I I I I I I I I I I I I I I I I I I I I I I I I I I I . . . 7 1 7 l \ % . \ M M i L c U h n I i i B v g R a e A s n r R S i Y t t a y ' _ g t e m a fi a * 7 T h i s i s t o c e r t i f y t h a t t h e . d i s s e r t a t i o n e n t i t l e d C H A R G E D E N S I T Y W A V E S A N D S T R U C T U R A L M O D U L A T I O N S i I N P O L Y T E L L U R I D E C O M P O U N D S 3 p r e s e n t e d b y C h r i s t o s D . M a l l i a k a s h a s b e e n a c c e p t e d t o w a r d s f u l fi l l m e n t o f t h e r e q u i r e m e n t s f o r t h e d e g r e e I n C h e m i s t r y M a j o r [ P r o f 7 s o r ’ 0 s i g n a t u r e D a t e M S U i s a n a f f i r m a t i v e - a c t i o n , e q u a l - o p p o r t u n i t y e m p l o y e r P L A C E I N R E T U R N B O X t o r e m o v e t h i s c h e c k o u t f r o m y o u r r e c o r d . T o A V O I D F I N E S r e t u r n o n o r b e f o r e d a t e d u e . M A Y B E R E C A L L E D w i t h e a r l i e r d u e d a t e i f r e q u e s t e d . D A T E D U E D A T E D U E D A T E D U E 5 / 0 8 K : l P r o fl A o c & P r e s / C I R C I D a t e D u e . i n d d C H A R G E D E N S I T Y W A V E S A N D S T R U C T U R A L M O D U L A T I O N S I N P O L Y T E L L U R I D E C O M P O U N D S V O L U M E I B y C h r i s t o s D . M a l l i a k a s A D I S S E R T A T I O N S u b m i t t e d t o M i c h i g a n S t a t e U n i v e r s i t y i n p a r t i a l f u l fi l l m e n t o f t h e r e q u i r e m e n t s f o r t h e d e g r e e o f D O C T O R O F P H I L O S O P H Y D e p a r t m e n t o f C h e m i s t r y 2 0 0 7 — A B S T R A C T C H A R G E D E N S I T Y W A V E S A N D S T R U C T U R A L M O D U L A T I O N S I N P O L Y T E L L U R I D E C O M P O U N D S b y C h r i s t o s D . M a l l i a k a s A l a t t i c e o f p o s i t i v e i o n s s u r r o u n d e d b y a c l o u d o f d e l o c a l i z e d e l e c t r o n s i s t h e c l a s s i c a l d e s c r i p t i o n o f a m e t a l . S u p e r c o n d u c t i v i t y a n d C h a r g e D e n s i t y W a v e s ( C D W s ) a r e t h e t w o k n o w i n s t a b i l i t i e s t h a t b r e a k t h i s d i f f u s e c h a r a c t e r o f t h e e l e c t r o n i c s e a i n t o a m o r e o r d e r e d p i c t u r e . T h e s e t w o c o m p e t i n g s t a t e s a r i s e i n l o w q u a s i - d i m e n s i o n a l s y s t e m s f r o m a p h o n o n - e l e c t r o n c o u p l i n g t h a t i s t h e r m o d y n a m i c a l l y s t a b l e u s u a l l y a t l o w t e m p e r a t u r e . C D W s d e v e l o p f r o m a p e r i o d i c m o d u l a t i o n o f t h e e l e c t r o n d e n s i t y t h a t c r e a t e s a n e w b r o k e n s y m m e t r y g r o u n d s t a t e t h r o u g h a s o - c a l l e d P e i e r l s d i s t o r t i o n . A l t h o u g h t h e C D W p h e n o m e n o n i s w e l l u n d e r s t o o d f o r o n e - d i m e n s i o n a l s y s t e m s t h e o r e t i c a l l y n o p r o p e r m o d e l s h a v e b e e n d e v e l o p e d f o r t h e t w o - d i m e n s i o n a l c a s e s . T h e s t u d y o f C D W s i s i m p o r t a n t , b e c a u s e a s u c c e s s f u l d e s c r i p t i o n o f t h e c o u p l e d e l e c t r o n i c l a t t i c e i n s t a b i l i t y r e fl e c t s o n t h e b r o a d e r i s s u e o f t h e e l e c t r o n i c a s p e c t s o f s t r u c t u r a l s t a b i l i t y w h i c h i s l i n k e d t o s e v e r a l i n t e r e s t i n g p h e n o m e n a i n c l u d i n g s u p e r c o n d u c t i v i t y . I n t h i s w o r k , a s y s t e m a t i c s t u d y o f C D W d i s t o r t e d p o l y t e l l u r i d e m a t e r i a l s w i l l b e r e p o r t e d i n o r d e r t o u n d e r s t a n d a n d e l u c i d a t e t h e i r s t r u c t u r a l m o d u l a t i o n s . C D W s a r e c r e a t e d i n t h e s e m a t e r i a l s d u e t o e x t e n d e d h y p e r v a l e n t T e - - - T e b o n d i n g t h a t o c c u r s i n t h e p l a n a r s q u a r e n e t s o f t e l l u r i u m . T h e fi r s t f a m i l y o f c o m p o u n d s t h a t w i l l b e p r e s e n t e d i n t h i s D i s s e r t a t i o n , R E T e 3 ( R E = R a r e e a r t h ) , r e v e a l e d f o r t h e fi r s t t i m e t h a t t h e n a t u r e o f " I t h e C D W i n t h e s e c o m p o u n d s v a r i e s s u b t l y b u t s i g n i fi c a n t l y w i t h R E e l e m e n t . S u r p r i s i n g l y , t h e t e m p e r a t u r e d e p e n d e n c e o f t h e m o d u l a t e d s t r u c t u r e s o f R E T e 3 c o m p o u n d s f o u n d t o b e a n o m a l o u s . A c h a n g e i n c e l l v o l u m e w i t h R E e l e m e n t h a s a n o p p o s i t e e f f e c t f r o m c o m p a r a b l e c h a n g e s i n v o l u m e c a u s e d b y t e m p e r a t u r e . F u r t h e r m o r e , i n v e s t i g a t i o n o f A M R E T e 4 ( A = N a , K ; M = C u , A g ; R E = L a , C e ) t h a t i s s t r u c t u r a l l y r e l a t e d t o R E T e 3 s h o w e d t h a t c r o s s - p l a n e i n t e r a c t i o n s p l a y a n i m p o r t r o l e o n d e fi n i n g t h e C D W d i s t o r t i o n s i n t h e s e m a t e r i a l s . A d d i t i o n a l l y , v a r i a t i o n o f t h e c r o s s - p l a n e i n t e r a c t i o n s i n A M z E u T e 4 ( A = N a , K , R b , C s ; M = C u , A g ) w i t h s u b s t i t u t i o n o f d i f f e r e n t a l k a l i m e t a l i o n s a n d e u r o p i u m a t o m s s u g g e s t e d t h a t i n - p l a n e a n d c r o s s - p l a n e s t r u c t u r a l c h a n g e s h a v e d i f f e r e n t e f f e c t s o n t h e C D W d i s t o r t i o n s . F u r t h e r m o r e , t h e i n t e r g r o w t h s z T c 5 . x t h a t i s c o m p o s e d b y t h e s u b s t r u c t u r e s o f S m T e h a n d S m T e ; r e p r e s e n t s a r a r e e x a m p l e o f c o m p o s i t e s t r u c t u r e a n d p o s s e s t w o T e n e t s w i t h d i f f e r e n t o x i d a t i o n s t a t e s s h o w e d a h y b r i d C D W d i s t o r t i o n w i t h t w o i n d e p e n d e n t m o d u l a t i o n v e c t o r s . A s i m i l a r b e h a v i o r o f c o e x i s t e n c e o f t w o m o d u l a t i o n v e c t o r s w a s f o u n d i n K z A g 4 L a 2 T e 1 0 - x . F i n a l l y , C D W d i s t o r t i o n s i n t h e l i n e a r T e c h a i n s o f C u x U T e 3 f o u n d t o d e p e n d s t r o n g l y o n t h e c o n c e n t r a t i o n o f i n t e r c a l a t e d C u a t o m s t o g e t h e r w i t h a n u n u s u a l l o n g r a n g e o r d e r i n g o f C u a t o m s a n d v a c a n c i e s i n t o c l u s t e r s . T h e C D W m o d u l a t i o n s i n t h e p o l y t e l l u r i d e s t h a t a r e r e p o r t e d i n t h i s t h e s i s a r e n o t e f f e c t e d o n l y b y t h e a v e r a g e e l e c t r o n c o u n t a s i t w a s o r i g i n a l l y a s s u m e d . T e m p e r a t u r e , s i z e o f a t o m s , a n d d i m e n s i o n a l i t y p l a y a v e r y i m p o r t a n t r o l e o n t h e f o r m a t i o n a n d s t a b i l i t y o f C D W m o d u l a t i o n s . I n t e r a c t i o n s a l o n g a l l t h r e e d i r e c t i o n s m u s t b e t a k e n i n t o a c c o u n t a n d t h e “ q u a s i ” d e s c r i p t i o n h a s t o b e u s e d w i t h c a u t i o n . C e p y r i g h t b y C h r i s t o s D . M a l l i a k a s 2 0 0 7 D e d i c a t e d t o m y f a m i l y A C K N O W L E D G E M E N T S F i r s t , I w i s h t o t h a n k t h e p e o p l e w h o h e l p e d a n d i n s p i r e d m e i n m y fi r s t s t e p s o f m y s c i e n t i fi c c a r e e r a s a n u n d e r g r a d u a t e s t u d e n t . T h e s e p e o p l e i n c l u d e P r o f . P a n a g i o t i s N i k i t a s a t t h e C h e m i s t r y D e p a r t m e n t a n d P r o f . K o n s t a n t i n o s M . P a r a s k e v o p o u l o s a t t h e P h y s i c s D e p a r t m e n t o f A r i s t o t l e U n i v e r s i t y o f T h e s s a l o n i k i . I w o u l d l i k e t o t h a n k m y P h . D . a d v i s o r P r o f . M e r c o u r i G . K a n a t z i d i s f o r t h e o p p o r t u n i t i e s a n d s u p p o r t h e g a v e m e . O v e r t h e p a s t 5 y e a r , h e h a s g i v e n m e a n e n o r m o u s a m o u n t o f e n c o u r a g e m e n t a n d g u i d a n c e . I w i l l a l w a y s r e m e m b e r h i s e n d l e s s l o v e f o r s c i e n c e t h a t m a d e m e t o w a k e u p e v e r y d a y a n d b e e x c i t e d t o g o t o w o r k i n t h e l a b . I t t o o k m e a c o u p l e o f m o n t h s a t t h e b e g i n n i n g t o r e a l i z e t h a t h i s “ w h a t ’ s u p ” e x p r e s s i o n w h e n w e c a m e a c r o s s e a c h o t h e r i n t h e h a l l w a y w a s n o t j u s t a c a s u a l g r e e t i n g b u t a c t u a l l y a q u e s t i o n f o r s c i e n t i fi c r e s u l t s . E v e n w h e n I k n e w t h a t , I k e p t t e a s i n g h i m b y g i v i n g t h e s a m e t y p e o f “ e v e r y t h i n g i s fi n e ” a n s w e r e x p e c t i n g a f t e r a f e w s e c o n d s t o e n d u p h a v i n g a m i n i g r o u p m e e t i n g . I w i l l n o t f o r g e t t h a t a t e n - m i n u t e d i s c u s s i o n w o u l d b e e n o u g h t o k e e p m e b u s y f o r a t l e a s t a y e a r . M e r c o u r i h a s c r e a t e d a n d s h a p e d t h e s c i e n t i s t I a m t o d a y a n d f o r t h a t I w i l l a l w a y s b e g r a t e f u l . N e x t , I w o u l d l i k e t o t h a n k o u r c o l l a b o r a t o r s i n t h e P h y s i c s D e p a r t m e n t a t M i c h i g a n S t a t e U n i v e r s i t y t h a t c o n t r i b u t e d s u b s t a n t i a l l y t o t h e w o r k p r e s e n t e d i n t h i s D i s s e r t a t i o n . T h e e x p e r t i s e a n d h e l p o f P r o f . S i m o n J . L . B i l l i n g e w a s i m p o r t a n t t o t h e a c c o m p l i s h m e n t o f t h e q u a l i t y o f t h i s w o r k . T e a m u p w i t h p a s t a n d p r e s e n t m e m b e r s i n B i l l i n g e ’ s g r o u p w a s v e r y u s e f u l . I n p a r t i c u l a r , D r . V a l e r i P e t k o v ( c u r r e n t l y A s s o c i a t e P r o f e s s o r i n t h e D e p a r t m e n t o f P h y s i c s a t C e n t r a l M i c h i g a n U n i v e r s i t y ) t a u g h t m e t h e V i P a i r D i s t r i b u t i o n F u n c t i o n t e c h n i q u e a n d X i a n g y u n Q i u w h o h e l p e d m e w i t h d a t a a n a l y s i s . F u r t h e r m o r e , I c a n n o t f o r g e t t h e g r u e l i n g o v e r n i g h t h o u r s I s p e n t a t t h e b e a m l i n e s o f A d v a n c e s P h o t o n S o u r c e ( A P S ) s y n c h r o t r o n f a c i l i t y a t A r g o n n e N a t i o n a l L a b o r a t o r y ( A N L ) w i t h H y u n j e o n g K i m , A h m a d M a s a d e n , D r . E m i l B o z i n , a n d D r . P a v o l J u h a s f o r c o l l e c t i n g d i f f r a c t i o n d a t a . I w o u l d a l s o l i k e t o e x p r e s s m y a p p r e c i a t i o n t o P r o f . S u b h e n d r a D . M a h a n t i a n d h i s s t u d e n t s , D a n i e l B i l c a n d Z s o l t R a k , f o r t h e i r h e l p w i t h t h e o r e t i c a l p h y s i c a l c o n c e p t s a n d u s e f u l d i s c u s s i o n s . F i n a l l y , m y t h a n k s t o P r o f . S t u a r t H . T e s s m e r a n d A l e k s a n d r a K . T o m i é f o r t h e S c a n n i n g T u n n e l i n g M i c r o s c o p y m e a s u r e m e n t s . I n a d d i t i o n , I w o u l d l i k e t o t h a n k t h e s t a f f a t M i c h i g a n S t a t e U n i v e r s i t y w h o h e l p e d m e w i t h t h e u s e o f i n s t r u m e n t s I n e e d e d f o r m y r e s e a r c h . T h e s e p e o p l e i n c l u d e D r . R e z a L o l o e e ( D e p a r t m e n t o f P h y s i c s , S Q U I D ) , D r . S t a n l e y L . F l e g l e r ( C e n t e r f o r A d v a n c e d M i c r o s c o p y , S E M ) , D r . C a r o l S . F l e g l e r ( S E M ) , D r . E w a D a n i e l e w i c z ( S E M ) , A l i c i a P a s t o r ( T E M ) , D r . X u d o n g F a n ( T E M ) , D r . R u i H u a n g ( C H N a n a l y s i s a n d X - r a y f a c i l i t i e s a t t h e C h e m i s t r y D e p a r t m e n t ) , P a u l R e e d , T h o m a s P . C a r t e r , a n d T o m a s V . A t k i n s o n ( I T s u p p o r t ) , S c o t t B a n k r o f f ( G l a s s b l o w i n g L a b ) , S c o t t S a n d e r s o n a n d D a v i d C e d a r s t a fi ‘ ( E l e c t r o n i c s h o p ) , G l e n n W e s l e y a n d T h o m a s B a r t l e t t ( M a c h i n e s h o p ) . P a r t o f t h e w o r k p r e s e n t e d i n t h i s t h e s i s w a s c a r r i e d o u t a t t h e f a c i l i t i e s o f A N L a n d A P S . I w o u l d l i k e t o t h a n k a l l t h e p e o p l e t h a t w e r e i n v o l v e d a n d h e l p e d m e w i t h t h e s e e x p e r i m e n t s . T h e s e p e o p l e i n c l u d e : M a r i a I a v a r o n e ( M S D / A N L ) f o r S T M m e a s u r e m e n t s , J o h n M i t c h e l l ( M S D / A N L ) f o r h e l p w i t h s o m e o f t h e r e s i s t i v i t y m e a s u r e m e n t s , G o r a n K a r a p e t r o v ( M S D / A N L ) f o r h e l p w i t h t h e e v a p o r a t i o n o f g o l d c o n t a c t s o n t h e s a m p l e s f o r r e s i s t i v i t y m e a s u r e m e n t s , a n d t h e b e a m s c i e n t i s t s a t A P S : v i i P e t e r L . L e e ( A P S / S e c t o r 1 ) , D o u g R o b i n s o n ( A P S / S e c t o r 6 ) , P e t e r C h u p a s ( A P S / S e c t o r 1 1 ) , a n d Y u - S h e n g C h e n ( A P S / S e c t o r 1 5 ) . L a s t b u t n o t l e a s t , I w o u l d l i k e t o t h a n k t h e m e m b e r s o f t h e K a n a t z i d i s ’ g r o u p , p a s t a n d p r e s e n t , f o r a l l o f t h e i r s u p p o r t a n d t o l e r a n c e . I w i l l a l w a y s r e m e m b e r t h e f a c e t h e y h a d d u r i n g m y g r o u p m e e t i n g s t r y i n g t o u n d e r s t a n d a n d v i s u a l i z e t h e d i s t o r t e d p a t t e r n s . I n p a r t i c u l a r , m y t h a n k s t o D r . D u c k - Y o u n g C h u n g w h o w a s n e x t t o m e i n e v e r y e x p e r i m e n t a n d w o r k I d i d a t m y fi r s t d a y s i n t h e l a b , D r . P a n t e l i s N . T r i k a l i t i s ( c u r r e n t l y A s s i s t a n t P r o f e s s o r i n t h e D e p a r t m e n t o f C h e m i s t r y a t U n i v e r s i t y o f C r e t e ) , D r . T h e o d o r a K y r a t s i ( c u r r e n t l y L e c t u r e r i n t h e D e p a r t m e n t o f M e c h a n i c a l a n d M a n u f a c t u r i n g E n g i n e e r i n g a t U n i v e r s i t y o f C y p r u s ) , a n d R a t n a s a b a p a t h y G . I y e r ( c u r r e n t l y A s s i s t a n t P r o f e s s o r i n t h e D e p a r t m e n t o f C h e m i s t r y a t C l a fl i n U n i v e r s i t y ) w h o m a d e m y l i f e e a s i e r i n E a s t L a n s i n g a n d M i c h i g a n S t a t e U n i v e r s i t y . F i n a l l y , t h e N a t i o n a l S c i e n c e F o u n d a t i o n ( D M R a n d N I R T ) i s g r a t e f u l l y a c k n o w l e d g e d f o r t h e fi n a n c i a l s u p p o r t a n d A m e r i c a n C h e m i c a l S o c i e t y ( A C S ) f o r t h e p e r m i s s i o n t o i n c l u d e t h e a r t i c l e s t h a t h a v e b e e n p u b l i s h e d i n A C S j o u r n a l s i n t h i s D i s s e r t a t i o n . v i i i T A B L E O F C O N T E N T S L I S T O F T A B L E S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x i v L I S T O F F I G U R E S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x x x v i i K E Y T O A B B R E V I A T I O N S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x l i x C h a p t e r 1 D i s t o r t i o n s i n P l a n a r N e t s o f T e l l m ' i u m : S y n t h e t i c a n d C h a r a c t e r i z a t i o n T e c h n i q u e s . . . . . . . 1 1 . 1 I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 . 2 P o l y c h a l c o g e n i d e a n d h a l i d e fl u x s y n t h e t i c t e c h n i q u e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 . 3 D i s t o r t i o n s i n p l a n a r n e t s o f t e l l u r i u m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1 . 4 C h a r g e - D e n s i t y - W a v e ( C D W ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 . 4 . 1 J a h n - T e l l e r d i s t o r t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 . 4 . 2 P e i e r l s d i s t o r t i o n a n d C h a r g e - D e n s i t y - W a v e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 1 . 5 T h e r m o e l e c t r i c p r o p e r t y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 1 . 6 P a i r D i s t r i b u t i o n F u n c t i o n a n a l y s i s ( P D F ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 1 . 7 S u p e r s p a c e a p p r o a c h f o r m o d u l a t e d s t r u c t u r e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 1 . 7 . 1 R e c i p r o c a l s p a c e a n d s u p e r s p a c e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 1 . 7 . 2 D i r e c t s p a c e a n d s u p e r s p a c e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 1 . 7 . 3 S y m m e t r y i n s u p e r s p a c e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 5 1 . 7 . 4 R e fi n e m e n t o f m o d u l a t e d s t r u c t u r e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 7 1 . 7 . 5 P o s i t i o n a l m o d u l a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 9 1 . 7 . 6 S u b s t i t u t i o n a l m o d u l a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 9 1 . 7 . 7 C r e n e l f u n c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 1 . 7 . 8 S a w t o o t h f u n c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 1 . 7 . 9 E x a m p l e s o f c o n t i n u e s a n d d i s c o n t i n u e s d i s t o r t i o n s i n r e a l s p a c e . . . . . . . . . . . . 3 2 1 . 7 . 1 0 S t r u c t u r e s o l u t i o n o f m o d u l a t e d c r y s t a l s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 7 1 . 7 . 1 1 S p e c i a l b o o k s , l i t e r a t u r e a n d r e s o u r c e s o n s u p e r s p a c e c o n c e p t . . . . . . . . . . . . . . . . . 3 8 1 . 8 C o n v e n t i o n s o f t h e t h e s i s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 9 C h a p t e r 2 R e a c t i o n s o f R a r e - E a r t h M e t a l s ( R E ) a n d T e l l u r i u m : S i z e E f f e c t o f R a r e E a r t h t o t h e D i s t o r t i o n s o f t h e T e l l u r i u m N e t o f R E T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4 2 . 1 . I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 5 2 . 2 . E x p e r i m e n t a l S e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 6 2 . 2 . 1 . R e a g e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 6 2 . 2 . 2 . S y n t h e s i s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 6 i x R E T e 3 ( R E = L a , C e , P r , N d , S m , G d , T b a n d D y ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 6 R E T e 3 ( R E = H o , E r , T m a n d Y ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 7 2 . 2 . 3 . P h y s i c a l M e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 7 S e m i q u a n t i t a t i v e E n e r g y D i s p e r s i v e S p e c t r o s c o p y ( E D S ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 7 S i n g l e C r y s t a l X - r a y D i f f r a c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 8 T r a n s m i s s i o n E l e c t r o n M i c r o s c o p y o f C e T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 9 I n f r a r e d ( I R ) S p e c t r o s c o p y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 9 P a i r D i s t r i b u t i o n F u n c t i o n o f R E T e 3 ( R E = C e , P r a n d N d ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 9 2 . 3 . R e s u l t s a n d D i s c u s s i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 0 S u b c e l l D e s c r i p t i o n o f R E T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 0 E l e c t r o n T r a n s m i s s i o n M i c r o s c o p y o f C e T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 C o m m e n s u r a t e S u p e r c e l l D e s c r i p t i o n o f R E T e 3 ( R E = C e , P r a n d N d ) . . . . . . . . . . . . . . . 5 1 S u p e r c e l l D e s c r i p t i o n o f R E T e 3 B a s e d o n 3 M o d u l a t i o n q - v e c t o r . . . . . . . . . . . . . . . . . . . . . . . 6 8 P a i r D i s t r i b u t i o n F u n c t i o n A n a l y s i s o f R E T e 3 ( R E = C e , P r a n d N d ) . . . . . . . . . . . . . . . . . . 7 2 B a n d s t r u c t u r e c a l c u l a t i o n o f L a T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 0 2 . 4 . C o n c l u s i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4 C h a p t e r 3 R e a c t i o n s o f R a r e - E a r t h M e t a l s ( R E ) a n d T e l l u r i u m : T e m p e r a t u r e D e p e n d e n c e o f t h e D i s t o r t i o n s o f t h e T e l l u r i u m N e t o f R E T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 1 3 . 1 . I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 2 3 . 2 . E x p e r i m e n t a l S e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 3 3 . 2 . 1 . R e a g e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 3 3 . 2 . 2 . S y n t h e s i s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 4 R E T e 3 ( R E = L a , C e , P r , N d , S m , G d , T b a n d D y ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 4 R E T e 3 ( R E = H o , E r , T m a n d Y ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 5 3 . 2 . 3 . P h y s i c a l M e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 5 S e m i q u a n t i t a t i v e E n e r g y D i s p e r s i v e S p e c t r o s c o p y ( E D S ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 5 S i n g l e C r y s t a l X - r a y D i f f r a c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 6 T e m p e r a t u r e D e p e n d e n t T r a n s m i s s i o n E l e c t r o n M i c r o s c o p y o f H o T e 3 . . . . . . . . . . . . . 1 2 7 3 . 3 . R e s u l t s a n d D i s c u s s i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 7 S u b c e l l D e s c r i p t i o n o f R E T e ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 7 S u p e r c e l l D e s c r i p t i o n o f R E T e 3 B a s e d o n a M o d u l a t i o n q - v e c t o r . . . . . . . . . . . . . . . . . . . . . 1 2 9 C o m p a r i s o n o f t h e s t r u c t u r e r e fi n e m e n t o f C e T e 3 i n c l u d i n g s a t e l l i t e r e fl e c t i o n s o f s e c o n d o r d e r i n r e s p e c t w i t h t h e r e fi n e m e n t c o n t a i n i n g o n l y fi r s t o r d e r r e fl e c t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 2 E l e c t r o n T r a n s m i s s i o n M i c r o s c o p y o f H o T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 9 3 . 4 . C o n c l u s i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 1 C h a p t e r 4 E f f e c t o f t h e T h r e e D i m e n s i o n a l C h a r a c t e r o n t h e C h a r g e D e n s i t y W a v e s o f t h e S q u a r e N e t s o f T e l l u r i u m o f A M R E T e 4 ( A = K , N a ; M = C u , A g ; R E = L a , C e ) . . . . . . . . . 2 0 2 4 . 1 . I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 3 4 . 2 . E x p e r i m e n t a l S e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 5 4 . 2 . 1 . R e a g e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 5 A l k a l i M e t a l T e l l u r i d e , A 2 T e ( A = K , N a ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 5 4 . 2 . 2 . S y n t h e s i s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 6 A M R E T e 4 ( A = K , N a ; M = C u , A g ; R E = L a , C e ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 6 4 . 2 . 3 . P h y s i c a l M e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 6 S e m i q u a n t i t a t i v e E n e r g y D i s p e r s i v e S p e c t r o s c o p y ( E D S ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 6 S i n g l e C r y s t a l X - r a y D i f f r a c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 6 C h a r g e t r a n s p o r t m e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 7 I n f r a r e d ( I R ) S p e c t r o s c o p y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 8 4 . 3 . R e s u l t s a n d D i s c u s s i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 8 S u b c e l l D e s c r i p t i o n o f A M R E T e 4 ( A = K , N a ; M = C u , A g ; R E = L a , C e ) . . . . . . . . 2 0 8 S u p e r c e l l D e s c r i p t i o n o f A M R E T e 4 ( A = K , N a ; M = C u , A g ; R E = L a , C e ) . . . . . 2 1 0 D i s o r d e r a n d p u r i t y o f A 1 - x M 1 + x R E T e 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 6 B a n d s t r u c t u r e c a l c u l a t i o n o f K C u L a T e 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 7 C h a r g e t r a n s p o r t m e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 2 I n f r a r e d ( I R ) S p e c t r o s c o p y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 3 4 . 4 . C o n c l u s i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 5 C h a p t e r 5 C h a r g e D e n s i t y W a v e D i s t o r t i o n s i n S q u a r e N e t s o f T e l l u r i u m i n L a y e r e d I n t e r g r o w t h P o l y t e l l u r i d e C o m p o u n d s : s z T e s a n d K z A g 4 L a 2 T e 1 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 9 8 5 . 1 . I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 9 9 5 . 2 . E x p e r i m e n t a l S e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 1 5 . 2 . 1 . R e a g e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 1 S i l v e r p o w d e r . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 1 P o t a s s i u m T e l l u r i d e , K z T e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 1 5 . 2 . 2 . S y n t h e s i s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 2 s z T e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 2 S m T e z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 2 K z A g 4 L a 2 T e 1 0 - x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 3 5 . 3 . P h y s i c a l M e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 5 S e m i q u a n t i t a t i v e E n e r g y D i s p e r s i v e S p e c t r o s c o p y ( E D S ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 5 S i n g l e C r y s t a l X - r a y D i f f r a c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 5 I n f r a r e d ( I R ) S p e c t r o s c o p y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 7 S c a n n i n g T u n n e l i n g M i c r o s c o p y ( S T M ) o f s z T e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 7 5 . 4 . R e s u l t s a n d D i s c u s s i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 7 S u b c e l l D e s c r i p t i o n o f R E T e z a n d R E z T e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 7 S u b c e l l D e s c r i p t i o n o f K z A g 4 L a 2 T e 1 0 - x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 0 S u p e r c e l l D e s c r i p t i o n o f s z T e s B a s e d o n a M o d u l a t i o n q - v e c t o r . . . . . . . . . . . . . . . . . . . . 3 1 2 O c c u p a t i o n a l m o d u l a t i o n w a v e s o f v a c a n c i e s i n t h e T e l ' n e t o f s z T e 4 . 9 o ( 1 ) . . . . . 3 1 6 S c a n n i n g T u n n e l i n g M i c r o s c o p y ( S T M ) S t u d y o f s z T e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 9 I n f r a r e d ( I R ) S p e c t r o s c o p y o f s z T e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 1 S u p e r c e l l D e s c r i p t i o n o f S m T e m w ) B a s e d o n a M o d u l a t i o n q - v e c t o r . . . . . . . . . . . . . . . 3 2 2 S u p e r c e l l D e s c r i p t i o n o f K 2 A g 4 L a 2 T e 9 , 6 1 ( 1 ) B a s e d o n a M o d u l a t i o n q - v e c t o r . . . . 3 2 4 B a n d s t r u c t u r e c a l c u l a t i o n o f L a z T e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 8 x i B a n d s t r u c t u r e c a l c u l a t i o n o f K 2 A g 4 L a 2 T e | 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 9 5 . 5 . C o n c l u s i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 0 C h a p t e r 6 R e a c t i o n s o f E u r o p i u m M e t a l ( E u ) w i t h C o i n a g e M e t a l s ( C H a n d A g ) i n P o l y c h a l c o g e n i d e F l u x : D i s t o r t e d T e l l u r i u m N e t s o f E u 2 + c o m p o u n d s . . . . . . . . . . . . . . . . . . . . . . . . . 3 9 3 6 . 1 . I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 9 4 6 . 2 . E x p e r i m e n t a l S e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 9 6 6 . 2 . 1 . R e a g e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 9 6 A c t i v a t e d C o p p e r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 9 6 P o t a s s i u m T e l l u r i d e , K z T e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 9 6 S o d i u m T e l l u r i d e , N a z T e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 9 7 R u b i d i u m T e l l u r i d e , s z T e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 9 7 C e s i u m T e l l u r i d e , C s z T e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 9 8 6 . 2 . 2 . S y n t h e s i s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 9 8 A M z E u T e 4 ( A = K , N a , R b , C s ; M = C u , A g ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 9 8 C u o _ 6 3 E u T e 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 9 8 6 . 2 . 3 . P h y s i c a l M e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 9 9 S e m i q u a n t i t a t i v e E n e r g y D i s p e r s i v e S p e c t r o s c o p y ( E D S ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 9 9 S i n g l e C r y s t a l X - r a y D i f f r a c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 9 9 I n f r a r e d ( I R ) S p e c t r o s c o p y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 0 0 M a g n e t i c S u s c e p t i b i l i t y M e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 0 0 6 . 3 . R e s u l t s a n d D i s c u s s i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 0 1 S u b c e l l D e s c r i p t i o n o f A M z E u T e 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 0 1 S u b c e l l D e s c r i p t i o n o f C u o _ 6 3 E u T e 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 0 4 S u p e r c e l l D e s c r i p t i o n o f A M z E u T e 4 B a s e d o n a M o d u l a t i o n q - v e c t o r . . . . . . . . . . . . . . 4 0 6 S u p e r c e l l D e s c r i p t i o n o f C u o , 6 3 E u T e 2 B a s e d o n a M o d u l a t i o n q - v e c t o r . . . . . . . . . . . . . 4 1 5 M a g n e t i c S u s c e p t i b i l i t y M e a s u r e m e n t s o f A M z E u T e 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 0 I n f r a r e d ( I R ) S p e c t r o s c o p y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 1 B a n d s t r u c t u r e c a l c u l a t i o n o f A C u z L u T e 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 2 B a n d s t r u c t u r e c a l c u l a t i o n o f C u x L u T e z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 4 6 . 4 . C o n c l u s i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 1 C h a p t e r 7 C l l e T e 3 ( O S x < 0 . 5 ) : E v o l u t i o n o f t h e I n c o m m e n s u r a t e C h a r g e D e n s i t y W a v e M o d u l a t i o n s i n t h e L i n e a r C h a i n s o f T e l l u r i u m a n d S t r i p e s o f C o p p e r v i a S u c c e s s i v e I n t e r c a l a t i o n o f C o p p e r i n a - U T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 0 7 7 . 1 . I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 0 8 7 . 2 . E x p e r i m e n t a l S e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 0 9 7 . 2 . 1 . R e a g e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 0 9 A c t i v a t e d C o p p e r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 0 9 7 . 2 . 2 . S y n t h e s i s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 0 a - U T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 0 B - U T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 0 x i i C I I X U T C 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 0 7 . 2 . 3 . P h y s i c a l M e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 1 S e m i q u a n t i t a t i v e E n e r g y D i s p e r s i v e S p e c t r o s c o p y ( E D S ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 1 S i n g l e C r y s t a l X - r a y D i f f r a c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 1 M a g n e t i c S u s c e p t i b i l i t y M e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 2 C h a r g e t r a n s p o r t m e a s u r e m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 3 7 . 3 . R e s u l t s a n d D i s c u s s i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 3 S u b c e l l D e s c r i p t i o n o f a - U T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 3 S u b c e l l D e s c r i p t i o n o f B - U T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 4 S u b c e l l D e s c r i p t i o n o f C u x U T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 4 S u p e r c e l l D e s c r i p t i o n o f C u x U T e 3 B a s e d o n a M o d u l a t i o n q - v e c t o r . . . . . . . . . . . . . . . . . 5 1 5 M a g n e t i c s u s c e p t i b i l i t y m e a s u r e m e n t s o f B - U T e 3 a n d C u o , 4 U T e 3 . . . . . . . . . . . . . . . . . . . . . 5 2 2 R e s i s t i v i t y m e a s u r e m e n t s o f a - U T e g , B - U T e ; a n d C u x U T e 3 ( x = 0 . 1 0 , 0 . 4 0 ) 5 2 5 7 . 4 . C o n c l u s i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 9 C h a p t e r 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4 6 C o n c l u s i o n s a n d O u t l o o k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4 6 8 . 1 . S i z e e f f e c t o n C h a r g e D e n s i t y W a v e m o d u l a t i o n s ( C h e m i c a l p r e s s u r e ) . . . . . . . . 5 4 7 8 . 2 . T e m p e r a t u r e e f f e c t o n C h a r g e D e n s i t y W a v e m o d u l a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4 9 8 . 3 . D i m e n s i o n a l i t y e f f e c t o n C h a r g e D e n s i t y W a v e d i s t o r t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5 0 8 . 4 . I n d e x i n g a n d p r o p e r c h a r a c t e r i z a t i o n o f m o d u l a t e d s t r u c t u r e s . . . . . . . . . . . . . . . . . . . . . . . 5 5 1 8 . 5 . D e s i g n o n n e w C h a r g e D e n s i t y W a v e m a t e r i a l s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5 6 8 . 6 . C h a r g e D e n s i t y W a v e s D i s t o r t i o n s a n d T h e r m o e l e c t r i c s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 6 2 8 . 7 . C l o s i n g r e m a r k s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 6 2 x i i i a . . . . ~ - . u m . ‘ 1 5 l I n t x . l . . ’ \ § . I L I S T O F T A B L E S T a b l e 1 . 1 . M e l t i n g p o i n t s o f s o m e k n o w n a l k a l i m e t a l p o l y c h a l c o g e n i d e ( A n y w h e r e Q = S , S e a n d T e ) s p e c i e s a n d h a l i d e s a l t s . ’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 T a b l e 2 . 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C e T e 3 , P r T e 3 a n d N d T e 3 u s i n g t h e c o m m e n s u r a t e s o l u t i o n a t 3 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 6 T a b l e 2 . 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r C e T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . 5 7 T a b l e 2 . 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r C e T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 7 T a b l e 2 . 4 . S e l e c t e d b o n d d i s t a n c e s [ A ] f o r C e T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 8 T a b l e 2 . 5 . S e l e c t e d b o n d a n g l e s [ ° ] f o r C e T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 9 T a b l e 2 . 6 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r P r T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . 6 0 T a b l e 2 . 7 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r P r T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1 T a b l e 2 . 8 . B o n d d i s t a n c e s [ A ] f o r P r T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 T a b l e 2 . 9 . S e l e c t e d b o n d a n g l e s [ ° ] f o r P r T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3 T a b l e 2 . 1 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r N d T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . 6 4 T a b l e 2 . 1 1 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r N d T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 5 T a b l e 2 . 1 2 . B o n d d i s t a n c e s [ A ] f o r N d T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 6 x i v T a b l e 2 . 1 3 . S e l e c t e d b o n d a n g l e s [ ° ] f o r N d T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 6 T a b l e 2 . 1 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r L a T e 3 a t 3 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5 T a b l e 2 . 1 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r L a T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 6 T a b l e 2 . 1 6 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r L a T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 6 T a b l e 2 . 1 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r L a T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 6 T a b l e 2 . 1 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r L a T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 7 T a b l e 2 . 1 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C e T e ; a t 3 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 8 T a b l e 2 . 2 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C e T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 9 T a b l e 2 . 2 1 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r C e T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 9 T a b l e 2 . 2 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C e T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 9 T a b l e 2 . 2 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C e T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 0 T a b l e 2 . 2 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r P r T e 3 a t 3 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1 T a b l e 2 . 2 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r P r T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 T a b l e 2 . 2 6 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r P r T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 X V T a b l e 2 . 2 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r P r T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 T a b l e 2 . 2 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r P r T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3 T a b l e 2 . 2 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N d T e 3 a t 3 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4 T a b l e 2 . 3 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r N d T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5 T a b l e 2 . 3 1 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r N d T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5 T a b l e 2 . 3 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N d T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5 T a b l e 2 . 3 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N d T C 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 6 T a b l e 2 . 3 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r S m T e 3 a t 3 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 7 T a b l e 2 . 3 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r S m T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 8 T a b l e 2 . 3 6 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r S m T e ; a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 8 T a b l e 2 . 3 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r S m T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 8 T a b l e 2 . 3 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r S m T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 9 T a b l e 2 . 3 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r G d T e 3 a t 3 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 0 T a b l e 2 . 4 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r G d T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 1 x v i . D 0 ' 0 ? ~ . \ . . . . . 5 . s P . J : - , 1 “ T a b l e 2 . 4 1 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r G d T e ; a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 1 T a b l e 2 . 4 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r G d T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 1 T a b l e 2 . 4 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r G d T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 2 T a b l e 2 . 4 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r T b T e 3 a t 3 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 3 T a b l e 2 . 4 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r T b T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 4 T a b l e 2 . 4 6 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r T b T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 4 T a b l e 2 . 4 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r T b T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 4 T a b l e 2 . 4 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r T b T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 5 T a b l e 2 . 4 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r D y T e 3 a t 3 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 6 T a b l e 2 . 5 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r D y T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 7 T a b l e 2 . 5 1 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r D y T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 7 T a b l e 2 . 5 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r D y T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 7 T a b l e 2 . 5 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r D y T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 8 T a b l e 2 . 5 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r H o T e 3 a t 3 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 9 x v i i T a b l e 2 . 5 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r H o T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 9 T a b l e 2 . 5 6 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r H o T e 3 a t 3 0 0 K w i t h e . s . d ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 0 T a b l e 2 . 5 7 . B o n d d i s t a n c e s [ A ] f o r H o T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . 1 1 0 T a b l e 2 . 5 8 . B o n d a n g l e s [ ° ] f o r H o T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . 1 1 0 T a b l e 2 . 5 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r E r T e 3 a t 3 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 T a b l e 2 . 6 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r E r T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 2 T a b l e 2 . 6 1 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r E r T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 2 T a b l e 2 . 6 2 . B o n d d i s t a n c e s [ A ] f o r E r T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . 1 1 2 T a b l e 2 . 6 3 . B o n d a n g l e s [ ° ] f o r E r T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . 1 1 2 T a b l e 2 . 6 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r T m T e 3 a t 3 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 3 T a b l e 2 . 6 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r T m T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 4 T a b l e 2 . 6 6 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r T m T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 4 T a b l e 2 . 6 7 . B o n d d i s t a n c e s [ A ] f o r T m T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . 1 1 4 T a b l e 2 . 6 8 . B o n d a n g l e s [ ° ] f o r T m T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . 1 1 5 T a b l e 2 . 6 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r Y T e 3 a t 3 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 6 T a b l e 2 . 7 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r W e ; a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 7 T a b l e 2 . 7 1 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r Y T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 7 x v i i i T a b l e 2 . 7 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r Y T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 7 T a b l e 2 . 7 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r Y T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 8 T a b l e 3 . 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r L a T e 3 a t 1 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 2 T a b l e 3 . 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r L a T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 3 T a b l e 3 . 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r L a T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 3 T a b l e 3 . 4 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r L a T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 3 T a b l e 3 . 5 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r L a T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 4 T a b l e 3 . 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r L a T e 3 a t 5 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 5 T a b l e 3 . 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r L a T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 6 T a b l e 3 . 8 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r L a T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 6 T a b l e 3 . 9 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r L a T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 6 T a b l e 3 . 1 0 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r L a T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 7 T a b l e 3 . 1 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C e T e ; a t 1 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 8 T a b l e 3 . 1 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C e T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 9 x i x T a b l e 3 . 1 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r C e T e 3 a t 1 0 0 K w i t h e . s . d ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 9 T a b l e 3 . 1 4 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C e T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 9 T a b l e 3 . 1 5 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C e T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 0 T a b l e 3 . 1 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C e T e 3 a t 1 0 0 K ( 2 " ‘ 1 o r d e r s a t e l l i t e s ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 1 T a b l e 3 . 1 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C e T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s ( 2 n d o r d e r s a t e l l i t e s ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 2 T a b l e 3 . 1 8 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r C e T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s ( 2 n d o r d e r s a t e l l i t e s ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 2 T a b l e 3 . 1 9 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C e T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s ( 2 ‘ r i d o r d e r s a t e l l i t e s ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 3 T a b l e 3 . 2 0 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C e T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s ( 2 n d o r d e r s a t e l l i t e s ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 3 T a b l e 3 . 2 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C e T e 3 a t 5 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 4 T a b l e 3 . 2 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C e T e ; a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 5 T a b l e 3 . 2 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r C e T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 5 T a b l e 3 . 2 4 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C e T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 5 T a b l e 3 . 2 5 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C e T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 6 T a b l e 3 . 2 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r P r T e 3 a t 1 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 7 T a b l e 3 . 2 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r P r T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 8 T a b l e 3 . 2 8 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r P r T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 8 T a b l e 3 . 2 9 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r P r T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 8 T a b l e 3 . 3 0 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r P r T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 9 T a b l e 3 . 3 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r P r T e 3 a t 5 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 0 T a b l e 3 . 3 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r P r T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 1 T a b l e 3 . 3 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r P r T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 1 T a b l e 3 . 3 4 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r P r T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 1 T a b l e 3 . 3 5 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r P r T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 2 T a b l e 3 . 3 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N d T e 3 a t 1 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 3 T a b l e 3 . 3 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r N d T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 4 T a b l e 3 . 3 8 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r N d T e 3 a t 1 0 0 K w i t h e . s . d ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 4 T a b l e 3 . 3 9 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N d T e ; a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 4 T a b l e 3 . 4 0 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N d T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 5 T a b l e 3 . 4 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N d T e 3 a t 4 7 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 6 T a b l e 3 . 4 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r N d T e 3 a t 4 7 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 7 T a b l e 3 . 4 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r N d T e 3 a t 4 7 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 7 T a b l e 3 . 4 4 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N d T e ; a t 4 7 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 7 T a b l e 3 . 4 5 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N d T e 3 a t 4 7 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 8 T a b l e 3 . 4 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N d T e 3 a t 5 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 9 T a b l e 3 . 4 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r N d T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 6 9 T a b l e 3 . 4 8 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r N d T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 0 T a b l e 3 . 4 9 . B o n d d i s t a n c e s [ A ] f o r N d T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . 1 7 0 T a b l e 3 . 5 0 . B o n d a n g l e s [ ° ] f o r N d T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . 1 7 0 T a b l e 3 . 5 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r S m T e 3 a t 1 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 1 T a b l e 3 . 5 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r S m T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 2 T a b l e 3 . 5 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r S m T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 2 T a b l e 3 . 5 4 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r S m T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 2 T a b l e 3 . 5 5 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r S m T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 3 T a b l e 3 . 5 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r S m T e 3 a t 4 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 4 T a b l e 3 . 5 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r S m T e 3 a t 4 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 5 T a b l e 3 . 5 8 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r S m T e 3 a t 4 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 5 T a b l e 3 . 5 9 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r S m T e 3 a t 4 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 5 T a b l e 3 . 6 0 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r S m T e 3 a t 4 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 6 T a b l e 3 . 6 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r S m T e 3 a t 5 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 7 T a b l e 3 . 6 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r S m T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 7 T a b l e 3 . 6 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r S m T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 8 T a b l e 3 . 6 4 . B o n d d i s t a n c e s [ A ] f o r S m T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . 1 7 8 T a b l e 3 . 6 5 . B o n d a n g l e s [ ° ] f o r S m T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . 1 7 8 T a b l e 3 . 6 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r G d T e 3 a t 1 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7 9 T a b l e 3 . 6 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r G d T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 0 T a b l e 3 . 6 8 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r G d T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 0 T a b l e 3 . 6 9 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r G d T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 0 T a b l e 3 . 7 0 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r G d T e ; a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 1 x x i i i T a b l e 3 . 7 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r T b T e 3 a t 1 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 2 T a b l e 3 . 7 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r T b T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 3 T a b l e 3 . 7 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r T b T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 3 T a b l e 3 . 7 4 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r T b T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 3 T a b l e 3 . 7 5 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r T b T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 4 T a b l e 3 . 7 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r D y T e 3 a t 1 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 5 T a b l e 3 . 7 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r D y T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 6 T a b l e 3 . 7 8 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r D y T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 6 T a b l e 3 . 7 9 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r D y T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 6 T a b l e 3 . 8 0 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r D y T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 7 T a b l e 3 . 8 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r H o T e 3 a t 1 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 8 T a b l e 3 . 8 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r H o T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 9 T a b l e 3 . 8 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r H o T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 9 T a b l e 3 . 8 4 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r H o T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 9 x x i v l i b l r ' t u I a T a b l e 3 . 8 5 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r H o T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 0 T a b l e 3 . 8 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r E r T e 3 a t 1 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 1 T a b l e 3 . 8 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r E r T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 2 T a b l e 3 . 8 8 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r E r T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 2 T a b l e 3 . 8 9 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r E r T e ; a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 2 T a b l e 3 . 9 0 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r E r T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 3 T a b l e 3 . 9 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r T m T e 3 a t 1 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 4 T a b l e 3 . 9 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r T m T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 5 T a b l e 3 . 9 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r T m T e ; a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 5 T a b l e 3 . 9 4 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r T m T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 5 T a b l e 3 . 9 5 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r T m T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 6 T a b l e 3 . 9 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r Y T e 3 a t 1 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 7 T a b l e 3 . 9 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r Y T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 8 T a b l e 3 . 9 8 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r Y T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 8 T a b l e 3 . 9 9 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r Y T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 8 T a b l e 3 . 1 0 0 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r Y T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 9 T a b l e 4 . 1 . A t o m i c c o o r d i n a t e s f o r K C u L a T e 4 i n P m m n u s e d f o r t h e D F T c a l c u l a t i o n . . 2 1 8 T a b l e 4 . 2 . C o m p a r i s o n o f t h e m i n i m u m a n d m a x i m u m d i s t a n c e s o f T e — T e w i t h i n t h e n e t ( X - r a y d i f f r a c t i o n a t 1 0 0 K ) a n d r o o m t e m p e r a t u r e e n e r g y g a p v a l u e s o f a l l A ] . m e R E T e 4 ( A = K , N a ; M = C u , A g ; R E = L a , C e ) q u a t e r n a r y c o m p o u n d s w i t h t h e b i n a r y R E T e 3 a n a l o g s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 4 T a b l e 4 . 3 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r u n d i s t o r t e d ( n o C D W ) K C u C e T e 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 6 T a b l e 4 . 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r K A g C e T e 4 a t 1 0 0 K . . . . . . . . . . . . . . . . . . . . . 2 2 7 T a b l e 4 . 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K A g C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 8 T a b l e 4 . 6 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K A g C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 9 T a b l e 4 . 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K A g C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 1 T a b l e 4 . 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K A g C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 1 T a b l e 4 . 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r K A g C e T e 4 a t 3 0 0 K . . . . . . . . . . . . . . . . . . . . . 2 3 7 T a b l e 4 . 1 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K A g C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 8 T a b l e 4 . 1 1 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K A g C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 9 T a b l e 4 . 1 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K A g C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4 1 x x v i T a b l e 4 . 1 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K A g C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4 1 T a b l e 4 . 1 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r K o , 7 1 ( 1 ) A g 1 , 2 9 ( 1 ) L a T e 4 a t 1 0 0 K . . . . 2 4 6 T a b l e 4 . 1 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A l e O 4 ) f o r K o _ 7 1 ( 1 ) A g 1 _ 2 9 ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4 7 T a b l e 4 . 1 6 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K o _ 7 1 ( 1 ) A g 1 . 2 9 ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4 8 T a b l e 4 . 1 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K o _ 7 1 ( 1 ) A g 1 , 2 9 ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4 9 T a b l e 4 . 1 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K o _ 7 1 ( | ) A g 1 _ 2 9 ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4 9 T a b l e 4 . 1 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r K C u C e T e 4 a t 1 0 0 K . . . . . . . . . . . . . . . . . . . . 2 5 4 T a b l e 4 . 2 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K C u C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 5 5 T a b l e 4 . 2 1 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K C u C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 5 5 T a b l e 4 . 2 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K C u C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 5 6 T a b l e 4 . 2 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K C u C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 5 7 T a b l e 4 . 2 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r K C u C e T e 4 a t 3 0 0 K . . . . . . . . . . . . . . . . . . . 2 5 9 T a b l e 4 . 2 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K C u C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 6 0 T a b l e 4 . 2 6 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K C u C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 6 0 x x v i i T a b l e 4 . 2 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K C u C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 6 1 T a b l e 4 . 2 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K C u C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 6 2 T a b l e 4 . 2 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r K C u L a T e 4 a t 1 0 0 K . . . . . . . . . . . . . . . . . . . . 2 6 4 T a b l e 4 . 3 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K O r L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 6 5 T a b l e 4 . 3 1 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K C u L a T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 6 5 T a b l e 4 . 3 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K C u L a T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 6 6 T a b l e 4 . 3 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K C u L a T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 6 7 T a b l e 4 . 3 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N a o , 7 g ( 1 ) A g 1 _ 2 2 ( 1 ) C e T e 4 a t 1 0 0 K . . 2 7 0 T a b l e 4 . 3 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r N a o _ 7 g ( 1 ) A g 1 , 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 7 1 T a b l e 4 . 3 6 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r N a o , 7 g ( 1 ) A g L 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 7 1 T a b l e 4 . 3 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N a o _ 7 g ( 1 ) A g 1 , 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 7 2 T a b l e 4 . 3 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o . 7 3 ( 1 ) A g 1 , 2 2 ( 1 ) C 8 T 8 4 a t 1 0 0 K . W l t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 7 3 T a b l e 4 . 3 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N a o , 7 o ( 1 ) A g 1 , 3 0 ( 1 ) L a T e 4 a t 1 0 0 K . . 2 7 6 T a b l e 4 . 4 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r N a o , 7 o ( 1 ) A g 1 , 3 0 ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 7 7 x x v i i i T a b l e 4 . 4 1 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r N a o , 7 o ( 1 ) A g 1 . 3 0 ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 7 7 T a b l e 4 . 4 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N a o . 7 o ( 1 ) A g 1 _ 3 0 ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 7 8 T a b l e 4 . 4 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o _ 7 0 ( 1 ) A g 1 _ 3 o ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 7 9 T a b l e 4 . 4 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N a o , 7 g ( 1 ) C u 1 , 2 2 ( 1 ) C e T e 4 a t 1 0 0 K . . 2 8 2 T a b l e 4 . 4 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r N a o _ 7 g ( 1 ) C u 1 _ 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 8 3 T a b l e 4 . 4 6 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r N a o , 7 g ( 1 ) C u 1 , 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 8 3 T a b l e 4 . 4 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N a o , 7 3 ( 1 ) C u 1 , 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 8 4 T a b l e 4 . 4 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o , 7 8 ( 1 ) C u 1 , 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 8 5 T a b l e 4 . 4 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N a o , 6 o ( 2 ) C u 1 , 4 o ( 2 ) L a T e 4 a t 1 0 0 K . . 2 8 9 T a b l e 4 . 5 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r N a o _ 6 o ( 2 ) C u 1 , 4 o ( 2 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 9 0 T a b l e 4 . 5 1 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r N a o _ 6 o ( 2 ) C u L 4 o ( 2 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 9 0 T a b l e 4 . 5 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N a 0 . 6 o ( 2 ) C u 1 _ 4 o ( 2 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 9 1 T a b l e 4 . 5 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o , 6 o ( 2 ) C u 1 , 4 o ( 2 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 9 2 T a b l e 5 . 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r s z T e 4 . 9 o ( 1 ) a t 1 0 0 K . . . . . . . . . . . . . . . . . . . . 3 4 0 x x i x T a b l e 5 . 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r s z T e 4 , 9 o ( 1 ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4 1 T a b l e 5 . 3 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r s z T e 4 _ 9 o ( 1 ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4 5 T a b l e 5 . 4 . F o u r i e r c o m p o n e n t s o f t h e o c c u p a t i o n a l m o d u l a t i o n f o r s z T e 4 _ 9 o ( 1 ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5 0 T a b l e 5 . 5 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r s z T e 4 , 9 o ( 1 ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5 0 T a b l e 5 . 6 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r s z T e 4 , 9 o ( 1 ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5 1 T a b l e 5 . 7 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r s z T e 4 , 9 o ( 1 ) a t 5 0 0 K . . . . . . . . . . . . . . . . . . . . 3 5 5 T a b l e 5 . 8 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r s z T e 4 , 9 o ( 1 ) a t 5 0 0 K w i t h e s t i m a t e d s t a n d a r d d e v i a t i o n s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . 3 5 6 T a b l e 5 . 9 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r s z T e 4 _ 9 o ( l ) a t 5 0 0 K w i t h e s t i m a t e d s t a n d a r d d e v i a t i o n s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . 3 5 7 T a b l e 5 . 1 0 . F o u r i e r c o m p o n e n t s o f t h e o c c u p a t i o n a l m o d u l a t i o n f o r s z T e 4 _ 9 o ( 1 ) a t 5 0 0 K w i t h e s t i m a t e d s t a n d a r d d e v i a t i o n s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5 8 T a b l e 5 . 1 1 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r s z T e 4 9 m ) a t 5 0 0 K w i t h e s t i m a t e d s t a n d a r d d e v i a t i o n s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5 9 T a b l e 5 . 1 2 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r s z T e 4 _ 9 o ( . ) a t 5 0 0 K w i t h e s t i m a t e d s t a n d a r d d e v i a t i o n s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 6 0 T a b l e 5 . 1 3 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r S m T e n g ) a t 1 0 0 K . . . . . . . . . . . . . . . . . . . . 3 6 4 T a b l e 5 . 1 4 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r S m T e L g é m a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 6 5 T a b l e 5 . 1 5 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r S m T e 1 _ 3 6 ( 1 ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 6 6 T a b l e 5 . 1 6 . F o u r i e r c o m p o n e n t s o f t h e o c c u p a t i o n a l m o d u l a t i o n f o r S m l T e 1 . 8 a t 1 0 0 . 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 6 8 T a b l e 5 . 1 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r S m T e 1 _ g 6 ( 1 ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 6 8 T a b l e 5 . 1 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r S m T e L s é m a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 6 9 T a b l e 5 . 1 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r K z A g 4 L a 2 T e 9 , 6 l ( 1 ) a t 1 0 0 K . . . . . . . . . 3 7 0 T a b l e 5 . 2 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K z A g 4 L a 2 T e 9 _ 6 1 ( 1 ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 7 1 T a b l e 5 . 2 1 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K z A g 4 L a 2 T e 9 , 6 1 ( 1 ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 7 7 T a b l e 5 . 2 2 . F o u r i e r c o m p o n e n t s o f t h e o c c u p a t i o n a l m o d u l a t i o n f o r K z A g 4 L a 2 T e 9 , 6 1 ( 1 ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 8 3 T a b l e 5 . 2 3 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K z A g 4 L a 2 T e 9 m m a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 8 3 T a b l e 5 . 2 4 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K z A g 4 L a 2 T e 9 _ 6 1 ( 1 ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 8 4 T a b l e 6 . 1 . M i n i m u m a n d m a x i m u m d i s t a n c e s o f T e - T e w i t h i n t h e n e t ( X - r a y d i f fi ‘ a c t i o n a t 1 0 0 K ) a n d r o o m t e m p e r a t u r e e n e r g y g a p v a l u e s o f a l l A 1 - x M 2 E u 1 + x T e 4 ( A = K , N a , R b , C s ; M = C u , A g ) q u a t e r n a r y c o m p o u n d s a n d C u o m m E u T e z . . . . . . . . . . . . . . . . 4 2 2 T a b l e 6 . 2 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N a o , 3 0 ( 2 ) C u 2 E u 1 _ 2 0 ( 2 ) T e 4 a t 1 0 0 K . . . 4 3 3 T a b l e 6 . 3 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) , o c c u p a n c i e s a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r N a o _ g o ( 2 ) C u 2 E u 1 , 2 0 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . 4 3 4 T a b l e 6 . 4 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r N a 0 _ g o ( 2 ) C u 2 E u 1 , 2 0 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 5 T a b l e 6 . 5 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N a o , 3 o ( 2 ) C U 2 E u 1 , 2 o ( 2 ) T e 4 a t 1 0 0 K W i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 6 x x x i T a b l e 6 . 6 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a 0 _ 3 0 ( 2 ) C u 2 E u 1 _ 2 0 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 6 T a b l e 6 . 7 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N a 0 _ 3 1 ( 2 ) A g 2 E u 1 , 1 9 ( 2 ) T e 4 a t 1 0 0 K . . . 4 4 0 T a b l e 6 . 8 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) , o c c u p a n c i e s a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A l e O 4 ) f o r N a o , 3 l ( 2 ) A g 2 E u 1 _ 1 9 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . 4 4 1 T a b l e 6 . 9 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r N a o , 3 1 ( 2 ) A g 2 E u 1 _ 1 9 ( z ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4 2 T a b l e 6 . 1 0 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N a o _ 3 1 ( 2 ) A g 2 E u 1 , 1 9 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4 3 T a b l e 6 . 1 1 . B o n d a n g l e s d i S t I ‘ i b u t i O I l S [ ° ] f o r N 3 0 , 3 1 ( 2 ) A g 2 E U 1 . 1 9 ( 2 ) T C 4 a t 1 0 0 K W i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4 3 T a b l e 6 . 1 2 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N a 0 _ 3 1 ( 2 ) A g 2 E u 1 , 1 9 ( 2 ) T e 4 a t 3 0 0 K . 4 4 7 T a b l e 6 . 1 3 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) , o c c u p a n c i e s a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r N a o _ 8 1 ( 2 ) A g 2 E u l , 1 9 ( 2 ) T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . 4 4 8 T a b l e 6 . 1 4 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r N a o , 3 1 ( 2 ) A g 2 E u 1 , 1 9 ( 2 ) T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4 9 T a b l e 6 . 1 5 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N a o _ g l ( 2 ) A g 2 E u 1 , 1 9 ( 2 ) T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 5 0 T a b l e 6 . 1 6 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o , g 1 ( 2 ) A g 2 E u 1 _ 1 9 ( 2 ) T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 5 0 T a b l e 6 . 1 7 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r K C q u u T e 4 a t 1 0 0 K . . . . . . . . . . . . . . . . . . 4 5 3 T a b l e 6 . 1 8 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) , o c c u p a n c i e s a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K C q u u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 5 4 T a b l e 6 . 1 9 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K C q u u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 5 5 x x x i i T a b l e 6 . 2 0 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K C q u u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 5 6 T a b l e 6 . 2 1 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K C q u u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 5 6 T a b l e 6 . 2 2 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r K o , 9 7 ( 2 ) A g 2 E u 1 _ o 3 ( 2 ) T e 4 a t 1 0 0 K . . 4 5 9 T a b l e 6 . 2 3 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) , o c c u p a n c i e s a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K o , 9 7 ( 2 ) A g 2 E u 1 , 0 3 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . 4 6 0 T a b l e 6 . 2 4 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K o , 9 7 ( 2 ) A g 2 E u 1 _ o 3 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 6 1 T a b l e 6 . 2 5 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K 0 , 9 7 ( 2 ) A g 2 E u 1 , 0 3 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 6 2 T a b l e 6 . 2 6 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K o , 9 7 ( 2 ) A g 2 E u L o 3 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 6 2 T a b l e 6 . 2 7 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r R b C q u u T e 4 a t 1 0 0 K . . . . . . . . . . . . . . . . 4 6 5 T a b l e 6 . 2 8 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) , o c c u p a n c i e s a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r R b C q u u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 6 6 T a b l e 6 . 2 9 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r R b C q u u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 6 7 T a b l e 6 . 3 0 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r R b C q u u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 6 8 T a b l e 6 . 3 1 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r R b C q u u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 6 8 T a b l e 6 . 3 2 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r R b A n g u T e 4 a t 1 0 0 K . . . . . . . . . . . . . . . . 4 7 2 T a b l e 6 . 3 3 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) , o c c u p a n c i e s a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r R b A n g u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 7 3 x x x i i i T a b l e 6 . 3 4 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r R b A n g u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 7 4 T a b l e 6 . 3 5 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r R b A n g u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 7 5 T a b l e 6 . 3 6 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r R b A n g u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 7 5 T a b l e 6 . 3 7 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C s A n g u T e 4 a t 1 0 0 K . . . . . . . . . . . . . . . . . 4 7 9 T a b l e 6 . 3 8 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) , o c c u p a n c i e s a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C s A n g u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 8 0 T a b l e 6 . 3 9 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r C s A n g u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 8 1 T a b l e 6 . 4 0 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C s A n g u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 8 2 T a b l e 6 . 4 1 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C s A n g u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 8 2 T a b l e 6 . 4 2 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C s A n g u T e 4 a t 3 0 0 K . . . . . . . . . . . . . . . . . 4 8 6 T a b l e 6 . 4 3 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C s A n g u T e 4 a t 3 0 0 K w i t h e . s . d . ’ s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 8 7 T a b l e 6 . 4 4 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r C s A n g u T e 4 a t 3 0 0 K w i t h e . s . d . ’ s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 8 8 T a b l e 6 . 4 5 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C s A n g u T e 4 a t 3 0 0 K w i t h e . s . d . ’ s . . . . . . . 4 8 9 T a b l e 6 . 4 6 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C s A n g u T e 4 a t 3 0 0 K w i t h e . s . d . ’ s . . . . . . . . . . 4 8 9 T a b l e 6 . 4 7 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C u o , 6 3 ( 2 ) E u T e 2 a t 1 0 0 K . . . . . . . . . . . . . . . 4 9 3 T a b l e 6 . 4 8 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C u o , 5 3 ( 2 ) E u T e 2 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 9 4 x x x i v T a b l e 6 . 4 9 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r C u o , 6 3 ( 2 ) E u T e 2 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 9 6 T a b l e 6 . 5 0 . F o u r i e r c o m p o n e n t s o f t h e o c c u p a t i o n a l m o d u l a t i o n f o r C u o _ 6 3 ( 2 ) E u T e 2 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 9 9 T a b l e 6 . 5 1 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C u o a m E u T e z a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 0 0 T a b l e 6 . 5 2 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C u o , 6 3 ( 2 ) E u T e 2 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 0 0 T a b l e 7 . 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C u o . 1 4 ( 1 ) U T e 3 a t 1 0 0 K . . . . . . . . . . . . . . . . . . 5 3 0 T a b l e 7 . 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C 1 1 0 , ] 4 ( 1 ) U T C 3 a t 1 0 0 K W i t h e . s . d . ’ s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 1 T a b l e 7 . 3 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r C u o , 1 4 ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 1 T a b l e 7 . 4 . F o u r i e r c o m p o n e n t s o f t h e o c c u p a t i o n a l m o d u l a t i o n f o r C u o , | 4 ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 2 T a b l e 7 . 5 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C u o . 1 4 ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s . . . . . . . . 5 3 2 T a b l e 7 . 6 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C u o _ 1 4 ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s . . . . . . . . . . . 5 3 2 T a b l e 7 . 7 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C q u g m U T e g a t 1 0 0 K . . . . . . . . . . . . . . . . . . 5 3 4 T a b l e 7 . 8 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C u o , 1 3 ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 5 T a b l e 7 . 9 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r C q u g m U T e g a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 5 T a b l e 7 . 1 0 . F o u r i e r c o m p o n e n t s o f t h e o c c u p a t i o n a l m o d u l a t i o n f o r C U o _ 1 8 ( 1 ) U T C 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 6 T a b l e 7 . 1 1 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C u o _ 2 0 ( 2 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 6 X X X V T a b l e 7 . 1 2 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C u o _ 1 8 ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 6 T a b l e 7 . 1 3 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C u o , 4 0 ( 1 ) U T e 3 a t 1 0 0 K . . . . . . . . . . . . . . . . 5 3 9 T a b l e 7 . 1 4 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C u o , 4 o ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4 0 T a b l e 7 . 1 5 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r C r r o _ 4 o ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4 0 T a b l e 7 . 1 6 . F o u r i e r c o m p o n e n t s o f t h e o c c u p a t i o n a l m o d u l a t i o n f o r C u o , 4 o ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4 1 T a b l e 7 . 1 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C u o _ 4 o ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4 1 T a b l e 7 . 1 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C u o . 4 o ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4 2 T a b l e 8 . 1 . S u m m a r y o f s u p e r c e l l p a r a m e t e r s o f R E T e 3 ( R E = L a , C e , P r , N d , S m , G d , T b , D y , Y ) a t 3 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5 7 T a b l e 8 . 2 . S u m m a r y o f s u p e r c e l l p a r a m e t e r s o f R E T e 3 ( R E = L a , C e , P r , N d , S m , G d , T b , D y , H o , E r , T m , Y ) a t 1 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5 8 T a b l e 8 . 3 . S u m m a r y o f s u p e r c e l l p a r a m e t e r s o f A M R E T e 4 ( A = N a , K ; M = C u , A g ; R E = L a , C e ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5 9 T a b l e 8 . 4 . S u m m a r y o f s u p e r c e l l p a r a m e t e r s o f A M z E u T e 4 ( A = N a , K , R b , C s ; M = C u , A g ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 6 0 x x x v i L I S T O F F I G U R E S F i g u r e 1 . 1 . S c h e m a t i c r e p r e s e n t a t i o n o f s o m e p o s s i b l e p a t t e r n s o f d i s t o r t i o n o f a n i d e a l s q u a r e n e t o f t e l l u r i u m a t o m s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0 F i g u r e 1 . 2 . S c h e m a t i c r e p r e s e n t a t i o n o f t h e l o c a l i z e d p i c t u r e o f J a h n - T e l l e r d i s t o r t i o n . ( A ) T h e u n d i s t o r t e d l i n e a r c h a i n o f a t o m s a n d t h e c o r r e s p o n d i n g m e t a l l i c s t a t e . ( B ) F o r m a t i o n o f d i m e r s a n d a g a p o p e n i n g a t t h e F e r m i l e v e l . T h i s p i c t u r e c r e a t e s f u l l y o c c u p i e d b o n d i n g o r b i t a l a n d u n o c c u p i e d a n t i b o n d i n g o r b i t a l s . . . . . . . . . . . . . . . . . . . . 1 2 F i g u r e 1 . 3 . ( A ) A q u a s i - o n e - d i m e n s i o n a l u n d i s t o r t e d m e t a l w i t h i n t e r a t o m i c s p a c i n g d ( B ) C D W m o d u l a t e d e l e c t r o n s a n d p h o n o n s a n d t h e c r e a t i o n o f a g a p a t t h e F e r m i l e v e l . T h e m o d u l a t i o n s a r e u s u a l l y q u i t e s m a l l w i t h a t o m i c d i s p l a c e m e n t s a b o u t 1 % o f t h e i n t e r a t o m i c s p a c i n g a n d t h e c o n d u c t i o n e l e c t r o n d e n s i t y v a r i e s b y s e v e r a l p e r c e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 F i g u r e 1 . 4 . ( A ) E x p e r i m e n t a l x - r a y d i f f r a c t i o n p a t t e r n o f C e T e ; p o w d e r . ( B ) T h e c o r r e c t e d a n d r e d u c e d Q [ S ( q ) - 1 ] p l o t a n d ( C ) t h e P D F G ( r ) a f t e r t h e F o u r i e r t r a n s f o r m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8 F i g u r e 1 . 5 . T y p i c a l d i f f r a c t i o n p a t t e r n ( r e c i p r o c a l s p a c e ) o f a m o d u l a t e d s y s t e m . T h e m a i n s t r o n g r e fl e c t i o n s a r e i n d e x e d a s t h O a n d t h e w e a k e r s a t e l l i t e r e fl e c t i o n s a r e i n d e x e d a s h k l m w h e r e m i s t h e ( 3 + 1 ) d i m e n s i o n a l i n d e x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 F i g u r e 1 . 6 . S c h e m a t i c r e p r e s e n t a t i o n o f r e a l d i f f r a c t i o n p a t t e r n ( 3 D ) b y a p r o j e c t i o n f r o m t h e ( 3 + 1 ) d i m e n s i o n a l s u p e r s p a c e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 F i g u r e 1 . 7 . V i s u a l i z a t i o n o f a ( 1 + 1 ) d i m e n s i o n a l s t r u c t u r e i n r e a l s p a c e . T h e s t r u c t u r e c a n b e b u i l d u p f r o m o n e f o u r - d i m e n s i o n a l b a s i c c e l l . I n d i v i d u a l a t o m s a r e n o w r e p r e s e n t e d b y a m o d u l a t i o n c u r v e ( a t o m i c s t r i n g s ) w h i c h h a s p e r i o d i c i t y f o l l o w i n g t h e f o u r d i m e n s i o n a l l a t t i c e . T h e q - v e c t o r c o m p o n e n t a l o n g c * i s n o t a t e d a s y . . . . . . . . . . . . . . . . 2 4 F i g u r e 1 . 8 . ( A ) I l l u s t r a t i o n o f a h a r m o n i c fi r n c t i o n c o m p o s e d o f a s i n g l e w a v e w i t h a n a m p l i t u d e A . T h e p e r i o d a n d p h a s e a r e i n d i c a t e d . ( B ) A c o m p l e x s q u a r e - l i k e h a r m o n i c f u n c t i o n c o m p o s e d o f t h r e e w a v e s . ( C ) A s q u a r e f u n c t i o n ( c r e n e l ) w i t h 2 a n d w i d t h A . ( D ) A s a w t o o t h f u n c t i o n w i t h c e n t e r x 2 , w i d t h A a n d m a x i m a l d i s p l a c e m e n t u 0 . B o t h c r e n e l a n d s a w t o o t h f u n c t i o n s r e p e a t p e r i o d i c a l l y c e n t e r x a l o n g t h e x 4 d i r e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 8 x x x v i i F i g u r e 1 . 9 . ( A ) U n d i s t o r t e d p a t t e r n o f a t o m s . ( B ) L o n g i t u d i n a l p o s i t i o n a l m o d u l a t i o n i n d i r e c t s p a c e . ( C ) T r a n s v e r s e p o s i t i o n a l m o d u l a t i o n i n d i r e c t s p a c e . ( D ) D i f f r a c t i o n p a t t e r n o f t h e m o d u l a t e d p a t t e r n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4 F i g u r e 1 . 1 0 . C o m b i n a t i o n o f a h a r m o n i c m o d u l a t i o n w a v e a n d a c r e n e l f u n c t i o n i n r e a l s p a c e . T h e r e s u l t i n g s e q u e n c e o f a t o m s i s s h o w n f o r t w o d i f f e r e n t t — s e c t i o n s w i t h a q - v e c t o r c o m p o n e n t o f 0 . 2 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 5 F i g u r e 1 . 1 1 . C o m b i n a t i o n o f a h a r m o n i c m o d u l a t i o n w a v e a n d a c r e n e l f u n c t i o n i n r e a l s p a c e . T h e r e s u l t i n g s e q u e n c e o f a t o m s i s s h o w n f o r t w o d i f f e r e n t t - s e c t i o n s w i t h a q - v e c t o r c o m p o n e n t o f 0 . 1 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 6 F i g u r e 2 . 1 . ( A ) U n d i s t o r t e d s t r u c t u r e o f C C T C 3 . ( B ) C o o r d i n a t i o n g e o m e t r y a n d e n v i r o n m e n t o f C e . ( C ) I d e a l s q u a r e n e t o f T e a t o m s i n t h e C e T e 3 s u b c e l l . . . . . . . . . . . . . . . . . . . . . . 5 0 F i g u r e 2 . 2 . O R T E P r e p r e s e n t a t i o n o f t h e ( A ) c o m m e n s u r a t e 7 - f o l d s u p e r c e l l o f C e T e 3 a s s e e n d o w n t h e c - a x i s ( 9 5 % p r o b a b i l i t y e l l i p s o i d s ) . ( B ) D i s t o r t e d t e l l u r i u m n e t a t a t h r e s h o l d o f 3 . 0 2 0 A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 F i g u r e 2 . 3 . ( A ) S e l e c t e d a r e a e l e c t r o n d i f f r a c t i o n ( S A E D ) p a t t e r n f o r C e T e 3 a t t h e [ 0 1 0 ] o r i e n t a t i o n s h o w i n g t h e 7 - f o l d s u p e r l a t t i c e . ( B ) I n t e n s i t y s c a n a l o n g t h e c * a x i s o f t h e S A E D p a t t e r n ( s h o w n i n r e c t a n g u l a r b o x ) a n d a p p r o x i m a t e i n d e x i n g b a s e d o n s u p e r c e l l . T h e q - v e c t o r i s a l s o i n d i c a t e d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4 F i g u r e 2 . 4 . ( A ) C r o s s s e c t i o n s e l e c t e d a r e a e l e c t r o n d i f f r a c t i o n ( S A E D ) p a t t e r n f o r C e T e 3 a t t h e [ 1 0 0 ] o r i e n t a t i o n . ( B ) T h e o r e t i c a l c a l c u l a t e d d i f f r a c t i o n p a t t e r n b a s e d o n t h e c o m m e n s u r a t e s u p e r c e l l m o d e l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5 F i g u r e 2 . 5 . P l o t o f t h e q - v e c t o r d e p e n d e n c e a s a fi m c t i o n o f R E s i z e a t 3 0 0 K . P a r a l l e l d a s h e d l i n e s n o t a t e s o m e p o s s i b l e l o w i n d e x c o m m e n s u r a t e a p p r o x i m a n t s . . . . . . . . . . . . . . . . . . . . . . 7 0 F i g u r e 2 . 6 . R e p r e s e n t a t i v e p l o t o f t h e T e [ 2 ] - T e [ 3 ] d i s t a n c e s f o u n d i n t h e d i s t o r t e d n e t o f C e T e ; f r o m t h e s u p e r s p a c e a n a l y s i s b a s e d o n a q - v e c t o r a s a f r m c t i o n o f t - d i r e c t i o n . D a s h e d l i n e s r e p r e s e n t t h e a v e r a g e ( u n d i s t o r t e d ) T e - T e d i s t a n c e s . . . . . . . . . . . . . . . . . . . . 7 0 F i g u r e 2 . 7 . P l o t o f t h e p o s i t i o n a l d i s p l a c e m e n t ( A ) a l o n g x - a x i s o f a l l t h e a t o m s i n t h e C e T e 3 s u p e r c e l l a s a f u n c t i o n o f t - d i r e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1 F i g u r e 2 . 8 . P l o t o f t h e p o s i t i o n a l d i s p l a c e m e n t ( A ) a l o n g y - a x i s o f a l l t h e a t o m s i n t h e C e T e 3 s u p e r c e l l a s a f u n c t i o n o f t - d i r e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1 ; F i g u r e 2 . 9 . P l o t o f t h e p o s i t i o n a l d i s p l a c e m e n t ( A ) a l o n g z - a x i s o f a l l t h e a t o m s i n t h e C e T e 3 s u p e r c e l l a s a f u n c t i o n o f t - d i r e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 I x x x v i i i F i g u r e 2 . 1 0 . G e n e r a l s c h e m e o f ( A ) C o m m e n s u r a t e , ( B ) I n c o m m e n s u r a t e a n d ( C ) D i s c o m m e n s u r a t e C h a r g e D e n s i t y W a v e . C i r c l e s r e p r e s e n t t h e c r y s t a l l a t t i c e a n d s o l i d l i n e s t h e e l e c t r o n d e n s i t y . A d i s c o m m e n s u r a t e w a v e c a n b e s e e n a s a c o m b i n a t i o n o f a c o m m e n s u r a t e w a v e a n d a p h a s e s l i p . T h e a v e r a g e l o n g r a n g e r e s u l t i s t h e s a m e w i t h a n i n c o m m e n s u r a t e w a v e b u t l o c a l l y t h e t w o c a s e s a r e v e r y d i f f e r e n t . . . 7 3 F i g u r e 2 . 1 1 . ( A ) R e s o l v e d s t r u c t u r e o f t h e T e n e t o f C e T e 3 a t a t h r e s h o l d o f 3 . 0 3 5 A s h o w i n g V - a n d N - s h a p e d o l i g o m e r s . ( B ) T e n e t o f P r T e 3 a t a t h r e s h o l d o f 3 . 0 2 9 A . ( C ) T e n e t o f N d T e 3 a t a t h r e s h o l d o f 3 . 0 2 8 A . T h e q - v e c t o r s c o r r e s p o n d t o a n a p p r o x i m a t e 2 5 — f o l d , 3 9 - f o l d a n d 6 3 - f o l d s u p e r c e l l r e s p e c t i v e l y . T h e b o x e d a r e a s r e p r e s e n t r e g i o n s w h e r e i d e n t i c a l d o m a i n s a r e e n c o u n t e r e d b e t w e e n R E T e 3 m e m b e r s . . . . 7 4 F i g u r e 2 . 1 2 . D i s t o r t e d T e n e t o f L a T e 3 a t 3 0 0 K w i t h q = 0 . 2 7 l 7 ( 6 ) a n d 3 . 0 4 3 A b o n d i n g t h r e s h o l d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5 F i g u r e 2 . 1 3 . D i s t o r t e d T e n e t o f S m T e 3 a t 3 0 0 K w i t h q = 0 . 2 8 7 4 ( 4 ) a n d 3 . 0 1 8 A b o n d i n g t h r e s h o l d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5 F i g u r e 2 . 1 4 . D i s t o r t e d T e n e t o f G d T e 3 a t 3 0 0 K w i t h q = 0 . 2 9 l 6 ( 3 ) a n d 3 . 0 0 3 A b o n d i n g t h r e s h o l d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5 F i g u r e 2 . 1 5 . D i s t o r t e d T e n e t o f T b T e 3 a t 3 0 0 K w i t h q = 0 . 2 9 5 7 ( 5 ) a n d 3 . 0 1 9 A b o n d i n g t h r e s h o l d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 6 F i g u r e 2 . 1 6 . D i s t o r t e d T e n e t o f D y T e 3 a t 3 0 0 K w i t h q = 0 . 2 9 8 4 ( 3 ) a n d 3 . 0 2 3 A b o n d i n g t h r e s h o l d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 6 F i g u r e 2 . 1 7 . T e n e t o f H o T e 3 , E r T e 3 a n d T m T e 3 a t 3 0 0 K w i t h n o o b s e r v a b l e q - v e c t o r . . 7 6 F i g u r e 2 . 1 8 . ( A ) F i t o f t h e e x p e r i m e n t a l P D F d a t a i n t h e r a n g e o f 2 - 2 0 A ( B ) F i r s t P D F p e a k w h i c h r e p r e s e n t s t h e l o c a l s t r u c t u r e o f t h e C 8 T C 3 . T h e s o l i d l i n e r e p r e s e n t s t h e a v e r a g e s t r u c t u r a l m o d e l a n d t h e c i r c l e s t h e e x p e r i m e n t a l d a t a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 7 F i g u r e 2 . 1 9 . T h e r e d u c e d Q [ S ( q ) - 1 ] a n d P D F G ( r ) p l o t s o f P r T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 8 F i g u r e 2 . 2 0 . T h e r e d u c e d Q [ S ( q ) - 1 ] a n d P D F G ( r ) p l o t s o f N d T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 9 F i g u r e 2 . 2 1 . B a n d s t r u c t u r e o f L a T e 3 n e a r t h e F e r m i l e v e l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1 F i g u r e 2 . 2 2 . ( A ) P a r t i a l d e n s i t y o f s t a t e ( D O S ) o f t h e p o r b i t a l o f T e [ 3 ] a n d ( B ) t o t a l D O S o f t h e L a T e 3 s u b c e l l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2 x x x i x F i g u r e 2 . 2 3 . ( A ) B r i l l o u i n z o n e o f C m c m s p a c e g r o u p ( B ) F e r m i s u r f a c e t o p o l o g y o f L a T e 3 w i t h a n a v e r a g e n e s t i n g v e c t o r o f 0 2 8 ( 2 ) ( s o l i d a r r o w s ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3 F i g u r e 3 . 1 . ( A ) U n d i s t o r t e d s t r u c t u r e o f C e T e 3 . ( B ) C o o r d i n a t i o n g e o m e t r y a n d e n v i r o n m e n t o f C e . ( C ) I d e a l s q u a r e n e t o f T e a t o m s i n t h e C e T e 3 s u b c e l l . . . . . . . . . . . . . . . . . . . . 1 2 8 F i g u r e 3 . 2 . q - v e c t o r d e p e n d e n c e a s a f r m c t i o n o f R E e l e m e n t a n d t e m p e r a t u r e . P a r a l l e l d a s h e d l i n e s n o t a t e s o m e p o s s i b l e l o w i n d e x c o m m e n s u r a t e a p p r o x i m a n t s . . . . . . 1 3 0 F i g u r e 3 . 3 . E v o l u t i o n o f t h e C D W i n t h e T e n e t o f S m T e 3 w i t h t e m p e r a t u r e . ( A ) t h e T e n e t o f S m T e 3 a t 1 0 0 K . V - a n d N - s h a p e d o l i g o m e r s a r e s h o w n u s i n g a b o n d i n g t h r e s h o l d o f 3 . 0 0 2 A . ( B ) T e n e t a t 3 0 0 K a t a t h r e s h o l d o f 3 . 0 1 8 A ( C ) T e n e t a t 4 0 0 K , m i n i m u m t h r e s h o l d o f 3 . 0 4 2 A a n d m a x i m u m a t 3 . 0 6 3 A . I n t r a - a n d i n t e r - c h a i n i n t e r a c t i o n s b e g i n t o b e m o r e c o m p a r a b l e . ( D ) P e r f e c t n e t d u e t o v a n i s h i n g o f t h e ' C D W a t 5 0 0 K a t a t h r e s h o l d o f 3 . 0 7 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 3 F i g u r e 3 . 4 . L a T e 3 a t 1 0 0 K w i t h q = 0 . 2 7 1 9 ( 4 ) a n d 3 . 0 3 4 A b o n d i n g t h r e s h o l d . . . . . . . . . . . . . . 1 3 4 F i g u r e 3 . 5 . L a T e ; a t 5 0 0 K w i t h q = 0 . 2 7 9 3 ( 4 ) a n d 3 . 0 6 5 A b o n d i n g t h r e s h o l d . . . . . . . . . . . . . . 1 3 4 F i g u r e 3 . 6 . C e T e 3 a t 1 0 0 K w i t h q = 0 . 2 7 9 0 ( 3 ) a n d 3 . 0 1 5 A b o n d i n g t h r e s h o l d . . . . . . . . . . . . . . 1 3 4 F i g u r e 3 . 7 . C e T e 3 a t 5 0 0 K w i t h q = 0 . 2 8 6 7 ( 5 ) a n d 3 . 0 6 6 A b o n d i n g t h r e s h o l d . . . . . . . . . . . . . . 1 3 5 F i g u r e 3 . 8 . P r T e 3 a t 1 0 0 K w i t h q = 0 . 2 8 2 5 ( 5 ) a n d 3 . 0 1 5 A b o n d i n g t h r e s h o l d . . . . . . . . . . . . . . . 1 3 5 F i g u r e 3 . 9 . P r T e 3 a t 5 0 0 K w i t h q = 0 . 2 8 6 4 ( 5 ) a n d 3 . 0 5 7 A b o n d i n g t h r e s h o l d . . . . . . . . . . . . . . . 1 3 5 F i g u r e 3 . 1 0 . N d T e 3 a t 1 0 0 K w i t h q = 0 . 2 8 2 4 ( 4 ) a n d 3 . 0 0 7 A b o n d i n g t h r e s h o l d . . . . . . . . . . . 1 3 6 F i g u r e 3 . 1 1 . N d T e 3 a t 4 7 0 K w i t h q = 0 . 2 8 7 4 ( 4 ) a n d 3 . 0 4 3 A b o n d i n g t h r e s h o l d . . . . . . . . . . . 1 3 6 F i g u r e 3 . 1 2 . N d T e 3 a t 5 0 0 K w i t h n o o b s e r v a b l e q - v e c t o r a n d 3 . 0 9 8 A b o n d i n g t h r e s h o l d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 6 F i g u r e 3 . 1 3 . G d T e 3 a t 1 0 0 K w i t h q = 0 . 2 8 8 4 ( 3 ) a n d 2 . 9 9 3 A b o n d i n g t h r e s h o l d . . . . . . . . . . . 1 3 7 F i g u r e 3 . 1 4 . T b T e 3 a t 1 0 0 K w i t h q = 0 . 2 9 1 2 ( 5 ) a n d 2 . 9 9 5 A b o n d i n g t h r e s h o l d . . . . . . . . . . . . 1 3 7 F i g u r e 3 . 1 5 . D y T e 3 a t 1 0 0 K w i t h q = 0 . 2 9 2 6 ( 3 ) a n d 2 . 9 9 3 A b o n d i n g t h r e s h o l d . . . . . . . . . . . 1 3 7 F i g u r e 3 . 1 6 . H o T e 3 a t 1 0 0 K w i t h q = 0 . 2 9 3 5 ( 3 ) a n d 2 . 9 9 2 A b o n d i n g t h r e s h o l d . . . . . . . . . . . 1 3 8 x 1 F i g u r e 3 . 1 7 . E r T e 3 a t 1 0 0 K w i t h q = 0 . 2 9 9 2 ( 4 ) a n d 2 . 9 8 8 A b o n d i n g t h r e s h o l d . . . . . . . . . . . . 1 3 8 F i g u r e 3 . 1 8 . T m T e ; a t 1 0 0 K w i t h q = 0 . 3 0 2 8 ( 4 ) a n d 2 . 9 8 0 A b o n d i n g t h r e s h o l d . . . . . . . . . . . 1 3 8 F i g u r e 3 . 1 9 . E x p e r i m e n t a l F o u r i e r m a p o f C e T e 3 a t 1 0 0 K p l o t t e d a l o n g t h e m o d u l a t i o n d i r e c t i o n ( t ) . T h e c e n t r a l l i n e r e p r e s e n t s t h e c a l c u l a t e d ( fi t t e d ) p o s i t i o n o f T e [ 2 ] ( A ) F o u r i e r m a p w i t h t h e fi r s t o r d e r s a t e l l i t e r e fl e c t i o n s . O n e c o n t o u r l i n e p e r 0 . 2 e ‘ A ' 3 . P o s i t i v e ( s o l i d l i n e ) c u t o f f 2 . 6 7 e ' A ' 3 a n d n e g a t i v e ( d a s h e d l i n e ) c u t o f f - 0 . 4 6 e ‘ A ' 3 . ( B ) F o u r i e r m a p i n c l u d i n g b o t h fi r s t a n d s e c o n d o r d e r s a t e l l i t e r e fl e c t i o n s . O n e c o n t o u r l i n e p e r 1 e ‘ A ’ 3 . P o s i t i v e c u t o f f 2 8 . 0 8 e ' A ' 3 a n d n e g a t i v e c u t o f f - 2 . 4 l e ' A ' 3 . . . . . . . 1 3 9 F i g u r e 3 . 2 0 . I n t e n s i t y s c a n a l o n g t h e c * - a x i s o f t h e t e m p e r a t u r e d e p e n d e n t ( 2 5 0 - 3 2 5 K ) S A E D p a t t e r n s o f t h e ( 1 0 1 ) f a m i l y o f r e fl e c t i o n f o r H o T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 4 0 F i g u r e 4 . 1 . ( A ) T h e l a y e r e d s t r u c t u r e o f R E T e ; ( N d T e g - t y p e ) . T h e v a n d e r W a a l s g a p i s i n d i c a t e d b y t h e a r r o w . ( B ) T h e u n d i s t o r t e d s q u a r e n e t o f T e a t o m s i n R E T e 3 a n d A M R E T e 4 . ( C ) T h e e l e c t r o n i c a l l y n e u t r a l A C u T e l a y e r w h i c h w h e n i n s e r t e d i n t h e s t r u c t u r e o f R E T e ; g i v e s A M R E T e 4 . ( D ) T h e s t r u c t u r e o f A M R E T e 4 ( A = K , N a ; M = C u , A g ; R E = L a , C e ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0 9 F i g u r e 4 . 2 . N a o _ 5 1 ( 2 ) C u 1 _ 3 9 ( 2 ) L a T e 4 a t 1 0 0 K w i t h q = 0 . 3 6 3 2 ( 8 ) b ‘ + 1 / 2 e ‘ a n d 3 . 0 7 5 A t h r e s h o l d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 2 F i g u r e 4 . 3 . N a o _ 7 5 ( 2 ) C U r . 2 5 ( 2 ) C e T e 4 a t 1 0 0 K w i t h q = 0 . 3 6 2 1 ( 7 ) b ' a n d 3 . 0 3 5 A t h r e s h o l d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 2 F i g u r e 4 . 4 . N a o , 7 2 ( 1 ) A g 1 , 2 3 ( 1 ) L a T e 4 a t 1 0 0 K W i t h ( 1 = 0 . 3 6 6 0 ( 8 ) b ‘ I + 1 / 2 0 . a n d 3 . 0 9 7 A t h r e s h o l d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 2 F i g u r e 4 . 5 . N a o , 7 9 ( 1 ) A g 1 _ 2 1 ( 1 ) C e T e 4 a t 1 0 0 K w i t h q = 0 . 3 6 8 1 ( 8 ) b i a n d 3 . 0 7 0 A t h r e s h o l d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 3 F i g u r e 4 . 6 . K C u L a T e 4 a t 1 0 0 K w i t h q = 0 . 3 8 6 1 ( 5 ) b i + l / 2 c ' a n d 3 . 1 0 9 A t h r e s h o l d . . . 2 1 3 F i g u r e 4 . 7 . K o , 7 1 ( 1 ) A g 1 , 2 9 ( 1 ) L a T e 4 a t 1 0 0 K w i t h q = 0 . 3 4 6 6 ( 7 ) b ' + 1 / 2 e ‘ a n d 3 . 0 6 2 A t h r e s h o l d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 4 F i g u r e 4 . 8 . K o _ 7 . ( 1 ) A g 1 _ 2 9 ( 1 ) L a T e 4 a t 3 0 0 K w i t h q = 0 . 3 4 5 0 ( 7 ) b ’ + 1 / 2 e ‘ a n d 3 . 1 0 0 A t h r e s h o l d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 4 F i g u r e 4 . 9 . K A g C e T e 4 a t 1 0 0 K w i t h q = 0 . 3 3 6 1 ( 6 ) b ' + 1 0 6 a n d 3 . 0 8 0 A t h r e s h o l d . . 2 1 5 F i g u r e 4 . 1 0 . K A g C e T e 4 a t 3 0 0 K w i t h q = 0 . 3 3 8 1 ( 8 ) b i + 1 / 2 e “ a n d 3 . 0 9 6 A t h r e s h o l d 2 1 5 x l i F i g u r e 4 . 1 1 . K C u C e T e 4 a t 1 0 0 K w i t h q = 0 . 3 5 5 0 ( 8 ) b ' + 1 / 2 c i a n d 3 . 0 5 5 A t h r e s h o l d 2 1 5 F i g u r e 4 . 1 2 . C o m p a r i s o n o f t h e e x p e r i m e n t a l X - r a y p o w d e r p a t t e r n o f N a A g C e T e 4 w i t h t h e c a l c u l a t e d p o w d e r p a t t e r n s o f t h e q u a t e r n a r y a n d C e T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 7 F i g u r e 4 . 1 3 . B a n d s t r u c t u r e o f K C u L a T e 4 n e a r t h e F e r m i l e v e l . C u d a n d T e [ 3 ] p b a n d s f r o m t h e [ K C u T e ] l a y e r a r e d r a w n i n o p e n c i r c l e s . T e [ l ] a n d T e [ 2 ] p b a n d s f r o m t h e d i s t o r t e d p l a n a r n e t a r e d r a w n i n c l o s e d c i r c l e s . T h e c o n t r i b u t i o n o f e a c h o r b i t a l i s p r o p o r t i o n a l t o t h e b r e a d t h o f t h e c i r c l e s t r a c i n g o u t t h e b a n d . O n l y t h e b a n d s t h a t c r o s s t h e F e r m i s u r f a c e a r e d r a w n i n c i r c l e s f o r c l a r i t y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 9 F i g u r e 4 . 1 4 . T o t a l d e n s i t y o f s t a t e s ( D O S ) o f K C u L a T e 4 n e a r t h e F e r m i l e v e l . T e [ l ] a n d T e [ 2 ] a r e t h e t e l l u r i u m a t o m s i n t h e [ R E T e 3 ] n e t , T e [ 3 ] i s i n t h e [ C u T e ] l a y e r a n d T e [ 4 ] i s i n t h e [ R E T e 3 ] s l a b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 0 F i g u r e 4 . 1 5 . B r i l l o u i n z o n e o f P m m n s p a c e g r o u p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 1 F i g u r e 4 . 1 6 . F e r m i s u r f a c e t o p o l o g y o f K C u L a T e 4 . P o s s i b l e n e s t i n g v e c t o r s ( q - v e c t o r s ) w i t h a n a v e r a g e l e n g t h o f 0 3 3 ( 2 ) a l o n g t h e b * - a x i s ( Y p o i n t ) a r e d r a w n i n a r r o w s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 1 F i g u r e 4 . 1 7 . T e m p e r a t u r e d e p e n d e n t r e s i s t i v i t y o f K C u L a T e 4 s i n g l e c r y s t a l . . . . . . . . . . . . . . . . . . 2 2 2 F i g u r e 4 . 1 8 . D e p e n d e n c e o f t h e r m o p o w e r w i t h t e m p e r a t u r e o f K C u L a T e 4 s i n g l e c r y s t a l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 3 F i g u r e 4 . 1 9 . T y p i c a l r o o m t e m p e r a t u r e i n f r a r e d a b s o r p t i o n s p e c t r u m o f N a o , 7 g C u 1 2 2 C e T e 4 s h o w i n g e n e r g y g a p a t a r o u n d 0 . 2 7 e V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 4 F i g u r e 5 . 1 . S E M i m a g e o f a t h i c k p l a t e - l i k e s z T e s s i n g l e c r y s t a l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 3 F i g u r e 5 . 2 . C o m p a r i s o n o f t h e e x p e r i m e n t a l p o w d e r d i f f r a c t i o n p a t t e r n o f t h e a s p r e p a r e d s z T e s c o m p o u n d w i t h t h e c a l c u l a t e d p a t t e r n s o f S m T e ; a n d s z T e s . R e l a t i v e i n t e n s i t y o f t h e e x p e r i m e n t a l p a t t e r n i s d i f f e r e n t f r o m t h e c a l c u l a t e d o n e d u e t o p r e f e r e n t i a l o r i e n t a t i o n o f t h e p l a t e - l i k e c r y s t a l s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 4 F i g u r e 5 . 3 . S E M i m a g e o f a p l a t e - l i k e K z A g 4 L a 2 T e 1 0 s i n g l e c r y s t a l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 4 F i g u r e 5 . 4 . C o m p a r i s o n o f t h e e x p e r i m e n t a l p o w d e r d i f f r a c t i o n p a t t e r n o f t h e a s p r e p a r e d K z A g 4 L a 2 T e 1 0 c o m p o u n d w i t h t h e c a l c u l a t e d p a t t e r n s o f K A g L a T e 4 a n d K z q u L a z T e l o . R e l a t i v e i n t e n s i t y o f t h e e x p e r i m e n t a l p a t t e r n i s d i f f e r e n t f r o m t h e c a l c u l a t e d o n e d u e t o p r e f e r e n t i a l o r i e n t a t i o n o f t h e p l a t e - l i k e c r y s t a l s . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0 5 x l i i F i g u r e 5 . 5 . ( A ) T h e a v e r a g e s t r u c t u r e o f R E T e z ( C u Z S b - t y p e ) w i t h s q u a r e n e t s o f ( B ) T h e a v e r a g e l a y e r e d s t r u c t u r e o f R E T e 3 ( N d T e 3 - t y p e ) w i t h s q u a r e n e t s o f T e l / 2 . ( C ) T h e h y b r i d a v e r a g e l l a y e r e d s t r u c t u r e o f R E z T e s ( N d z T e s - t y p e ) w i t h s q u a r e n e t s o f b o t h T e a n d T e " . T h e v a n d e r W a a l s ( v d W ) g a p s a r e i n d i c a t e d . . . . . . . . . . 3 0 9 F i g u r e 5 . 6 . T h e a v e r a g e s t r u c t u r e o f K z A g 4 L a 2 T e 1 0 w i t h s q u a r e n e t s o f T e l / L a n d T e l ' . 3 1 1 F i g u r e 5 . 7 . ( A ) T r a n s f o r m e d c e l l o f s z T e s a n d l a b e l i n g s c h e m e u s e d i n t h e s u p e r s p a c e r e fi n e m e n t . ( B ) C e l l l a b e l i n g s c h e m e i n S m T e z s u p e r c e l l . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 4 F i g u r e 5 . 8 . T o ” n e t o f s z T e s a t 1 0 0 K w i t h 3 . 0 1 7 A b o n d i n g t h r e s h o l d . . . . . . . . . . . . . . . . . . . 3 1 5 F i g u r e 5 . 9 . T e l ' n e t o f s z T e s a t 1 0 0 K w i t h 3 . 1 1 0 A b o n d i n g t h r e s h o l d a n d 8 0 % o c c u p a t i o n a l c u t o f f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 5 F i g u r e 5 . 1 0 . T o ” n e t o f s z T e s a t 5 0 0 K w i t h 3 . 0 7 4 A b o n d i n g t h r e s h o l d . . . . . . . . . . . . . . . . . 3 1 6 F i g u r e 5 . 1 1 . T e " n e t o f s z T e s a t 5 0 0 K w i t h 3 . 0 8 0 A b o n d i n g t h r e s h o l d a n d 8 0 % o c c u p a t i o n a l c u t o f f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 6 F i g u r e 5 . 1 2 . P r o fi l e o f t h e o c c u p a n c y o f T e [ 3 a ] i n s z T e 4 , 9 o ( 1 ) a t 1 0 0 K a l o n g t h e t - d i r e c t i o n a t a fi x e d u = 0 . 5 s e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 7 F i g u r e 5 . 1 3 . C o n t o u r p l o t o f t h e o c c u p a n c y o f T e [ 3 a ] i n s z T e 4 , 9 o ( 1 ) a l o n g t h e t - u s p a c e . O n e c o n t o u r l i n e p e r 0 . 1 ( o c c u p a t i o n a l fi a c t i o n ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 8 F i g u r e 5 . 1 4 . P r o fi l e o f t h e o c c u p a n c y o f T e [ 3 a ] i n s z T e 4 , 9 o ( 1 ) a t 5 0 0 K a l o n g t h e t - d i r e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 8 F i g u r e 5 . 1 5 . E x p e r i m e n t a l F o u r i e r m a p o f s z T e 4 9 0 ( 1 ) a t 1 0 0 K p l o t t e d a l o n g t h e m o d u l a t i o n d i r e c t i o n ( t ) . T h e c e n t r a l b l u e l i n e r e p r e s e n t s t h e c a l c u l a t e d ( fi t t e d ) p o s i t i o n o f T e [ 3 a ] . O n e c o n t o u r l i n e p e r 0 . 7 5 e “ ' 3 . A S u m m a t i o n o f x 2 a l o n g 0 . 5 - 1 . 0 a n d x 5 = 0 . 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1 9 F i g u r e 5 . 1 6 . ( A ) S T M i m a g e o f t h e s z T e s s u r f a c e o f T e l ” . ( B ) F F T o f t h e S T M i m a g e . T h e p e a k s L c o r r e s p o n d t o t h e T e s q u a r e l a t t i c e . ( C ) L i n e c u t p l o t f r o m O t o A , a l o n g t h e d i a g o n a l o f t h e T e s q u a r e n e t . ( D ) L i n e c u t p l o t f r o m O t o L . . . . . . . . . . . . . . . . . . . . . 3 2 0 F i g u r e 5 . 1 7 . R o o m t e m p e r a t u r e i n f r a r e d a b s o r p t i o n s p e c t r u m o f s z T e s s i n g l e c r y s t a l s . E n e r g y g a p a t ~ 0 . 2 5 e V c o r r e s p o n d s t o t h e C D W d i s t o r t e d T e n e t s . . . . . . . . . . . . . . . . 3 2 1 F i g u r e 5 . 1 8 . T e l ' n e t o f S m T e z a t 1 0 0 K w i t h 3 . 1 1 0 A b o n d i n g t h r e s h o l d a n d 8 6 % o c c u p a t i o n a l c u t o f f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 3 x l i i i F i g u r e 5 . 1 9 . C o n t o u r p l o t o f t h e o c c u p a n c y o f T e [ 2 ] i n S m T e L g s m a l o n g t h e t - u s p a c e . O n e c o n t o u r l i n e p e r 0 . 0 5 ( o c c u p a t i o n a l f r a c t i o n ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 4 F i g u r e 5 . 2 0 . T r a n s f o r m e d c e l l o f K z A g 4 L a 2 T e o g m ) a n d l a b e l s u s e d i n t h e s u p e r s p a c e r e fi n e m e n t a t 1 0 0 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 6 F i g u r e 5 . 2 1 . T e l / 2 ' n e t o f K 2 A g 4 L a 2 T e o , 6 1 ( 1 ) a t 1 0 0 K w i t h 3 . 0 1 7 A b o n d i n g t h r e s h o l d s h o w i n g t r i m e r s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 6 F i g u r e 5 . 2 2 . T e l ‘ n e t o f K z A g 4 L a 2 T e o 6 m ) a t 1 0 0 K w i t h 3 . 1 1 0 A b o n d i n g t h r e s h o l d a n d 6 0 % o c c u p a t i o n a l c u t o f f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 7 F i g u r e 5 . 2 3 . C o n t o u r p l o t o f t h e o c c u p a n c y o f T e [ 2 ] i n S m T e L g m ) a l o n g t h e t — u s p a c e . O n e c o n t o u r l i n e p e r 0 . 0 5 ( o c c u p a t i o n a l f r a c t i o n ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 8 F i g u r e 5 . 2 4 . B a n d s t r u c t u r e o f L a z T e s n e a r t h e F e r m i l e v e l . T e [ 3 ] p b a n d s f r o m t h e T e ’ n e t a r e d r a w n i n o p e n c i r c l e s . T h e c o n t r i b u t i o n o f e a c h o r b i t a l i s p r o p o r t i o n a l t o t h e b r e a d t h o f t h e c i r c l e s t r a c i n g o u t t h e b a n d . O n l y t h e b a n d s t h a t c r o s s t h e F e r m i s u r f a c e a r e d r a w n i n c i r c l e s f o r c l a r i t y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 1 F i g u r e 5 . 2 5 . T o t a l d e n s i t y o f s t a t e s ( D O S ) o f L a z T e s n e a r t h e F e r m i l e v e l . T e [ l ] a n d T e [ 2 ] a r e t h e t e l l u r i u m a t o m s i n t h e [ R E T e ] p u c k e r e d l a y e r s , T e [ 3 ] i s i n t h e T e l ' n e t a n d T e [ 4 ] , T e [ 5 ] a r e i n t h e r e ” n e t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 2 F i g u r e 5 . 2 6 . P a r t i a l d e n s i t y o f s t a t e s ( D O S ) o f a l l T e p b a n d s i n L a z T e s n e a r t h e F e r m i l e v e l . T e [ l ] a n d T e [ 2 ] a r e t h e t e l l u r i u m a t o m s i n t h e [ R E T e ] p u c k e r e d l a y e r s , T e [ 3 ] i s i n t h e T e ' n e t a n d T e [ 4 ] , T e [ 5 ] a r e i n t h e T e l / 2 ' n e t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 3 F i g u r e 5 . 2 7 . ( A - F ) F e r m i s u r f a c e t o p o l o g y o f t h e s i x i n d i v i d u a l b a n d s t h a t c r o s s t h e F e r m i l e v e l o f L a z T e 5 . S u p e r p o s i t i o n o f a l l s i x b a n d s w i l l g i v e t h e t o t a l F e r m i s u r f a c e s h o w n i n F i g u r e 5 . 2 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 4 F i g u r e 5 . 2 8 . C a l c u l a t e d F e r m i s u r f a c e t o p o l o g y o f L a g T e s . P o s s i b l e n e s t i n g v e c t o r s w i t h a n a v e r a g e l e n g t h o f q ] = 0 3 2 ( 2 ) a l o n g t h e b * a x i s ( Y p o i n t ) a n d q ; = 0 3 5 ( 2 ) a l o n g t h e d i a g o n a l a r e d r a w n i n a r r o w s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 5 F i g u r e 5 . 2 9 . B r i l l o u i n z o n e o f C m c m s p a c e g r o u p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 5 F i g u r e 5 . 3 0 . B a n d s t r u c t u r e o f K z A g 4 L a 2 T e 1 0 n e a r t h e F e r m i l e v e l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 6 F i g u r e 5 . 3 1 . P a r t i a l d e n s i t y o f s t a t e s ( D O S ) o f a l l T e p b a n d s K 2 A g 4 L a 2 T e l o n e a r t h e F e r m i l e v e l . T e [ l ] a n d T e [ 2 ] a r e t h e t e l l u r i u m a t o m s i n t h e [ R E T e ] p u c k e r e d l a y e r s , T e [ 3 ] a n d T e [ 4 ] a r e i n t h e T e l / 2 ' n e t a n d T e [ 5 ] , T e [ 6 ] a r e i n t h e T e ' n e t . . . . . . . . . . . . . . . . . . . . . . . . 3 3 7 x l i v F i g u r e 5 . 3 2 . ( A - G ) F e r m i s u r f a c e t o p o l o g y o f t h e s e v e n i n d i v i d u a l b a n d s t h a t c r o s s t h e F e r m i l e v e l o f K z A g 4 L a 2 T e 1 0 . S u p e r p o s i t i o n o f a l l s e v e n b a n d s w i l l g i v e t h e F e r m i s u r f a c e ( H ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 8 F i g u r e 5 . 3 3 . B r i l l o u i n z o n e o f I m m m s p a c e g r o u p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 9 F i g u r e 6 . 1 . U n d i s t o r t e d s t r u c t u r e o f A M z E u T e 4 . T h e i n t e r p l a n a r s e p a r a t i o n d c h a n g e s f r o m ~ 3 . 7 A i n t h e N a + , t o ~ 4 . 2 A i n t h e K + , t o ~ 4 . 7 A i n t h e R b : a n d t o ~ 5 . 1 A i n t h e C s + a n a l o g u e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 0 2 F i g u r e 6 . 2 . ( A ) C o o r d i n a t i o n g e o m e t r y a n d e n v i r o n m e n t o f E u i n N a A n g u T e 4 . ( B ) C o o r d i n a t i o n g e o m e t r y a n d e n v i r o n m e n t o f N a i n N a A n g u T e 4 . ( C ) S q u a r e n e t o f T e a t o m s i n t h e s u b c e l l o f N a A n g u T e 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 0 3 F i g u r e 6 . 3 . U n d i s t o r t e d s t r u c t u r e o f C u x E u T e z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 0 5 F i g u r e 6 . 4 . R e p r e s e n t a t i v e p l o t o f t h e T e [ 3 ] - T e [ 4 ] d i s t a n c e s f o u n d i n t h e d i s t o r t e d n e t o f C s A n g u T e 4 f r o m t h e s u p e r s p a c e a n a l y s i s b a s e d o n a q - v e c t o r a s a f u n c t i o n o f t - d i r e c t i o n . D a s h e d l i n e s r e p r e s e n t t h e a v e r a g e ( u n d i s t o r t e d ) T e - T e d i s t a n c e s . . . . . . . . . . . . . . . . . . 4 0 9 F i g u r e 6 . 5 . P l o t o f t h e p o s i t i o n a l d i s p l a c e m e n t ( A ) a l o n g x - a x i s o f a l l t h e a t o m s i n t h e C s A n g u T e 4 s u p e r c e l l a s a f u n c t i o n o f t - d i r e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 0 9 F i g u r e 6 . 6 . P l o t o f t h e p o s i t i o n a l d i s p l a c e m e n t ( A ) a l o n g y - a x i s o f a l l t h e a t o m s i n t h e C s A n g u T e 4 s u p e r c e l l a s a f u n c t i o n o f t - d i r e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1 0 F i g u r e 6 . 7 . P l o t o f t h e p o s i t i o n a l d i s p l a c e m e n t ( A ) a l o n g z - a x i s o f a l l t h e a t o m s i n t h e C s A n g u T e 4 s u p e r c e l l a s a f u n c t i o n o f t - d i r e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1 0 F i g u r e 6 . 8 . T h e T e [ 3 ] - T e [ 4 ] d i s t a n c e s f o u n d i n t h e d i s t o r t e d n e t o f C u o m m E u T e z f r o m t h e s u p e r s p a c e a n a l y s i s b a s e d o n a q - v e c t o r a s a f u n c t i o n o f t - d i r e c t i o n . D a s h e d l i n e s r e p r e s e n t t h e a v e r a g e ( u n d i s t o r t e d ) T e - T e d i s t a n c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1 8 F i g u r e 6 . 9 . P l o t o f t h e p o s i t i o n a l d i s p l a c e m e n t ( A ) a l o n g x - a x i s o f a l l t h e a t o m s i n t h e C u o , 5 3 ( 2 ) E u T e 2 s u p e r c e l l a s a f u n c t i o n o f t - d i r e c t i o n f o r u = 0 . 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1 8 F i g u r e 6 . 1 0 . P l o t o f t h e p o s i t i o n a l d i s p l a c e m e n t ( A ) a l o n g y - a x i s o f a l l t h e a t o m s i n t h e C u o , 6 3 ( 2 ) E u T e 2 s u p e r c e l l a s a fi m c t i o n o f t - d i r e c t i o n f o r u = 0 . 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1 9 F i g u r e 6 . 1 1 . P l o t o f t h e p o s i t i o n a l d i s p l a c e m e n t ( A ) a l o n g z - a x i s o f a l l t h e a t o m s i n t h e C u o s s m E u T e z s u p e r c e l l a s a f u n c t i o n o f t — d i r e c t i o n f o r u = 0 . 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1 9 x l v F i g u r e 6 . 1 2 . T h e C u [ l a ] - C u [ l b ] d i s t a n c e s f o u n d i n t h e d i s t o r t e d n e t o f C u o m m E u T e z f r o m t h e s u p e r s p a c e a n a l y s i s b a s e d o n a q — v e c t o r a s a f u n c t i o n o f t - d i r e c t i o n . D a s h e d l i n e s r e p r e s e n t t h e a v e r a g e ( u n d i s t o r t e d ) C u - C u d i s t a n c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 0 F i g u r e 6 . 1 3 . T e m p e r a t u r e d e p e n d e n t m a g n e t i c s u s c e p t i b i l i t y f o r N a A n g u T e 4 . . . . . . . . . . . . . 4 2 1 F i g u r e 6 . 1 4 . T y p i c a l r o o m t e m p e r a t u r e i n f r a r e d a b s o r p t i o n s p e c t r u m o f . . . . . . . . . . . . . . . . . . . . . . . 4 2 2 F i g u r e 6 . 1 5 . B a n d s t r u c t u r e o f N a C u z L u T e 4 n e a r t h e F e r m i l e v e l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 6 F i g u r e 6 . 1 6 . F e r m i s u r f a c e t o p o l o g y o f t h e t w o i n d i v i d u a l b a n d s ( A a n d B ) t h a t c r o s s t h e F e r m i l e v e l o f N a C u z L u T e 4 . ( C ) S u p e r p o s i t i o n o f t h e s e b a n d s w i l l g i v e t h e t o t a l F e r m i s u r f a c e . P o s s i b l e n e s t i n g v e c t o r s a r e d r a w n i n a r r o w s . 5 1 x 5 1 k p o i n t s w e r e u s e d f o r t h e c a l c u l a t i o n o f t h e F e r m i s u r f a c e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 7 F i g u r e 6 . 1 7 . B a n d s t r u c t u r e o f C u L u T e z n e a r t h e F e r m i l e v e l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 8 F i g u r e 6 . 1 8 . F e r m i s u r f a c e t o p o l o g y f o r C u x L u T e z . ( A ) x = 1 . ( B ) x = 2 / 3 . ( C ) x = 1 / 3 . ( D ) T h e fi r s t b a n d t h e c r o s s e s t h e F e r m i s u r f a c e f o r x = 0 . ( E ) T h e s e c o n d b a n d t h a t c r o s s e s t h e F e r m i s u r f a c e f o r x = 0 . ( F ) S u p e r p o s i t i o n o f b a n d s ( D a n d E ) t h a t g i v e s t h e t o t a l F e r m i s u r f a c e t o p o l o g y f o r x = 0 w i t h p o s s i b l e n e s t i n g v e c t o r s d r a w n i n a r r o w s . 5 1 x 5 1 k p o i n t s w e r e u s e d f o r t h e c a l c u l a t i o n o f t h e F e r m i s u r f a c e . . . . . . . . . . . . . . 4 2 9 F i g u r e 6 . 1 9 . B r i l l o u i n z o n e o f P m m 2 s p a c e g r o u p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 0 F i g u r e 6 . 2 0 . B r i l l o u i n z o n e o f P m m n s p a c e g r o u p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 0 F i g u r e 7 . 1 . S E M i m a g e o f a s i n g l e c r y s t a l o f C u o , 1 4 ( 1 ) U T e 3 u s e d f o r r e s i s t i v i t y m e a s u r e m e n t . T y p i c a l c r y s t a l s i z e i s ~ 3 m m i n l e n g t h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 1 F i g u r e 7 . 2 . ( A ) S t r u c t u r e o f a — U T e 3 ( Z r S e g - t y p e ) . ( B ) L i n e a r c h a i n s o f T e i n a - U T e ; ( b o n d l e n g t h s a r e i n d i c a t e d ) . ( C ) S t r u c t u r e o f B - U T e 3 ( N d T e 3 - t y p e ) . ( B ) S q u a r e n e t o f T e i n B - U T e 3 ( b o n d l e n g t h s a r e i n d i c a t e d ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 6 F i g u r e 7 . 3 . ( A ) A v e r a g e u n d i s t o r t e d s t r u c t u r e o f C u x U T e g . ( B ) U n d i s t o r t e d l i n e a r c h a i n s o f T e i n C u x U T e 3 . B o n d l e n g t h s a r e i n d i c a t e d ( C ) L i n e a r c h a i n s o f C u i n t h e a v e r a g e C u x U T e 3 s t r u c t u r e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 7 F i g u r e 7 . 4 . T e [ 2 ] - T e [ 3 ] d i s t a n c e s f o u n d i n t h e d i s t o r t e d n e t o f C u x U T e g ( x = 0 . 1 4 ( 1 ) , 0 . 1 8 ( 1 ) a n d 0 . 4 0 ( 1 ) ) f r o m t h e s u p e r s p a c e a n a l y s i s b a s e d o n a q - v e c t o r a s a f u n c t i o n o f t - d i r e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 l 7 x l v i F i g u r e 7 . 5 . O c c u p a t i o n a l c u r v e s o f C u a t o m s f o u n d i n C u x U T e 3 ( x = 0 . 1 4 ( 1 ) , 0 1 8 ( 1 ) a n d 0 . 4 0 ( l ) ) f r o m t h e s u p e r s p a c e a n a l y s i s b a s e d o n a q — v e c t o r a s a f u n c t i o n o f t - d i r e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 9 F i g u r e 7 . 6 . ( A ) D i s t o r t e d T e p a t t e r n o f C u 0 1 3 ( 1 ) U T e 3 a t 1 0 0 K w i t h q = 0 . 1 0 4 0 ( 4 ) a - 0 . 0 2 8 4 ( 7 ) c a n d 2 . 9 A b o n d i n g t h r e s h o l d v i e w e d d o w n t h e b - a x i s . T h e f o r m a t i o n o f T e - T e d i m e s 1 n t h e r e g i o n s w h e r e t h e r e 1 8 n o C u a t o m s i s a p p a r e n t . ( B ) D i s t o r t e d T e p a t t e r n o f C u o , 1 g ( 1 ) U T e 3 a t 1 0 0 K v i e w e d d o w n t h e c - a x i s a t a b o n d i n g t h r e s h o l d o f 2 . 9 A . T h e o c c u p a n c y c u t o f f w a s s e t t o t h e a v e r a g e v a l u e o f 0 . 1 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 1 F i g u r e 7 . 7 . D i s t o r t e d T e p a t t e r n o f C u 0 1 4 ( 1 ) U T e 3 a t 1 0 0 K w i t h q = 0 . 1 0 4 0 ( 4 ) a - 0 . 0 2 8 4 ( 7 ) c a n d 2 . 9 A b o n d i n g t h r e s h o l d . T h e o c c u p a n c y c u t o f f w a s s e t t o t h e a v e r a g e v a l u e o f 0 . l 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 1 F i g u r e 7 . 8 . D i s t o r t e d T e p a t t e r n o f C u 0 . 4 0 ( 1 ) U T e 3 w i t h q = 0 . 1 0 4 0 ( 4 ) a * - 0 . 0 2 8 4 ( 7 ) c ' a t 1 0 0 K a n d 2 . 9 A b o n d i n g t h r e s h o l d . T h e o c c u p a n c y c u t o f f w a s s e t t o t h e a v e r a g e v a l u e o f 0 . 4 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 2 F i g u r e 7 . 9 . T e m p e r a t u r e d e p e n d e n t m a g n e t i c s u s c e p t i b i l i t y f o r B - U T C 3 . . . . . . . . . . . . . . . . . . . . . . . . 5 2 3 F i g u r e 7 . 1 0 . F i e l d d e p e n d e n t m a g n e t i z a t i o n c u r v e f o r B — U T 6 3 a t 5 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 4 F i g u r e 7 . 1 1 . T e m p e r a t u r e d e p e n d e n t m a g n e t i c s u s c e p t i b i l i t y f o r C u o , 4 U T e 3 . . . . . . . . . . . . . . . . . 5 2 4 F i g u r e 7 . 1 2 . F i e l d d e p e n d e n t m a g n e t i z a t i o n c u r v e f o r C u o , 4 U T e 3 a t 5 K . . . . . . . . . . . . . . . . . . . . . . . 5 2 5 F i g u r e 7 . 1 3 . R e s i s t i v i t y v s . l o w t e m p e r a t u r e p l o t f o r a - U T e 3 a n d C U O _ 2 U T C 3 . . . . . . . . . . . . . . . . 5 2 6 F i g u r e 7 . 1 4 . A r r h e n i u s p l o t o f t h e r e s i s t i v i t y f o r C m . 2 U T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 6 F i g u r e 7 . 1 5 . R e s i s t i v i t y v s . h i g h t e m p e r a t u r e p l o t f o r C u o ‘ z U T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 7 F i g u r e 7 . 1 6 . R e s i s t i v i t y v s . l o w t e m p e r a t u r e p l o t f o r C 1 1 0 . 4 U T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 8 F i g u r e 7 . 1 7 . R e s i s t i v i t y v s . l o w t e m p e r a t u r e p l o t f o r B - U T e 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 8 F i g u r e 8 . 1 . ( A ) S e l e c t e d a r e a e l e c t r o n d i f fi ' a c t i o n ( S A E D ) p a t t e r n f o r C e T e 3 a t t h e [ 0 1 0 ] . o r i e n t a t i o n s h o w i n g t h e 7 - f o l d s u p e r l a t t i c e . ( B ) I n t e n s i t y s c a n a l o n g t h e c * a x i s o f t h e S A E D p a t t e r n ( s h o w n 1 n r e c t a n g u l a r b o x ) a n d a p p r o x i m a t e i n d e x i n g b a s e d o n s u p e r c e l l . T h e q - v e c t o r i s a l s o i n d i c a t e d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5 4 x l v i i F i g u r e 8 . 2 . P r e c e s s i o n p h o t o g r a p h o f C e T e 3 a t 1 0 0 K o f ( A ) T h e h 0 1 l a y e r . ( B ) T h e h l l l a y e r . ( C ) T h e h 2 1 l a y e r . R o w s o f r e fl e c t i o n s w i t h h = 2 n a r e a b s e n t s i n c e t h e s t r u c t u r e i s C - c e n t e r e d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5 5 F i g u r e 8 . 3 . O v e r v i e w o f t h e m o d u l a t i o n v e c t o r s o f m o s t o f t h e k n o w n C D W d i s t o r t e d p o l y t e l l u r i d e p h a s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 6 1 x l v i i i C D W D M F E D S P D F R A - P D F S A E D S E M T E M S T M L T - S T M F F T S Q U I D P P M S D F T F S 1 c N I C e . s . d . A C K E Y T O A B B R E V I A T I O N S C h a r g e D e n s i t y W a v e N , N - D i m e t h y l f o r m a m i d e E n e r g y D i s p e r s i v e S p e c t r o s c o p y I n f r a R e d P a i r D i s t r i b u t i o n F u n c t i o n R a p i d A c q u i s i t i o n - P a i r D i s t r i b u t i o n F u n c t i o n S e l e c t e d A r e a E l e c t r o n D i f f r a c t i o n S c a n n i n g E l e c t r o n M i c r o s c o p y T r a n s m i s s i o n E l e c t r o n M i c r o s c o p y S c a n n i n g T u n n e l i n g M i c r o s c o p y L o w T e m p e r a t u r e S c a n n i n g T u n n e l i n g M i c r o s c o p y F a s t F o u r i e r T r a n s f o r m S u p e r c o n d u c t i n g Q U a n t u m I n t e r f e r e n c e D e v i c e P h y s i c a l P r o p e r t y M e a s u r e m e n t S y s t e m D e n s i t y F u n c t i o n a l T h e o r y F e r m i S u r f a c e I n C o m m e n s u r a t e C o m m e n s u r a t e N e a r I n C o m m e n s u r a t e E s t i m a t e d S t a n d a r d D e v i a t i o n A l t e r n a t i n g C u r r e n t x l i x C h a p t e r 1 D i s t o r t i o n s i n P l a n a r N e t s o f T e l l u r i u m : S y n t h e t i c a n d C h a r a c t e r i z a t i o n T e c h n i q u e s 1 . 1 I n t r o d u c t i o n P o l y c h a l c o g e n i d e c o m p o u n d s a r e d e fi n e d b y t h e o c c u r r e n c e o f Q — Q b o n d s ( Q = S , S e , T e ) i n t h e s t r u c t u r e . T h e s e c o m p o u n d s h a v e r e c o g n i z a b l e p o l y c h a l c o g e n i d e ( Q x ) 2 ' u n i t s . A s t h e c h a l c o g e n a t o m s b e c o m e l a r g e r a n d h e a v i e r i n a d d i t i o n t o Q - Q b o n d s , t e r n a r y h y p e r v a l e n t Q - - - Q b o n d i n g i n t e r a c t i o n s c a n d e v e l o p . 1 T h e s e i n t e r a c t i o n s e v o l v e f r o m b e i n g e s s e n t i a l l y v a n d e r W a a l s i n n a t u r e i n t h e l i g h t e r c o n g e n e r s , t o b e c o m i n g s i g n i fi c a n t a n d p r e v a l e n t i n t h e t e l l u i i d e s g i v i n g r i s e t o u n u s u a l n o n - c l a s s i c a l a r r a n g e m e n t s s u c h a s o l i g o m e r i c o r p o l y m e r i c a n i o n s a n d s q u a r e n e t s ( s e c t i o n 1 . 3 ) . C o m p o u n d s w i t h t h e s e f e a t u r e s c a n g i v e r i s e t o i n t e r e s t i n g p h y s i c a l p r o p e r t i e s s u c h a s c h a r g e d e n s i t y w a v e s ( C D W , s e c t i o n 1 . 4 ) , a n i s o t r o p i c o p t i c a l p r o p e r t i e s , a n d m a y e v e n b e i n t e r e s t i n g f o r t h e r m o e l e c t r i c i n v e s t i g a t i o n s ( s e c t i o n 1 . 5 ) . I n p o l y t e l l u r i d e s e x t e n d e d h y p e r v a l e n t T e - " T e b o n d i n g i s f r e q u e n t l y o b s e r v e d w i t h f l a t s q u a r e n e t s o f t e l l u r i u m . A t fi r s t g l a n c e t h e s e n e t s a r e h i g h l y s y m m e t r i c b u t a c l o s e r l o o k a l m o s t a l w a y s r e v e a l s s u b t l e d i s t o r t i o n s a s s o c i a t e d w i t h c o m m e n s u r a t e l y o r i n c o m m e n s u r a t e l y m o d u l a t e d s u p e r s t r u c t u r e s . l A v a r i e t y o f e x p e r i m e n t a l t e c h n i q u e s l i k e E l e c t r o n D i f f r a c t i o n ( E D ) , S u p e r s p a c e c r y s t a l l o g r a p h y , a n d P a i r D i s t r i b u t i o n F u n c t i o n a n a l y s i s ( P D F ) a l o n g w i t h t h e o r e t i c a l c a l c u l a t i o n s a t t h e D e n s i t y F u n c t i o n a l T h e o r y ( D F T ) l e v e r w e r e u s e d t o p r o p e r l y c h a r a c t e r i z e t h e C D W m a t e r i a l s r e p o r t e d h e r e . S i n c e s o m e o f t h o s e t e c h n i q u e s a r e n o t s t a n d a r d a n d c o m m o n l y u s e d a b r i e f i n t r o d u c t i o n f o r P D F a n a l y s i s ( s e c t i o n 1 . 6 ) a n d s u p e r s p a c e a p p r o a c h ( s e c t i o n 1 . 7 ) w i l l b e g i v e n i n t h i s C h a p t e r . 1 . 2 P o l y c h a l c o g e n i d e a n d h a l i d e fl u x s y n t h e t i c t e c h n i q u e A c o n v e n t i o n a l s o l i d s t a t e s y n t h e s i s i n v o l v e s u s e o f v e r y h i g h t e m p e r a t u r e ( u s u a l l y m o r e t h a n 1 0 0 0 ° C ) a n d h e a t i n g o f e l e m e n t s o r s i m p l e b i n a r i e s p h a s e s a t s t o i c h i o m e t r i c a m o u n t s b a s e d o n t h e t a r g e t c o m p o u n d . T h i s s o - c a l l e d “ h e a t a n d b e a t ” s y n t h e t i c m e t h o d h o w e v e r h a s s o m e l i m i t a t i o n s . T h e r e a c t i o n o f t h e s t a r t i n g m a t e r i a l s d e p e n d s o n t h e d i f f u s i o n b e t w e e n t h e s o l i d p a r t i c l e s . T h e r e f o r e h o m o g e n e i t y i s d i f fi c u l t t o a c h i e v e s i n c e m o s t o f t h e t i m e s e i t h e r o n e o f t h e r e a c t i o n c o m p o n e n t s o r t h e fi n a l p r o d u c t r e m a i n s t i l l i n t h e s o l i d s t a t e a t t h e c o n d i t i o n s o f t h e r e a c t i o n . S u c c e s s i v e g r i n d i n g a n d c o m p r e s s i o n ( p e l l e t ) o f t h e m i x t u r e o f r e a c t a n t s / p r o d u c t s b e t w e e n h e a t i n g c y c l e s m a y b e t h e o n l y w a y t o o b t a i n h o m o g e n e o u s p r o d u c t s . S i n c e h i g h t e m p e r a t u r e i s r e q u i r e d t o f a c i l i t a t e a s m u c h a s p o s s i b l e t h e d i fi u s i o n b e t w e e n r e a c t a n t s t h e fi n a l p r o d u c t s a r e u s u a l l y t h e m o s t t h e r m o d y n a m i c a l l y s t a b l e o n e s . C o m p o u n d s t h a t a r e m e t a s t a b l e a n d d e c o m p o s e a t r e l a t i v e h i g h t e m p e r a t u r e o r w h o s e f o r m a t i o n i s k i n e t i c a l l y c o n t r o l l e d a r e a l m o s t i m p o s s i b l e t o o b t a i n v i a t h i s c l a s s i c a l s y n t h e t i c a p p r o a c h . G r o w t h o f s i n g l e c r y s t a l s a n d c h a r a c t e r i z a t i o n o f t h o s e b y X - r a y d i f f r a c t i o n m e t h o d s i s t h e “ b a c k b o n e ” o f a n y s o l i d s t a t e s c i e n c e a n d e s s e n t i a l t o o b t a i n s t r u c t u r e s i n r e a l s p a c e . T h e l a r g e n u m b e r o f r e fl e c t i o n s i n t h e t h r e e - d i m e n s i o n a l r e c i p r o c a l s p a c e o b t a i n e d b y s i n g l e c r y s t a l d i f f r a c t i o n i s p r e f e r a b l e t h a n t h e l i m i t e d n u m b e r o f r e fl e c t i o n s p r e s e n t i n a t w o - d i m e n s i o n a l p r o j e c t i o n o f a p o w d e r d i f f r a c t i o n e x p e r i m e n t . S i n c e d i f f u s i o n i s r e l a t i v e l i m i t e d i n a t y p i c a l s o l i d s t a t e e x p e r i m e n t s i n g l e c r y s t a l g r o w t h i s a m a j o r p r o b l e m t h a t m a k e s t h e s t r u c t u r a l c h a r a c t e r i z a t i o n o f n e w p h a s e s r a t h e r d i f fi c u l t i f n o t i m p o s s i b l e . M o l t e n s a l t s h a v e b e e n u s e d f o r o v e r 1 0 0 y e a r s a s a h i g h t e m p e r a t u r e r e c r y s t a l l i z a t i o n m e d i a f o r v a r i o u s b i n a r y a n d t e r n a r y c o m p o u n d s 2 t o o v e r c o m e t h e l i m i t e d d i fi u s i o n p r o b l e m o f t h e c o n v e n t i o n a l s o l i d s t a t e s y n t h e s i s . I t w a s n o t u n t i l 1 9 8 7 w h e n a m o l t e n s a l t w a s u s e d a t l o w e r t e m p e r a t u r e t o s y n t h e s i z e n e w c o m p o u n d s . 3 S i n c e t h e n a l a r g e n u m b e r o f n e w c o m p o u n d s h a v e b e e n r e p o r t e d . I n t h i s w o r k , a r a r e e a r t h m e t a l i s r e a c t e d w i t h t e l l u r i u m m e t a l . T h e r e a c t i o n b e t w e e n t h e s e t w o e l e m e n t s i s e x t r e m e l y e x o t h e r m i c a n d t h e d i r e c t c o m b i n a t i o n o f t h e m w i l l a l w a y s c r e a t e a n e x p l o s i o n o f t h e g l a s s c o n t a i n e r ( > 4 0 0 ° C ) . T h e u s e o f a h a l i d e ( o r p o l y t e l l u r i d e ) fl u x i n t h i s c a s e i s i m p o r t a n t n o t o n l y f o r c r y s t a l g r o w t h p u r p o s e s b u t a l s o a s a h e a t a b s o r b e r . A l i s t o f r e l a t i v e l o w m e l t i n g p o i n t h a l i d e s a l t s ( a n d e u t e c t i c m i x t u r e s o f t h e m ) a n d t h e i r c o r r e s p o n d i n g m e l t i n g p o i n t t e m p e r a t u r e a r e p r e s e n t e d a t t h e b o t t o m o f T a b l e 1 . 1 . T h e u s e o f m o l t e n a l k a l i m e t a l p o l y c h a l c o g e n i d e A 2 Q x ( A = A l k a l i m e t a l , Q = S , S e , T e ) fl u x a s s o l v e n t h a s b e e n v e r y u s e f u l f o r t h e d i s c o v e r y o f n e w ( p o l y ) c h a 1 c o g e n i d e m a t e r i a l s . 4 T h e r e a s o n f o r t h a t i s m a i n l y t h e f a c t t h a t t h e fl u x h a s a l o w m e l t i n g p o i n t a n d t h e r e a c t i o n s i m m e r s e d i n t o i t c a n b e c a r r i e d o u t a t r e l a t i v e l o w e r t e m p e r a t u r e s ( l o w e r t h a n 7 0 0 ° C ) . T h e m e l t i n g p o i n t s o f s e v e r a l a l k a l i m e t a l / p o l y c h a l c o g e n i d e s a l t s ( A z Q x ) a r e g i v e n i n T a b l e 1 . 1 . I t i s w o r t h n o t e d t h a t m o s t o f t h e A z Q x ( x > 2 ) s p e c i e s h a v e a m e l t i n g p o i n t l e s s t h a n 5 0 0 ° C a n d i n s o m e c a s e s e v e n l e s s t h a n 2 0 0 ° C . T h e m o l t e n fl u x a c t s a s s o l v e n t a n d i n m a n y c a s e s a s r e a c t a n t t o o , p r o v i d i n g a n d i n c o r p o r a t i n g t h e c h a l c o g e n i d e a n d / o r t h e a l k a l i m e t a l i n t o t h e fi n a l p r o d u c t . I m p o r t a n t l y , t h e A 2 Q x fl u x e s r e m a i n n o n v o l a t i l e o v e r a w i d e t e m p e r a t u r e r a n g e w h i c h i s a n e c e s s a r y r e q u i r e m e n t f o r a s o l v e n t . I t c a n b e u s e d f o r v a r i o u s r e a c t i o n t e m p e r a t u r e s a b o v e t h e i r m e l t i n g p o i n t w i t h o u t c o n c e r n i n g s o l v e n t l o s s . I n a d d i t i o n , c r y s t a l g r o w t h i s e n h a n c e d . T h r o u g h a m i n e r a l i z a t i o n e f f e c t , s m a l l o r p o o r l y f o r m e d c r y s t a l l i t e s c a n b e r e d i s s o l v e d i n t h e fl u x a n d r e p r e c i p i t a t e a s l a r g e r s i n g l e c r y s t a l s . F i n a l l y , t h e e x c e s s A n y s a l t t h a t r e m a i n e d f r o m t h e fl u x c a n b e e a s i l y w a s h e d o f f u s i n g a n y p o l a r s o l v e n t s u c h a s m e t h a n o l , N , N - D i m e t h y l f o r m a m i d e o r w a t e r . T a b l e 1 . 1 . M e l t i n g p o i n t s o f s o m e k n o w n a l k a l i m e t a l p o l y c h a l c o g e n i d e ( A x Q y w h e r e Q = S , 3 6 a n d T e ) s p e c i e s a n d h a l i d e s a l t s . 5 ' 6 ’ 7 A n y A z Q A 2 Q 2 A 2 Q 3 A 2 Q 4 A z Q s A 2 Q 5 L i 2 8 L i 2 8 2 9 0 0 - 9 7 5 ° C 3 6 9 ° C N 3 2 8 N a 2 8 2 N a 2 8 3 N 2 1 2 8 1 : , N 3 2 8 5 1 1 8 0 ° C 4 9 0 ° C 2 2 8 ° C 2 7 5 ° C 2 5 2 ° C A S K 2 8 K 2 8 2 K 2 8 3 K 2 8 4 K 2 8 5 K 2 3 6 x y 8 4 0 0 C 4 7 0 ° C 2 5 2 ° C 1 4 5 ° C 2 0 6 ° C 1 8 9 ° C R b 2 8 R b 2 8 2 R b 2 8 3 R b 2 8 4 R b 2 8 5 R b 2 8 5 5 3 0 ° C 4 2 0 ° C 2 1 3 ° C 1 6 0 ° C 2 2 5 ° C 2 0 1 ° C C 8 2 8 2 C 8 2 3 3 C 8 2 5 4 C 8 2 8 5 C 8 2 8 5 4 6 0 ° C 2 1 7 ° C 1 6 0 ° C 2 1 0 ° C 1 8 6 ° C N a Z S e N a 2 8 e 2 N a 2 8 e 3 N a 2 8 e 4 N a 2 8 e 6 A x S e y > 8 7 5 ° C 4 9 5 ° C 3 1 3 ° C 2 9 0 ° C 2 5 8 ° C K 2 8 6 2 K 2 3 6 3 K 2 3 6 4 K 2 3 6 5 4 6 0 ° C 3 8 0 0 C 2 0 5 ° C 1 9 0 ° C N a 2 T 6 N 3 2 T 6 2 N 3 2 T 6 5 9 5 3 ° C 3 4 8 ° C 4 3 6 K 2 T 6 K 2 T 6 3 K 2 T 6 4 K 2 T 6 5 K 2 T 6 6 A T e y 9 0 0 ° C 4 2 9 ° C 2 6 6 ° C 2 6 8 ° C 2 6 4 ° C x s z T e R b 2 T 6 3 R b 2 T 6 5 7 7 5 ° C 4 0 0 ° C 2 7 0 ° C C S 2 T 6 C 8 2 T 6 3 C 8 2 T 6 4 C S 2 T 6 5 C 8 2 T 6 6 8 2 0 ° C 3 9 5 ° C 2 2 1 - 2 3 7 ° C 2 3 5 ° C 2 2 6 ° C L i F L i C l L i B r L i I E u t e c t i c m i x t u r e s 8 4 8 ° C 6 1 0 ° C 5 5 2 ° C 6 8 1 ° C ( m o l a r f r a c t i o n ) N a F N a C l N a B r N a I R b C l ( 4 2 . 2 ) — L i C l 9 9 6 ° C 8 0 1 ° C 7 4 7 ° C 6 6 0 ° C 3 1 3 ° C H a l i d e K F K C l K B r K I L i I ( 3 6 . 6 ) — K I 8 5 8 ° C 7 7 1 ° C 7 3 4 ° C 4 6 9 ° C 2 8 6 ° C R b F R b C l R b B r R b I L i C l ( 5 8 ) - C s C l 8 3 3 ° C 7 2 0 ° C 6 9 3 ° C 6 4 7 ° C 3 2 6 ° C C s F C s C l C s B r C 8 1 7 0 3 ° C 6 4 6 ° C 6 3 6 ° C 6 2 6 ° C T h e r e a c t i o n b e t w e e n A 2 Q a n d Q ( s t a r t i n g m a t e r i a l s o f t h e fl u x ) o c c u r s i n s i t u a n d p o l y c h a l c o g e n i d e c h a i n s ( Q x ) 2 ‘ w i t h v a r i o u s l e n g t h s a r e f o r m e d . T h e s e c h a i n s c o n s i s t o f t w o t e r m i n a l a t o m s t h a t c a r r y a c h a r g e o f 1 - a n d x - 2 i n t e r n a l a t o m s w i t h z e r o - v a l e n t c h a r g e . T h e n e g a t i v e c h a r g e d t e r m i n a l a t o m s b e h a v e l i k e a L e w i s b a s e a n d c o o r d i n a t e t o t h e m e t a l ( r e a c t a n t ) a n d t h e i n t e r n a l Q a t o m s a t t h e s a m e t i m e o x i d i z e t h e m e t a l w h i l e t h e y a r e b e i n g r e d u c e d . T h e i n t e r n a l a t o m s n o w b e c o m e t e r m i n a l c h a l c o g e n s a n d t h e c h a i n s a r e s p l i t t e d i n t o s m a l l e r ( Q x ) 2 ' f r a g m e n t s . F u r t h e r m o r e , t h e p o l y c h a l c o g e n i d e c h a i n s c a n u n d e r g o a l s o s e l f - r e d o x e q u i l i b r i a o f t h e t y p e s h o w n i n S c h e m e 1 . 1 . 0 ' 0 ° ° Q ‘ — Q ’ + \ o / \ 2 / \ Q Q ' Q ’ Q ’ ( s z ' ( 0 0 2 ‘ ( 0 3 % S c h e m e 1 . 1 : S e l f - r e d o x e q u i l i b r i u m o f t h e p o l y c h a l c o g e n i d e fl u x . T h e r e l a t i v e b a s i c i t y o f t h e r e a c t i o n d e p e n d s o n t h e l e n g t h o f t h e s e p o l y c h a l c o g e n i d e c h a i n s a n d i t c a n b e c o n t r o l l e d b y c h a n g i n g t h e A 2 Q / Q r a t i o . I f l e s s A z Q ( o r m o r e Q ) i s u s e d i n t h e r e a c t i o n m i x t u r e , l o n g e r p o l y c h a l c o g e n i d e c h a i n s w i l l f o r m . T h e Q o / Q l ' r a t i o w i l l i n c r e a s e a n d t h e r e f o r e t h e r e s u l t i n g fl u x w i l l b e m o r e o x i d i z i n g ( l e s s b a s i c ) , S c h e m e 1 . 2 . Q Q ” A W “ 4 6 + Q / Q O \ Q _ + \ 0 / Q 0 o M 2 . + Q / Q O \ Q O / Q \ 2 A 2 Q 3 4 Q ( m o r e b a s i c ) Q a d d i t ' o o o A Q + 4 Q m 1 Q Q Q 2 2 . + / \ 0 / \ 0 / \ Q ' Q Q Q " A Z Q + 6 Q ( l e s s b a s i c ) S c h e m e 1 . 2 : C o n t r o l o f t h e b a s i c i t y w i t h v a r i a t i o n o f t h e A 2 Q / Q r a t i o . T h e a l k a l i m e t a l p o l y c h a l c o g e n i d e fl u x m e t h o d b e c a m e o n e o f t h e m o s t p o w e r f u l s y n t h e t i c t o o l f o r e x p l o r a t o r y s y n t h e s i s i n t h e s o l i d s t a t e c o m m u n i t y . T h e a b i l i t y t o c o n t r o l t h e b a s i c i t y o f t h e fl u x b y v a r y i n g t h e A 2 Q / Q r a t i o g a v e t h e p o s s i b i l i t y t o e x p l o r e d i f f e r e n t c h e m i c a l s y s t e m s u n d e r a w i d e r a n g e o f s y n t h e t i c c o n d i t i o n s . T h e fl u x c o n d i t i o n s a l l o w t h e r e a c t i o n s y s t e m t o e v o l v e w i t h o u t c o n s t r a i n s a n d f o r m e i t h e r k i n e t i c o r t h e r m o d y n a m i c s t a b l e p r o d u c t s . T h e e x c e s s fl u x f a c i l i t a t e s t h e s y n t h e s i s o f n e w c o m p o u n d s w i t h n o p r e d e fi n e d s t o i c h i o m e t r i e s a n d s t r u c t u r e t y p e s . M e t a s t a b l e p h a s e s t h a t c o u l d n o t b e s y n t h e s i z e d o f p r e d i c t e d p r e v i o u s l y a r e n o w a c c e s s i b l e . 1 . 3 D i s t o r t i o n s i n p l a n a r n e t s o f t e l l u r i u m M o v i n g a c r o s s t h e V I g r o u p o f e l e m e n t s i n t h e p e r i o d i c t a b l e , f r o m S t o S e a n d T e , t h e s i z e a n d d i f f u s e n a t u r e o f t h e p - o r b i t a l s i n c r e a s e s . T e l l u r i u m i s t h e l e a s t e l e c t r o n e g a t i v e e l e m e n t a m o n g t h e c h a l c o g e n s a n d c a n s t a b i l i z e l o n g e r t h a n n o r m a l b o n d d i s t a n c e s h a v i n g a g r e a t t e n d e n c y t o a s s o c i a t e t h r o u g h T e - T e b o n d i n g i n t e r a c t i o n s . R o a l d H o f f m a n n d e s c r i b e d t h i s b e h a v i o r o f t e l l u r i u m a s a “ c o n s t a n t fl i r t a t i o n w i t h o t h e r t e l l u r i u m p a r t n e r s , i n t h e r a n g e b e t w e e n a b o n d a n d n o b o n d ” . 8 T h i s h a s b e e n i l l u s t r a t e d i n t h e a l k a l i m e t a l r i c h t e l l u r i d e s 9 w h e r e s u c h T e - T e “ h y p e r - i n t e r a c t i o n s ” h a s r e s u l t e d i n t h e f o r m a t i o n o f o n e - d i m e n s i o n a l i n fi n i t e 1 0 a n d s p i r o c y c l i c l l c h a i n s , c y c l o h e x a n e - l i k e T e 6 r i n g s 1 2 a n d p u c k e r e d c r o w n s h a p e d T 6 3 r i n g s . l 3 L o w d i m e n s i o n a l c o m p o u n d s w i t h p l a n a r T e n e t s h a v e b e e n o b s e r v e d w h e n a t r a n s i t i o n m e t a l o r a r a r e e a r t h m e t a l i s a d d e d i n t h e s y n t h e s i s . T h e s e c o m p o u n d s h a v e b e e n f o u n d t o u n d e r g o s t r u c t u r a l d i s t o r t i o n s l o c a t e d m a m e i n t h e p l a n a r n e t s o f t e l l u r i u m . D u e t o t h i s d i s t o r t i o n t h e p l a n a r T e n e t f r o m a n i d e a l s q u a r e g e o m e t r y b r a k e s d o w n i n t o o l i g o m e r s o f t h e f o r m ( Q x ) 2 ' . S o m e r e p r e s e n t a t i v e e x a m p l e s o f c o m p o u n d s w i t h p l a n a r T e n e t s i n c l u d e K o , 3 3 B a o _ 6 7 A g T e 2 , ” N d T e 3 , ” m u m . . . l 6 A R E 3 T e 8 ( A = K , R b , C s ; R E = C e , N d ) , ” K C u C e T e 4 , 1 8 R b C u C e T e 4 , 2 ° N a o , 3 A g 1 , 2 C e T e 4 , 2 ° K 2 _ 5 A g 4 , 5 C e 2 T e 9 , 2 0 2 0 1 9 1 9 1 9 2 0 K 2 . 5 A g 4 . s L 3 2 T € 9 , C u o . s e E U T 6 2 , K C q u U T C 4 , N a o . 2 A g z . s E U T € 4 , K o . 6 5 A n g u 1 . 3 5 T € 4 a n d C u x U T e g , ( x = 0 . 2 5 , 0 . 3 3 ) . 2 1 I n s o m e c a s e s t h e u n d i s t o r t e d o r d i s t o r t e d c o m p o u n d s p o s s e s o n e d i m e n s i o n a l l i n e a r c h a i n s l i k e a - U T e g , 2 2 a n d A T h z T e 6 ( A = C s , C u ) . 2 3 M o r e 2 6 a n d e x a m p l e s o f p l a n a r c h a l c o g e n i d e n e t s i n c l u d e K 3 C u 3 8 6 , 2 4 L a S e l g , 2 5 D Y S 6 1 3 4 , R b D y 3 8 e 3 . 2 7 T h e s e s t r u c t u r a l d i s t o r t i o n s a r e n o t s p e c i fi c t o s q u a r e n e t s o n l y b u t r a t h e r t o t h e l o w - d i m e n s i o n a l n a t u r e o f t h e c o m p o u n d s t h a t m a k e s t h e m s u s c e p t i b l e t o d i s t o r t . S o m e t y p i c a l e x a m p l e s i n c l u d e t h e c h a i n - l i k e t r a n s i t i o n m e t a l t r i c h a l c o g e n i d e s , 2 8 t h e l a y e r e d t r a n s i t i o n m e t a l d i c h a l c o g e n i d e s , 2 9 t h e r e d 3 0 a n d p u r p l e 3 1 b r o n z e s . T h e p h y s i c a l p r o p e r t i e s o f a s y s t e m u n d o u b t e d l y d e p e n d o n i t s s t r u c t u r e . A n “ i d e a l ” s q u a r e n e t o f T e a t o m s s h o u l d c o n t a c t e l e c t r o n s a n d b e m e t a l l i c i n n a t u r e . T h e e l e c t r o n i c p r o p e r t i e s o f c o m p o u n d s t h a t c o n t a i n p l a n a r T e n e t s s h o u l d d e p e n d m a m e o n t h i s d i f f u s e n a t u r e o f t h e T e p - o r b i t a l s w h i c h a r e c o n s i d e r e d t o b e d e l o c a l i z e d a c r o s s t h e n e t . I n d e e d , f r o m t h e o r e t i c a l c a l c u l a t i o n s o n m o s t o f t h e c o m p o u n d s m e n t i o n e d a b o v e , t h e F e r m i l e v e l i s p r i m a r i l y m a d e u p o f T e p - o r b i t a l s . W h e n t h e f o r m a l o x i d a t i o n s t a t e o f a l l T e a t o m s i n t h e n e t i s - 2 , a s t a b l e s q u a r e n e t i s o b s e r v e d ( e . g . , N a C u T e ) . 3 2 H o w e v e r , w h e n t h e f o r m a l o x i d a t i o n s t a t e i s < - 2 , o r w h e n t h e r e a r e a t o m i c v a c a n c i e s i n t h e s q u a r e n e t , s t r u c t u r a l d i s t o r t i o n s a r e p o s s i b l e l e a d i n g t o T e - T e b o n d i n g i n t e r a c t i o n s a n d t h e f o r m a t i o n o f ( T e x ) 2 ' s p e c i e s w i t h i n t h e n e t , F i g u r e 1 . 1 . T h e d i s t o r t i o n s i n t h e s e e l e c t r o n d e fi c i e n t T e n e t s l o w e r t h e t o t a l e n e r g y o f t h e s y s t e m b y d e c r e a s i n g t h e e n e r g y o f t h e fi l l e d T e p - o r b i t a l s a n d b r i n g i n g t h e e l e c t r o n s i n t o f u l l y o c c u p i e d b o n d i n g o r b i t a l s ( J a h n - T e l l e r t y p e d i s t o r t i o n ) . C o n s e q u e n t l y , a g a p o p e n s u p a t t h e F e r m i l e v e l a n d t h e m a t e r i a l b e c o m e s a s e m i c o n d u c t o r o r i n s u l a t o r . T h e d i s t o r t i o n s i n p l a n a r n e t s o f T e c a n b e c r e a t e d i n a f o r m o f a C h a r g e D e n s i t y W a v e ( C D W ) o r S i t e O c c u p a n c y W a v e ( S O W ) o r c o m b i n a t i o n o f t h e s e t w o w a v e s . I n t h e c a s e o f C D W , a n e l e c t r o n - p h o t o n c o u p l i n g c r e a t e s a s i n u s o i d a l ( o r c o m b i n a t i o n o f s e v e r a l s i n u s o i d a l w a v e s ) a t o m i c d i s p l a c e m e n t o f t h e T e a t o m s . T h i s c o u p l i n g l o w e r s t h e t o t a l e n e r g y a n d a g a p i s p r o d u c e d i n t h e F e r m i s u r f a c e ( P e i e r l s d i s t o r t i o n ) . T h e w a v e v e c t o r o f t h e m o d u l a t i o n ( q - v e c t o r ) c a n o r i e n t i n p r i n c i p l e t o a n y d i r e c t i o n i n t h e r e c i p r o c a l s p a c e . T h e e n e r g e t i c a l l y p r e f e r r e d o r i e n t a t i o n o f t h e q - v e c t o r i s t h e o n e t h a t w i l l c r e a t e a g r e a t e r s t a b i l i t y ( l o w e r e n e r g y ) o r b i g g e r b a n d g a p . T h e F e r m i s u r f a c e t o p o l o g y w i l l d e t e r m i n e t h i s l o w e r e n e r g y p a t h a n d b a n d s w i l l s p a n a l o n g t h a t d i r e c t i o n i n o r d e r t o c r e a t e a g a p . T h i s n e s t i n g e f f e c t i s t h e r m o d y n a m i c a l l y f a v o r a b l e a n d t h e c o r r e s p o n d i n g n e s t i n g v e c t o r d i c t a t e s t h e w a v e v e c t o r o f t h e e l e c t r o n d e n s i t y . E s s e n t i a l l y , t h e q - v e c t o r o f t h e d i s t o r t i o n i s t h e s a m e w i t h t h e n e s t i n g v e c t o r o f t h e F e r m i s u r f a c e . T h e r e s u l t o f t h i s C D W m o d u l a t i o n i n t h e p a t t e r n o f t h e T e n e t i s t h e c r e a t i o n o f o l i g o m e r i c f r a g m e n t s o f ( T e x ) 2 ' , F i g u r e 1 . 1 . T h e l e n g t h o f e a c h o l i g o m e r x w i l l d e p e n d o n t h e p e r i o d o f t h e m o d u l a t i o n w a v e ( 1 / 2 , 1 / 3 , 1 / 4 e t c . ) a n d t h e a v e r a g e o x i d a t i o n s t a t e o f t h e n e t . I n a c o m m e n s u r a t e c a s e , a r e g u l a r s e q u e n c e o f o l i g o m e r s w i l l f o r m w h i l e e l e c t r o n s c a n b e l o c a l i z e d o n t h e w e l l s e p a r a t e d f r a g m e n t s , F i g u r e s 1 . 1 A , 1 . 1 B . F o r e x a m p l e , L a T e z p o s s e s a 2 x 2 s u p e r c e l l i n t h e p l a n e t h a t c o n t a i n s t h e p l a n a r n e t a n d a n a v e r a g e o x i d a t i o n o f 1 - o n t h e T e a t o m s i n t h e n e t . 3 3 A s e x p e c t e d , t h e s u p e r c e l l c o n t a i n s d i m e r s o f ( T e 2 ) 2 ' . I n a n i n c o m m e n s u r a t e c a s e , t h e r a t i o n a l i z a t i o n m e n t i o n e d a b o v e i s m o r e d i f fi c u l t s i n c e t h e r e i s n o o b v i o u s “ c o m m e n s u r a t e ” p e r i o d i c i t y i n t h e s y s t e m . T h e r e f o r e , t h e c a l c u l a t i o n o f t h e a v e r a g e n u m b e r o f e l e c t r o n s i s n o t t r i v i a l a n d i t w i l l a l w a y s d e p e n d o n t h e a r b i t r a r y r a t i o n a l a p p r o x i m a t i o n o f t h e s u p e r c e l l . T h e r e i s n o e a s y w a y t o l o c a l i z e e l e c t r o n s a n d t h e p a t t e r n o f t h e ( T e x ) 2 ' s p e c i e s i s m o r e d i f f u s e w i t h a p e r i o d i c s e q u e n c e s , F i g u r e 1 . 1 C . S i t e O c c u p a n c y W a v e s ( S O W s ) i s a n o t h e r w a y o f d i s t o r t i o n . U s u a l l y v a c a n c i e s m a y o r d e r i n t h e n e t a n d c r e a t e p e r i o d i c h o l e s i n i t . A r o u n d t h e s e v a c a n t s i t e s , T e a t o m s m a y m o v e a n d d i s p l a c e i n o r d e r t o fi n d a r e l a x e d ( e n e r g e t i c a l l y f a v o r a b l e ) p o s i t i o n . T h e r e f o r e , S O W s a r e m o s t o f t h e t i m e s a c c o m p a n i e d w i t h p o s i t i o n a l m o d u l a t i o n s a n d i n t h e c a s e o f p l a n a r T e n e t s c o u p l e d w i t h C D W s . S o m e p o s s i b l e d i s t o r t e d T e p a t t e r n s o f S O W s a n d C D W s a r e s h o w n i n F i g u r e s 1 . 1 D , 1 . 1 E . ( w w n x ( 0 5 . 1 ; _ _ ‘ _ I ‘ I [ I ] ; I “ . I Z L I I “ 1 ’ I “ . l ' " _ l _ 7 f n % n \ / 9 i fi r m — J j [ — l — _ _ 1 1 ‘ 1 I I — F C I I J I J _ I _ ' P e r f e c t s q u a r e n e t ( D ) I / \ e ~ n a E E L J - L U F i g u r e 1 . 1 . S c h e m a t i c r e p r e s e n t a t i o n o f s o m e p o s s i b l e p a t t e r n s o f d i s t o r t i o n o f a n i d e a l s q u a r e n e t o f t e l l u r i u m a t o m s . 1 0 — — 1 . 4 C h a r g e - D e n s i t y - W a v e ( C D W ) A l m o s t 5 0 y e a r s a g o R . P e i e r l s 3 4 a n d H . F r o h l i c h 3 5 i n d e p e n d e n t l y s u g g e s t e d t h a t a c o u p l i n g o f t h e e l e c t r o n a n d p h o n o n s y s t e m s i n a o n e - d i m e n s i o n a l m e t a l i s u n s t a b l e w i t h r e s p e c t t o a s t a t i c l a t t i c e d e f o r m a t i o n o f w a v e v e c t o r Q = 2 k . A C D W i s a m o d u l a t i o n o f f t h e c o n d u c t i o n e l e c t r o n d e n s i t y i n a m e t a l a n d a n a s s o c i a t e d m o d u l a t i o n o f t h e l a t t i c e a t o m s p o s i t i o n s . T h e s e k i n d s o f m o d u l a t i o n s , w h i c h a r e g i v i n g r i s e t o t h e u n u s u a l p r o p e r t i e s o f q u a s i - o n e - d i m e n s i o n a l m e t a l s , h a v e t h r e e s p a t i a l f e a t u r e s : 1 . T h e y a r e c a u s e d b y i n s t a b i l i t y o f t h e m e t a l l i c F e r m i s u r f a c e d u e t o t h e e l e c t r o n - p h o n o n i n t e r a c t i o n 2 . T h e y r e s u l t i n e n e r g y g a p s a t t h e F e r m i s u r f a c e a n d 3 . T h e i r w a v e l e n g t h A c i s n / k f w h e r e k f i s t h e F e r m i w a v e v e c t o r I n a n e l e c t r o n - l o c a l i z e d d e s c r i p t i o n , J a h n - T e l l e r d i s t o r t i o n , t h e s y s t e m u s u a l l y a d o p t s a c o m m e n s u r a t e s u p e r s t r u c t u r e i n w h i c h c o v a l e n t b o n d i n g b e t w e e n n e a r n e i g h b o r s l e a d s t o a n i n s u l a t i n g s y s t e m . I n a m o r e e l e c t r o n - d i f f u s e d e s c r i p t i o n , P e i e r l s d i s t o r t i o n , t h e F e r m i s u r f a c e d r i v e n d i s t o r t i o n i s s t a b i l i z e d b y t h e f o r m a t i o n o f t h e C D W g a p . T h e n e s t i n g v e c t o r m a y b e i n c o m m e n s u r a t e a n d t h e g a p m a y r e m o v e s t a t e s f r o m o n l y p a r t o f t h e F e r m i s u r f a c e . 1 . 4 . 1 J a h n — T e l l e r d i s t o r t i o n H e r e t h e s y s t e m i s d e s c r i b e d a s h a v i n g l o c a l b o n d i n g b e t w e e n n e a r e s t n e i g h b o r s a n d t h e d i s t o r t i o n i s e n e r g e t i c a l l y s t a b i l i z e d b y t h e o v e r l a p o f p a r t i a l l y fi l l e d d e g e n e r a t e m o l e c u l a r o r b i t a l s . W h e n t h e n u m b e r o f b o n d i n g n e i g h b o r s i n t h e d i s t o r t e d s t r u c t u r e i s e q u a l t o t h e n u m b e r o f u n o c c u p i e d s t a t e s , o n l y e n e r g e t i c a l l y l o w e r e d s t a t e s a r e o c c u p i e d , 1 1 F i g u r e 1 . 2 . F u l l y o c c u p i e d b o n d i n g a n d u n o c c u p i e d a n t i b o n d i n g o r b i t a l s a r e s e p a r a t e d b y a n e n e r g y g a p i n t h e p r e s e n c e o f t h e c o o r d i n a t i o n - l o w e r i n g d i s t o r t i o n , l e a d i n g t o i n s u l a t i n g b e h a v i o r . T h i s g a p i s e q u i v a l e n t t o t h a t d e r i v e d f r o m t h e F e r m i s u r f a c e d r i v e n s i n u s o i d a l d i s t o r t i o n c r e a t e d f r o m t h e P e i e r l s t r a n s i t i o n . I n b o t h c a s e s t h e d i s t o r t i o n i s s t a b i l i z e d b y t h e l o w e r i n g o f o c c u p i e d s t a t e s . 3 6 u n d i s t o r t e d l i n e a r c h a i n ( A ) k . a e e e d i s t o r t e d l i n e a r c h a i n ( d i m e r s ) ( B ) — e £ — — e — e — e — e — 0 k — — > 1 1 / ( 2 1 1 ) A n t i b o n d i n g o r b i t a l s : > E n e r g y g a p B o n d i n g o r b i t a l s ' ' . 4 " . . 1 ‘ — . — O — O O O O — — . - G — . - O — . - O - — F i g u r e 1 . 2 . S c h e m a t i c r e p r e s e n t a t i o n o f t h e l o c a l i z e d p i c t u r e o f J a h n - T e l l e r d i s t o r t i o n . ( A ) T h e u n d i s t o r t e d l i n e a r c h a i n o f a t o m s a n d t h e c o r r e s p o n d i n g m e t a l l i c s t a t e . ( B ) F o r m a t i o n o f d i m e r s a n d a g a p o p e n i n g a t t h e F e r m i l e v e l . T h i s p i c t u r e c r e a t e s f u l l y o c c u p i e d b o n d i n g o r b i t a l a n d u n o c c u p i e d a n t i b o n d i n g o r b i t a l s . 1 2 1 . 4 . 2 P e i e r l s d i s t o r t i o n a n d C h a r g e - D e n s i t y — W a v e s C o n s i d e r a q u a s i - o n e - d i m e n s i o n a l m e t a l w i t h c h a i n s o f e q u a l l y s p a c e d a t o m s . T h e c o n d u c t i o n s t a t e s f o r m a b a n d a s s h o w n i n F i g u r e 1 . 3 A . I f t h e r e i s c o u p l i n g b e t w e e n t h e c o n d u c t i o n e l e c t r o n s a n d t h e l a t t i c e t h e n a p e r i o d i c d i s p l a c e m e n t o f t h e i o n s d r i = A i c o s ( q - r l . ) ( 1 . 1 ) w i l l p r o d u c e a p e r t u r b a t i o n p o t e n t i a l W ) = V 0 c o s ( q - r ) ( 1 . 2 ) s e e n b y t h e c o n d u c t i o n e l e c t r o n s . H e r e q i s t h e w a v e v e c t o r o f t h e d i s t o r t i o n , l a t t i c e p o s i t i o n s a r e g i v e n b y r a n d t h e p o t e n t i a l V 0 5 g | A | i s p r o p o r t i o n a l t o t h e d i s t o r t i o n a m p l i t u d e a n d t h e e l e c t r o n - p h o n o n c o u p l i n g c o n s t a n t . T h i s p e r t u r b a t i o n s p l i t s t h e d e g e n e r a t e l e v e l s a n d p r o d u c e s a g a p i n t h e b a n d s t r u c t u r e a t i q / 2 . S t a t e s w i t h w a v e v e c t o r s j u s t l e s s t h a n q / 2 w i l l b e l o w e r e d i n e n e r g y w h i l e t h o s e w i t h w a v e v e c t o r g r e a t e r t h a n q / 2 w i l l b e r a i s e d . T h e d i s t o r t i o n i s m o s t f a v o r a b l e w h e n q = 2 k f t h e r e f o r e t h e g a p i s p r o d u c e d a t t h e F e r m i s u r f a c e . I n t h i s c a s e t h e o c c u p i e d s t a t e s b e l o w k f a r e l o w e r e d i n e n e r g y w h i l e t h e r a i s e d s t a t e s a r e u n o c c u p i e d a n d t h e o n l y e n e r g e t i c c o s t i s t h e l a t t i c e s t r a i n . T h e e n e r g e t i c r e q u i r e m e n t f o r t h e d i s t o r t i o n h a s i m p l i c i t t e m p e r a t u r e d e p e n d e n c e s i n c e i n c r e a s i n g t e m p e r a t u r e w i l l p r o g r e s s i v e l y p o p u l a t e t h e r a i s e d e l e c t r o n i c s t a t e s . U l t i m a t e l y , a b o v e a t r a n s i t i o n t e m p e r a t u r e T C D W t h e d i s t o r t i o n w i l l b e l o s t a n d t h e s y s t e m w i l l r e t u r n t o i t s m e t a l l i c u n d i s t o r t e d c o n d i t i o n . I n t h i s o n e - d i m e n s i o n a l c a s e a n y fi n i t e e l e c t r o n - p h o n o n c o u p l i n g l e a d s t o t h e a d o p t i o n o f a s u p e r s t r u c t u r e a n d a g a p a t E . 3 7 f 1 3 ) k ( E y / g r e n E 1 3 J \ ( A ) S ? ' L I - l E l e m “ d e n s ‘ t y a . . . . . . . . . . . . . . . . . { 5 f 0 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 g 5 , A t o m i c p o s i t i o n l ? m I I l l - E - k f + k f . 1 W a v e c t o r k ( B ) . A c = fl / k f E l e c t r o n d e n s i t y . H — — — 4 W 0 0 e 0 0 0 e 0 0 0 e 0 0 A t o m i c p o s i t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I I I - l - k f + k f l W a v e c t o r k F i g u r e 1 . 3 . ( A ) A q u a s i - o n e - d i m e n s i o n a l u n d i s t o r t e d m e t a l w i t h i n t e r a t o m i c s p a c i n g d ( B ) C D W m o d u l a t e d e l e c t r o n s a n d p h o n o n s a n d t h e c r e a t i o n o f a g a p a t t h e F e r m i l e v e l . T h e m o d u l a t i o n s a r e u s u a l l y q u i t e s m a l l w i t h a t o m i c d i s p l a c e m e n t s a b o u t 1 % o f t h e i n t e r a t o m i c s p a c i n g a n d t h e c o n d u c t i o n e l e c t r o n d e n s i t y v a r i e s b y s e v e r a l p e r c e n t . 1 . 5 T h e r m o e l e c t r i c p r o p e r t y I n o r d e r f o r a m a t e r i a l t o b e u s e f u l f o r t h e r m o e l e c t r i c a p p l i c a t i o n s i t m u s t h a v e a h i g h fi g u r e o f m e r i t , Z T : 2 = S ” T ( 1 . 3 ) K Z T w h e r e S i s t h e t h e r m o p o w e r , a i s t h e e l e c t r i c a l c o n d u c t i v i t y a n d 1 c i s t h e t h e r m a l c o n d u c t i v i t y . F r o m e q u a t i o n ( ( 1 . 3 ) ) i s a p p a r e n t t h a t i n o r d e r t o o b t a i n a h i g h Z T , t h e m a t e r i a l m u s t p o s s e s s h i g h t h e r m o p o w e r , h i g h e l e c t r i c a l c o n d u c t i v i t y a n d l o w t h e r m a l 1 4 c o n d u c t i v i t y . A l t h o u g h t h i s a p p e a r s t o b e v e r y s t r a i g h t f o r w a r d t h e p r o b l e m i s a c t u a l m o r e c o m p l i c a t e d b e c a u s e t h e s e v a r i a b l e s a r e d e p e n d e n t o f e a c h o t h e r . R i s i n g o f t h e r m o p o w e r i s u s u a l l y f o l l o w e d b y d e c r e a s i n g o f e l e c t r i c a l c o n d u c t i v i t y a n d i n c r e a s i n g o f e l e c t r i c a l c o n d u c t i v i t y i s u s u a l l y f o l l o w e d b y i n c r e a s i n g o f t h e r m a l c o n d u c t i v i t y . 3 8 A l t h o u g h m e t a l l i c m a t e r i a l s m a y h a v e h i g h e l e c t r i c a l c o n d u c t i v i t y , t h e y g e n e r a l l y h a v e l o w t h e r m o p o w e r . W i d e b a n d g a p s e m i c o n d u c t o r s m a y p o s s e s s h i g h e r t h e r m o p o w e r b u t t h e i r e l e c t r i c a l c o n d u c t i v i t y i s t o o l o w d u e t o f e w e r c a r r i e r s . S e m i r n e t a l s o r n a r r o w b a n d g a p s e m i c o n d u c t o r s w i t h h e a v y m e t a l s s e e m s t o b e t h e m o r e p r o m i s i n g m a t e r i a l s f o r t h e r m o e l e c t r i c a p p l i c a t i o n s . 3 8 T h e y h a v e h i g h e l e c t r i c a l c o n d u c t i v i t y a n d l o w t h e r m a l c o n d u c t i v i t y d u e t o l o w f r e q u e n c y l a t t i c e v i b r a t i o n s o f t h e h e a v y e l e m e n t s . T h e t h e r m o p o w e r i s g i v e n b y t h e e q u a t i o n : d 1 n 0 ' ( E ) _ . — — d E a t E — E f ( 1 - 4 ) S = K w h e r e K i s a c o n s t a n t a n d 0 ( E ) i s t h e e l e c t r i c a l c o n d u c t i v i t y a s a f u n c t i o n o f F e r m i e n e r g y , E f ' T h e t h e r m o p o w e r c a n b e s e e n a s a m e a s u r e o f t h e d i f f e r e n c e o f 0 ( E ) b e l o w a n d a b o v e t h e F e r m i s u r f a c e . T h e c o m p l e x i t y o f a b a n d s t r u c t u r e i n c r e a s e s w i t h t h e c o m p l e x i t y o f t h e e l e c t r o n i c s t r u c t u r e a n d f u r t h e r m o r e t h e c h a n c e s f o r a h i g h 0 ( E ) a t t h e F e r m i l e v e l . T h e r e b y , t h e t h e r m o p o w e r c a n b e i n c r e a s e d . 1 . 6 P a i r D i s t r i b u t i o n F u n c t i o n a n a l y s i s ( P D F ) K n o w i n g t h e r e a l s t r u c t u r e o f a m a t e r i a l i s v e r y i m p o r t a n t i n d e t e r m i n i n g a n d e x p l a i n i n g i t s p r o p e r t i e s a n d c h a r a c t e r i s t i c s . T h e s t r u c t u r e c h a r a c t e r i z a t i o n o f a s o l i d u s u a l l y i n v o l v e s X - r a y d i f f r a c t i o n s t u d y a n d c r y s t a l l o g r a p h i c a n a l y s i s . H o w e v e r , t h e c r y s t a l s t r u c t u r e r e p r e s e n t s o n l y t h e l o n g - r a n g e o r d e r a n d t h e a v e r a g e u n i t c e l l . 1 5 — y D e v i a t i o n s f r o m i d e a l “ p e r f e c t ” c r y s t a l s - l i k e m i x e d s i t e o c c u p a t i o n , i m p u r i t i e s , d i s t o r t i o n s a n d d e f e c t s — a r e v e r y i m p o r t a n t f o r t h e p r o p e r t i e s o f t h e m a t e r i a l s . S o m e t i m e s , t h e s e s t r u c t u r a l d e v i a t i o n s a r e b e i n g h i d d e n i n t o t h e a v e r a g e s t r u c t u r e a n d s o r t - r a n g e o r d e r c h a r a c t e r i z a t i o n t e c h n i q u e s a r e n e c e s s a r y t o p r o b e t h i s k i n d o f d e f e c t s . T h e p a i r d i s t r i b u t i o n fi m c t i o n m e t h o d ( P D F ) i s a p o w e r f u l t e c h n i q u e f o r l o c a l s t r u c t u r e s t u d i e s . B a s i c a l l y , t h e P D F d e s c r i b e s t h e d i s t r i b u t i o n o f i n t e r a t o m i c d i s t a n c e s i n a m a t e r i a l . T h e p o w e r a n d t h e d i f f e r e n c e o f P D F f r o m o t h e r c r y s t a l l o g r a p h i c t e c h n i q u e s l i k e R i e t v e l d i s t h a t P D F i s a t o t a l s c a t t e r i n g t e c h n i q u e w h i c h m e a n s b o t h t h e B r a g g a n d d i f f u s e s c a t t e r i n g a r e t r e a t e d o n a n e q u a l b a s i c . T h e e x p e r i m e n t s a r e s t r a i g h t f o r w a r d X - r a y o r n e u t r o n p o w d e r d i f fi ' a c t i o n m e a s u r e m e n t s , F i g u r e 1 . 4 A . F r o m t h e c o h e r e n t p a r t , 1 c 0 h ( Q ) , o f t h e m e a s u r e d t o t a l d i f f r a c t e d i n t e n s i t y o f t h e m a t e r i a l w e fi n d t h e t o t a l s c a t t e r i n g s t r u c t u r e f u n c t i o n , S ( Q ) 1 6 " ” ( Q > — Z c I f ( Q ) | 2 i i , + 1 S ( Q ) = 2 ‘ 2 C i f i ( Q ) l ( 1 . 5 ) w h e r e t h e c o h e r e n t i n t e n s i t y i s c o r r e c t e d f o r b a c k g r o u n d a n d o t h e r e x p e r i m e n t a l e f f e c t s a n d n o r m a l i z e d b y t h e fl u x a n d n u m b e r o f a t o m s i n t h e s a m p l e , F i g u r e 1 . 4 B . H e r e , C i a n d f i a r e t h e a t o m i c c o n c e n t r a t i o n a n d X - r a y a t o m i c f o r m f a c t o r , r e s p e c t i v e l y , f o r t h e a t o m i c s p e c i e s o f t y p e i . M o m e n t u m t r a n s f e r , Q , i s g i v e n b y Q = 4 7 r s i n r 9 / / i ( 1 . 6 ) B y F o u r i e r t r a n s f o r m i n g t h e e x p r e s s i o n Q [ S ( Q ) — I ] w e h a v e 1 6 Q m a x G ( r ) = ( 2 / r r ) j Q [ S ( Q ) - 1 ] s i n ( Q - r ) d Q ( 1 . 7 ) Q = o w h e r e G ( r ) i s t h e a t o m i c p a i r d i s t r i b u t i o n f u n c t i o n w h i c h i s a l s o d e fi n e d a s G ( r ) = 4 n - r [ p ( r ) - p 0 ] ( 1 . 8 ) w h e r e p 0 i s t h e a v e r a g e a t o m i c n u m b e r d e n s i t y , p ( r ) i s t h e a t o m i c p a i r - d e n s i t y a n d r i s a r a d i a l d i s t a n c e . T h e f u n c t i o n G ( r ) g i v e s i n f o r m a t i o n a b o u t t h e n u m b e r o f a t o m s i n a s p h e r i c a l s h e l l o f u n i t t h i c k n e s s a t a d i s t a n c e r f r o m a r e f e r e n c e a t o m , F i g u r e 1 . 4 C . F i n a l l y , t h e e x p e r i m e n t a l G ( r ) c a n b e c o m p a r e d a n d r e fi n e d a g a i n s t a t h e o r e t i c a l G ( r ) f r o m a s t r u c t u r a l m o d e l g i v e n b y f ( 0 ) v f ( 0 ) ” 6 ( r — r ) ( 1 . 9 ) G ( r ) + 4 7 z - r - p = — 0 r V ’ u < f ( 0 ) > 2 V 1 “ I n t h e o r y , Q m a x f r o m e q u a t i o n ( 1 . 7 ) s h o u l d b y i n fi n i t e b u t e x p e r i m e n t a l l y i s a l w a y s a fi n i t e n u m b e r . I n o r d e r t o h a v e g o o d r e s o l u t i o n , v a l u e s o f Q ’ s > 3 0 A ' 1 a r e d e s i r a b l e t h e r e f o r e s h o r t w a v e l e n g t h s a r e n e c e s s a r y a c c o r d i n g t o e q u a t i o n ( 1 . 6 ) . X - r a y s o f > 4 5 K e V ( k = 0 . 2 7 A ) a n d u p t o l 3 0 K e V ( k = 0 . 0 9 A ) o r n e u t r o n s a r e t y p i c a l l y u s e d . A s c a n b e s e e n P D F i s b a s e d o n a c o n v e n t i o n a l X - r a y o r n e u t r o n p o w d e r d i f fi ' a c t i o n e x p e r i m e n t a n d i t ’ s s i m p l y a n o t h e r r e p r e s e n t a t i o n o f t h e d i f f r a c t i o n d a t a . T h e o n l y d i f f e r e n c e i s t h a t P D F r e fl e c t s b o t h t h e l o n g - r a n g e a t o m i c s t r u c t u r e , m a n i f e s t i n t h e B r a g g r e fl e c t i o n s , a n d t h e l o c a l s t r u c t u r e i m p e r f e c t i o n s , m a n i f e s t i n t h e d i f f u s e c o m p o n e n t o f t h e d i f fi a c t i o n p a t t e r n . T h e d a t a a n a l y s i s d o e s n o t p r e s u m e a n y p e r i o d i c i t y t h e r e f o r e t h e P D F t e c h n i q u e i s v e r y u s e f u l f o r e x a m i n i n g i f t h e d i s t o r t i o n s f o u n d i n a s p e c i fi c s i n g l e c r y s t a l a r e r e p r e s e n t a t i v e o f t h e t o t a l b u l k o f t h e s a m p l e . 3 9 1 7 A 1 . 0 1 ' 1 ' 1 r 1 1 1 1 ) . 0 . 8 - _ : 5 £ 0 6 — — . é ‘ ‘ 2 0 . 4 - - 8 a ' « 0 . 2 " M J 0 0 r 1 1 1 . 1 1 1 1 1 . 0 5 1 0 2 0 d 1 5 2 0 2 5 3 0 6 6 6 8 ( B ) 1 2 . 1 1 T 1 r 1 1 1 ( ' [ g r ' ) 1 1 ' 1 1 1 ' 1 1 0 - - 1 3 . _ a . O i _ 4 n 1 L 1 . 1 . 1 1 1 1 4 n m . 1 m 1 . 1 n r A ‘ 0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 W a v e v e c t o r Q ( A ' l ) ( C ) 5 1 l i I i I 7 I ' I ' 1 ' 1 ' T j F ‘ q 4 0 m o d e l _ fi t 2 3 _ A 2 - . , _ b ' : " - - O 1 5 ' : ‘ 5 0 ’ 1 ‘ e - ‘ 7 ' : ‘ ' 1 ' " - 1 - 3 L - l 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 l 6 1 7 1 8 1 9 2 0 R a d i a l d i s t a n c e r ( A ) F i g u r e 1 . 4 . ( A ) E x p e r i m e n t a l x - r a y d i f f r a c t i o n p a t t e r n o f C e T e 3 p o w d e r . ( B ) T h e c o r r e c t e d a n d r e d u c e d Q [ S ( q ) - l ] p l o t a n d ( C ) t h e P D F G ( r ) a f t e r t h e F o u r i e r t r a n s f o r m . 1 8 1 . 7 S u p e r s p a c e a p p r o a c h f o r m o d u l a t e d s t r u c t u r e s L a t t i c e p e r i o d i c i t y i s a f u n d a m e n t a l c o n c e p t i n c r y s t a l l o g r a p h y . T h i s p r o p e r t y i s w i d e l y c o n s i d e r e d a s e s s e n t i a l f o r t h e c h a r a c t e r i z a t i o n o f t h e c o n c e p t o f a c r y s t a l . I n r e c e n t d e c a d e s , h o w e v e r , m o r e a n d m o r e l o n g - r a n g e - o r d e r e d c o n d e n s e d - m a t t e r p h a s e s h a v e b e e n o b s e r v e d i n n a t u r e t h a t d o n o t h a v e l a t t i c e p e r i o d i c i t y , s o - c a l l e d a p e r i o d i c s y s t e m s . T h e y o n l y d i f f e r f r o m n o r m a l c r y s t a l p h a s e s i n v e r y s u b t l e a n d n o t e a s y t o o b s e r v e s t r u c t u r a l a n d p h y s i c a l p r o p e r t i e s . T h e r e a r e t h r e e m a i n c l a s s e s o f c o m p o u n d s w i t h a p e r i o d i c c h a r a c t e r . O n e i s t h e f a m i l y o f c o m m e n s u r a t e o r i n c o m m e n s u r a t e m o d u l a t e d s y s t e m s . A n o t h e r o n e i s t h e g r o u p o f c o m p o s i t e c r y s t a l s i n w h i c h a t l e a s t t w o d i f f e r e n t s t r u c t u r a l m o t i f s ( s u b s t r u c t u r e s ) a r e c r y s t a l l i z e d t o g e t h e r a n d f o r m a n i n t e r g r o w t h m o d u l a t e d s y s t e m . I n t h a t c a s e , t h e r e fl e c t i o n s i n r e c i p r o c a l s p a c e o f o n e s u b s t r u c t u r e b e c o m e s u p e r c e l l r e fl e c t i o n s o f t h e o t h e r o n e a n d v i s e v e r s a . Q u a s i c r y s t a l s b e l o n g t o t h e t h i r d f a m i l y o f a p e r i o d i c c r y s t a l s . I n t h a t c a s e s y m m e t r y e l e m e n t s l i k e 5 - f o l d , 7 - f o l d , 9 - f o l d e t c . r o t a t i o n a x i s a r e p r e s e n t i n t h e d i f f r a c t i o n p a t t e r n t h a t c a n n o t b e d e s c r i b e d b y t h e c o n v e n t i o n a l c r y s t a l l o g r a p h i c t h e o r y . I n t h i s w o r k w e w i l l d e a l o n l y w i t h t h e fi r s t c l a s s o f i n c o m m e n s u r a t e m o d u l a t e d s y s t e m s . A m o d u l a t i o n i s c o n s i d e r e d t o b e a p e r i o d i c d e f o r m a t i o n o f a “ b a s i c s t r u c t u r e ” h a v i n g s p a c e g r o u p s y m m e t r y . I f t h e p e r i o d i c i t y o f t h e m o d u l a t i o n d o e s n o t b e l o n g t o t h e p e r i o d i c i t i e s o f t h e b a s i c s t r u c t u r e , t h e m o d u l a t e d c r y s t a l s t r u c t u r e i s c a l l e d i n c o m m e n s u r a t e . O n t h e o t h e r h a n d , i f t h e p e r i o d o f t h e d i s t o r t i o n c a n b e g e n e r a t e d b y a r e l a t i v e s m a l l i n t e g e r n u m b e r o f r e p e t i t i o n s o f t h e b a s i c s t r u c t u r e , t h e s u p e r c e l l i s c a l l e d c o m m e n s u r a t e . T h i s d e s c r i p t i o n i s b a s e d o n t h e o b s e r v a t i o n i n t h e d i f f r a c t i o n p a t t e r n o f 1 9 m o d u l a t e d s t r u c t u r e s o f m a i n r e fl e c t i o n s , s i t u a t e d o n a r e c i p r o c a l l a t t i c e , a n d a d d i t i o n a l r e fl e c t i o n s , g e n e r a l l y o f w e a k e r i n t e n s i t y , c a l l e d s a t e l l i t e s . 1 . 7 . 1 R e c i p r o c a l s p a c e a n d s u p e r s p a c e I n c o m m e n s u r a t e c r y s t a l s a r e c h a r a c t e r i z e d b y B r a g g r e fl e c t i o n p e a k s i n t h e d i f f r a c t i o n p a t t e r n w h i c h a r e w e l l s e p a r a t e d b u t d o n o t b e l o n g t o a l a t t i c e a n d c a n n o t b e i n d e x e d b y t h r e e - i n t e g e r i n d i c e s , F i g u r e 1 . 5 . S a t e l l i t e s a r e r e g u l a r l y s p a c e d b u t t h e y c a n n o t b e i n d e x e d w i t h t h r e e r e c i p r o c a l v e c t o r s . D i f f r a c t i o n p a t t e r n h a s n o m o r e t h r e e d i m e n s i o n a l l a t t i c e c h a r a c t e r a n d t h e b a s i c p r o p e r t y o f c r y s t a l , t h r e e d i m e n s i o n a l t r a n s l a t i o n s y m m e t r y , i s v i o l a t e d b u t i n a s p e c i fi c r e g u l a r w a y . O n e o r m o r e a d d i t i o n a l , m o d u l a t i o n v e c t o r s ( q - v e c t o r s ) h a v e t o b e a d d e d t o i n d e x a l l d i f fi ' a c t i o n s p o t s . 4 0 0 0 0 o e - 0 0 0 0 . 4 _ E - q + q : 0 . 2 _ 0 0 4 0 + - . . . . . . e . - 0 . 2 _ . - O . L : c o o c o o 0 0 0 - 9 . 4 4 5 . 2 3 1 1 . 0 6 . 2 5 . 4 F i g u r e 1 . 5 . T y p i c a l d i f f r a c t i o n p a t t e r n ( r e c i p r o c a l s p a c e ) o f a m o d u l a t e d s y s t e m . T h e m a i n s t r o n g r e fl e c t i o n s a r e i n d e x e d a s h k l O a n d t h e w e a k e r s a t e l l i t e r e fl e c t i o n s a r e i n d e x e d a s h k l m w h e r e m i s t h e ( 3 + 1 ) d i m e n s i o n a l i n d e x . 2 0 q - — — — h ‘ — — - T h e p o s i t i o n s o f a l l t h e B r a g g r e fl e c t i o n s c a n b e d e s c r i b e d b y Q = h a * + k b * + l c * + m q = H + m q ( 1 . 1 0 ) w h e r e t h e m o d u l a t i o n v e c t o r q c a n b e e x p r e s s e d a s a l i n e a r c o m b i n a t i o n o f a * , b * , c " ' q = q l a * + q z b * + q 3 c * ( 1 . 1 1 ) W h e n m = 0 t h e n t h e r e fl e c t i o n b e l o n g s t o t h e u n d i s t o r t e d s u b c e l l a n d i s c a l l e d m a i n r e fl e c t i o n . W h e n m 9 6 0 t h e n t h e r e fl e c t i o n i s c h a r a c t e r i z e d a s s a t e l l i t e d u e t o t h e s u p e r c e l l f o r m a t i o n . I n o t h e r w o r d s , i f q 1 , q 2 a n d q 3 a r e r a t i o n a l n u m b e r s t h e n w e h a v e a c o m m e n s u r a t e m o d u l a t i o n o t h e r w i s e f o r i r r a t i o n a l q 1 , q 2 a n d q 3 n u m b e r s t h e m o d u l a t i o n i s i n c o m m e n s u r a t e . I t i s d i f fi c u l t t o p r o v e i r r a t i o n a l i t y o n l y f r o m t h e m e a s u r e d v a l u e s o f t h e l e n g t h o f t h e v e c t o r s . T h e h i g h e r t h e d e n o m i n a t o r s t h e s m a l l e r d i f f e r e n c e b e t w e e n c o m m e n s u r a t e a n d i n c o m m e n s u r a t e s i t u a t i o n . B u t t h e r e a r e c a s e s l i k e 1 / 2 , 1 / 3 w h e r e c o m m e n s u r a b i l i t y i s e a s y t o i d e n t i f y . 0 M a i n r e fl e c t i o n s e S a t e l l i t e s F i g u r e 1 . 6 . S c h e m a t i c r e p r e s e n t a t i o n o f r e a l d i f f r a c t i o n p a t t e r n ( 3 D ) b y a p r o j e c t i o n f r o m t h e ( 3 + 1 ) d i m e n s i o n a l s u p e r s p a c e . 2 1 M o d u l a t e d , c o m p o s i t e , a n d q u a s i c r y s t a l s c a n b e d e s c r i b e d i n a ( 3 + d ) d i m e n s i o n a l s u p e r s p a c e . T h e t h e o r y h a s d e v e l o p e d b y P M . D e W o l f f , A . J a n n e r a n d T . J a n s s e n 4 0 ( A m i n o f f p r i z e 1 9 9 8 ) . T h i s t h e o r y a l l o w s t o g e n e r a l i z e c o n c e p t o f s y m m e t r y a n d a l s o t o m o d i f y a l l m e t h o d u s e d f o r s t r u c t u r e d e t e r m i n a t i o n a n d r e fi n e m e n t o f t h r e e d i m e n s i o n a l s y s t e m s f o r a p e r i o d i c c r y s t a l s . T h e b a s i c i d e a i s t h a t a r e a l d i f f r a c t i o n p a t t e r n c a n b e s e e n a s a p r o j e c t i o n f r o m t h e ( 3 + d ) d i m e n s i o n a l s u p e r s p a c e , F i g u r e 1 . 6 . T h e a d d i t i o n a l v e c t o r e , p e r p e n d i c u l a r t o t h e r e a l s p a c e R 3 , a l l o w s t h e d e s c r i p t i o n o f t h e d i f f r a c t i o n p a t t e r n a s a f o u r - d i m e n s i o n a l l a t t i c e . T h e r e f o r e , r e a l r e fl e c t i o n s i n t h e o b s e r v e d t h r e e - d i m e n s i o n a l s p a c e c a n b e u n d e r s t o o d a s a p r o j e c t i o n a l o n g v e c t o r e f r o m a f o u r - d i m e n s i o n a l l a t t i c e . T h u s , t h e n e w f o u r - d i m e n s i o n a l r e c i p r o c a l b a s i s c a n b e w r i t t e n a s : 1 | : : 1 : : 1 : . A = a . f o r z = l , 2 , 3 a n d A 4 = q + e ( 1 . 1 2 ) i 1 1 . 7 . 2 D i r e c t s p a c e a n d s u p e r s p a c e A s t h e d i f f r a c t i o n p a t t e r n h a s a f o u r - d i m e n s i o n a l l a t t i c e c h a r a c t e r , i t s F o u r i e r t r a n s f o r m a t i o n ( d i r e c t o r r e a l s p a c e ) , w h i c h r e p r e s e n t s s o m e g e n e r a l i z e d f o u r - d i m e n s i o n a l d e n s i t y , m u s t f u l fi l l t h e p e r i o d i c i t y c o n d i t i o n . D e p e n d i n g o n t h e c h a r a c t e r o f t h e m o d u l a t i o n w e s h a l l g e t d i f f e r e n t f o u r - d i m e n s i o n a l m a p s . F o r a p o s i t i o n a l m o d u l a t i o n w e ' c a n g e t a m a p s i m i l a r t o t h a t i n F i g u r e 1 . 7 . T h e m a p h a s a t r a n s l a t i o n a l c h a r a c t e r a n d t h e w h o l e s t r u c t u r e c a n b e b u i l d u p f r o m o n e f o u r - d i m e n s i o n a l b a s i c c e l l . I n d i v i d u a l a t o m s a r e n o w r e p r e s e n t e d b y a m o d u l a t i o n c u r v e w h i c h h a s p e r i o d i c i t y f o l l o w i n g t h e f o u r - d i m e n s i o n a l l a t t i c e . T h e d i r e c t f o u r - d i m e n s i o n a l b a s i c v e c t o r s a r e r e l a t e d t o t h e r e c i p r o c a l o n e s b y t h e o r t h o n o r m a l i t y c o n d i t i o n A i A ; = 6 1 . ] . ( w h e r e 5 1 . 1 . 1 3 K r o n e c k e r ’ s d e l t a : 2 2 A i z a i — l q - a i l e f o r i = 1 , 2 , 3 a n d A 4 = e ( 1 . 1 3 ) 6 i ] . = 1 w h e n i = j , a n d 5 1 . ] . = 0 w h e n i 7 E j ) w h i c h a l l o w s t h e d e r i v a t i o n o f r e l a t i o n s h i p s b e t w e e n t h r e e a n d f o u r - d i m e n s i o n a l b a s i s v e c t o r s : T h e s u p e r s p a c e d e s c r i p t i o n g i v e s t h e p o s s i b i l i t y t o d e s c r i b e a m o d u l a t e d s t r u c t u r e i n a s i m i l a r w a y a s a r e g u l a r s t r u c t u r e , F i g u r e 1 . 7 . T h e d e n s i t y c a n b e a g a i n d i v i d e d i n t o " a t o m s " b u t t h e y a r e n o t c o n c e n t r a t e d a n y m o r e i n a r e l a t i v e l y s m a l l v o l u m e b u t i n a s o - c a l l e d a t o m i c d o m a i n s ( a t o m i c s t r i n g s ) . I n a n a l o g y t o a r e g u l a r s t r u c t u r e , t h e a t o m i c d o m a i n s a r e a g a i n d e s c r i b e d b y a s e t o f p a r a m e t e r s w h i c h a r e n o w a f u n c t i o n o f t h e i n t e r n a l c o o r d i n a t e x 4 . F o r t h e i n c o m m e n s u r a t e c a s e a l l s e c t i o n s t h r o u g h t h e a t o m i c d o m a i n a r e r e a l i z e d i n s o m e c e l l i n R 3 , f o r t h e c o m m e n s u r a t e c a s e o n l y s o m e s p e c i fi c v a l u e s a r e r e a l i z e d . A u s e f u l c o o r d i n a t e t t h a t c h a r a c t e r i z e s a n d d e s c r i b e s t h e r e a l t h r e e d i m e n s i o n a l s t r u c t u r e c o n s t r u c t e d a s a p e r p e n d i c u l a r i n t e r s e c t i o n w i t h t h e A 4 a x i s i s d e fi n e d a s : t = x 4 — q - r ( 1 . 1 4 ) A l l d i f f e r e n t t s e c t i o n s f o r t h e i n c o m m e n s u r a t e c a s e a r e e q u i v a l e n t t o o n l y t h e " fi r s t " c e l l c h o s e n i n a d i f f e r e n t w a y . O n t h e o t h e r h a n d s e l e c t i o n o f t h e t c o o r d i n a t e p l a y s a c r u c i a l r o l e i n c o m m e n s u r a t e c a s e s w h e r e i t c a n l e a d t o d i f f e r e n t s p a c e g r o u p s . T h e s u p e r s p a c e a p p r o a c h i n c l u d e s a l l m e t h o d s f o r s o l u t i o n a n d r e fi n e m e n t o f a p e r i o d i c c r y s t a l s . I t e n a b l e s t h e u s e o f t h e t o o l s u s e d i n s t r u c t u r e a n a l y s i s o f r e g u l a r c r y s t a l s s u c h a s d i r e c t m e t h o d s , F o u r i e r m a p s , l e a s t s q u a r e s , d i s t a n c e a n d a n g l e c a l c u l a t i o n s , b o n d v a l e n c e s u m m a t i o n s , m a x i m u m e n t r o p y m e t h o d e t c . s o t h a t t h e y c a n b e u s e d i n a s i m i l a r w a y l i k e i n s t a n d a r d c r y s t a l l o g r a p h y . 2 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . t - p e r i o d 2 4 4 F i g u r e 1 . 7 . V i s u a l i z a t i o n o f a ( 1 + 1 ) d i m e n s i o n a l s t r u c t u r e i n r e a l s p a c e . T h e s t r u c t u r e c a n b e b u i l d u p f r o m o n e f o u r - d i m e n s i o n a l b a s i c c e l l . I n d i v i d u a l a t o m s a r e n o w r e p r e s e n t e d b y a m o d u l a t i o n c u r v e ( a t o m i c s t r i n g s ) w h i c h h a s p e r i o d i c i t y f o l l o w i n g t h e f o u r d i m e n s i o n a l l a t t i c e . T h e q — v e c t o r c o m p o n e n t a l o n g c * i s n o t a t e d a s y . 1 . 7 . 3 S y m m e t r y i n s u p e r s p a c e T h e r e a r e 7 7 5 s u p e r s p a c e g r o u p s a n d t h e y w e r e d e r i v e d a n d l i s t e d b y d e W o l f f , J a n s s e n a n d J a n n e r i n t h e I n t e r n a t i o n a l T a b l e s o f C r y s t a l l o g r a p h y , V o l u m e C f o r ( 3 + 1 ) d i m e n s i o n a l m o d u l a t e d s y s t e m s . T h e r e a r e s e v e r a l n o t a t i o n s , f o r e x a m p l e : B P m n _ a s o r B : P m n a : 3 1 T T h e fi r s t s y m b o l d e n o t e s a B r a v a i s c l a s s w h e r e t h e f o u r - d i m e n s i o n a l c e n t e r i n g v e c t o r s f o r e a c h s y m b o l a r e : 1 1 P ( 0 0 0 ) A ( — , 0 , 0 ) B ( 0 , 1 , 0 ) C ( 0 . 0 . — ) 2 2 2 R ( % , % , O ) L ( 1 , 0 , 0 ) M ( 0 , 1 , 0 ) N ( 0 , 0 , 1 ) 1 1 1 1 1 1 U 0 , — 2 — V — 9 0 9 _ W _ 9 _ 9 O ( 2 2 ) ( 2 2 ) ( 2 2 ) W h e n t h e r e i s n o t h r e e - d i m e n s i o n a l a n a l o g o f a c e r t a i n c e n t e r i n g v e c t o r u s u a l l y a l o n g t h e x 4 , f o r e x a m p l e ( 0 , 0 , % , - ; — ) , t h e B r a v a i s c l a s s n o t a t i o n b e c o m e s “ X ” . T h e s y m b o l s i n t r o d u c e d i n t h e o r i g i n a l p a p e r w e r e l a t e r m o d i fi e d a n d , a c c o r d i n g t o I n t e r n a t i o n a l T a b l e s V o l . C , t h e s u p e r s p a c e g r o u p m e n t i o n e d a b o v e i s w r i t t e n a s a n a ( 0 1 / 2 y ) s 0 0 . T h i s m e a n s t h a t b o t h , t h e r a t i o n a l a n d i r r a t i o n a l p a r t o f t h e m o d u l a t i o n v e c t o r a r e g i v e n e x p l i c i t l y . I n t h i s n o t a t i o n , t h e fi r s t s y m b o l s b e f o r e t h e p a r e n t h e s e s c o n t a i n t h e e l e m e n t s o f t h e t h r e e - d i m e n s i o n a l s p a c e g r o u p , a n a . I n t h e p a r e n t h e s e s , t h e c o m p o n e n t s o f t h e m o d u l a t i o n q - v e c t o r ( a , , 6 , ) 2 p a r a m e t e r s o f e q u a t i o n ( 1 . 1 1 ) ) a r e i n t r o d u c e d . F i n a l l y , a f t e r p a r e n t h e s e s v a l u e s o f t r a n s l a t i o n a l v e c t o r s t i n t h e f o u r t h - 2 5 d i m e n s i o n f o r e a c h g e n e r a t o r t h a t a p p e a r s i n t h e t h r e e - d i m e n s i o n a l s p a c e g r o u p a r e i n t r o d u c e d . A l e t t e r s y m b o l i z e s t h e v a l u e o f 1 ' a c c o r d i n g t o : 1 : 0 1 / 2 : t l / 3 i l / 4 i 1 / 6 s y m b o l 0 s t q h I n o u r e x a m p l e , t h e n o t a t i o n o f t h e s u p e r s p a c e g r o u p a n a ( 0 ‘ / 2 7 ) S O O m e a n s t h a t t h e u n d i s t o r t e d s u b c e l l s t r u c t u r e h a s a a n a s y m m e t r y w i t h a r a t i o n a l c o m p o n e n t o f t h e q - v e c t o r o f 1 / 2 a l o n g t h e b * a n d a n i n c o m m e n s u r a t e c o m p o n e n t ( 7 ) a l o n g t h e 0 * . F u r t h e r m o r e , t h e r e i s a n o n - p r i m i t i v e t r a n s l a t i o n o f 1 / 2 a s s o c i a t e d o n t h e n - g l i d e p l a n e a l o n g t h e a * a x i s ( 1 / 2 a , 0 ) = ( V 2 0 0 0 ) . T h e r e a r e n o e x t r a c e n t e r i n g c o n d i t i o n s a l o n g t h e m i r r o r p l a n e a n d a - g l i d e p l a n e o f b * a n d c * a x i s r e s p e c t i v e l y . S i m i l a r f o r m a l i s m h a s b e e n a d o p t e d f o r m o d u l a t i o n w i t h t w o a n d t h r e e q - v e c t o r s . A l t h o u g h t h e c o r r e s p o n d i n g s u p e r s p a c e g r o u p s w e r e d e r i v e d b y A k i j i Y a m a m o t o f o r ( 3 + 2 ) - d i m e n s i o n s 4 1 a n d ( 3 + 3 ) - d i m e n s i o n s 4 2 s t i l l t h e y a r e n o t t a b u l a t e d i n t h e I n t e r n a t i o n a l T a b l e s o f C r y s t a l l o g r a p h y . 2 6 1 . 7 . 4 R e fi n e m e n t o f m o d u l a t e d s t r u c t u r e s T h e c a l c u l a t i o n o f t h e s t r u c t u r e f a c t o r s f o r a m o d u l a t e d c r y s t a l c o m e s f r o m a n i n t e g r a t i o n p r o c e d u r e s i n c e t h e c e l l s i n t h r e e - d i m e n s i o n a l s p a c e a r e g e n e r a l l y d i f f e r e n t a l o n g t h e m o d u l a t i o n . T h i s c a n b e d o n e e i t h e r n u m e r i c a l l y o r a n a l y t i c a l l y . T h e n u m e r i c a l p r o c e d u r e s a r e b a s e d o n G a u s s i a n , 4 3 o r F F T 4 4 i n t e g r a t i o n a n d t h e a n a l y t i c a l o n e s u s u a l l y o n B e s s e l f u n c t i o n s . 4 5 T h r e e d i f f e r e n t p r o g r a m s R E M O S , 4 3 M S R 4 6 a n d J a n a 3 6 ’ 4 7 w e r e d e v e l o p e d f o r t h e r e fi n e m e n t o f m o d u l a t e d s t r u c t u r e s . T h e r e fi n e m e n t p r o g r a m s u s e a p e r i o d i c m o d u l a t i o n f u n c t i o n p i x 4 ) = p i x 4 + n ) , w h e r e n i s a n i n t e g e r n u m b e r , t o d e s c r i b e t h e c h a n g e s o f t h e b a s i c s t r u c t u r a l p a r a m e t e r s a l o n g t h e m o d u l a t i o n v e c t o r . D u e t o t h e p e r i o d i c i t y , t h e d i s t o r t i o n ( p o s i t i o n a l , o c c u p a t i o n a l , t e m p e r a t u r e p a r a m e t e r , e t c . ) o f a g i v e n a t o m i c p a r a m e t e r x o f t h e s u b c e l l 4 c a n b e e x p r e s s e d b y a p e r i o d i c m o d u l a t i o n f u n c t i o n p 1 x 4 ) i n a f o r m o f a F o u r i e r e x p a n s i o n : m m p ( k + x 4 ) = Z A s n s i n [ 2 n - fi n ( k + x 4 ) ] + Z A c n c o s [ 2 7 r - fi n ( k + x 4 ) ( 1 . 1 5 ) " = 1 n = l w h e r e A S ” i s t h e s i n u s o i d a l c o e f f i c i e n t o f t h e g i v e n F o u r i e r t e r m , A c n t h e c o s i n e c o e f f i c i e n t , n t h e n u m b e r o f m o d u l a t i o n w a v e s u s e d f o r t h e r e fi n e m e n t a n d k t h e l a t t i c e d t r a n s l a t i o n . i n = Z a n i q i w h e r e a m . i n t e g e r n u m b e r s f o r t h e l i n e a r c o m b i n a t i o n o f t h e 1 : 1 i n c o m m e n s u r a t e m o d u l a t i o n v e c t o r s q i . T h e n u m b e r o f t e r m s u s e d d e p e n d s o n t h e c o m p l e x i t y o f t h e m o d u l a t i o n f u n c t i o n a n d t h e r e f o r e o n t h e o r d e r o f t h e o b s e r v e d s a t e l l i t e s , F i g u r e 1 . 8 A - B . 2 7 p h a s e # 7 : p e r i o d / A ( A ) ( B ) A ( C ) , ( D ) > X 4 F i g u r e 1 . 8 . ( A ) I l l u s t r a t i o n o f a h a r m o n i c f u n c t i o n c o m p o s e d o f a s i n g l e w a v e w i t h a n a m p l i t u d e A . T h e p e r i o d a n d p h a s e a r e i n d i c a t e d . ( B ) A c o m p l e x s q u a r e - l i k e h a r m o n i c 0 4 w i d t h A . ( D ) A s a w t o o t h f u n c t i o n w i t h c e n t e r x 2 , w i d t h A a n d m a x i m a l d i s p l a c e m e n t u B o t h c r e n e l a n d s a w t o o t h f u n c t i o n s r e p e a t p e r i o d i c a l l y a l o n g t h e x 4 d i r e c t i o n . f u n c t i o n c o m p o s e d o f t h r e e w a v e s . ( C ) A s q u a r e f u n c t i o n ( c r e n e l ) w i t h c e n t e r x a n d O ' 2 8 1 . 7 . 5 P o s i t i o n a l m o d u l a t i o n T h e p o s i t i o n a l m o d u l a t i o n a f f e c t s i n t e n s i t i e s i n a r e l a t i v e c o m p l e x w a y . T h e k i n e m a t i c a l t h e o r y o f d i f f r a c t i o n a l l o w s d e r i v a t i o n o f d i f fi ‘ a c t e d i n t e n s i t i e s f o r h a r m o n i c m o d u l a t i o n w a v e s . A c o m b i n a t i o n o f s t a t i c w a v e s i s u s e d f o r d e s c r i b i n g m o d u l a t e d s t r u c t u r e s i n a s i m i l a r d e r i v a t i o n f a s h i o n l i k e t h e e x p r e s s i o n o f t h e r m a l v i b r a t i o n s i n t h e c r y s t a l . T h e i n d e p e n d e n t d e r i v a t i o n s f o r v a r i o u s c a s e s w e r e m a d e b y s e v e r a l a u t h o r s . 3 4 ’ 3 6 ' 4 8 ’ 4 9 F o r a s i m p l e h a r m o n i c m o d u l a t i o n w a v e t h e m o d u l a t i o n d i s p l a c e m e n t u a n d t h e c o r r e s p o n d i n g s t r u c t u r e f a c t o r F c a n b e e x p r e s s e d a s : u = U c o s ( 2 7 r q - r ) a n d F = f e x p ( 2 7 t - i - Q - r ) . l m ( 2 7 t U - H ) ( 1 . 1 6 ) T h e s y m b o l J m s t a n d s f o r t h e m - t h o r d e r B e s s e l f u n c t i o n , m b e i n g t h e s a t e l l i t e i n d e x . T h e a r g u m e n t i s a s c a l a r p r o d u c t o f t h e d i f f r a c t i o n v e c t o r H w i t h t h e m o d u l a t i o n a m p l i t u d e U . T h e r e f o r e , a l l s a t e l l i t e s w i t h H p e r p e n d i c u l a r t o U a r e u n o b s e r v e d . T h i s m a k e s i t p o s s i b l e t o d r a w s o m e c o n c l u s i o n s c o n c e r n i n g t h e m o d u l a t i o n a m p l i t u d e d i r e c t l y f r o m t h e d i f f r a c t i o n p a t t e r n . 1 . 7 . 6 S u b s t i t u t i o n a l m o d u l a t i o n T h e r e a r e c a s e s t h a t a s i n g l e c r y s t a l l o g r a p h i c s i t e i s o c c u p i e d b y t w o o r m o r e a t o m s . A s s u m i n g t h a t t h e p r o b a b i l i t y o f fi n d i n g a g i v e n a t o m o n t h a t s i t e i s a h a r m o n i c fi r n c t i o n o f t h e x 4 c o o r d i n a t e , t h e a t o m i c f o r m f a c t o r c a n b e d e s c r i b e d a s f = f l v + f 2 v + f 1 v — f 2 v V 2 2 s i n ( 2 7 r - q - r v ) ( 1 - 1 7 ) T h i s g i v e s r i s e t o m a i n r e fl e c t i o n s a n d fi r s t o r d e r s a t e l l i t e s : 2 9 f + f F v ( h k 1 0 ) = $ 3 . 2 1 ! . e x p ( 2 n - i - Q - r v ) 1 . 1 8 F ( h k l i l ) = - f l — V - f i e x p ( 2 7 t - i - Q - r ) ( ) v 2 v T h e d i f f r a c t i o n p a t t e r n h a s i s o t r o p i c c h a r a c t e r a n d s a t e l l i t e s a r e g e n e r a l l y p r e s e n t i n a l l p o s i t i o n s p r e d i c t e d b y t h e q v e c t o r . T h e i r i n t e n s i t y d e p e n d s o n d i f f e r e n c e s i n t h e f o r m f a c t o r s o f t w o a t o m s . T h e m a i n r e fl e c t i o n s a r e a l s o m o d i fi e d a n d t h e i r s t r u c t u r e f a c t o r s a r e t h e a v e r a g e o f t w o l i m i t i n g c a s e s . F u r t h e r m o r e , i t i s p o s s i b l e t o h a v e p o s i t i o n a l a n d o c c u p a t i o n a l m o d u l a t i o n s o n t h e s a m e s t r u c t u r e . T h i s s i t u a t i o n c r e a t e s a m o r e o r d e r e d p i c t u r e w i t h t h e p r e s e n c e o f h i g h e r o r d e r s a t e l l i t e r e fl e c t i o n s . T h e s h a p e o f t h e o v e r a l l m o d u l a t i o n f u n c t i o n i s r a t h e r c o m p l e x a n d i n g e n e r a l i t t a k e s a c o m b i n a t i o n o f a l o t o f h a r m o n i c w a v e s i n o r d e r t o f u l l y d e s c r i b e t h e o b s e r v e d d i s t o r t i o n . S p e c i a l fi r n c t i o n s h a v e b e e n d e p l o y e d f o r d e s c r i b i n g p o s s i b l e d i s c o n t i n u e s s u b s t i t u t i o n a l p a t t e r n s ( C r e n e l f u n c t i o n ) o r d i s c o n t i n u e s p o s i t i o n a l a n d o c c u p a t i o n a l d i s t o r t i o n s ( S a w t o o t h f u n c t i o n ) . 1 . 7 . 7 C r e n e l f u n c t i o n O c c u p a t i o n a l d i s t o r t i o n s s o m e t i m e s c a n n o t b e d e s c r i b e d b y a r e l a t i v e s m a l l n u m b e r o f h a r m o n i c w a v e s a s w e a s s u m e d i n t h e p r e v i o u s c a s e . T h e o c c u p a t i o n a l m o d u l a t i o n p a t t e r n m a y l o o k l i k e a s t e p - l i k e d i s c o n t i n u o u s f u n c t i o n w i t h s h a r p c h a n g e s o n t h e o c c u p i e d f r a c t i o n f r o m 0 t o 1 , F i g u r e 1 . 8 C . T h e s o - c a l l e d c r e n e l f u n c t i o n s a r e d i s c o n t i n u o u s p e r i o d i c f u n c t i o n s c o n s t r u c t e d f o r t h e d e s c r i p t i o n o f s u c h c a s e s . T h e o c c u p a t i o n a l m o d u l a t i o n o f t e n o c c u r s a s a t o m i c b l o c k s t h a t a r e o c c u p i e d b y o n e k i n d o f 3 0 a t o m . T h e s e b l o c k s c a n h a v e d i f f e r e n t w i d t h a n d o r d e r . S u c h a m o d e l c a n b e d e s c r i b e d b y a p e r i o d i c d i s c o n t i n u o u s m o d u l a t i o n f u n c t i o n : 5 0 0 0 p 1 x 4 1 = 1 f o r x 4 e < x 4 — A / 2 , x 4 + A / 2 > ( 1 1 9 ) _ _ 0 0 . 0 4 a r e t h e w i d t h a n d c e n t e r o f t h e c r e n e l f r m c t i o n . T h e F o u r i e r w h e r e A a n d x t r a n s f o r m o f t h i s f u n c t i o n g i v e s 0 . 0 . P m ( A , x 4 ] = e x p ( 2 7 t - 1 - m - x 4 ) s r n ( 7 t - m - A ) r t - m ( 1 . 2 0 ) t h a t m o d i fi e s t h e a t o m i c c o n t r i b u t i o n t o t h e s t r u c t u r e f a c t o r . S u c h a m o d u l a t i o n i n d u c e s s t r o n g s a t e l l i t e s u p t o v e r y h i g h o r d e r . S i m i l a r l y a s f o r t h e h a r m o n i c m o d u l a t i o n , t h e d i f f r a c t i o n p a t t e r n h a s i s o t r o p i c c h a r a c t e r b u t t h e n u m b e r o f o b s e r v a b l e s a t e l l i t e s i s m u c h h i g h e r . A c c o r d i n g t o e q u a t i o n ( 1 . 2 0 ) i n t e n s i t i e s o f s a t e l l i t e s a r e d r o p p i n g o f f a s 1 / m 2 . T h e c r e n e l l i k e m o d u l a t i o n w a s o r i g i n a l l y i n t r o d u c e d t o a c c o u n t f o r a s t r o n g o c c u p a t i o n m o d u l a t i o n i n o n e s p e c i a l s t r u c t u r e 5 I b u t n o w a d a y s p l a y s a v e r y i m p o r t a n t r o l e a s i t a l l o w s t h e d e s c r i p t i o n o f a g e n e r a l d i s c o n t i n u i t y i n a m o d u l a t e d s t r u c t u r e . T h e s u b s t i t u t i o n a l m o d u l a t i o n n a t u r a l l y i n d u c e s s o m e p e r i o d i c i n c o m m e n s u r a t e t e n s i o n i n t h e c r y s t a l a s t h e t w o d i f f e r e n t a t o m s c a n n o t g e n e r a l l y fi t t o t h e s a m e p o s i t i o n a n d c o o r d i n a t i o n . T h i s o fi e n c a u s e s a n a d d i t i o n a l p o s i t i o n a l m o d u l a t i o n . T h e C r e n e l f u n c t i o n i s a p p l i e d o n t h e l a s t w a v e o f t h e o v e r a l l m o d u l a t i o n ( p o s s i b l e c o m b i n a t i o n o f w a v e s f o r p o s i t i o n a l d i s t o r t i o n ) a n d i t s i g n i fi c a n t l y r e d u c e s t h e n u m b e r o f p a r a m e t e r s c o m p a r e d t o t h e u s e o f a l a r g e n u m b e r o f F o u r i e r s e r i e s o f h a r m o n i c w a v e s . 3 1 1 . 7 . 8 S a w t o o t h f u n c t i o n S i m i l a r t o t h e p i c t u r e o f d i s t o r t i o n s w i t h d i s c o n t i n u o u s o c c u p a t i o n a l w a v e s , w e m a y h a v e c a s e s i n w h i c h t h e p o s i t i o n a l p a r a m e t e r s b e h a v e d i s c o n t i n u o u s l y . T h e c o r r e s p o n d i n g f u n c t i o n t h a t c a n d e s c r i b e t h i s b e h a v i o r i s c a l l e d s a w t o o t h f t m c t i o n , F i g u r e 1 . 8 D . T h e w i d t h A x 4 i s d e fi n e d a s t h e l e n g t h o f t h e p r o j e c t i o n o f t h e s a w t o o t h f u n c t i o n o n t h e x 4 - a x i s . I t r e p e a t s p e r i o d i c a l l y a l o n g t h e h o r i z o n t a l d i r e c t i o n x c a u s i n g a l i n e a r 4 9 d i s p l a c e m e n t o f — A r i t o + A x i i n a r a n g e o f w i d t h A x c e n t e r e d a t x 0 o n t h e i n t e r n a l 4 4 d i r e c t i o n w h e r e i = l , 2 , 3 f o r x 4 6 < x 2 — A / 2 , x 2 + A / 2 > . 0 p ( x 4 ) = 2 A x O x 0 ( 1 . 2 1 ) I n a d d i t i o n , t h e s a w t o o t h f u n c t i o n h a s a n o c c u p a t i o n a l c h a r a c t e r . T h e v a l u e o f t h e w i d t h A c a n b e l e s s t h a n o n e a n d i n t h a t c a s e t h e o c c u p a t i o n w i l l h a v e a s t e p - l i k e c h a r a c t e r a s w e s a w i n t h e c r e n e l c a s e . S i m i l a r l y , t h e n u m b e r o f s a t e l l i t e r e fl e c t i o n s i s m u c h h i g h e r t h a n t h o s e o b s e r v e d f o r a s i n g l e h a r m o n i c w a v e . 1 . 7 . 9 E x a m p l e s o f c o n t i n u e s a n d d i s c o n t i n u e s d i s t o r t i o n s i n r e a l s p a c e A f e w i l l u s t r a t i o n s o f h o w d i s t o r t i o n s m a y l o o k l i k e i n r e a l s p a c e c a n b e f o u n d i s F i g u r e s 1 . 9 - 1 . 1 l . A s i n g l e h a r m o n i c p o s i t i o n a l w a v e o f a t o m s m a y o c c u r a t a n y d i r e c t i o n i n t h e t h r e e - d i m e n s i o n a l s p a c e . O n a n u n d i s t o r t e d s q u a r e p a t t e r n o f a t o m s , F i g u r e 1 . 9 A , a p o s i t i o n a l d i s t o r t i o n c a n b e a l o n g a l o n g i t u d i n a l d i r e c t i o n a n d c r e a t e i n - p l a n e 3 2 d i s p l a c e m e n t s a l o n g t h e d i r e c t i o n o f t h e n e t , F i g u r e 1 . 9 B . A n o t h e r p o s s i b i l i t y i s t o h a v e a t r a n s v e r s e d i s t o r t i o n a n d t h e c r e a t i o n o f o u t - o f — p l a n e d i s p l a c e m e n t s a s c a n b e s e e n i n F i g u r e 1 . 9 C . T h e o v e r a l l m o d u l a t i o n w i l l c r e a t e a n e w p e r i o d i c i t y i n t h e s y s t e m a n d t h i s c a n b e a p p a r e n t f r o m t h e e x a m i n a t i o n o f t h e r e c i p r o c a l d i f f r a c t i o n p a t t e r n o f F i g u r e 1 . 9 D . E x t r a s a t e l l i t e r e fl e c t i o n s w i l l b e p r e s e n t i n d i c a t i v e o f t h e p e r i o d i c d i s t o r t i o n . I n a m o r e c o m p l e x s y s t e m w e c a n h a v e a c o m b i n a t i o n o f p o s i t i o n a l a n d o c c u p a t i o n a l m o d u l a t i o n w i t h d i s c o n t i n u e c h a r a c t e r , F i g u r e s 1 . 1 0 - 1 . 1 1 . L e t ’ s a s s u m e d o m a i n 1 w i t h a c o n c e n t r a t i o n o f 2 / 3 w h i c h p o s s e s a p o s i t i o n a l m o d u l a t i o n o f t h e c o m p l e x s h a p e s h o w n i n F i g u r e 1 . 1 0 . T h e c o m p l e m e n t a r y f r a c t i o n o f 1 / 3 i s o c c u p i e d b y d o m a i n 2 w h i c h i s n o t d i s t o r t e d ( fl a t l i n e ) . T h e f o u r - d i m e n s i o n a l u n i t c e l l i s n o t a t e d ( s e e F i g u r e 1 . 7 a s w e l l ) . T h e r e s u l t e d s e q u e n c e o f a t o m s ( p o s i t i o n a n d o c c u p a t i o n ) i n t h e r e a l s p a c e w i l l d e p e n d o n t h e s p e c i fi c v a l u e o f t h e t - c o o r d i n a t e w e c h o o s e . T h e “ c u t s ” f o r t w o T - v a l u e s o f 0 . 2 6 a n d 0 . 5 9 a r e s h o w n a t t h e b o t t o m o f F i g u r e 1 . 1 0 . T h e c o m p o n e n t o f t h e q - v e c t o r i n t h i s c a s e i s 0 . 2 4 . N o t e t h e d i f f e r e n c e o f t h e a t o m i c s e q u e n c e s b e t w e e n t h e t w o T - v a l u e s i n t e r m s o f p o s i t i o n a n d o c c u p a n c y . L e t ’ s e x a m i n e n o w a s i t u a t i o n i n w h i c h t h e l e n g t h o f t h e q — v e c t o r c h a n g e s , F i g u r e 1 . 1 1 . T h e a t o m i c d o m a i n s a n d f o u r - d i m e n s i o n a l u n i t c e l l a r e e x a c t l y t h e s a m e l i k e i n t h e p r e v i o u s e x a m p l e . T h e o b s e r v e d s e q u e n c e o f a t o m s n o w i s q u i t e d i f f e r e n t fi o m t h e o n e o b s e r v e d b e f o r e e v e n i f w e c h o o s e t h e s a m e t - s e c t i o n s . T h e q - v e c t o r c o m p o n e n t i n t h e l a t e r c a s e i s 0 . 1 3 . I t i s a m a z i n g h o w a s m a l l v a r i a t i o n o f m o d u l a t i o n p a r a m e t e r s ( q - v e c t o r , o c c u p a n c y . e t c . ) c a n d r a m a t i c a l l y a f f e c t t h e r e a l s p a c e p i c t u r e . F r o m t h e o t h e r h a n d , i t ’ s a p p a r e n t h o w t h e s u p e r s p a c e a p p r o a c h c a n s u c c e s s f u l l y d e s c r i b e a c o m p l e x m o d u l a t e d s t r u c t u r e w i t h a s m a l l n u m b e r o f p a r a m e t e r s . 3 3 ) D ( . I O I I I O C O I I . . ) ) ) A B C ( ( ( 3 4 F i g u r e 1 . 9 . ( A ) U n d i s t o r t e d p a t t e r n o f a t o m s . ( B ) L o n g i t u d i n a l p o s i t i o n a l m o d u l a t i o n i n d i r e c t s p a c e . ( C ) T r a n s v e r s e p o s i t i o n a l m o d u l a t i o n i n d i r e c t s p a c e . ( D ) D i f f r a c t i o n p a t t e r n o f t h e m o d u l a t e d p a t t e r n s . s i s m o t a f o e c n e u q e s g n i t l u s e r e h T . e c a p s l a e r n i n o i t c n u f l e n . e 4 r 2 c . 0 a f d o n t a n e e n . v . . . . . . . . . . . . . . a o w p m n . o . . . . . . o . . l . . . . . . . . . . . . . . . . . . . y y c c n n a a p p u u . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c c . . c c o o 3 3 / / 2 1 : : 1 2 n n i i a a m m o o d d . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [ . . . . . . . . . . 6 2 9 5 . 0 0 = : e e c c u u i i l ] m m a a o o t t A A V v - - T T c i t r a o t c u e d v o - m q c a i h n t i w o m r a s h n o a i t f c o e s n - o t i t t n a e r n e i f b f m i d o C o . w 0 t 1 . r 1 o f e n r u w g o i h F s 3 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I R e s u l t i n g s e q u e n c e f o r : T - v a l u e = 0 . 2 6 O C C C C . T - v a l u e = 0 . 5 9 O O C C C C s i s m o t a f o e c n e u q e s g n i t l C C . . . . . . . . . . . . . . . . u . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . s e r e h T . e c a C C p s l a e r n i n o i C C . t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c n u f l e n e r C 3 c . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a . C 0 d n f a o t e . . n y y c c . . . . . . . . . . . _ . . . . . . . . . . . . . . . . . . . . . . . C . . . . . . . . n n . . . . . . v e a n w o C p a a p p . . . . . . . . u . u c c c c o o 3 3 / / 2 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l . . . . . . . . . . . . . . . . . . . n o m i o t c a r l o u t d c o e m v - c q i a n o h m t r i w . . . . . . . . . . . . . . . . C C . a . . . : h s . r . . . . . . . . . . o n . o f a . . 6 9 i . . . . . . 2 5 f t . . e : : 1 2 l . . . . . . . . . . . n n 6 i i 2 a a . 9 5 m m o o d d 0 0 : : = e e c c u u c . . o c e 0 0 n s e = = t o u i n - q e e t e a u u t n e s n r l l a a i e g f v v b n i t - - m f i T T o d i i C l l m m a a o o t t V v _ - T T A A R l o u w . s t 1 e 1 . r 1 o f e n r u w g o i h F s 3 6 A 1 . . . . . . . . . u - . . o . . . - . . . . . . . n . . . 1 r . 9 2 . 1 1 . 3 I i i i f ' i f " " " " 2 . . — c . d 1 . 7 . 1 0 S t r u c t u r e s o l u t i o n o f m o d u l a t e d c r y s t a l s T h e s t r u c t u r e s o l u t i o n o f m o d u l a t e d s y s t e m s c a n b e d i v i d e d i n t o t w o s t e p s . F i r s t w e h a v e t o fi n d t h e s t r u c t u r e o f t h e s u b c e l l t h a t i s d e s c r i b e d b y t h e e l e c t r o n d e n s i t y c o m i n g f r o m t h e m a i n r e fl e c t i o n s o f t h e e x p e r i m e n t a l r e c i p r o c a l s p a c e . T h e a v e r a g e u n d i s t o r t e d c e l l o f t h e m a i n r e fl e c t i o n s c a n b e s o l v e d u s i n g t r a d i t i o n a l w a y s f o r s o l u t i o n l i k e d i r e c t a n d h e a v y a t o m m e t h o d s . T h e s t r u c t u r e s o l u t i o n c a n b e p e r f o r m e d b y p r o g r a m s s u c h a s S H E L X 5 2 o r S I R . 5 3 T h e q u a l i t y o f t h e r e fi n e m e n t o f t h e s u b c e l l d e p e n d s o n t h e m a g n i t u d e o f t h e d i s t o r t i o n . F o r w e a k l y m o d u l a t e d s y s t e m s ( a t o m i c d i s p l a c e m e n t s l e s s t h a n 0 . 1 A ) t h e r e fi n e m e n t i s u s u a l l y r e a s o n a b l e o r s o m e t i m e s s o g o o d t h a t n o e v i d e n c e o f d i s t o r t i o n i s p r e s e n t . U s u a l l y s t r u c t u r a l i n d i c a t i o n s r e m i n i s c e n t o f d i s t o r t i o n i n t h e r e fi n e d s u b c e l l c a n b e r e l a t i v e l a r g e h a r m o n i c A D P p a r a m e t e r s , a n h a r m o n i c i t y o r s p l i t t i n g . F o r s t r o n g l y m o d u l a t e d s y s t e m s t h e s o l u t i o n o f t h e a v e r a g e s t r u c t u r e c a n b e a b i g p r o b l e m . I n t h a t c a s e , t h e i n t e n s i t i e s o f t h e m a i n r e fl e c t i o n s h a v e t o b e c o r r e c t e d f o r t h e p r e s e n c e o f s a t e l l i t e s . T h e s i m p l e s t m e t h o d t h a t w o r k s w e l l f o r s i m p l e m o d u l a t i o n s i s t o a d d t h e i n t e n s i t i e s o f t h e s a t e l l i t e r e fl e c t i o n s t o t h e i n t e n s i t y o f m a i n r e fl e c t i o n s . S i n c e t h e s t r u c t u r e o f t h e s u b c e l l h a s b e e n f o u n d t h e n e x t s t e p i s t o d e s c r i b e t h e m o d u l a t i o n c o m i n g f r o m t h e i n t e n s i t y o f t h e s a t e l l i t e r e fl e c t i o n s . T r i a l a n d e r r o r i s a t y p i c a l t o o l i n o r d e r t o fi n d a p r o p e r s t a r t i n g p o i n t ( s u p e r s p a c e g r o u p , m o d u l a t i o n w a v e s , e t c . ) f o r t h e r e fi n e m e n t o f m o d u l a t e d s t r u c t u r e s . T h e s m a l l e r t h e d i s p l a c e m e n t s i n t h e d i s t o r t e d s t r u c t u r e , t h e m o r e i n s e n s i t i v e t h e r e fi n e m e n t t o t h e q u a l i t y o f t h e s t a r t i n g p o i n t . O f t e n w e s t a r t r e fi n i n g t h e m o d u l a t e d s t r u c t u r e j u s t f r o m s m a l l d i s p l a c e m e n t s . T h e s i t u a t i o n i s s i m i l a r t o t h e r e fi n e m e n t o f A D P h a r m o n i c p a r a m e t e r s f o r a r e g u l a r s t r u c t u r e . 3 7 I n a n a l o g y t o r e g u l a r s t r u c t u r e s , b o t h d i r e c t 5 4 a n d h e a v y a t o m 5 5 m e t h o d s f o r s o l u t i o n o f m o d u l a t e d s t r u c t u r e s h a v e b e e n d e v e l o p e d . B o t h m e t h o d s s t a r t f r o m t h e k n o w n a v e r a g e s t r u c t u r e . I f a l l t r i a l s t o s o l v e a m o d u l a t e d s t r u c t u r e f a i l , w e h a v e t o u s e s o m e s u p e r c e l l a p p r o x i m a t i o n a n d t r y t o s o l v e t h e s t r u c t u r e i n a l a r g e c e l l . T h i s c a n b e a d i f f i c u l t t a s k t h a t o f t e n r e q u i r e s a d v a n c e d d i r e c t m e t h o d s . T h e s u p e r c e l l s o l u t i o n t h e n c a n b e u s e d a s a s t a r t i n g p o i n t f o r t h e fi n a l m o d u l a t e d r e fi n e m e n t . 1 . 7 . 1 1 S p e c i a l b o o k s , l i t e r a t u r e a n d r e s o u r c e s o n s u p e r s p a c e c o n c e p t T h e b a s i c p h y s i c a l a n d m a t h e m a t i c a l c o n c e p t s o f m o d u l a t e d s t r u c t u r e s w e r e b r i e fl y d e s c r i b e d i n t h i s c h a p t e r i n o r d e r t o h e l p t h e r e a d e r t o u n d e r s t a n d t h e r e s u l t s r e p o r t e d i n t h i s t h e s i s . F o r a d e t a i l e d d e s c r i p t i o n o f t h e t h e o r y o f a p e r i o d i c s y s t e m s I s t r o n g l y r e c o m m e n d t h e f o l l o w i n g m a t e r i a l : 0 v a n S m a a l e n , S . " I n c o m m e n s u r a t e C r y s t a l l o g r a p h y " , O x f o r d U n i v e r s i t y P r e s s , 2 0 0 7 . 0 J a n s s e n , T . ; C h a p u i s , G . a n d d e B o i s s i e u , M . " A p e r i o d i c C r y s t a l s : F r o m M o d u l a t e d P h a s e s t o Q u a s i c r y s t a l s " , O x f o r d U n i v e r s i t y P r e s s , 2 0 0 7 . S o m e m o r e r e f e r e n c e s c a n b e f o u n d i n t h e r e v i e w a r t i c l e s b e l l o w : 0 I n t e r n a t i o n a l T a b l e s f o r C r y s t a l l o g r a p h y , V o l u m e C - M a t h e m a t i c a l , P h y s i c a l a n d C h e m i c a l T a b l e s i n t h e c h a p t e r " I n c o m m e n s u r a t e a n d C o m m e n s u r a t e M o d u l a t e d S t r u c t u r e s " b y J a n s s e n , T . ; J a n n e r , A . ; L o o i j e n g a - V o s , A . ; d e W o l f f , P . M . 0 Y a m a m o t o , A . " D e t e r m i n a t i o n o f c o m p o s i t e c r y s t a l s t r u c t u r e s a n d s u p e r s p a c e g r o u p s " , A c t a C r y s t . 1 9 9 3 , A 4 9 , 8 3 1 . 3 8 o P e ’ r e z - M a t o , J . ; Z r ' r f l i g a , F . a n d M a d a r i a g a , G . E . " S u p e r s p a c e d e s c r i p t i o n o f c o m m e n s u r a t e l y m o d u l a t e d s t r u c t u r e s . M e t h o d s o f s t r u c t u r a l a n a l y s i s o f m o d u l a t e d s t r u c t u r e s a n d q u a s i c r y s t a l s " , W o r l d S c i e n t i fi c . S i n g a p o r e , N e w J e r s e y , L o n d o n , H o n g K o n g , 1 9 9 1 , p . 1 1 7 . 0 P é r e z - M a t o , J . M . ; M a d a r i a g a , G . ; Z t ' r fi i g a , F . J . a n d G a r c i a A r r i b a s , A . " O n t h e s t r u c t u r e a n d s y m m e t r y o f i n c o m m e n s u r a t e p h a s e s . A p r a c t i c a l f o r m u l a t i o n " , A c t a C r y s t . 1 9 8 7 , A 4 3 , 2 1 6 . F i n a l l y , s o m e r e s o u r c e s t h a t I f o u n d v e r y h e l p f u l f o r p r e p a r i n g t h i s i n t r o d u c t o r y p a r t : 0 W e b s i t e o f I v a n O r l o v a n d G e r v a i s C h a p u i s a t h t m z / x ’ l c r . e p fl . c w . 0 I v a n O r l o v ’ s t h e s i s . E P F L , S w i t z e r l a n d , 2 0 0 7 . 0 H a n n a L i n d ’ s t h e s i s . U n i v e r s i t y o f S t o c k h o l m , S t o c k h o l m , 2 0 0 4 . 1 . 8 C o n v e n t i o n s o f t h e t h e s i s D e t a i l e d c r y s t a l l o g r a p h i c d a t a r e p o r t s f o r a l l t h e s o l v e d a n d r e fi n e d m o d u l a t e d s t r u c t u r e s c a n b e f o u n d i n t h e i n d i v i d u a l c h a p t e r o f t h i s t h e s i s . A l l t h e F o u r i e r c o e f fi c i e n t s o f t h e g e n e r a l h a r m o n i c e q u a t i o n ( 1 . 1 5 ) w h e r e fi e e l y r e fi n e d b a s e d o n t h e s u p e r s p a c e s y m m e t r y c o n d i t i o n s f o r e v e r y c a s e . T h e F o u r i e r t e r m A c " w a s n o t a t e d a s c o s , n i n t h e c r y s t a l l o g r a p h i c t a b l e s a n d t h e t e r m A S ” a s s i n , n . F o r e x a m p l e s , t h e s i n u s o i d a l c o e f fi c i e n t o f t h e s e c o n d h a r m o n i c w a v e s w a s s y m b o l i z e d a s “ s i n , 2 ” . T h e m i n i m u m , m a x i m u m a n d a v e r a g e v a l u e s o f t h e d i s t r i b u t i o n o f b o n d d i s t a n c e s a n d a n g l e s b e t w e e n a t o m s a r e g i v e n i n s t e a d o f “ s t a t i c ” t h r e e d i m e n s i o n a l l e n g t h s . E a c h d i s t r i b u t i o n w a s c a l c u l a t e d f o r t h e fi r s t p e r i o d o f t h e t — s e c t i o n w i t h a r e s o l u t i o n o f 0 . 1 . T h e b o n d i n g c u t o f f b e t w e e n a t o m s w a s 3 . 5 A . 3 9 R e f e r e n c e s 1 P a p o i a n , G . ; H o f f m a n n , R . , A n g e w . C h e m . I n t . E d . 2 0 0 0 , 3 9 , 2 4 0 8 . 2 ( a ) S c h e e l , H . J . C r y s t . G r o w t h 1 9 7 4 , 2 4 / 2 5 , 6 6 9 . ( b ) S a n j i n e s , R ; B e r g e r , R ; L e v y , F . J . M a t e r . R e s . B u l l . 1 9 8 8 , 2 3 , 5 4 9 . ( c ) G a r n e r , R . W . ; W h i r e , W . B . J . C r y s t . G r o w t h 1 9 7 0 , 7 , 3 4 3 . 3 S u n s h i n e , 8 . A . ; K a n g , D ; I b e r s , J . A . J . A m . C h e m . S o c . 1 9 8 7 , 1 0 9 , 6 2 0 2 . 4 ( a ) K a n a t z i d i s , M . G . C h e m . M a t e r . 1 9 9 0 , 2 , 3 5 3 . ( b ) S u t o r k i , A . C . ; K a n a t z i d i s , M . G . P r o g . I n o r g . C h e m . 1 9 9 5 , 4 3 , 1 5 1 . ( c ) W u , P . ; I b e r s , J . A . J . A l l o y s . C o m p . 1 9 9 5 , 2 2 9 , 2 0 6 . ( d ) P e l l , M . A . ; I b e r s , J . A . C h e m . B e r . / R e c u e i l 1 9 9 7 , I 3 0 , 1 . ( e ) N a r d u c c i , A . A . ; I b e r s , J . A . C h e m . M a t e r . 1 9 9 8 , 1 0 , 2 8 1 1 . 5 ( 3 ) P e a r s o n , T . G . ; R o b i n s o n , P . L . J . C h e m . S o c . 1 9 3 1 , 1 3 0 4 . ( b ) M a t h e w s o n , G . H . J . A m . C h e m . S o c . 1 9 0 7 , 2 9 , 8 6 7 . ( c ) K l e m m , W . ; S o d o m a n n , H . ; L a n g m e s s e r , P . Z . A n o r g . A l l g . C h e m . 1 9 3 9 , 2 4 1 , 2 8 1 . ( d ) G m e l i n ’ s H a n d b u c h d e r A n o r g a n i s c h e n C h e m i e , V e r l a g C h e m i e , W e i h e i m / B r g s t r , F R G 1 9 6 6 , S o d i u m , S u p p l . P a r t 3 , 1 2 0 2 a n d r e f e r e n c i e s t h e r e i n . 6 B i n a r y A l l o y P h a s e D i a g r a m s ( E d . : T . B . M a s s a l s k i ) , W i l l i a m W . S c o t t , J r . , M a t e r i a l s P a r k , O h i o 1 9 9 0 , p 1 3 9 5 , 2 3 9 2 , 2 7 3 7 a n d 3 1 9 3 . 7 w w w . w e b e l e m e n t s . c o m . 8 H o f f m a n , R . A m e r i c a n S c i e n t i s t 1 9 9 6 , 8 4 , 3 2 7 . 9 ( a ) S h e l d r i c k , W . 8 . ; W a c h h o l d , M ; J o b i c , 8 . ; B r e c , R . ; C a n a d e l l , E . A d v a n c e d M a t e r i a l s 1 9 9 7 , 9 , 6 6 9 . ( b ) K a n a t z i d i s , M . G . A n g e w . C h e m . I n t . E d . E n g l . 1 9 9 5 , 3 4 , 2 1 0 9 . 1 0 L i z T e 6 : B o t t c h e r , P . ; K e l l e r , R . J . L e s s C o m m o n M e t . 1 9 8 5 , 1 0 9 , 3 1 1 a n d r e f e r e n c e s t h e r e i n . 1 1 s z T e s : B o t t c h e r , P . ; K r e t s c h m a n n , U . J . L e s s C o m m o n M e t . 1 9 8 3 , 9 5 , 8 1 . 1 2 R q u : S h e l d r i c k , W . S . ; S c h a a f , B . Z . N a t u r f o r s c h . B 1 9 9 4 , 4 9 , 9 9 3 . 1 3 C s 3 T e 2 2 : S h e l d r i c k , W . 8 . ; W a c h h o l d , M . A n g e w . C h e m . 1 9 9 5 , 1 0 7 , 4 9 0 ; A n g e w . C h e m . I n t . E d . E n g l . 1 9 9 5 , 3 4 , 4 5 0 . 4 0 1 4 ( a ) Z h a n g , Z . ; L i . J . ; F o r a n , B . ; L e e , 8 . ; G u o , H . - Y . ; H o g a n , T . ; K a n n e w u r f , C . R . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 1 9 9 5 , 1 1 7 , 1 0 5 1 3 . ( b ) H a n k o , J . A . ; K a n a t z i d i s , M . G . E v a i n , M . ; G o u r d o n , O . ; B o u c h e r , G . ; P e t r i c e k , V . I n o r g . C h e m . 2 0 0 0 , 3 9 , 1 3 9 8 . 1 5 ( a ) N o r l i n g , B . K . ; S t e i n fi n k , H . I n o r g . C h e m . 1 9 6 6 , 5 , 1 4 8 8 . ( b ) N o e l , H . ; L e v e t , J . C . J . S o l i d S t a t e C h e m . 1 9 8 9 , 7 9 , 2 8 . 1 6 P a r k , S . — M . ; P a r k , S . - J . ; K i m , S . — J . J . S o l i d S t a t e C h e m . 1 9 9 8 , I 4 6 , 3 0 0 . 1 7 P a t s c h k e , R . ; H e i s i n g , J . ; S c h i n d l e r , J . ; K a n n e w u r f , C . R . ; K a n a t z i d i s , M . G . J . S o l i d S t a t e C h e m . 1 9 9 8 , I 3 5 , 1 1 1 . 1 8 P a t s c h k e , R . ; H e i s i n g , J . ; S c h i n d l e r , J . ; K a n n e w u r f , C . R . ; K a n a t z i d i s , M . G . C h e m . M a t e r . 1 9 9 8 , 1 0 , 6 9 5 . 1 9 P a t s c h k e , R . ; B r a z i s , P . ; K a n n e w u r f , C . R . ; K a n a t z i d i s , M . G . M a t e r . C h e m . 1 9 9 9 , 9 , 2 2 9 3 . 2 0 P a t s c h k e , R . ; K a n a t z i d i s M . G . P h y s . C h e m . C h e m . P h y s . 2 0 0 2 , 4 , 3 2 6 6 . 2 1 P a t s c h k e , R . ; B r e s h e a r s , J . D . ; B r a z i s , P . ; K a n n e w u r f , C . R . ; B i l l i n g e , S . J . L . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 1 , 1 2 3 , 4 7 5 5 . 2 2 B r e e z e , E . W . ; B r e t t , N . H . ; W h i t e , J . J . N u c l . M a t . 1 9 7 1 , 3 9 , 1 5 7 2 3 ( a ) C o d y , J . A . ; I b e r s , J . A . I n o r g . C h e m . 1 9 9 6 , 3 5 , 3 8 3 6 . ( b ) N a r d u c c i , A . A . ; I b e r s , J . A . I n o r g . C h e m . 1 9 9 8 , 3 7 , 3 7 9 8 2 4 S a t o , H . ; K o j i m a , N . ; S u z u k i , K . ; E n o k i , T . J . P h y s . S o c . J a p a n 1 9 9 3 , 6 2 , 6 4 5 . 2 5 L e e , S . ; F o r a n , B . J . A m . C h e m . S o c . 1 9 9 4 , 1 1 6 , 1 5 4 . 2 6 ( a ) L e e , 8 . ; F o r a n , B . J . A m . C h e m . S o c . 1 9 9 6 , 1 1 8 , 9 1 3 9 . ( b ) F o r a n , B . ; L e e , 8 . ; A r o n s o n , M . C . C h e m . M a t e r . 1 9 9 3 , 5 , 9 7 4 . 2 7 v a n d e r L e e , A . ; H o i s t a d , L . M . ; E v a i n , M . ; F o r a n , B . J . ; L e e , 8 . C h e m . M a t e r . 1 9 9 7 , 9 , 2 1 8 . 4 1 2 8 ( a ) N b 8 e 3 : C o m e ’ s , R . ; L a m b e r t , M . ; L a u n o i s , H . ; Z e l l e r , H . R . P h y s . R e v . B 1 9 7 3 , 8 , 5 7 1 . ( b ) Z r T e 3 : E a g l e s h a m , D . J . ; S t e e d s , J . W . ; W i l s o n , J . A . J . P h y s . C : S o l i d S t a t e P h y s . 1 9 8 4 , I 7 , 6 9 7 . 2 9 ( a ) E l e c t r o n i c P r o p e r t i e s o f I n o r g a n i c Q u a s i - O n e — D i m e n s i o n a l C o m p o u n d s , E d s . P . M o n c e a u 1 9 8 5 . ( b ) W h a n g b o , M . - H . ; C a n a d e l l , E . J . A m . C h e m . S o c . 1 9 9 2 , 1 1 4 , 9 5 8 7 . ( c ) R o v i r a , C . ; W h a n g b o , M . - H . I n o r g . C h e m . 1 9 9 3 , 3 2 , 4 0 9 4 . ( d ) W h a n g b o , M . - H . ; R e n , J . ; C a n a d e l l , E . ; L o u d e r , D . ; P a r k i n s o n , B . A . ; B e n g e l , H . ; M a g a n o v , S . N . J . A m . C h e m . S o c . 1 9 9 3 , 1 1 5 , 3 7 6 0 . ( e ) L i a n g , X . ; L i e b e r , C . M . S c i e n c e 1 9 8 9 , 2 4 3 , 1 7 0 3 . ( f ) B u r k , B . ; T h o m p s o n , R E . ; C l a r k e , J . ; Z e t t l , A . S c i e n c e 1 9 9 2 , 2 5 7 , 3 6 2 . 3 0 A o _ 3 3 M o O 3 ( A = A l k a l i m e t a l ) : H i l l e n i u m , S . J . ; C o l e m a n , R . V . ; F l e m i n g , R . M . ; C a v a , R . J . P h y s . R e v . B 1 9 8 1 , 2 3 , 1 5 6 7 . ( b ) B a o , 1 5 W O 3 : C a n a d e l l , E . ; W h a n g b o , M . - H . I n o r g . C h e m . 1 9 9 4 , 3 3 , 1 8 6 4 . 3 1 ( a ) K M O 6 0 1 7 , N a o g M O G O n , L 1 0 , 9 M O 5 O 1 7 2 D u m a s , J . ; S C t h D k C I ’ , C . I n t . J . M a t . P h y s . 1 9 9 3 , 7 , 4 0 4 5 . ( b ) W h a n g b o , M . — H . C a n a d e l l , E . ; F o u r y , P . ; P o u g e t , J . — P . S c i e n c e 1 9 9 1 , 2 5 2 , 9 6 . 3 2 S a v e l s b e r g , G . ; S c h a e f e r , H . Z . N a t u r f o r s c h . B 1 9 7 8 , 3 3 B , 3 7 0 . 3 3 S t o w e , K . J . S o l i d S t a t e C h e m . 2 0 0 0 , 1 4 9 , 1 5 5 . 3 4 P e i e r l s , R . B , Q u a n t u m T h e o r y o f S o l i d s , O x f o r d U n i v e r s i t y P r e s s , E n g l a n d , 1 9 5 5 . 3 5 F r o h l i c h , H . , P r o c . R . S o c . 1 9 5 4 , A 2 2 3 , 2 9 6 . 3 6 H o f f a m a n n , R . , S o l i d s a n d S u r f a c e s : A C h e m i s t ’ s v i e w o f b o n d i n g i n e x t e n d i n g s t r u c t u r e s , W i l e y - V C H , 1 9 8 9 . 3 7 G o r ’ k o v , L . P . ; G r u n e r , G . , C h a r g e D e n s i t y w a v e s i n s o l i d s , N o r t h - H o l l a n d , 1 9 8 9 . 3 8 R o w e , D . M . , C R C H a n d b o o k o f t h e r m o e l e c t r i c s , C R C P r e s s , 1 9 9 4 . 3 9 B i l l i n g e , S . J . L . ; K a n a t z i d i s , M . G . C h e m . C o m m u n . 2 0 0 4 , 7 , 7 4 9 . 4 0 J a n s s e n , T . ; J a n n e r , A . ; L o o i j e n g a - V o s , A . ; d e W o l f f , P . M . , I n t e r n a t i o n a l T a b l e s o f C r y s t a l l o g r a p h y , V o l u m e C , 7 9 7 . 4 1 Y a m a m o t o , A . A c t a C r y s t . 1 9 8 6 , A 5 2 , 5 0 9 . 4 2 4 2 Y a m a m o t o , A . F e r r o e l e c t r i c s 2 0 0 1 , 3 2 , 1 3 9 . 4 3 Y a m a m o t o A . A c t a C r y s t . 1 9 8 2 , B 4 1 , 5 2 8 . 4 4 P a c i o r e k , W . A . ; C h a p u i s G . J . A p p l . C r y s t . 1 9 9 2 , 2 5 , 3 1 7 . 4 5 P e t i i c e k V . ; C o p p e n s , P ; B e c k e r P . A c t a C r y s t . 1 9 8 5 , A 4 1 , 4 7 8 . 4 6 P a c i o r e k , W . A . ; K u c h a r c z y k , D . A c t a C r y s t . 1 9 8 5 , A 4 1 , 4 6 2 . 4 7 P e t i i é e k V . ; D u s e k , M . Z . K r i s t a l l o g r . 2 0 0 4 , 2 1 9 , 6 9 2 . 4 8 d e W o l f f , P . M . A c t a C r y s t . 1 9 7 4 , A 3 0 , 7 7 7 . 4 9 P e r e z - M a t o , J . M . ; M a d a r i a g a , G . ; T e l l o , M . J . J . P h y s . C . 1 9 8 6 , 1 9 , 2 6 1 3 . 5 0 P e t i i é e k , V . ; v a n d e r L e e , A . ; E v a i n , M . A c t a C r y s t . 1 9 9 5 , A 5 1 , 5 2 2 9 5 1 B o u c h e r , F . ; E v a i n , M . ; P e t r ' i é e k , V . A c t a C r y s t . 1 9 9 6 , B 5 2 , 1 0 0 . 5 2 ( a ) S h e l d r i c k , G . M . S H E L X . A p r o g r a m f o r c r y s t a l s t r u c t u r e d e t e r m i n a t i o n 1 9 7 6 , U n i v . o f C a m b r i d g e , E n g l a n d . ( b ) R o b i n s o n , W . T . ; S h e l d r i c k , G . M . C r y s t a l l o g r a p h i c C o m p u t i n g 4 . T e c h n i q u e s a n d N e w T e c h n o l o g i e s . 1 9 8 8 e d i t e d b y N . W . I s a a c s & M . R . T a y l o r , p p . 3 6 6 - 3 7 7 . I n t e r n a t i o n a l U n i o n o f C r y s t a l l o g r a p h y , O x f o r d U n i v . P r e s s 5 3 ( a ) A l t o m a r e , A . ; C a s c a r a n o , G . ; G i a c o v a z z o , C . ; G u a g l i a r d i , A . ; B u r l a , M . C . ; P o l i d o r i , G . ; C a m a l l i , M . J . A p p l . C r y s t . 1 9 9 4 , 2 7 , 4 3 5 . ( b ) A l t o m a r e , A . ; B u r l a , M . C . ; C a m a l l i , M . ; C a s c a r a n o , G . L . ; G i a c o v a z z o , C . ; G u a g l i a r d i , A . ; M o l i t e m i , A . G . G . ; P o l i d o r i , G . ; S p a g n a , R . J . A p p l . C r y s t . 1 9 9 9 , 3 2 , 1 1 5 - 1 1 9 . 5 4 ( a ) H a o Q . ; L i u , Y . - W ; F a n , H . - F . A c t a C r y s t . 1 9 8 7 , A 4 3 , 8 2 0 . ( b ) F a n , H . - F . ; v a n S m a a l e n , 8 . ; L a m , E . J . W . ; B e u r s k e n s , P . T . A c t a C r y s t . 1 9 9 3 , A 4 9 , 7 0 4 . 5 5 ( a ) S t e u r e r , W . A c t a C r y s t . 1 9 8 7 , A 4 3 , 3 6 . ( b ) P e t t i é e k , V . “ T h e h e a v y a t o m m e t h o d f o r m o d u l a t e d a n d c o m p o s i t e c r y s t a l s ” , A p e r i o d i c 9 4 , 3 8 8 - 3 9 2 , W o r l d S c i e n t i fi c 1 9 9 5 E d i t e d b y G . C h a p u i s a n d W . P a c i o r e k 4 3 C h a p t e r 2 R e a c t i o n s o f R a r e - E a r t h M e t a l s ( R E ) a n d T e l l u r i u m : S i z e E f f e c t o f R a r e E a r t h t o t h e D i s t o r t i o n s o f t h e T e l l u r i u m N e t o f R E T e 3 “ S q u a r e N e t s o f T e l l u r i u m : R a r e - E a r t h D e p e n d e n t V a r i a t i o n i n t h e C h a r g e - D e n s i t y W a v e o f R E T e 3 ( R E = R a r e - E a r t h E l e m e n t ) ” , M a l l i a k a s , C . D . ; B i l l i n g e , S . J . L . ; K i m , H . J . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 5 , 1 2 7 , 6 5 1 0 - 6 5 1 1 . A m e r i c a n C h e m i c a l S o c i e t y ( A C S ) i s g r a t e f u l l y a c k n o w l e d g e d f o r t h e p e r m i s s i o n t o i n c l u d e t h i s r e p r i n t i n t h e T h e s i s . 4 4 2 . 1 . I n t r o d u c t i o n T h e t r i t e l l u r i d e s R E T e 3 ( R E = r a r e e a r t h e l e m e n t ) " 2 w e r e o r i g i n a l l y r e p o r t e d t o c r y s t a l l i z e i n t h e l a y e r e d s o — c a l l e d N d T e 3 s t r u c t u r e t y p e , h o w e v e r r e c e n t l y t h e y w e r e r e c o g n i z e d t o b e t w o - d i m e n s i o n a l C D W m a t e r i a l s . A s a l i e n t f e a t u r e o f t h i s s t r u c t u r e i s m o n o l a y e r s o f T e a t o m s t h a t a p p e a r t o d e fi n e “ p e r f e c t ” s q u a r e n e t s . A l l T e - T e d i s t a n c e s i n t h e n e t a r e ~ 3 . 1 A , t o o l o n g t o b e n o r m a l b o n d s y e t t o o s h o r t t o b e i g n o r e d a s n o n - b o n d i n g . B e c a u s e o f t h e n o v e l b o n d i n g i m p l i c a t i o n s o f a s q u a r e n e t i t w o u l d b e r a t h e r e x c i t i n g i f i d e a l s q u a r e n e t s o f T e a c t u a l l y e x i s t e d i n t h e e n t i r e a b s o l u t e t e m p e r a t u r e r a n g e . T h i s p i c t u r e , h o w e v e r , i s i n c o r r e c t a n d d e c e p t i v e a s i t m a s k s c o m p l e t e l y t h e t r u e u n d e r l y i n g s t r u c t u r e . 3 S q u a r e n e t a r r a n g e m e n t s o f a t o m s a r e p r e d i c t e d t h e o r e t i c a l l y 4 t o b e u n s t a b l e a n d p r o n e t o c h a r g e d e n s i t y w a v e s ( C D W ) a n d t h e r e f o r e s y s t e m s w h i c h f e a t u r e t h e m , s u c h a s R E T 6 3 , a r e o f g r e a t i n t e r e s t . E l e c t r o n d i f f r a c t i o n s t u d i e s o n s e v e r a l R E T e 3 c o m p o u n d s r e v e a l e d e v i d e n c e f o r t h e p r e s e n c e o f l o n g r a n g e o r d e r i n g . 5 T h i s c a s t s d o u b t o n t h e “ p e r f e c t ” s q u a r e n e t p i c t u r e a n d r a i s e s t h e p o s s i b i l i t y o f l a t t i c e d i s t o r t i o n s o f t h e c h a r g e d e n s i t y w a v e ( C D W ) t y p e i n R E T e 3 , . 6 E l e c t r i c a l c o n d u c t i v i t y m e a s u r e m e n t s o n R E T e 3 s y s t e m s i n d i c a t e m e t a l l i c b e h a v i o r a n d a b s e n c e o f a b a n d g a p i n t h e s e m a t e r i a l s . 7 T h e r e f o r e d e t a i l e d k n o w l e d g e o f t h e l o n g r a n g e m o d u l a t i o n s i s n e c e s s a r y t o c o r r e c t l y u n d e r s t a n d t h e p r o p e r t i e s o f R E T e 3 . M o d u l a t i o n s i n T e n e t s h a v e b e e n f o u n d i n m o r e c o m p l e x m u l t i n a r y c o m p o u n d s s u c h a s K B a A g T e 2 3 , a n d L a T e 2 8 e 8 w h i c h s h o w o l i g o m e r i z a t i o n w i t h i n t h e n e t t o T e x z ' f r a g m e n t s w h e r e x v a r i e s d e p e n d i n g o n e l e c t r o n s p e r T e a t o m . C o m p l i c a t i n g f u r t h e r t h e s t r u c t u r a l i s s u e i s t h a t t h e d i s t o r t i o n s c a n b e i n c o m m e n s u r a t e w i t h t h e u n d e r l y i n g s u b l a t t i c e , w h i c h h i s t o r i c a l l y h a s fi ' u s t r a t e d a t t e m p t s a t a c o m p l e t e c r y s t a l l o g r a p h i c a n a l y s i s . 4 5 2 . 2 . E x p e r i m e n t a l S e c t i o n 2 . 2 . 1 . R e a g e n t s T h e f o l l o w i n g r e a g e n t s w e r e u s e d a s o b t a i n e d . A l l r a r e - e a r t h m e t a l s , 9 9 . 9 % p u r e , fi l l i n g s f r o m i n g o t , C h i n e s e R a r e E a r t h I n f o r m a t i o n C e n t e r , I n n e r M o n g o l i a , C h i n a ; T e l l u r i u m s h o t s , 9 9 . 9 % p u r e , T e l l u r e x C o r p o r a t i o n , T r a v e r s e C i t y , M I ; R u b i d i u m C h l o r i d e , 9 9 . 8 % p u r e , 2 0 m e s h , C e r a c S p e c i a l t y I n o r g a n i c s , M i l w a u k e e , W I ; L i t h i u m C h l o r i d e , 9 9 . 8 % p u r e , 2 0 m e s h , C e r a c S p e c i a l t y I n o r g a n i c s , M i l w a u k e e , W I ; L i t h i u m I o d i d e , 9 9 . 8 % p u r e , 2 0 m e s h , C e r a c S p e c i a l t y I n o r g a n i c s , M i l w a u k e e , W I ; P o t a s s i u m I o d i d e , 9 9 . 8 % p u r e , 2 0 m e s h , C e r a c S p e c i a l t y I n o r g a n i c s , M i l w a u k e e , W I ; N , N — D i m e t h y l f o r m a m i d e ( D M F ) , A C 8 r e a g e n t g r a d e , S p e c t r u m C h e m i c a l s , N e w B r u n s w i c k , N J ; D i e t h y l e t h e r a n h y d r o u s , A C S r e a g e n t g r a d e , C o l u m b u s C h e m i c a l I n d u s t r i e s , C o l u m b u s , W I . 2 . 2 . 2 . S y n t h e s i s R E T e 3 ( R E = L a , C e , P r , N d , S m , G d , 7 7 ) a n d D y ) — A l l m a n i p u l a t i o n s w e r e c a r r i e d o u t u n d e r d r y n i t r o g e n a t m o s p h e r e i n a V a c u u m A t m o s p h e r e s D r i - L a b g l o v e b o x . S t o i c h i o m e t r i c a m o u n t s o f r a r e e a r t h ( ~ 0 . 3 g ) a n d t e l l u r i u m ( ~ 0 . 8 2 g ) w e r e l o a d e d i n t o q u a r t z t u b e s u n d e r n i t r o g e n t o g e t h e r w i t h a d o u b l e a m o u n t ( ~ 2 g ) o f h a l i d e fl u x ( 0 . 4 2 : 0 . 5 8 m o l a r m i x t u r e s o f R b C l a n d L i C l ) . T h e t u b e s w e r e s e a l e d u n d e r v a c u u m ( < 1 0 ‘ 1 t o r r ) a n d h e a t e d t o 6 5 0 ° C a t 1 2 h o u r s f o r 6 d a y s . T h e t u b e s w e r e t h e n c o o l e d d o w n t o r o o m t e m p e r a t u r e a t a r a t e o f 4 ° C ‘ m i n ' 1 . T h e h a l i d e fl u x w a s d i s s o l v e d i n w a t e r a n d t h e c r y s t a l s w e r e w a s h e d w i t h a c e t o n e a n d d r i e d u n d e r n i t r o g e n e n v i r o n m e n t . T h e m o r p h o l o g y o f t h e c r y s t a l s i s t h a t o f t h i n p l a t e s w i t h a b r o w n ( c o p p e r - l i k e ) c o l o r . 4 6 E l e c t r o n m i c r o p r o b e e n e r g y d i s p e r s i v e s p e c t r o s c o p y ( E D S ) w a s p e r f o r m e d o n s e v e r a l c r y s t a l s o f t h e c o m p o u n d a n d c o n fi r m e d t h e 1 : 3 r a t i o o f t h e r a r e e a r t h t o t e l l u r i u m a n d t h e a b s e n c e o f o t h e r e l e m e n t s o f t h e fl u x . C o m p o u n d s f o u n d t o b e X - r a y p u r e a n d m o i s t u r e s e n s i t i v e a f t e r e x p o s u r e t o a i r f o r a f e w d a y s . R E T e 3 ( R E = H o , E r , T m a n d I ? — I n t h e c a s e o f t h e h e a v i e r r a r e e a r t h s t h e R b C l / L i C l h a l i d e fl u x r e a c t s w i t h t h e e l e m e n t s p r o d u c i n g b e R E y T e z c o m p o u n d s . I n s t e a d , a n e u t e c t i c h a l i d e o f L i I a n d K 1 ( 0 . 3 7 : 0 . 6 3 m o l a r m i x t u r e s ) w a s u s e d t o s y n t h e s i z e t h e t a r g e t R E T e 3 b i n a r i e s . S i m i l a r l y , s t o i c h i o m e t r i c a m o u n t s o f r a r e e a r t h ( ~ 0 . 3 g ) a n d t e l l u r i u m ( ~ 0 . 8 2 g ) w e r e l o a d e d i n t o q u a r t z t u b e s u n d e r n i t r o g e n t o g e t h e r w i t h a d o u b l e a m o u n t ( ~ 2 g ) o f t h e h a l i d e fl u x . T h e t u b e s w e r e s e a l e d u n d e r v a c u u m ( < 1 0 4 t o r r ) a n d h e a t e d t o 6 5 0 ° C a t 1 2 h o u r s f o r 6 d a y s . T h e t u b e s w e r e t h e n c o o l e d d o w n t o r o o m t e m p e r a t u r e a t a r a t e o f 4 ° C ‘ m i n ' l . T h e h a l i d e fl u x w a s d i s s o l v e d i n D M F s i n c e t h e c r y s t a l s f o u n d t o b e e x t r e m e l y m o i s t u r e s e n s i t i v e ( s u r f a c e b e c o m e s b l a c k a f t e r a f e w s e c o n d s o f e x p o s u r e t o w a t e r / m o i s t u r e ) a n d t h e c r y s t a l s w e r e w a s h e d w i t h e t h e r a n d d r i e d u n d e r n i t r o g e n e n v i r o n m e n t . T h e m o r p h o l o g y o f t h e c r y s t a l s i s t h a t o f t h i n p l a t e s w i t h a b r o w n ( c o p p e r - l i k e ) c o l o r . E l e c t r o n m i c r o p r o b e e n e r g y d i s p e r s i v e s p e c t r o s c o p y ( E D S ) w a s p e r f o r m e d o n s e v e r a l c r y s t a l s o f t h e c o m p o u n d a n d c o n fi r m e d t h e 1 : 3 r a t i o o f t h e r a r e e a r t h t o t e l l u r i u m a n d t h e a b s e n c e o f o t h e r e l e m e n t s o f t h e fl u x . C o m p o u n d s f o u n d t o b e X - r a y p u r e . 2 . 2 . 3 . P h y s i c a l M e a s u r e m e n t s S e m i q u a n t i t a t i v e E n e r g y D i s p e r s i v e S p e c t r o s c o p y ( E D S ) — T h e a n a l y s e s w e r e p e r f o r m e d w i t h a J E O L I S M - 3 5 C s c a n n i n g e l e c t r o n m i c r o s c o p e e q u i p p e d w i t h a N o r a n 4 7 V a n t a g e E D S ( S i z L i ) d e t e c t o r . C r y s t a l s w e r e m o u n t e d o n a n a l u m i n u m s t a g e w i t h c a r b o n t a p e . D a t a w e r e a c q u i r e d o n s e v e r a l c r y s t a l s a n d d i f f e r e n t r e g i o n s o f e a c h c r y s t a l u s i n g a n a c c e l e r a t i n g v o l t a g e o f 2 5 k V a n d a c c u m u l a t i o n t i m e o f 4 0 s . S i n g l e C r y s t a l X - r a y D i fi r a c t i o n — A s i n g l e c r y s t a l o f e a c h R E T e 3 m e m b e r w a s m o u n t e d w i t h g l u e o n t h e t i p o f a g l a s s fi b e r . I n t e n s i t y d a t a w e r e c o l l e c t e d o n a S T O E I P D S H d i f fi a c t o m e t e r e q u i p p e d w i t h a g r a p h i t e m o n o c h r o m a t i z e d M o r a d i a t i o n ( 3 » = 0 . 7 1 0 7 3 A ) a n d a n I m a g e P l a t e ( 1 P ) d e t e c t o r . T h e d a t a w e r e c o l l e c t e d w i t h a n c o - s c a n t e c h n i q u e f r o m 0 - 1 8 0 ° a n d a n a r b i t r a r y ( p - a n g l e . D a t a r e d u c t i o n w a s p e r f o r m e d w i t h t h e X - A r e a p a c k a g e . 9 T h e l e n g t h d e t e r m i n a t i o n a n d r e fi n e m e n t o f t h e q - v e c t o r s w a s p e r f o r m e d w i t h t h e P e a k l i s t 1 . 0 6 s o f t w a r e p a r t o f t h e X - A r e a s u i t e u s i n g a l e a s t s q u a r e r e fi n e m e n t a l g o r i t h m . A n a n a l y t i c a l a b s o r p t i o n c o r r e c t i o n w a s p e r f o r m e d ( X - S h a p e w i t h i n X - A r e a ) a n d a l l s t r u c t u r e s w e r e r e fi n e d w i t h J A N A 2 0 0 0 s o f t w a r e . l o D i r e c t m e t h o d s o f S H E L X T L s o f t w a r e l l w e r e u s e d t o fi n d t h e a t o m i c p o s i t i o n s i n t h e s u b c e l l . S a t e l l i t e r e fl e c t i o n s o f fi r s t o r d e r w e r e o b s e r v e d a n d u s e d f o r t h e r e fi n e m e n t . A s i n g l e m o d u l a t i o n w a v e f o r p o s i t i o n a l p a r a m e t e r s w a s u s e d . O n l y t h e s y m m e t r y a l l o w e d F o u r i e r t e r m s w e r e r e fi n e d . T h e p s e u d o - t e t r a g o n a l c h a r a c t e r o f t h e c r y s t a l s y s t e m a l l o w s t h e p l a t e s t o s t a c k a n d t w i n i n a m e r o h e d r a l f a s h i o n . T h e r e f o r e h i g h e l e c t r o n i c d e n s i t i e s w e r e o b s e r v e d i n d i f f e r e n t p o s i t i o n s fi ' o m t h e c a l c u l a t e d o n e s f o r s o m e o f t h e R E T e 3 m e m b e r s . B y a p p l y i n g a t w i n l a w o f a r o t a t i o n o f 9 0 ° a l o n g b - a x i s a ' a 0 0 1 b ' = b - 0 1 0 t h e R f a c t o r s f o r a l l t h e r e fl e c t i o n s ( R l / s z ) i n t h e r e fi n e m e n t c ' c - l 0 0 s i g n i fi c a n t l y d r o p p e d ( f o r t h e c a s e o f t h e N d T e 3 s u b c e l l f r o m 1 1 9 7 / 2 8 9 0 t o 2 6 2 / 5 . 8 3 ) . T h e c o m p l e t e d a t a c o l l e c t i o n p a r a m e t e r s a n d d e t a i l s o f t h e s t r u c t u r e s o l u t i o n a n d 4 8 r e fi n e m e n t f o r a l l R E T e 3 m e m b e r s a t 3 0 0 K a r e g i v e n i n T a b l e s 2 . 1 - 2 . 7 3 . T e m p e r a t u r e w a s c o n t r o l l e d b y a n O x f o r d C r y o s t r e a m 7 0 0 P l u s c r y o s t a t . T r a n s m i s s i o n E l e c t r o n M i c r o s c o p y o f C e T e 3 — S e l e c t e d a r e a e l e c t r o n d i f f r a c t i o n ( S A E D ) s t u d i e s w e r e c a r r i e d o u t o n a J E O L 2 0 1 0 F ( J a p a n E l e c t r o n O p t i c s L a b o r a t o r i e s ) 2 0 0 k V fi e l d e m i s s i o n T E M a t t h e C e n t e r f o r A d v a n c e d M i c r o s c o p y o f M i c h i g a n S t a t e U n i v e r s i t y . A t h i n p l a t e c r y s t a l o f C e T e ; w a s p o l i s h e d a n d i o n - m i l l e d i n o r d e r t o b e t h i n e n o u g h f o r T E M s t u d y . T h e c r y s t a l w a s m o u n t e d o n a c o p p e r a p e r t u r e g r i d . F o r t h e c r o s s s e c t i o n d i f f r a c t i o n e x p e r i m e n t a s t a c k o f p l a t e c r y s t a l s w a s s a n d w i c h e d b e t w e e n t w o t h i n c a r b o n p l a t e s a n d p o l i s h e d / i o n - m i l l e d . I n fi a r e d ( I R ) S p e c t r o s c o p y — O p t i c a l d i f f u s e r e fl e c t a n c e m e a s u r e m e n t s w e r e p e r f o r m e d o n s i n g l e c r y s t a l s o f a l l R E T e 3 m e m b e r s a t r o o m t e m p e r a t u r e . T h e s p e c t r a w e r e r e c o r d e d i n t h e M i d - I R r e g i o n ( 6 0 0 0 — 4 0 0 c m ' l ) w i t h a N i c o l e t 6 7 0 0 F T - I R S p e c t r o m e t e r e q u i p p e d w i t h a d i f f u s e r e fl e c t a n c e c o l l e c t o r f r o m S p e c t r a - T e c h I n c . P a i r D i s t r i b u t i o n F u n c t i o n o f R E T e 3 ( R E = C e , P r a n d N d ) — P o w d e r s a m p l e s o f R E T e 3 ( R = C e , P r a n d N d ) w e r e p a c k e d i n 1 . 0 m m t h i c k fl a t p l a t e s s e a l e d b e t w e e n k a p t o n t a p e s . T h e X - r a y s c a t t e r i n g e x p e r i m e n t s w e r e c o n d u c t e d o n t h e R E T e 3 s a m p l e s w i t h 9 9 . 8 K e V ( i t = 0 . 1 2 4 2 A ) X - r a y a t t h e 6 - I D - D b e a m l i n e a t t h e A d v a n c e d P h o t o n S o u r c e ( A P S ) a t A r g o n n e N a t i o n a l L a b o r a t o r y ( A N L ) . P o w d e r d i f f r a c t i o n d a t a w e r e c o l l e c t e d a t 3 0 0 K u s i n g t h e r e c e n t l y d e v e l o p e d r a p i d a c q u i s i t i o n p a i r d i s t r i b u t i o n f u n c t i o n ( R A - P D F ) t e c h n i q u e . I n o r d e r t o a v o i d t h e s a t u r a t i o n o f t h e d e t e c t o r , e a c h m e a s u r e m e n t w a s m a d e f o r 4 s e c o n d s , a n d r e p e a t e d 5 t i m e s t o i m p r o v e c o u n t i n g s t a t i s t i c s . A l l t h e c o r r e c t i o n s , t h e t o t a l s c a t t e r i n g s t r u c t u r e f u n c t i o n 8 ( Q ) a n d P D F G ( r ) w e r e o b t a i n e d u s i n g t h e p r o g r a m P D F g e t X 2 . 0 . 1 2 4 9 2 . 3 . R e s u l t s a n d D i s c u s s i o n S u b c e l l D e s c r i p t i o n o f R E T e 3 — T h e a v e r a g e s t r u c t u r e o f R E T e 3 a d o p t s t h e s p a c e g r o u p C m c m . I t c o n s i s t s o f p u c k e r e d d o u b l e l a y e r s o f ( R E T e ) t h a t a r e s a n d w i c h e d b y t h e p l a n a r n e t s o f T e m a k i n g a R E T e 3 s l a b . T h e s l a b s t h e n s t a c k a l o n g t h e b - a x i s c r e a t i n g v a n d e r W a a l s g a p s . T h e f o r m u l a c a n b e m o r e e x p r e s s l y w r i t t e n a s ( R E T e ) + ( T e 2 ) ' , F i g u r e 2 . 1 A . T h e R E a t o m i s i n a m o n o c a p p e d t e t r a g o n a l a n t i p r i s m o f T e a t o m s , F i g u r e 2 . 1 B . T h e a p p a r e n t T e - T e d i s t a n c e s i n t h e s q u a r e n e t a r e 3 . 1 0 3 4 ( 6 ) A ( f o r C e T e 3 ) , F i g u r e 2 . 1 C . ( A ) 3 . 6 A v a n d e r W a a l s g a p ( C ) F i g u r e 2 . 1 . ( A ) U n d i s t o r t e d s t r u c t u r e o f C e T e 3 . ( B ) C o o r d i n a t i o n g e o m e t r y a n d e n v i r o n m e n t o f C e . ( C ) I d e a l s q u a r e n e t o f T e a t o m s i n t h e C e T e 3 s u b c e l l . 5 0 E l e c t r o n T r a n s m i s s i o n M i c r o s c o p y o f C e T e 3 — E l e c t r o n d i f f r a c t i o n s t u d i e s o n C e T e 3 r e v e a l e d a c o m m e n s u r a t e 7 - f o l d s u p e r s t r u c t u r e a l o n g t h e a c - p l a n e , F i g u r e 2 . 3 A . T h e s u p e r s t r u c t u r e h a s a n a p p r o x i m a t e c e l l o f c s u p = 7 c m d u e t o t h e p r e s e n c e o f r e l a t i v e w e a k i n i n t e n s i t y s a t e l l i t e r e fl e c t i o n s a l o n g t h e c * d i r e c t i o n . A d e n s i t o m e t r i c i n t e n s i t y s c a n a l o n g t h e ( h l - l ) r o w o f r e fl e c t i o n s i s s h o w n i n F i g u r e 2 . 3 B w i t h t h e s a t e l l i t e r e fl e c t i o n s l o c a t e d a t a d i s t a n c e o f 0 2 8 5 0 “ f r o m t h e m a i n ( 0 1 - 1 ) s p o t . T h e e l e c t r o n d i f f r a c t i o n p a t t e r n a l o n g t h e a b - p l a n e ( c r o s s - s e c t i o n ) s h o w s t h a t t h e r e i s n o m o d u l a t i o n a l o n g t h e b * d i r e c t i o n s i n c e t h e r e a r e n o s u p p l e m e n t a r y s u p e r c e l l s p o t s , F i g u r e 2 . 4 A . C o m m e n s u r a t e S u p e r c e l l D e s c r i p t i o n o f R E T e 3 ( R E = C e , P r a n d N d ) - T h e T E M r e s u l t s l e d u s t o s i n g l e c r y s t a l x - r a y d i f f r a c t i o n s t u d i e s w h i c h c o n fi r m e d t h e s u p e r c e l l o f c = 7 c m a x i s i n s p a c e g r o u p A m a 2 ( F i g u r e 2 . 2 A ) f o r R E T e 3 ( R E = C e , P r a n d N d ) a n a l o g s , T a b l e 2 . 1 . T h e m o d u l a t i o n i s m o s t l y l o c a t e d o n t h e t e l l u r i u m n e t a n d r e s u l t s i n a w i d e d i s t r i b u t i o n o f d i s t a n c e s b e t w e e n t h e T e a t o m s . F o r C e T e 3 t h e m i n i m u m T e - T e d i s t a n c e i n t h e n e t i s 2 . 9 3 9 ( 8 ) A a n d t h e m a x i m u m 3 . 2 6 6 ( 3 ) A . F o r P r T e 3 t h e s e d i s t a n c e s a r e 2 . 9 3 9 ( 6 ) A a n d 3 . 2 0 1 ( 6 ) A r e s p e c t i v e l y , a n d f o r N d T e 3 t h e y a r e 2 . 9 5 9 ( 7 ) A a n d 3 . 2 1 4 ( 7 ) A r e s p e c t i v e l y . B y t a k i n g l e s s t h a n 3 . 0 2 0 A t o b e t h e T e - T e b o n d i n g t h r e s h o l d , t h e s q u a r e n e t c o n t a i n s V - s h a p e d t r i m e r s a n d N - s h a p e d t e t r a m e r s , F i g u r e 2 . 2 B . F o r t h e C e a n a l o g , t h e T e - T e d i s t a n c e s w i t h i n t h e t w o d i f f e r e n t V - s h a p e d t r i m e r s a r e 2 . 9 8 5 ( 8 ) a n d 2 . 9 7 9 ( 8 ) A r e s p e c t i v e l y , w h e r e a s w i t h i n t h e N - s h a p e d t e t r a m e r s a r e 2 . 9 3 9 ( 8 ) , 3 . 0 0 1 ( 8 ) a n d 3 . 0 0 2 ( 9 ) A . T h e s e q u e n c e o f t r i m e r s a n d t e t r a m e r s f o u n d t o b e t h e s a m e f o r t h e R E T e ; ( R E = C e , P r a n d N d ) m e m b e r s u s i n g t h e c o m m e n s u r a t e s o l u t i o n . T h e s e T e - T e d i s t a n c e s a r e m u c h l o n g e r t h a n t h o s e f o u n d i n c l a s s i c a l i s o l a t e d T e 3 2 ' a n d R . ; ” p o l y t e l l u r i d e a n i o n s . l 3 I n t h e l a t t e r n o r m a l T e - T e b o n d s a r e i n t h e o r d e r o f 2 . 8 A . T h e 5 1 l o n g e r T e - T e d i s t a n c e s o b s e r v e i n t h e V - s h a p e d t r i m e r s a n d N - s h a p e d t e t r a m e r s o f t h e n e t m a y b e t h e r e s u l t o f a v e r a g i n g o v e r a w i d e r d i s t r i b u t i o n o f d i f f e r e n t o l i g o m e r s t h a n t h o s e o b s e r v e d c r y s t a l l o g r a p h i c a l l y a n d a l s o d u e t o s i g n i fi c a n t i n t e r - p o l y t e l l u r i d e i n t e r a c t i o n s 3 t h a t t e n d t o d i s t u r b t h e n o r m a l o r d e r o f t h e i n t r a - p o l y t e l l u r i d e b o n d i n g . T h e c a l c u l a t e d e l e c t r o n d i f f r a c t i o n p a t t e r n o f t h e m o d e l w e o b t a i n e d f r o m t h e s i n g l e c r y s t a l X - r a y r e fi n e m e n t m a t c h e s w i t h t h e e x p e r i m e n t a l o n e , F i g u r e 2 . 4 B . B y u s i n g t h e Z i n t l - K l e m m c o n c e p t a n d c o n s i d e r i n g r a r e - e a r t h a t o m s t o b e R E 3 + i o n s a n d t h e T e a t o m s i n t h e ( R E T e ) + p a r t t o b e 2 - , e a c h T e a t o m i n t h e n e t m u s t h a v e a n a v e r a g e c h a r g e o f - 0 . 5 a c c o r d i n g t o t h e f o r m u l a [ ( C e T e ) + ] 7 [ T e 1 4 ] 7 ' . H o w e v e r i f w e a s s u m e t h e V - s h a p e d t r i m e r s a n d N - s h a p e d t e t r a m e r s t o b e T e 3 2 ' a n d T e 4 2 ' p o l y t e l l u r i d e s u n i t s t h e n w e c a n e x p e c t t h e o v e r a l l c h a r g e o f t h e T e - n e t t o b e [ T e 1 4 ] 8 ’ w h i c h i s o n e e l e c t r o n r i c h c o m p a r e d t o t h e e x p e c t e d [ ( C e T e ) + ] 7 [ T e 1 4 ] 7 ' . I f t h e e x t r a e l e c t r o n i s l o c a t e d r a n d o m l y o n T e 3 2 ' o r T e 4 2 ‘ u n i t s t h e n t h i s w i l l a l s o b e a n a d d i t i o n a l r e a s o n f o r l e n g t h e n i n g t h e a v e r a g e T e - T e b o n d s i n t h e n e t . 5 2 F i g u r e 2 . 2 . O R T E P r e p r e s e n t a t i o n o f t h e ( A ) c o m m e n s u r a t e 7 - f o l d s u p e r c e l l o f C e T e 3 a s s e e n d o w n t h e c - a x i s ( 9 5 % p r o b a b i l i t y e l l i p s o i d s ) . ( B ) D i s t o r t e d t e l l u r i u m n e t a t a t h r e s h o l d o f 3 . 0 2 0 A . . O o ¢ 1 1 * 3 A : » ? g " 9 , I 3 5 g g " . Q . . 0 . - - * - . . C 1 ) 1 5 0 1 A _ . 1 w _ N 2 8 5 0 * 5 ' f , 0 O R ” e o Q o r i G 1 - - . - . ' . o o 7 1 1 - _ 0 1 1 2 a 1 c \ p " _ 1 5 c 1 W 2 , 8 5 / . 1 . 0 . . \ M M e c i p r o c a l s 9 1 1 F i g u r e 2 . 3 . ( A ) S e l e c t e d a r e a e l e c t r o n d i f f r a c t i o n ( S A E D ) p a t t e r n f o r C e T e 3 a t t h e [ 0 1 0 ] o r i e n t a t i o n s h o w i n g t h e 7 - f o l d s u p e r l a t t i c e . ( B ) I n t e n s i t y s c a n a l o n g t h e c * a x i s o f t h e S A E D p a t t e r n ( s h o w n i n r e c t a n g u l a r b o x ) a n d a p p r o x i m a t e i n d e x i n g b a s e d o n s u p e r c e l l . T h e q - v e c t o r i s a l s o i n d i c a t e d . 5 4 . 0 0 . 4 . c o . C e - . - 0 5 ’ . . . . o . - 6 . 4 - 6 . 2 6 . 0 6 . 2 6 . 4 F i g u r e 2 . 4 . ( A ) C r o s s s e c t i o n s e l e c t e d a r e a e l e c t r o n d i f f r a c t i o n ( S A E D ) p a t t e r n f o r C e T e 3 a t t h e [ 1 0 0 ] o r i e n t a t i o n . ( B ) T h e o r e t i c a l c a l c u l a t e d d i f f r a c t i o n p a t t e r n b a s e d o n t h e c o m m e n s u r a t e s u p e r c e l l m o d e l . 5 5 ° ° ° 0 0 0 9 9 3 4 1 2 2 1 4 . 1 0 . 0 9 = . a 3 [ y K = = = ] 8 4 s = b . 3 o . 0 A A A 0 w . , , , 4 R 0 3 ° , ) ) ) 0 7 3 1 A 2 , 6 9 5 t ( ( ( = a 9 1 3 m ) m . 4 1 1 4 2 . c 8 0 3 " 6 8 0 9 n 1 6 6 5 5 5 8 / m 2 , . . 1 o ( R 0 3 0 . 5 t 4 . 3 . g o 7 9 ( e 2 3 4 1 = . 6 8 = l T 7 1 % 2 1 7 1 3 . 4 d 2 5 7 4 . . 7 2 = = = 4 1 . 0 3 . . , . 9 . N c 7 a 3 b 2 5 5 1 1 4 9 R M 4 ° < 6 n 4 = < 1 = 2 F 9 . A k 6 w . d 0 n a . 0 . , c 3 0 9 0 ° 0 0 0 0 0 0 . 0 i b m 9 9 = = = 3 y 5 4 o 2 ~ 1 s e r a u 1 . 2 0 . 0 = 3 = = q < s h h a 8 = , t o 1 2 - a k t r , , A m A A 2 < 6 R 1 a w s R g n o A ) 3 e w 0 h , 3 ° 0 0 ) ) 1 3 l 5 , i - t 8 7 1 A 5 8 . 4 s r ( ( ( ) i m . 4 + 6 3 3 " 6 x 3 7 9 0 u m O 0 5 8 , 1 4 9 1 0 / t 1 5 r c ) 8 0 5 - 3 6 5 9 1 ( / m 2 . d I 4 . a 1 e o 0 = m 1 9 8 / 2 T 7 . 4 9 < = 3 - 0 5 . t a . . 3 g 0 ( n 6 4 3 2 l 4 = 6 1 3 9 h 3 4 ( . 9 N ‘ = = = u 6 0 . 3 = 7 l 5 . . . . 4 / d 5 P a c b 3 7 2 = 4 R R 3 1 1 I 2 4 . . 6 2 . , < . l F . . n a 3 0 4 - w d n e a 1 d . T 3 , ) b . 3 2 o . 1 A . 6 T 0 r 0 P 1 0 i t u o s e t a r u s n e m m o c e , 3 6 T 0 0 ° 0 9 0 9 9 = = = 2 " } ] ) . 0 " = | , . 6 | 3 1 . 3 y F ] C r a 1 , , , A A A 5 ( . 3 0 . 1 A k 6 1 1 1 1 £ o w ) f 3 ° ) ) 2 . 0 t n e 8 7 1 A 8 ( ( ( = 3 4 " 3 7 . / 2 3 0 5 0 m 1 9 - ) m . ] 6 f c 8 m 0 1 5 / 0 2 5 , 8 m / 8 8 0 1 a m 2 ( R 1 e g . 3 . . 4 d n 7 8 3 [ / 1 o 0 n ; 0 . 6 t 7 a 9 . 2 3 [ fi e 4 3 2 9 8 8 = . 5 1 0 2 9 e T 9 5 2 5 1 3 9 . 7 . = = = 5 r e 2 5 2 . 6 2 . 2 . 9 7 . % 3 - . . C 5 a 3 c b 6 2 1 1 1 | 4 9 4 2 R e r u t c u r t s d n a a t a d a l l a t s u t m r o h m g e y p i t r e s f o F | ( w [ Z { = R w , m 1 2 / l u l C w y l o . a a s r 1 g c . i l l 2 u e a e s r i m c t p y r a m r o p E F C S l b a T h c - l o F e l = R 5 6 U n i t c e l l d i m e n s i o n s V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 8 . 4 8 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ 1 > 2 6 ( I ) ] R i n d i c e s ( a l l d a t a ) L a r g e s t d i f f . p e a k a n d h o l e R o b , = 0 . 0 3 7 9 , w R o b , = 0 . 0 8 8 1 1 7 7 2 8 4 2 5 4 [ 1 1 . . . = 0 . 0 9 6 0 ] 9 7 % 4 2 0 1 / 1 / 1 3 5 1 . 7 4 T a b l e 2 . 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r C e T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l x y 2 O c c u p a n c y U s ; C e [ l ] 3 2 1 4 ( 1 ) 3 3 0 6 ( 1 ) 4 1 2 8 1 9 ( 1 ) C e [ 2 ] 3 9 2 9 ( 1 ) 1 6 8 5 ( 1 ) 9 1 7 8 ( 1 2 ) 1 9 ( 1 ) C e [ 3 ] 2 5 4 9 1 6 8 6 ( 2 ) 9 0 9 6 ( 1 9 ) 1 1 0 ( 1 ) C e [ 4 ] 4 6 4 3 ( 1 ) 3 3 1 0 ( 1 ) 4 2 2 6 ( 1 2 ) 1 7 ( 1 ) T e [ l ] 3 9 3 1 ( 1 ) 2 9 5 4 ( 1 ) 9 1 8 1 ( 1 6 ) 1 9 ( 1 ) T e [ 2 ] 3 2 1 4 ( 1 ) 2 0 3 6 ( 1 ) 4 1 6 7 ( 9 ) 1 9 ( 1 ) T e [ 3 ] 2 5 4 9 2 9 5 6 ( 2 ) 9 1 6 9 ( 1 9 ) 1 1 2 ( 1 ) T e [ 4 ] 4 6 4 1 ( 1 ) 2 0 4 1 ( 1 ) 4 1 7 7 ( 1 3 ) 1 7 ( 1 ) T e [ 5 ] 2 5 4 9 4 3 0 0 ( 3 ) 4 4 9 5 ( 2 0 ) 1 1 6 ( 2 ) T e [ 6 ] 3 2 1 3 ( 2 ) 6 9 4 ( 1 ) 9 3 7 7 ( 1 1 ) 1 1 5 ( 1 ) T e [ 7 ] 4 6 4 4 ( 2 ) 4 3 0 0 ( 2 ) 9 4 5 9 ( 1 4 ) 1 1 4 ( 1 ) T e [ 8 ] 3 9 3 0 ( 1 ) 6 9 7 ( 2 ) 4 2 8 3 ( 1 8 ) 1 1 3 ( 1 ) T e [ 9 ] 3 9 2 9 ( 1 ) 4 2 9 8 ( 2 ) 4 1 2 5 ( 2 0 ) 1 1 2 ( 1 ) T e [ 1 0 ] 3 2 1 2 ( 2 ) 4 2 9 6 ( 1 ) 9 0 8 8 ( 9 ) 1 1 0 ( 1 ) T e [ l l ] 2 5 4 9 6 9 4 ( 2 ) 3 9 9 5 ( 2 0 ) 1 7 ( 1 ) T e [ 1 2 ] 4 6 4 5 ( 1 ) 6 9 7 ( 2 ) 8 9 3 5 ( 1 6 ) 1 7 ( 1 ) * U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 2 . 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r C e T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 C e [ l ] 1 1 ( 1 ) 9 ( 1 ) 7 ( 1 ) 1 ( 1 ) 1 ( 2 ) 8 ( 1 ) C e [ 2 ] 6 ( 1 ) 1 2 ( 1 ) 8 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 3 ( 2 ) C e [ 3 ] 5 ( 2 ) 1 3 ( 2 ) 1 1 ( 2 ) 0 0 - 1 ( 2 ) C e [ 4 ] 9 ( 1 ) 9 ( 1 ) 5 ( 1 ) 0 ( 1 ) 1 ( 2 ) 6 ( 1 ) T e [ l ] 1 3 ( 2 ) 8 ( 2 ) 5 ( 1 ) 2 ( 1 ) 2 ( 1 ) 2 ( 2 ) T e [ 2 ] 3 ( 1 ) 1 2 ( 1 ) 1 1 ( 1 ) 1 ( 2 ) 0 ( 2 ) 4 ( 1 ) T e [ 3 ] 1 8 ( 2 ) 1 2 ( 2 ) 6 ( 1 ) 0 0 3 ( 3 ) T e [ 4 ] 5 ( 1 ) 9 ( 1 ) 6 ( 1 ) 2 ( 1 ) — 1 ( 2 ) 0 ( 2 ) T e [ 5 ] 1 9 ( 3 ) 1 7 ( 2 ) 1 3 ( 3 ) 0 0 5 ( 2 ) T e [ 6 ] 9 ( 1 ) 2 0 ( 1 ) 1 7 ( 2 ) 0 ( 2 ) - 1 ( 2 ) 2 ( 1 ) T e [ 7 ] 1 4 ( 2 ) 1 5 ( 2 ) 1 3 ( 2 ) 1 ( 2 ) 1 ( 2 ) 2 ( 2 ) 5 7 T a b l e 2 . 3 . ( c o n t ’ d ) A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r C e T e ; ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 8 ] 9 ( 2 ) 1 6 ( 2 ) 1 4 ( 2 ) 0 ( 1 ) 2 ( 2 ) 1 ( 2 ) T e [ 9 ] 1 2 ( 2 ) 1 5 ( 2 ) 1 0 ( 1 ) 0 ( 2 ) - 3 ( 1 ) 3 ( 2 ) T e [ 1 0 ] 1 3 ( 1 ) 9 ( 1 ) 7 ( 1 ) 0 ( 2 ) 1 ( 2 ) 5 ( 1 ) T e [ l l ] 5 ( 2 ) 6 ( 2 ) 9 ( 2 ) 0 0 1 ( 2 ) T e [ 1 2 ] 5 ( 2 ) 7 ( 1 ) 9 ( 2 ) 0 ( 1 ) 1 ( 2 ) 1 ( 1 ) T a b l e 2 . 4 . S e l e c t e d b o n d d i s t a n c e s [ A ] f o r C e T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l D i s t a n c e s L a b e l D i s t a n c e s C e [ l ] - T e [ 1 ] 3 . 2 2 6 ( 6 ) C e [ 3 ] - T e [ l 1 ] 3 . 3 6 0 ( 1 0 ) C e [ l ] - T e [ 1 ] 3 . 2 5 8 ( 6 ) C e [ 4 ] - T e [ 1 ] 3 . 2 5 0 ( 7 ) C e [ l ] - T e [ 2 ] 3 . 3 0 9 ( 3 ) C e [ 4 ] - T e [ 1 ] 3 . 2 2 3 ( 7 ) C e [ l ] - T e [ 3 ] 3 . 2 2 4 ( 6 ) C e [ 4 ] - T e [ 4 ] 3 . 3 0 7 ( 4 ) C e [ l ] - T e [ 3 ] 3 . 2 4 8 ( 6 ) C e [ 4 ] - T e [ 4 ] 3 . 2 5 4 ( 6 ) C e [ l ] - T e [ 5 ] 3 . 4 0 1 ( 6 ) C e [ 4 ] - T e [ 4 ] 3 . 2 2 5 ( 6 ) C e [ l ] - T e [ 9 ] 3 . 3 9 6 ( 5 ) C e [ 4 ] - T e [ 7 ] 3 . 3 1 8 ( 6 ) C e [ l ] - T e [ 1 0 ] 3 . 3 9 5 ( 4 ) C e [ 4 ] - T e [ 7 ] 3 . 4 5 1 ( 7 ) C e [ l ] - T e [ 1 0 ] 3 . 3 7 3 ( 4 ) C e [ 4 ] - T e [ 9 ] 3 . 3 8 7 ( 5 ) C e [ 2 ] - T e [ 1 ] 3 . 3 0 7 ( 5 ) C e [ 4 ] - T e [ 1 2 ] 3 . 3 9 4 ( 5 ) C e [ 2 ] - T e [ 2 ] 3 . 2 4 1 ( 5 ) T e [ 5 ] - T e [ 1 0 ] x 2 3 . 2 2 7 ( 8 ) C e [ 2 ] - T e [ 2 ] 3 . 2 3 4 ( 5 ) T e [ 5 ] - T e [ 1 0 ] x 2 2 . 9 7 9 ( 8 ) C e [ 2 ] - T e [ 4 ] 3 . 2 3 7 ( 6 ) T e [ 6 ] - T e [ 8 ] 3 . 1 3 8 ( 8 ) C e [ 2 ] - T e [ 4 ] 3 . 2 3 6 ( 6 ) T e [ 6 ] - T e [ 8 ] 3 . 0 8 0 ( 8 ) C e [ 2 ] - T e [ 6 ] 3 . 3 9 6 ( 5 ) T e [ 6 ] - T e [ l 1 ] 3 . 2 2 2 ( 9 ) C e [ 2 ] - T e [ 8 ] 3 . 3 4 9 ( 8 ) T e [ 6 ] - T e [ l 1 ] 2 . 9 8 6 ( 8 ) C e [ 2 ] - T e [ 8 ] 3 . 4 0 8 ( 8 ) T e [ 7 ] - T e [ 9 ] 3 . 2 1 3 ( 9 ) C e [ 2 ] - T e [ 1 2 ] 3 . 3 9 1 ( 5 ) T e [ 7 ] - T e [ 9 ] 3 . 0 0 2 ( 9 ) C e [ 3 ] - T e [ 2 ] x 2 3 . 2 1 4 ( 7 ) T e [ 7 ] - T e [ 1 2 ] 3 . 2 6 4 ( 8 ) C e [ 3 ] - T e [ 2 ] x 2 3 . 2 5 7 ( 7 ) T e [ 7 ] - T e [ 1 2 ] 2 . 9 4 0 ( 8 ) C e [ 3 ] - T e [ 3 ] 3 . 3 0 8 ( 6 ) T e [ 8 ] - T e [ 1 2 ] 3 . 2 1 6 ( 9 ) C e [ 3 ] - T e [ 6 ] x 2 3 . 3 9 4 ( 5 ) T e [ 8 ] - T e [ 1 2 ] 3 . 0 0 1 ( 8 ) C e [ 3 ] - T e [ l 1 ] 3 . 4 1 7 ( 1 0 ) T e [ 9 ] - T e [ 1 0 ] 3 . 1 1 9 ( 9 ) 5 8 T a b l e 2 . 5 . S e l e c t e d b o n d a n g l e s [ ° ] f o r C e T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l A n g l e s L a b e l A n g l e s C e [ l ] - T e [ 5 ] - C e [ l ] x 2 8 0 . 6 0 ( l 6 ) C e [ 4 ] - T e [ 7 ] - T e [ 1 2 ] 6 5 . 3 5 ( 1 5 ) C e [ l ] - T e [ 5 ] - T e [ 1 0 ] x 2 6 1 . 5 6 ( 1 1 ) T e [ 9 ] - T e [ 7 ] - T e [ 9 ] x 2 8 9 . 6 ( 2 ) C e [ l ] - T e [ 5 ] - T e [ 1 0 ] x 2 6 3 . 4 l ( l l ) T e [ 9 ] - T e [ 7 ] - T e [ 1 2 ] 8 5 . 4 ( 2 ) C e [ l ] - T e [ 5 ] - T e [ 1 0 ] x 2 1 1 3 . 8 ( 2 ) T e [ 9 ] - T e [ 7 ] - T e [ 1 2 ] 1 7 5 . 1 ( 3 ) C e [ l ] - T e [ 5 ] - T e [ 1 0 ] x 2 1 2 0 . 3 ( 3 ) T e [ 9 ] - T e [ 7 ] - T e [ 1 2 ] 1 7 5 . 0 ( 3 ) T e [ 1 0 ] - T e [ 5 ] - T e [ 1 0 ] x 4 8 9 . 7 2 ( 1 3 ) T e [ 9 ] - T e [ 7 ] - T e [ 1 2 ] 9 5 . 3 ( 3 ) T e [ 1 0 ] - T e [ 5 ] - T e [ 1 0 ] x 2 8 5 . 7 ( 3 ) T e [ 1 2 ] - T e [ 7 ] - T e [ 1 2 ] x 2 8 9 . 7 ( 2 ) T e [ 1 0 ] - T e [ 5 ] - T e [ 1 0 ] x 4 1 7 5 . 4 ( 3 ) C e [ 2 ] - T e [ 8 ] - C e [ 2 ] x 2 8 0 . 8 2 ( 1 6 ) T e [ 1 0 ] - T e [ 5 ] - T e [ 1 0 ] x 2 9 4 . 9 ( 3 ) C e [ 2 ] — T e [ 8 ] - T e [ 6 ] 6 2 . 8 7 ( l 6 ) C e [ 2 ] - T e [ 6 ] - C e [ 3 ] 8 0 8 0 ( 9 ) C e [ 2 ] - T e [ 8 ] - T e [ 6 ] 1 1 7 . 9 2 ( 1 7 ) C e [ 2 ] - T e [ 6 ] — T e [ 8 ] 6 1 . 5 2 ( 1 6 ) C e [ 2 ] - T e [ 8 ] - T e [ 1 2 ] 6 1 . 5 0 ( 1 6 ) C e [ 2 ] - T e [ 6 ] - T e [ 8 ] 6 3 . 2 9 ( l 6 ) C e [ 2 ] - T e [ 8 ] - T e [ 1 2 ] 1 1 6 . 5 1 ( 1 8 ) C e [ 2 ] - T e [ 6 ] - T e [ l 1 ] 1 1 5 . 0 7 ( 1 8 ) C e [ 2 ] - T e [ 8 ] - T e [ 6 ] 1 1 6 . 6 6 ( 1 7 ) C e [ 2 ] - T e [ 6 ] - T e [ l 1 ] l 1 9 . 6 6 ( 1 9 ) C e [ 2 ] - T e [ 8 ] - T e [ 6 ] 6 3 . 0 3 ( 1 6 ) C e [ 3 ] - T e [ 6 ] - T e [ 8 ] 1 1 5 . 2 7 ( 1 9 ) C e [ 2 ] - T e [ 8 ] - T e [ 1 2 ] l l 7 . 8 6 ( 1 7 ) C e [ 3 ] - T e [ 6 ] - T e [ 8 ] 1 1 9 . 1 1 ( 1 9 ) C e [ 2 ] - T e [ 8 ] - T e [ 1 2 ] 6 4 . 2 8 ( 1 7 ) C e [ 3 ] - T e [ 6 ] - T e [ l 1 ] 6 2 . 1 3 ( 1 9 ) T e [ 6 ] - T e [ 8 ] - T e [ 6 ] x 2 8 9 . 5 7 ( 1 7 ) C e [ 3 ] - T e [ 6 ] - T e [ l l ] 6 3 . 1 7 ( l 9 ) T e [ 6 ] - T e [ 8 ] - T e [ 1 2 ] 8 9 . 0 ( 3 ) T e [ 8 ] - T e [ 6 ] - T e [ 8 ] x 2 8 9 . 6 ( 2 ) T e [ 6 ] - T e [ 8 ] - T e [ 1 2 ] 1 7 8 . 5 ( 3 ) T e [ 8 ] - T e [ 6 ] - T e [ l 1 ] 8 7 . 6 ( 2 ) T e [ 6 ] - T e [ 8 ] - T e [ 1 2 ] 1 7 8 . 6 ( 3 ) T e [ 8 ] - T e [ 6 ] - T e [ l 1 ] 1 7 7 . 3 ( 3 ) T e [ 6 ] - T e [ 8 ] - T e [ 1 2 ] 9 1 . 9 ( 3 ) T e [ 8 ] - T e [ 6 ] - T e [ l 1 ] 1 7 7 . 2 ( 3 ) T e [ 1 2 ] - T e [ 8 ] - T e [ 1 2 ] x 2 8 9 . 5 2 ( 1 8 ) T e [ 8 ] - T e [ 6 ] - T e [ l 1 ] 9 3 . 1 ( 2 ) C e [ l ] - T e [ 9 ] - C e [ 4 ] 8 0 . 9 2 ( 1 2 ) T e [ l l ] - T e [ 6 ] - T e [ l 1 ] x 2 8 9 . 7 ( 2 ) C e [ l ] - T e [ 9 ] - T e [ 7 ] 1 1 8 . 5 ( 2 ) C e [ 4 ] - T e [ 7 ] - C e [ 4 ] x 2 8 0 . 6 4 ( 1 4 ) C e [ l ] - T e [ 9 ] - T e [ 7 ] 1 1 6 . 4 ( 2 ) C e [ 4 ] - T e [ 7 ] - T e [ 9 ] 6 0 . 9 7 ( 1 5 ) C e [ l ] - T e [ 9 ] - T e [ 1 0 ] 6 2 . 6 5 ( 1 2 ) C e [ 4 ] - T e [ 7 ] - T e [ 9 ] 1 1 6 . 7 6 ( l 9 ) C e [ l ] - T e [ 9 ] - T e [ 1 0 ] 6 2 . 3 6 ( 1 2 ) C e [ 4 ] - T e [ 7 ] - T e [ 1 2 ] 6 0 . 6 4 ( 1 4 ) C e [ 4 ] - T e [ 9 ] - T e [ 7 ] 6 2 . 2 4 ( 1 5 ) C e [ 4 ] - T e [ 7 ] - T e [ 1 2 ] 1 1 6 . 4 6 ( 1 8 ) C e [ 4 ] - T e [ 9 ] - T e [ 7 ] 6 2 . 9 9 ( 1 5 ) C e [ 4 ] - T e [ 7 ] - T e [ 9 ] 1 1 7 . 1 8 ( 1 8 ) C e [ 4 ] - T e [ 9 ] - T e [ 1 0 ] 1 1 7 . 9 ( 2 ) C e [ 4 ] - T e [ 7 ] - T e [ 9 ] 6 4 . 5 7 ( 1 6 ) C e [ 4 ] - T e [ 9 ] — T e [ 1 0 ] 1 1 6 . 8 ( 2 ) C e [ 4 ] - T e [ 7 ] - T e [ 1 2 ] 1 1 7 . 9 6 ( 1 7 ) T e [ 7 ] - T e [ 9 ] - T e [ 7 ] x 2 8 9 . 5 8 ( l 8 ) 5 9 T a b l e 2 . 5 . ( c o n t ’ d ) S e l e c t e d b o n d a n g l e s [ ° ] f o r C e T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 7 ] - T e [ 9 ] - T e [ 1 0 ] T e [ 7 ] - T e [ 9 ] - T e [ 1 0 ] x 2 T e [ 7 ] - T e [ 9 ] - T e [ 1 0 ] T e [ 1 0 ] - T e [ 9 ] - T e [ 1 0 ] x 2 C e [ 1 ] - T e [ 1 0 ] - C e [ 1 ] x 2 C e [ l ] - T e [ 1 0 ] - T e [ 5 ] C e [ l ] - T e [ 1 0 ] - T e [ 5 ] C e [ l ] - T e [ 1 0 ] - T e [ 9 ] C e [ l ] - T e [ 1 0 ] - T e [ 9 ] C e [ l ] - T e [ 1 0 ] - T e [ 5 ] C e [ l ] - T e [ 1 0 ] - T e [ 5 ] C e [ l ] - T e [ 1 0 ] - T e [ 9 ] C e [ l ] - T e [ 1 0 ] - T e [ 9 ] T e [ 5 ] - T e [ 1 0 ] - T e [ 5 ] x 2 T e [ 5 ] - T e [ 1 0 ] - T e [ 9 ] T e [ 5 ] - T e [ 1 0 ] - T e [ 9 ] T e [ 5 ] - T e [ 1 0 ] - T e [ 9 ] T e [ 5 ] - T e [ 1 0 ] - T e [ 9 ] T e [ 9 ] - T e [ 1 0 ] - T e [ 9 ] x 2 C e [ 3 ] - T e [ l 1 ] - C e [ 3 ] x 2 C e [ 3 ] - T e [ l l ] - T e [ 6 ] x 2 C e [ 3 ] - T e [ l 1 ] - T e [ 6 ] x 2 9 2 . 2 ( 3 ) 1 7 8 . 2 ( 3 ) 8 8 . 7 ( 3 ) 8 9 . 5 6 ( 1 6 ) 8 0 6 8 ( 6 ) 6 4 . 4 1 ( 1 6 ) 1 1 8 . 4 2 ( 1 8 ) 6 3 . 1 2 ( 1 4 ) 1 1 7 . 1 1 ( 1 7 ) 1 1 6 . 3 4 ( 1 9 ) 6 1 . 7 5 ( 1 4 ) 1 1 7 . 2 0 ( 1 7 ) 6 2 . 6 7 ( 1 3 ) 8 9 . 7 ( 2 ) 9 2 . 8 ( 2 ) 1 7 7 . 6 ( 3 ) 1 7 7 . 4 ( 2 ) 8 7 . 9 ( 2 ) 8 9 . 6 ( 2 ) 8 0 . 5 ( 2 ) 6 4 . 3 5 ( 1 8 ) 1 1 7 . 8 7 ( 1 7 ) C e [ 3 ] - T e [ l 1 ] - T e [ 6 ] x 2 C e [ 3 ] - T e [ l 1 ] - T e [ 6 ] x 2 T e [ 6 ] - T e [ l l ] - T e [ 6 ] x 4 T e [ 6 ] - T e [ l 1 ] - T e [ 6 ] x 2 T e [ 6 ] - T e [ l 1 ] - T e [ 6 ] x 4 T e [ 6 ] - T e [ l 1 ] - T e [ 6 ] x 2 C e [ 2 ] - T e [ 1 2 ] - C e [ 4 ] C e [ 2 ] - T e [ 1 2 ] - T e [ 7 ] C e [ 2 ] - T e [ 1 2 ] - T e [ 7 ] C e [ 2 ] - T e [ 1 2 ] - T e [ 8 ] C e [ 2 ] - T e [ 1 2 ] - T e [ 8 ] C e [ 4 ] - T e [ 1 2 ] - T e [ 7 ] C e [ 4 ] - T e [ 1 2 ] - T e [ 7 ] C e [ 4 ] - T e [ 1 2 ] - T e [ 8 ] C e [ 4 ] - T e [ 1 2 ] - T e [ 8 ] T e [ 7 ] - T e [ 1 2 ] - T e [ 7 ] x 2 T e [ 7 ] - T e [ 1 2 ] - T e [ 8 ] T e [ 7 ] - T e [ 1 2 ] - T e [ 8 ] T e [ 7 ] - T e [ 1 2 ] - T e [ 8 ] T e [ 7 ] - T e [ 1 2 ] - T e [ 8 ] T e [ 8 ] - T e [ 1 2 ] - T e [ 8 ] x 2 1 1 6 . 3 0 ( 1 7 ) 6 1 . 4 1 ( 1 7 ) 8 9 . 6 9 ( 1 4 ) 9 4 . 7 ( 3 ) 1 7 5 . 6 ( 3 ) 8 5 . 9 ( 3 ) 8 0 . 8 2 ( 1 1 ) 1 2 0 . 2 ( 2 ) 1 1 4 . 3 ( 2 ) 6 2 . 8 4 ( 1 6 ) 6 2 . 0 4 ( 1 5 ) 6 2 . 7 1 ( 1 5 ) 6 2 . 4 0 ( 1 4 ) 1 2 0 . 0 ( 2 ) 1 1 4 . 5 ( 2 ) 8 9 . 6 8 ( 1 9 ) 9 5 . 4 ( 3 ) 1 7 5 . 1 ( 3 ) 1 7 4 . 9 ( 3 ) 8 5 . 4 ( 2 ) 8 9 . 5 ( 2 ) T a b l e 2 . 6 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r P r T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l x y 2 O c c u p a n c y c h ' P r [ l ] 3 2 1 4 ( 1 ) 3 3 0 5 ( 1 ) 3 1 5 1 ( 8 ) 1 1 1 ( 1 ) P r [ 2 ] 3 9 2 9 ( 1 ) 1 6 8 7 ( 1 ) 8 2 2 9 ( 9 ) 1 1 0 ( 1 ) P r [ 3 ] 2 5 0 0 1 6 8 7 ( 2 ) - 1 8 4 7 ( 1 0 ) 1 1 2 ( 1 ) P r [ 4 ] 4 6 4 6 ( 1 ) 3 3 0 8 ( 1 ) 3 2 5 2 ( 5 ) 1 9 ( 1 ) T e [ 1 ] 3 9 3 0 ( 1 ) 2 9 5 2 ( 2 ) 8 1 9 8 ( 1 0 ) 1 1 0 ( 1 ) T e [ 2 ] 3 2 1 6 ( 1 ) 2 0 3 8 ( 1 ) 3 1 8 0 ( 9 ) 1 1 0 ( 1 ) T e [ 3 ] 2 5 0 0 2 9 5 0 ( 3 ) 8 1 9 4 ( 1 3 ) 1 1 3 ( 1 ) 6 0 T a b l e 2 . 6 . ( c o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r P r T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 4 ] 4 6 4 2 ( 1 ) 2 0 4 1 ( 2 ) 1 3 1 8 8 ( 7 ) 1 8 ( 1 ) T e [ 5 ] 2 5 0 0 4 2 9 3 ( 3 ) 3 4 7 1 ( 1 6 ) 1 1 7 ( 2 ) T e [ 6 ] 3 2 1 5 ( 2 ) 6 9 6 ( 2 ) 8 3 8 8 ( 1 0 ) 1 1 7 ( 1 ) T e [ 7 ] 4 6 4 5 ( 2 ) 4 2 9 7 ( 2 ) 4 5 3 0 ( 9 ) 1 1 6 ( 1 ) T e [ 8 ] 3 9 2 9 ( 2 ) 6 9 9 ( 2 ) 3 3 4 7 ( 1 4 ) 1 1 5 ( 1 ) T e [ 9 ] 3 9 2 9 ( 1 ) 4 2 9 6 ( 2 ) 3 1 3 5 ( 1 3 ) 1 1 3 ( 1 ) T e [ 1 0 ] 3 2 1 3 ( 1 ) 4 2 9 2 ( 2 ) - 1 8 4 9 ( 9 ) 1 1 0 ( 1 ) T e [ 1 1 ] 2 5 0 0 6 9 6 ( 3 ) - 6 9 1 2 ( 1 4 ) 1 8 ( 1 ) T e [ 1 2 ] 4 6 4 4 ( 1 ) 7 0 1 ( 2 ) 7 9 9 2 ( 1 0 ) 1 9 ( 1 ) ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 2 . 7 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r P r T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 P r [ l ] 8 ( 1 ) 1 3 ( 2 ) 1 3 ( 1 ) 1 ( 1 ) 0 ( 1 ) 2 ( 2 ) P r [ 2 ] 6 ( 2 ) 1 4 ( 2 ) 9 ( 1 ) - 1 ( 1 ) 0 ( 1 ) - 3 ( 2 ) P r [ 3 ] 7 ( 2 ) 1 4 ( 2 ) 1 4 ( 2 ) 0 0 - 3 ( 2 ) P r [ 4 ] 6 ( 1 ) 1 4 ( 2 ) 5 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 4 ( 1 ) T e [ 1 ] 1 1 ( 2 ) 9 ( 2 ) 8 ( 1 ) 0 ( 2 ) 1 ( 1 ) - 4 ( 2 ) T e [ 2 ] 5 ( 2 ) 1 3 ( 2 ) 1 2 ( 2 ) 0 ( 2 ) - 1 ( 2 ) 2 ( 2 ) T e [ 3 ] 1 2 ( 3 ) 1 4 ( 3 ) 1 4 ( 2 ) 0 0 - 7 ( 2 ) T e [ 4 ] 3 ( 1 ) 1 2 ( 2 ) 7 ( 1 ) 1 ( 2 ) 1 ( 2 ) 0 ( 2 ) T e [ 5 ] 1 2 ( 3 ) 1 7 ( 4 ) 2 2 ( 4 ) 0 0 1 ( 3 ) T e [ 6 ] 1 4 ( 2 ) 2 0 ( 2 ) 1 8 ( 3 ) 0 ( 2 ) - 1 ( 2 ) 2 ( 2 ) T e [ 7 ] 1 2 ( 2 ) 1 8 ( 3 ) 1 8 ( 3 ) 1 ( 2 ) 1 ( 2 ) 1 ( 2 ) T e [ 8 ] 1 2 ( 2 ) 1 8 ( 2 ) 1 3 ( 2 ) - 1 ( 2 ) 1 ( 2 ) - 2 ( 2 ) T e [ 9 ] 7 ( 2 ) 1 8 ( 2 ) 1 5 ( 2 ) 1 ( 2 ) - 2 ( 2 ) 0 ( 2 ) T e [ 1 0 ] 1 0 ( 2 ) 1 1 ( 2 ) 9 ( 2 ) 0 ( 2 ) 1 ( 2 ) 0 ( 2 ) T e [ l l ] 5 ( 2 ) 7 ( 3 ) 1 2 ( 3 ) 0 0 - 8 ( 2 ) T e [ 1 2 ] 6 ( 1 ) 1 4 ( 2 ) 8 ( 2 ) - 1 ( 2 ) - 2 ( 2 ) 2 ( 1 ) 6 1 T a b l e 2 . 8 . B o n d d i s t a n c e s [ A ] f o r P r T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l D i s t a n c e s L a b e l D i s t a n c e s P r [ 1 ] - T e [ 1 ] 3 . 2 1 0 ( 5 ) T e [ 1 ] - P r [ l ] 3 . 2 1 0 ( 5 ) P r [ l ] - T e [ 3 ] 3 . 2 0 9 ( 5 ) T e [ 1 ] - P r [ 4 ] 3 . 2 4 3 ( 5 ) P r [ l ] - T e [ 3 ] 3 . 2 3 4 ( 6 ) T e [ 2 ] - P r [ 3 ] 3 . 2 1 5 ( 5 ) P r [ l ] - T e [ 1 ] 3 . 2 3 8 ( 5 ) T e [ 2 ] - P r [ 2 ] 3 . 2 0 2 ( 5 ) P r [ l ] - T e [ 2 ] 3 . 2 8 4 ( 5 ) T e [ 3 ] - P r [ l ] x 2 3 . 2 0 9 ( 5 ) P r [ l ] - T e [ 1 0 ] x 2 3 . 3 6 1 ( 5 ) T e [ 3 ] - P r [ l ] 3 . 2 3 4 ( 6 ) P r [ l ] - T e [ 9 ] 3 . 3 7 5 ( 6 ) T e [ 3 ] - P r [ 3 ] 3 . 2 7 5 ( 9 ) P r [ l ] - T e [ 5 ] 3 . 3 7 1 ( 6 ) T e [ 4 ] - P r [ 4 ] 3 . 1 9 6 ( 5 ) P r [ 2 ] - T e [ 2 ] 3 . 2 0 2 ( 5 ) T e [ 4 ] - P r [ 2 ] 3 . 2 3 3 ( 5 ) P r [ 2 ] - T e [ 4 ] 3 . 2 0 8 ( 5 ) T e [ 4 ] - P r [ 4 ] 3 . 2 3 4 ( 5 ) P r [ 2 ] - T e [ 2 ] 3 . 2 3 1 ( 5 ) T e [ 4 ] - P r [ 4 ] 3 . 2 8 5 ( 6 ) P r [ 2 ] - T e [ 4 ] 3 . 2 3 3 ( 5 ) T e [ 5 ] - T e [ 1 0 ] x 2 2 . 9 9 0 ( 6 ) P r [ 2 ] - T e [ 1 ] 3 . 2 7 9 ( 6 ) T e [ 5 ] - T e [ 1 0 ] x 2 3 . 1 8 7 ( 6 ) P r [ 2 ] - T e [ 8 ] 3 . 3 3 1 ( 6 ) T e [ 5 ] - P r [ l ] 3 . 3 7 2 ( 6 ) P r [ 2 ] - T e [ 6 ] 3 . 3 7 3 ( 6 ) T e [ 6 ] - T e [ l 1 ] 2 . 9 9 9 ( 5 ) P r [ 2 ] - T e [ 1 2 ] 3 . 3 6 9 ( 6 ) T e [ 6 ] - T e [ 8 ] 3 . 0 7 7 ( 6 ) P r [ 2 ] - T e [ 8 ] 3 . 3 9 7 ( 6 ) T e [ 6 ] - T e [ 8 ] 3 . 1 0 2 ( 7 ) P r [ 3 ] - T e [ 2 ] x 2 3 . 2 1 4 ( 5 ) T e [ 6 ] - T e [ l 1 ] 3 . 1 8 4 ( 6 ) P r [ 3 ] - T e [ 2 ] x 2 3 . 2 3 1 ( 5 ) T e [ 6 ] - P r [ 3 ] 3 . 3 7 6 ( 6 ) P r [ 3 ] - T e [ 3 ] 3 . 2 7 5 ( 9 ) T e [ 7 ] - T e [ 1 2 ] 2 . 9 3 9 ( 6 ) P r [ 3 ] - T e [ l 1 ] 3 . 3 4 9 ( 8 ) T e [ 7 ] - T e [ 9 ] 2 . 9 9 2 ( 6 ) P r [ 3 ] - T e [ 6 ] x 2 3 . 3 7 6 ( 6 ) T e [ 7 ] - T e [ 9 ] 3 . 1 9 8 ( 6 ) P r [ 3 ] - T e [ l 1 ] 3 . 3 8 6 ( 8 ) T e [ 7 ] - P r [ 4 ] 3 . 4 2 6 ( 5 ) P r [ 4 ] - T e [ 4 ] 3 . 1 9 6 ( 5 ) T e [ 8 ] - T e [ 1 2 ] 2 . 9 8 2 ( 6 ) P r [ 4 ] - T e [ 1 ] 3 . 2 1 1 ( 5 ) T e [ 8 ] - T e [ 6 ] 3 . 0 7 7 ( 6 ) P r [ 4 ] - T e [ 4 ] 3 . 2 3 4 ( 5 ) T e [ 8 ] - T e [ 1 2 ] 3 . 2 0 1 ( 6 ) P r [ 4 ] - T e [ 1 ] 3 . 2 4 3 ( 5 ) T e [ 8 ] - P r [ 2 ] 3 . 3 9 7 ( 6 ) P r [ 4 ] - T e [ 4 ] 3 . 2 8 5 ( 6 ) T e [ 9 ] - T e [ 1 0 ] x 2 3 . 0 8 6 ( 6 ) P r [ 4 ] - T e [ 7 ] 3 . 3 0 3 ( 5 ) T e [ 9 ] - T e [ 7 ] 3 . 1 9 8 ( 6 ) P r [ 4 ] - T e [ 9 ] 3 . 3 7 3 ( 6 ) T e [ 1 0 ] - T e [ 5 ] 2 . 9 9 0 ( 6 ) P r [ 4 ] - T e [ 1 2 ] 3 . 3 6 9 ( 5 ) T e [ 1 0 ] - T e [ 9 ] 3 . 0 9 6 ( 6 ) P r [ 4 ] - T e [ 7 ] 3 . 4 2 6 ( 5 ) T e [ 1 0 ] - P r [ l ] 3 . 3 6 1 ( 5 ) 6 2 T a b l e 2 . 8 . ( c o n t ’ d ) B o n d d i s t a n c e s [ A ] f o r P r T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ l 1 ] - T e [ 6 ] x 2 2 . 9 9 9 ( 5 ) T e [ 1 2 ] - T e [ 7 ] 2 . 9 3 9 ( 6 ) T e [ l 1 ] - T e [ 6 ] x 2 3 . 1 8 4 ( 6 ) T e [ 1 2 ] - T e [ 8 ] 3 . 2 0 1 ( 6 ) r 6 1 1 1 ] - P r [ 3 ] 3 . 3 4 9 ( 8 ) T a b l e 2 . 9 . S e l e c t e d b o n d a n g l e s [ ° ] f o r P r T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l A n g l e s L a b e l A n g l e s T e [ 1 0 ] - T e [ 5 ] - T e [ 1 0 ] 9 3 . 9 ( 2 ) T e [ 9 ] - T e [ 7 ] - P r [ 4 ] 1 1 6 . 8 2 ( 1 7 ) T e [ 1 0 ] — T e [ 5 ] - T e [ 1 0 ] x 2 l 7 6 . 3 3 ( l 8 ) T e [ 9 ] - T e [ 7 ] - P r [ 4 ] 6 1 . 1 0 ( 1 2 ) T e [ 1 0 ] - T e [ 5 ] - T e [ 1 0 ] x 2 8 9 . 7 4 ( 1 2 ) P r [ 4 ] - T e [ 7 ] - P r [ 4 ] 8 0 . 7 5 ( 1 2 ) T e [ 1 0 ] - T e [ 5 ] - T e [ 1 0 ] 8 6 . 6 ( 2 ) T e [ 1 2 ] - T e [ 8 ] - T e [ 6 ] 1 7 8 . 1 ( 2 ) T e [ 1 0 ] - T e [ 5 ] - P r [ l ] x 2 6 3 . 4 7 ( 1 3 ) T e [ 1 2 ] - T e [ 8 ] - T e [ 6 ] 9 2 . 1 2 ( 1 8 ) T e [ 1 0 ] - T e [ 5 ] - P r [ l ] x 2 1 2 0 . 1 ( 2 ) T e [ 6 ] - T e [ 8 ] - T e [ 6 ] 8 9 . 7 5 ( l 6 ) T e [ 1 0 ] - T e [ 5 ] - P r [ l ] x 2 1 1 4 . 5 ( 2 ) T e [ 1 2 ] - T e [ 8 ] - T e [ 1 2 ] 8 9 . 6 0 ( l 6 ) T e [ 1 0 ] - T e [ 5 ] - P r [ l ] x 2 6 1 . 5 9 ( 1 2 ) T e [ 6 ] - T e [ 8 ] - T e [ 1 2 ] 8 8 . 5 2 ( 1 8 ) P r [ l ] - T e [ 5 ] - P r [ l ] 8 0 . 9 1 ( l 9 ) T e [ 6 ] - T e [ 8 ] - T e [ 1 2 ] 1 7 8 . 3 ( 2 ) T e [ l l ] - T e [ 6 ] - T e [ 8 ] 9 2 . 2 6 ( l 4 ) T e [ 1 2 ] - T e [ 8 ] - P r [ 2 ] 6 4 . 2 2 ( 1 4 ) T e [ l l ] - T e [ 6 ] - T e [ 8 ] 1 7 7 . 9 8 ( 1 9 ) T e [ 6 ] - T e [ 8 ] - P r [ 2 ] l 1 6 . 7 5 ( 1 7 ) T e [ 8 ] - T e [ 6 ] - T e [ 8 ] 8 9 . 7 5 ( l 6 ) T e [ 6 ] - T e [ 8 ] - P r [ 2 ] 6 3 . 1 4 ( 1 4 ) T e [ l l ] - T e [ 6 ] - T e [ l 1 ] 8 9 . 6 3 ( 1 2 ) T e [ 1 2 ] - T e [ 8 ] - P r [ 2 ] 1 1 7 . 7 3 ( 1 7 ) T e [ 8 ] - T e [ 6 ] - T e [ l l ] 1 7 8 . 1 0 ( 1 7 ) T e [ 1 2 ] - T e [ 8 ] - P r [ 2 ] 1 1 6 . 4 3 ( 1 7 ) T e [ 8 ] - T e [ 6 ] - T e [ l l ] 8 8 . 3 5 ( l 4 ) T e [ 6 ] - T e [ 8 ] - P r [ 2 ] 6 2 . 5 8 ( 1 4 ) T e [ l 1 ] — T e [ 6 ] - P r [ 3 ] 6 3 . 0 6 ( l 6 ) T e [ 6 ] - T e [ 8 ] - P r [ 2 ] 1 1 7 . 8 0 ( 1 7 ) T e [ 8 ] - T e [ 6 ] - P r [ 3 ] 1 1 8 . 7 8 ( 1 7 ) T e [ 1 2 ] - T e [ 8 ] - P r [ 2 ] 6 1 . 3 2 ( 1 3 ) T e [ 8 ] - T e [ 6 ] - P r [ 3 ] 1 1 5 . 7 7 ( l 7 ) P r [ 2 ] - T e [ 8 ] - P r [ 2 ] 8 0 . 7 8 ( 1 3 ) T e [ l l ] - T e [ 6 ] - P r [ 3 ] 6 2 . 0 6 ( 1 5 ) T e [ 7 ] - T e [ 9 ] - T e [ 1 0 ] 9 2 . 4 3 ( 1 9 ) T e [ l 1 ] - T e [ 6 ] - P r [ 2 ] 1 1 9 . 1 6 ( 1 7 ) T e [ 7 ] - T e [ 9 ] - T e [ 1 0 ] 1 7 7 . 9 ( 2 ) T e [ 8 ] - T e [ 6 ] - P r [ 2 ] 6 3 . 3 6 ( 1 4 ) T e [ 1 0 ] - T e [ 9 ] - T e [ 1 0 ] 8 9 . 6 9 ( 1 5 ) T e [ 8 ] - T e [ 6 ] - P r [ 2 ] 6 1 . 7 4 ( 1 3 ) T e [ 7 ] - T e [ 9 ] - T e [ 7 ] 8 9 . 4 9 ( 1 6 ) T e [ l 1 ] - T e [ 6 ] - P r [ 2 ] 1 1 5 . 5 2 ( 1 7 ) T e [ 1 0 ] - T e [ 9 ] - T e [ 7 ] 1 7 8 . 1 ( 2 ) P r [ 3 ] - T e [ 6 ] - P r [ 2 ] 8 0 . 8 6 ( 1 2 ) T e [ 1 0 ] - T e [ 9 ] - T e [ 7 ] 8 8 . 4 0 ( 1 6 ) T e [ 1 2 ] - T e [ 7 ] - T e [ 9 ] 9 5 . 0 6 ( 1 6 ) T e [ 7 ] - T e [ 9 ] - P r [ 4 ] 6 2 . 1 8 ( l 3 ) T e [ 1 2 ] - T e [ 7 ] - T e [ 9 ] 1 7 5 . 4 5 ( 1 9 ) T e [ 1 0 ] - T e [ 9 ] - P r [ 4 ] 1 1 8 . 0 8 ( l 7 ) 6 3 T a b l e 2 . 9 . ( c o n t ’ d ) S e l e c t e d b o n d a n g l e s [ ° ] f o r P r T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 9 ] - T e [ 7 ] - T e [ 9 ] 8 9 . 4 9 ( 1 6 ) T e [ 1 0 ] - T e [ 9 ] - P r [ 4 ] 1 1 6 . 6 1 ( 1 9 ) T e [ 1 2 ] - T e [ 7 ] - P r [ 4 ] 6 5 . 0 3 ( 1 3 ) T e [ 7 ] - T e [ 9 ] - P r [ 4 ] 6 2 . 7 9 ( 1 3 ) T e [ 9 ] - T e [ 7 ] - P r [ 4 ] 6 4 . 5 8 ( 1 4 ) T e [ 7 ] - T e [ 9 ] - P r [ l ] 1 1 8 . 5 5 ( 1 7 ) T e [ 9 ] - T e [ 7 ] - P r [ 4 ] 1 1 7 . 3 2 ( 1 8 ) T e [ 1 0 ] - T e [ 9 ] - P r [ l ] x 2 6 2 . 5 0 ( 1 3 ) T e [ 1 2 ] - T e [ 7 ] - P r [ 4 ] 1 1 6 . 5 2 ( 1 7 ) T e [ 7 ] - T e [ 9 ] - P r [ l ] 1 1 6 . 3 8 ( 1 9 ) P r [ 4 ] - T e [ 9 ] - P r [ l ] 8 1 . 0 9 ( 1 3 ) T e [ 6 ] - T e [ l 1 ] - T e [ 6 ] x 2 8 9 . 6 3 ( 1 2 ) T e [ 5 ] - T e [ 1 0 ] - T e [ 9 ] 1 7 8 . 2 6 ( 1 7 ) T e [ 6 ] - T e [ l 1 ] - T e [ 6 ] 8 6 . 9 2 ( 1 9 ) T e [ 5 ] - T e [ 1 0 ] - T e [ 9 ] 9 2 . 0 3 ( 1 3 ) T e [ 6 ] - T e [ l 1 ] - P r [ 3 ] x 2 6 3 . 9 7 ( 1 5 ) T e [ 9 ] - T e [ 1 0 ] - T e [ 9 ] 8 9 . 6 9 ( 1 5 ) T e [ 6 ] - T e [ l 1 ] - P r [ 3 ] x 2 1 1 7 . 8 1 ( 1 7 ) T e [ 5 ] - T e [ 1 0 ] - T e [ 5 ] 8 9 . 7 4 ( 1 2 ) T e [ 6 ] - T e [ l 1 ] - P r [ 3 ] x 2 1 1 6 . 4 7 ( 1 7 ) T e [ 9 ] - T e [ 1 0 ] - T e [ 5 ] 8 8 . 5 4 ( 1 3 ) T e [ 6 ] - T e [ l 1 ] - P r [ 3 ] x 2 6 1 . 7 5 ( 1 3 ) T e [ 9 ] - T e [ 1 0 ] - T e [ 5 ] 1 7 8 . 2 1 ( 1 7 ) P r [ 3 ] - T e [ l 1 ] - P r [ 3 ] 8 0 . 6 9 ( 1 8 ) T e [ 5 ] - T e [ 1 0 ] - P r [ l ] 6 3 . 8 1 ( 1 4 ) T e [ 7 ] - T e [ 1 2 ] - T e [ 8 ] 9 5 . 1 1 ( 1 7 ) T e [ 9 ] - T e [ 1 0 ] - P r [ l ] x 2 1 1 7 . 2 9 ( 1 6 ) T e [ 7 ] - T e [ 1 2 ] - T e [ 8 ] 1 7 5 . 3 ( 2 ) T e [ 9 ] - T e [ 1 0 ] - P r [ l ] x 2 6 2 . 8 7 ( 1 3 ) T e [ 8 ] - T e [ 1 2 ] - T e [ 8 ] 8 9 . 6 0 ( 1 6 ) T e [ 5 ] - T e [ 1 0 ] - P r [ l ] 1 1 8 . 2 4 ( 1 7 ) T e [ 7 ] - T e [ 1 2 ] - P r [ 4 ] 6 2 . 7 1 ( 1 3 ) T e [ 5 ] - T e [ 1 0 ] - P r [ l ] 1 1 6 . 3 5 ( 1 9 ) T e [ 8 ] - T e [ 1 2 ] - P r [ 4 ] 1 1 9 . 9 2 ( 1 7 ) T e [ 5 ] - T e [ 1 0 ] - P r [ l ] 6 1 . 9 1 ( 1 5 ) T e [ 8 ] - T e [ 1 2 ] - P r [ 4 ] 1 1 4 . 7 6 ( 1 6 ) P r [ l ] - T e [ 1 0 ] - P r [ l ] 8 0 . 8 6 ( 1 1 ) T e [ 7 ] - T e [ 1 2 ] - P r [ 2 ] 1 2 0 . 1 0 ( 1 7 ) T e [ 6 ] - T e [ l 1 ] - T e [ 6 ] 9 3 . 8 ( 2 ) T e [ 8 ] - T e [ 1 2 ] - P r [ 2 ] 6 2 . 9 1 ( 1 4 ) T e [ 6 ] - T e [ l 1 ] - T e [ 6 ] x 2 1 7 6 . 5 6 ( 1 7 ) T e [ 8 ] - T e [ 1 2 ] - P r [ 2 ] 6 2 . 2 1 ( 1 3 ) T a b l e 2 . 1 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r N d T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . I L a b e l x y 2 O c c u p a n c y c h N d [ l ] 7 5 4 9 3 3 1 0 ( 2 ) 2 7 7 5 1 8 ( 1 ) N d [ 2 ] 6 7 8 6 ( 2 ) 1 6 9 3 ( 1 ) 7 7 6 5 ( 2 0 ) 1 7 ( 1 ) N d [ 3 ] 6 0 7 1 ( 1 ) 3 3 1 0 ( 2 ) 2 7 2 5 ( 3 0 ) 1 1 0 ( 1 ) N d [ 4 ] 5 3 5 7 ( 2 ) 1 6 9 3 ( 1 ) 7 6 8 3 ( 1 1 ) 1 1 1 ( 1 ) T e [ 1 ] 7 5 4 9 2 0 4 3 ( 3 ) 2 7 0 5 ( 3 0 ) 1 6 ( 2 ) T e [ 2 ] 6 7 8 6 ( 3 ) 2 9 6 0 ( 1 ) - 2 2 8 5 ( 2 0 ) 1 8 ( 1 ) T e [ 3 ] 6 0 7 3 ( 1 ) 2 0 4 7 ( 2 ) 2 7 1 5 ( 3 0 ) 1 9 ( 2 ) T e [ 4 ] 5 3 5 6 ( 2 ) 2 9 5 3 ( 2 ) - 2 2 8 5 ( 2 0 ) 1 1 2 ( 1 ) 6 4 T a b l e 2 . 1 0 . ( c o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r N d T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 5 ] 7 5 4 9 4 3 0 6 ( 5 ) 2 1 2 5 ( 3 0 ) 1 1 1 ( 2 ) T e [ 6 ] 6 7 8 6 ( 4 ) 7 0 3 ( 2 ) 2 8 1 5 ( 2 0 ) 1 1 1 ( 1 ) T e [ 7 ] 7 5 4 9 7 1 5 ( 4 ) 7 4 6 5 ( 4 0 ) 1 1 1 ( 2 ) T e [ 8 ] 6 0 7 1 ( 2 ) 4 2 9 8 ( 5 ) 2 3 5 5 ( 3 0 ) 1 1 5 ( 2 ) T e [ 9 ] 6 7 8 8 ( 5 ) 4 2 9 5 ( 2 ) 2 5 7 5 ( 2 0 ) 1 1 5 ( 1 ) T e [ 1 0 ] 6 0 7 2 ( 2 ) 7 0 5 ( 4 ) 7 7 7 5 ( 3 0 ) 1 1 2 ( 2 ) T e [ l l ] 5 3 5 7 ( 4 ) 7 0 9 ( 3 ) 2 5 1 5 ( 2 0 ) 1 1 3 ( 2 ) T e [ 1 2 ] 5 3 5 7 ( 3 ) 4 3 0 3 ( 3 ) 2 9 2 5 ( 2 0 ) 1 8 ( 1 ) " U . q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 2 . 1 1 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r N d T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 N d [ l ] 1 0 ( 3 ) 1 0 ( 2 ) 3 ( 2 ) 0 0 - 3 ( 2 ) N d [ 2 ] 3 ( 1 ) 1 1 ( 1 ) 7 ( 2 ) 1 ( 2 ) 1 ( 3 ) — 2 ( 1 ) N d [ 3 ] 1 1 ( 3 ) 1 0 ( 2 ) 8 ( 2 ) 1 ( 1 ) 0 ( 2 ) - 3 ( 2 ) N d [ 4 ] 9 ( 2 ) 1 1 ( 2 ) 1 3 ( 1 ) 2 ( 2 ) 0 ( 3 ) 0 ( 2 ) T e [ 1 ] 0 ( 3 ) 9 ( 3 ) 8 ( 3 ) 0 0 - 6 ( 3 ) T e [ 2 ] 1 6 ( 1 ) 3 ( 1 ) 4 ( 2 ) 0 ( 2 ) 1 ( 3 ) 0 ( 1 ) T e [ 3 ] 4 ( 3 ) 1 4 ( 3 ) 9 ( 2 ) - 1 ( 2 ) 0 ( 2 ) - 5 ( 3 ) T e [ 4 ] 1 2 ( 3 ) 1 4 ( 2 ) 9 ( 2 ) - 1 ( 2 ) 0 ( 4 ) 2 ( 2 ) T e [ 5 ] 7 ( 5 ) 1 3 ( 3 ) 1 2 ( 4 ) 0 0 - 1 8 ( 3 ) T e [ 6 ] 6 ( 2 ) 1 4 ( 2 ) 1 4 ( 2 ) 0 ( 4 ) 0 ( 4 ) 8 ( 1 ) T e [ 7 ] 9 ( 5 ) 4 ( 3 ) 2 1 ( 4 ) 0 0 0 ( 3 ) T e [ 8 ] 1 3 ( 5 ) 1 8 ( 3 ) 1 2 ( 3 ) 1 ( 2 ) 1 ( 2 ) - 1 3 ( 3 ) T e [ 9 ] 1 4 ( 2 ) 1 4 ( 2 ) 1 6 ( 2 ) 0 ( 4 ) - 1 ( 4 ) - 1 ( 2 ) T e [ 1 0 ] 8 ( 4 ) 1 4 ( 3 ) 1 5 ( 3 ) 1 ( 2 ) - 2 ( 3 ) - 6 ( 2 ) T e [ l l ] 1 2 ( 4 ) 1 4 ( 2 ) 1 4 ( 3 ) 1 ( 3 ) 0 ( 4 ) 1 3 ( 2 ) T e [ 1 2 ] 7 ( 3 ) 1 0 ( 2 ) 8 ( 2 ) 0 ( 3 ) - 1 ( 3 ) 0 ( 2 ) 6 5 T a b l e 2 . 1 2 . B o n d d i s t a n c e s [ A ] f o r N d T e ; ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l D i s t a n c e s L a b e l D i s t a n c e s N d [ l ] - T e [ 1 ] 3 . 2 7 6 ( 9 ) N d [ 3 ] - T e [ 1 2 ] 3 . 3 7 1 ( 1 0 ) N d [ l ] - T e [ 2 ] x 2 3 . 2 3 4 ( 9 ) N d [ 4 ] - T e [ 3 ] x 2 3 . 2 1 3 ( 1 1 ) N d [ l ] - T e [ 2 ] x 2 3 . 1 9 5 ( 9 ) N d [ 4 ] - T e [ 4 ] 3 . 2 5 8 ( 6 ) N d [ l ] - T e [ 5 ] 3 . 3 4 8 ( 1 4 ) N d [ 4 ] - T e [ 4 ] x 2 3 . 2 0 7 ( 1 0 ) N d [ l ] - T e [ 5 ] 3 . 3 9 9 ( 1 4 ) N d [ 4 ] - T e [ 1 0 ] 3 . 3 6 2 ( 1 0 ) N d [ l ] - T e [ 9 ] x 2 3 . 3 5 1 ( 1 1 ) N d [ 4 ] - T e [ l 1 ] 3 . 3 9 9 ( 1 0 ) N d [ 2 ] - T e [ 1 ] 3 . 2 3 2 ( 1 2 ) N d [ 4 ] - T e [ l l ] 3 . 3 0 0 ( 1 0 ) N d [ 2 ] - T e [ 1 ] 3 . 1 9 6 ( 1 2 ) N d [ 4 ] - T e [ 1 2 ] 3 . 3 7 8 ( 1 0 ) N d [ 2 ] - T e [ 2 ] 3 . 2 7 5 ( 4 ) T e [ 5 ] - T e [ 9 ] x 2 3 . 1 7 3 ( 1 5 ) N d [ 2 ] - T e [ 3 ] 3 . 2 3 1 ( 1 3 ) T e [ 5 ] - T e [ 9 ] x 2 2 . 9 8 9 ( 1 5 ) N d [ 2 ] - T e [ 3 ] 3 . 1 9 8 ( 1 2 ) T e [ 6 ] - T e [ 7 ] 3 . 1 9 0 ( 1 6 ) N d [ 2 ] - T e [ 6 ] 3 . 3 4 9 ( 1 0 ) T e [ 6 ] - T e [ 7 ] 2 . 9 8 0 ( 1 6 ) N d [ 2 ] - T e [ 6 ] 3 . 3 7 4 ( 1 0 ) T e [ 6 ] - T e [ 1 0 ] x 2 3 . 0 9 4 ( 1 5 ) N d [ 2 ] - T e [ 7 ] 3 . 3 4 4 ( 9 ) T e [ 8 ] — T e [ 9 ] 3 . 1 1 0 ( 1 6 ) N d [ 2 ] - T e [ 1 0 ] 3 . 3 6 0 ( 1 0 ) T e [ 8 ] - T e [ 9 ] 3 . 0 6 7 ( 1 6 ) N d [ 3 ] - T e [ 2 ] x 2 3 . 2 1 7 ( 1 3 ) T e [ 8 ] - T e [ 1 2 ] 2 . 9 9 7 ( 1 5 ) N d [ 3 ] - T e [ 3 ] 3 . 2 6 5 ( 8 ) T e [ 8 ] - T e [ 1 2 ] 3 . 1 7 3 ( 1 5 ) N d [ 3 ] - T e [ 4 ] x 2 3 . 2 2 3 ( 1 3 ) T e [ 1 0 ] - T e [ l 1 ] 3 . 1 6 8 ( 1 5 ) N d [ 3 ] - T e [ 8 ] 3 . 3 8 1 ( 1 6 ) T e [ 1 0 ] - T e [ l 1 ] 3 . 0 0 7 ( 1 5 ) N d [ 3 ] - T e [ 8 ] 3 . 3 3 5 ( 1 6 ) T e [ l l ] - T e [ 1 2 ] 2 . 9 5 8 ( 1 5 ) N d [ 3 ] - T e [ 9 ] 3 . 3 6 1 ( 1 1 ) T a b l e 2 . 1 3 . S e l e c t e d b o n d a n g l e s [ ° ] f o r N d T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l A n g l e L a b e l A n g l e N d [ l ] - T e [ 5 ] - N d [ l ] x 2 8 0 . 4 ( 3 ) N d [ 3 ] - T e [ 8 ] - T e [ 1 2 ] 6 4 . 1 ( 3 ) N d [ l ] - T e [ 5 ] - T e [ 9 ] x 2 6 1 . 2 ( 3 ) N d [ 3 ] - T e [ 8 ] - T e [ 1 2 ] x 2 1 1 8 . 0 ( 4 ) N d [ l ] - T e [ 5 ] - T e [ 9 ] x 2 1 1 6 . 1 ( 3 ) N d [ 3 ] - T e [ 8 ] - T e [ 1 2 ] 6 1 . 8 ( 3 ) N d [ l ] - T e [ 5 ] - T e [ 9 ] x 2 1 1 7 . 2 ( 3 ) T e [ 9 ] - T e [ 8 ] - T e [ 9 ] x 3 8 9 . 7 ( 4 ) N d [ l ] - T e [ 5 ] - T e [ 9 ] x 2 6 3 . 6 ( 3 ) T e [ 9 ] - T e [ 8 ] - T e [ 1 2 ] 9 1 . 5 ( 5 ) T e [ 9 ] - T e [ 5 ] - T e [ 9 ] x 4 8 9 . 9 ( 3 ) T e [ 9 ] - T e [ 8 ] - T e [ 1 2 ] x 2 1 7 8 . 7 ( 5 ) T e [ 9 ] - T e [ 5 ] - T e [ 9 ] x 2 8 6 . 6 ( 4 ) N d [ 3 ] - T e [ 9 ] - T e [ 8 ] 6 1 . 9 ( 4 ) 6 6 T a b l e 2 . 1 3 . ( c o n t ’ d ) S e l e c t e d b o n d a n g l e s [ ° ] f o r N d T e 3 ( c o m m e n s u r a t e ) a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 9 ] - T e [ 5 ] - T e [ 9 ] x 4 T e [ 9 ] — T e [ 5 ] - T e [ 9 ] x 2 N d [ 2 ] - T e [ 1 ] - N d [ 2 ] x 4 N d [ 2 ] - T e [ 6 ] - T e [ 1 0 ] x 2 N d [ 2 ] - T e [ 6 ] - T e [ 1 0 ] x 3 N d [ 2 ] - T e [ 6 ] - T e [ 7 ] T e [ 7 ] - T e [ 6 ] - T e [ 7 ] x 2 T e [ 7 ] - T e [ 6 ] - T e [ 1 0 ] T e [ 7 ] - T e [ 6 ] - T e [ 1 0 ] x 2 T e [ 7 ] - T e [ 6 ] - T e [ 1 0 ] T e [ 1 0 ] - T e [ 6 ] - T e [ 1 0 ] x 2 N d [ 2 ] - T e [ 7 ] - N d [ 2 ] x 2 N d [ 2 ] - T e [ 7 ] - T e [ 6 ] x 2 N d [ 2 ] - T e [ 7 ] - T e [ 6 ] x 2 N d [ 2 ] - T e [ 7 ] - T e [ 6 ] x 2 N d [ 2 ] - T e [ 7 ] - T e [ 6 ] x 2 T e [ 6 ] - T e [ 7 ] - T e [ 6 ] x 4 T e [ 6 ] - T e [ 7 ] - T e [ 6 ] x 2 T e [ 6 ] - T e [ 7 ] - T e [ 6 ] x 4 T e [ 6 ] - T e [ 7 ] - T e [ 6 ] x 2 N d [ 3 ] - T e [ 8 ] - N d [ 3 ] x 2 N d [ 3 ] - T e [ 8 ] - T e [ 9 ] x 2 N d [ 3 ] - T e [ 8 ] - T e [ 9 ] x 2 N d [ 3 ] - T e [ 9 ] - T e [ 5 ] N d [ 3 ] - T e [ 9 ] - T e [ 5 ] N d [ 3 ] - T e [ 9 ] - T e [ 8 ] N d [ 4 ] - T e [ l l ] - T e [ 1 2 ] N d [ 4 ] - T e [ 1 1 ] - T e [ 1 0 ] x 2 T e [ 1 0 ] - T e [ l 1 ] - T e [ 1 0 ] x 2 T e [ 1 0 ] - T e [ l l ] - T e [ 1 2 ] T e [ 1 0 ] - T e [ l l ] - T e [ 1 2 ] x 2 T e [ 1 0 ] - T e [ 1 1 ] - T e [ 1 2 ] T e [ 1 2 ] - T e [ 1 1 ] - T e [ 1 2 ] x 2 N d [ 3 ] - T e [ 1 2 ] - N d [ 4 ] 1 7 6 . 4 ( 5 ) 9 3 . 5 ( 5 ) 1 4 7 . 3 ( 3 ) 6 2 . 4 ( 3 ) 1 1 7 2 ( 4 ) 6 3 . 5 ( 3 ) 8 9 . 8 ( 4 ) 8 8 . 0 ( 4 ) 1 7 7 . 8 ( 5 ) 9 2 . 3 ( 4 ) 8 9 . 9 ( 4 ) 8 1 . 5 ( 3 ) 6 3 . 6 ( 2 ) 6 2 . 1 ( 2 ) 1 2 0 . 8 ( 4 ) 1 1 5 . 2 ( 4 ) 8 9 . 8 ( 3 ) 9 4 . 2 ( 5 ) 1 7 5 . 9 ( 5 ) 8 6 . 3 ( 5 ) 8 0 . 9 ( 4 ) 6 2 . 8 ( 3 ) 1 1 6 . 6 ( 4 ) 1 1 9 . 7 ( 4 ) 1 1 6 . 1 ( 4 ) 6 3 . 3 ( 4 ) 1 1 8 . 4 ( 3 ) 6 1 . 5 ( 3 ) 8 9 . 7 ( 4 ) 9 4 . 2 ( 4 ) 1 7 6 . 0 ( 5 ) 8 6 . 4 ( 4 ) 8 9 . 7 ( 4 ) 8 0 . 5 7 ( 1 8 ) T e [ 5 ] - T e [ 9 ] - T e [ 5 ] x 2 T e [ 5 ] - T e [ 9 ] - T e [ 8 ] N d [ 2 ] - T e [ 1 0 ] - T e [ l 1 ] N d [ 2 ] - T e [ 1 0 ] - T e [ l 1 ] N d [ 4 ] - T e [ 1 0 ] - T e [ 6 ] N d [ 4 ] - T e [ 1 0 ] - T e [ 6 ] N d [ 4 ] - T e [ 1 0 ] - T e [ l l ] N d [ 4 ] - T e [ 1 0 ] - T e [ l 1 ] T e [ 6 ] - T e [ 1 0 ] - T e [ 6 ] x 2 T e [ 6 ] - T e [ 1 0 ] - T e [ l 1 ] T e [ 6 ] - T e [ 1 0 ] - T e [ l l ] x 2 T e [ 6 ] - T e [ 1 0 ] - T e [ l 1 ] T e [ 1 1 ] - T e [ 1 0 ] - T e [ 1 1 ] x 2 N d [ 4 ] - T e [ l 1 ] - N d [ 4 ] x 2 N d [ 4 ] - T e [ l 1 ] - T e [ 1 0 ] N d [ 4 ] - T e [ 1 1 ] - T e [ 1 0 ] x 3 N d [ 4 ] - T e [ l 1 ] - T e [ 1 2 ] T e [ 1 2 ] - T e [ 8 ] - T e [ 1 2 ] x 2 N d [ l ] - T e [ 9 ] - N d [ 3 ] N d [ l ] - T e [ 9 ] - T e [ 5 ] N d [ l ] - T e [ 9 ] - T e [ 5 ] N d [ l ] - T e [ 9 ] - T e [ 8 ] N d [ l ] - T e [ 9 ] - T e [ 8 ] N d [ 3 ] - T e [ 1 2 ] - T e [ 8 ] x 2 N d [ 3 ] - T e [ 1 2 ] - T e [ l 1 ] N d [ 3 ] - T e [ 1 2 ] - T e [ l l ] N d [ 4 ] - T e [ 1 2 ] - T e [ 8 ] N d [ 4 ] - T e [ 1 2 ] - T e [ 8 ] N d [ 4 ] - T e [ 1 2 ] - T e [ 1 1 ] x 2 T e [ 8 ] - T e [ 1 2 ] - T e [ 8 ] x 2 T e [ 8 ] - T e [ 1 2 ] - T e [ l l ] T e [ 8 ] - T e [ 1 2 ] - T e [ 1 1 ] x 2 T e [ 8 ] - T e [ 1 2 ] - T e [ l 1 ] T e [ 1 1 ] - T e [ 1 2 ] - T e [ 1 1 ] x 2 8 9 . 9 ( 4 ) 9 2 . 3 ( 4 ) 1 1 6 . 4 ( 4 ) 1 1 8 . 0 ( 4 ) 1 1 7 . 0 ( 4 ) 1 1 7 . 9 ( 4 ) 6 2 . 6 ( 2 ) 6 2 . 1 ( 2 ) 8 9 . 9 ( 3 ) 8 8 . 9 ( 4 ) 1 7 8 . 6 ( 5 ) 9 1 . 5 ( 4 ) 8 9 . 7 ( 3 ) 8 1 . 1 ( 2 ) 6 4 . 2 ( 3 ) 1 1 7 . 6 ( 4 ) 6 5 . 1 ( 3 ) 8 9 . 8 ( 3 ) 8 1 . 2 0 ( 1 3 ) 6 3 . 4 ( 3 ) 6 2 . 7 ( 3 ) 1 1 9 . 0 ( 3 ) 1 1 6 . 1 ( 3 ) 6 2 . 1 ( 3 ) 1 1 4 . 3 ( 4 ) 1 1 9 . 1 ( 4 ) 1 1 4 . 8 ( 3 ) 1 1 9 . 2 ( 4 ) 6 2 . 0 ( 3 ) 8 9 . 8 ( 4 ) 8 6 . 2 ( 4 ) 1 7 5 . 9 ( 5 ) 9 4 . 3 ( 4 ) 8 9 . 7 ( 4 ) 6 7 S u p e r c e l l D e s c r i p t i o n o f R E T e 3 B a s e d o n a M o d u l a t i o n q - v e c t o r — A l t h o u g h t h e c o m m e n s u r a t e s u p e r c e l l a p p r o a c h g a v e a m u c h b e t t e r v i e w o f t h e d i s t o r t i o n s i n t h e s e c o m p o u n d s i t i s , h o w e v e r , s t i l l i n a d e q u a t e a s i t “ g l o s s e s o v e r ” s o m e i m p o r t a n t d e t a i l s o f t h e s t r u c t u r e . A m o r e a c c u r a t e d e s c r i p t i o n w a s o b t a i n e d w h e n t h e f o u r - d i m e n s i o n a l s u p e r s p a c e c r y s t a l l o g r a p h i c a p p r o a c h w a s u s e d t o r e fi n e t h e s t r u c t u r e s b a s e d o n t h e e x i s t e n c e o f a m o d u l a t i o n q v e c t o r . X — r a y d i f f r a c t i o n g a v e a c c u r a t e q v a l u e s w h i c h i n f a c t v a r y s l i g h t l y b u t s i g n i fi c a n t l y w i t h t h e R E e l e m e n t ( e . g . q = 0 . 2 8 0 1 ( 4 ) , 0 . 2 8 2 1 ( 4 ) a n d 0 . 2 8 3 1 ( 4 ) r e s p e c t i v e l y f o r C e , P r a n d N d ) a n d t h i s h a s c o n s e q u e n c e s o n t h e o b s e r v e d d i s t o r t i o n . T h e l e n g t h o f t h e q - v e c t o r i n c r e a s e s w i t h d e c r e a s i n g R E s i z e ( f r o m L a t o D y ) a s c a n b e s e e n i n F i g u r e 2 . 5 . I n t e r e s t i n g l y , t h e C D W f o r t h e t h r e e h e a v i e s t R E ( H o , B r a n d T m ) d i s a p p e a r s j u d g i n g f r o m t h e v a n i s h i n g o f t h e q - v e c t o r . T h e s u p e r s p a c e c r y s t a l l o g r a p h i c a n a l y s i s g a v e f o r C e T e 3 t h e m i n i m u m T e - T e d i s t a n c e i n t h e n e t t o b e 2 . 9 9 9 ( 2 ) A a n d t h e m a x i m u m 3 . 1 9 8 ( 2 ) A . F o r P r T e 3 t h e s e d i s t a n c e s a r e 2 . 9 5 6 ( 3 ) A a n d 3 . 2 1 4 ( 3 ) A r e s p e c t i v e l y , a n d f o r N d T e 3 2 . 9 4 5 4 ( 1 4 ) A a n d 3 . 2 1 0 4 ( 1 5 ) A r e s p e c t i v e l y . B y a r b i t r a r i l y t a k i n g 3 . 0 3 5 A t o b e t h e T e - T e b o n d i n g t h r e s h o l d , t h e s q u a r e n e t o f C e T e 3 c a n b e e a s i l y v i e w e d a s a s e q u e n c e o f V - s h a p e d “ t r i m e r s ” a n d N - s h a p e d “ t e t r a m e r s ” a n d , i n f r e q u e n t l y , e v e n “ s i n g l e ” T e a t o m s , F i g u r e 2 . 1 1 . T h e T e - T e d i s t a n c e s w i t h i n t h e o l i g o m e r s a r e s h o r t e r t h a n t h e a v e r a g e 3 . 1 0 3 4 ( 6 ) A f o u n d i n t h e o r i g i n a l C m c m s t r u c t u r e . T h e m o s t s u r p r i s i n g fi n d i n g o f t h e s u p e r s p a c e a n a l y s i s i s t h a t t h e R E T e 3 a n a l o g s d o n o t h a v e i d e n t i c a l C D W d i s t o r t i o n s . A c l o s e r l o o k a t t h e p a t t e r n o f t h e T e n e t s r e v e a l s s u b s t a n t i a l d i f f e r e n c e s i n t h e w a y t h e n e t s d i s t o r t a s t h e R E e l e m e n t c h a n g e s , F i g u r e s 2 . 1 1 - 2 . 1 7 . T h e n e t d o e s n o t s i m p l y s h r i n k t o f o l l o w t h e l a n t h a n i d e c o n t r a c t i o n . I n s t e a d , 6 8 t h e l o n g - s h o r t b o n d a l t e r n a t i o n a m o n g t h e T e a t o m s v a r i e s f r o m C e t o P r t o N d e . g . f o r m i n g d i f f e r e n t o l i g o m e r i c p a t t e r n s . S t a r t i n g f r o m t h e l e f t o f F i g u r e 2 . 1 1 , w e c a n s e e t h a t t h e n e t f o r t h e t h r e e c o m p o u n d s i s i d e n t i c a l u p t o a c e r t a i n d i s t a n c e ( s h o w n b y t h e b o x e d a r e a ) . A f t e r t h a t p o i n t t h e r e i s d i v e r g e n c e ; i n C e T e 3 f o r e x a m p l e , T e a t o m s f o r m t w o t e t r a m e r s t h e r e b y b r e a k i n g t h e t r i m e r - t o - t e t r a m e r o r d e r , F i g u r e 2 . 1 1 A . I n c o n t r a s t , t h e o r d e r o f o l i g o m e r s i n P r T e 3 a n d N d T e 3 c o n t i n u e s i d e n t i c a l u n t i l t h e a p p e a r a n c e o f s i n g l e T e a t o m s i n P r T e 3 ( s h o w n i n t h e d o t t e d b o x e d a r e a ) , F i g u r e 2 . 1 1 B a n d F i g u r e 2 . 1 1 C . A t t h i s p o i n t t h e p a t t e r n s o f P r T e 3 a n d N d T e 3 d i v e r g e . E v e r y d i s t o r t e d T e n e t w i t h i n t h e R E T e 3 s e r i e s i s u n i q u e a s c a n b e s e e n i n F i g u r e s 2 . 1 1 — 2 . 1 7 . T h e d i s t o r t i o n i s m a i n l y l o c a t e d a t t h e t e l l u r i u m p l a n a r n e t c r e a t i n g a w i d e d i s t r i b u t i o n o f T e - T e d i s t a n c e s a s c a n b e s e e n i n F i g u r e 2 . 6 . T h e a t o m i c d i s p l a c e m e n t o f t h e T e a t o m s ( T e [ 2 ] a n d T e [ 3 ] ) i n t h e p l a n a r n e t a l o n g t h e a - a x i s ( x d i r e c t i o n ) i s a t l e a s t t w o o r d e r s o f m a g n i t u d e l a r g e r t h a n t h e d i s p l a c e m e n t s f o u n d a l o n g t h e o t h e r t w o d i r e c t i o n s , F i g u r e 2 . 7 . A l o n g t h e b a n d c - a x i s ( y a n d 2 d i r e c t i o n s r e s p e c t i v e l y ) , C e a n d T e l h a v e t h e l a r g e s t d i s p l a c e m e n t a s a r e s u l t o f t h e r e s p o n d o f t h e [ R E T e ] l a y e r t o t h e C D W d i s t o r t i o n o f t h e T e n e t , F i g u r e s 2 . 8 - 2 . 9 . 6 9 ) A ( ” e 5 5 c n a t s i D . 0 - 3 0 4 1 1 1 1 T 1 1 1 1 1 1 1 : 0 . 3 0 2 - 3 0 . 3 0 0 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 3 2 4 1 - 0 : 0 . 2 9 8 I _ 0 . 2 9 6 I I _ . A 0 2 9 4 " - 5 7 1 7 ; * : o 0 . 2 9 2 I _ € 0 , 2 9 0 9 0 1 . ] 3 0 . 2 8 8 I _ . ’ 5 : 0 . 2 8 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 n ? g 0 . 2 8 4 _ = 3 0 . 2 8 2 5 I - : 7 / 2 = g 0 . 2 8 0 - - - - - - - - - - I - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - : c " 0 . 2 7 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 5 1 1 % 0 . 2 7 6 _ . 0 . 2 7 4 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 3 m g 0 . 2 7 2 . . - : 0 . 2 7 0 I 1 L l l I l l l 1 1 1 L a C e P r N d S m G d T b D y H o E r T m Y R a r e E a r t h F i g u r e 2 . 5 . P l o t o f t h e q - v e c t o r d e p e n d e n c e a s a f u n c t i o n o f R E s i z e a t 3 0 0 K . P a r a l l e l d a s h e d l i n e s n o t a t e s o m e p o s s i b l e l o w i n d e x c o m m e n s u r a t e a p p r o x i m a n t s . 3 . 3 0 I I U I I _ I T I T I l ' I 1 I U I I T ’ T e [ 2 ] - T e [ 3 ] d i s t a n c e s 1 3 . 2 5 — 1 3 . 2 0 3 . 1 5 1 ” O u : . 8 2 . 9 5 2 . 9 0 1 l 1 l 1 i a l n l a 1 1 l L l 1 1 1 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 t - d i r e c t i o n F i g u r e 2 . 6 . R e p r e s e n t a t i v e p l o t o f t h e T e [ 2 ] - T e [ 3 ] d i s t a n c e s f o u n d i n t h e d i s t o r t e d n e t o f C e T e 3 f r o m t h e s u p e r s p a c e a n a l y s i s b a s e d o n a q - v e c t o r a s a f u n c t i o n o f t - d i r e c t i o n . D a s h e d l i n e s r e p r e s e n t t h e a v e r a g e ( u n d i s t o r t e d ) T e - T e d i s t a n c e s . 7 0 ) A ( t n e m e c a l p s i o d b ' x d 0 - 1 5 1 1 ' 1 1 1 0 . 1 0 p O U 1 9 8 - 0 . 1 0 _ O . 1 5 1 l 1 l 1 l 1 l % 1 4 l 1 l 1 l 1 I 1 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 t - d i r e c t i o n F i g u r e 2 . 7 . P l o t o f t h e p o s i t i o n a l d i s p l a c e m e n t ( A ) a l o n g x - a x i s o f a l l t h e a t o m s i n t h e C e T e 3 s u p e r c e l l a s a f u n c t i o n o f t - d i r e c t i o n . 0 . 0 2 f r . 1 . . T 1 1 T f 1 1 r r r 0 . 0 1 - 1 A ‘ 3 1 , . T e l . é T e 2 ' E . _ . . 0 ) ' 5 > 1 " D - O D I - q 1 - 1 . C e _ 0 . 0 2 1 1 g 1 1 1 1 1 1 1 1 1 1 1 L 1 + 1 1 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 t - d i r e c t i o n F i g u r e 2 . 8 . P l o t o f t h e p o s i t i o n a l d i s p l a c e m e n t ( A ) a l o n g y - a x i s o f a l l t h e a t o m s i n t h e C e T e 3 s u p e r c e l l a s a f u n c t i o n o f t - d i r e c t i o n . 7 1 ) A ( t n e i g e c a l p s i d z d § % 0 . 0 1 0 . 1 1 1 1 T . , § 1 - 0 . 0 1 0 1 l 1 I 4 l 1 l 1 l 1 l 1 l 1 l 1 l 1 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 t - d i r e c t i o n F i g u r e 2 . 9 . P l o t o f t h e p o s i t i o n a l d i s p l a c e m e n t ( A ) a l o n g z - a x i s o f a l l t h e a t o m s i n t h e C e T e ; s u p e r c e l l a s a f u n c t i o n o f t - d i r e c t i o n . P a i r D i s t r i b u t i o n F u n c t i o n A n a l y s i s o f R E T e 3 ( R E = C e , P r a n d N d ) — I n o r d e r t o e n s u r e t h a t t h e o b s e r v e d m o d u l a t i o n s w e r e r e p r e s e n t a t i v e o f t h e b u l k a n d n o t o f i s o l a t e d s i n g l e c r y s t a l d o m a i n s s a m p l e d s e l e c t i v e l y b y o u r e l e c t r o n o r X - r a y d i f f r a c t i o n e x p e r i m e n t s , w e s o u g h t a t o t a l s c a t t e r i n g t e c h n i q u e t o c h e c k t h e e n t i r e s a m p l e . T h e P D F t e c h n i q u e i s a p o w e r f u l a n d u n i q u e t o o l f o r t h e c h a r a c t e r i z a t i o n a n d s t r u c t u r e r e fi n e m e n t o f c r y s t a l l i n e m a t e r i a l s w i t h i n t r i n s i c d i s o r d e r . 1 4 T h e t e c h n i q u e h a s p r o v e n s u c c e s s f u l i n d e t e r m i n i n g t h e s t r u c t u r e o f c r y s t a l l i n e m a t e r i a l s e x h i b i t i n g l o c a l d e v i a t i o n s f r o m t h e a v e r a g e s t r u c t u r e a r i s i n g f r o m d i f f e r e n t d e g r e e s o f d i s o r d e r o r l o n g r a n g e m o d u l a t i o n s . T h e e x p e r i m e n t a l P D F o f a l l t h r e e R E T e 3 s y s t e m s w e r e s t u d i e d s h o w a p r o n o u n c e d s h o u l d e r o n t h e fi r s t p e a k a t ~ 2 . 9 A a n d i t i s d u e t o t h e T e - T e b o n d s i n t h e o l i g o m e r s . T h e a v e r a g e C m c m s t r u c t u r e c a n n o t a c c o u n t f o r t h i s p e a k b e c a u s e i t h a s n o d i s t a n c e < 3 . 1 A , 7 2 F i g u r e 2 . 1 8 B . T h i s f e a t u r e i s m u c h l a r g e r t h a n t h e n o i s e a n d i s a l s o a p p a r e n t i n d a t a c o l l e c t e d f r o m P r T e 3 a n d N d T e 3 ( F i g u r e 2 . 1 9 a n d F i g u r e 2 . 2 0 ) . T h i s p r o v e s t h a t t h e d i s t o r t i o n i n t h e T e - n e t i s a b u l k p h e n o m e n o n o f t h e R E T e 3 s y s t e m s . F u r t h e r m o r e , t h e a m p l i t u d e o f l o c a l d i s t o r t i o n s i n t h e m o d e l o b t a i n e d f r o m P D F a n a l y s i s f o u n d t o b e l a r g e r t h a n t h o s e d e t e r m i n e d c r y s t a l l o g r a p h i c a l l y . T h e r e s u l t s w e r e r e c o n c i l e d w i t h i n t h e d i s c o m m e n s u r a t i o n m o d e l w h e r e p h a s e s l i p s o f t h e C D W e x i s t b e t w e e n c o m m e n s u r a t e r e g i o n s r e s u l t i n g i n a n i n c o m m e n s u r a t e w a v e v e c t o r o n t h e a v e r a g e , F i g u r e 2 . 1 0 . T h i s w o r k w a s d o n e i n c o l l a b o r a t i o n w i t h H y u n J e o n g K i m a n d S i m o n J . L . B i l l i n g e a t t h e D e p a r t m e n t o f P h y s i c s a t M i c h i g a n S t a t e U n i v e r s i t y . 1 5 ( A ) C o m m e n s u r a t e O O O O O O O O O O O O O O O O . ( B ) I n c o m m e n s u r a t e O O O O G O O O O O O O O C O Q O ( C ) D i s c o m m e n s u r a t e o o o o o o o o o o o q p o o q o C o m m e n s u r a t e r e g i o n I I P h a s e s l i p I F i g u r e 2 . 1 0 . G e n e r a l s c h e m e o f ( A ) C o m m e n s u r a t e , ( B ) I n c o m m e n s u r a t e a n d ( C ) D i s c o m m e n s u r a t e C h a r g e D e n s i t y W a v e . C i r c l e s r e p r e s e n t t h e c r y s t a l l a t t i c e a n d s o l i d l i n e s t h e e l e c t r o n d e n s i t y . A d i s c o m m e n s u r a t e w a v e c a n b e s e e n a s a c o m b i n a t i o n o f a c o m m e n s u r a t e w a v e a n d a p h a s e s l i p . T h e a v e r a g e l o n g r a n g e r e s u l t i s t h e s a m e w i t h a n i n c o m m e n s u r a t e w a v e b u t l o c a l l y t h e t w o c a s e s a r e v e r y d i f f e r e n t . 7 3 3 . c : 5 a 1 > n . . . . 3 > > \ 1 1 > \ ( ( 1 ) \ \ < < ( < x 5 . o 5 g x 3 ) H - . x 0 ( 0 . / o 8 c 3 \ . x : : 1 I ( 8 2 O » 1 ) 1 > ( 1 8 \ 8 $ \ ( . . . . ( ) 1 < 1 \ > \ 1 r . 3 3 3 — . 1 < < \ ” \ ” 3 0 n = 8 i ( ) ( m . m . ( ( — 5 1 < 1 ( ( < ( \ \ . 1 s > o a : s m g 8 . ( 1 a 8 . > a ( . m m m \ . 1 . \ 1 1 : 1 \ ( ( d \ s s n w a a ( o o . o E 1 ( _ . ( c 8 . 1 . 1 ( » 1 c \ » . < . \ ( % m > > ( 3 N > . ( < . . . . ( ( . . . > 1 \ . \ a 1 E 3 \ 2 n \ c . 1 1 . m 8 w 5 . o 1 m > 1 1 ( a 1 ( > \ x 1 o < b 8 3 ( \ 1 ( ( . < \ < ( P w — . 1 8 m m Y < 8 8 3 1 > < < a a \ > \ . 8 : 5 ( ) \ \ m m . 8 0 3 5 > 5 . > ) < 1 c 1 1 k ( 1 1 ( . z w \ > . v 9 - fi c 3 fl 5 3 0 3 . ( _ < . < > > ( 5 m . m 2 . . m H / b > 1 1 ) o 1 ( \ \ 1 > . b ? m 8 1 s o o . . ( ( . 9 m w m / n n m ( o ) ( a ( a o c n < / ( ( ( \ 1 . < S P 1 5 « 2 : 1 \ . 9 \ \ \ . ( 0 w : o 0 5 1 1 2 1 \ > 3 8 1 1 — g . / _ . . . ( ( ( ( ( ( / . ( \ ( 1 ( w \ 3 a . 9 " n p 1 1 w 3 \ ( ( < < ( > ( 8 9 3 a n n » m 9 . 1 m 2 “ a . w . \ < v . ) 1 \ > . 2 ( d n n n \ x \ a > \ x 1 . v a 9 o . . 5 » . > . z o / . . m . > R . 5 . ( 1 $ 1 < . ( . ( ( \ 1 ( . 1 ) \ ( > 1 < > ( 3 ~ 2 2 : 3 m c . o " H o n . q o g d n o S . e 9 o A v 8 m 8 o . > H 8 z x $ ¢ 2 x m » x : 1 1 1 8 \ \ \ 3 > 6 < 1 < £ ( . . \ 3 . . . 1 > . \ ( » o ) ( \ X 1 ( \ . : : . h 1 2 0 3 c \ 2 < 8 \ 9 8 > m < % 1 < 5 \ e 3 . 3 — 3 ) e € < \ > w . 3 1 x . . 1 1 ( : fl 6 3 m g a n 5 ( C \ . 3 3 : - _ _ . z ( 8 . 1 2 3 $ A . 0 V H . 9 ) 5 > g , 1 \ . : . 3 a 1 3 > ( m « 1 N ( , 8 v ( ( C 6 6 1 < V . 5 9 — 3 3 . . > g a O 3 3 . n . A v A E 3 3 3 7 4 \ l ( I \ I ( I . l \ \ / I X \ I I ) . \ < ( I . / \ . \ I < \ 1 I ) 1 . . ) 1 ‘ 1 ) , \ I \ . ‘ / \ / _ . \ l \ 1 2 \ / _ . ‘ < 1 ) > 1 \ / \ / p \ l \ ( l ) \ l \ . . . \ l . . \ / . . . / \ / . \ I \ . . / \ / . \ 1 \ . . \ / . . < . . \ l . . . < l . \ 1 \ . 1 \ . ( l . \ ( \ . \ l b n o ? 2 : : “ 1 3 8 : 3 2 a $ 3 . 3 . 3 5 9 3 1 9 8 1 3 5 ( 1 . < \ 1 < \ 1 1 x \ 1 1 } \ < ( 1 \ ( ( . ( v ) . . < . < 1 \ . 1 > \ . < . 1 > \ . 1 ) \ . . ( I . < \ l < \ / I x . \ / 1 \ . . \ ( ( I \ 1 \ I ) . . < \ l ( ( 1 ) \ / \ ( I \ 1 \ ” \ r . ) \ l \ . 0 . 0 o > > ( 0 . ( 1 . . ) 1 . . I x f ) \ / \ 1 ‘ / \ / ) \ I \ . x / \ l ) \ l \ . m \ / ) ‘ < . ) \ I ) x l \ . ) \ l . \ $ ) ) \ ; \ I \ / ) > \ 1 ‘ / \ / ) \ o \ \ l ) x < 1 ( 0 0 ) . . o $ o z . o $ o z . 0 5 0 z . 9 H 0 > o o < | > n o < ) 0 O S . 2 0 o $ 9 z - o $ 0 2 K 0 > 0 0 < a > > > > > > > > > > 2 2 2 2 2 2 2 2 2 2 < < < < < < < < < 0 0 0 0 0 0 0 0 0 0 < < < < < < < < < < S S S S S S S S S > > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < < < . . . . . . . . . . > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 S S S S S S S S S > > > > > > > > > > 2 2 2 2 2 2 2 2 2 2 < < < < < < < < < S S S S S S S S S : > > > > > > > > > > 3 3 3 3 3 3 3 3 3 : > > > > > > > > > > 2 2 2 2 2 2 2 2 2 2 < < < < < < < < < S S S S S S S S S > > > > > > > > > > 2 2 2 2 2 2 2 2 2 2 < < < < < < < < < < < < < < < < < < < S S S S S S S S S > > > > > > > > > > 2 2 2 2 2 2 2 2 2 2 < < < < < < < < < S S S S S S S S S 2 2 2 2 2 2 2 2 2 2 3 F i g u r e 2 . 1 2 . D i s t o r t e d T e n e t 0 f L a T e 3 a t 3 0 0 K w i t h q = 0 . 2 7 l 7 ( 6 ) a n d 3 . 0 4 3 A b o n d i n g t h r e s h o l d . < < < < < < < < < < . < < < < < < < < < > > > > > > > > > > > > > > > > > > > . 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < . . . . . . . . . . > > > > > > > > > > > > > > > > > > > . 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < S S S S S S S S S S > > > > > > > > > z 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < S S S S S S S S S S - > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < S S S S S S S S S S > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < S S S S S S S S S S > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < S S S S S S S S S S > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < S S S S S S S S S S > > > > > > > > > z 2 2 2 2 2 2 2 2 2 2 m : < < < < < < < < < S S S S S S S S S S 7 5 F i g u r e 2 . 1 3 . D i s t o r t e d T e n e t o f S m T e 3 a t 3 0 0 K w i t h q = 0 . 2 8 7 4 ( 4 ) a n d 3 . 0 1 8 A b o n d i n g t h r e s h o l d . 3 3 3 2 3 3 3 2 3 S S S S S S S S S > > > > > > > > . 2 2 2 2 2 2 2 2 2 : < < < < < < < < - S S S S S S S S S - > > > > > > > > : 2 2 2 2 2 2 2 2 2 : < < < < < < < < S S S S S S S S S > > > > > > > > : > > > > > > > > > / / / / / / / / . 3 3 3 3 3 3 3 3 3 . \ \ \ \ \ \ \ \ ' S S S S S S S S S > > > > > > > > : 2 2 2 2 2 2 2 2 2 : < < < < < < < < S S S S S S S S S > > > > > > > > : 2 2 2 2 2 2 2 2 2 : < < < < < < < < S S S S S S S S S > > > > > > > > : 2 2 2 2 2 2 2 2 2 / / / / / / / / . 3 3 3 3 3 3 3 3 3 . \ \ \ \ \ \ \ \ S S S S S S S S S > > > > > > > > : 2 2 2 2 2 2 2 2 2 a : < < < < < < < S S S S S S S S S F i g u r e 2 . 1 4 . D i s t o r t e d T e n e t o f G d T e 3 a t 3 0 0 K w i t h q = 0 . 2 9 l 6 ( 3 ) a n d 3 . 0 0 3 A b o n d i n g t h r e s h o l d . > > > > > > > > > > > > > > > > > > > I 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < S S S S S S S S S S > > > > > > > > > : > > > > > > > > > > > > > > > > > > > : 0 0 0 0 0 0 0 0 0 0 < < < < < < < < < < I < < < < < < < < < S S S S S S S S S S > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < S S S S S S S S S S > > > > > > > > > : > > > > > > > > > > > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < 3 S S S S S S S S S > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < 2 < < < < < < < < < > > > > > > > > > I > > > > > > > > > > > > > > > > > > > I 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < S S S S S S S S S S - > > > > > > > > > : > > > > > > > > > > > > > > > > > > > € 3 < < < < < < < < < < I < < < < < < < < < 0 . 2 9 5 7 ( 5 ) a n d 3 . 0 1 9 A b o n d i n g t h r e s h o l d . F i g u r e 2 . 1 5 . D i s t o r t e d T e n e t o f T b T e 3 a t 3 0 0 K w i t h q - > > > > > > > > : 2 2 2 2 2 2 2 2 2 ° / / / / / / / / . 3 3 3 3 3 3 3 3 3 . \ \ \ \ \ \ \ \ ' S S S S S S S S S ~ > > > > > > > > : 2 2 2 2 2 2 2 2 2 / / / / / / / / . 3 3 3 3 3 3 3 3 3 . \ \ \ \ \ \ \ \ S S S S S S S S S - > > > > > > > > : 2 2 2 2 2 2 2 2 2 ° / / / / / / / / . 3 3 3 3 3 3 3 3 3 . \ \ \ \ \ \ \ \ ' S S S S S S S S S - > > > > > > > > : 2 2 2 2 2 2 2 2 2 ' / / / / / / / / . 3 3 3 3 3 3 3 3 3 . \ \ \ \ \ \ \ \ ' 0 0 0 0 0 0 0 0 0 ' / / / / / / / / . 2 2 2 2 2 2 2 2 2 : < < < < < < < < ~ S S S S S S S S S . \ \ \ \ \ \ \ \ ° / / / / / / / / . 3 3 3 3 3 3 3 3 3 - > > > > > > > > : 2 2 2 2 2 2 2 2 2 7 6 C D ( A ) l l T I T I I l l I 3 - ° P D F ‘ . ; — — F I T 2 - 3 1 E 3 3 fi fi l ( D 1 ' S f ‘ i ’ , « i f ; 5 : d E “ i i 3 ’ 5 . 2 1 : ~ I : 0 — ‘ 1 ‘ 3 ’ : - 2 : i : § : : J . 4 , . L 4 . + l . L l + % 4 N W 2 4 6 8 . 1 0 . 1 2 1 4 1 6 1 8 2 0 R a d l a l d l s t a n c e r ( A ) I O E x p e r i m e n t a l P D F 0 0 % . . S u b c e l l fi t ° 0 O O 2 . 6 2 . 8 3 . 0 L 3 . 2 3 . 4 3 . 6 3 . 8 R a d i a l d i s t a n c e r ( A ) F i g u r e 2 . 1 8 . ( A ) P i t o f t h e e x p e r i m e n t a l P D F d a t a i n t h e r a n g e o f 2 - 2 0 A ( B ) F i r s t P D F p e a k w h i c h r e p r e s e n t s t h e l o c a l s t r u c t u r e o f t h e C e T e 3 . T h e s o l i d l i n e r e p r e s e n t s t h e a v e r a g e s t r u c t u r a l m o d e l a n d t h e c i r c l e s t h e e x p e r i m e n t a l d a t a . 7 7 1 0 ' _ _ 8 — _ l ' _ l 6 + - - ' 7 ' 4 r P _ 3 T m 2 — _ O 0 - { L . ~ ’ ‘ ' - 2 — J a . 4 - a 1 l 1 l 1 l 1 1 1 I 1 l 1 l 1 l 1 l 1 l 1 1 1 l 4 O 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6 W a v e v e c t o r Q ( A ' l ) r 1 ' I ' - 1 4 . . A 2 " M t } ( D E 0 1 m U 1 l 1 1 l - 2 . 1 4 l 1 I 1 l 1 O 1 0 2 O 3 O 4 0 R a d i a l d i s t a n c e r ( A ) F i g u r e 2 . 1 9 . T h e r e d u c e d Q [ S ( q ) - l ] a n d P D F G ( r ) p l o t s o f P r T e 3 7 8 6 I l i l i l l l U r U r U l T l l l l ' l l fi i r T 4 ~ - l — l v — l é v 2 . . . 2 C l ) 0 ’ J l L l l l l l l l l l l l l l l l l l L l l l l O 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6 W a v e v e c t o r Q ( 1 3 ( 1 ) 4 - P 3 8 2 _ . . . . . . . . . . . . D [ L 1 Q G a 0 U A J 1 1 1 U _ 2 . 1 . 1 1 1 0 1 0 2 0 3 0 I 4 0 R a d i a l d i s t a n c e r ( A ) F i g u r e 2 . 2 0 . T h e r e d u c e d Q [ S ( q ) - 1 ] a n d P D F G ( r ) p l o t s o f N d T e 3 7 9 B a n d s t r u c t u r e c a l c u l a t i o n o f L a T e 3 — T h e c a l c u l a t i o n s w e r e p e r f o r m e d u s i n g t h e s e l f - c o n s i s t e n t f u l l - p o t e n t i a l l i n e a r i z e d a u g m e n t e d p l a n e w a v e m e t h o d ( L A P W ) 1 6 a n d t h e g e n e r a l i z e d g r a d i e n t a p p r o x i m a t i o n ( G G A ) l 7 f o r t h e e x c h a n g e a n d c o r r e l a t i o n p o t e n t i a l . T h e e x p e r i m e n t a l c e l l c o n s t a n t s ( T a b l e 2 . 1 4 ) a n d a t o m i c c o o r d i n a t e s ( T a b l e 2 . 1 5 ) f r o m t h e c r y s t a l s t r u c t u r e r e fi n e m e n t o f L a T e 3 i n C m c m w e r e u s e d . D i r e c t i o n s i n t h e B r i l l o u i n z o n e ( B Z ) a r e s h o w n i n F i g u r e 2 . 2 3 A . 1 8 I n t e r a t o m i c f o r c e s w e r e m i n i m i z e d w i t h i n 0 . 1 m R y / b o h r u s i n g a r e v e r s e - c o m m u n i c a t i o n t r u s t - r e g i o n q u a s i - N e w t o n m e t h o d f r o m t h e P o r t l i b r a r y . 1 9 S c a l a r r e l a t i v i s t i c c o r r e c t i o n s w e r e i n c l u d e d a n d a s p i n - o r b i t i n t e r a c t i o n w a s i n c o r p o r a t e d u s i n g a s e c o n d v a r i a t i o n a l p r o c e d u r e . 2 0 T h e v a l u e s o f t h e a t o m i c r a d i i w e r e t a k e n t o b e : 2 . 7 a . u . f o r L a a t o m a n d 2 . 5 a . u . f o r T e a t o m s , w h e r e a . u . i s t h e a t o m i c u n i t ( 0 . 5 2 9 A ) . C o n v e r g e n c e o f t h e s e l f - c o n s i s t e n t i t e r a t i o n s w a s p e r f o r m e d f o r 3 0 k p o i n t s i n s i d e t h e i r r e d u c i b l e B Z t o w i t h i n 0 . 0 0 0 1 R y w i t h a c u t o f f o f - 6 . 0 R y b e t w e e n t h e v a l e n c e a n d t h e c o r e s t a t e s . T h e c a l c u l a t i o n s w e r e p e r f o r m e d u s i n g W I E N Z K p r o g r a m . 2 1 T h e b a n d s o f p , a n d p 2 o r b i t a l s o f T e [ 2 ] a n d T e [ 3 ] ( a t o m s i n t h e n e t ) a r e h i g h l y d i s p e r s i v e c r o s s i n g t h e F e r m i s u r f a c e , F i g u r e 2 . 2 1 . T h i s i s a c l e a r i n d i c a t i o n o f t h e m e t a l l i c c h a r a c t e r o f L a T e g . P a r t i a l d e n s i t y o f s t a t e s ( D O S ) o f t h e p o r b i t a l o f T e [ 3 ] ( F i g u r e 2 . 2 2 A ) a n d t o t a l D O S o f t h e s u b c e l l ( F i g u r e 2 . 2 2 B ) w e r e a l s o c a l c u l a t e d s h o w i n g n o g a p a t t h e F e r m i l e v e l . T h e F e r m i s u r f a c e t o p o l o g y f a v o r s t h e f o r m a t i o n o f a n e s t i n g v e c t o r ( q - v e c t o r ) a l o n g t h e c * d i r e c t i o n w i t h a v a l u e o f ~ 0 2 8 ( 2 ) w h i c h i s c o n s i s t e n t w i t h o u r e x p e r i m e n t a l o b s e r v a t i o n , F i g u r e 2 2 3 8 8 0 3 . 0 2 . 0 0 . 0 E n e r g y ( C V ) 1 1 1 1 j u n / ' - 4 . o — \ - 6 . 0 F Z T Y F T R S Y R Z F i g u r e 2 . 2 1 . B a n d s t r u c t u r e o f L a T e 3 n e a r t h e F e r m i l e v e l . 3 0 . 8 D p a r t i a l D O S : T e 3 t d t _ 2 . 5 . 1 . 5 - D O S 0 . 5 . I 1 b P 0 I l l 5 0 E n e r g y [ e V ] ( B ) 6 0 . T . 5 0 - 1 O t o t a l D O S — 4 0 - 2 0 + 1 0 - 0 - i o 3 5 6 1 ' 0 E n e r g y [ e V ] F i g u r e 2 . 2 2 . ( A ) P a r t i a l d e n s i t y o f s t a t e ( D O S ) o f t h e p o r b i t a l o f T e [ 3 ] a n d ( B ) t o t a l D O S o f t h e L a T e 3 s u b c e l l . 8 2 Z B A o n ' t ~ 1 5 T 1 R J 4 O E B A H 2 0 J 1 z r A _ , ( B ) 2 r I I I I I I I I I I I I I I " " J \ A / F i g u r e 2 . 2 3 . ( A ) B r i l l o u i n z o n e o f C m c m s p a c e g r o u p ( B ) F e r m i s u r f a c e t o p o l o g y o f L a T e 3 w i t h a n a v e r a g e n e s t i n g v e c t o r o f 0 2 8 ( 2 ) ( s o l i d a r r o w s ) . 8 3 2 . 4 . C o n c l u s i o n s C h a r g e d e n s i t y w a v e s ( C D W s ) a r e b r o k e n s y m m e t r y s t a t e s o f m o s t l y s t r o n g l y a n i s o t r o p i c q u a s i - o n e d i m e n s i o n a l m e t a l s . 2 2 A s a r e s u l t o f a P e i e r l s i n s t a b i l i t y t h e i r g r o u n d s t a t e i s a c o h e r e n t s u p e r p o s i t i o n o f e l e c t r o n - h o l e p a i r s w h i c h r e s u l t s i n a p e r i o d i c s p a t i a l m o d u l a t i o n o f t h e c h a r g e d e n s i t y . T h e s t u d y o f C D W s i s i m p o r t a n t , b e c a u s e a s u c c e s s f u l d e s c r i p t i o n o f t h e c o u p l e d e l e c t r o n i c l a t t i c e i n s t a b i l i t y r e fl e c t s o n t h e b r o a d e r i s s u e o f t h e e l e c t r o n i c a s p e c t s o f s t r u c t u r a l s t a b i l i t y w h i c h i s l i n k e d t o s e v e r a l i n t e r e s t i n g p h e n o m e n a i n c l u d i n g s u p e r c o n d u c t i v i t y . T h e C D W s t a t e h a s n o t r e c e i v e d t h e s a m e l e v e l o f a t t e n t i o n a s s u p e r c o n d u c t i v i t y , a l t h o u g h t h e p h e n o m e n o n i s p o t e n t i a l l y e q u a l l y i m p o r t a n t . T h e v a s t m a j o r i t y o f C D W s t u d i e s f o c u s e d o n q u a s i o n e - d i m e n s i o n a l s y s t e m s p a r t l y b e c a u s e t w o - d i m e n s i o n a l c o u n t e r p a r t s a r e s c a r c e . T h e r e s o l u t i o n o f t h e m o d u l a t e d s t r u c t u r e s o f R E T e 3 c o m p o u n d s s h e d s l i g h t o n t h e s u b t l e d e t a i l s o f t h e i r C D W d i s t o r t i o n ( s ) . F u r t h e r m o r e , i t r e v e a l s f o r t h e fi r s t t i m e t h a t t h e n a t u r e o f t h e C D W w a v e i n t h e s e c o m p o u n d s v a r i e s s u b t l y y e t d e t e c t a b l y w i t h R E e l e m e n t . T h i s r e s u l t i s s u r p r i s i n g g i v e n t h a t t h e s u b s t i t u t i o n o f o n e R E f o r t h e n e x t i s i s o e l e c t r o n i c i n n a t u r e a n d t h e r e f o r e s h o u l d p r e s a g e a n i d e n t i c a l d i s t o r t i o n p a t t e r n . 2 3 B e c a u s e o f t h e fi n e d i f f e r e n c e s f o u n d i n C D W d i s t o r t i o n s a c r o s s t h e R E s e r i e s , t h e s t r u c t u r a l c h a r a c t e r i z a t i o n o f t h e r e m a i n i n g m e m b e r s o f t h e R E T e 3 f a m i l y i s n o w j u s t i fi e d . I t i s n e c e s s a r y t o a p p l y t h e s u p e r s p a c e g r o u p c r y s t a l l o g r a p h i c a p p r o a c h i n o r d e r t o s u c c e s s f u l l y d e c i p h e r t h e s e s u b t l e d i f f e r e n c e s . T h e n e w i n f o r m a t i o n r e p o r t e d h e r e r e g a r d i n g t h e C D W d i s t o r t i o n s o p e n s f r e s h p e r s p e c t i v e s o n h o w t o t h i n k a b o u t t h e s e s y s t e m s a n d p r o v i d e s n e w p o s s i b i l i t i e s f o r m o r e i n f o r m e d t h e o r e t i c a l i n t e r p r e t a t i o n s o f t h e i r p h y s i c a l p r o p e r t i e s . 8 4 T a b l e 2 . 1 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r L a T e 3 a t 3 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 2 6 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 0 ’ ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T M a n d T m c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e L a T e 3 5 2 1 . 7 3 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c c 2 c m ( 0 0 y ) 0 0 0 a = 4 . 3 9 4 4 ( 8 ) A , 0 1 = 9 0 0 b = 2 6 . 2 2 7 ( 4 ) A , 0 = 9 0 0 c = 4 . 4 0 7 6 ( 7 ) A , y = 9 0 0 0 . 2 7 5 1 ( 4 ) c ‘ 5 0 7 9 9 0 4 ) A 3 4 6 . 8 1 9 3 g / c m 3 2 5 . 0 7 5 m m " 8 5 2 0 . 1 0 x 0 . 0 6 x 0 0 1 1 1 1 1 1 1 3 2 . 0 0 t o 2 9 . 2 6 ° - 6 < = h < = 6 , - 3 6 < = k < = 3 0 , - 6 < = l < = 6 , - 1 < = m < = 1 7 1 9 5 ( 2 3 9 7 m a i n + 4 7 9 8 s a t e l l i t e s ) 2 1 2 3 ( 7 5 8 m a i n + 1 3 6 5 s a t e l l i t e S ) [ R i m = 0 . 0 7 8 3 ] 9 9 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 2 1 2 3 / 0 / 3 8 1 . 6 8 R o b , = 0 . 0 5 1 4 , w R o b , = 0 . 1 1 9 0 R , " = 0 . 0 8 2 7 , w R , 1 1 = 0 . 1 2 6 7 R 0 , , = 0 . 0 4 1 0 , w R o b s = 0 . 1 0 5 4 R a n = 0 . 0 4 3 0 , W R a n = 0 . 1 0 5 9 R o b , = 0 . 1 1 4 6 , w R o b , = 0 . 1 7 2 3 R , “ = 0 . 2 5 3 3 , w R a u = 0 . 2 0 0 4 0 . 0 0 0 5 0 ( 6 ) 0 . 1 1 8 9 a n d 0 . 9 3 3 3 3 . 4 1 a n d 3 2 2 6 A 3 R = 2 1 1 F 0 1 - 1 F c 1 1 / 2 1 8 , 1 , w R = { 2 1 w ( 1 F 0 1 2 - 1 F c 1 2 ) 2 1 / 2 1 w < 1 F o 1 ‘ ) 1 1 ” 2 a n d “ = 1 / ( 6 2 ( I ) + 0 . 0 0 1 6 I Z ) 8 5 T a b l e 2 . 1 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r L a T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . a L a b e l W a v e x y z U e q L a 0 9 3 4 9 1 6 8 8 ( 1 ) 2 5 4 9 1 7 ( 1 ) s i n , 1 0 0 - 1 ( 5 ) c o s , 1 5 9 ( 2 ) 2 ( 1 ) 0 T e [ 1 ] 0 9 2 9 6 ( 8 ) 2 9 6 0 ( 1 ) 2 5 4 9 1 7 ( 1 ) s i n , 1 0 0 1 3 ( 6 ) c o s , 1 1 0 ( 2 ) - 1 ( 1 ) 0 T e [ 2 ] 0 9 2 8 2 ( 1 1 ) 6 9 1 ( 1 ) 7 5 4 9 2 1 ( 1 ) s i n , 1 0 0 - 2 0 ( 8 ) c o s , 1 - 3 0 8 ( 4 ) - 3 ( 1 ) 0 T e [ 3 ] 0 9 3 3 9 ( 9 ) 4 3 0 6 ( 1 ) 7 5 4 9 2 1 ( 1 ) s i n , 1 0 0 - 5 1 ( 8 ) c o s , 1 2 4 0 ( 4 ) - 1 1 ( 1 ) 0 ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 2 . 1 6 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r L a T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 L a 1 3 ( 1 ) 2 5 ( 1 ) 1 3 ( 1 ) 0 ( 1 ) 0 0 T e [ 1 ] 1 3 ( 1 ) 2 5 ( 1 ) 1 4 ( 1 ) 0 ( 1 ) 0 0 T e [ 2 ] 2 0 ( 1 ) 2 8 ( 1 ) 1 6 ( 1 ) 4 ( 2 ) 0 0 T e [ 3 ] 1 8 ( 1 ) 2 7 ( 1 ) 1 7 ( 1 ) - 2 ( 1 ) 0 0 T a b l e 2 . 1 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r L a T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e L a - T e [ 1 ] 3 . 3 3 6 ( 3 ) 3 . 3 2 8 ( 5 ) 3 . 3 4 3 ( 5 ) L a - T e [ 1 ] x 4 3 . 2 4 7 ( 3 ) 3 . 2 2 9 ( 3 ) 3 . 2 6 4 ( 3 ) L a - T e [ 2 ] x 2 3 . 4 2 3 ( 3 ) 3 . 4 1 4 ( 3 ) 3 . 4 3 3 ( 3 ) L a - T e [ 3 ] 3 . 3 9 8 ( 3 ) 3 . 3 2 9 ( 5 ) 3 . 4 6 8 ( 5 ) L a - T e [ 3 ] 3 . 4 2 1 ( 3 ) 3 . 3 8 8 ( 5 ) 3 . 4 5 4 ( 5 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 9 5 ( 5 ) 2 . 9 3 4 ( 5 ) 3 . 2 6 1 ( 5 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 1 3 3 ( 5 ) 2 . 9 8 8 ( 5 ) 3 . 2 8 0 ( 5 ) 8 6 T a b l e 2 . 1 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r L a T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - L a - T e [ 1 ] x 8 7 3 4 8 ( 6 ) 7 3 4 0 ( 7 ) 7 3 5 7 ( 7 ) T e [ 1 ] - L a - T e [ 2 ] x 2 1 3 9 . 8 5 ( 7 ) 1 3 9 . 5 9 ( 6 ) l 4 0 . 0 3 ( 6 ) T e [ 1 ] - L a - T e [ 3 ] x 2 1 4 0 . 0 8 ( 8 ) 1 3 9 . 6 8 ( 9 ) 1 4 0 . 4 8 ( 9 ) T e [ 1 ] - L a - T e [ 1 ] x 8 8 5 4 9 ( 7 ) 8 5 1 4 ( 7 ) 8 5 8 5 ( 8 ) T e [ 1 ] - L a - T e [ 1 ] x 4 1 4 7 . 0 0 ( 7 ) 1 4 6 . 7 9 ( 1 0 ) 1 4 7 . l 9 ( 1 0 ) T e [ 1 ] - L a - T e [ 2 ] x 4 7 7 . 1 8 ( 8 ) 7 5 5 2 ( 9 ) 7 8 8 8 ( 9 ) T e [ 1 ] - L a - T e [ 2 ] x 4 1 3 0 . 7 5 ( 1 0 ) 1 2 8 . 1 5 ( 9 ) l 3 3 . 3 7 ( 9 ) T e [ 1 ] - L a - T e [ 3 ] x 4 7 7 5 0 ( 7 ) 7 7 1 4 ( 7 ) 7 7 8 6 ( 7 ) T e [ 1 ] - L a - T e [ 3 ] x 4 1 3 0 . 9 1 ( 9 ) 1 3 0 . 2 7 ( 8 ) 1 3 1 . 5 4 ( 8 ) T e [ 2 ] - L a - T e [ 2 ] x 2 8 0 2 1 ( 7 ) 7 9 7 5 ( 8 ) 8 0 . 5 7 ( 8 ) T e [ 2 ] - L a - T e [ 3 ] x 4 5 3 9 6 ( 9 ) 5 1 8 2 ( 9 ) 5 6 . 6 7 ( 1 0 ) T e [ 3 ] - L a - T e [ 3 ] x 2 8 0 2 4 ( 9 ) 7 9 7 2 ( 1 1 ) 8 0 . 7 3 ( 1 1 ) L a - T e [ 1 ] - L a x 8 1 0 6 . 5 3 ( 7 ) l O 6 . 2 4 ( 8 ) 1 0 6 8 l ( 8 ) L a - T e [ 1 ] - L a x 8 8 5 5 7 ( 9 ) 8 5 2 8 ( 9 ) 8 5 8 5 ( 9 ) L a - T e [ 1 ] - L a x 4 1 4 7 . 0 0 ( 7 ) 1 4 6 . 8 4 ( 4 ) 1 4 7 . 1 5 ( 4 ) L a - T e [ 2 ] - L a x 2 8 0 1 7 ( 6 ) 7 9 8 6 ( 8 ) 8 0 8 8 ( 8 ) L a - T e [ 2 ] - T e [ 3 ] x 4 6 2 5 7 ( 6 ) 6 1 9 2 ( 6 ) 6 3 8 4 ( 7 ) L a - T e [ 2 ] - T e [ 3 ] x 4 1 1 7 2 3 ( 1 2 ) 1 1 4 . 4 5 ( l 3 ) 1 1 9 . 9 0 ( l 4 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 9 0 . 9 8 ( 1 6 ) 8 6 . l 4 ( 1 5 ) 9 6 . 0 0 ( 1 8 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 6 8 9 . 6 8 ( 1 1 ) 8 9 1 9 ( 9 ) 9 0 . 1 8 ( l 1 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 6 . 5 2 ( 1 6 ) 1 7 3 . 8 6 ( 1 6 ) 1 7 9 . 7 9 ( 8 ) L a - T e [ 3 ] - L a x 2 8 0 2 4 ( 5 ) 7 9 7 2 ( 8 ) 8 0 7 3 ( 8 ) L a - T e [ 3 ] - T e [ 2 ] x 2 6 2 8 0 ( 8 ) 6 1 2 0 ( 8 ) 6 4 4 3 ( 9 ) L a - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 1 2 ( 8 ) 1 1 6 . 9 7 ( 8 ) 1 1 7 . 3 8 ( 9 ) L a - T e [ 3 ] - T e [ 2 ] x 2 6 3 4 6 ( 8 ) 6 1 . 0 1 ( 8 ) 6 5 9 9 ( 9 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 6 8 9 6 4 ( 1 5 ) 8 4 . 5 7 ( 1 4 ) 9 4 . 9 0 ( l 7 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 6 . 6 4 ( 1 5 ) 1 7 4 . 0 6 ( 1 5 ) 1 8 0 T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 9 0 . 9 8 ( 1 5 ) 8 6 . 1 1 ( 1 4 ) 9 5 9 7 ( 1 7 ) 8 7 T a b l e 2 . 1 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C e T e 3 a t 3 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( O O O ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 3 1 . 6 8 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ’ ( 1 ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 0 ' ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m . . . a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e C e T e 3 5 2 2 . 9 3 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 0 m ( 0 0 y ) 0 0 0 a = 4 . 3 7 3 2 ( 5 ) A , 0 1 = 9 0 0 b = 2 5 . 9 7 3 ( 4 ) A , ( 3 = 9 0 ° c = 4 . 3 8 4 9 ( 5 ) A , y = 9 0 0 0 . 2 8 0 1 ( 3 ) c " 4 9 8 . 0 7 ( 1 1 ) A 3 4 6 . 9 7 1 4 g / c m 3 2 6 . 2 4 2 m m " 8 5 6 0 . 7 9 x 0 . 3 4 x 0 . 0 1 m m 3 3 . 1 3 t o 3 1 . 6 8 ° - 6 < = h < = 6 , - 3 8 < = k < = 3 8 , - 6 < = l < = 6 , - 1 < = m < = 1 7 3 5 6 ( 2 1 6 7 m a i n + 5 1 8 9 s a t e l l i t e s ) 2 4 7 5 ( 8 2 2 m a i n + 1 6 5 3 s a t e l l i t e s ) [ R i m = 0 . 0 2 8 6 ] 9 6 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 2 4 7 5 / 0 / 3 8 1 . 5 0 k . . . = 0 . 0 3 3 4 , w k . . . = 0 . 0 9 1 9 R . . . = 0 . 0 5 8 4 , w R . u = 0 . 1 0 2 8 R . . . = 0 . 0 1 7 1 , w k . . . = 0 . 0 5 9 2 R . “ = 0 . 0 1 8 1 , w R . u = 0 . 0 6 0 0 R . . . = 0 . 0 9 9 6 , w k . . . = 0 . 1 4 9 6 R . " = 0 . 1 9 3 2 , W K . " = 0 . 1 7 3 2 0 . 0 3 3 ( 8 ) 0 . 0 7 2 2 a n d 0 . 7 3 6 8 2 . 9 5 a n d - 2 . 6 8 e . A ' 3 R = 2 1 1 1 3 0 1 1 1 3 1 / X I F O I . w R = { 2 [ W ( | F o | 2 - 1 1 1 1 0 2 1 / 2 [ W ( | F o l 4 ) ] } " 2 a n d w = 1 / ( o Z ( I ) + 0 . 0 0 1 6 1 2 ) 8 8 T a b l e 2 . 2 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C e T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . L a b e l W a v e x y z U . q C e 0 9 2 4 9 1 6 8 9 ( 1 ) 2 5 4 9 7 ( 1 ) s i n , 1 0 0 - 2 0 ( 4 ) c o s , 1 5 8 ( 1 ) 7 ( 1 ) 0 T e [ 1 ] 0 9 1 7 9 ( 3 ) 2 9 5 8 ( 1 ) 2 5 4 9 7 ( 1 ) s i n , 1 0 0 1 0 ( 4 ) c o s , 1 7 ( 1 ) - l ( 1 ) 0 T e [ 2 ] 0 9 2 3 4 ( 4 ) 6 9 7 ( 1 ) 7 5 4 9 1 1 ( 1 ) s i n , 1 0 0 1 ( 5 ) c o s , 1 - 2 7 4 ( 1 ) 0 ( 1 ) 0 T e [ 3 ] 0 9 2 2 2 ( 3 ) 4 3 0 0 ( 1 ) 7 5 4 9 1 1 ( 1 ) s i n , 1 0 0 7 ( 5 ) c o s , 1 2 2 1 ( 1 ) 0 ( 1 ) 0 T U . q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 2 . 2 1 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r C e T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 C e 7 ( 1 ) 9 ( 1 ) 6 ( 1 ) 0 ( 1 ) 0 0 T e [ 1 ] 7 ( 1 ) 9 ( 1 ) 6 ( 1 ) 0 ( 1 ) 0 0 T e [ 2 ] 1 1 ( 1 ) 1 2 ( 1 ) 1 0 ( 1 ) 4 ( 1 ) 0 0 T e [ 3 ] 1 1 ( 1 ) 1 1 ( 1 ) 1 1 ( 1 ) - l ( 1 ) 0 0 T a b l e 2 . 2 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C e T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e C e — T e [ 1 ] 3 . 2 9 6 3 ( 1 1 ) 3 . 2 7 5 0 ( 1 9 ) 3 . 3 1 8 0 ( 1 9 ) C e - T e [ l ] x 2 3 . 2 3 5 3 ( 1 5 ) 3 . 2 1 9 0 ( 1 7 ) 3 . 2 5 1 5 ( 1 7 ) C e - T e [ 1 ] x 2 3 . 2 2 2 8 ( 1 5 ) 3 . 2 0 4 2 ( 1 2 ) 3 . 2 4 1 8 ( 1 2 ) C e - T e [ 2 ] x 2 3 . 3 8 4 7 ( 1 5 ) 3 . 3 6 9 0 ( 1 6 ) 3 . 3 9 8 5 ( 1 5 ) C e - T e [ 3 ] 3 . 3 6 7 0 ( 1 3 ) 3 . 3 3 5 5 ( 1 8 ) 3 . 3 9 9 8 ( 1 8 ) C e - T e [ 3 ] 3 . 3 8 0 1 ( 1 3 ) 3 . 3 1 9 8 ( 1 8 ) 3 . 4 3 9 5 ( 1 8 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 1 0 1 ( 2 ) 2 . 9 6 6 2 ( 1 6 ) 3 . 2 4 0 7 ( 1 8 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 9 5 ( 2 ) 2 . 9 5 6 4 ( 1 6 ) 3 . 2 3 5 0 ( 1 7 ) 8 9 T a b l e 2 . 2 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C e T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - C e - T e [ 1 ] x 8 7 3 4 4 ( 3 ) 7 3 3 5 ( 3 ) 7 3 5 4 ( 3 ) T e [ 1 ] - C e - T e [ 2 ] x 2 l 3 9 . 5 7 ( 5 ) 1 3 9 . 1 5 ( 5 ) 1 3 9 . 9 4 ( 7 ) T e [ 1 ] - C e - T e [ 3 ] x 2 l 3 9 . 5 7 ( 3 ) 1 3 8 . 8 4 ( 4 ) l 4 0 2 9 ( 4 ) T e [ 1 ] - C e - T e [ 1 ] x 6 8 5 3 2 ( 4 ) 8 5 0 3 ( 4 ) 8 5 6 2 ( 4 ) T e [ 1 ] - C e - T e [ 1 ] x 4 1 4 7 . 0 5 ( 3 ) 1 4 6 . 5 1 ( 4 ) 1 4 7 . 5 8 ( 4 ) T e [ 1 ] - C e - T e [ 2 ] x 2 7 7 2 4 ( 4 ) 7 5 7 3 ( 4 ) 7 8 7 8 ( 4 ) T e [ 1 ] - C e - T e [ 2 ] x 2 1 3 1 . 1 2 ( 4 ) 1 2 8 . 6 0 ( 4 ) 1 3 3 . 6 7 ( 4 ) T e [ 1 ] - C e - T e [ 3 ] x 4 7 7 . 1 3 ( 4 ) 7 6 7 2 ( 4 ) 7 7 5 4 ( 4 ) T e [ 1 ] - C e - T e [ 3 ] x 4 1 3 1 . 0 1 ( 5 ) l 3 0 . 6 3 ( 5 ) 1 3 1 . 3 9 ( 5 ) T e [ 1 ] - C e - T e [ 1 ] x 2 8 5 7 4 ( 4 ) 8 4 9 8 ( 4 ) 8 6 4 9 ( 4 ) T e [ 1 ] - C e - T e [ 2 ] x 2 7 6 8 7 ( 4 ) 7 5 1 9 ( 4 ) 7 8 5 2 ( 4 ) T e [ 1 ] - C e - T e [ 2 ] x 2 l 3 0 . 8 6 ( 4 ) 1 2 8 . 7 8 ( 4 ) 1 3 2 . 8 9 ( 4 ) T e [ 2 ] - C e - T e [ 2 ] x 2 8 0 7 9 ( 4 ) 8 0 3 7 ( 4 ) 8 1 . 1 2 ( 4 ) T e [ 2 ] - C e - T e [ 3 ] x 4 5 4 6 7 ( 4 ) 5 2 2 6 ( 4 ) 5 7 . l 7 ( 4 ) T e [ 3 ] - C e - T e [ 3 ] x 2 8 0 8 0 ( 3 ) 8 0 3 9 ( 4 ) 8 1 2 0 ( 4 ) C e - T e [ 1 ] - C e x 4 1 0 6 . 6 2 ( 4 ) 1 0 6 . 2 0 ( 4 ) 1 0 7 . 0 4 ( 4 ) C e - T e [ 1 ] - C e x 4 1 0 6 . 3 3 ( 4 ) 1 0 5 . 6 8 ( 4 ) 1 0 6 . 9 9 ( 4 ) C e - T e [ 1 ] - C e x 8 8 5 2 4 ( 4 ) 8 5 0 1 ( 3 ) 8 5 4 8 ( 3 ) C e - T e [ 1 ] - C e x 4 1 4 7 . 0 5 ( 3 ) 1 4 6 . 8 0 ( 4 ) 1 4 7 . 2 9 ( 4 ) C e - T e [ 2 ] - C e x 2 8 0 . 7 5 ( 4 ) 8 0 3 0 ( 5 ) 8 1 . 1 2 ( 5 ) C e - T e [ 2 ] - T e [ 3 ] x 2 6 2 8 5 ( 3 ) 6 1 5 9 ( 3 ) 6 3 0 8 ( 3 ) C e - T e [ 2 ] - T e [ 3 ] x 2 1 1 6 . 9 3 ( 5 ) 1 1 3 . 9 6 ( 6 ) 1 1 9 . 8 4 ( 6 ) C e - T e [ 2 ] - T e [ 3 ] x 2 6 2 6 8 ( 3 ) 6 2 1 1 ( 3 ) 6 3 2 6 ( 3 ) C e - T e [ 2 ] - T e [ 3 ] x 2 1 1 7 . 4 1 ( 5 ) 1 1 4 . 2 4 ( 6 ) 1 2 0 . 5 6 ( 6 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 9 0 1 4 ( 6 ) 8 5 4 0 ( 6 ) 9 5 0 2 ( 7 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 8 9 7 3 ( 5 ) 8 9 5 8 ( 4 ) 8 9 9 2 ( 7 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 6 . 9 6 ( 7 ) 1 7 5 . 0 9 ( 7 ) 1 7 9 . 6 9 ( 3 ) C e - T e [ 3 ] - C e x 2 8 0 8 0 ( 2 ) 8 0 3 9 ( 4 ) 8 1 2 0 ( 4 ) C e - T e [ 3 ] - T e [ 2 ] x 4 6 2 8 7 ( 3 ) 6 1 . 1 3 ( 3 ) 6 4 7 0 ( 3 ) C e - T e [ 3 ] - T e [ 2 ] x 4 l 1 7 . 4 2 ( 4 ) 1 1 6 . 3 0 ( 4 ) 1 1 8 . 4 8 ( 4 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 9 0 4 0 ( 6 ) 8 5 9 3 ( 6 ) 9 5 0 1 ( 6 ) T e [ 2 ] — T e [ 3 ] - T e [ 2 ] x 4 8 9 7 3 ( 6 ) 8 9 5 8 ( 5 ) 8 9 9 2 ( 7 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 7 . 1 0 ( 7 ) 1 7 5 . 3 1 ( 6 ) l 7 9 . 7 0 ( 3 ) 9 O T a b l e 2 . 2 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r P r T e 3 a t 3 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 1 7 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( 1 ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 3 t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 “ o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m . . . a n d T m . . . c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e P r T e 3 5 2 3 . 7 3 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 c m ( 0 0 y ) 0 0 0 a = 4 . 3 5 6 9 ( 9 ) A , a = 9 0 0 b = 2 5 . 8 9 6 ( 5 ) A , B = 9 0 0 c = 4 . 3 6 6 6 ( 9 ) A , y = 9 0 0 0 . 2 8 1 8 ( 4 ) e ‘ 4 9 2 . 6 7 ( 1 7 ) A 3 4 7 . 0 5 8 g / c m 3 2 6 . 9 4 5 m m " 8 6 0 0 . 3 2 x 0 . 3 1 x 0 . 0 2 m m 3 2 . 0 5 t o 2 9 . 1 7 ° - 5 < = h < = 5 , - 3 4 < = k < = 3 4 , - 6 < = l < = 6 , - 1 < = m < = 1 5 7 5 3 ( 3 1 1 6 m a i n + 6 6 6 7 s a t e l l i t e s ) 1 9 1 4 ( 1 0 9 4 m a i n + 2 0 4 6 s a t e l l i t e s ) [ R i m = 0 . 0 3 3 7 ] 9 6 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 1 9 1 4 / 0 / 3 8 1 . 5 7 k . . . = 0 . 0 3 0 8 , w k . . . = 0 . 0 9 6 4 R . . . = 0 . 0 5 3 0 , w k . . . = 0 . 1 0 7 7 R . . . = 0 . 0 4 0 2 , w k . . . = 0 . 1 1 9 1 R . . . = 0 . 0 4 1 9 , W K . " = 0 . 1 2 2 4 R . . . = 0 . 1 2 0 0 , w k . . . = 0 . 2 1 7 8 R . " = 0 . 2 4 5 3 , w R . u = 0 . 3 1 0 3 0 . 0 0 1 8 4 ( 9 ) 0 . 0 0 9 1 a n d 0 . 5 9 3 1 2 . 3 0 a n d - 2 0 7 e . A ' 3 R = l e F o I - c h l l / 2 l F o l , W R = { ‘ Z [ W ( | F o | 2 - c h | 2 ) 2 ] / E [ W ( | F o | 4 ) ] } " 2 a n d W = 1 / ( 0 7 ( I ) + 0 - 0 0 1 6 1 2 ) 9 1 T a b l e 2 . 2 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r P r T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e x y z U . q P r 0 9 2 4 9 1 6 9 1 ( 1 ) 2 5 4 9 5 ( 1 ) s i n , 1 0 0 3 ( 3 ) c o s , 1 5 3 ( 1 ) 1 ( 1 ) 0 T e [ 1 ] O 9 1 8 8 ( 5 ) 2 9 5 7 ( 1 ) 2 5 4 9 5 ( 1 ) s i n , 1 0 0 4 ( 4 ) c o s , 1 6 ( 1 ) 0 ( 1 ) 0 T e [ 2 ] 0 9 2 1 3 ( 5 ) 7 0 1 ( 1 ) 7 5 4 9 9 ( 1 ) s i n , 1 0 0 - 1 3 ( 5 ) c o s , 1 - 2 4 6 ( 2 ) 6 ( 1 ) 0 T e [ 3 ] 0 9 2 6 7 ( 4 ) 4 2 9 7 ( 1 ) 7 5 4 9 8 ( 1 ) s i n , 1 0 0 - 5 ( 5 ) c o s , 1 2 0 5 ( 2 ) 1 ( 1 ) 0 ‘ U . q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 2 . 2 6 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r P r T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 P r 5 ( 1 ) 6 ( 1 ) 5 ( 1 ) - 1 ( 1 ) 0 0 T e [ 1 ] 5 ( 1 ) 6 ( 1 ) 5 ( 1 ) 2 ( 1 ) 0 0 T e [ 2 ] 1 0 ( 1 ) 9 ( 1 ) 8 ( 1 ) 0 ( 1 ) 0 0 T e [ 3 ] 8 ( 1 ) 9 ( 1 ) 8 ( 1 ) 3 ( 1 ) 0 0 T a b l e 2 2 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r P r T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e P r - T e [ 1 ] 3 . 2 7 7 2 ( 1 4 ) 3 . 2 7 5 ( 2 ) 3 . 2 7 9 ( 2 ) P r - T e [ 1 ] x 2 3 . 2 2 0 1 ( 1 7 ) 3 . 2 0 5 1 ( 1 6 ) 3 . 2 3 4 9 ( 1 6 ) P r - T e [ 1 ] x 2 3 . 2 1 2 7 ( 1 7 ) 3 . 1 9 8 4 ( 1 6 ) 3 . 2 2 7 4 ( 1 6 ) P r - T e [ 2 ] x 2 3 . 3 6 9 0 ( 1 5 ) 3 . 3 5 8 9 ( 1 5 ) 3 . 3 8 1 5 ( 1 5 ) P r - T e [ 3 ] 3 . 3 4 2 4 ( 1 7 ) 3 . 3 0 4 ( 2 ) 3 . 3 8 2 ( 2 ) P r - T e [ 3 ] 3 . 3 8 0 8 ( 1 7 ) 3 . 3 3 4 ( 2 ) 3 . 4 2 8 ( 2 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 6 8 ( 3 ) 2 . 9 4 3 ( 2 ) 3 . 1 9 7 ( 2 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 1 0 3 ( 3 ) 2 . 9 8 0 ( 2 ) 3 . 2 2 7 ( 2 ) 9 2 T a b l e 2 . 2 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r P r T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - P r - T e [ 1 ] x 8 7 3 4 7 ( 3 ) 7 3 3 4 ( 4 ) 7 3 6 0 ( 4 ) T e [ 1 ] - P r - T e [ 2 ] x 2 1 3 9 . 5 6 ( 4 ) 1 3 9 . 3 5 ( 5 ) 1 3 9 . 7 7 ( 6 ) T e [ 1 ] - P r - T e [ 3 ] 1 3 9 . 9 0 ( 5 ) 1 3 9 . 3 4 ( 5 ) 1 4 0 . 4 6 ( 5 ) T e [ 1 ] - P r - T e [ 3 ] l 3 9 . 3 2 ( 4 ) 1 3 8 . 9 0 ( 5 ) 1 3 9 . 7 6 ( 5 ) T e [ 1 ] - P r - T e [ 1 ] x 6 8 5 3 8 ( 4 ) 8 4 9 6 ( 4 ) 8 5 8 1 ( 4 ) T e [ 1 ] - P r - T e [ 1 ] x 4 l 4 7 . 0 3 ( 4 ) 1 4 6 . 9 4 ( 6 ) 1 4 7 . 1 2 ( 5 ) T e [ 1 ] - P r - T e [ 2 ] x 4 7 7 . 1 2 ( 4 ) 7 5 5 5 ( 5 ) 7 8 7 1 ( 5 ) T e [ 1 ] - P r - T e [ 2 ] x 4 1 3 1 . 0 1 ( 5 ) 1 2 8 . 9 9 ( 5 ) 1 3 3 . 0 4 ( 5 ) T e [ 1 ] - P r - T e [ 3 ] x 2 7 7 8 6 ( 4 ) 7 6 9 2 ( 4 ) 7 7 7 9 ( 4 ) T e [ 1 ] - P r - T e [ 3 ] x 2 1 3 1 . 1 1 ( 5 ) 1 3 0 . 7 0 ( 5 ) 1 3 1 . 5 2 ( 5 ) T e [ 1 ] - P r - T e [ 1 ] x 2 8 5 6 2 ( 4 ) 8 5 0 8 ( 4 ) 8 6 . 1 6 ( 4 ) T e [ 1 ] - P r - T e [ 3 ] x 2 l 3 0 7 2 ( 5 ) 1 . 3 0 1 6 ( 5 ) 1 3 l 2 8 ( 5 ) T e [ 1 ] - P r - T e [ 3 ] x 2 7 6 9 0 ( 4 ) 7 6 5 0 ( 4 ) 7 7 8 2 ( 4 ) T e [ 2 ] - P r - T e [ 2 ] x 2 8 0 8 2 ( 4 ) 8 0 7 2 ( 5 ) 8 0 8 8 ( 3 ) T e [ 2 ] - P r - T e [ 3 ] x 2 5 4 4 0 ( 5 ) 5 2 3 8 ( 5 ) 5 6 4 7 ( 5 ) T e [ 2 ] - P r - T e [ 3 ] x 2 5 4 7 4 ( 5 ) 5 2 6 2 ( 5 ) 5 6 8 5 ( 5 ) T e [ 3 ] - P r - T e [ 3 ] x 2 8 0 7 8 ( 4 ) 8 0 6 4 ( 5 ) 8 0 9 0 ( 5 ) P r - T e [ 1 ] - P r x 8 1 0 6 . 5 7 ( 4 ) 1 0 6 . 3 0 ( 5 ) 1 0 6 . 8 3 ( 5 ) P r - T e [ 1 ] - P r x 8 8 5 2 6 ( 3 ) 8 5 2 5 ( 2 ) 8 5 2 7 ( 2 ) P r - T e [ 1 ] - P r x 4 1 4 7 . 0 4 ( 4 ) 1 4 6 . 8 9 ( 2 ) 1 4 7 . 1 8 ( 2 ) P r - T e [ 2 ] - P r x 2 8 0 7 9 ( 3 ) 8 0 4 0 ( 5 ) 8 1 . 1 2 ( 5 ) P r - T e [ 2 ] - T e [ 3 ] x 4 “ 7 8 4 ( 6 ) l l 4 . l 8 ( 7 ) 1 2 0 . 4 8 ( 7 ) P r - T e [ 2 ] - T e [ 3 ] x 4 6 2 8 1 ( 3 ) 6 2 3 2 ( 3 ) 6 3 3 4 ( 3 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 9 0 8 5 ( 8 ) 8 6 5 9 ( 8 ) 9 5 2 3 ( 9 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 6 8 9 7 7 ( 6 ) 8 9 6 3 ( 5 ) 8 9 9 6 ( 7 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 7 . 1 8 ( 8 ) 1 7 5 . 0 4 ( 8 ) 1 7 9 . 7 2 ( 4 ) P r - T e [ 3 ] - P r x 2 8 0 7 8 ( 3 ) 8 0 6 4 ( 4 ) 8 0 9 0 ( 4 ) P r - T e [ 3 ] - T e [ 2 ] x 2 6 2 4 6 ( 4 ) 6 0 5 9 ( 4 ) 6 4 4 2 ( 4 ) P r - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 3 2 ( 4 ) 1 1 6 . 2 0 ( 4 ) 1 1 8 . 3 8 ( 4 ) P r - T e [ 3 ] - T e [ 2 ] x 2 6 3 2 5 ( 4 ) 6 1 8 0 ( 4 ) 6 4 7 1 ( 4 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 6 8 9 6 0 ( 7 ) 8 5 4 5 ( 7 ) 9 3 8 7 ( 8 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 7 . 3 1 ( 8 ) 1 7 5 . 2 3 ( 8 ) 1 7 9 . 7 7 ( 3 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 9 0 8 5 ( 7 ) 8 6 8 3 ( 7 ) 9 4 9 6 ( 8 ) 9 3 T a b l e 2 . 2 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N d T e 3 a t 3 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( l ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 1 4 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 6 ( 1 ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ' ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 0 ’ ( I ) ] R l S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f f i c i e n t T . . . a n d T m . . . c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e N d T e 3 5 2 7 3 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 c m ( 0 0 y ) 0 0 0 a = 4 . 3 4 3 3 ( 6 ) A , a = 9 0 ° b = 2 5 . 8 0 9 ( 4 ) A , B = 9 0 ° c = 4 . 3 5 3 8 ( 5 ) A , y = 9 0 ° 0 . 2 8 2 7 ( 3 ) e ’ 4 8 8 . 0 4 0 2 ) A 3 4 7 . 1 7 0 5 g / c m 3 2 8 . 0 0 4 m m " 8 6 4 0 . 3 4 x 0 . 2 3 x 0 . 0 1 m m 3 2 . 0 5 t o 2 9 . 1 4 0 - 5 < = h < = 5 , - 3 4 < = k < = 3 4 , - 6 < = l < = 5 , - 1 < = m < = 1 1 2 4 1 0 ( 1 8 6 5 m a i n + 4 3 4 0 s a t e l l i t e s ) 1 9 9 1 ( 6 8 5 m a i n + 1 3 0 1 s a t e l l i t e S ) [ R i m - 1 0 . 0 2 5 6 ] 9 8 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 1 9 9 1 / 0 / 3 8 1 . 5 9 R . . . = 0 . 0 2 5 9 , w R . . . = 0 . 0 8 9 9 R . “ = 0 . 0 4 3 1 , w R . . . = 0 . 1 0 1 9 R . . . = 0 . 0 1 7 2 , w R . . . = 0 . 0 6 5 3 R . “ = 0 . 0 1 7 4 , w R . u = 0 . 0 6 5 3 R . . . = 0 . 0 8 4 7 , w R . . . = 0 . 1 4 1 4 R . " = 0 . 2 0 1 9 , W K . " = 0 . 1 7 2 9 0 . 0 0 0 9 6 ( 7 ) 0 . 0 1 5 1 a n d 0 . 6 9 1 3 2 . 2 3 a n d - 1 9 5 e . A ' 3 R = Z | | F . | - | F . | | / 2 | F . | , w k = { 2 [ w ( | F . | 2 - | F . | 2 ) 2 ] / 2 [ w ( | l = . | ‘ ) ] ) ” 2 a n d w = 1 / ( 6 2 ( I ) + 0 . 0 0 1 6 1 2 ) 9 4 T a b l e 2 . 3 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r N d T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e x y 2 U . . . N d 0 9 2 4 9 1 6 9 2 ( 1 ) 2 5 4 9 6 ( 1 ) s i n , 1 0 0 - 1 ( 3 ) c o s , 1 5 3 ( 1 ) 0 ( 1 ) 0 T e [ 1 ] 0 9 2 0 2 ( 3 ) 2 9 5 6 ( 1 ) 2 5 4 9 6 ( 1 ) s i n , 1 0 0 - 4 ( 3 ) c o s , 1 6 ( 1 ) 0 ( 1 ) 0 T e [ 2 ] 0 9 2 6 4 ( 4 ) 7 0 3 ( 1 ) 7 5 4 9 9 ( 1 ) s i n , 1 0 0 - 6 ( 4 ) c o s , 1 - 2 3 0 ( 1 ) 8 ( 1 ) 0 T e [ 3 ] 0 9 2 0 9 ( 3 ) 4 2 9 5 ( 1 ) 7 5 4 9 9 ( 1 ) s i n , 1 0 0 2 0 ( 4 ) c o s , 1 1 9 1 ( 2 ) 0 ( 1 ) 0 ' U . q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 2 . 3 1 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r N d T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 N d 6 ( 1 ) 7 ( 1 ) 5 ( 1 ) - 1 ( 1 ) 0 0 T e [ 1 ] 6 ( 1 ) 7 ( 1 ) 6 ( 1 ) - 3 ( 1 ) 0 0 T e [ 2 ] 1 0 ( 1 ) 1 0 ( 1 ) 8 ( 1 ) 0 ( 1 ) 0 0 T e [ 3 ] 9 ( 1 ) 9 ( 1 ) 9 ( 1 ) 4 ( 1 ) 0 0 T a b l e 2 . 3 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N d T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e N d - T e [ 1 ] 3 . 2 6 1 8 ( 1 0 ) 3 . 2 6 0 5 ( 1 7 ) 3 . 2 6 3 2 ( 1 7 ) N d - T e [ 1 ] x 4 3 . 2 0 6 3 ( 1 2 ) 3 . 1 9 2 8 ( 1 2 ) 3 . 2 1 9 6 ( 1 2 ) N d - T e [ 2 ] x 2 3 . 3 5 4 4 ( 1 1 ) 3 . 3 3 9 3 ( 1 1 ) 3 . 3 7 1 7 ( 1 1 ) N d - T e [ 3 ] 3 . 3 4 5 1 ( 1 2 ) 3 . 3 0 8 0 ( 1 6 ) 3 . 3 8 3 2 ( 1 6 ) N d - T e [ 3 ] 3 . 3 5 0 7 ( 1 2 ) 3 . 3 1 0 0 ( 1 6 ) 3 . 3 9 0 8 ( 1 6 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 9 2 2 ( 1 9 ) 2 . 9 7 8 7 ( 1 6 ) 3 . 2 0 9 5 ( 1 7 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 5 9 8 ( 1 8 ) 2 . 9 4 2 0 ( 1 6 ) 3 . 1 7 8 6 ( 1 7 ) 9 5 T a b l e 2 . 3 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N d T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - N d — T e [ 1 ] x 8 7 3 5 2 ( 3 ) 7 3 3 5 ( 3 ) 7 3 6 9 ( 3 ) T e [ 1 ] - N d - T e [ 2 ] x 2 1 3 9 . 4 9 ( 3 ) 1 3 9 . 2 6 ( 4 ) 1 3 9 . 7 0 ( 5 ) T e [ 1 ] - N d - T e [ 3 ] x 2 1 3 9 . 6 3 ( 3 ) 1 3 9 . 1 8 ( 3 ) 1 4 0 . 0 8 ( 3 ) T e [ 1 ] - N d - T e [ 1 ] x 4 8 5 5 2 ( 3 ) 8 5 0 2 ( 3 ) 8 6 0 3 ( 3 ) T e [ 1 ] - N d - T e [ 1 ] x 4 8 5 2 5 ( 4 ) 8 5 2 1 ( 3 ) 8 5 2 9 ( 3 ) T e [ 1 ] - N d - T e [ 1 ] x 4 1 4 7 . 0 2 ( 3 ) 1 4 7 . 0 1 ( 3 ) 1 4 7 . 0 4 2 ( 1 8 ) T e [ 1 ] - N d - T e [ 2 ] x 2 7 7 8 2 ( 3 ) 7 5 8 5 ( 3 ) 7 8 8 0 ( 4 ) T e [ 1 ] - N d - T e [ 2 ] x 2 1 3 1 . 4 5 ( 4 ) 1 2 9 . 5 7 ( 4 ) 1 3 3 . 3 3 ( 4 ) T e [ 1 ] - N d - T e [ 3 ] x 4 7 7 . 1 5 ( 3 ) 7 6 7 5 ( 3 ) 7 7 5 4 ( 3 ) T e [ 1 ] - N d - T e [ 3 ] x 4 1 3 0 . 9 6 ( 4 ) 1 3 0 . 4 9 ( 4 ) 1 3 1 . 4 2 ( 3 ) ‘ T e [ 1 ] - N d - T e [ 2 ] x 2 7 6 7 0 ( 3 ) 7 5 5 0 ( 3 ) 7 7 8 7 ( 3 ) T e [ 1 ] - N d - T e [ 2 ] x 2 1 3 0 . 6 2 ( 4 ) 1 2 8 . 5 8 ( 4 ) l 3 2 . 6 4 ( 4 ) T e [ 2 ] - N d - T e [ 2 ] x 2 8 0 9 6 ( 3 ) 8 0 7 0 ( 4 ) 8 1 . 1 5 ( 4 ) T e [ 2 ] - N d - T e [ 3 ] x 2 5 4 9 6 ( 4 ) 5 3 2 0 ( 4 ) 5 6 7 8 ( 4 ) T e [ 2 ] - N d - T e [ 3 ] x 2 5 4 8 1 ( 4 ) 5 2 1 8 ( 4 ) 5 6 4 2 ( 4 ) T e [ 3 ] - N d - T e [ 3 ] x 2 8 0 8 8 ( 3 ) 8 0 8 3 ( 4 ) 8 0 9 1 ( 4 ) N d - T e [ 1 ] - N d x 8 1 0 6 . 4 8 ( 3 ) 1 0 6 . 1 7 ( 3 ) 1 0 6 . 7 8 ( 3 ) N d - T e [ 1 ] - N d x 8 8 5 4 9 ( 4 ) 8 5 2 3 ( 4 ) 8 5 . 7 4 ( 4 ) N d - T e [ 1 ] - N d x 4 1 4 7 . 0 2 ( 3 ) 1 4 6 . 8 9 9 ( 1 9 ) 1 4 7 . 1 5 2 ( 1 9 ) N d - T e [ 2 ] - N d x 2 8 0 9 3 ( 3 ) 8 0 4 5 ( 3 ) 8 1 8 5 ( 3 ) N d - T e [ 2 ] - T e [ 3 ] x 4 6 2 8 5 ( 3 ) 6 1 6 4 ( 2 ) 6 3 0 4 ( 2 ) N d - T e [ 2 ] - T e [ 3 ] x 2 1 1 6 . 7 9 ( 4 ) 1 1 3 . 6 8 ( 5 ) 1 1 9 . 8 8 ( 5 ) N d - T e [ 2 ] - T e [ 3 ] x 2 1 1 7 . 8 2 ( 4 ) 1 1 5 . 7 2 ( 5 ) 1 1 9 . 8 6 ( 5 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 6 8 9 6 0 ( 6 ) 8 5 4 9 ( 6 ) 9 3 8 0 ( 6 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 7 . 3 8 ( 6 ) 1 7 5 . 2 5 ( 6 ) 1 7 9 . 8 9 ( 6 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 9 0 8 4 ( 6 ) 8 7 0 3 ( 6 ) 9 4 7 9 ( 6 ) N d - T e [ 3 ] - N d x 2 8 0 . 8 7 8 ( 1 9 ) 8 0 8 3 ( 3 ) 8 0 9 1 ( 3 ) N d - T e [ 3 ] - T e [ 2 ] x 2 6 2 9 3 ( 3 ) 6 1 0 7 ( 3 ) 6 4 8 8 ( 3 ) N d - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 0 8 ( 3 ) 1 1 6 7 1 ( 3 ) 1 1 7 . 3 8 ( 3 ) N d - T e [ 3 ] - T e [ 2 ] x 2 6 2 6 7 ( 3 ) 6 1 . 4 2 ( 3 ) 6 3 9 3 ( 3 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 9 0 8 5 ( 6 ) 8 6 9 5 ( 5 ) 9 4 8 5 ( 6 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 6 8 9 7 7 ( 5 ) 8 9 5 6 ( 5 ) 9 0 1 3 ( 5 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 7 . 5 1 ( 6 ) 1 7 5 . 4 7 ( 6 ) 1 8 0 9 6 T a b l e 2 . 3 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r S m T e 3 a t 3 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 1 9 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( 1 ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f f i c i e n t T m . . . a n d T m . . . c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e S m T e 3 5 3 3 . 2 3 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c c z e m ( 0 0 y ) 0 0 0 a = 4 . 3 2 1 8 ( 6 ) A , a = 9 0 ° b = 2 5 . 6 0 9 ( 5 ) A , 1 3 = 9 0 ° c = 4 . 3 3 4 2 ( 8 ) A , y = 9 0 ° 0 . 2 8 7 4 ( 4 ) e ' 4 7 9 . 6 9 ( 1 4 ) A 3 4 7 . 3 8 0 g / e m 3 2 9 . 8 8 9 m m " 8 7 2 0 . 1 7 x 0 . 1 1 x 0 . 0 1 m m 3 2 . 0 8 t o 2 9 . 1 9 ° - 5 < = h < = 5 , - 3 4 < = k < = 3 4 , - 6 < = 1 < = 6 , - 1 < = m < = 1 6 5 9 9 ( 2 0 4 8 m a i n + 4 5 5 1 s a t e l l i t e s ) 1 9 3 7 ( 6 6 3 m a i n + 1 2 7 4 s a t e l l i t e S ) [ R i m = 0 . 0 2 8 5 ] 9 8 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 1 9 3 7 / 0 / 3 7 1 . 6 1 k . . . = 0 . 0 2 6 7 , w k . . . = 0 . 1 0 4 4 R . . . = 0 . 0 5 0 7 , w k . . . = 0 . 1 1 2 3 R . . . = 0 . 0 1 5 7 , w k . . . = 0 . 0 6 5 0 R . . . = 0 . 0 1 5 9 , w k . . . = 0 . 0 6 5 1 R . . . = 0 . 1 1 7 7 , w k . . . = 0 . 2 3 0 7 R . . . = 0 . 2 5 4 4 , w R . . . = 0 . 2 5 5 1 0 . 0 0 1 6 9 ( 8 ) 0 . 0 5 0 1 a n d 0 . 6 4 0 4 2 . 3 5 a n d - 2 . 3 3 e . A ' 3 R = 2 1 1 1 3 1 - 1 1 1 1 / Z I F o I , w R = { 2 1 w ( 1 1 = . 1 2 - 1 1 3 1 2 1 2 1 / 2 1 . 4 4 1 . 1 0 1 . 1 0 a n d w l / ( o ’ ( 1 ) + 0 . 0 0 1 6 1 2 ) 9 7 T a b l e 2 . 3 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r S m T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . l L a b e l W a v e x y z U . q S m 0 9 4 4 9 1 6 9 4 ( 1 ) 2 5 4 9 7 ( 1 ) s i n , 1 0 0 - 1 8 ( 4 ) c o s , 1 4 2 ( 1 ) 6 ( 1 ) 0 T e [ 1 ] 0 9 3 9 9 ( 5 ) 2 9 5 2 ( 1 ) 2 5 4 9 6 ( 1 ) s i n , 1 0 0 - 6 ( 4 ) c o s , 1 4 ( 1 ) 0 ( 1 ) 0 T e [ 2 ] 0 9 3 9 4 ( 6 ) 7 0 8 ( 1 ) 7 5 4 9 1 0 ( 1 ) s i n , 1 O 0 1 4 ( 5 ) c o s , 1 - 1 4 4 ( 2 ) - 2 ( 1 ) 0 T e [ 3 ] 0 4 3 5 4 ( 5 ) 7 0 9 ( 1 ) 2 5 4 9 9 ( 1 ) s i n , 1 0 0 1 3 ( 5 ) c o s , 1 1 8 7 ( 2 ) 0 ( 1 ) 0 ‘ U . q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 2 . 3 6 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r S m T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 S m 7 ( 1 ) 7 ( 1 ) 7 ( 1 ) 1 ( 1 ) 0 0 T e [ 1 ] 6 ( 1 ) 6 ( 1 ) 7 ( 1 ) 1 ( 1 ) 0 0 T e [ 2 ] 1 1 ( 1 ) 1 0 ( 1 ) 9 ( 1 ) 2 ( 1 ) 0 0 T e [ 3 ] 8 ( 1 ) 1 0 ( 1 ) 9 ( 1 ) 3 ( 1 ) 0 0 T a b l e 2 . 3 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r S m T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e S m - T e [ 1 ] 3 . 2 2 1 6 ( 1 3 ) 3 . 2 0 7 ( 2 ) 3 . 2 3 6 ( 2 ) S m - T e [ 1 ] x 4 3 . 1 9 1 7 ( 1 8 ) 3 . 1 8 3 9 ( 1 9 ) 3 . 1 9 9 6 ( 1 9 ) S m - T e [ 2 ] x 2 3 . 3 2 8 9 ( 1 6 ) 3 . 3 1 1 7 ( 1 6 ) 3 . 3 4 5 5 ( 1 6 ) S m - T e [ 3 ] 3 . 3 3 5 9 ( 1 9 ) 3 . 3 0 6 ( 2 ) 3 . 3 6 7 ( 2 ) S m - T e [ 3 ] 3 . 3 1 0 7 ( 1 9 ) 3 . 2 5 9 ( 2 ) 3 . 3 6 2 ( 2 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 7 3 ( 3 ) 2 . 9 8 6 ( 2 ) 3 . 1 6 2 ( 3 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 5 0 ( 3 ) 2 . 9 5 5 ( 2 ) 3 . 1 4 4 ( 3 ) 9 8 T a b l e 2 . 3 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r S m T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - S m - T e [ 1 ] x 8 7 3 5 2 ( 4 ) 7 3 4 1 ( 4 ) 7 3 6 3 ( 4 ) T e [ 1 ] - S m - T e [ 2 ] x 2 1 3 9 . 3 6 ( 4 ) 1 3 9 . 0 5 ( 5 ) l 3 9 . 6 7 ( 6 ) T e [ 1 ] - S m - T e [ 3 ] 1 3 9 . 1 8 ( 5 ) 1 3 8 . 4 9 ( 5 ) 1 3 9 . 8 7 ( 5 ) T e [ 1 ] - S m - T e [ 3 ] 1 3 9 . 7 1 ( 5 ) 1 3 9 . 3 3 ( 5 ) 1 4 0 . 1 0 ( 5 ) T e [ 1 ] - S m - T e [ 1 ] x 4 8 5 5 3 ( 4 ) 8 5 2 3 ( 5 ) 8 5 8 2 ( 5 ) T e [ 1 ] - S m - T e [ 1 ] x 4 8 5 2 4 ( 5 ) 8 5 0 1 ( 5 ) 8 5 4 7 ( 5 ) T e [ 1 ] - S m - T e [ 1 ] x 4 1 4 7 . 0 6 ( 4 ) 1 4 6 . 5 7 ( 5 ) 1 4 7 . 5 4 ( 5 ) T e [ 1 ] - S m - T e [ 2 ] x 4 7 6 8 4 ( 5 ) 7 6 0 1 ( 4 ) 7 7 6 9 ( 4 ) T e [ 1 ] - S m - T e [ 2 ] x 4 1 3 l . 0 4 ( 5 ) 1 2 9 . 5 0 ( 5 ) 1 3 2 . 6 1 ( 5 ) T e [ 1 ] - S m — T e [ 3 ] x 2 7 6 8 2 ( 4 ) 7 6 4 7 ( 5 ) 7 7 . 1 7 ( 5 ) T e [ 1 ] - S m - T e [ 3 ] x 4 l 3 0 . 8 6 ( 5 ) 1 3 0 . 5 3 ( 5 ) 1 3 1 . 1 9 ( 5 ) T e [ 1 ] - S m - T e [ 3 ] x 2 7 7 . 1 9 ( 4 ) 7 6 6 3 ( 4 ) 7 7 . 7 7 ( 4 ) T e [ 2 ] - S m - T e [ 2 ] x 2 8 1 2 5 ( 4 ) 8 0 9 7 ( 5 ) 8 1 5 0 ( 5 ) T e [ 2 ] - S m - T e [ 3 ] x 4 5 4 9 0 ( 5 ) 5 3 3 5 ( 5 ) 5 6 4 9 ( 5 ) T e [ 3 ] - S m - T e [ 3 ] x 2 8 1 . 1 1 ( 5 ) 8 0 8 0 ( 6 ) 8 1 . 4 1 ( 6 ) S m - T e [ 1 ] - S m x 8 1 0 6 . 4 8 ( 5 ) 1 0 6 . 2 4 ( 4 ) 1 0 6 . 7 2 ( 5 ) S m - T e [ 1 ] - S m x 4 8 5 5 5 ( 5 ) 8 5 4 2 ( 6 ) 8 5 6 8 ( 6 ) S m - T e [ 1 ] - S m x 4 8 5 2 4 ( 3 ) 8 5 0 1 ( 3 ) 8 5 4 7 ( 3 ) S m - T e [ 1 ] - S m x 4 1 4 7 . 0 6 ( 4 ) 1 4 6 . 7 7 ( 6 ) 1 4 7 . 3 4 ( 6 ) S m - T e [ 2 ] - S m x 2 8 1 2 4 ( 4 ) 8 0 7 7 ( 5 ) 8 1 6 9 ( 5 ) S m - T e [ 2 ] - T e [ 3 ] x 2 6 2 6 5 ( 4 ) 6 2 2 8 ( 4 ) 6 3 0 6 ( 4 ) S m - T e [ 2 ] - T e [ 3 ] x 4 1 1 7 . 3 4 ( 6 ) 1 1 5 . 7 2 ( 7 ) 1 1 8 . 9 4 ( 8 ) S m - T e [ 2 ] - T e [ 3 ] x 2 6 2 8 5 ( 4 ) 6 2 0 7 ( 4 ) 6 2 . 6 5 ( 4 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 6 8 9 7 7 ( 9 ) 8 6 7 2 ( 8 ) 9 2 8 6 ( 9 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 8 . 0 9 ( 9 ) 1 7 6 . 5 6 ( 9 ) 1 7 9 . 9 0 ( 5 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 9 0 6 6 ( 9 ) 8 7 8 1 ( 8 ) 9 3 5 9 ( 9 ) S m - T e [ 3 ] - S m x 2 8 1 . 1 1 ( 3 ) 8 0 8 0 ( 5 ) 8 1 . 4 1 ( 5 ) S m - T e [ 3 ] - T e [ 2 ] x 2 6 2 9 7 ( 5 ) 6 1 . 7 6 ( 4 ) 6 4 2 3 ( 5 ) S m - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 2 8 ( 5 ) 1 1 6 . 6 7 ( 4 ) 1 1 7 . 8 9 ( 4 ) S m - T e [ 3 ] - T e [ 2 ] x 2 6 2 4 5 ( 5 ) 6 0 9 4 ( 5 ) 6 3 9 5 ( 5 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 9 0 6 4 ( 8 ) 8 7 . 6 4 ( 8 ) 9 3 7 8 ( 9 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 6 8 9 7 8 ( 7 ) 8 9 6 3 ( 6 ) 8 9 8 6 ( 6 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 7 . 9 6 ( 9 ) 1 7 6 . 3 8 ( 9 ) 1 7 9 . 9 1 ( 4 ) 9 9 T a b l e 2 . 3 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r G d T e 3 a t 3 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( l ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 0 9 0 R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 6 ( 1 ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 6 ( I ) ] R 1 s t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T . . . a n d T . . . c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e G d T e 3 5 4 0 3 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 c m ( 0 0 y ) 0 0 0 a = 4 . 3 0 8 3 ( 4 ) A , a = 9 0 ° b = 2 5 . 5 2 8 ( 2 ) A , B = 9 0 ° c = 4 . 3 1 5 4 ( 5 ) A , y = 9 0 ° 0 . 2 9 1 6 ( 3 ) e ‘ 4 7 4 . 6 1 ( 8 ) A 3 4 7 . 5 5 5 6 g / c m 3 3 1 . 8 2 1 m m ' 1 8 8 0 0 . 1 1 x 0 . 1 0 x 0 . 0 1 m m 3 2 . 1 0 t o 2 9 . 0 9 ° - 5 < = h < = 5 , - 3 4 < = k < = 3 4 , - 6 < = l < = 6 , - 1 < = m < = 1 6 8 5 1 ( 2 2 4 6 m a i n + 4 6 0 5 s a t e l l i t e s ) 1 9 3 2 ( 6 8 2 m a i n + 1 2 5 0 s a t e l l i t e S ) [ R i m = 0 . 0 8 9 8 ] 9 9 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 1 9 3 2 / O / 3 9 1 . 4 7 R . . . = 0 . 0 4 0 6 , w R . . . = 0 . 1 0 2 5 R . . . = 0 . 0 6 5 2 , w R . . . = 0 . 1 0 8 1 R . . . = 0 . 0 3 7 6 , w R . . . = 0 . 0 9 9 1 R . . . = 0 . 0 3 7 9 , w R . . . = 0 . 0 9 9 4 R . . . = 0 . 0 8 6 7 , w R . . . = 0 . 1 5 1 6 R . . . = 0 . 2 9 0 7 , w R . . . = 0 . 2 0 9 5 0 . 0 0 0 2 0 ( 5 ) 0 . 0 5 9 0 a n d 0 . 8 1 8 8 2 . 6 2 a n d - 2 . 1 0 e . A ' 3 R = l e F o I - l F e l l / X l F o l . w R = { E l m / ( I 1 3 1 2 - I F c | 2 ) 2 ] / ‘ Z [ \ ? V ( l 1 “ e | 4 ) l } " 2 a n d W = 1 / ( 6 2 ( N O - 0 0 1 6 1 ? ) 1 0 0 T a b l e 2 . 4 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r G d T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e x y 2 U . . . G d 0 9 0 0 0 1 6 9 6 ( 1 ) 2 5 4 9 1 1 ( 1 ) s i n , 1 O 0 2 ( 3 ) c o s , 1 - 4 0 ( 1 ) 0 ( 1 ) 0 T e [ 1 ] 0 8 9 8 9 ( 5 ) 2 9 4 8 ( 1 ) 2 5 4 9 1 0 ( 1 ) s i n , 1 0 0 - 8 ( 5 ) c o s , 1 - 5 ( 2 ) 0 ( 1 ) 0 T e [ 2 ] 0 9 0 1 5 ( 5 ) 7 1 1 ( 1 ) 7 5 4 9 1 4 ( 1 ) s i n , 1 0 0 5 ( 5 ) c o s , 1 1 5 0 ( 4 ) 9 ( 1 ) 0 T e [ 3 ] 0 4 0 8 2 ( 5 ) 7 1 2 ( 1 ) 2 5 4 9 1 3 ( 1 ) s i n , 1 0 0 4 0 ( 5 ) c o s , 1 - 1 3 2 ( 4 ) 0 ( 1 ) 0 # U . . . i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 2 . 4 1 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r G d T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 G d 1 0 ( 1 ) 1 6 ( 1 ) 6 ( 1 ) 0 ( 1 ) 0 0 T e [ 1 ] 9 ( 1 ) 1 5 ( 1 ) 6 ( 1 ) 3 ( 1 ) 0 0 T e [ 2 ] 1 4 ( 1 ) 1 8 ( 1 ) 8 ( 1 ) - 3 ( 1 ) 0 0 T e [ 3 ] 1 3 ( 1 ) 1 9 ( 1 ) 8 ( 1 ) - 1 ( 1 ) 0 0 T a b l e 2 . 4 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r G d T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e G d - T e [ l ] 3 . 1 9 5 1 ( 1 8 ) 3 . 1 9 5 ( 3 ) 3 . 1 9 6 ( 3 ) G d - T e [ 1 ] x 2 3 . 1 8 4 7 ( 1 8 ) 3 . 1 7 1 9 ( 1 9 ) 3 . 1 9 7 8 ( 1 9 ) G d - T e [ 1 ] x 2 3 . 1 7 8 4 ( 1 8 ) 3 . 1 6 9 6 ( 1 7 ) 3 . 1 8 7 1 ( 1 7 ) G d - T e [ 2 ] x 2 3 . 3 1 4 6 ( 1 8 ) 3 . 2 9 9 ( 2 ) 3 . 3 3 1 ( 2 ) G d - T e [ 3 ] 3 . 2 8 7 ( 2 ) 3 . 2 6 1 ( 3 ) 3 . 3 1 3 ( 3 ) G d - T e [ 3 ] 3 . 3 3 2 ( 2 ) 3 . 3 0 7 ( 3 ) 3 . 3 5 9 ( 3 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 3 0 ( 3 ) 2 . 9 4 6 ( 2 ) 3 . 1 1 3 ( 3 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 6 9 ( 3 ) 2 . 9 9 9 ( 2 ) 3 . 1 4 2 ( 3 ) 1 0 1 T a b l e 2 . 4 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r G d T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - G d - T e [ 1 ] x 8 7 3 3 5 ( 4 ) 7 3 2 3 ( 4 ) 7 3 4 8 ( 4 ) T e [ 1 ] - G d - T e [ 2 ] x 2 1 3 9 . 3 6 ( 5 ) 1 3 9 . 0 4 ( 5 ) 1 3 9 . 6 7 ( 5 ) T e [ 1 ] - G d - T e [ 3 ] x 2 1 3 9 . 0 2 ( 5 ) 1 3 8 . 7 7 ( 5 ) 1 3 9 . 2 8 ( 5 ) T e [ 1 ] - G d - T e [ 1 ] x 8 8 5 8 0 ( 5 ) 8 5 0 2 ( 5 ) 8 5 5 8 ( 5 ) T e [ 1 ] - G d - T e [ 1 ] x 4 1 4 6 . 7 9 ( 5 ) 1 4 6 . 7 7 ( 5 ) l 4 6 8 2 ( 4 ) T e [ 1 ] - G d - T e [ 2 ] x 4 7 7 . 1 2 ( 5 ) 7 6 4 0 ( 5 ) 7 7 8 2 ( 5 ) T e [ 1 ] - G d - T e [ 2 ] x 4 l 3 1 2 3 ( 5 ) 1 2 9 . 8 1 ( 5 ) 1 3 2 . 6 5 ( 5 ) T e [ 1 ] - G d - T e [ 3 ] x 2 7 7 8 6 ( 5 ) 7 7 0 5 ( 4 ) 7 7 . 6 7 ( 4 ) T e [ 1 ] - G d - T e [ 3 ] x 2 1 3 1 . 3 4 ( 5 ) l 3 0 9 8 ( 5 ) 1 3 1 . 7 0 ( 5 ) T e [ 1 ] - G d - T e [ 3 ] x 2 1 3 0 . 8 9 ( 6 ) 1 3 0 . 4 8 ( 6 ) 1 3 1 . 2 9 ( 6 ) T e [ 1 ] - G d - T e [ 3 ] x 2 7 6 7 9 ( 5 ) 7 6 4 7 ( 5 ) 7 7 . 1 0 ( 5 ) T e [ 2 ] - G d - T e [ 2 ] x 2 8 1 2 4 ( 5 ) 8 0 8 9 ( 6 ) 8 1 5 7 ( 6 ) T e [ 2 ] - G d - T e [ 3 ] x 2 5 4 6 4 ( 5 ) 5 3 0 4 ( 5 ) 5 6 2 2 ( 5 ) T e [ 2 ] - G d - T e [ 3 ] x 2 5 5 0 0 ( 5 ) 5 3 9 5 ( 5 ) 5 6 0 8 ( 5 ) T e [ 3 ] - G d - T e [ 3 ] x 2 8 1 2 0 ( 5 ) 8 1 . 1 9 ( 7 ) 8 1 2 1 ( 4 ) G d - T e [ 1 ] - G d x 8 1 0 6 . 6 8 ( 5 ) 1 0 6 . 4 6 ( 6 ) 1 0 6 . 9 0 ( 6 ) G d - T e [ 1 ] - G d x 8 8 5 5 1 ( 5 ) 8 5 3 4 ( 6 ) 8 5 6 8 ( 6 ) G d - T e [ 1 ] - G d x 4 1 4 6 . 8 0 ( 5 ) 1 4 6 . 7 0 ( 3 ) 1 4 6 . 8 9 ( 3 ) G d - T e [ 2 ] - G d x 2 8 1 2 3 ( 4 ) 8 0 7 2 ( 6 ) 8 1 . 7 2 ( 6 ) G d - T e [ 2 ] - T e [ 3 ] x 4 6 2 2 1 ( 4 ) 6 1 9 3 ( 4 ) 6 2 5 1 ( 4 ) G d - T e [ 2 ] - T e [ 3 ] x 4 1 1 7 . 4 8 ( 6 ) 1 1 6 . 3 4 ( 8 ) 1 1 8 . 6 0 ( 8 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 9 0 9 0 ( 8 ) 8 8 6 0 ( 9 ) 9 3 2 5 ( 9 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 8 9 8 6 ( 6 ) 8 9 4 8 ( 5 ) 9 0 2 8 ( 6 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 8 . 1 7 ( 8 ) 1 7 6 . 4 4 ( 9 ) 1 8 0 T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 8 9 8 7 ( 8 ) 8 6 4 2 ( 8 ) 9 2 8 6 ( 9 ) G d - T e [ 3 ] - G d x 2 8 1 2 0 ( 3 ) 8 1 . 1 9 ( 6 ) 8 1 2 1 ( 2 ) G d - T e [ 3 ] - T e [ 2 ] x 2 6 2 2 1 ( 5 ) 6 1 . 4 3 ( 5 ) 6 2 9 8 ( 5 ) G d - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 4 8 ( 5 ) 1 1 7 . 2 1 ( 5 ) 1 1 7 . 7 9 ( 5 ) G d - T e [ 3 ] - T e [ 2 ] x 2 6 3 1 5 ( 5 ) 6 1 . 7 6 ( 4 ) 6 4 6 0 ( 5 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 8 9 8 9 ( 8 ) 8 6 8 1 ( 8 ) 9 1 9 7 ( 9 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 8 9 8 6 ( 6 ) 8 9 4 8 ( 7 ) 9 0 2 8 ( 8 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 8 . 2 4 ( 8 ) 1 7 6 . 5 9 ( 9 ) 1 8 0 T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 9 0 8 8 ( 8 ) 8 8 8 7 ( 8 ) 9 3 4 7 ( 9 ) 1 0 2 T a b l e 2 . 4 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r T b T e 3 a t 3 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 0 9 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( 1 ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R l S t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 s t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T . . . a n d T . . . c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e T b T e 3 5 4 1 . 7 3 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 c m ( 0 0 y ) 0 0 0 a = 4 . 2 9 9 5 ( 8 ) A , a = 9 0 ° b = 2 5 . 4 2 0 ( 6 ) A , 1 3 = 9 0 ° c = 4 . 3 0 7 8 ( 9 ) A , y = 9 0 0 0 . 2 9 5 7 ( 5 ) e ‘ 4 7 0 . 8 2 ( 1 7 ) A 3 4 7 . 6 4 0 g / c m 3 3 3 . 1 1 m m " 8 8 4 0 . 2 8 x 0 . 2 0 x 0 . 0 3 m m 3 2 . 1 2 t o 2 9 . 0 9 ° - 5 < = h < = 5 , - 3 4 < = k < = 3 4 , - 6 < = l < = 6 , - 1 < = m < = 1 6 0 6 1 ( 1 8 8 6 m a i n + 4 1 7 5 s a t e l l i t e s ) 1 9 1 2 ( 6 6 4 m a i n + 1 2 4 8 s a t e l l i t e s ) [ R i n 1 = 0 . 0 9 5 3 ] 9 9 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 1 9 1 2 / 0 / 3 9 2 . 3 2 k . . . = 0 . 0 6 8 0 , w R . . . = 0 . 1 6 5 8 R . . . = 0 . 0 9 3 1 , w k . . . = 0 . 1 7 1 1 R . . . = 0 . 0 6 4 7 , w k . . . = 0 . 1 6 4 6 R . . . = 0 . 0 6 4 8 , w k . . . = 0 . 1 6 4 6 R . . . = 0 . 1 3 4 6 , w k . . . = 0 . 1 9 5 9 R . . . = 0 . 3 7 1 7 , w k . . . = 0 . 2 9 2 5 0 . 0 0 0 9 3 ( 9 ) 0 . 0 2 8 6 a n d 0 . 3 1 9 8 7 . 8 0 a n d - 5 . 9 3 e . A ' 3 R = 2 1 1 F . 1 - 1 F . 1 1 / 2 1 F . 1 . w R = { 2 1 w ( 1 1 = . 1 2 - 1 1 7 . 1 7 1 2 ] / 2 1 w ( 1 F . 1 ‘ ) 1 } " 2 a n d w = 1 / ( o z ( 1 ) + 0 . 0 0 1 6 1 2 ) 1 0 3 T a b l e 2 . 4 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r T b T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . l L a b e l W a v e x y 2 U . . . T b 0 9 0 0 0 1 6 9 7 ( 1 ) 2 5 4 9 1 0 ( 1 ) s i n , 1 0 0 - 1 3 ( 7 ) c o s , 1 2 6 ( 2 ) 6 ( 1 ) 0 T e [ 1 ] 0 9 0 1 4 ( 7 ) 2 9 4 8 ( 1 ) 2 5 4 9 9 ( 1 ) s i n , 1 0 0 9 ( 9 ) c o s , 1 2 ( 2 ) - 1 ( 1 ) 0 T e [ 2 ] 0 9 0 4 3 ( 7 ) 7 1 4 ( 1 ) 7 5 4 9 1 2 ( 1 ) s i n , 1 0 0 9 ( 9 ) c o s , 1 - 1 0 4 ( 5 ) 0 ( 1 ) 0 T e [ 3 ] 0 9 0 2 6 ( 7 ) 4 2 8 5 ( 1 ) 7 5 4 9 1 2 ( 1 ) s i n , 1 0 0 0 ( 9 ) c o s , 1 8 3 ( 5 ) - l ( 1 ) 0 " U . ( . i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 2 . 4 6 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r T b T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 T b 6 ( 1 ) 1 8 ( 1 ) 6 ( 1 ) 8 ( 1 ) 0 0 T e [ 1 ] 4 ( 1 ) 1 8 ( 1 ) 5 ( 1 ) - 1 ( 1 ) 0 0 T e [ 2 ] 7 ( 1 ) 2 2 ( 1 ) 7 ( 1 ) 2 ( 1 ) 0 0 T e [ 3 ] 7 ( 1 ) 2 1 ( 1 ) 8 ( 1 ) 2 ( 1 ) 0 0 T a b l e 2 . 4 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r T b T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e T b - T e [ 1 ] x 3 3 . 1 7 8 ( 2 ) 3 . 1 6 1 ( 4 ) 3 . 1 9 6 ( 4 ) T b - T e [ 1 ] x 2 3 . 1 7 0 ( 3 ) 3 . 1 6 2 ( 4 ) 3 . 1 7 8 ( 4 ) T b - T e [ 2 ] x 2 3 . 2 9 9 ( 3 ) 3 . 2 8 5 ( 3 ) 3 . 3 1 2 ( 3 ) T b - T e [ 3 ] 3 . 2 8 8 ( 3 ) 3 . 2 8 1 ( 4 ) 3 . 2 9 5 ( 4 ) T b - T e [ 3 ] 3 . 3 0 3 ( 3 ) 3 . 2 7 7 ( 4 ) 3 . 3 2 8 ( 4 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 4 8 ( 4 ) 2 . 9 9 9 ( 4 ) 3 . 0 9 9 ( 4 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 3 9 ( 4 ) 2 . 9 8 7 ( 4 ) 3 . 0 9 0 ( 4 ) 1 0 4 T a b l e 2 . 4 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r T b T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] — T b — T e [ 1 ] x 8 7 3 5 3 ( 6 ) 7 3 8 9 ( 6 ) 7 3 6 6 ( 6 ) T e [ 1 ] - T b - T e [ 2 ] x 2 1 3 9 2 3 ( 9 ) 1 3 8 . 9 1 ( 1 1 ) 1 3 9 . 5 3 ( 1 1 ) T e [ 1 ] - T b - T e [ 3 ] 1 3 9 . 5 4 ( 7 ) 1 3 9 . 2 6 ( 8 ) 1 3 9 . 8 1 ( 8 ) T e [ 1 ] - T b - T e [ 3 ] 1 3 9 . 0 2 ( 7 ) 1 3 9 . 0 2 ( 7 ) 1 3 9 . 0 3 ( 8 ) T e [ 1 ] - T b - T e [ 1 ] x 8 8 5 5 9 ( 8 ) 8 5 5 5 ( 8 ) 8 5 6 4 ( 8 ) T e [ 1 ] - T b - T e [ 1 ] x 4 1 4 6 . 9 5 ( 6 ) 1 4 6 . 5 0 ( 8 ) 1 4 7 . 3 8 ( 8 ) T e [ 1 ] - T b - T e [ 2 ] x 4 7 7 0 4 ( 8 ) 7 6 4 4 ( 7 ) 7 7 6 6 ( 7 ) T e [ 1 ] - T b - T e [ 2 ] x 2 1 3 1 . 5 4 ( 8 ) 1 3 0 . 4 5 ( 7 ) 1 3 2 . 6 4 ( 7 ) T e [ 1 ] - T b - T e [ 3 ] x 4 7 7 0 9 ( 7 ) 7 6 9 8 ( 8 ) 7 7 2 0 ( 8 ) T e [ 1 ] - T b - T e [ 3 ] x 4 1 3 1 . 1 4 ( 9 ) 1 3 0 9 2 ( 1 0 ) 1 3 1 . 3 5 ( 1 0 ) T e [ 1 ] - T b - T e [ 2 ] x 2 1 3 0 . 8 4 ( 8 ) 1 3 0 . 1 0 ( 7 ) 1 3 1 . 5 6 ( 7 ) T e [ 2 ] - T b - T e [ 2 ] x 2 8 1 5 3 ( 7 ) 8 1 2 9 ( 8 ) 8 1 . 7 7 ( 8 ) T e [ 2 ] - T b - T e [ 3 ] x 4 5 5 1 3 ( 8 ) 5 4 1 4 ( 8 ) 5 6 1 5 ( 8 ) T e [ 3 ] - T b — T e [ 3 ] x 2 8 1 . 4 4 ( 7 ) 8 1 . 1 6 ( 9 ) 8 1 . 7 2 ( 9 ) T b - T e [ 1 ] - T b x 8 1 0 6 . 4 3 ( 8 ) 1 0 6 . 1 1 ( 9 ) 1 0 6 . 7 5 ( 9 ) T b - T e [ 1 ] - T b x 8 8 5 3 3 ( 9 ) 8 5 2 6 ( 9 ) 8 5 8 9 ( 9 ) T b - T e [ 1 ] - T b x 4 1 4 6 . 9 4 ( 7 ) 1 4 6 . 7 8 ( 1 0 ) 1 4 7 . 1 0 ( 1 0 ) T b - T e [ 2 ] - T b x 2 8 1 5 3 ( 7 ) 8 1 2 1 ( 9 ) 8 1 8 3 ( 1 0 ) T b - T e [ 2 ] - T e [ 3 ] x 2 6 2 2 5 ( 6 ) 6 1 9 0 ( 6 ) 6 2 5 9 ( 6 ) T b - T e [ 2 ] - T e [ 3 ] x 2 1 1 7 . 2 1 ( 1 0 ) 1 1 6 . l 4 ( 1 2 ) 1 1 8 2 6 ( 1 2 ) T b - T e [ 2 ] - T e [ 3 ] x 2 6 2 6 6 ( 6 ) 6 2 4 7 ( 6 ) 6 2 8 4 ( 6 ) T b - T e [ 2 ] - T e [ 3 ] x 2 1 1 7 . 8 2 ( 1 0 ) 1 1 6 5 3 ( 1 2 ) 1 1 9 . l l ( 1 2 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 8 8 9 9 4 ( 1 3 ) 8 8 . 1 9 ( 1 3 ) 9 1 . 7 0 ( 1 4 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 8 . 8 8 ( 1 4 ) 1 7 8 . 0 4 ( 1 3 ) 1 8 0 T b - T e [ 3 ] - T b x 2 8 1 . 4 4 ( 5 ) 8 1 . 1 6 ( 9 ) 8 1 . 7 2 ( 9 ) T b - T e [ 3 ] — T e [ 2 ] x 4 6 2 5 3 ( 7 ) 6 1 9 5 ( 7 ) 6 3 1 4 ( 7 ) T b - T e [ 3 ] - T e [ 2 ] x 4 l 1 7 5 8 ( 8 ) 1 1 7 . 1 5 ( 7 ) 1 1 8 . 0 2 ( 7 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 8 9 0 8 2 ( 1 3 ) 8 8 . 7 4 ( 1 3 ) 9 1 9 2 ( 1 4 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 8 . 9 4 ( 1 4 ) 1 7 8 . 1 4 ( l 3 ) 1 8 0 1 0 5 T a b l e 2 . 4 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r D y T e 3 a t 3 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 8 . 9 6 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ’ ( 1 ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f f i c i e n t T . . . a n d T m . . . c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e D y T e 3 5 4 5 . 3 3 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 c m ( 0 0 y ) 0 0 0 a = 4 . 2 9 9 4 ( 6 ) A , a = 9 0 0 b = 2 5 . 3 5 3 ( 5 ) A , B = 9 0 0 c = 4 . 2 9 3 0 ( 6 ) A , y = 9 0 ° 0 . 2 9 8 4 ( 3 ) e ' 4 6 7 . 9 5 ( 1 3 ) A 3 4 7 . 7 3 8 g / e m 3 3 4 . 1 3 9 m m " 8 8 8 0 . 2 3 x 0 . 1 5 x 0 . 0 3 m m 3 2 . 1 4 t o 2 8 . 9 6 ° - 5 < = h < = 5 , - 3 4 < = k < = 3 4 , - 5 < = l < = 6 , - 1 < = m < = 1 5 8 3 5 ( 1 6 4 3 m a i n + 4 1 9 2 s a t e l l i t e s ) 1 8 5 9 ( 6 1 4 m a i n + 1 2 4 5 s a t e l l i t e S ) [ R i m = 0 . 0 3 6 1 ] 9 7 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 1 8 5 9 / 0 / 3 7 1 . 6 4 k . . . = 0 . 0 3 0 8 , w k . . . = 0 . 1 0 7 0 R . . . = 0 . 0 6 5 5 , w R . . . = 0 . 1 2 2 8 R . . . = 0 . 0 2 4 4 , w k . . . = 0 . 0 9 9 6 R . . . = 0 . 0 2 4 5 , w k . . . = 0 . 0 9 9 6 R . . . = 0 . 2 0 3 2 , w R . . . = 0 . 3 5 3 5 R . . . = 0 . 4 9 1 1 , w R . . . = 0 . 5 5 1 7 0 . 0 0 1 1 5 ( 1 0 ) 0 . 0 2 3 4 a n d 0 . 3 0 7 9 2 . 8 1 a n d - 2 4 0 e . A ' 3 R = 2 | | F . | - | F . | | / > : | 1 = . 1 , w k = { 2 : [ w ( | 1 = . | 2 - | F . | 2 ) 2 ] / 2 [ w ( | F . | 4 ) ] } ” 2 a n d w = 1 / ( o z ( 1 ) + 0 . 0 0 1 6 1 2 ) 1 0 6 T a b l e 2 . 5 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r D y T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . L a b e l W a v e x y 2 U . . . D y 0 9 4 4 9 1 6 9 9 ( 1 ) 2 5 4 9 7 ( 1 ) s i n , 1 0 0 1 3 ( 4 ) c o s , 1 1 6 ( 2 ) 5 ( 1 ) 0 T e [ 1 ] 0 9 3 6 6 ( 3 ) 2 9 4 6 ( 1 ) 2 5 4 9 6 ( 1 ) s i n , 1 0 0 - 1 2 ( 5 ) c o s , 1 - 9 ( 2 ) - l ( 1 ) 0 T e [ 2 ] 0 9 4 0 7 ( 4 ) 7 1 5 ( 1 ) 7 5 4 9 9 ( 1 ) s i n , 1 0 0 9 ( 5 ) c o s , 1 - 6 7 ( 5 ) 1 ( 1 ) 0 T e [ 3 ] 0 4 4 5 0 ( 4 ) 7 1 6 ( 1 ) 2 5 4 9 9 ( 1 ) s i n , 1 0 0 - 9 ( 5 ) c o s , 1 5 7 ( 5 ) 0 ( 1 ) 0 ' U . . . i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 2 . 5 1 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r D y T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 D y 8 ( 1 ) 6 ( 1 ) 7 ( 1 ) 0 ( 1 ) 0 0 T e [ 1 ] 7 ( 1 ) 5 ( 1 ) 6 ( 1 ) 3 ( 1 ) 0 0 T e [ 2 ] 1 0 ( 1 ) 1 0 ( 1 ) 9 ( 1 ) - 1 ( 1 ) 0 0 T e [ 3 ] 1 0 ( 1 ) 9 ( 1 ) 9 ( 1 ) - 1 ( 1 ) 0 0 T a b l e 2 . 5 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r D y T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e D y - T e [ 1 ] 3 . 1 6 1 6 ( 1 2 ) 3 . 1 4 8 ( 2 ) 3 . 1 7 6 ( 2 ) D y - T e [ 1 ] x 2 3 . 1 7 8 2 ( 1 6 ) 3 . 1 7 0 0 ( 1 7 ) 3 . 1 8 6 3 ( 1 7 ) D y - T e [ 1 ] x 2 3 . 1 5 8 0 ( 1 6 ) 3 . 1 4 5 2 ( 1 8 ) 3 . 1 7 1 0 ( 1 8 ) D y - T e [ 2 ] x 2 3 . 2 9 0 7 ( 1 6 ) 3 . 2 8 0 1 ( 1 4 ) 3 . 3 0 1 2 ( 1 4 ) D y - T e [ 3 ] 3 . 2 7 7 1 ( 1 8 ) 3 . 2 7 5 ( 3 ) 3 . 2 7 9 ( 3 ) D y - T e [ 3 ] 3 . 3 0 5 6 ( 1 8 ) 3 . 2 8 4 ( 3 ) 3 . 3 2 6 ( 3 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 2 5 ( 3 ) 2 . 9 9 1 ( 2 ) 3 . 0 5 9 ( 3 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 5 1 ( 3 ) 3 . 0 1 7 ( 2 ) 3 . 0 8 5 ( 3 ) 1 0 7 T a b l e 2 . 5 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r D y T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - D y - T e [ 1 ] x 4 7 3 3 8 ( 3 ) 7 3 2 4 ( 3 ) 7 3 5 2 ( 3 ) T e [ 1 ] - D y - T e [ 1 ] x 4 7 3 6 5 ( 3 ) 7 3 8 3 ( 3 ) 7 3 9 7 ( 3 ) T e [ 1 ] - D y - T e [ 2 ] x 4 1 3 9 . 2 8 ( 5 ) 1 3 9 . 0 1 ( 7 ) 1 3 9 . 5 5 ( 7 ) T e [ 1 ] - D y - T e [ 1 ] x 2 8 4 9 7 ( 4 ) 8 4 7 6 ( 5 ) 8 5 1 7 ( 5 ) T e [ 1 ] - D y - T e [ 1 ] x 6 8 5 4 6 ( 5 ) 8 5 1 7 ( 5 ) 8 5 7 5 ( 5 ) T e [ 1 ] - D y - T e [ 1 ] x 4 l 4 7 . 0 3 ( 3 ) 1 4 6 . 6 6 ( 4 ) 1 4 7 . 4 0 ( 4 ) T e [ 1 ] - D y - T e [ 2 ] x 4 7 6 9 6 ( 4 ) 7 6 4 6 ( 4 ) 7 7 . 4 7 ( 4 ) T e [ 1 ] - D y - T e [ 2 ] x 4 1 3 0 . 9 6 ( 4 ) 1 3 0 . 1 8 ( 4 ) 1 3 1 . 7 4 ( 4 ) T e [ 1 ] - D y - T e [ 3 ] x 4 7 6 8 7 ( 4 ) 7 6 7 7 ( 4 ) 7 6 9 6 ( 4 ) T e [ 1 ] - D y - T e [ 3 ] x 2 l 3 1 . 3 5 ( 5 ) 1 3 1 . 1 4 ( 6 ) 1 3 1 . 5 6 ( 6 ) T e [ 1 ] - D y - T e [ 3 ] x 2 1 3 0 . 9 5 ( 5 ) 1 3 0 . 5 5 ( 5 ) l 3 l . 3 5 ( 5 ) T e [ 2 ] - D y - T e [ 2 ] x 2 8 1 . 4 3 ( 4 ) 8 1 2 6 ( 5 ) 8 1 6 0 ( 5 ) T e [ 2 ] - D y - T e [ 3 ] x 4 5 4 8 4 ( 5 ) 5 4 1 1 ( 5 ) 5 5 5 9 ( 5 ) T e [ 3 ] - D y - T e [ 3 ] x 2 8 1 5 6 ( 4 ) 8 1 2 7 ( 6 ) 8 1 8 5 ( 6 ) D y - T e [ 1 ] - D y x 4 1 0 6 . 7 3 ( 4 ) 1 0 6 . 6 8 ( 4 ) 1 0 6 . 7 7 ( 4 ) D y - T e [ 1 ] - D y x 4 1 0 6 . 2 4 ( 4 ) 1 0 5 . 9 6 ( 4 ) 1 0 6 . 5 2 ( 4 ) D y — T e [ 1 ] - D y x 6 8 5 6 4 ( 5 ) 8 5 2 9 ( 5 ) 8 5 9 8 ( 5 ) D y - T e [ 1 ] - D y x 4 1 4 7 . 0 3 ( 4 ) 1 4 6 . 8 0 ( 6 ) 1 4 7 . 2 6 ( 6 ) D y - T e [ 1 ] - D y x 2 8 4 9 7 ( 5 ) 8 4 9 7 ( 5 ) 8 4 9 7 ( 5 ) D y - T e [ 2 ] - D y x 2 8 1 . 4 3 ( 4 ) 8 1 . 4 3 ( 5 ) 8 1 . 4 3 ( 3 ) D y - T e [ 2 ] - T e [ 3 ] x 2 6 2 3 5 ( 4 ) 6 2 1 3 ( 4 ) 6 2 5 6 ( 4 ) D y - T e [ 2 ] - T e [ 3 ] x 4 1 1 7 . 5 0 ( 5 ) 1 1 6 . 7 1 ( 7 ) 1 1 8 . 2 9 ( 7 ) D y - T e [ 2 ] - T e [ 3 ] x 2 6 2 6 9 ( 4 ) 6 2 5 6 ( 3 ) 6 2 8 2 ( 3 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 6 9 0 4 2 ( 7 ) 8 9 8 4 ( 9 ) 9 1 5 1 ( 9 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 9 . 1 7 ( 8 ) 1 7 8 . 3 3 ( 9 ) 1 7 9 . 9 1 ( 4 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 8 9 4 2 ( 7 ) 8 8 2 0 ( 8 ) 9 0 6 6 ( 9 ) D y - T e [ 3 ] - D y x 2 8 1 5 6 ( 3 ) 8 1 2 7 ( 5 ) 8 1 8 5 ( 5 ) D y - T e [ 3 ] - T e [ 2 ] x 2 6 2 2 0 ( 4 ) 6 1 8 5 ( 5 ) 6 2 5 6 ( 5 ) D y - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 6 0 ( 5 ) 1 1 7 . 3 1 ( 5 ) 1 1 7 . 8 8 ( 5 ) D y - T e [ 3 ] - T e [ 2 ] x 2 6 2 8 1 ( 4 ) 6 2 2 4 ( 5 ) 6 3 8 7 ( 5 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 8 9 4 2 ( 8 ) 8 8 4 2 ( 9 ) 9 0 4 4 ( 9 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 6 9 0 0 8 ( 6 ) 8 9 9 0 ( 7 ) 9 0 2 7 ( 7 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 9 . 2 0 ( 8 ) 1 7 8 . 3 9 ( 9 ) 1 7 9 . 9 1 ( 5 ) 1 0 8 T a b l e 2 . 5 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r H o T e 3 a t 3 0 0 K E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 0 9 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ 1 > 2 6 ( 1 ) ] R i n d i c e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t L a r g e s t d i f f . p e a k a n d h o l e H O T 6 3 5 4 7 . 7 3 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C m c m a = 4 . 2 8 6 2 ( 6 ) A , a = 9 0 ° b = 2 5 . 3 0 4 ( 3 ) A , B = 9 0 ° c = 4 . 2 8 8 3 ( 4 ) A , y = 9 0 ° 4 6 5 . 0 9 ( 1 0 ) A 3 4 7 . 8 1 9 8 g / e m 3 3 5 . 3 3 m m “ 8 9 2 0 . 2 4 x 0 . 2 0 x 0 . 0 4 m m 3 3 . 2 2 t o 2 9 . 0 9 0 - 5 < = h < = 5 , - 3 4 < = k < = 3 4 , - 5 < = 1 < = 5 1 9 9 9 3 8 0 [ k . . . = 0 . 1 0 2 4 ] 9 5 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 3 8 0 / 0 / 1 9 2 . 9 7 k . . s = 0 . 0 4 1 5 , w k . . . = 0 . 1 2 1 7 R . . . = 0 . 0 4 1 5 , w R . . . = 0 . 1 2 1 7 0 . 0 9 0 ( 1 2 ) 3 . 0 5 a n d - 4 3 7 e . A ' 3 k = 2 | | F . | - | F . | ] / 2 | 1 = . 1 , w k = { 2 : [ w ( | 1 = . | 2 - | F . | 2 ) 2 ] / > : [ w ( | 1 = . | 4 ) ] ) ‘ ” a n d w = 1 / ( 0 2 ( I ) + 0 . 0 0 1 6 1 2 ) T a b l e 2 . 5 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r H o T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l x 2 O c c u p a n c y U . . . H o 0 1 7 0 1 ( 1 ) 2 5 4 9 1 1 2 ( 1 ) T e [ 1 ] 0 2 9 4 6 ( 1 ) 2 5 4 9 1 1 0 ( 1 ) 1 0 9 T a b l e 2 . 5 5 . ( c o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r H o T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 2 ] 0 4 2 8 2 ( 1 ) 7 5 4 9 1 T e [ 3 ] 0 7 1 7 ( 1 ) 7 5 4 9 1 ' U . . . i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U . . - t e n s o r . 1 4 ( 1 ) 1 4 ( 1 ) T a b l e 2 . 5 6 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r H o T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 H o 1 0 ( 1 ) 1 3 ( 1 ) 1 2 ( 1 ) 0 0 0 T e [ 1 ] 7 ( 1 ) 1 3 ( 1 ) 1 1 ( 1 ) 0 0 0 T e [ 2 ] 1 1 ( 1 ) 1 6 ( 1 ) 1 5 ( 1 ) 0 0 0 T e [ 3 ] 9 ( 1 ) 1 9 ( 1 ) 1 4 ( 1 ) 0 0 0 T a b l e 2 . 5 7 . B o n d d i s t a n c e s [ A ] f o r H o T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l D i s t a n c e s L a b e l D i s t a n c e s H o - T e [ 1 ] 3 . 1 4 9 6 ( 1 0 ) H o - T e [ 3 ] x 2 3 . 2 8 5 2 ( 8 ) H o - T e [ 1 ] x 4 3 . 1 6 0 8 ( 3 ) T e [ 2 ] - T e [ 3 ] x 4 3 . 0 3 1 5 H o - T e [ 2 ] x 2 3 . 2 8 2 5 ( 8 ) T a b l e 2 . 5 8 . B o n d a n g l e s [ ° ] f o r H o T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l A n g l e s L a b e l A n g l e s T e [ 1 ] - H o - T e [ 1 ] x 8 7 3 5 5 5 ( 1 8 ) H o - T e [ 1 ] - H o x 4 8 5 . 3 7 8 ( 9 ) T e [ 1 ] - H o - T e [ 2 ] x 2 1 3 9 2 4 1 ( 1 1 ) H o - T e [ 1 ] - H o x 4 1 4 7 . 1 1 ( 3 ) T e [ 1 ] - H o - T e [ 3 ] x 2 1 3 9 2 5 7 ( 1 1 ) H o - T e [ 2 ] - H o x 2 8 1 5 2 ( 2 ) T e [ 1 ] - H o - T e [ 1 ] x 4 8 5 . 4 2 9 ( 8 ) H o - T e [ 2 ] - T e [ 3 ] x 4 6 2 . 5 5 6 ( 1 6 ) T e [ 1 ] - H o - T e [ 1 ] x 4 8 5 . 3 7 8 ( 8 ) H o - T e [ 2 ] - T e [ 3 ] x 4 1 1 7 . 5 3 ( 2 ) T e [ 1 ] - H o - T e [ 1 ] x 4 1 4 7 . 1 1 ( 3 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 9 0 . 0 2 8 T e [ 1 ] - H o - T e [ 2 ] x 4 7 6 . 8 0 7 ( 1 5 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 8 9 . 9 7 2 T e [ 1 ] - H o - T e [ 2 ] x 4 1 3 1 . 0 7 8 ( 1 6 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 9 . 9 0 ( 4 ) T e [ 1 ] - H o - T e [ 3 ] x 4 7 6 . 8 0 6 ( 1 5 ) H o - T e [ 3 ] - H o x 2 8 1 . 4 9 ( 2 ) T e [ 1 ] - H o - T e [ 3 ] x 4 1 3 1 . 0 8 8 ( 1 6 ) H o - T e [ 3 ] - T e [ 2 ] x 4 6 2 . 4 6 6 ( 1 6 ) T e [ 2 ] - H o - T e [ 2 ] x 2 8 1 . 5 1 8 ( 1 9 ) H o - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 4 5 ( 2 ) 1 1 0 T a b l e 2 . 5 8 . ( c o n t ’ d ) B o n d a n g l e s [ ° ] f o r H o T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 2 ] - H o - T e [ 3 ] x 4 5 4 . 9 7 8 ( 1 1 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 T e [ 3 ] - H o - T e [ 3 ] x 2 8 1 . 4 8 5 ( 1 9 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 H o - T e [ 1 ] - H o x 8 1 0 6 . 4 4 5 ( 1 8 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 H o - T e [ 1 ] - H o x 4 8 5 . 4 2 9 ( 9 ) 9 0 . 0 2 8 8 9 . 9 7 2 1 7 9 . 9 0 ( 4 ) T a b l e 2 . 5 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r E R ; a t 3 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 3 1 8 2 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 o ( 1 ) ] R i n d i c e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t L a r g e s t d i f f . p e a k a n d h o l e E I T C 3 5 5 0 . 1 3 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C m c m a = 4 . 2 9 9 4 ( 6 ) A , a = 9 0 ° b = 2 5 . 2 7 5 ( 6 ) A , ( 3 = 9 0 ° c = 4 . 2 7 8 7 ( 8 ) A , y = 9 0 ° 4 6 2 . 5 5 ( 1 6 ) A 3 4 7 . 8 9 6 g / c m 3 3 6 . 6 0 3 m m ‘ 1 8 9 6 0 . 5 0 x 0 . 3 2 x 0 . 0 3 m m 3 3 . 2 2 t o 3 1 8 2 ° - 6 < = h < = 6 , - 3 7 < = k < = 3 7 , - 6 < = l < = 6 2 7 1 8 4 9 2 [ R i m = 0 . 1 1 2 5 ] 9 9 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 4 9 2 / 0 / 1 9 3 . 6 2 k . . . = 0 . 0 5 9 1 , w k . . . = 0 . 1 7 6 4 R . . . = 0 . 0 6 1 6 , w k . . . = 0 . 1 7 7 0 0 . 0 2 9 ( 8 ) 1 0 . 6 4 a n d - 6 . 9 4 e . A ' 3 R = l e F o l - c h l l / 2 i l F o l , w R = { 2 [ W ( I F 0 1 2 - l F e l z ) Z l / l e t l F o I T H W 2 a n d W = 1 / ( 0 2 ( 1 ) + 0 - 0 0 1 6 1 2 ) 1 1 1 T a b l e 2 . 6 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r E r T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . t L a b e l x y 2 O c c u p a n c y U . . . B r 0 3 2 9 8 ( 1 ) 7 5 4 9 1 1 7 ( 1 ) T e [ 1 ] 0 2 0 5 7 ( 1 ) 7 5 4 9 1 1 5 ( 1 ) T e [ 2 ] 5 0 0 0 4 2 8 0 ( 1 ) 7 5 4 9 1 2 2 ( 1 ) T e [ 3 ] 0 4 2 8 2 ( 1 ) 2 5 4 9 1 2 1 ( 1 ) T U . . . i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U . . - t e n s o r . T a b l e 2 . 6 1 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r E r T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 E r 1 5 ( 1 ) 2 4 ( 1 ) 1 3 ( 1 ) 0 0 0 T e [ 1 ] 1 4 ( 1 ) 2 2 ( 1 ) 1 1 ( 1 ) 0 0 0 T e [ 2 ] 2 3 ( 1 ) 2 6 ( 1 ) 1 7 ( 1 ) 0 0 0 T e [ 3 ] 2 1 ( 1 ) 2 6 ( 1 ) 1 6 ( 1 ) 0 0 0 T a b l e 2 . 6 2 . B o n d d i s t a n c e s [ A ] f o r E r T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l D i s t a n c e s L a b e l D i s t a n c e s E r - T e [ 1 ] 3 . 1 3 8 ( 2 ) E r - T e [ 3 ] x 2 3 . 2 7 9 6 ( 1 6 ) E r - T e [ 1 ] x 4 3 . 1 5 5 0 ( 6 ) T e [ 2 ] - T e [ 3 ] x 4 3 . 0 2 5 E r - T e [ 2 ] x 2 3 . 2 7 6 7 ( 1 7 ) T a b l e 2 . 6 3 . B o n d a n g l e s [ ° ] f o r E r T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l A n g l e s L a b e l A n g l e s T e [ 1 ] - E r - T e [ 1 ] x 8 7 3 5 0 ( 3 ) E r - T e [ 1 ] - E r x 4 8 5 . 3 5 3 ( 1 7 ) T e [ 1 ] - E r - T e [ 2 ] x 2 1 3 9 2 6 ( 3 ) E r - T e [ 1 ] - E r x 4 1 4 6 . 9 9 ( 6 ) T e [ 1 ] - E r - T e [ 3 ] x 2 1 3 9 2 8 ( 2 ) E r - T e [ 2 ] - E r x 2 8 1 . 4 9 ( 5 ) T e [ 1 ] - E r - T e [ 1 ] x 4 8 5 . 3 9 0 ( 1 6 ) E r - T e [ 2 ] - T e [ 3 ] x 4 6 2 5 7 ( 4 ) T e [ 1 ] - E r - T e [ 1 ] x 4 8 5 . 3 5 3 ( 1 6 ) E r - T e [ 2 ] - T e [ 3 ] x 4 1 1 7 . 5 3 ( 5 ) T e [ 1 ] - E r — T e [ 1 ] x 4 1 4 6 . 9 9 ( 6 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 9 0 . 0 2 T e [ 1 ] - E r - T e [ 2 ] x 4 7 6 8 7 ( 3 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 8 9 . 9 8 T e [ 1 ] - E r - T e [ 2 ] x 4 1 3 l . 1 2 ( 3 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 9 . 8 7 ( 9 ) 1 1 2 T a b l e 2 . 6 3 . ( c o n t ’ d ) B o n d a n g l e s [ ° ] f o r E r T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 1 ] - E r - T e [ 3 ] x 4 7 6 8 8 ( 3 ) E r - T e [ 3 ] - E r x 2 T e [ 1 ] - E r - T e [ 3 ] x 4 1 3 l . 1 2 ( 3 ) E r - T e [ 3 ] - T e [ 2 ] x 4 T e [ 2 ] - E r — T e [ 2 ] x 2 8 1 . 4 9 ( 4 ) E r - T e [ 3 ] - T e [ 2 ] x 4 T e [ 2 ] - E r - T e [ 3 ] x 4 5 4 9 5 ( 2 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 T e [ 3 ] - E r - T e [ 3 ] x 2 8 1 . 4 3 ( 4 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 B r - T e [ 1 ] - E r x 8 1 0 6 . 5 0 ( 3 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 E r - T e [ 1 ] - E r x 4 8 5 . 3 9 0 ( 1 7 ) 8 1 . 4 3 ( 5 ) 6 2 4 7 ( 4 ) 1 1 7 4 2 ( 5 ) 9 0 . 0 2 8 9 . 9 8 1 7 9 . 8 7 ( 8 ) T a b l e 2 . 6 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r T m T e 3 a t 3 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 3 1 . 6 9 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 6 ( 1 ) ] R i n d i c e s ( a l l d a t a ) L a r g e s t d i f f . p e a k a n d h o l e T m T e 3 5 5 1 . 7 3 0 0 . 0 ( 3 ) K O r t h o r h o m b i c C m c m a = 4 . 2 9 9 5 ( 8 ) A , a = 9 0 ° b = 2 5 . 1 9 0 ( 3 ) A , 1 3 = 9 0 0 c = 4 . 2 8 0 4 ( 7 ) A , y = 9 0 0 4 6 0 . 6 0 ( 1 1 ) A 3 4 7 . 9 5 3 7 g / c m 3 3 7 . 7 6 3 m m ’ 1 0 . 4 3 x 0 . 4 0 x 0 . 0 4 m m 3 3 . 2 3 t o 3 1 . 6 9 ° - 5 < = h < = 6 , - 3 6 < = k < = 3 6 , - 5 < = 1 < = 6 2 3 6 9 4 3 7 [ k . m = 0 . 0 3 8 6 ] 9 0 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 4 3 7 / 0 / 1 8 3 . 0 2 k . . . = 0 . 0 3 1 2 , w k . . . = 0 . 1 2 5 9 R . . . = 0 . 0 3 1 2 , w R . . . = 0 . 1 2 5 9 4 . 1 7 a n d - 2 . 6 3 e . A ' 3 R = E l l F o l - l F e l l / 2 l l F s l . w R = { Z N / 0 1 % | 2 - I F c | 2 ) 2 ] / 2 [ W ( | F s | 4 ) ] } " 2 a n d W = 1 / ( 6 2 ( I ) + 0 - 0 0 1 6 1 2 ) 1 1 3 T a b l e 2 . 6 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r T m T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l x y 2 O c c u p a n c y U . . . T m 0 1 7 0 4 ( 1 ) 2 5 4 9 1 1 1 ( 1 ) T e [ 1 ] 0 2 9 4 3 ( 1 ) 2 5 4 9 1 9 ( 1 ) T e [ 2 ] 0 4 2 7 9 ( 1 ) 7 5 4 9 1 1 3 ( 1 ) T e [ 3 ] 0 7 2 1 ( 1 ) 7 5 4 9 1 1 3 ( 1 ) ' U . . . i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U . . - t e n s o r . T a b l e 2 . 6 6 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r T m T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 T m 1 0 ( 1 ) 1 0 ( 1 ) 1 2 ( 1 ) 0 0 0 T e [ 1 ] 8 ( 1 ) 1 0 ( 1 ) 1 0 ( 1 ) 0 0 0 T e [ 2 ] 1 2 ( 1 ) 1 4 ( 1 ) 1 3 ( 1 ) 0 0 0 T e [ 3 ] 1 0 ( 1 ) 1 5 ( 1 ) 1 2 ( 1 ) 0 0 0 T a b l e 2 . 6 7 . B o n d d i s t a n c e s [ A ] f o r T m T e ; a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l D i s t a n c e s L a b e l D i s t a n c e s T m - T e [ 1 ] 3 . 1 2 2 3 ( 9 ) T m - T e [ 3 ] x 2 3 . 2 7 3 4 ( 7 ) T m - T e [ 1 ] x 4 3 . 1 5 1 7 ( 3 ) T e [ 2 ] — T e [ 3 ] x 4 3 . 0 2 3 7 ( 5 ) T m - T e [ 2 ] x 2 3 . 2 7 0 1 ( 7 ) 1 1 4 T a b l e 2 . 6 8 . B o n d a n g l e s [ ° ] f o r T m T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l A n g l e s L a b e l A n g l e s T e [ 1 ] - T m - T e [ 1 ] x 8 T e [ 1 ] - T m - T e [ 2 ] x 2 T e [ 1 ] - T m - T e [ 3 ] x 2 T e [ 1 ] - T m - T e [ 1 ] x 4 T e [ 1 ] - T m - T e [ 1 ] x 4 T e [ 1 ] - T m - T e [ 1 ] x 4 T e [ 1 ] - T m - T e [ 2 ] x 4 T e [ 1 ] - T m - T e [ 2 ] x 4 T e [ 1 ] - T m - T e [ 3 ] x 4 T e [ 1 ] - T m - T e [ 3 ] x 4 T e [ 2 ] - T m - T e [ 2 ] x 2 T e [ 2 ] - T m - T e [ 3 ] x 4 T e [ 3 ] - T m - T e [ 3 ] x 2 T m - T e [ 1 ] - m e 8 T m - T e [ l ] - m e 4 7 3 . 6 1 1 ( 1 6 ) 1 3 9 . 2 2 0 ( 1 0 ) 1 3 9 . 1 7 0 ( 1 1 ) 8 5 . 5 4 0 ( 7 ) 8 5 . 3 2 7 ( 7 ) 1 4 7 . 2 2 ( 3 ) 7 6 . 7 6 2 ( 1 4 ) 1 3 1 . 0 1 8 ( 1 5 ) 7 6 . 6 7 4 ( 1 4 ) 1 3 1 . 1 0 7 ( 1 5 ) 8 1 . 5 6 0 ( 1 6 ) 5 5 . 0 4 4 ( 1 0 ) 8 1 . 6 6 1 ( 1 7 ) 1 0 6 . 3 8 9 ( 1 6 ) 8 5 . 5 4 0 ( 8 ) T m - T e [ 1 ] - T m x 4 T m - T e [ 1 ] - T m x 4 T m - T e [ 2 ] - T m x 2 T m - T e [ 2 ] - T e [ 3 ] x 4 T m - T e [ 2 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 T m - T e [ 3 ] - T m x 2 T m - T e [ 3 ] - T e [ 2 ] x 4 T m - T e [ 3 ] - T e [ 2 ] x 4 T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 8 5 . 3 2 7 ( 8 ) 1 4 7 . 2 2 ( 3 ) 8 1 . 5 6 0 ( 1 9 ) 6 2 . 5 3 3 ( 1 5 ) 1 1 7 4 9 ( 2 ) 9 0 . 1 1 5 8 9 . 8 8 5 1 8 0 8 1 . 6 6 1 ( 2 0 ) 6 2 . 4 2 4 ( 1 5 ) 1 1 7 5 6 ( 2 ) 9 0 . 1 1 5 8 9 . 8 8 5 1 8 0 1 1 5 T a b l e 2 . 6 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r Y T e 3 a t 3 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 2 2 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( 1 ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 s t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 3 3 ! o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T . . . a n d T . . . c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e Y T e 3 4 7 1 . 7 3 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 0 m ( 0 0 ' y ) 0 0 0 a = 4 . 2 9 4 7 ( 7 ) A , a = 9 0 ° b = 2 5 . 4 0 4 ( 4 ) A , 1 3 = 9 0 0 c = 4 . 2 9 6 8 ( 9 ) A , y = 9 0 ° 0 . 2 9 6 9 ( 5 ) e ‘ 4 6 8 . 7 9 ( 1 5 ) A 3 4 6 . 6 8 1 g / c m 3 3 0 . 8 2 6 m m " 7 8 0 0 . 2 9 x 0 . 2 7 x 0 . 0 2 m m 3 1 . 6 0 t o 2 9 . 2 2 ° - 5 < = h < = 5 , - 3 4 < = k < = 3 4 , - 6 < = l < = 6 , - 1 < = m < = 1 6 5 2 1 ( 2 0 8 6 m a i n + 4 4 3 5 s a t e l l i t e s ) 1 9 2 9 ( 6 6 7 m a i n + 1 2 6 2 s a t e l l i t e S ) [ R i n t = 0 . 0 4 8 2 ] 9 8 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 1 9 2 9 / 0 / 3 9 1 . 2 5 k . . . = 0 . 0 3 0 7 , w k . . . = 0 . 0 8 1 8 R . . . = 0 . 0 5 1 6 , w k . . . = 0 . 0 8 9 0 R . . . = 0 . 0 2 4 8 , w k . . . = 0 . 0 6 9 3 R . . . = 0 . 0 2 5 1 , w k . . . = 0 . 0 6 9 6 R . . . = 0 . 1 1 5 1 , w k . . . = 0 . 1 4 9 6 R . . . = 0 . 2 8 8 7 , w k . . . = 0 . 1 8 1 5 0 . 0 0 0 5 4 ( 8 ) 0 . 0 4 1 0 a n d 0 . 7 0 9 2 1 . 4 9 a n d - 1 . 8 4 e . A ’ 3 R = l e F o l - c h l l / Z l F o l . W R = { E [ W ( | F o l 2 - c h | 2 ) 2 ] / Z [ W ( | F o | 4 ) ] } " 2 a n d W = 1 / ( 0 2 ( 1 ) + 0 - 0 0 1 6 1 2 ) 1 1 6 T a b l e 2 . 7 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r Y T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . t L a b e l W a v e x y 2 U . . . Y 0 9 0 1 2 ( 3 ) 1 7 0 1 ( 1 ) 2 5 4 9 1 2 ( 1 ) s i n , 1 0 0 2 ( 4 ) c o s , 1 2 5 ( 1 ) 1 ( 1 ) 0 T e [ 1 ] O 9 0 0 0 2 9 4 6 ( 1 ) 2 5 4 9 1 1 ( 1 ) s i n , 1 0 0 - 2 ( 3 ) c o s , 1 2 ( 1 ) 0 ( 1 ) 0 T e [ 2 ] 0 9 0 1 5 ( 2 ) 7 1 4 ( 1 ) 7 5 4 9 1 4 ( 1 ) s i n , 1 0 0 - 5 ( 3 ) c o s , 1 - 1 0 1 ( 2 ) 6 ( 1 ) 0 T e [ 3 ] 0 9 0 4 5 ( 2 ) 4 2 8 5 ( 1 ) 7 5 4 9 1 4 ( 1 ) s i n , 1 0 0 - 2 6 ( 3 ) c o s , 1 8 6 ( 2 ) 1 ( 1 ) 0 ' U . . . i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 2 . 7 1 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r Y T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 Y 1 1 ( 1 ) 1 4 ( 1 ) 1 3 ( 1 ) - 1 ( 1 ) 0 0 T e [ 1 ] 9 ( 1 ) 1 3 ( 1 ) 1 0 ( 1 ) 2 ( 1 ) 0 0 T e [ 2 ] 1 3 ( 1 ) 1 5 ( 1 ) 1 3 ( 1 ) 1 ( 1 ) 0 0 T e [ 3 ] 1 3 ( 1 ) 1 6 ( 1 ) 1 3 ( 1 ) 0 ( 1 ) 0 0 T a b l e 2 . 7 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r Y T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e Y - T e [ 1 ] x 3 3 . 1 6 4 6 ( 1 1 ) 3 . 1 6 0 8 ( 1 9 ) 3 . 1 6 8 6 ( 1 9 ) Y - T e [ 1 ] x 2 3 . 1 7 0 9 ( 1 4 ) 3 . 1 6 5 1 ( 1 2 ) 3 . 1 7 6 5 ( 1 2 ) Y - T e [ 2 ] x 2 3 . 3 0 1 1 ( 1 3 ) 3 . 2 9 1 2 ( 1 2 ) 3 . 3 1 1 6 ( 1 2 ) Y - T e [ 3 ] 3 . 2 8 9 4 ( 1 4 ) 3 . 2 7 6 0 ( 1 9 ) 3 . 3 0 3 2 ( 1 9 ) Y - T e [ 3 ] 3 . 3 0 8 3 ( 1 4 ) 3 . 2 8 7 4 ( 1 9 ) 3 . 3 2 8 9 ( 1 9 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 2 8 3 ( 1 2 ) 2 . 9 7 3 3 ( 1 1 ) 3 . 0 8 4 2 ( 1 1 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 4 7 4 ( 1 2 ) 3 . 0 0 0 2 ( 1 1 ) 3 . 0 9 4 4 ( 1 1 ) 1 1 7 T a b l e 2 . 7 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r Y T e 3 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - Y - T e [ 1 ] x 8 7 3 4 9 ( 3 ) 7 3 4 4 ( 3 ) 7 3 5 5 ( 3 ) T e [ 1 ] - Y - T e [ 2 ] x 2 1 3 9 . 3 9 ( 4 ) 1 3 9 . 1 8 ( 6 ) 1 3 9 . 5 9 ( 6 ) T e [ 1 ] - Y - T e [ 3 ] x 2 1 3 9 . 4 8 ( 5 ) 1 3 9 . 2 6 ( 5 ) 1 3 9 . 7 1 ( 5 ) T e [ 1 ] - Y - T e [ 1 ] x 6 8 5 8 0 ( 4 ) 8 5 0 8 ( 4 ) 8 5 5 3 ( 4 ) T e [ 1 ] - Y - T e [ 1 ] x 4 1 4 7 . 0 8 ( 4 ) 1 4 6 . 9 9 ( 6 ) 1 4 7 . 1 7 ( 6 ) T e [ 1 ] - Y - T e [ 2 ] x 4 7 6 9 4 ( 3 ) 7 6 2 1 ( 3 ) 7 7 6 8 ( 3 ) T e [ 1 ] - Y - T e [ 2 ] x 4 1 3 1 . 0 0 ( 5 ) 1 3 0 . 1 4 ( 5 ) 1 3 1 . 8 5 ( 5 ) T e [ 1 ] - Y - T e [ 3 ] x 4 7 7 0 1 ( 4 ) 7 6 8 2 ( 3 ) 7 7 2 1 ( 3 ) T e [ 1 ] - Y - T e [ 3 ] x 4 1 3 l . 1 3 ( 4 ) 1 3 0 . 8 9 ( 4 ) 1 3 1 . 3 8 ( 4 ) T e [ 1 ] - Y - T e [ 1 ] x 2 8 5 5 4 ( 4 ) 8 5 3 0 ( 4 ) 8 5 7 8 ( 4 ) T e [ 2 ] - Y - T e [ 2 ] x 2 8 1 2 1 ( 3 ) 8 1 . 1 0 ( 4 ) 8 1 8 0 ( 4 ) T e [ 2 ] - Y - T e [ 3 ] x 2 5 4 7 0 ( 3 ) 5 3 8 1 ( 3 ) 5 5 6 1 ( 3 ) T e [ 2 ] - Y - T e [ 3 ] x 2 5 4 9 1 ( 3 ) 5 4 0 8 ( 3 ) 5 5 7 4 ( 3 ) T e [ 3 ] - Y - T e [ 3 ] x 2 8 1 2 2 ( 3 ) 8 1 . 1 1 ( 4 ) 8 1 8 3 ( 4 ) Y - T e [ 1 ] - Y x 8 1 0 6 . 5 4 ( 3 ) 1 0 6 . 4 2 ( 3 ) 1 0 6 . 6 7 ( 3 ) Y - T e [ 1 ] — Y x 8 8 5 5 4 ( 4 ) 8 5 8 9 ( 4 ) 8 5 6 9 ( 4 ) Y - T e [ 1 ] - Y x 4 1 4 7 . 0 8 ( 3 ) 1 4 7 . 0 1 ( 2 ) 1 4 7 . 1 6 ( 2 ) Y - T e [ 2 ] - Y x 2 8 1 2 0 ( 3 ) 8 0 8 7 ( 4 ) 8 1 5 3 ( 4 ) Y - T e [ 2 ] - T e [ 3 ] x 2 6 2 4 5 ( 3 ) 6 1 9 8 ( 3 ) 6 2 9 1 ( 3 ) Y - T e [ 2 ] - T e [ 3 ] x 4 1 1 7 . 4 5 ( 4 ) 1 1 5 . 9 9 ( 4 ) 1 1 8 . 9 2 ( 4 ) Y - T e [ 2 ] - T e [ 3 ] x 2 6 2 6 6 ( 3 ) 6 2 5 5 ( 3 ) 6 2 7 8 ( 3 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 9 0 3 9 ( 4 ) 8 8 8 7 ( 4 ) 9 1 9 3 ( 4 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 8 9 9 5 ( 3 ) 8 9 7 0 ( 3 ) 9 0 2 2 ( 3 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 8 . 7 7 ( 4 ) 1 7 7 . 8 2 ( 4 ) 1 7 9 . 8 5 ( 2 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 8 9 6 9 ( 4 ) 8 7 2 3 ( 4 ) 9 1 6 8 ( 4 ) Y - T e [ 3 ] - Y x 2 8 1 2 2 ( 3 ) 8 1 . 1 1 ( 4 ) 8 1 8 3 ( 4 ) Y - T e [ 3 ] - T e [ 2 ] x 2 6 2 4 3 ( 3 ) 6 1 5 7 ( 3 ) 6 3 8 2 ( 3 ) Y - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 4 4 ( 3 ) 1 1 6 . 9 5 ( 3 ) 1 1 7 . 9 2 ( 3 ) Y - T e [ 3 ] - T e [ 2 ] x 2 6 2 8 4 ( 3 ) 6 2 3 3 ( 3 ) 6 3 3 5 ( 3 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 8 9 . 6 9 ( 4 ) 8 7 9 9 ( 4 ) 9 1 . 4 2 ( 4 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 8 9 9 6 ( 3 ) 8 9 7 0 ( 4 ) 9 0 2 2 ( 4 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 8 . 8 5 ( 4 ) 1 7 7 . 9 3 ( 4 ) 1 7 9 . 9 0 5 ( 1 9 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 9 0 4 0 ( 4 ) 8 8 7 5 ( 4 ) 9 2 0 5 ( 4 ) 1 1 8 R e f e r e n c e s 1 L i n , W . ; S t e i n fi n k , H . ; W e i s s , E . J . I n o r g . C h e m . 1 9 6 5 , 4 , 8 7 7 . 2 K u z ’ m i c h e v a , G . M . ; M a t v e e n k o , I . A . R u s s . J . C o o r d . C h e m . 2 0 0 1 , 2 7 , 7 3 . 3 P a t s c h k e , R . ; K a n a t z i d i s M . P h y s . C h e m . C h e m . P h y s . 2 0 0 2 , 4 , 3 2 6 6 . 4 T r e m e l , W . ; H o f f m a n n R . J . A m . C h e m . S o c 1 9 8 7 , 1 0 9 , 1 2 4 - 1 4 0 . 5 D i M a s i , E . ; A r o n s o n , M . C . ; M a n s fi e l d , J . F . ; F o r a n , B . ; L e e S . P h y s . R e v B 1 9 9 5 , 5 2 , 1 4 5 1 6 . 6 ( a ) B r o u e t , V ; Y a n g , W . L . ; Z h o u , X . J . ; H u s s a i n , Z . ; R u , N . ; S h i n , K . Y . ; F i s h e r , I . R . ; S h e n , Z . X . P h y s . R e v . L e t t . 2 0 0 4 , 9 3 , 1 2 6 4 0 5 . ( c ) L a v e r o c k , J . ; D u g d a l e , S . B . ; M a j o r , Z s . ; A l a m , M . A . ; R u , N . ; F i s h e r , I . R . ; S a n t i G . ; B r u n o , E . P h y s . R e v . B 2 0 0 5 , B 7 1 , 0 8 5 1 1 4 ( a n d r e f e r e n c e s t h e r e i n ) . 7 I y e i r i , Y . ; O k u m u r a , T . ; M i c h i o k a , C . ; S u z u k i , K . P h y s . R e v . B 2 0 0 3 , 6 7 , 1 4 4 4 1 7 . 8 D o e r t , T . ; F o k w a , B . P . T . ; S i m o n , P . ; L i d i n , S . ; S o h n e l T . C h e m . E u r . J . 2 0 0 3 , 9 , 5 8 6 5 - 5 8 7 2 . 9 X - A R E A , I P D S S o f t w a r e , S T O E & C i e G m b H , D a r m s t a d t , 2 0 0 6 . 1 0 P e t r i c e k , V . ; D u s e k , M . I n s t i t u t e o f P h y s i c s , P r a h a , C z e c h R e p u b l i c , 2 0 0 0 . 1 1 S h e l d r i c k , G . M . S H E I X L - 9 7 : P r o g r a m f o r C r y s t a l S t r u c t u r e R e fi n e m e n t ; U n i v e r s i t y o f t h t i n g e n , G d t t i n g e n , G e r m a n y , 1 9 9 7 . 1 2 Q i u , X . ; T h o m p s o n , J . W . ; B i l l i n g e , S . J . L . J . A p p l . C r y s t . 2 0 0 4 , 3 7 , 6 7 8 . 1 3 P a t s c h k e , R . ; B r a z i s , P . ; K a n n e w u r f , C . R . ; K a n a t z i d i s , M . G . J . M a t e r . C h e m . 1 9 9 8 , 8 , 2 5 8 7 - 2 5 8 9 . 1 4 B i l l i n g e , S . J . L . ; K a n a t z i d i s , M . G . C h e m . C o m m u n . 2 0 0 4 , 7 , 7 4 9 . 1 5 K i m , H . J . ; M a l l i a k a s , C . D . ; T o m i c , A . ; T e s s m e r , S . H . ; K a n a t z i d i s M . G . ; B i l l i n g e , S . J . L . P h y s . R e v . L e t t . 2 0 0 6 , 9 6 , 2 2 6 4 0 1 . 1 6 S i n g h , D . P l a n e w a v e s , P s e u d o p o t e n t i a l s , a n d t h e L A P W m e t h o d ; K l u w e r A c a d e m i c : B o s t o n , M A , 1 9 9 4 . 1 1 9 1 7 P e r d e w , J . P . , B u r k e , K . , E r n z e r h o f , M . P h y s . R e v . L e t t . 1 9 9 6 , 7 7 , 3 8 6 5 - 3 8 6 8 . 1 8 B i l b a o C r y s t a l l o g r a p h i c S e r v e r , ( h t t p : / / w w w . c r v s t . e h u . e s ) . 1 9 h t t p : / / w w w . b e l l - l a b s . c o m / p r o j e c t / P O R T / d o c / p o r t 3 d o c . t a r . g z , G a y 1 9 8 3 . 2 0 K o e l l i n g , D . D . , H a r m o n , B . J . P h y s . C 1 9 7 7 , 1 0 , 3 1 0 7 . 2 1 B l a h a , P . , S c h w a r z , K . , M a d s e n , G . , K v a s n i c k a , D . , L u i t z , J . , W I E N Z K , A n A u g m e n t e d P l a n e W a v e + L o c a l O r b i t a l s P r o g r a m f o r C a l c u l a t i n g C r y s t a l P r o p e r t i e s ; K a r l h e i n z S c h w a r z , T e c h . U n i v . , W i e n , V i e n n a , 2 0 0 1 . 2 2 G r i i n e r , G . D e n s i t y W a v e s i n S o l i d s , A d d i s o n - W e s l e y , R e a d i n g , M A , 1 9 9 4 2 3 M a l l i a k a s , C . D . ; B i l l i n g e , S . J . L . ; K i m , H . J . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 5 , 1 2 7 , 6 5 1 0 . 1 2 0 C h a p t e r 3 R e a c t i o n s o f R a r e - E a r t h M e t a l s ( R E ) a n d T e l l u r i u m : T e m p e r a t u r e D e p e n d e n c e o f t h e D i s t o r t i o n s o f t h e T e l l u r i u m N e t o f R E T e . D i v e r g e n c e i n t h e B e h a v i o r o f t h e C h a r g e D e n s i t y W a v e i n R E T e 3 ( R E = R a r e - E a r t h E l e m e n t ) w i t h T e m p e r a t u r e a n d R E E l e m e n t ” , M a l l i a k a s , C . D . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 6 , 1 2 8 , 1 2 6 1 2 - 1 2 6 1 3 . A m e r i c a n C h e m i c a l S o c i e t y ( A C S ) i s g r a t e f u l l y a c k n o w l e d g e d f o r t h e p e r m i s s i o n t o i n c l u d e t h i s r e p r i n t i n t h e T h e s i s . 1 2 1 3 . 1 . I n t r o d u c t i o n I n c o m m e n s u r a b i l i t y i n m o d u l a t e d s y s t e m s i s o f t e n l i n k e d t o h i g h - t r a n s i t i o n - t e m p e r a t u r e s u p e r c o n d u c t i v i t y l a n d d e n s i t y w a v e m a t e r i a l s . 2 I n c o m m e n s u r a t e ( I C ) t o c o m m e n s u r a t e ( C ) o r n e a r - i n c o m m e n s u r a t e ( N I C ) t r a n s i t i o n s m a y g i v e r i s e t o i n t e r e s t i n g a n d o f t e n u n e x p l a i n e d a n o m a l i e s i n p h y s i c a l p r o p e r t i e s . 3 C h a r g e d e n s i t y w a v e ( C D W ) s t a t e s c a n b e c r e a t e d t h r o u g h a F e r m i s u r f a c e n e s t i n g e f f e c t a n d t h e c r e a t i o n o f a n e w g r o u n d s t a t e w i t h b r o k e n t r a n s l a t i o n a l s y m m e t r y . A b a n d g a p o p e n s a t t h e F e r m i l e v e l a n d a n o v e r a l l e n e r g y l o w e r i n g i s a c h i e v e d c o m p e n s a t i n g t h e p o t e n t i a l l y e n e r g e t i c a l l y u n f a v o r a b l e i n c o m m e n s u r a t e t r a n s i t i o n . A w i d e v a r i e t y o f p h y s i c a l c h a r a c t e r i z a t i o n t e c h n i q u e s h a v e b e e n u s e d t o p r o b e a n d s t u d y C D W t r a n s i t i o n s . T e m p e r a t u r e d e p e n d e n t t r a n s p o r t , m a g n e t i c a n d t h e r m a l p r o p e r t i e s a r e s o m e o f t h e t y p i c a l m e t h o d s a p p l i e d . 4 S i n c e t h e C D W d i s t o r t i o n a f f e c t s t h e F e r m i s u r f a c e s , a n g l e - r e s o l v e d p h o t o e m i s s i o n s p e c t r o s c o p y ( A R P E S ) h a s p r o v e n t o b e a u s e f u l c h a r a c t e r i z a t i o n m e t h o d f o r t h i s c l a s s o f m a t e r i a l s . 5 A d i r e c t o b s e r v a t i o n o f t h e e l e c t r o n i c b a n d s t r u c t u r e n e a r t h e F e r m i s u r f a c e ( o b t a i n e d t h r o u g h A R P E S ) g i v e s i n f o r m a t i o n o f t h e n a t u r e o f t h e C D W s t a t e . I n s o m e t w o - d i m e n s i o n a l s y s t e m s , h o w e v e r , t h i s d i s t o r t i o n l e a d s o n l y t o a p s e u d o g a p k e e p i n g t h e R E T e 3 s y s t e m i n t h e m e t a l l i c s t a t e . 6 T h e r e f o r e , s t r u c t u r a l t r a n s i t i o n s c o r r e l a t e d w i t h t h e s e e l e c t r o n b a n d c h a n g e s c a n b e d i f fi c u l t t o e x a m i n e . T e m p e r a t u r e d e p e n d e n t X - r a y s c a t t e r i n g s t u d i e s o f i n c o m m e n s u r a t e t w o d i m e n s i o n a l s y s t e m s r e m a i n b u t a f e w 7 a n d i n c l u d e 2 H - N b S e 2 a n d 2 H - T a S e 2 8 , N b S e 3 9 a n d l T - T a S Z . l o I n a l l c a s e s t h e s y s t e m s t e n d t o “ l o c k - i n ” i n a m o r e t h e r m o d y n a m i c a l l y s t a b l e c o m m e n s u r a t e s t a t e a s t h e t e m p e r a t u r e d e c r e a s e s . I n o t h e r w o r d s , 1 2 2 i n c o m m e n s u r a b i l i t y ( 5 ) d e fi n e d a s t h e d e p a r t u r e f r o m t h e c o m m e n s u r a t e s t a t e t e n d s t o z e r o w i t h f a l l i n g t e m p e r a t u r e ( i n c o m m e n s u r a b i l i t y i s d e fi n e d a s 5 = c h - q l c l w h e r e q c a n d q l c a r e t h e m o d u l a t i o n v e c t o r s o f t h e c o m m e n s u r a t e a n d i n c o m m e n s u r a t e p h a s e s r e s p e c t i v e l y ) . A p h e n o m e n o l o g i c a l L a n d a u t h e o r y d e v e l o p e d b y M c M i l l a n l l c a n d e s c r i b e t h e i n c o m m e n s u r a t e t o c o m m e n s u r a t e t r a n s i t i o n s a n d e x p l a i n t h e i n s t a b i l i t i e s i n t r a n s p o r t p r o p e r t i e s e t c . H e r e w e r e p o r t t h e t e m p e r a t u r e d e p e n d e n c e o f t h e i n c o m m e n s u r a t e C D W s t a t e o f R E T e 3 ( R E = L a , C e , P r , N d , S m , G d , T b , D y , H o , B r , a n d T m ) . T h e r e s u l t s a r e u n e x p e c t e d i n t h a t t h e C D W m o d u l a t i o n d e p e n d e n c e a s a f u n c t i o n o f d e c r e a s i n g R E r a d i u s a n d d e c r e a s i n g t e m p e r a t u r e f o l l o w s o p p o s i t e t r e n d s , e v e n t h o u g h b o t h f a c t o r s c a u s e a u n i t c e l l c o n t r a c t i o n . T h e s o l u t i o n o f C D W s t r u c t u r e s o f R E T e 3 a t 3 0 0 K w a s d e s c r i b e d i n t h e s e c o n d c h a p t e r u s i n g s u p e r s p a c e c r y s t a l l o g r a p h i c t e c h n i q u e s . 1 2 T h e m o d u l a t i o n s o r i g i n a t e fi o m d i s t o r t i o n i n t h e i d e a l s q u a r e T e n e t w i t h a q - v e c t o r a l o n g t h e c - a x i s o f t h e s o - c a l l e d s u b c e l l . A l t h o u g h t h e R E T e 3 e x h i b i t F e r m i s u r f a c e n e s t i n g “ , t r a n s p o r t a n d m a g n e t i c p r o p e r t i e s i n t h e r a n g e o f 1 . 8 - 3 0 0 K s h o w n o i n d i c a t i o n o f a n i n c o m m e n s u r a t e t o c o m m e n s u r a t e t r a n s i t i o n . T e m p e r a t u r e d e p e n d e n t X - r a y d i f f r a c t i o n e x p e r i m e n t s o n t h e i s o s t r u c t u r a l L a S e T e z , s h o w e d n o t e m p e r a t u r e d e p e n d e n c e o f i t s q - v e c t o r . l 3 3 . 2 . E x p e r i m e n t a l S e c t i o n 3 . 2 . ] . R e a g e n t s T h e f o l l o w i n g r e a g e n t s w e r e u s e d a s o b t a i n e d . A l l r a r e - e a r t h m e t a l s , 9 9 . 9 % p u r e , fi l l i n g s f r o m i n g o t , C h i n e s e R a r e E a r t h I n f o r m a t i o n C e n t e r , I n n e r M o n g o l i a , C h i n a ; 1 2 3 T e l l u r i u m s h o t s , 9 9 . 9 % p u r e , T e l l u r e x C o r p o r a t i o n , T r a v e r s e C i t y , M I ; R u b i d i u m C h l o r i d e , 9 9 . 8 % p u r e , 2 0 m e s h , C e r a c S p e c i a l t y I n o r g a n i c s , M i l w a u k e e , W I ; L i t h i u m C h l o r i d e , 9 9 . 8 % p u r e , 2 0 m e s h , C e r a c S p e c i a l t y I n o r g a n i c s , M i l w a u k e e , W I ; L i t h i u m I o d i d e , 9 9 . 8 % p u r e , 2 0 m e s h , C e r a c S p e c i a l t y I n o r g a n i c s , M i l w a u k e e , W I ; P o t a s s i u m I o d i d e , 9 9 . 8 % p u r e , 2 0 m e s h , C e r a c S p e c i a l t y I n o r g a n i c s , M i l w a u k e e , W I ; N , N — D i m e t h y l f o r m a m i d e ( D M F ) , A C S r e a g e n t g r a d e , S p e c t r u m C h e m i c a l s , N e w B r u n s w i c k , N J ; D i e t h y l e t h e r a n h y d r o u s , A C S r e a g e n t g r a d e , C o l u m b u s C h e m i c a l I n d u s t r i e s , C o l u m b u s , W I . 3 . 2 . 2 . S y n t h e s i s R E T e 3 ( R E = L a , C e , P r , N d , S m , G d , T b a n d D y ) — A l l m a n i p u l a t i o n s w e r e c a r r i e d o u t u n d e r d r y n i t r o g e n a t m o s p h e r e i n a V a c u u m A t m o s p h e r e s D r i - L a b g l o v e b o x . S t o i c h i o m e t r i c a m o u n t s o f r a r e e a r t h ( ~ 0 . 3 g ) a n d t e l l u r i u m ( ~ 0 . 8 2 g ) w e r e l o a d e d i n t o q u a r t z t u b e s u n d e r n i t r o g e n t o g e t h e r w i t h a d o u b l e a m o u n t ( ~ 2 g ) o f h a l i d e fl u x ( 0 . 4 2 : 0 . 5 8 m o l a r m i x t u r e s o f R b C l a n d L i C l ) . T h e t u b e s w e r e s e a l e d u n d e r v a c u u m ( < 1 0 ‘ 4 t o r r ) a n d h e a t e d t o 6 5 0 ° C a t 1 2 h o u r s f o r 6 d a y s . T h e t u b e s w e r e t h e n c o o l e d d o w n t o r o o m t e m p e r a t u r e a t a r a t e o f 4 ° C ‘ m i n " . T h e h a l i d e fl u x w a s d i s s o l v e d i n w a t e r a n d t h e c r y s t a l s w e r e w a s h e d w i t h a c e t o n e a n d d r i e d u n d e r n i t r o g e n e n v i r o n m e n t . T h e m o r p h o l o g y o f t h e c r y s t a l s i s t h a t o f t h i n p l a t e s w i t h a b r o w n ( c o p p e r - l i k e ) c o l o r . E l e c t r o n m i c r o p r o b e e n e r g y d i s p e r s i v e s p e c t r o s c o p y ( E D S ) w a s p e r f o r m e d o n s e v e r a l c r y s t a l s o f t h e c o m p o u n d a n d c o n fi r m e d t h e 1 : 3 r a t i o o f t h e r a r e e a r t h t o t e l l u r i u m a n d t h e a b s e n c e o f o t h e r e l e m e n t s o f t h e fl u x . C o m p o u n d s f o u n d t o b e X - r a y p u r e a n d m o i s t u r e s e n s i t i v e a f t e r e x p o s u r e t o a i r f o r a f e w d a y s . 1 2 4 R E T e 3 ( R E = H o , E r , T m a n d Y ) — I n t h e c a s e o f t h e h e a v i e r r a r e e a r t h s t h e R b C l / L i C l h a l i d e fl u x r e a c t s w i t h t h e e l e m e n t s p r o d u c i n g R b , . R E y T e z c o m p o u n d s . I n s t e a d , a n e u t e c t i c h a l i d e o f L i I a n d K 1 ( 0 . 3 7 : 0 . 6 3 m o l a r m i x t u r e s ) w a s u s e d t o s y n t h e s i z e t h e t a r g e t R E T e 3 b i n a r i e s . S i m i l a r l y , s t o i c h i o m e t r i c a m o u n t s o f r a r e e a r t h ( ~ 0 . 3 g ) a n d t e l l u r i u m ( ~ 0 . 8 2 g ) w e r e l o a d e d i n t o q u a r t z t u b e s u n d e r n i t r o g e n t o g e t h e r w i t h a d o u b l e a m o u n t ( ~ 2 g ) o f t h e h a l i d e fl u x . T h e t u b e s w e r e s e a l e d u n d e r v a c u u m ( < 1 0 “ 4 t o r r ) a n d h e a t e d t o 6 5 0 ° C a t 1 2 h o u r s f o r 6 d a y s . T h e t u b e s w e r e t h e n c o o l e d d o w n t o r o o m t e m p e r a t u r e a t a r a t e o f 4 ° C ' m i n ' 1 . T h e h a l i d e fl u x w a s d i s s o l v e d i n D M F s i n c e t h e c r y s t a l s f o u n d t o b e e x t r e m e l y m o i s t u r e s e n s i t i v e ( s u r f a c e b e c o m e s b l a c k a f t e r a f e w s e c o n d s o f e x p o s u r e t o w a t e r / m o i s t u r e ) a n d t h e c r y s t a l s w e r e w a s h e d w i t h e t h e r a n d d r i e d u n d e r n i t r o g e n e n v i r o n m e n t . T h e m o r p h o l o g y o f t h e c r y s t a l s i s t h a t o f t h i n p l a t e s w i t h a b r o w n ( c o p p e r - l i k e ) c o l o r . E l e c t r o n m i c r o p r o b e e n e r g y d i s p e r s i v e s p e c t r o s c o p y ( E D S ) w a s p e r f o r m e d o n s e v e r a l c r y s t a l s o f t h e c o m p o u n d a n d c o n fi r m e d t h e 1 : 3 r a t i o o f t h e r a r e e a r t h t o t e l l u r i u m a n d t h e a b s e n c e o f o t h e r e l e m e n t s o f t h e fl u x . C o m p o u n d s f o u n d t o b e X - r a y p u r e . 3 . 2 . 3 . P h y s i c a l M e a s u r e m e n t s S e m i q u a n t i t a t i v e E n e r g y D i s p e r s i v e S p e c t r o s c o p y ( E D S ) - T h e a n a l y s e s w e r e p e r f o r m e d w i t h a J E O L J S M - 3 5 C s c a n n i n g e l e c t r o n m i c r o s c o p e e q u i p p e d w i t h a N o r a n V a n t a g e E D S ( S i z L i ) d e t e c t o r . C r y s t a l s w e r e m o u n t e d o n a n a l u m i n u m s t a g e w i t h c a r b o n t a p e . D a t a w e r e a c q u i r e d o n s e v e r a l c r y s t a l s a n d d i f f e r e n t r e g i o n s o f e a c h c r y s t a l u s i n g a n a c c e l e r a t i n g v o l t a g e o f 2 5 k V a n d a c c u m u l a t i o n t i m e o f 4 0 s . 1 2 5 S i n g l e C r y s t a l X - r a y D i fl r a c t i o n - - A l l t h e t e m p e r a t u r e d e p e n d e n t m e a s u r e m e n t s w e r e p e r f o r m e d o n t h e s a m e s i n g l e c r y s t a l f o r e a c h R E T e 3 c o m p o u n d ( R E = L a , C e , P r , N d , S m , G d , T b , D y , H o , E r a n d T m ) . S i n g l e c r y s t a l s w e r e q u e n c h e d fi ' o m r o o m t e m p e r a t u r e t o 1 0 0 K . T h e h e a t i n g r a t e f o r w a r m i n g r a m p s w a s ~ 2 0 0 K / h . T y p i c a l a c q u i s i t i o n t i m e w a s 1 2 - 2 4 h . I n t e n s i t y d a t a w e r e c o l l e c t e d o n a S T O E I P D S I I d i f f r a c t o m e t e r e q u i p p e d w i t h a g r a p h i t e m o n o c h r o m a t i z e d M o r a d i a t i o n ( A = 0 . 7 1 0 7 3 A ) a n d a n I m a g e P l a t e ( I P ) d e t e c t o r . T h e d a t a w e r e c o l l e c t e d w i t h a n w - s c a n t e c h n i q u e f r o m 0 - 1 8 0 ° a n d a n a r b i t r a r y ( p - a n g l e . D a t a r e d u c t i o n w a s p e r f o r m e d w i t h t h e X - A r e a p a c k a g e . 1 4 T h e l e n g t h d e t e r m i n a t i o n a n d r e fi n e m e n t o f t h e q - v e c t o r s w a s p e r f o r m e d w i t h t h e P e a k l i s t 1 . 0 6 s o f t w a r e p a r t o f t h e X - A r e a s u i t e u s i n g a l e a s t s q u a r e r e fi n e m e n t a l g o r i t h m . A n a n a l y t i c a l a b s o r p t i o n c o r r e c t i o n w a s p e r f o r m e d ( X - S h a p e W i t h i n X - A r e a ) a n d a l l s t r u c t u r e s w e r e r e fi n e d w i t h J A N A 2 0 0 0 s o f t w a r e . l 5 D i r e c t m e t h o d s o f S H E L X T L s o f t w a r e 1 6 w e r e u s e d t o fi n d t h e a t o m i c p o s i t i o n s i n t h e s u b c e l l . S a t e l l i t e r e fl e c t i o n s o f fi r s t o r d e r w e r e o b s e r v e d a n d u s e d f o r t h e r e fi n e m e n t . A s i n g l e m o d u l a t i o n w a v e f o r p o s i t i o n a l p a r a m e t e r s w a s u s e d . O n l y t h e s y m m e t r y a l l o w e d F o u r i e r t e r m s w e r e r e fi n e d . T h e p s e u d o - t e t r a g o n a l c h a r a c t e r o f t h e c r y s t a l s y s t e m a l l o w s t h e p l a t e s t o s t a c k a n d t w i n i n a m e r o h e d r a l f a s h i o n . T h e r e f o r e h i g h e l e c t r o n i c d e n s i t i e s w e r e o b s e r v e d i n d i f f e r e n t p o s i t i o n s f r o m t h e c a l c u l a t e d o n e s f o r s o m e o f t h e R E T e ; m e m b e r s . B y a p p l y i n g a t w i n l a w o f a r o t a t i o n o f 9 0 ° a l o n g b — a x i s a ' a O 0 1 b ' = b - 0 l 0 t h e R f a c t o r s f o r a l l t h e r e fl e c t i o n s ( R . / w R 2 ) i n t h e r e fi n e m e n t c ' c - 1 0 0 s i g n i fi c a n t l y d r o p p e d ( f o r t h e c a s e o f t h e N d T e 3 s u b c e l l f r o m 1 1 9 7 / 2 8 9 0 t o 2 . 6 2 / 5 . 8 3 ) . D e t a i l e d c r y s t a l l o g r a p h i c t a b l e r e p o r t s ( b o n d d i s t a n c e s a n d a n g l e s ) f o r e a c h i n d i v i d u a l 1 2 6 R E T e 3 a n a l o g u e a n d t e m p e r a t u r e c a n b e f o u n d i n t a b l e s 3 . 1 - 3 . 9 5 . T e m p e r a t u r e w a s c o n t r o l l e d b y a n O x f o r d C r y o s t r e a m 7 0 0 P l u s c r y o s t a t . T e m p e r a t u r e D e p e n d e n t T r a n s m i s s i o n E l e c t r o n M i c r o s c o p y o f H O T e 3 — S e l e c t e d a r e a e l e c t r o n d i f fi ' a c t i o n ( S A E D ) s t u d i e s a t v a r i a b l e t e m p e r a t u r e s w e r e c a r r i e d o u t o n a J E O L 2 0 1 0 F ( J a p a n E l e c t r o n O p t i c s L a b o r a t o r i e s ) 2 0 0 k V fi e l d e m i s s i o n T E M a t t h e C e n t e r f o r A d v a n c e d M i c r o s c o p y o f M i c h i g a n S t a t e U n i v e r s i t y . A t h i n p l a t e c r y s t a l o f H o T e ; w a s p o l i s h e d a n d i o n - m i l l e d i n o r d e r t o b e t h i n e n o u g h f o r T E M s t u d y . T h e c r y s t a l w a s m o u n t e d o n a c o p p e r a p e r t u r e g r i d . T e m p e r a t u r e d e p e n d e n t ( 2 5 0 - 3 2 5 K ) s e l e c t e d a r e a e l e c t r o n d i f f r a c t i o n ( S A E D ) p a t t e r n s f o r H o T e 3 a r e s h o w n i n F i g u r e 3 . 2 0 . A G A T A N l i q u i d n i t r o g e n a u t o m a t i c a l l y c o n t r o l l e d l o w t e m p e r a t u r e s t a g e w a s u s e d f o r t h e t e m p e r a t u r e d e p e n d e n t T E M s t u d y . 3 . 3 . R e s u l t s a n d D i s c u s s i o n S u b c e l l D e s c r i p t i o n o f R E T e 3 - — T h e a v e r a g e s t r u c t u r e o f R E T e 3 a d o p t s t h e s p a c e g r o u p C m c m . I t c o n s i s t s o f p u c k e r e d d o u b l e l a y e r s o f ( R E T e ) t h a t a r e s a n d w i c h e d b y t h e p l a n a r n e t s o f T e m a k i n g a R E T e 3 s l a b . T h e s l a b s t h e n s t a c k a l o n g t h e b - a x i s c r e a t i n g v a n d e r W a a l s g a p s . T h e f o r m u l a c a n b e m o r e e x p r e s s l y w r i t t e n a s ( R E T e ) + ( T e 2 ) ' , F i g u r e 3 1 A . T h e R E a t o m i s i n a m o n o c a p p e d t e t r a g o n a l a n t i p r i s m o f T e a t o m s , F i g u r e 3 . 1 B . T h e a p p a r e n t T e - T e d i s t a n c e s i n t h e s q u a r e n e t a r e 3 . 1 0 3 4 ( 6 ) A ( f o r C e T e 3 ) , F i g u r e 3 . 1 C . 1 2 7 3 . 6 A v a n d e r W a a l s g a p ( C ) F i g u r e 3 . 1 . ( A ) U n d i s t o r t e d s t r u c t u r e o f C e T e 3 . ( B ) C o o r d i n a t i o n g e o m e t r y a n d e n v i r o n m e n t o f C e . ( C ) I d e a l s q u a r e n e t o f T e a t o m s i n t h e C e T e 3 s u b c e l l . 1 2 8 S u p e r c e l l D e s c r i p t i o n o f R E T e 3 B a s e d o n a M o d u l a t i o n q - v e c t o r — A l l c r y s t a l l o g r a p h i c r e fi n e m e n t s a t v a r i a b l e t e m p e r a t u r e s c o n v e r g e d s u c c e s s f u l l y b y u s i n g t h e a v e r a g e s t r u c t u r e o f N d T e 3 a s a s t a r t i n g m o d e l . T h e R E T e 3 s e r i e s a d o p t t h e C 2 c m ( 0 0 ~ y ) 0 0 0 s u p e r s p a c e g r o u p . A g e n e r a l c h a r a c t e r i s t i c i s t h a t t h e d i r e c t i o n o f t h e q - v e c t o r i s a l w a y s a l o n g t h e c * a x i s . D e s p i t e t h e p s e u d o - t e t r a g o n a l s y m m e t r y t h e r e i s n o b i d i r e c t i o n a l i t y a t a l l . O f t e n t h e p r e s e n c e o f t w i n d o m a i n s , w h i c h i s c o m m o n f o r t h e s e s y s t e m s , c a n p r o d u c e a n a p p a r e n t s e c o n d q - v e c t o r n o r m a l t o t h e r e a l o n e . T h i s a r t i f a c t c a n b e e a s i l y d e t e c t e d f r o m t h e h i g h r e s i d u a l e l e c t r o n d e n s i t y p e a k s o f t h e r e fi n e d s u b c e l l . T h e q - v e c t o r a s a f u n c t i o n o f R E f o r a g i v e n t e m p e r a t u r e i n c r e a s e s f r o m L a t o T m , F i g u r e 1 B . A t 1 0 0 K , a l l a n a l o g s p o s s e s s a C D W w i t h q v a l u e s v a r y i n g f r o m 0 . 2 7 1 9 ( 3 ) t o 0 . 3 0 2 8 ( 4 ) f o r L a a n d T m r e s p e c t i v e l y . A t 3 0 0 K , t h e C D W f o r t h e t h r e e h e a v i e s t R E ( H o , B r a n d T m ) d i s a p p e a r s j u d g i n g f r o m t h e v a n i s h i n g o f t h e q - v e c t o r . A t 5 0 0 K , o n l y L a , C e a n d P r s t i l l h a v e a m o d u l a t i o n q - v e c t o r . N d h a s a q - v e c t o r o f 0 . 2 8 7 4 ( 4 ) a t 4 7 0 K a n d f o r S m i s 0 . 2 9 3 6 ( 4 ) a t 4 0 0 K . I n t e r e s t i n g l y , e v i d e n c e o f a l o c k - i n t r a n s i t i o n t o a l o w i n d e x c o m m e n s u r a t e s t a t e a t l o w t e m p e r a t u r e s ( 1 0 0 K ) , a c c o r d i n g t o M c M i l l a n ” , w a s n o t o b s e r v e d a s a l l q - v e c t o r v a l u e s t e n d t o s t a b i l i z e t o a n i n c o m m e n s u r a t e s t a t e . F o r a g i v e n t e m p e r a t u r e t h e C D W s t a t e s e e m s t o f a d e w i t h d e c r e a s i n g R E e l e m e n t r a d i u s . F o r e x a m p l e H o , B r a n d T m d o n o t e x h i b i t a C D W s t a t e a t a l l a t r o o m t e m p e r a t u r e . T h i s C D W s u p p r e s s i o n c a n b e a t t r i b u t e d t o “ c h e m i c a l p r e s s u r e ” w h e r e t h e T e n e t i s s q u e e z e d b y t h e d e c r e a s i n g u n i t c e l l s i z e c a u s e d b y t h e s h r i n k i n g R E a t o m s . I n d e e d i t i s k n o w n t h a t p r e s s u r e c a n s u p p r e s s t h e C D W s t a t e a n d i t s o m e c a s e s c a n t u r n o n a s u p e r c o n d u c t i n g s t a t e . 1 7 1 2 9 \ 0 . 3 — ° — 1 0 0 K ’ 0 6 - o — 3 0 0 K . . . . . ‘ ' 0 - 3 0 3 . H T ( K ) - - . 3 4 1 9 ‘ 0 . . l ‘ . ' . 3 0 0 4 0 0 K - . : . ~ ~ ~ ~ ~ ~ ~ ‘ 0 . 2 9 7 Q . 0 . L ‘ ~ : ~ ~ ~ ~ ~ ~ 5 / 1 7 u r . 0 . ‘ . “ “ - “ . 0 . 2 9 o 5 0 0 K 4 7 0 K ° ° - . ° ~ ~ ~ ~ ' 4 2 : ” q . . o . . o “ ' s ‘ ~ ‘ 9 ~ / 3 ‘ 1 : 0 2 9 § 4 a , - ~ ~ ~ ~ ~ ~ I v . . . . . . . . \ \ “ ‘ ~ § / 7 : 0 . 2 8 8 2 3 5 0 0 K . ° “ x . “ ‘ x : 0 - 2 8 5 1 % q . . . . . . \ “ ‘ \ “ ‘ . o . . o . . . . . . . . . ‘ s \ ‘ s “ ‘ 7 ~ 0 - o . . . . . . “ ‘ \ \ ‘ ‘ 5 1 2 ‘ 5 ; 2 8 2 U ! x ‘ x / J ‘ \ “ “ 8 ; 0 ' 2 7 9 “ ~ . ‘ 0 2 5 0 0 ~ 4 4 . 7 6 2 . 4 0 0 0 . 2 7 3 0 e 0 0 « 9 9 8 8 . 2 7 3 0 4 ° 0 1 0 0 . 9 . 4 2 . , “ 9 0 : Q 7 0 6 w e w m 4 9 F i g u r e 3 . 2 . q - v e c t o r d e p e n d e n c e a s a f u n c t i o n o f R E e l e m e n t a n d t e m p e r a t u r e . P a r a l l e l d a s h e d l i n e s n o t a t e s o m e p o s s i b l e l o w i n d e x c o m m e n s u r a t e a p p r o x i m a n t s . T h e s y s t e m a t i c c h a n g e o f q - v e c t o r w i t h R E e l e m e n t c a n b e n a i v e l y e x p l a i n e d b y c o n s i d e r i n g t h e b r o a d e n i n g o f f r o n t i e r o r b i t a l b a n d s n e a r t h e F e r m i l e v e l w i t h d e c r e a s i n g u n i t c e l l v o l u m e ( i . e . i n c r e a s e d o r b i t a l o v e r l a p ) r e s u l t i n g i n a c h a n g e i n t h e n e s t i n g v e c t o r . 5 B e c a u s e t e m p e r a t u r e v a r i a t i o n c a u s e s s i m i l a r c h a n g e s i n t h e c e l l v o l u m e i t i s r e a s o n a b l e t o e x p e c t t h e s a m e t r e n d i n t h e c h a n g e o f q - v e c t o r a s t h e o n e o b s e r v e d w i t h R E v a r i a t i o n . S u r p r i s i n g l y , o u r e x p e r i m e n t s s h o w t h e q - v e c t o r f o r a l l R E T e 3 a s a f u n c t i o n o f t e m p e r a t u r e f o l l o w s t h e o p p o s i t e t r e n d , F i g u r e 3 . 2 . F o r t h e l i g h t e r b u t l a r g e r R E e l e m e n t s ( C e - S m ) t h e c h a n g e o f q - v e c t o r fi o m 1 0 0 t o 3 0 0 K i s n e g l i g i b l e b u t i t i s s i g n i fi c a n t b e t w e e n 3 0 0 a n d 5 0 0 K . S p e c i fi c a l l y , f o r C e T e 3 t h e q - v e c t o r d r o p s f r o m 0 . 2 8 6 7 ( 5 ) a t 5 0 0 K t o 0 . 2 8 0 1 ( 3 ) a t 3 0 0 K a n d f o r P r T e 3 f r o m 0 . 2 8 6 4 ( 4 ) t o 0 . 2 8 1 8 ( 5 ) . F o r 1 3 0 N d a n d S m t h e q - v e c t o r v a n i s h e s a t 5 0 0 K . T h e s a m e i r r e g u l a r t r e n d i s m o r e a p p a r e n t f r o m 3 0 0 K t o 1 0 0 K f o r t h e o t h e r R E ( R E = G d , T b , D y , H o , B r a n d T m ) a n a l o g u e s . A p o s s i b l e r e a s o n f o r t h i s b e h a v i o r i s t h a t v o l u m e s h r i n k a g e a s s o c i a t e d w i t h a t e m p e r a t u r e d e c r e a s e i n d u c e s a c h a r g e r e d i s t r i b u t i o n f o l l o w e d w i t h a T e - T e b o n d l e n g t h c h a n g e d u e t o t h e fl e x i b i l i t y o f t e l l u r i d e t o e x h i b i t a w i d e r a n g e o f T e - T e b o n d s . A l t h o u g h b o t h p a r a m e t e r s c a u s e s i m i l a r c h a n g e s i n t h e c e l l v o l u m e , t h e r e a s o n f o r t h e d i v e r g e n t t r e n d s o b s e r v e d f o r R E a n d t e m p e r a t u r e v a r i a t i o n i s n o t c l e a r . T h i s s u g g e s t s t h a t s u b t l e c h a n g e s i n R E - T e b o n d i n g a c r o s s t h e s e r i e s p l a y a k e y r o l e t h a t c a n n o t b e a c c o u n t e d f o r b y c e l l v o l u m e c h a n g e s a l o n e . D e t a i l e d e x a m i n a t i o n o f t h e d i s t o r t e d T e n e t i n S m T e 3 a t f o u r d i f f e r e n t t e m p e r a t u r e s i s s h o w n i n F i g u r e 3 . 3 . A t 1 0 0 K t h e m i n i m u m T e - T e d i s t a n c e i n t h e n e t i s 2 . 9 1 8 9 ( 1 8 ) A a n d t h e m a x i m u m 3 . 1 8 5 ( 2 ) A . B y a r b i t r a r i l y t a k i n g 3 . 0 0 2 A t o b e t h e T e - T e b o n d i n g t h r e s h o l d , t h e n e t c a n b e c o n v e n i e n t l y v i e w e d a s a s e q u e n c e o f t r i m e r s a n d t e t r a m e r s , F i g u r e 3 . 3 A . A t 3 0 0 K , t h e m i n i m u m a n d m a x i m u m T e - T e d i s t a n c e i s 2 . 9 5 5 ( 2 ) A a n d 3 . 1 6 2 ( 3 ) A a n d t h e T e p a t t e r n l o o k s a l m o s t i d e n t i c a l w i t h t h e o n e a t l o w t e m p e r a t u r e s h o w i n g , t o a l a r g e e x t e n t , t h e s a m e s e q u e n c e o f t r i m e r s - t o - t e t r a m e r s a t a t h r e s h o l d o f 3 . 0 1 8 A b u t u p t o a p o i n t , F i g u r e 3 . 3 B . T h e t w o T e n e t s b e g i n t o d i f f e r a f t e r a c e r t a i n n u m b e r o f u n i t s u b c e l l s ( s e e f r o m r i g h t t o l e f t ) . T h e d i s t r i b u t i o n o f T e - T e b o n d s h a s c h a n g e d a n d t h e c o n n e c t i v i t y o f t h e o l i g o m e r s n o w r e s u l t s i n a d i f f e r e n t s e q u e n c e . T e t r a m e r s b e c o m e t r i m e r s a n d s i n g l e T e a t o m s r e s u l t i n g i n m o r e t r i m e r s i n t h e n e t . I n c r e a s i n g t h e t e m p e r a t u r e t o 4 0 0 K , t h e c o n t r a s t b e t w e e n m i n i m u m a n d m a x i m u m T e - T e d i s t a n c e b e c o m e s e v e n s m a l l e r a t 3 . 0 1 1 ( 3 ) A a n d 3 . 1 1 3 ( 3 ) A a n d m o r e a p p a r e n t c h a n g e s a r e o b s e r v e d i n t h e s e q u e n c e o f o l i g o m e r s . M o r e o v e r , t h e d i f f e r e n c e b e t w e e n t h e T e - T e 1 3 1 d i s t a n c e s w i t h i n a n d b e t w e e n t h e c h a i n s a l s o d i m i n i s h e s a n d i n t e r a c t i o n s d e v e l o p b e t w e e n c h a i n s , s e e F i g u r e 3 8 C . B o n d i n g i n t e r a c t i o n s b e t w e e n t h e o l i g o m e r s i s a l s o v e r i fi e d b y t h e o b s e r v e d m e t a l l i c c h a r a c t e r o f t h e s y s t e m . 1 8 F i n a l l y , a t 5 0 0 K t h e C D W v a n i s h e s t o y i e l d a p e r f e c t s q u a r e n e t o f T e a t o m s a n d t h e s t r u c t u r e d e g e n e r a t e s t o t h e i d e a l s u b - c e l l C m c m , F i g u r e 3 . 3 D . S i m i l a r c h a n g e s o c c u r i n t h e T e n e t s o f a l l R E T e 3 m e m b e r s w i t h i n c r e a s i n g t e m p e r a t u r e . C o m p a r i s o n o f t h e s t r u c t u r e r e fi n e m e n t o f C e T e 3 i n c l u d i n g s a t e l l i t e r e fl e c t i o n s o f s e c o n d o r d e r i n r e s p e c t w i t h t h e r e fi n e m e n t c o n t a i n i n g o n l y fi r s t o r d e r r e fl e c t i o n s — I n o r d e r t o v e r i f y i f t h e e x t r e m e l y w e a k s a t e l l i t e r e fl e c t i o n s o f s e c o n d o r d e r , d e t e c t e d b y e l e c t r o n d i f f r a c t i o n ( F i g u r e 2 3 A ) a n d h i g h e n e r g y X - r a y s ( F i g u r e 4 b i n r e f e r e n c e 1 9 ) , e f f e c t t h e s t r u c t u r e r e fi n e m e n t a n d b o n d d i s t r i b u t i o n s , w e u s e d a n e v e n l o n g e r e x p o s u r e t i m e o n C e T e 3 a t 1 0 0 K t o d e t e c t t h e s e c o n d o r d e r s a t e l l i t e r e fl e c t i o n s . C o m p a r i n g t h e s t a t i s t i c s o f T e — T e b o n d l e n g t h s i n t h e n e t , T a b l e 3 . 1 4 a n d T a b l e 3 . 1 9 , w e c a n c o n c l u d e t h a t t h e i n t r o d u c t i o n o f s e c o n d o r d e r s a t e l l i t e r e fl e c t i o n s i n t h e s t r u c t u r e r e fi n e m e n t d o e s n o t c h a n g e t h e r e s u l t i n t h e b o n d d i s t r i b u t i o n c o n s i d e r i n g t h e c a l c u l a t e d e r r o r b a r s . S p e c i fi c a l l y , t h e m i n i m u m T e - T e b o n d i n t h e d i s t o r t e d n e t f o r t h e c a s e o f t a k i n g i n a c c o u n t o n l y fi r s t o r d e r s a t e l l i t e r e fl e c t i o n s i s 2 . 9 2 5 ( 2 ) A w i t h a n a v e r a g e o f 3 . 0 7 9 ( 3 ) A a n d f o r t h e c a s e w i t h s e c o n d o r d e r s a t e l l i t e r e fl e c t i o n s t h e m i n i m u m b o n d i n g l e n g t h i s 2 . 9 1 7 ( 4 ) A w i t h a n a v e r a g e o f 3 . 0 8 9 ( 5 ) A . T h e s a m e c o n c l u s i o n c a n b e d r a w n f r o m t h e e x p e r i m e n t a l F o u r i e r m a p s o f t h e t w o c a s e s i n F i g u r e 3 1 9 A - B . I n b o t h c a s e s t h e e x p e r i m e n t a l e l e c t r o n i c d e n s i t y o f T e a t o m s i n t h e n e t c a n b e s e e n a n d d e s c r i b e d ( m o d e l e d ) a s a s i n g l e s i n u s o i d a l w a v e . 1 3 2 ) r 4 ( 6 3 9 2 . 0 q h t i w K 0 0 4 t a 3 e T m o t c e v - q e l b a v r e s b o o n h t i w K 0 S 0 5 t a 3 e T m S ? n 3 d a v M x A A A A 2 v v A A » v . . A 2 » . ) v m w N . W ) . m a . « x ” 2 m . u v m v v . v . . . m . x ” “ 8 3 3 x A 3 A N v A & N a 3 x A 1 N . w 1 m m 3 a . v fl a m e r s “ ? c . v v v a % . v v v v u o fl . W x x m . . . . x x x m . M 2 2 6 6 3 2 2 4 . r a m 3 3 % x x x . x x x . ” A R A . ” ” A 2 6 4 . . . ” A A A A . ” A A A A . a n a n d . . v v v v ” . M N . W A N A N A N A N . m e s s e s . . . w . w a s 4 . . . » . . . . M 5 w 0 F i g u r e 3 3 . E v o l u t i o n o f t h e C D W i n t h e T e n e t o f S m T e 3 w i t h t e m p e r a t u r e . ( A ) t h e T e n e t o f S m T e ; a t 1 0 0 K . V - a n d N - s h a p e d m i n i m u m t h r e s h o l d o f 3 . 0 4 2 A a n d m a x i m u m a t 3 . 0 6 3 A . I n t r a - a n d i n t e r - c h a i n i n t e r a c t i o n s b e g i n t o b e m o r e c o m p a r a b l e . ( D ) P e r f e c t o l i g o m e r s a r e s h o w n u s i n g a b o n d i n g t h r e s h o l d o f 3 . 0 0 2 A . ( B ) T e n e t a t 3 0 0 K a t a t h r e s h o l d o f 3 . 0 1 8 A ( C ) T e n e t a t 4 0 0 K , n e t d u e t o v a n i s h i n g o f t h e C D W a t 5 0 0 K a t a t h r e s h o l d o f 3 . 0 7 0 . . d l o h s e r h t g n i d n o b A 5 1 0 . 3 d n a ) 3 ( 0 9 7 2 . 0 = q h t i w K 0 0 1 t a 3 e T e C . 6 . 3 e r u g i 3 e r u g i F F > > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < < < < < < < < < < < < < 5 5 5 5 5 5 5 5 5 > > > > > > > > > > 2 2 2 2 2 2 2 2 2 2 < < < < < < < < < 5 5 5 5 5 5 5 5 5 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < 5 5 5 5 5 5 5 5 5 5 2 2 2 2 2 2 2 2 2 2 < < < < < < < < < 5 5 5 5 5 5 5 5 5 : > > > > > > > > > > 2 2 2 2 2 2 2 2 2 2 < < < < < < < < < < < < < < < < < < < 5 5 5 5 5 5 5 5 5 > > > > > > > > > > 2 2 2 2 2 2 2 2 2 2 < < < < < < < < < 5 5 5 5 5 5 5 5 5 . 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < 5 5 5 5 5 5 5 5 5 5 2 2 2 2 2 2 2 2 2 < < < < < < < < < < 0 . 3 5 5 5 : 5 5 5 5 ] > > > > > > > > > > F i g u r e 3 . 4 . L a T e 3 a t 1 0 0 K w i t h q = 0 . 2 7 1 9 ( 4 ) a n d 3 . 0 3 4 A b o n d i n g t h r e s h o l d . > > > > > > > > > > 2 2 2 2 2 2 2 2 2 2 < < < < < < < < < - 5 5 5 5 5 5 5 5 5 : < < < < < < < < < < I < < < < < < < < < < < < < < < < < < < 2 2 2 2 2 2 2 2 2 2 < < < < < < < < < < 3 5 5 5 5 5 5 5 5 : > > > > > > > > > > 2 2 2 2 2 2 2 2 2 2 < < < < < < < < < 5 5 5 5 5 5 5 5 5 : > > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < < < 2 2 2 2 2 2 2 2 2 2 < < < < < < < < < < - 5 5 5 5 5 5 5 5 5 : \ \ \ \ \ \ \ \ \ \ : 2 2 2 2 2 2 2 2 2 < < < < < < < < < < 5 5 5 5 5 5 5 5 5 > > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < < < 3 5 5 5 5 5 5 5 5 5 : / / / / / / / / / / 2 2 2 2 2 2 2 2 2 2 - 2 < < < < < < < < < 0 § 2 2 2 2 2 2 2 2 2 « 2 < < < < < < < < 1 3 4 L a T e 3 a t 5 0 0 K w i t h q = 0 . 2 7 9 3 ( 4 ) a n d 3 . 0 6 5 A b o n d i n g t h r e s h o l d . 5 5 5 5 5 5 5 5 5 - > > > > > > > > : > > > > > > > > > I < < < < < < < < 5 5 5 5 5 5 5 5 5 > > > > > > > > z 2 2 2 2 2 2 2 2 2 : < < < < < < < < > > > > > > > > > > > > > > > > > I 2 2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 5 : > > > > > > > > > I < < < < < < < < 5 5 5 5 5 5 5 5 5 > > > > > > > > z 2 2 2 2 2 2 2 2 2 : < < < < < < < < 5 5 5 5 5 5 5 5 5 > > > > > > > > z 2 2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 5 > > > > > > > > > 2 2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 5 5 > > > > > > > > : > > > > > > > > > I < < < < < < < < 5 5 5 5 5 5 5 5 5 > > > > > > > > z 2 2 2 2 2 2 2 2 2 0 5 5 5 5 5 5 5 5 : > > > > fi g > > > . d l o h s e r h t g n i d n o b A 7 5 0 . 3 d n a ) 5 ( 4 6 8 2 . 0 = q h t i w K 0 0 5 t a 3 e T r P . 9 . 3 e r u g i F > > - > > > > > > > > I > > > > > > > > > 0 0 0 0 0 0 0 0 0 \ \ \ \ \ \ \ \ \ 3 5 5 5 5 5 5 5 5 : > > > > > > > > > I < < < < < < < < < < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > . . . . . . . . . I < < < < < < < < < < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > I < < < < < < < < < < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > : 2 2 2 2 2 2 2 2 3 2 < < < < < < < < o 5 5 5 5 5 5 5 5 > > > > > > > > > > F i g u r e 3 . 7 . C e T e 3 a t 5 0 0 K w i t h q = 0 . 2 8 6 7 ( 5 ) a n d 3 . 0 6 6 A b o n d i n g t h r e s h o l d . < < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > K < < < < < < < 5 5 5 5 5 5 5 5 5 > > > > > > > > : 2 2 2 2 2 2 2 2 2 : < < < < < < < < 5 5 5 5 5 5 5 5 5 . 2 2 2 2 2 2 2 2 ; 2 2 2 2 2 2 2 2 2 : < < < < < < < < > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < 3 5 5 5 5 5 5 5 5 : > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < 5 5 5 5 5 5 5 5 < 2 8 . P r T e 3 a t 1 0 0 K w i t h q = 0 . 2 8 2 5 ( 5 ) a n d 3 . 0 1 5 A b o n d i n g t h r e s h o l d . > > > > > > > > > A ~ = K < < < < < < < 1 3 5 . 3 I n > > > > > > > > I 2 2 2 2 2 2 2 2 2 2 < < < < < < < 5 5 5 5 5 5 5 5 5 > > > > > > > > : 2 2 2 2 2 2 2 2 2 : < < < < < < < < 5 5 5 5 5 5 5 5 5 - > > > > > > > > : 2 2 2 2 2 2 2 2 2 : < < < < < < < < 5 5 5 5 5 5 5 5 5 . > > > > > > > > : 2 2 2 2 2 2 2 2 2 : < < < < < < < < 5 5 5 5 5 5 5 5 5 > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 < < < < < < < 5 5 5 5 5 5 5 5 5 . 2 2 2 2 2 2 2 2 ; 2 2 2 2 2 2 2 2 2 : < < < < < < < < 5 5 5 5 5 5 5 5 5 > > > > > > > > : ‘ 2 2 2 2 2 2 2 2 2 K < < < < < < < 5 5 5 5 5 5 5 5 5 > > > > > > > > z > > > > > > > > > K < < < < < < < 5 5 5 5 5 5 5 5 5 3 > > > > > > > > : > > > > > > > > 6 < < < < < < < < < S S S S S S S S > > > > > > > > > . < < < < < < < < S S S S S S S S S - > > > > > > > > : 2 2 2 2 2 2 2 2 2 : < < < < < < < < S S S S S S S S S - > > > > > > > > : 2 2 2 2 2 2 2 2 2 : < < < < < < < < S S S S S S S S S > > > > > > > > : 2 2 2 2 2 2 2 2 2 ; < < < < < < < < . S S S S S S S S S > > > > > > > > : 2 2 2 2 2 2 2 2 2 : < < < < < < < < > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < S S S S S S S S > > > > > > > > > 2 2 2 2 2 2 2 2 < < < < < < < < < S S S S S S S S > > > > > > > > > . < < < < < < < < S S S S S S S S S > > > > > > > > z < 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < F i g u r e 3 . 1 0 . N d T e ; a t 1 0 0 K w i t h q = 0 . 2 8 2 4 ( 4 ) a n d 3 . 0 0 7 A b o n d i n g t h r e s h o l d . 2 2 2 2 2 2 2 2 2 2 / / / / / / / / / . 2 2 2 2 2 2 2 2 2 2 . \ \ \ \ \ \ \ \ \ ' 2 2 2 2 2 2 2 2 2 2 ° / / / / / / / / / . 2 2 2 2 2 2 2 2 2 2 . . . . . . . . . . . \ \ \ \ \ \ \ \ \ 2 2 2 2 2 2 2 2 2 2 ° / / / / / / / / / . 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < - 2 2 2 2 2 2 2 2 2 2 ° / / / / / / / / / . 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < - S S S S S S S S S S - > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < - S S S S S S S S S S i ° > > > > > > > > > I 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < - S S S S S S S S S S - > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < - S S S S S S S S S S > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < v M S S S S S S S S S S c a g . \ \ \ \ \ \ \ \ \ 2 2 2 2 2 2 2 2 2 2 § a 1 3 6 . d l o h s e r h t g n i d n o b A 3 9 9 . 2 d n a ) 3 ( 6 2 9 2 . 0 = q h t i w K 0 0 1 t a 3 e T y D . 5 1 . 3 e r u g i F > > > > > > > > I > > > > > > > > > : 2 2 2 2 2 2 2 2 3 2 < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > > > > > > > > > : > > > > > > > > > I < < < < < < < < 5 5 5 5 5 5 5 5 5 > > > > > > > > z > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > > > > > > > > > : 2 2 2 2 2 2 2 2 2 : < < < < < < < < . > > > > > > > > > > > > > > > > > I > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > ° Q > > > > > > > > I > > > > > > > > > 0 . 2 8 8 4 ( 3 ) a n d 2 . 9 9 3 A b o n d i n g t h r e s h o l d . F i g u r e 3 . 1 3 . G d T e 3 a t 1 0 0 K w i t h q > > > > > > > > I > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < : < < < < < < < < > > > > > > > > > > > > > > > > > I > > > > > > > > > I < < < < < < < < < < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > o > > > > > > > > z > > > > > > > > > I < < < < < < < < < < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < 5 5 5 5 5 5 5 5 > > > > > > > > > > > > > > > > > : 2 2 2 2 2 2 2 2 2 : < < < < < < < < 5 5 5 5 5 5 5 5 5 o > > > > > > > X I > > > > > > > > > 1 3 7 F i g u r e 3 . 1 4 . T b T € 3 a t 1 0 0 K w i t h q = 0 . 2 9 1 2 ( 5 ) a n d 2 . 9 9 5 A b o n d i n g t h r e s h o l d . 5 5 5 5 5 5 5 5 5 5 > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < 2 < < < < < < < < < : < < < < < < < < < 5 5 5 s 5 5 s $ $ s > > > > > > > > > I 2 2 3 3 / 2 3 / 2 3 } ; 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < 5 5 5 5 5 5 5 5 5 5 > > > > > > > > > : > > > > > > > > > > > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < 5 5 5 5 5 5 5 5 5 5 > > > > > > > > > : > > > > > > > > > > > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < 2 < < < < < < < < < 0 0 0 0 0 0 0 0 0 0 . \ \ \ \ \ \ \ \ \ ' 5 5 5 5 5 5 5 5 5 5 > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < 2 < < < < < < < < < : < < < < < < < < < 5 5 5 5 5 5 5 5 5 5 > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 / / / / / / / / / . 2 2 2 2 2 2 2 2 2 2 c ® < . d l o h s e r h t g n i d n o b A 2 9 9 . 2 d n a ) 3 ( 5 3 9 2 . 0 q h t i w K 0 0 1 t a 3 e T o . d l o h s e r h t g n i d n o b A 8 8 9 . 2 d n a ) 4 ( 2 9 9 2 . 0 q h t i w K 0 0 1 t a 3 e T r H E . 6 . 7 1 1 . . 3 3 e e r r u u g g i i F F - > > > > > > > > I > > > > > > > > > : 2 2 2 2 2 2 2 2 3 < < < < < < < < < 3 $ $ S $ $ $ $ S z > > > > > > > > > : 2 2 2 2 2 2 2 2 3 < < < < < < < < < : < < < < < < < < > > > > > > > > > > > > > > > > > I > > > > > > > > > I < < < < < < < < ° < < < < < < < < < 3 S 5 $ $ $ $ $ $ z > > > > > > > > > : 2 2 2 2 2 2 2 2 3 2 < < < < < < < < $ $ $ $ $ $ $ $ > > > > > > > > > > > > > > > > > : > > > > > > > > > I < < < < < < < < < < < < < < < < < $ $ $ $ S $ $ $ > > > > > > > > > 2 2 2 2 2 2 2 2 2 < < < < < < < < $ $ $ $ $ $ $ $ > > > > > > > > > > > > > > > > > : 2 2 2 2 2 2 2 2 2 : < < < < < < < < $ $ $ $ $ $ S $ $ “ > > > > > > > > j r > > > > > > > > > > > > > > > > > > > > > > > > > > > > I 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < < < < < < < < < < < . . . . . . . . . . ° > > > > > > > > > I > > > > > > > > > > > > > > > > > > > I 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < 2 < < < < < < < < < > > > > > > > > > I > > > > > > > > > > > > > > > > > > > I 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < < < < < < < < < < < 0 0 0 0 0 0 0 0 0 0 > > > > > > > > > I > > > > > > > > > > > > > > > > > > > I 0 0 0 0 0 0 0 0 0 0 < < < < < < < < < < I < < < < < < < < < - $ $ $ $ S $ $ $ S S > > > > > > > > > : > > > > > > > > > > > > > > > > > > > : . . . . . . . . . . < < < < < < < < < < I < < < < < < < < < $ $ $ $ S $ S $ S $ > > > > > > > > > : > > > > > > > > > > o > > > > > > > > > z < < < < < < < < < < I < < < < < < < < < 5 5 $ $ $ 5 $ $ 5 $ > > > > > > > > > I > > > > > i ? > > > 1 3 8 $ $ S $ $ $ S S S $ > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < 2 < < < < < < < < < : < < < < < < < < < s $ $ $ s s s s $ $ > > > > > > > > > I 2 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < $ $ $ $ $ 5 S S $ $ > > > > > > > > > z > > > > > > > > > > > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 ; < < < < < < < < < . 5 $ 5 $ $ $ $ S $ $ . > > > > > > > > > : > > > > > > > > > > - > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < - < < < < < < < < < < . \ \ \ \ \ \ \ \ \ ° S $ S $ $ $ S S $ $ > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < . 2 < < < < < < < < < : < < < < < < < < < $ $ $ $ $ 5 $ S S $ - > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 “ ' / / / / / / / / / . 2 2 2 2 2 2 2 2 2 2 0 . 3 0 2 8 ( 4 ) a n d 2 . 9 8 0 A b o n d i n g t h r e s h o l d . F i g u r e 3 . 1 8 . T m T e 3 a t 1 0 0 K w i t h q ( 1 & ) x z - o . 0 7 0 , x 3 - o . s o o : 1 _ _ _ _ _ ‘ _ _ _ _ _ _ ‘ ’ _ _ _ _ _ ‘ 1 . 1 0 1 - - ‘ ~ ) \ Q ’ I - - - - - - - - \ S ’ f - - - _ ' _ ’ 4 ‘ , ~ I « - - - \ o l o ' 0 . 4 0 . 3 1 . 2 1 . 6 x i 2 L 0 F i g u r e 3 . 1 9 . E x p e r i m e n t a l F o u r i e r m a p o f C e T e 3 a t 1 0 0 K p l o t t e d a l o n g t h e m o d u l a t i o n d i r e c t i o n ( t ) . T h e c e n t r a l l i n e r e p r e s e n t s t h e c a l c u l a t e d ( fi t t e d ) p o s i t i o n o f T e [ 2 ] ( A ) F o u r i e r m a p w i t h t h e fi r s t o r d e r s a t e l l i t e r e fl e c t i o n s . O n e c o n t o u r l i n e p e r 0 . 2 e ' A ' 3 . P o s i t i v e ( s o l i d l i n e ) c u t o f f 2 . 6 7 e - A ' 3 a n d n e g a t i v e ( d a s h e d l i n e ) c u t o f f - 0 . 4 6 e - A ' 3 . ( B ) F o u r i e r m a p i n c l u d i n g b o t h fi r s t a n d s e c o n d o r d e r s a t e l l i t e r e fl e c t i o n s . O n e c o n t o u r l i n e p e r 1 e ' A ' 3 . P o s i t i v e c u t o fi 2 8 . 0 8 e ' A ‘ 3 a n d n e g a t i v e c u t o f f - 2 . 4 1 e ' A ' 3 . E l e c t r o n T r a n s m i s s i o n M c r o s c o p y o f H o T e 3 — T e m p e r a t u r e d e p e n d e n t s e l e c t e d a r e a e l e c t r o n d i f f r a c t i o n s t u d y w a s p e r f o r m e d o n H o T e ; i n o r d e r t o v e r i f y t h e d i s a p p e a r a n c e o f t h e s a t e l l i t e s u p e r c e l l r e fl e c t i o n s a b o v e t h e C D W t r a n s i t i o n t e m p e r a t u r e 1 3 9 ) . u . a ( y t i s n e t n I E k L K . . ( T c p w ) , F i g u r e 3 . 2 0 . T h e m o d u l a t i o n q - v e c t o r ( d o t t e d l i n e s ) d i s a p p e a r s a t t h e t e m p e r a t u r e o f 3 0 0 K a n d a b o v e . T h e b r e a k i n g o f t r a n s l a t i o n a l s y m m e t r y s t i l l e x i s t s s i n c e t h e ( 1 0 0 ) r e fl e c t i o n a t z e r o p o s i t i o n v i o l a t e s t h e C m c m s u b c e l l s y m n i e t r y . T h e r e a r e 2 5 r e fl e c t i o n s ( 1 8 a b o v e 2 0 ) o u t o f 2 0 2 4 t h a t v i o l a t e t h e C m c m s y m m e t r y b a s e d o n s i n g l e c r y s t a l x — r a y d i fi r a c t i o n d a t a a t 3 0 0 K . T h e s e v i o l a t i o n s b e l o n g t o t h e h 0 1 g r o u p w i t h l = l , 3 , 5 . T h e s u b c e l l r e fl e c t i o n s a r e o v e r e x p o s e d , i n o r d e r t o d e t e c t t h e s u p e r c e l l r e fl e c t i o n s , a n d a l s o t w i n n i n g i s i n m o s t o f t h e c a s e s p r e s e n t . T a k i n g t h e s e i n t o a c c o u n t , t h i s v e r y s m a l l f r a c t i o n o f v i o l a t e d r e fl e c t i o n s ( i n r e s p e c t w i t h t h e t o t a l n u m b e r o f c o l l e c t e d r e fl e c t i o n s i n c l u d i n g s a t e l l i t e s ) w a s n o t c o n s i d e r e d i m p o r t a n t i n o r d e r t o r e d u c e t h e s y m m e t r y . 2 5 0 i 2 2 5 - 2 0 0 k 3 2 5 K 1 7 5 3 0 0 K p — a L I I C 2 7 5 K § \ 1 U I 5 0 2 5 0 K x E 2 5 I H O R e c i p r o c a l s p a c e ( a l o n g c * ) F i g u r e 3 . 2 0 . I n t e n s i t y s c a n a l o n g t h e c * - a x i s o f t h e t e m p e r a t u r e d e p e n d e n t ( 2 5 0 - 3 2 5 K ) S A E D p a t t e r n s o f t h e ( 1 0 1 ) f a m i l y o f r e fl e c t i o n f o r H o T e 3 . 1 4 0 3 . 4 . C o n c l u s i o n s T h e e l e c t r o n i c c o n fi g u r a t i o n o f t h e R E a t o m a p p e a r s t o p l a y a s u b t l e b u t i m p o r t a n t r o l e i n t h e C D W o f t h e R E T e 3 s e r i e s , p r o b a b l y t h r o u g h v a r y i n g i n v o l v e m e n t o f f - a n d d - o r b i t a l s a t d i f f e r e n t t e m p e r a t u r e s . U n f o r t u n a t e l y , a t t h i s s t a g e w e h a v e n o t h e o r e t i c a l e x p l a n a t i o n f o r t h i s b e h a v i o r s i n c e a b - i n i t i o c a l c u l a t i o n s c a n n o t h a n d l e t e m p e r a t u r e v a r i a t i o n s , n o r c a n t h e y t r e a t e a s i l y o p e n f - s h e l l s y s t e m s . I n a d d i t i o n a l g o r i t h m s t h a t c a n c a l c u l a t e b a n d s t r u c t u r e s o f “ a p e r i o d i c ” s y s t e m s a r e n o t a v a i l a b l e . T h e c o m b i n a t i o n o f a b - i n i t i o a n d m o d e l i n g s t u d i e s h o w e v e r c a n c o n t r i b u t e t o t h e u n d e r s t a n d i n g o f t h e r o l e o f t h e f - e l e c t r o n s . T h e e x p e r i m e n t a l d a t a r e p o r t e d h e r e r e g a r d i n g t h e C D W d i s t o r t i o n s r e v e a l u n i q u e b e h a v i o r a m o n g C D W s y s t e m s a n d u n d e r s c o r e s t h e i n c o m p l e t e l e v e l o f c u r r e n t u n d e r s t a n d i n g o f C D W p h y s i c s . 1 9 T h e t e m p e r a t u r e d e p e n d e n c e o f t h e m o d u l a t e d s t r u c t u r e s o f R E T e 3 c o m p o u n d s i s a n o m a l o u s . A c h a n g e i n c e l l v o l u m e w i t h R E e l e m e n t h a s a n o p p o s i t e e f f e c t f r o m c o m p a r a b l e c h a n g e s i n v o l u m e c a u s e d b y t e m p e r a t u r e . 2 0 T h e e v o l u t i o n o f C D W a c r o s s t h e R E T e 3 s e r i e s a n d w i t h t e m p e r a t u r e i s s o s u b t l e t h a t n o o t h e r c h a r a c t e r i z a t i o n t e c h n i q u e , s u c h a s A R P E S , s c a n n i n g p r o b e , a n d t r a n s m i s s i o n e l e c t r o n m i c r o s c o p y c a n p r o b e t h e m w i t h t h e r e q u i r e d p r e c i s i o n . O n l y t h e e x c e l l e n t s t a t i s t i c s o f h u n d r e d s o f s a t e l l i t e r e fl e c t i o n s p r o v i d e d b y s i n g l e c r y s t a l s c a t t e r i n g a r e a b l e t o d e t e r m i n e t h e s e fi n e d i f f e r e n c e s . 1 4 1 T a b l e 3 . 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r L a T e 3 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( O O O ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 1 6 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ l > 2 o ( 1 ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 0 ( 1 ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m i n a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e L a T e 3 5 2 1 . 7 1 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 c m ( 0 0 y ) 0 0 0 a = 4 . 3 7 7 9 ( 1 0 ) A , a = 9 0 ° b = 2 6 . 1 4 9 ( 5 ) A , [ 3 = 9 0 ° c = 4 . 3 9 6 8 ( 8 ) A , y = 9 0 ° 0 . 2 7 5 7 ( 4 ) c ‘ 5 0 3 . 3 4 ( 1 7 ) A 3 4 6 . 8 8 2 g / c m 3 2 5 . 3 0 6 m m " 8 5 2 0 . 1 0 x 0 . 0 6 x 0 . 0 1 m m 3 2 . 0 1 t o 2 9 . 1 6 ° - 6 < = h < = 5 , - 3 5 < = k < = 3 0 , - 6 < = l < = 6 , - l < = m < = 1 7 1 4 4 ( 2 3 7 8 m a i n + 4 7 6 6 s a t e l l i t e s ) 2 0 9 9 ( 7 4 9 m a i n + 1 3 5 0 s a t e l l i t e S ) [ R i m = 0 . 1 1 8 9 ] 9 9 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 2 0 9 9 / 0 / 3 8 1 . 7 8 R . , , = 0 . 0 5 8 9 , w R . . . , s = 0 . 1 3 5 6 R , " = 0 . 0 9 4 0 , w k . “ = 0 . 1 4 2 9 R o b , = 0 . 0 5 1 0 , w R o b s = 0 . 1 2 8 2 R , " = 0 . 0 5 4 6 , w k , “ = 0 . 1 2 8 9 R o b , = 0 . 1 1 3 5 , w R o b , = 0 . 1 8 3 1 R , " = 0 . 2 6 9 8 , w R . . . = 0 . 2 1 4 6 0 . 0 0 0 3 4 ( 4 ) 0 . 1 1 8 9 a n d 0 . 9 3 3 3 4 . 7 7 a n d - 2 . 7 8 e . A ' 3 R = 2 | | F o | - | F c | | / ) : | 1 = , | , w R = { > : [ w ( | 1 = , | 2 - | F , | 2 ) 2 ] / > : [ w ( | 1 = , | 4 ) ] } ‘ ” a n d w = 1 / ( o z ( I ) + O . 0 0 1 6 1 2 ) 1 4 2 T a b l e 3 . 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r L a T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e x y z U e q L a 0 9 2 4 9 1 6 8 6 ( 1 ) 2 5 4 9 2 4 ( 1 ) s i n , 1 0 0 8 ( 8 ) c o s , 1 5 9 ( 2 ) 0 ( 1 ) 0 T e [ 1 ] 0 9 2 0 2 ( 1 2 ) 2 9 5 9 ( 1 ) 2 5 4 9 2 4 ( 1 ) s i n , 1 0 0 - 8 ( 9 ) c o s , 1 8 ( 2 ) 1 ( 2 ) 0 T e [ 2 ] 0 9 1 5 4 ( 1 5 ) 6 8 9 ( 1 ) 7 5 4 9 2 5 ( 1 ) s i n , 1 0 0 - 4 6 ( 1 0 ) c o s , 1 - 3 2 5 ( 5 ) - l 7 ( 1 ) O T e [ 3 ] 0 9 1 9 8 ( 1 3 ) 4 3 0 6 ( 1 ) 7 5 4 9 2 5 ( 1 ) s i n , 1 0 0 - 1 1 ( 1 0 ) c o s , 1 2 3 6 ( 4 ) 1 ( 2 ) 0 ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r L a T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 L a 1 6 ( 1 ) 3 8 ( 1 ) 1 7 ( 1 ) 1 ( 1 ) 0 0 T e [ 1 ] 1 5 ( 1 ) 3 9 ( 1 ) 1 7 ( 1 ) 1 ( 2 ) 0 0 T e [ 2 ] 1 9 ( 1 ) 3 8 ( 1 ) 1 8 ( 1 ) 4 ( 1 ) 0 0 T e [ 3 ] 1 9 ( 1 ) 3 8 ( 1 ) 1 8 ( 1 ) - 1 ( 2 ) 0 0 T a b l e 3 . 4 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r L a T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e L a - T e [ 1 ] 3 . 3 2 9 ( 3 ) 3 . 3 2 6 ( 6 ) 3 . 3 3 1 ( 6 ) L a - T e [ 1 ] x 4 3 . 2 3 8 ( 4 ) 3 . 2 2 4 ( 4 ) 3 . 2 5 2 ( 4 ) L a - T e [ 2 ] x 2 3 . 4 1 3 ( 3 ) 3 . 3 7 5 ( 3 ) 3 . 4 5 2 ( 3 ) L a - T e [ 3 ] x 2 3 . 3 9 5 ( 5 ) 3 . 3 4 7 ( 6 ) 3 . 4 4 4 ( 6 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 9 0 ( 7 ) 2 . 9 2 9 ( 6 ) 3 . 2 5 6 ( 7 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 1 1 9 ( 7 ) 2 . 9 6 9 ( 6 ) 3 . 2 7 2 ( 7 ) 1 4 3 T a b l e 3 . 5 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r L a T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - L a - T e [ 1 ] x 8 7 3 3 4 ( 9 ) 7 3 1 4 ( 9 ) 7 3 5 4 ( 9 ) T e [ 1 ] - L a - T e [ 2 ] x 2 1 3 9 . 8 2 ( 1 0 ) 1 3 9 . 3 1 ( 7 ) 1 4 0 . 2 9 ( 7 ) T e [ 1 ] - L a - T e [ 3 ] x 2 1 3 9 . 8 7 ( 1 2 ) 1 3 9 . 2 5 ( l 3 ) 1 4 0 . 4 9 ( 1 3 ) T e [ 1 ] - L a - T e [ l ] x 8 8 5 . 5 2 ( 1 1 ) 8 4 . 9 4 ( l l ) 8 6 . 1 2 ( 1 1 ) T e [ 1 ] - L a - T e [ 1 ] x 4 1 4 6 . 6 6 ( 9 ) 1 4 6 . 6 5 ( 1 0 ) 1 4 6 . 6 9 ( 8 ) T e [ 1 ] - L a - T e [ 2 ] x 4 7 7 . 1 5 ( 1 1 ) 7 5 . 6 4 ( 1 2 ) 7 8 . 7 1 ( 1 2 ) T e [ 1 ] - L a - T e [ 2 ] x 4 1 3 0 . 7 6 ( 1 3 ) 1 2 7 . 9 4 ( 1 3 ) 1 3 3 6 3 ( 1 3 ) T e [ 1 ] - L a - T e [ 3 ] x 4 7 7 . 5 0 ( 1 0 ) 7 7 . 0 0 ( 1 0 ) 7 8 . 0 1 ( 1 0 ) T e [ 1 ] — L a - T e [ 3 ] x 4 1 3 0 . 9 2 ( 1 1 ) 1 3 0 . 3 1 ( 1 1 ) 1 3 1 . 5 1 ( 1 1 ) T e [ 2 ] - L a - T e [ 2 ] x 2 8 0 2 6 ( 9 ) 7 9 . 2 0 ( 1 1 ) 8 1 . 2 2 ( 1 1 ) T e [ 2 ] - L a - T e [ 3 ] x 4 5 3 9 7 ( 1 2 ) 5 1 . 0 5 ( 1 2 ) 5 6 . 9 9 ( 1 3 ) T e [ 3 ] - L a - T e [ 3 ] x 2 8 0 . 2 9 ( 1 2 ) 8 0 . 2 4 ( 1 4 ) 8 0 . 3 l ( 1 1 ) L a - T e [ 1 ] - L a x 8 1 0 6 . 6 6 ( 1 1 ) 1 0 6 . 3 l ( 1 1 ) 1 0 7 . 0 0 ( 1 1 ) L a - T e [ 1 ] - L a x 8 8 5 . 5 0 ( 1 3 ) 8 5 . 1 2 ( 1 4 ) 8 5 . 8 6 ( 1 4 ) L a - T e [ 1 ] - L a x 4 1 4 6 . 6 7 ( 1 0 ) 1 4 6 . 5 1 ( 4 ) 1 4 6 . 8 2 ( 4 ) L a - T e [ 2 ] - L a x 2 8 0 2 2 ( 8 ) 7 9 . 2 8 ( 1 0 ) 8 1 . 0 6 ( 1 0 ) L a - T e [ 2 ] - T e [ 3 ] x 4 6 2 6 8 ( 8 ) 6 2 3 0 ( 8 ) 6 2 . 9 1 ( 8 ) L a - T e [ 2 ] - T e [ 3 ] x 4 1 1 7 . 3 1 ( 1 5 ) 1 1 4 . 7 1 ( 1 7 ) 1 1 9 . 7 5 ( 1 6 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 9 0 . 9 ( 2 ) 8 5 . 6 ( 2 ) 9 6 . 4 ( 2 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 8 9 . 6 0 ( 1 4 ) 8 9 . l 7 ( 1 4 ) 9 0 . l 6 ( 1 7 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 6 . 3 ( 2 ) 1 7 3 . 7 ( 2 ) 1 7 9 . 7 8 ( 1 8 ) L a - T e [ 3 ] - L a x 2 8 0 . 2 9 ( 5 ) 8 0 . 2 4 ( 1 0 ) 8 0 3 1 ( 3 ) L a - T e [ 3 ] - T e [ 2 ] x 4 6 3 0 4 ( 1 1 ) 6 1 . 4 7 ( 1 1 ) 6 4 . 6 5 ( 1 2 ) L a - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 0 6 ( 1 0 ) 1 1 6 . 7 4 ( 1 0 ) 1 1 7 . 2 9 ( 1 0 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 8 8 9 . 9 ( 2 ) 8 4 . 4 9 ( 1 9 ) 9 5 . 4 ( 2 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 6 . 6 ( 2 ) 1 7 4 . 2 ( 2 ) l 7 9 . 6 7 ( 7 ) 1 4 4 T a b l e 3 . 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r L a T e 3 a t 5 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 3 0 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ’ ( 1 ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ' ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 0 ( 1 ) ] R 1 8 t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f f i c i e n t T m i n a n d T m c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e L a T e 3 5 2 1 . 7 5 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 0 m ( 0 0 y ) 0 0 0 a = 4 . 4 0 7 0 ( 8 ) A , a = 9 0 0 b = 2 6 . 3 1 3 ( 4 ) A , 1 3 = 9 0 0 c = 4 . 4 2 0 3 ( 7 ) A , y = 9 0 ° 0 2 7 9 3 0 6 “ 5 1 2 . 5 9 ( 1 4 ) A 3 4 6 . 7 5 8 1 g / c m 3 2 4 . 8 4 9 m m " 8 5 2 0 . 1 0 x 0 . 0 6 x 0 . 0 1 m m 3 2 . 0 1 t o 2 9 . 3 0 ° - 6 < = h < = 6 , - 3 5 < = k < = 3 2 , - 6 < = l < = 6 , - 1 < = m < = 1 7 1 9 6 ( 2 3 7 4 m a i n + 4 8 2 2 s a t e l l i t e s ) 2 1 2 7 ( 7 5 8 m a i n + 1 3 6 9 s a t e l l i t e S ) [ R i m = 0 . 0 7 5 8 ] 9 9 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 2 1 2 7 / 0 / 3 8 1 . 5 7 R o b , = 0 . 0 4 5 7 , w R o b s = 0 . 1 1 1 4 R , “ = 0 . 0 7 8 2 , w k , “ = 0 . 1 2 0 3 R 0 , , = 0 . 0 3 3 2 , w R o b s = 0 . 0 8 7 9 R , “ = 0 . 0 3 5 7 , w k , " = 0 . 0 8 8 8 R o b , = 0 . 1 3 5 7 , w R o b s = 0 . 2 0 4 6 R , 1 1 = 0 . 2 8 6 6 , w R . . . 1 = 0 . 2 3 4 8 0 . 0 0 0 5 8 0 ) 0 . 1 1 8 9 a n d 0 . 9 3 3 3 3 . 0 5 a n d - 2 4 2 6 A " 3 R = 2 1 1 1 2 1 — 1 1 3 , ” / 2 | F o l , w R = { 2 “ [ w ( | 1 = , | 2 - | F , | 2 ) 2 ] / 2 [ w ( | 1 ~ ‘ , , | “ ) ] } " 2 a n d w = 1 / ( 0 ' 2 ( I ) + 0 . 0 0 1 6 I Z ) 1 4 5 T a b l e 3 . 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o m ' i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r L a T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . u p L a b e l W a v e x y z U e q L a 0 9 3 4 9 1 6 8 9 ( 1 ) 2 5 4 9 1 6 ( 1 ) s i n , 1 0 0 3 ( 4 ) c o s , 1 4 7 ( 2 ) 0 ( 1 ) 0 T e [ 1 ] 0 9 2 7 9 ( 5 ) 2 9 6 0 ( 1 ) 2 5 4 9 1 6 ( 1 ) s i n , 1 0 0 1 9 ( 5 ) c o s , 1 2 ( 2 ) 4 ( 1 ) 0 T e [ 2 ] 0 9 2 1 6 ( 7 ) 6 9 4 ( 1 ) 7 5 4 9 2 3 ( 1 ) s i n , 1 0 0 - 7 0 ( 6 ) c o s , 1 - 2 6 1 ( 4 ) - 2 ( 1 ) 0 T e [ 3 ] 0 9 2 9 4 ( 6 ) 4 3 0 2 ( 1 ) 7 5 4 9 2 3 ( 1 ) s i n , 1 0 0 - 2 1 ( 6 ) c o s , 1 2 0 9 ( 4 ) - 9 ( 1 ) 0 ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 8 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r L a T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 L a 1 4 ( 1 ) 1 8 ( 1 ) 1 4 ( 1 ) 1 ( 1 ) 0 0 T e [ 1 ] 1 5 ( 1 ) 1 8 ( 1 ) 1 5 ( 1 ) 2 ( 1 ) 0 0 T e [ 2 ] 2 4 ( 1 ) 2 3 ( 1 ) 2 1 ( 1 ) 2 ( 1 ) 0 0 T e [ 3 ] 2 4 ( 1 ) 2 1 ( 1 ) 2 3 ( 1 ) - 2 ( 1 ) 0 0 T a b l e 3 . 9 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r L a T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e L a - T e [ 1 ] 3 . 3 4 5 ( 2 ) 3 . 3 3 6 ( 4 ) 3 . 3 5 4 ( 4 ) L a - T e [ 1 ] x 2 3 . 2 6 1 ( 2 ) 3 . 2 4 4 ( 2 ) 3 . 2 7 7 ( 2 ) L a - T e [ 1 ] x 2 3 . 2 4 8 ( 2 ) 3 . 2 3 6 1 ( 1 9 ) 3 . 2 6 0 5 ( 1 9 ) L a - T e [ 2 ] x 2 3 . 4 2 7 ( 2 ) 3 . 4 0 4 8 ( 1 9 ) 3 . 4 4 7 4 ( 1 8 ) L a - T e [ 3 ] x 2 3 . 4 1 6 ( 3 ) 3 . 3 5 3 ( 4 ) 3 . 4 8 0 ( 4 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 9 7 ( 3 ) 2 . 9 5 6 ( 3 ) 3 . 2 4 3 ( 3 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 1 4 8 ( 3 ) 3 . 0 2 6 ( 3 ) 3 . 2 7 2 ( 3 ) 1 4 6 T a b l e 3 . 1 0 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r L a T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - L a - T e [ 1 ] x 8 7 3 4 5 ( 4 ) 7 3 2 6 ( 4 ) 7 3 6 5 ( 4 ) T e [ 1 ] - L a - T e [ 2 ] x 2 1 3 9 . 7 9 ( 5 ) 1 3 9 . 4 4 ( 4 ) 1 4 0 . 1 5 ( 4 ) T e [ 1 ] - L a - T e [ 3 ] x 2 1 3 9 . 6 3 ( 6 ) 1 3 9 . 3 0 ( 6 ) 1 3 9 . 9 5 ( 6 ) T e [ 1 ] - L a - T e [ 1 ] x 6 8 5 3 5 ( 5 ) 8 5 . 1 3 ( 5 ) 8 5 5 6 ( 6 ) T e [ 1 ] - L a - T e [ 1 ] x 4 1 4 7 . 0 6 ( 6 ) 1 4 6 . 7 7 ( 9 ) 1 4 7 . 3 4 ( 9 ) T e [ 1 ] - L a - T e [ 2 ] x 2 7 6 7 8 ( 6 ) 7 5 2 3 ( 7 ) 7 8 3 7 ( 7 ) T e [ 1 ] - L a - T e [ 2 ] x 2 1 3 0 . 2 4 ( 6 ) 1 2 8 . 0 9 ( 6 ) 1 3 2 . 4 1 ( 6 ) T e [ 1 ] - L a - T e [ 3 ] x 4 1 3 0 . 8 4 ( 7 ) 1 3 0 . 3 3 ( 6 ) 1 3 1 . 3 3 ( 6 ) T e [ 1 ] - L a - T e [ 1 ] x 2 8 5 . 7 6 ( 5 ) 8 5 0 7 ( 5 ) 8 6 4 3 ( 6 ) T e [ 1 ] - L a - T e [ 2 ] x 2 7 7 . 6 2 ( 6 ) 7 6 2 2 ( 6 ) 7 8 9 9 ( 6 ) T e [ 1 ] - L a - T e [ 2 ] x 2 1 3 1 . 5 5 ( 7 ) 1 2 9 . 4 7 ( 6 ) 1 3 3 . 6 0 ( 6 ) T e [ 2 ] - L a - T e [ 2 ] x 2 8 0 3 5 ( 5 ) 7 9 5 6 ( 7 ) 8 1 0 7 ( 7 ) T e [ 2 ] - L a - T e [ 3 ] x 2 5 3 8 1 ( 6 ) 5 1 6 3 ( 7 ) 5 6 0 4 ( 7 ) T e [ 2 ] - L a - T e [ 3 ] x 2 5 4 8 0 ( 6 ) 5 2 . 7 0 ( 7 ) 5 6 . 9 1 ( 7 ) T e [ 3 ] - L a - T e [ 3 ] x 2 8 0 3 8 ( 6 ) 7 9 8 7 ( 8 ) 8 0 . 8 6 ( 8 ) L a - T e [ 1 ] - L a x 8 1 0 6 . 6 1 ( 6 ) 1 0 6 . 4 8 ( 5 ) 1 0 6 . 7 4 ( 5 ) L a - T e [ 1 ] - L a x 8 8 5 2 3 ( 4 ) 8 5 0 6 ( 5 ) 8 5 . 4 0 ( 5 ) L a - T e [ 1 ] - L a x 4 1 4 7 . 0 6 ( 6 ) 1 4 6 . 6 9 ( 9 ) 1 4 7 . 4 3 ( 9 ) L a - T e [ 2 ] - L a x 2 8 0 3 2 ( 5 ) 8 0 1 1 ( 7 ) 8 0 4 6 ( 7 ) L a - T e [ 2 ] - T e [ 3 ] x 2 6 2 8 8 ( 5 ) 6 2 5 9 ( 4 ) 6 3 1 8 ( 4 ) L a - T e [ 2 ] - T e [ 3 ] x 2 1 1 7 . 7 4 ( 8 ) 1 1 5 . 3 l ( 1 0 ) 1 2 0 . 0 8 ( 1 0 ) L a - T e [ 2 ] - T e [ 3 ] x 2 6 2 3 7 ( 5 ) 6 1 . 4 7 ( 4 ) 6 3 2 9 ( 4 ) L a - T e [ 2 ] - T e [ 3 ] x 2 1 1 6 . 3 2 ( 8 ) 1 1 3 . 0 0 ( 1 0 ) 1 1 9 . 6 4 ( 1 0 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 9 1 . l 9 ( 1 0 ) 8 6 8 4 ( 1 0 ) 9 5 . 6 6 ( 1 2 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 6 8 9 . 7 2 ( 7 ) 8 9 0 9 ( 8 ) 9 0 4 2 ( 9 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 6 . 9 9 ( 1 1 ) 1 7 4 . 4 4 ( 1 1 ) 1 7 9 . 8 5 ( 1 0 ) L a - T e [ 3 ] - L a x 2 8 0 3 8 ( 4 ) 7 9 8 7 ( 7 ) 8 0 8 6 ( 7 ) L a - T e [ 3 ] - T e [ 2 ] x 2 6 2 . 8 4 ( 6 ) 6 1 3 1 ( 6 ) 6 4 4 0 ( 6 ) L a - T e [ 3 ] - T e [ 2 ] x 4 1 1 6 . 9 5 ( 6 ) 1 1 6 . 5 2 ( 6 ) 1 1 7 . 4 9 ( 6 ) L a - T e [ 3 ] - T e [ 2 ] x 2 6 3 3 1 ( 6 ) 6 1 3 0 ( 6 ) 6 5 3 6 ( 6 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 6 8 9 3 7 ( 1 0 ) 8 4 . 5 7 ( 1 0 ) 9 4 3 0 ( 1 1 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 7 . 1 1 ( 1 1 ) 1 7 4 . 5 9 ( 1 1 ) 1 7 9 . 8 9 ( 9 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 9 1 . 1 8 ( 1 0 ) 8 7 . 4 8 ( 1 0 ) 9 4 . 9 8 ( 1 1 ) T a b l e 3 . 1 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C e T e 3 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 2 4 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 o ( 1 ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 0 ’ ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m a n d T m c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e C e T e 3 5 2 2 . 9 1 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 0 m ( 0 0 y ) 0 0 0 a = 4 . 3 5 6 6 ( 6 ) A , a = 9 0 0 b = 2 5 . 9 2 0 ( 3 ) A , 1 3 = 9 0 ° c = 4 . 3 7 2 2 ( 5 ) A , y = 9 0 0 0 . 2 7 9 0 ( 3 ) c ‘ 4 9 3 . 7 3 ( 1 0 ) A 3 4 7 . 0 3 2 6 g / c m 3 2 6 . 4 7 3 m m " 8 5 6 0 . 7 9 x 0 . 3 4 x 0 . 0 1 m m 3 2 . 0 3 t o 2 9 . 2 4 0 - 5 < = h < = 5 , - 3 4 < = k < = 3 4 , - 5 < = l < = 5 , - 1 < = m < = 1 6 8 3 2 ( 2 1 4 7 m a i n + 4 6 8 5 s a t e l l i t e s ) 1 9 2 3 ( 6 5 9 m a i n + 1 2 6 4 s a t e l l i t e S ) [ R i m = 0 . 0 2 6 6 ] 9 4 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 1 9 2 3 / 0 / 3 8 1 . 9 1 R . , , = 0 . 0 2 9 3 , w R o b s = 0 . 0 8 4 4 R , “ = 0 . 0 4 5 4 , w k . " = 0 . 1 1 8 3 R . , , s = 0 . 0 2 3 9 , w R o b s = 0 . 0 8 1 4 R , “ = 0 . 0 2 4 8 , w R . . . ] = 0 . 1 2 5 1 R o b , = 0 . 0 5 2 8 , w R o b s = 0 . 0 9 0 5 R 3 1 1 : 0 . 1 2 0 6 , W R a n = 0 . 1 0 1 7 0 . 0 0 0 1 0 ( 8 ) 0 . 0 7 2 2 a n d 0 . 7 3 6 8 3 . 4 3 a n d - 2 . 8 9 e . A ' 3 R = E l l F o l - I F e l l / 2 1 8 . 1 , w R = { X [ W ( | F o | 2 - c h | 2 ) 2 ] / > : 1 w ( I F . I ‘ ) 1 T ’ 2 a n d w = 1 / ( o z a ) + 0 . 0 0 1 6 1 2 > 1 4 8 T a b l e 3 . 1 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C e T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e x y 2 U 6 ; C e 0 9 2 4 9 1 6 8 8 ( 1 ) 2 5 4 9 3 ( 1 ) s i n , 1 0 0 6 ( 4 ) c o s , 1 - 6 6 ( 1 ) 0 ( 1 ) 0 T e [ 1 ] 0 9 1 9 9 ( 5 ) 2 9 5 8 ( 1 ) 2 5 4 9 4 ( 1 ) s i n , 1 0 0 4 3 ( 5 ) c o s , 1 - 1 1 ( 1 ) 7 ( 1 ) 0 T e [ 2 ] 0 9 2 0 9 ( 6 ) 6 9 6 ( 1 ) 7 5 4 9 5 ( 1 ) s i n , 1 0 0 - 1 1 ( 5 ) c o s , 1 3 0 7 ( 2 ) 1 ( 1 ) 0 T e [ 3 ] 0 9 2 4 2 ( 5 ) 4 3 0 1 ( 1 ) 7 5 4 9 5 ( 1 ) s i n , 1 0 0 1 4 ( 5 ) c o s , 1 - 2 4 9 ( 2 ) 1 ( 1 ) 0 " U . q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 1 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r C e T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 C e 3 ( 1 ) 4 ( 1 ) 2 ( 1 ) - 1 ( 1 ) 0 0 T e [ 1 ] 2 ( 1 ) 4 ( 1 ) 5 ( 1 ) 2 ( 1 ) 0 0 T e [ 2 ] 3 ( 1 ) 6 ( 1 ) 6 ( 1 ) - 3 ( 1 ) 0 0 T e [ 3 ] 2 ( 1 ) 5 ( 1 ) 7 ( 1 ) 3 ( 1 ) 0 0 T a b l e 3 . 1 4 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C e T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e C e - T e [ 1 ] 3 . 2 9 0 4 ( 1 3 ) 3 . 2 7 0 ( 2 ) 3 . 3 1 0 ( 2 ) C e - T e [ 1 ] x 4 3 . 2 2 0 2 ( 1 9 ) 3 . 2 0 6 9 ( 1 6 ) 3 . 2 3 3 6 ( 1 7 ) C e - T e [ 2 ] x 2 3 . 3 7 6 5 ( 1 7 ) 3 . 3 6 9 8 ( 1 8 ) 3 . 3 8 0 7 ( 1 6 ) C e - T e [ 3 ] 3 . 3 5 2 7 ( 1 7 ) 3 . 3 0 0 ( 2 ) 3 . 4 0 5 ( 2 ) C e - T e [ 3 ] 3 . 3 7 5 4 ( 1 7 ) 3 . 3 2 6 ( 2 ) 3 . 4 2 7 ( 2 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 7 9 ( 3 ) 2 . 9 2 5 ( 2 ) 3 . 2 3 5 ( 3 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 9 7 ( 3 ) 2 . 9 4 5 ( 2 ) 3 . 2 5 5 ( 3 ) 1 4 9 T a b l e 3 . 1 5 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C e T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - C e - T e [ 1 ] x 8 7 3 4 3 ( 4 ) 7 2 8 1 ( 4 ) 7 4 0 4 ( 4 ) T e [ 1 ] - C e - T e [ 2 ] x 2 1 3 9 . 5 8 ( 5 ) l 3 9 . 3 7 ( 6 ) 1 3 9 . 8 0 ( 7 ) T e [ 1 ] - C e - T e [ 3 ] 1 3 9 . 8 7 ( 5 ) 1 3 9 . 2 7 ( 5 ) 1 4 0 . 4 9 ( 5 ) T e [ 1 ] - C e - T e [ 3 ] l 3 9 . 4 3 ( 5 ) 1 3 8 . 8 1 ( 5 ) l 4 0 . 0 6 ( 5 ) T e [ 1 ] - C e - T e [ 1 ] x 4 8 5 5 2 ( 5 ) 8 4 4 6 ( 5 ) 8 6 5 7 ( 5 ) T e [ 1 ] - C e - T e [ 1 ] x 4 8 3 1 4 ( 6 ) 8 4 . 7 4 ( 6 ) 8 5 5 6 ( 6 ) T e [ 1 ] - C e - T e [ 1 ] x 4 1 4 6 . 8 6 ( 4 ) 1 4 6 . 3 8 ( 5 ) 1 4 7 . 3 3 ( 5 ) T e [ 1 ] - C e - T e [ 2 ] x 4 7 7 2 0 ( 5 ) 7 5 . 7 6 ( 5 ) 7 8 6 2 ( 5 ) T e [ 1 ] - C e - T e [ 2 ] x 4 l 3 l . 1 3 ( 5 ) 1 2 8 . 4 2 ( 5 ) 1 3 3 . 8 0 ( 5 ) T e [ 1 ] - C e - T e [ 3 ] x 2 7 7 . 4 1 ( 4 ) 7 6 7 6 ( 4 ) 7 8 0 9 ( 4 ) T e [ 1 ] - C e - T e [ 3 ] x 4 1 3 l . 0 4 ( 5 ) l 3 0 . 1 7 ( 5 ) 1 3 1 . 9 3 ( 5 ) T e [ 1 ] - C e - T e [ 3 ] x 2 7 7 0 9 ( 4 ) 7 6 6 7 ( 4 ) 7 7 5 2 ( 4 ) T e [ 2 ] - C e - T e [ 2 ] x 2 8 0 7 5 ( 4 ) 8 0 . 6 4 ( 5 ) 8 0 . 8 2 ( 4 ) T e [ 2 ] - C e - T e [ 3 ] x 4 5 4 . 4 7 ( 5 ) 5 1 8 5 ( 5 ) 5 7 0 6 ( 5 ) T e [ 3 ] - C e - T e [ 3 ] x 2 8 0 7 0 ( 4 ) 8 0 6 7 ( 5 ) 8 0 7 2 ( 4 ) C e - T e [ 1 ] - C e x 8 1 0 6 . 5 7 ( 5 ) 1 0 5 . 8 5 ( 4 ) 1 0 7 . 3 2 ( 4 ) C e - T e [ 1 ] - C e x 4 8 5 5 4 ( 6 ) 8 5 . 4 5 ( 6 ) 8 5 6 2 ( 6 ) C e - T e [ 1 ] - C e x 4 8 5 1 4 ( 4 ) 8 4 . 7 4 ( 5 ) 8 5 5 6 ( 5 ) C e - T e [ 1 ] - C e x 4 1 4 6 . 8 7 ( 4 ) 1 4 6 . 2 1 ( 6 ) l 4 7 5 1 ( 6 ) C e - T e [ 2 ] - C e x 2 8 0 7 0 ( 4 ) 8 0 5 5 ( 5 ) 8 0 . 7 8 ( 4 ) C e - T e [ 2 ] - T e [ 3 ] x 2 6 2 3 6 ( 4 ) 6 1 5 7 ( 3 ) 6 3 1 7 ( 4 ) C e - T e [ 2 ] - T e [ 3 ] x 4 1 1 7 . 2 1 ( 7 ) 1 1 3 . 8 8 ( 7 ) 1 2 0 . 4 9 ( 8 ) C e - T e [ 2 ] - T e [ 3 ] x 2 6 2 6 6 ( 4 ) 6 1 9 5 ( 4 ) 6 3 3 1 ( 4 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 9 0 7 1 ( 9 ) 8 5 5 7 ( 8 ) 9 6 0 9 ( 1 0 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 6 8 9 6 5 ( 6 ) 8 9 4 3 ( 6 ) 9 0 0 6 ( 7 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 6 . 5 8 ( 9 ) 1 7 4 . 2 4 ( 9 ) 1 7 9 . 7 2 ( 3 ) C e - T e [ 3 ] - C e x 2 8 0 7 0 ( 3 ) 8 0 6 7 ( 5 ) 8 0 . 7 2 0 ( 1 3 ) C e - T e [ 3 ] - T e [ 2 ] x 2 6 2 7 3 ( 4 ) 6 0 7 7 ( 4 ) 6 4 . 7 5 ( 5 ) C e - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 3 0 ( 5 ) 1 1 6 . 3 4 ( 5 ) 1 1 8 . 1 3 ( 4 ) C e - T e [ 3 ] - T e [ 2 ] x 2 6 3 1 9 ( 4 ) 6 1 0 9 ( 4 ) 6 5 3 9 ( 5 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 6 8 9 9 9 ( 8 ) 8 5 0 8 ( 8 ) 9 5 0 3 ( 9 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 6 . 7 3 ( 9 ) 1 7 4 . 5 0 ( 8 ) 1 7 9 . 7 3 ( 3 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 9 0 7 1 ( 8 ) 8 5 5 7 ( 8 ) 9 6 0 5 ( 9 ) 1 5 0 T a b l e 3 . 1 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C e T e 3 a t 1 0 0 K ( 2 n d o r d e r s a t e l l i t e s ) E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 2 4 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 6 ( 1 ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 c ( 1 ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) F i n a l R 2 n d o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 2 ' ” I d o r d e r s a t e l l i t e s ( a l l d a t a ) T m a n d T m c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e C e T e 3 5 2 2 . 9 1 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A O r t h o r h o m b i c C 2 c m ( 0 0 y ) 0 0 0 a = 4 . 3 5 6 6 ( 6 ) A , 0 1 = 9 0 ° b = 2 5 . 9 2 0 ( 3 ) A , [ 3 = 9 0 ° c = 4 . 3 7 2 2 ( 5 ) A , y = 9 0 0 0 . 2 7 9 0 ( 3 ) c ‘ 4 9 3 . 7 3 ( 1 0 ) A 3 4 7 . 0 3 2 6 g / c m 3 2 6 . 4 7 3 m m " 8 5 6 0 . 7 9 x 0 . 3 4 x 0 . 0 1 m m 3 2 . 0 3 t o 2 9 . 2 4 ° - 5 < = h < = 5 , - 3 4 < = k < = 3 5 , - 5 < = l < = 5 , - 2 < = m < = 2 9 1 0 6 ( 2 1 4 7 m a i n + 6 9 5 9 s a t e l l i t e s ) 2 7 6 9 ( 6 5 9 m a i n + 2 1 1 0 s a t e l l i t e s ) [ R i m = 0 . 0 3 3 5 ] 9 4 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 2 7 6 9 / 0 / 7 3 1 . 7 0 R o b , = 0 . 0 3 7 2 , w R o b , = 0 . 0 9 1 0 R a n = 0 . 0 6 3 7 , W R a n = 0 . 1 2 3 9 R o b , = 0 . 0 3 5 4 , w R . . . , = 0 . 0 9 8 3 R 3 “ = 0 . 0 3 6 3 , W R a n = 0 . 1 3 5 4 R 0 , , = 0 . 0 3 5 0 , w R . . . , = 0 . 0 6 6 3 R . , . = 0 . 0 9 2 4 , w R a u = 0 . 0 7 7 3 R . , . . . = 0 . 1 5 2 0 , w R o b s = 0 . 2 1 8 2 R , “ = 0 . 3 9 3 3 , m e = 0 . 3 4 7 1 0 . 0 7 2 2 a n d 0 . 7 3 6 8 5 . 1 0 a n d - 3 . 3 9 e . A ' 3 R = 2 | | F o | - | F c | | / 2 | F , | , w R = { 1 : [ w ( | 1 = . | 2 - [ 1 3 4 2 3 2 ] / > : [ w ( | l = , | 4 ) ] } ” 2 a n d w = l / ( o Z ( I ) + 0 . 0 0 1 6 I Z ) 1 5 1 T a b l e 3 . 1 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C e T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s ( 2 n d o r d e r s a t e l l i t e s ) . L a b e l W a v e x y z U e q C e 0 9 2 4 9 1 6 8 8 ( 1 ) 2 5 4 9 3 ( 1 ) s i n , 1 0 0 0 ( 3 ) c o s , 1 - 6 4 ( 1 ) 0 ( 1 ) 0 s i n , 2 0 0 2 ( 4 ) c o s , 2 1 ( 3 ) 1 ( 1 ) 0 T e [ 1 ] 0 9 1 7 9 ( 5 ) 2 9 5 8 ( 1 ) 2 5 4 9 4 ( 1 ) s i n , 1 0 0 - 5 ( 4 ) c o s , 1 - 1 1 ( 1 ) - 1 ( 1 ) 0 s i n , 2 0 0 9 ( 5 ) c o s , 2 - 5 ( 3 ) 0 ( 1 ) 0 T e [ 2 ] 0 9 2 0 9 ( 8 ) 6 9 6 ( 1 ) 7 5 4 9 6 ( 1 ) s i n , 1 0 0 - 1 0 ( 4 ) c o s , 1 2 9 2 ( 2 ) 1 ( 1 ) 0 s i n , 2 O 0 - 3 8 ( 8 ) c o s , 2 - 1 9 ( 8 ) 1 ( 1 ) 0 T e [ 3 ] 0 9 1 9 6 ( 6 ) 4 3 0 1 ( 1 ) 7 5 4 9 6 ( 1 ) s i n , 1 0 0 5 4 ( 4 ) c o s , 1 - 2 4 2 ( 2 ) 5 ( 1 ) 0 s i n , 2 0 0 - 1 2 ( 8 ) c o s , 2 1 6 ( 7 ) 6 ( 1 ) 0 ” U . . . I i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 1 8 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r C e T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s ( 2 n d o r d e r s a t e l l i t e s ) . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 C e 5 ( 1 ) 3 ( 1 ) 2 ( 1 ) - 1 ( 1 ) 0 0 T e [ 1 ] 4 ( 1 ) 4 ( 1 ) 6 ( 1 ) 4 ( 1 ) 0 0 T e [ 2 ] 5 ( 1 ) 5 ( 1 ) 7 ( 1 ) - 1 ( 1 ) 0 0 T e [ 3 ] 5 ( 1 ) 4 ( 1 ) 8 ( 1 ) 2 ( 1 ) 0 0 1 5 2 T a b l e 3 . 1 9 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C e T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s ( 2 n d o r d e r s a t e l l i t e s ) . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e C e - T e [ 1 ] 3 . 2 9 1 7 ( 1 8 ) 3 . 2 8 8 ( 3 ) 3 . 2 9 4 1 ( 1 5 ) C e - T e [ 1 ] x 2 3 . 2 2 6 ( 3 ) 3 . 2 0 7 ( 2 ) 3 . 2 4 5 ( 3 ) C e - T e [ 1 ] x 2 3 . 2 1 3 ( 3 ) 3 . 1 9 9 ( 3 ) 3 . 2 3 1 ( 3 ) C e - T e [ 2 ] x 2 3 . 3 7 7 ( 3 ) 3 . 3 6 5 ( 4 ) 3 . 3 8 6 ( 3 ) C e - T e [ 3 ] x 2 3 . 3 6 6 ( 3 ) 3 . 3 1 6 ( 4 ) 3 . 4 3 3 ( 4 ) T e [ 2 ] - T e [ 3 ] x 4 3 . 0 9 3 ( 5 ) 2 . 9 2 0 ( 4 ) 3 . 2 3 5 ( 5 ) T a b l e 3 . 2 0 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C e T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s ( 2 “ d o r d e r s a t e l l i t e s ) . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - C e - T e [ 1 ] x 8 7 3 3 8 ( 5 ) 7 3 1 7 ( 5 ) 7 3 5 8 ( 5 ) T e [ 1 ] - C e - T e [ 2 ] x 2 1 3 9 . 5 9 ( 1 0 ) 1 3 9 . 2 7 ( 9 ) 1 3 9 . 8 5 ( 8 ) T e [ 1 ] - C e - T e [ 3 ] x 2 1 3 9 . 4 7 ( 6 ) 1 3 9 . 1 1 ( 5 ) 1 4 0 . 1 9 ( 8 ) T e [ 1 ] - C e - T e [ 1 ] x 8 8 5 3 4 ( 7 ) 8 4 9 6 ( 8 ) 8 5 9 7 ( 8 ) T e [ 1 ] - C e - T e [ 1 ] x 4 1 4 6 . 9 1 ( 5 ) 1 4 6 . 7 7 ( 4 ) 1 4 7 . 0 6 ( 8 ) T e [ 1 ] - C e - T e [ 2 ] x 4 7 7 2 1 ( 8 ) 7 5 4 0 ( 9 ) 7 8 8 4 ( 8 ) T e [ 1 ] - C e - T e [ 2 ] x 4 l 3 1 . 0 3 ( 8 ) 1 2 8 . 4 2 ( 7 ) 1 3 3 . 3 5 ( 7 ) T e [ 1 ] - C e - T e [ 3 ] x 4 7 7 . 1 3 ( 8 ) 7 6 6 6 ( 8 ) 7 7 . 7 9 ( 8 ) T e [ 1 ] - C e - T e [ 3 ] x 4 1 3 0 . 9 6 ( 1 0 ) l 3 0 . 2 3 ( 1 0 ) 1 3 1 . 7 5 ( 1 1 ) T e [ 2 ] - C e - T e [ 2 ] x 2 8 0 7 3 ( 9 ) 8 0 1 5 ( 1 1 ) 8 1 2 7 ( 9 ) T e [ 2 ] - C e - T e [ 3 ] x 4 5 4 . 6 l ( 1 0 ) 5 1 . 7 1 ( 1 0 ) 5 7 0 2 ( 1 1 ) T e [ 3 ] - C e - T e [ 3 ] x 2 8 0 7 0 ( 6 ) 8 0 0 5 ( 9 ) 8 1 . 1 2 ( 7 ) C e - T e [ 1 ] - C e x 8 8 5 . 7 4 ( 7 ) 8 5 5 0 ( 8 ) 8 6 1 2 ( 8 ) C e - T e [ 1 ] - C e x 4 1 4 6 . 9 1 ( 6 ) 1 4 6 . 7 5 ( 4 ) 1 4 7 . 0 8 ( 4 ) C e - T e [ 2 ] - C e x 2 8 0 6 9 ( 6 ) 8 0 6 4 ( 8 ) 8 0 7 7 ( 8 ) C e - T e [ 2 ] - T e [ 3 ] x 4 1 1 7 . 0 6 ( 1 0 ) 1 1 4 . 1 9 ( 1 3 ) 1 2 0 . 2 2 ( 1 2 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 8 9 0 1 7 ( 1 5 ) 8 5 . 6 8 ( 1 6 ) 9 4 . 9 9 ( 1 9 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 6 . 6 9 ( 1 6 ) 1 7 4 . 7 4 ( 1 6 ) 1 7 9 . 7 4 ( 9 ) C e - T e [ 3 ] - T e [ 2 ] x 4 6 3 0 2 ( 8 ) 6 0 9 5 ( 8 ) 6 4 5 6 ( 7 ) C e - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 2 9 ( 9 ) 1 1 6 . 6 2 ( 9 ) 1 1 7 . 7 6 ( 9 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 9 0 5 0 ( 1 4 ) 8 5 . 1 7 ( 1 6 ) 9 4 8 2 ( 1 8 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 8 9 6 5 ( 1 3 ) 8 8 6 0 ( 1 2 ) 9 0 1 9 ( 1 5 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 6 . 7 2 ( 1 5 ) 1 7 5 0 0 ( 1 7 ) 1 7 9 . 2 2 ( 7 ) 1 5 3 T a b l e 3 . 2 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C e T e 3 a t 5 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 2 8 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 o ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 < 3 ( 1 ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 s t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m i n a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e C e T e 3 5 2 2 . 9 5 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 0 m ( 0 0 y ) 0 0 0 a = 4 . 3 8 3 7 ( 1 1 ) A , a = 9 0 ° b = 2 6 . 0 5 0 ( 7 ) A , [ 3 = 9 0 ° c = 4 . 4 0 3 3 ( 9 ) A , y = 9 0 ° 0 . 2 8 6 7 ( 5 ) c ‘ 5 0 2 . 8 ( 2 ) A 3 4 6 . 9 0 5 g / c m 3 2 5 . 9 9 3 m m " 8 5 6 0 . 7 9 x 0 . 3 4 x 0 . 0 1 m m 3 2 . 0 5 t o 2 9 . 2 8 ° - 6 < = h < = 6 , - 3 5 < = k < = 3 5 , - 6 < = l < = 5 , - 1 < = m < = 1 7 1 4 2 ( 2 3 4 8 m a i n + 4 7 9 4 s a t e l l i t e s ) 2 0 9 2 ( 7 3 9 m a i n + 1 3 5 3 s a t e l l i t e S ) [ R i m = 0 . 0 6 5 6 ] 9 9 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 2 0 9 2 / 0 / 3 8 1 . 3 6 R o b s = 0 . 0 3 9 4 , w R o b , = 0 . 0 9 6 5 R , “ = 0 . 0 7 5 9 , w R a n = 0 . 1 0 5 2 R o b s = 0 . 0 3 2 0 , w R o b s = 0 . 0 8 3 3 R , " = 0 . 0 3 4 2 , w R a u = 0 . 0 8 3 9 R o b s = 0 . 1 3 6 4 , w R o b s = 0 . 1 8 9 5 R , " = 0 . 3 6 4 6 , m e = 0 . 2 3 4 5 0 . 0 0 0 3 4 ( 4 ) 0 . 0 7 2 2 a n d 0 . 7 3 6 8 1 . 6 0 a n d - 2 0 7 6 A 3 R = l e F o l - I F c I I / E l F o l . W R = { Z [ W ( | F o l r - c h l l e ] / 2 3 1 ‘ 1 / ( l l : o | 4 ) ] } " 2 a n d W = 1 / ( 0 2 ( 1 ) + 0 - 0 0 1 6 1 2 ) 1 5 4 T a b l e 3 . 2 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C e T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . 1 p L a b e l W a v e x y 2 H . , , C e 0 9 2 4 9 1 6 9 0 ( 1 ) 2 5 4 9 2 2 ( 1 ) s i n , 1 0 0 2 8 ( 5 ) c o s , 1 3 4 ( 1 ) 8 ( 1 ) 0 T e [ 1 ] 0 9 2 0 2 ( 8 ) 2 9 5 9 ( 1 ) 2 5 4 9 2 2 ( 1 ) s i n , 1 0 0 0 ( 5 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 0 T e [ 2 ] 0 9 2 1 0 ( 1 2 ) 6 9 9 ( 1 ) 7 5 4 9 2 9 ( 1 ) s i n , 1 0 0 1 2 ( 6 ) c o s , 1 - 1 7 5 ( 3 ) - 1 ( 1 ) 0 T e [ 3 ] 0 9 1 7 6 ( 1 0 ) 4 2 9 9 ( 1 ) 7 5 4 9 2 9 ( 1 ) s i n , 1 0 0 1 6 ( 6 ) c o s , 1 1 3 3 ( 3 ) - 2 ( 1 ) 0 U “ , i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 2 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r C e T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 C e 1 8 ( 1 ) 3 0 ( 1 ) 1 9 ( 1 ) - 1 ( 1 ) 0 0 T e [ 1 ] 1 8 ( 1 ) 3 0 ( 1 ) 1 9 ( 1 ) 1 ( 1 ) 0 0 T e [ 2 ] 2 6 ( 1 ) 3 4 ( 1 ) 2 7 ( 1 ) - 1 ( 1 ) 0 0 T e [ 3 ] 2 5 ( 1 ) 3 5 ( 1 ) 2 8 ( 1 ) - 5 ( 1 ) 0 0 T a b l e 3 . 2 4 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C e T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e C e - T e [ 1 ] 3 . 3 0 5 1 ( 1 8 ) 3 . 2 8 5 ( 3 ) 3 . 3 2 5 ( 3 ) C e - T e [ 1 ] x 4 3 . 2 3 8 ( 3 ) 3 . 2 2 9 ( 3 ) 3 . 2 4 7 ( 3 ) C e - T e [ 2 ] x 2 3 . 3 9 5 ( 2 ) 3 . 3 7 4 ( 2 ) 3 . 4 1 6 ( 2 ) C e - T e [ 3 ] 3 . 3 9 0 ( 3 ) 3 . 3 7 4 ( 4 ) 3 . 4 0 8 ( 4 ) C e - T e [ 3 ] 3 . 3 7 7 ( 3 ) 3 . 3 3 8 ( 4 ) 3 . 4 1 6 ( 4 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 1 1 8 ( 5 ) 3 . 0 3 7 ( 5 ) 3 . 2 0 1 ( 5 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 9 7 ( 5 ) 3 . 0 0 8 ( 5 ) 3 . 1 8 7 ( 5 ) 1 5 5 T a b l e 3 . 2 5 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C e T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - C e - T e [ 1 ] x 8 7 3 6 3 ( 6 ) 7 3 3 7 ( 6 ) 7 3 8 8 ( 6 ) T e [ 1 ] - C e - T e [ 2 ] x 2 1 3 9 . 5 4 ( 6 ) 1 3 9 . 2 0 ( 7 ) 1 3 9 . 9 1 ( 7 ) T e [ 1 ] - C e - T e [ 3 ] x 2 1 3 9 . 5 1 ( 9 ) 1 3 9 . 0 5 ( 9 ) 1 3 9 . 9 6 ( 9 ) T e [ 1 ] - C e - T e [ 1 ] x 4 8 5 6 9 ( 7 ) 8 5 5 6 ( 7 ) 8 5 8 1 ( 7 ) T e [ 1 ] - C e - T e [ 1 ] x 4 8 5 2 0 ( 8 ) 8 4 8 8 ( 8 ) 8 5 5 3 ( 8 ) T e [ 1 ] - C e - T e [ 1 ] x 4 1 4 7 . 2 5 ( 5 ) 1 4 6 . 5 0 ( 7 ) 1 4 7 . 9 8 ( 7 ) T e [ 1 ] - C e - T e [ 2 ] x 4 7 6 9 5 ( 8 ) 7 3 7 1 ( 8 ) 7 8 2 2 ( 8 ) T e [ 1 ] - C e - T e [ 2 ] x 4 1 3 l . 0 4 ( 1 0 ) 1 2 9 . 3 l ( 1 0 ) 1 3 2 . 7 9 ( 1 0 ) T e [ 1 ] - C e - T e [ 3 ] x 4 7 6 9 9 ( 7 ) 7 6 9 3 ( 6 ) 7 7 0 5 ( 6 ) T e [ 1 ] - C e - T e [ 3 ] x 4 1 3 0 . 7 3 ( 7 ) 1 3 0 . 5 1 ( 8 ) 1 3 0 . 9 5 ( 8 ) T e [ 2 ] - C e - T e [ 2 ] x 2 8 0 8 9 ( 5 ) 8 0 4 9 ( 6 ) 8 1 2 6 ( 6 ) T e [ 2 ] - C e - T e [ 3 ] x 4 5 4 7 0 ( 9 ) 5 3 1 1 ( 9 ) 5 6 3 4 ( 9 ) T e [ 3 ] - C e - T e [ 3 ] x 2 8 0 7 4 ( 9 ) 8 0 4 3 ( 1 0 ) 8 1 . 0 6 ( 1 0 ) C e - T e [ 1 ] - C e x 8 1 0 6 . 3 7 ( 7 ) 1 0 6 . 2 8 ( 6 ) 1 0 6 . 4 6 ( 6 ) C e - T e [ 1 ] - C e x 4 8 5 6 7 ( 9 ) 8 5 0 8 ( 9 ) 8 6 2 4 ( 9 ) C e - T e [ 1 ] - C e x 4 8 5 2 0 ( 4 ) 8 4 8 8 ( 6 ) 8 5 5 3 ( 6 ) C e - T e [ 1 ] - C e x 4 1 4 7 . 2 4 ( 5 ) 1 4 6 . 6 9 ( 8 ) 1 4 7 . 7 9 ( 8 ) C e - T e [ 2 ] - C e x 2 8 0 8 7 ( 5 ) 8 0 7 7 ( 7 ) 8 0 9 5 ( 7 ) C e - T e [ 2 ] - T e [ 3 ] x 4 6 2 5 7 ( 6 ) 6 2 2 5 ( 6 ) 6 2 8 7 ( 6 ) C e - T e [ 2 ] - T e [ 3 ] x 4 1 1 7 . 1 2 ( 1 2 ) 1 1 5 . 2 7 ( 1 3 ) l l 8 . 9 3 ( 1 3 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 8 8 9 9 1 ( 1 7 ) 8 6 8 6 ( 1 6 ) 9 3 0 1 ( 1 8 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 8 . 0 9 ( 1 7 ) 1 7 6 . 6 6 ( 1 7 ) 1 7 9 . 7 7 ( 5 ) C e - T e [ 3 ] - C e x 2 8 0 . 7 5 ( 4 ) 8 0 4 3 ( 6 ) 8 1 0 6 ( 6 ) C e - T e [ 3 ] - T e [ 2 ] x 4 6 3 0 8 ( 8 ) 6 2 2 4 ( 8 ) 6 3 9 5 ( 8 ) C e - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 2 7 ( 7 ) 1 1 6 . 7 7 ( 6 ) 1 1 7 . 7 5 ( 6 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 9 0 6 9 ( 1 6 ) 8 8 0 4 ( 1 6 ) 9 3 3 9 ( 1 7 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 8 9 7 0 ( 1 2 ) 8 9 5 3 ( 1 1 ) 8 9 8 1 ( 1 3 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 8 2 0 ( 1 6 ) l 7 6 . 8 4 ( 1 6 ) 1 7 9 . 7 8 ( 5 ) 1 5 6 T a b l e 3 . 2 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r P r T e 3 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 1 3 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( 1 ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 o ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e P r T e 3 5 2 3 . 7 1 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 c m ( 0 0 y ) 0 0 0 a = 4 . 3 4 7 5 ( 9 ) A , 0 1 = 9 0 ° b = 2 5 . 8 0 0 ( 5 ) A , B = 9 0 ° c = 4 . 3 5 4 8 ( 9 ) A , y = 9 0 ° 0 . 2 8 2 5 ( 5 ) c ‘ 4 8 8 . 4 6 ( l 7 ) A 3 4 7 . 1 1 9 g / o m 3 2 7 . 1 7 7 m m " 8 6 0 0 . 3 2 x 0 . 3 1 x 0 . 0 2 m m 3 2 . 0 5 t o 2 9 . 1 3 ° - 5 < = h < = 5 , - 3 4 < = k < = 3 4 , - 6 < = l < = 6 , - 1 < = m < = 1 6 1 2 1 ( 1 7 5 6 m a i n + 4 3 6 5 s a t e l l i t e s ) 1 9 4 4 ( 6 4 0 m a i n + 1 3 0 4 s a t e l l i t e S ) [ R i o t = 0 . 0 2 9 3 ] 9 7 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 1 9 4 4 / 0 / 3 7 1 . 4 2 R o b , = 0 . 0 2 8 4 , w R o b , = 0 . 0 8 3 0 R , “ = 0 . 0 4 4 0 , w R a u = 0 . 0 9 0 0 R o b s = 0 . 0 2 2 6 , w R o b , = 0 . 0 7 6 9 R a n = 0 . 0 2 3 2 , w R a n = 0 . 0 7 7 1 R o b s = 0 . 0 5 3 4 , w R o b s = 0 . 0 9 5 2 R , " = 0 . 1 2 0 1 , w R a u = 0 . 1 1 3 5 0 . 0 0 1 8 4 ( 7 ) 0 . 0 0 9 1 a n d 0 . 5 9 3 1 2 . 0 9 a n d - l . 8 0 e . A ' 3 R = l e F o l - l F e l l / Z I F o I , w R = { 2 [ W ( | F o | 2 - I F c l e ] / 2 3 [ W ( | F o l 4 ) ] } ” 2 a n d W = 1 / ( 0 2 ( 1 ) + 0 - 0 0 1 6 T Z ) 1 5 7 T a b l e 3 . 2 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r P r T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . a L a b e l W a v e x y z U e q P r 0 9 0 0 0 1 6 9 0 ( 1 ) 2 5 4 9 1 ( 1 ) s i n , 1 0 0 - 5 ( 2 ) c o s , 1 - 6 1 ( 1 ) 0 ( 1 ) 0 T e [ 1 ] 0 8 9 7 2 ( 3 ) 2 9 5 7 ( 1 ) 2 5 4 9 1 ( 1 ) s i n , 1 0 0 1 5 ( 3 ) c o s , 1 - 9 ( 1 ) 5 ( 1 ) 0 T e [ 2 ] 0 9 0 4 5 ( 4 ) 6 9 9 ( 1 ) 7 5 4 9 2 ( 1 ) s i n , 1 0 0 - 3 ( 3 ) c o s , 1 2 7 8 ( 1 ) 0 ( 1 ) 0 T e [ 3 ] 0 9 0 1 8 ( 3 ) 4 2 9 8 ( 1 ) 7 5 4 9 2 ( 1 ) s i n , 1 0 0 - 7 ( 3 ) c o s , 1 - 2 2 7 ( 1 ) 1 ( 1 ) 0 ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 2 8 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r P r T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 P r 2 ( 1 ) 1 ( 1 ) 1 ( 1 ) 1 ( 1 ) 0 0 T e [ 1 ] 2 ( 1 ) 1 ( 1 ) 1 ( 1 ) 2 ( 1 ) 0 0 T e [ 2 ] 2 ( 1 ) 3 ( 1 ) 2 ( 1 ) 4 ( 1 ) 0 0 T e [ 3 ] 3 ( 1 ) 3 ( 1 ) 2 ( 1 ) - 2 ( 1 ) 0 0 T a b l e 3 . 2 9 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r P r T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e P r - T e [ 1 ] 3 . 2 6 9 2 ( 1 0 ) 3 . 2 5 6 6 ( 1 6 ) 3 . 2 8 1 7 ( 1 6 ) P r - T e [ 1 ] x 2 3 . 2 1 7 3 ( 1 2 ) 3 . 2 0 0 9 ( 1 1 ) 3 . 2 3 4 0 ( 1 1 ) P r — T e [ 1 ] x 2 3 . 2 0 1 0 ( 1 2 ) 3 . 1 8 1 6 ( 1 3 ) 3 . 2 2 0 1 ( 1 3 ) P r - T e [ 2 ] x 2 3 . 3 5 9 1 ( 1 0 ) 3 . 3 5 6 8 ( 1 0 ) 3 . 3 6 0 9 ( 1 1 ) P r - T e [ 3 ] 3 3 4 5 7 ( 1 2 ) 3 . 2 9 5 6 ( 1 6 ) 3 . 3 9 5 3 ( 1 6 ) P r - T e [ 3 ] 3 . 3 5 5 2 ( 1 2 ) 3 . 3 1 1 7 ( 1 6 ) 3 . 4 0 0 0 ( 1 6 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 8 7 3 ( 1 8 ) 2 . 9 4 8 9 ( 1 6 ) 3 . 2 2 7 2 ( 1 8 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 6 9 4 ( 1 8 ) 2 . 9 3 0 6 ( 1 6 ) 3 . 2 1 3 1 ( 1 8 ) 1 5 8 T a b l e 3 . 3 0 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r P r T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - P r - T e [ 1 ] x 8 7 3 3 8 ( 3 ) 7 2 9 1 ( 3 ) 7 3 8 4 ( 3 ) T e [ 1 ] - P r - T e [ 2 ] x 2 l 3 9 . 5 3 ( 3 ) 1 3 9 . 3 5 ( 3 ) 1 3 9 . 7 2 ( 4 ) T e [ 1 ] - P r - T e [ 3 ] x 2 1 3 9 . 4 4 ( 3 ) 1 3 8 . 9 4 ( 4 ) l 3 9 . 9 5 ( 4 ) T e [ 1 ] - P r — T e [ 1 ] x 6 8 5 . 1 9 ( 3 ) 8 4 4 3 ( 3 ) 8 5 9 4 ( 3 ) T e [ 1 ] - P r — T e [ 1 ] x 4 l 4 6 9 7 ( 3 ) 1 4 6 . 5 9 ( 4 ) 1 4 7 . 3 3 ( 4 ) T e [ 1 ] - P r - T e [ 2 ] x 2 7 7 3 6 ( 3 ) 7 5 9 2 ( 3 ) 7 8 7 7 ( 3 ) T e [ 1 ] - P r - T e [ 2 ] x 2 1 3 1 . 1 9 ( 4 ) 1 2 8 . 8 2 ( 4 ) 1 3 3 . 5 4 ( 4 ) T e [ 1 ] - P r - T e [ 3 ] x 4 7 7 0 7 ( 3 ) 7 6 4 8 ( 3 ) 7 7 6 8 ( 3 ) T e [ 1 ] - P r - T e [ 3 ] x 2 1 3 1 . 0 7 ( 3 ) 1 3 0 . 3 4 ( 3 ) 1 3 1 . 8 1 ( 3 ) T e [ 1 ] - P r - T e [ 1 ] x 2 8 5 . 7 2 ( 3 ) 8 5 4 1 ( 3 ) 8 6 0 5 ( 3 ) T e [ 1 ] - P r - T e [ 2 ] x 2 7 6 8 0 ( 3 ) 7 5 0 2 ( 3 ) 7 8 6 0 ( 3 ) T e [ 1 ] - P r - T e [ 2 ] x 2 1 3 0 . 8 4 ( 4 ) 1 2 8 . 5 1 ( 4 ) 1 3 3 . 1 8 ( 4 ) T e [ 1 ] - P r - T e [ 3 ] x 2 1 3 0 . 8 8 ( 3 ) 1 3 0 . 5 3 ( 3 ) 1 3 1 . 2 2 ( 3 ) T e [ 2 ] - P r - T e [ 2 ] x 2 8 0 8 6 ( 3 ) 8 0 7 5 ( 3 ) 8 0 9 1 ( 2 ) T e [ 2 ] - P r - T e [ 3 ] x 2 5 4 8 4 ( 4 ) 5 2 5 3 ( 4 ) 5 7 . 1 3 ( 4 ) T e [ 2 ] - P r - T e [ 3 ] x 2 5 4 3 9 ( 4 ) 5 2 0 5 ( 4 ) 5 6 8 1 ( 4 ) T e [ 3 ] - P r - T e [ 3 ] x 2 8 0 8 9 ( 3 ) 8 0 8 0 ( 4 ) 8 0 9 6 ( 4 ) P r - T e [ 1 ] - P r x 8 1 0 6 . 7 0 ( 3 ) 1 0 6 . 1 0 ( 3 ) 1 0 7 . 3 1 ( 3 ) P r - T e [ 1 ] - P r x 8 8 5 2 8 ( 2 ) 8 5 . 0 3 5 ( 1 9 ) 8 5 . 5 1 8 ( 1 9 ) P r - T e [ 1 ] - P r x 4 1 4 6 . 9 7 ( 3 ) 1 4 6 . 4 7 ( 4 ) 1 4 7 . 4 7 ( 4 ) P r - T e [ 2 ] - P r x 2 8 0 8 1 ( 2 ) 8 0 7 0 ( 3 ) 8 0 . 8 7 2 ( 1 8 ) P r - T e [ 2 ] - T e [ 3 ] x 4 6 2 3 4 ( 2 ) 6 1 . 7 2 ( 2 ) 6 2 9 7 ( 2 ) P r - T e [ 2 ] - T e [ 3 ] x 2 1 1 6 . 8 5 ( 5 ) 1 1 3 . 7 3 ( 5 ) l 1 9 9 4 ( 5 ) P r - T e [ 2 ] - T e [ 3 ] x 2 1 1 7 . 5 4 ( 5 ) 1 1 4 . 4 2 ( 5 ) 1 2 0 . 6 3 ( 5 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 6 8 9 9 0 ( 6 ) 8 5 . 1 2 ( 6 ) 9 4 8 7 ( 7 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 l 7 6 9 l ( 6 ) 1 7 4 . 8 5 ( 6 ) 1 7 9 . 7 4 ( 3 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 9 0 5 3 ( 6 ) 8 5 8 1 ( 6 ) 9 5 . 4 0 ( 7 ) P r - T e [ 3 ] - P r x 2 8 0 . 8 9 5 ( 1 9 ) 8 0 8 0 ( 3 ) 8 0 9 6 ( 3 ) P r - T e [ 3 ] - T e [ 2 ] x 4 6 2 8 8 ( 3 ) 6 1 0 4 ( 3 ) 6 4 7 5 ( 3 ) P r - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 4 8 ( 3 ) 1 1 6 . 5 7 ( 3 ) 1 1 8 . 2 9 ( 3 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 9 0 5 3 ( 5 ) 8 5 9 6 ( 5 ) 9 5 2 1 ( 6 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 6 8 9 7 8 ( 5 ) 8 9 6 4 ( 4 ) 8 9 9 5 ( 5 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 7 . 0 4 ( 6 ) 1 7 5 . 0 7 ( 6 ) 1 7 9 . 7 2 ( 3 ) T a b l e 3 . 3 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r P r T e 3 a t 5 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q — v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 2 2 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( 1 ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( 1 ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e P r T e 3 5 2 3 . 7 5 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 c m ( 0 0 y ) 0 0 0 a = 4 . 3 6 3 0 ( 9 ) A , 0 1 = 9 0 ° b = 2 6 . 0 2 6 ( 7 ) A , 1 3 = 9 0 ° c = 4 . 3 7 2 1 ( 8 ) A , y = 9 0 ° 0 . 2 8 6 4 ( 4 ) o ‘ 4 9 6 . 4 6 ( 1 8 ) A 3 4 7 . 0 0 4 g / c m 3 2 6 . 7 3 9 m m " 8 6 0 0 . 3 2 x 0 . 3 1 x 0 . 0 2 m m 3 2 . 0 5 t o 2 9 . 2 2 ° - 5 < = h < = 6 , - 3 4 < = k < = 3 5 , - 6 < = 1 < = 6 , - 1 < = m < = 1 6 5 9 2 ( 2 0 2 9 m a i n + 4 5 6 3 s a t e l l i t e s ) 2 0 2 4 ( 6 9 3 m a i n + 1 3 3 1 s a t e l l i t e s ) [ R i m = 0 . 0 4 0 8 ] 9 8 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 2 0 2 4 / 0 / 3 8 1 . 2 9 R o b , = 0 . 0 2 9 9 , w R . . . , s = 0 . 0 8 2 8 R , " = 0 . 0 6 0 7 , w R . . . , = 0 . 0 9 4 0 R . , , = 0 . 0 2 2 6 , w R o b , = 0 . 0 6 2 6 R , “ = 0 . 0 2 3 2 , w R , “ = 0 . 0 6 2 9 R o b , = 0 . 1 2 6 0 , w R o b s = 0 . 1 7 3 1 R . , . = 0 . 3 5 1 3 , w R a u = 0 . 2 1 5 7 0 . 0 0 1 5 8 ( 7 ) 0 . 0 0 9 1 a n d 0 . 5 9 3 1 2 . 0 7 a n d - 2 . 7 1 e . A ' 3 R = l e F o l - I F C H / 2 | F , | , w R = { 2 [ w ( | l = , | 2 - | F c | 2 ) 2 ] / 2 [ w ( | F , | “ ) ] } ” 2 a n d w = 1 / ( 6 2 ( I ) + 0 0 0 1 6 1 2 ) 1 6 0 T a b l e 3 . 3 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r P r T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e x y z U e q ‘ P r 0 9 0 0 0 1 6 9 2 ( 1 ) 2 5 4 9 1 2 ( 1 ) s i n , 1 0 0 7 ( 4 ) c o s , 1 2 7 ( 1 ) 0 ( 1 ) 0 T e [ 1 ] 0 9 0 2 4 ( 3 ) 2 9 5 7 ( 1 ) 2 5 4 9 1 2 ( 1 ) s i n , 1 0 0 - 2 4 ( 4 ) c o s , 1 - 5 ( 1 ) 0 ( 1 ) 0 T e [ 2 ] 0 8 9 5 1 ( 4 ) 7 0 2 ( 1 ) 7 5 4 9 1 8 ( 1 ) s i n , 1 0 0 6 ( 6 ) c o s , 1 - 1 3 3 ( 2 ) 0 ( 1 ) 0 T e [ 3 ] 0 8 9 7 1 ( 3 ) 4 2 9 6 ( 1 ) 7 5 4 9 1 8 ( 1 ) s i n , 1 0 0 - 7 ( 6 ) c o s , 1 1 1 3 ( 2 ) 8 ( 1 ) 0 ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 3 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r P r T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 P r 1 1 ( 1 ) 1 4 ( 1 ) 1 1 ( 1 ) - l ( 1 ) 0 o T e [ 1 ] 1 1 ( 1 ) 1 4 ( 1 ) 1 0 ( 1 ) - 1 ( 1 ) 0 0 T e [ 2 ] 1 9 ( 1 ) 1 8 ( 1 ) 1 8 ( 1 ) 4 ( 1 ) 0 0 T e [ 3 ] 1 8 ( 1 ) 1 8 ( 1 ) 1 8 ( 1 ) 0 ( 1 ) 0 0 T a b l e 3 . 3 4 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r P r T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e P r - T e [ 1 ] 3 . 2 9 2 3 ( 1 2 ) 3 . 2 9 2 ( 2 ) 3 . 2 9 2 ( 2 ) P r - T e [ 1 ] x 2 3 . 2 1 3 4 ( 1 5 ) 3 . 2 0 4 3 ( 1 4 ) 3 . 2 2 2 4 ( 1 4 ) P r - T e [ 1 ] x 2 3 2 2 7 5 ( 1 5 ) 3 . 2 1 2 5 ( 1 5 ) 3 . 2 4 2 7 ( 1 5 ) P r - T e [ 2 ] x 2 3 . 3 7 9 0 ( 1 6 ) 3 . 3 7 8 3 ( 1 7 ) 3 . 3 8 0 0 ( 1 4 ) P r - T e [ 3 ] 3 . 3 8 0 6 ( 1 3 ) 3 . 3 7 2 0 ( 1 8 ) 3 . 3 8 9 7 ( 1 8 ) P r - T e [ 3 ] 3 . 3 6 4 5 ( 1 3 ) 3 . 3 2 4 4 ( 1 8 ) 3 . 4 0 4 0 ( 1 8 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 8 2 ( 2 ) 3 . 0 1 4 4 ( 1 7 ) 3 . 1 5 1 5 ( 1 8 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 9 5 ( 2 ) 3 . 0 2 7 1 ( 1 7 ) 3 . 1 6 3 7 ( 1 8 ) 1 6 1 T a b l e 3 . 3 5 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r P r T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - P r - T e [ 1 ] x 6 7 3 6 2 ( 3 ) 7 3 3 8 ( 3 ) 7 3 8 6 ( 3 ) T e [ 1 ] - P r - T e [ 1 ] x 2 7 3 4 4 ( 3 ) 7 3 2 7 ( 3 ) 7 3 6 1 ( 3 ) T e [ 1 ] - P r - T e [ 2 ] x 2 1 3 9 . 6 7 ( 5 ) 1 3 9 . 4 0 ( 7 ) 1 3 9 . 9 4 ( 7 ) T e [ 1 ] - P r - T e [ 3 ] x 2 l 3 9 . 7 2 ( 3 ) 1 3 9 . 2 5 ( 3 ) 1 4 0 . 1 7 ( 3 ) T e [ 1 ] - P r - T e [ 1 ] x 8 8 5 2 8 ( 4 ) 8 5 0 0 ( 5 ) 8 5 5 6 ( 5 ) T e [ 1 ] - P r - T e [ 1 ] x 4 1 4 7 . 0 6 ( 3 ) l 4 6 9 3 ( 5 ) 1 4 7 . 1 8 ( 5 ) T e [ 1 ] - P r - T e [ 2 ] x 2 7 6 8 2 ( 4 ) 7 6 0 6 ( 5 ) 7 7 6 0 ( 5 ) T e [ 1 ] - P r - T e [ 2 ] x 2 1 3 0 . 7 2 ( 4 ) 1 2 9 . 6 1 ( 4 ) 1 3 1 . 8 4 ( 4 ) T e [ 1 ] - P r - T e [ 3 ] x 4 7 7 . 1 6 ( 4 ) 7 6 7 6 ( 4 ) 7 7 5 5 ( 4 ) T e [ 1 ] - P r - T e [ 3 ] x 4 1 3 0 . 7 5 ( 6 ) l 3 0 . 4 1 ( 5 ) 1 3 1 . 0 9 ( 5 ) T e [ 1 ] - P r - T e [ 2 ] x 2 7 7 . 4 0 ( 4 ) 7 6 6 5 ( 4 ) 7 8 1 4 ( 4 ) T e [ 1 ] - P r - T e [ 2 ] x 2 1 3 1 . 1 7 ( 4 ) 1 3 0 . 0 9 ( 4 ) 1 3 2 . 2 4 ( 4 ) T e [ 2 ] - P r - T e [ 2 ] x 2 8 0 . 6 4 ( 5 ) 8 0 5 4 ( 5 ) 8 0 7 1 ( 5 ) T e [ 2 ] - P r - T e [ 3 ] x 4 5 4 2 5 ( 5 ) 5 3 0 2 ( 5 ) 5 5 5 1 ( 5 ) T e [ 3 ] - P r - T e [ 3 ] x 2 8 0 6 1 ( 3 ) 8 0 1 6 ( 4 ) 8 1 0 5 ( 4 ) P r - T e [ 1 ] - P r x 8 1 0 6 . 3 1 ( 4 ) 1 0 5 . 9 5 ( 3 ) 1 0 6 . 6 6 ( 3 ) P r - T e [ 1 ] - P r x 6 8 5 2 7 ( 4 ) 8 5 0 0 ( 4 ) 8 5 5 3 ( 4 ) P r - T e [ 1 ] - P r x 4 1 4 7 . 0 6 ( 4 ) 1 4 6 . 9 7 ( 3 ) 1 4 7 . 1 5 ( 3 ) P r - T e [ 1 ] - P r x 2 8 5 . 7 3 ( 4 ) 8 5 5 6 ( 4 ) 8 5 9 1 ( 4 ) P r - T e [ 2 ] - P r x 2 8 0 6 2 ( 3 ) 8 0 5 3 ( 4 ) 8 0 7 0 ( 4 ) P r - T e [ 2 ] - T e [ 3 ] x 4 6 2 9 0 ( 4 ) 6 2 3 9 ( 3 ) 6 3 3 8 ( 3 ) P r - T e [ 2 ] - T e [ 3 ] x 2 1 1 7 . 5 4 ( 5 ) 1 1 5 . 7 7 ( 5 ) 1 1 9 . 3 1 ( 6 ) P r - T e [ 2 ] - T e [ 3 ] x 2 1 1 6 . 8 3 ( 5 ) 1 1 5 . 5 8 ( 6 ) 1 1 8 . 0 7 ( 6 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 9 0 3 8 ( 7 ) 8 8 1 2 ( 7 ) 9 2 6 7 ( 7 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 6 8 9 8 5 ( 6 ) 8 9 7 5 ( 8 ) 9 0 0 1 ( 8 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 8 . 4 5 ( 7 ) 1 7 7 . 4 1 ( 7 ) 1 7 9 . 8 2 ( 3 ) P r - T e [ 3 ] - P r x 2 8 0 6 1 ( 2 ) 8 0 1 6 ( 4 ) 8 1 0 5 ( 4 ) P r - T e [ 3 ] - T e [ 2 ] x 4 6 2 9 3 ( 4 ) 6 1 8 4 ( 3 ) 6 4 0 5 ( 4 ) P r - T e [ 3 ] - T e [ 2 ] x 2 1 1 7 0 8 ( 5 ) 1 1 6 . 2 6 ( 4 ) 1 1 7 . 8 8 ( 4 ) P r - T e [ 3 ] - T e [ 2 ] x 2 1 1 7 . 4 1 ( 5 ) l 1 6 9 5 ( 5 ) 1 1 7 . 8 8 ( 5 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 6 8 9 9 1 ( 6 ) 8 7 . 7 5 ( 6 ) 9 2 1 1 ( 7 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 8 . 4 5 ( 7 ) 1 7 7 . 4 3 ( 7 ) 1 7 9 . 8 1 ( 3 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 9 0 3 8 ( 6 ) 8 8 0 8 ( 6 ) 9 2 7 0 ( 7 ) 1 6 2 T a b l e 3 . 3 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N d T e 3 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 1 8 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( 1 ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 “ t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m a n d T m c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e N d T e 3 5 2 7 1 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 0 m ( 0 0 y ) 0 0 0 a = 4 . 3 3 1 6 ( 7 ) A , 0 1 = 9 0 ° b = 2 5 . 7 0 5 ( 5 ) A , 1 3 = 9 0 ° c = 4 . 3 4 1 9 ( 7 ) A , y = 9 0 ° 0 . 2 8 2 4 ( 4 ) o ‘ 4 8 3 4 4 ( 1 5 ) A 3 4 7 . 2 3 9 g / c m 3 2 8 . 2 7 1 m m ' 1 8 6 4 0 . 3 4 x 0 . 2 3 x 0 . 0 1 m m 3 2 . 0 6 t o 2 9 . 1 8 ° - 5 < = h < = 5 , - 3 4 < = k < = 3 4 , - 6 < = l < = 5 , - 1 < = m < = 1 6 6 0 1 ( 2 0 5 1 m a i n + 4 5 5 0 s a t e l l i t e s ) 1 9 8 8 ( 6 9 2 m a i n + 1 2 9 6 s a t e l l i t e s ) [ R i m = 0 . 0 2 5 9 ] 9 8 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 1 9 8 8 / 0 / 3 8 1 . 4 0 R o b s = 0 . 0 2 2 1 , w R o b , = 0 . 0 8 1 8 R , “ = 0 . 0 3 7 5 , w R . . . = 0 . 0 8 8 4 R o b s = 0 . 0 1 6 5 , W R o b s = 0 . 0 8 0 4 R , 1 1 = 0 . 0 1 7 2 , w R , u = 0 . 0 8 2 0 R . , . . . = 0 . 0 5 3 0 , w R o b s = 0 . 0 8 5 7 R a n = 0 . 1 2 9 6 , w k . “ = 0 . 1 0 4 4 0 . 0 0 0 9 5 ( 5 ) 0 . 0 1 5 1 a n d 0 . 6 9 1 3 1 . 5 9 a n d - 2 . 0 2 e . A ' 3 R = E I I F o l - I F c I I / 2 1 F . 1 . w R = { 2 [ W ( | F o | 2 - c h | 2 ) 2 ] m i m fl ‘ m ‘ ” a n d “ F l / ( « 2 ( I ) + o . 0 0 1 6 1 2 ) 1 6 3 T a b l e 3 . 3 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r N d T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . L a b e l W a v e x y z U s q N d 0 9 2 4 9 1 6 9 0 ( 1 ) 2 5 4 9 2 ( 1 ) s i n , 1 0 0 2 0 ( 2 ) c o s , 1 - 6 1 ( 1 ) 5 ( 1 ) 0 T e [ 1 ] 0 9 2 2 4 ( 3 ) 2 9 5 5 ( 1 ) 2 5 4 9 2 ( 1 ) s i n , 1 0 0 0 ( 3 ) c o s , 1 - 1 0 ( 1 ) 0 ( 1 ) 0 T e [ 2 ] O 9 1 6 2 ( 4 ) 7 0 1 ( 1 ) 7 5 4 9 3 ( 1 ) s i n , 1 0 0 0 ( 3 ) c o s , 1 2 6 1 ( 1 ) 1 ( 1 ) 0 T e [ 3 ] 0 9 1 8 2 ( 3 ) 4 2 9 6 ( 1 ) 7 5 4 9 3 ( 1 ) s i n , 1 0 0 - 3 ( 3 ) c o s , 1 - 2 1 7 ( 1 ) 1 ( 1 ) 0 ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 3 8 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r N d T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 N d 2 ( 1 ) 2 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 0 T e [ 1 ] 2 ( 1 ) 2 ( 1 ) 1 ( 1 ) - l ( 1 ) 0 0 T e [ 2 ] 2 ( 1 ) 3 ( 1 ) 2 ( 1 ) 4 ( 1 ) 0 0 T e [ 3 ] 3 ( 1 ) 3 ( 1 ) 2 ( 1 ) 1 ( 1 ) 0 0 T a b l e 3 . 3 9 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N d T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e N d - T e [ 1 ] 3 . 2 5 1 3 ( 1 0 ) 3 . 2 4 0 1 ( 1 8 ) 3 . 2 6 2 9 ( 1 8 ) N d - T e [ 1 ] x 2 3 . 1 9 1 7 ( 1 2 ) 3 . 1 7 0 6 ( 1 2 ) 3 . 2 1 3 2 ( 1 2 ) N d - T e [ 1 ] x 2 3 . 2 0 6 2 ( 1 2 ) 3 . 1 9 2 9 ( 1 1 ) 3 . 2 1 9 2 ( 1 1 ) N d - T e [ 2 ] x 2 3 . 3 4 4 6 ( 1 1 ) 3 . 3 3 6 5 ( 1 2 ) 3 . 3 5 4 7 ( 1 2 ) N d - T e [ 3 ] 3 . 3 4 1 3 ( 1 3 ) 3 . 2 8 6 9 ( 1 7 ) 3 . 3 9 5 1 ( 1 7 ) N d - T e [ 3 ] 3 . 3 3 0 3 ( 1 3 ) 3 . 2 9 7 3 ( 1 7 ) 3 . 3 6 4 5 ( 1 7 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 6 2 7 ( 1 7 ) 2 . 9 3 2 1 ( 1 5 ) 3 . 1 9 4 7 ( 1 6 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 7 3 2 ( 1 7 ) 2 . 9 4 2 7 ( 1 5 ) 3 . 2 0 8 2 ( 1 6 ) 1 6 4 T a b l e 3 . 4 0 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N d T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - N d - T e [ 1 ] x 8 7 3 5 6 ( 3 ) 7 3 1 4 ( 3 ) 7 3 9 6 ( 3 ) T e [ 1 ] - N d - T e [ 2 ] x 2 1 3 9 . 4 7 ( 3 ) 1 3 9 . 2 0 ( 4 ) 1 3 9 . 8 1 ( 3 ) T e [ 1 ] - N d - T e [ 3 ] x 2 1 3 9 . 5 9 ( 3 ) 1 3 9 . 2 7 ( 4 ) 1 3 9 . 9 4 ( 4 ) T e [ 1 ] - N d - T e [ 1 ] x 8 8 5 2 2 ( 3 ) 8 5 0 1 ( 4 ) 8 5 . 4 4 ( 4 ) T e [ 1 ] - N d - T e [ 1 ] x 4 1 4 6 . 9 2 ( 3 ) 1 4 6 . 4 9 ( 4 ) 1 4 7 . 3 4 ( 4 ) T e [ 1 ] — N d - T e [ 2 ] x 2 7 6 8 3 ( 3 ) 7 5 . 4 9 ( 3 ) 7 8 1 4 ( 3 ) T e [ 1 ] - N d - T e [ 2 ] x 2 l 3 0 9 4 ( 4 ) 1 2 8 . 8 5 ( 3 ) 1 3 3 . 0 0 ( 3 ) T e [ 1 ] - N d - T e [ 3 ] x 4 7 7 . 1 3 ( 3 ) 7 6 6 3 ( 3 ) 7 7 6 5 ( 3 ) T e [ 1 ] - N d - T e [ 3 ] x 2 1 3 0 . 9 0 ( 3 ) 1 3 0 . 1 2 ( 3 ) 1 3 1 . 6 7 ( 3 ) T e [ 1 ] - N d - T e [ 2 ] x 2 7 7 2 6 ( 3 ) 7 5 5 6 ( 3 ) 7 8 9 9 ( 3 ) T e [ 1 ] - N d - T e [ 2 ] x 2 1 3 1 . 2 2 ( 4 ) 1 2 8 . 8 2 ( 3 ) 1 3 3 . 6 3 ( 3 ) T e [ 1 ] - N d - T e [ 3 ] x 2 1 3 l . 1 0 ( 3 ) 1 3 0 . 7 2 ( 3 ) 1 3 1 . 4 7 ( 3 ) T e [ 2 ] - N d - T e [ 2 ] x 2 8 0 9 9 ( 3 ) 8 0 7 1 ( 3 ) 8 1 . 1 8 ( 3 ) T e [ 2 ] - N d - T e [ 3 ] x 2 5 4 5 3 ( 3 ) 5 2 4 8 ( 3 ) 5 6 5 6 ( 3 ) T e [ 2 ] - N d - T e [ 3 ] x 2 5 4 8 2 ( 3 ) 5 2 4 7 ( 3 ) 5 7 2 5 ( 3 ) T e [ 3 ] - N d - T e [ 3 ] x 2 8 0 9 7 ( 3 ) 8 0 6 5 ( 4 ) 8 1 2 6 ( 4 ) N d - T e [ 1 ] - N d x 8 1 0 6 . 7 1 ( 3 ) 1 0 6 . 5 4 ( 3 ) 1 0 6 . 8 7 ( 3 ) N d - T e [ 1 ] - N d x 8 8 5 2 4 ( 4 ) 8 5 2 1 ( 4 ) 8 5 2 7 ( 4 ) N d - T e [ 1 ] - N d x 4 1 4 6 . 9 2 ( 3 ) 1 4 6 . 5 6 ( 4 ) 1 4 7 . 2 8 ( 4 ) N d - T e [ 2 ] - N d x 2 8 0 9 5 ( 3 ) 8 0 8 6 ( 4 ) 8 0 9 9 9 ( 1 9 ) N d - T e [ 2 ] - T e [ 3 ] x 4 6 2 6 7 ( 2 ) 6 2 0 3 ( 2 ) 6 3 3 2 ( 2 ) N d - T e [ 2 ] - T e [ 3 ] x 2 1 1 7 . 5 4 ( 4 ) 1 1 4 . 6 5 ( 5 ) 1 2 0 . 4 1 ( 5 ) N d - T e [ 2 ] - T e [ 3 ] x 2 1 1 6 . 9 9 ( 4 ) 1 1 3 . 9 6 ( 5 ) 1 1 9 . 9 7 ( 5 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 9 0 4 6 ( 5 ) 8 5 9 3 ( 5 ) 9 5 . 1 6 ( 6 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 6 8 9 7 6 ( 4 ) 8 9 6 1 ( 3 ) 8 9 9 0 ( 5 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 7 . 1 0 ( 6 ) 1 7 5 . 2 0 ( 6 ) 1 7 9 . 7 9 ( 2 ) N d - T e [ 3 ] - N d x 2 8 0 9 7 ( 2 ) 8 0 6 5 ( 4 ) 8 1 2 6 ( 4 ) N d - T e [ 3 ] - T e [ 2 ] x 4 6 2 . 8 4 ( 3 ) 6 0 9 9 ( 3 ) 6 4 7 1 ( 3 ) N d - T e [ 3 ] - T e [ 2 ] x 2 1 1 7 2 2 ( 3 ) 1 1 6 . 3 1 ( 3 ) 1 1 8 . 0 6 ( 3 ) N d - T e [ 3 ] - T e [ 2 ] x 2 1 1 7 . 4 5 ( 3 ) 1 1 6 . 5 4 ( 3 ) 1 1 8 . 2 7 ( 3 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 6 9 0 0 3 ( 5 ) 8 5 . 7 1 ( 5 ) 9 4 4 4 ( 6 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 7 2 1 ( 6 ) 1 7 5 . 3 8 ( 5 ) 1 7 9 . 7 9 ( 3 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 9 0 4 6 ( 5 ) 8 6 1 3 ( 5 ) 9 4 9 3 ( 6 ) 1 6 5 T a b l e 3 . 4 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N d T e ; a t 4 7 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 2 3 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( 1 ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( 1 ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R l " t o r d e r s a t e l l i t e s [ I > 2 0 ( 1 ) ] R 1 “ o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m i n a n d T m c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e N d T e 3 5 2 7 4 7 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 0 m ( 0 0 y ) 0 0 0 a = 4 . 3 5 6 2 ( 7 ) A , 0 1 = 9 0 ° b = 2 5 . 8 6 0 ( 6 ) A , B = 9 0 ° c = 4 . 3 5 8 2 ( 7 ) A , y = 9 0 ° 0 . 2 8 7 4 ( 4 ) c ' 4 9 0 . 9 5 0 5 ) A 3 4 7 . 1 2 8 g / c m 3 2 7 . 8 3 8 m m " 8 6 4 0 . 3 4 x 0 . 2 3 x 0 . 0 1 m 3 2 . 0 7 t o 2 9 . 2 3 ° - 5 < = h < = 5 , - 3 5 < = k < = 3 4 , - 6 < = 1 < = 6 , - l < = m < = 1 6 8 1 6 ( 2 1 5 5 m a i n + 4 6 6 1 s a t e l l i t e s ) 2 0 3 0 ( 7 0 6 m a i n + 1 3 2 4 s a t e l l i t e s ) [ R i o t = 0 . 0 5 4 9 ] 9 9 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 2 0 3 0 / 0 / 3 8 1 . 2 4 R o b , = 0 . 0 2 9 0 , w R o b , = 0 . 0 8 2 7 R 3 1 1 = 0 . 0 5 1 7 , W R a u = 0 . 0 9 0 0 R o b s = 0 . 0 2 5 7 , w R o t , S = 0 . 0 7 5 4 R 8 1 1 = 0 . 0 2 6 1 , w R a n = 0 . 0 7 5 6 R o b s = 0 . 0 9 5 3 , w R o i , s = 0 . 1 6 5 0 R , “ = 0 . 3 1 3 4 , w R a n = 0 . 2 1 9 6 0 . 0 0 0 5 8 ( 5 ) 0 . 0 1 5 1 a n d 0 . 6 9 1 3 1 . 4 2 a n d - 1 . 6 1 e . A ' 3 R = r u m — I F , “ / £ | F o | , w R = { 2 [ w ( | F o | 2 - 1 1 2 , 1 5 2 ] / r _ [ w ( | 1 3 , | ‘ ) ] } ” 2 a n d w = l / ( 0 2 ( I ) + 0 . 0 0 1 6 I Z ) 1 6 6 T a b l e 3 . 4 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r N d T e 3 a t 4 7 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e x y 2 U s ; N d 0 9 2 4 9 1 6 9 3 ( 1 ) 2 5 4 9 1 5 ( 1 ) s i n , 1 0 0 3 ( 2 ) c o s , 1 2 1 ( 1 ) 0 ( 1 ) 0 T e [ 1 ] 0 9 2 1 4 ( 3 ) 2 9 5 6 ( 1 ) 2 5 4 9 1 5 ( 1 ) s i n , 1 O 0 - 3 ( 2 ) c o s , 1 - 1 ( 1 ) 1 ( 1 ) 0 T e [ 2 ] 0 9 1 9 2 ( 3 ) 7 0 4 ( 1 ) 7 5 4 9 2 0 ( 1 ) s i n , 1 0 0 3 ( 3 ) c o s , 1 - 1 1 1 ( 2 ) 6 ( 1 ) 0 T e [ 3 ] O 9 1 3 7 ( 3 ) 4 2 9 5 ( 1 ) 7 5 4 9 2 0 ( 1 ) s i n , 1 0 0 2 2 ( 3 ) c o s , 1 8 4 ( 2 ) 1 ( 1 ) 0 ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 4 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r N d T e 3 a t 4 7 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 N d 1 4 ( 1 ) 1 8 ( 1 ) 1 3 ( 1 ) 0 ( 1 ) 0 0 T e [ 1 ] 1 4 ( 1 ) 1 7 ( 1 ) 1 3 ( 1 ) - 1 0 ) 0 0 T e [ 2 ] 2 1 ( 1 ) 2 2 ( 1 ) 1 8 ( 1 ) 3 ( 1 ) 0 0 T e [ 3 ] 1 9 ( 1 ) 2 2 ( 1 ) 1 9 ( 1 ) - 2 ( 1 ) 0 0 T a b l e 3 . 4 4 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N d T e 3 a t 4 7 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e N d - T e [ 1 ] 3 . 2 6 6 3 ( 1 1 ) 3 . 2 6 5 3 ( 1 9 ) 3 . 2 6 7 3 ( 1 9 ) N d - T e [ 1 ] x 2 3 . 2 0 8 1 ( 1 1 ) 3 . 2 0 2 7 ( 1 1 ) 3 . 2 1 3 4 ( 1 1 ) N d - T e [ 1 ] x 2 3 . 2 1 6 4 ( 1 1 ) 3 . 2 0 8 6 ( 1 1 ) 3 . 2 2 4 4 ( 1 1 ) N d - T e [ 2 ] x 2 3 . 3 5 8 8 ( 1 1 ) 3 . 3 4 9 2 ( 1 2 ) 3 . 3 6 8 9 ( 1 2 ) N d - T e [ 3 ] 3 . 3 7 4 2 ( 1 3 ) 3 . 3 5 8 2 ( 1 8 ) 3 . 3 9 0 5 ( 1 8 ) N d - T e [ 3 ] 3 . 3 3 8 7 ( 1 2 ) 3 . 3 1 9 3 ( 1 8 ) 3 . 3 5 7 9 ( 1 8 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 9 8 0 ( 1 6 ) 3 . 0 4 7 6 ( 1 5 ) 3 . 1 4 9 7 ( 1 6 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 6 4 6 ( 1 6 ) 3 . 0 0 6 6 ( 1 5 ) 3 . 1 2 2 4 ( 1 6 ) 1 6 7 T a b l e 3 . 4 5 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N d T e 3 a t 4 7 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - N d - T e [ 1 ] x 8 7 3 6 2 ( 2 ) 7 3 5 6 ( 3 ) 7 3 6 8 ( 3 ) T e [ 1 ] - N d - T e [ 2 ] x 2 1 3 9 . 5 4 ( 3 ) 1 3 9 . 3 4 ( 3 ) 1 3 9 7 4 ( 3 ) T e [ 1 ] - N d — T e [ 3 ] x 2 1 3 9 2 9 ( 3 ) l 3 9 . 0 9 ( 3 ) 1 3 9 5 0 ( 3 ) T e [ 1 ] - N d - T e [ 1 ] x 8 8 5 5 7 ( 3 ) 8 5 3 5 ( 3 ) 8 5 8 0 ( 3 ) T e [ 1 ] - N d - T e [ 1 ] x 4 1 4 7 . 1 3 ( 3 ) 1 4 7 . 0 7 ( 4 ) 1 4 7 . l 9 ( 4 ) T e [ 1 ] - N d - T e [ 2 ] x 4 7 6 9 4 ( 3 ) 7 6 1 6 ( 3 ) 7 7 . 7 3 ( 3 ) T e [ 1 ] - N d - T e [ 2 ] x 4 1 3 0 . 9 6 ( 3 ) 1 3 0 . 1 0 ( 3 ) 1 3 1 . 8 2 ( 3 ) T e [ 1 ] - N d - T e [ 3 ] x 2 7 6 8 1 ( 3 ) 7 6 6 4 ( 3 ) 7 6 9 8 ( 3 ) T e [ 1 ] - N d - T e [ 3 ] x 2 1 3 0 . 7 5 ( 3 ) l 3 0 . 5 5 ( 3 ) 1 3 0 . 9 5 ( 3 ) T e [ 1 ] - N d - T e [ 3 ] x 2 1 3 1 . 1 3 ( 3 ) 1 3 0 . 8 8 ( 3 ) 1 3 1 . 3 7 ( 3 ) T e [ 1 ] - N d - T e [ 3 ] x 2 7 7 2 1 ( 3 ) 7 7 0 1 ( 2 ) 7 7 . 4 2 ( 2 ) T e [ 2 ] - N d - T e [ 2 ] x 2 8 0 . 9 1 ( 3 ) 8 0 7 0 ( 3 ) 8 1 . 1 0 ( 3 ) T e [ 2 ] - N d - T e [ 3 ] x 4 5 4 7 9 ( 3 ) 5 4 0 2 ( 3 ) 5 5 5 7 ( 3 ) T e [ 3 ] - N d - T e [ 3 ] x 2 8 0 9 2 ( 3 ) 8 0 8 8 ( 4 ) 8 0 9 6 ( 4 ) N d - T e [ 1 ] - N d x 4 1 0 6 . 3 4 ( 3 ) 1 0 6 . 2 2 ( 3 ) 1 0 6 . 4 5 ( 3 ) N d - T e [ 1 ] - N d x 4 1 0 6 . 5 3 ( 3 ) 1 0 6 . 3 5 ( 3 ) 1 0 6 . 7 2 ( 3 ) N d - T e [ 1 ] - N d x 6 8 5 3 0 ( 3 ) 8 5 . 1 1 ( 4 ) 8 5 . 4 8 ( 4 ) N d - T e [ 1 ] - N d x 4 1 4 7 . 1 3 ( 3 ) 1 4 7 . 0 3 ( 4 ) 1 4 7 . 2 3 ( 4 ) N d - T e [ 1 ] - N d x 2 8 5 5 7 ( 3 ) 8 5 . 4 8 ( 4 ) 8 5 6 7 ( 4 ) N d - T e [ 2 ] - N d x 2 8 0 9 0 ( 3 ) 8 0 5 7 ( 4 ) 8 1 2 2 ( 4 ) N d - T e [ 2 ] - T e [ 3 ] x 4 6 2 8 6 ( 2 ) 6 2 5 0 ( 2 ) 6 3 2 0 ( 2 ) N d - T e [ 2 ] - T e [ 3 ] x 4 1 1 7 . 1 7 ( 4 ) 1 1 5 . 5 6 ( 5 ) 1 1 8 . 7 8 ( 5 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 6 8 9 9 5 ( 4 ) 8 9 7 3 ( 3 ) 9 0 1 9 ( 4 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 8 . 6 9 ( 5 ) 1 7 7 . 4 1 ( 5 ) 1 8 0 T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 9 0 6 8 ( 5 ) 8 9 0 0 ( 5 ) 9 2 3 8 ( 6 ) N d - T e [ 3 ] - N d x 2 8 0 9 2 ( 2 ) 8 0 8 8 ( 3 ) 8 0 9 6 ( 3 ) N d - T e [ 3 ] - T e [ 2 ] x 2 6 3 1 1 ( 3 ) 6 2 1 7 ( 3 ) 6 4 0 8 ( 3 ) N d - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 2 7 ( 3 ) l 1 6 5 4 ( 3 ) 1 1 8 0 0 ( 3 ) N d - T e [ 3 ] - T e [ 2 ] x 2 6 2 3 5 ( 3 ) 6 1 8 3 ( 3 ) 6 2 . 8 7 ( 3 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 9 0 6 8 ( 5 ) 8 8 9 5 ( 5 ) 9 2 4 3 ( 5 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 8 9 9 5 ( 4 ) 8 9 7 3 ( 4 ) 9 0 1 9 ( 4 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 8 . 7 8 ( 5 ) l 7 7 . 5 6 ( 5 ) 1 8 0 T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 8 9 4 2 ( 5 ) 8 7 6 7 ( 5 ) 9 1 . 1 8 ( 5 ) 1 6 8 T a b l e 3 . 4 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N d T e 3 a t 5 0 0 K E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f f i c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 0 3 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( I ) ] R i n d i c e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t L a r g e s t d i f f . p e a k a n d h o l e N d T e 3 5 2 7 5 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C m c m a = 4 . 4 0 2 ( 3 ) A , 0 1 = 9 0 ° b = 2 5 7 2 ( 2 ) A , 0 = 9 0 0 c = 4 . 3 6 0 ( 3 ) A , y = 9 0 0 4 9 3 . 6 ( 6 ) A 3 4 7 . 0 8 9 g / c m 3 2 7 . 6 8 7 m i t t l 8 6 4 0 . 3 4 x 0 . 2 3 x 0 . 0 1 m m 3 3 . 1 7 t o 2 9 . 0 3 ° - 5 < = h < = 5 , - 3 4 < = k < = 3 4 , - 5 < = 1 < = 5 2 1 8 7 3 8 8 [ R i m = 0 . 0 4 7 6 ] 9 4 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 3 8 8 / 0 / 1 8 1 . 6 7 R o b s = 0 . 0 2 4 3 , w R o b s = 0 . 0 7 4 0 R , " = 0 . 0 2 4 9 , w R . . . = 0 . 0 7 4 1 0 . 0 7 6 ( 9 ) 1 . 6 5 a n d - 1 . 6 0 e . A ' 3 R = 2 J I I F o I - l F t l l / z I F o l . w R = { ‘ Z [ W ( | F o | 7 - c h | 2 ) 2 ] / > 3 [ W ( | F o | 4 ) ] } v 2 a n d W = 1 / ( 0 2 ( I ) + 0 - 0 0 1 6 1 2 ) T a b l e 3 . 4 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r N d T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . ‘ L a b e l x y 2 O c c u p a n c y U , q N d 5 0 0 0 3 3 0 7 ( 1 ) 2 5 4 9 1 1 2 ( 1 ) T e [ 1 ] 5 0 0 0 2 0 4 5 ( 1 ) 2 5 4 9 1 1 2 ( 1 ) T e [ 2 ] O 4 2 9 4 ( 1 ) 2 5 4 9 1 1 8 ( 1 ) 1 6 9 T a b l e 3 . 4 7 . ( C o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r N d T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 3 ] 5 0 0 0 4 2 9 5 ( 1 ) 7 5 4 9 1 1 8 ( 1 ) ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 4 8 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r N d T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 N d 1 1 ( 1 ) 1 4 ( 1 ) 1 1 ( 1 ) 0 0 0 T e [ 1 ] 1 1 ( 1 ) 1 3 ( 1 ) 1 1 ( 1 ) 0 0 0 T e [ 2 ] 1 8 ( 1 ) 1 8 ( 1 ) 1 8 ( 1 ) 0 0 0 T e [ 3 ] 1 8 ( 1 ) 1 9 ( 1 ) 1 7 ( 1 ) 0 0 0 T a b l e 3 . 4 9 . B o n d d i s t a n c e s [ A ] f o r N d T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l D i s t a n c e s L a b e l D i s t a n c e s N d - T e [ 1 ] 3 . 2 4 6 8 ( 7 ) N d - T e [ 2 ] x 2 3 . 3 5 9 9 ( 6 ) N d - T e [ 1 ] x 4 3 . 2 2 7 1 ( 2 ) N d - T e [ 3 ] x 2 3 . 3 4 7 5 ( 6 ) T a b l e 3 . 5 0 . B o n d a n g l e s [ ° ] f o r N d T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l A n g l e s L a b e l A n g l e s T e [ 1 ] - N d - T e [ 1 ] x 8 7 3 7 1 2 ( 1 3 ) N d - T e [ 1 ] - N d x 4 8 5 . 9 9 7 ( 6 ) T e [ 1 ] - N d - T e [ 2 ] x 2 1 3 9 . 0 7 7 ( 9 ) N d - T e [ 1 ] - N d x 4 1 4 7 . 4 2 ( 2 ) T e [ 1 ] - N d - T e [ 1 ] x 4 8 4 9 7 9 ( 6 ) N d - T e [ 2 ] - T e [ 3 ] x 4 6 2 2 9 4 ( 1 2 ) T e [ 1 ] - N d - T e [ 1 ] x 4 8 5 . 9 9 7 ( 6 ) N d - T e [ 2 ] - T e [ 3 ] x 4 1 1 7 . 7 6 7 ( 1 7 ) T e [ 1 ] - N d - T e [ 1 ] x 4 1 4 7 . 4 2 ( 2 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 8 9 . 4 4 9 T e [ 1 ] - N d - T e [ 2 ] x 4 7 6 . 4 2 0 ( 1 0 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 9 0 . 5 5 1 T e [ 1 ] - N d - T e [ 2 ] x 4 1 3 1 . 1 9 7 ( 1 2 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 8 0 T e [ 1 ] - N d - T e [ 3 ] x 4 7 6 8 8 1 ( 1 0 ) N d - T e [ 3 ] - N d x 2 8 1 . 2 5 9 ( 1 6 ) T e [ 1 ] - N d - T e [ 3 ] x 4 1 3 0 . 7 4 5 ( 1 2 ) N d - T e [ 3 ] - T e [ 2 ] x 4 6 2 . 6 9 7 ( 1 2 ) T e [ 2 ] - N d - T e [ 2 ] x 2 8 1 . 8 4 6 ( 1 4 ) N d - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 2 4 3 ( 1 7 ) T e [ 2 ] - N d - T e [ 3 ] x 4 5 5 . 0 0 9 ( 9 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 8 9 . 4 4 9 T e [ 3 ] - N d - T e [ 3 ] x 2 8 1 . 2 5 9 ( 1 4 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 9 0 . 5 5 1 N d - T e [ 1 ] - N d x 8 1 0 6 . 2 8 8 ( 1 3 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 8 0 1 7 0 T a b l e 3 . 5 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r S m T e ; a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 3 1 . 9 0 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ’ ( 1 ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( 1 ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 “ o r d e r s a t e l l i t e s [ I > 2 0 ( 1 ) ] R 1 “ o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m i n a n d T m c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e S m T e 3 5 3 3 . 2 1 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 c m ( 0 0 y ) 0 0 0 a = 4 . 3 0 5 5 ( 6 ) A , 0 1 = 9 0 ° b = 2 5 . 5 5 3 ( 5 ) A , B = 9 0 ° c = 4 . 3 2 4 7 ( 6 ) A , y = 9 0 ° 0 . 2 8 6 5 ( 3 ) o ‘ 4 7 5 . 8 0 0 3 ) A 3 4 7 . 4 4 0 g / o m 3 3 0 . 1 3 4 m m “ 8 7 2 0 . 1 7 x 0 . 1 1 x 0 . 0 1 6 1 6 1 3 3 . 1 8 t o 3 1 9 0 ° - 5 < = h < = 6 , - 3 7 < = k < = 3 7 , - 6 < = l < = 6 , - 1 < = m < = 1 8 2 3 4 ( 2 5 3 5 m a i n + 5 6 9 9 s a t e l l i t e s ) 2 4 0 8 ( 8 2 6 m a i n + 1 5 8 2 s a t e l l i t e S ) [ R i m = 0 . 0 2 9 2 ] 9 8 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 2 4 0 8 / 0 / 3 7 2 . 0 5 R o b , = 0 . 0 3 1 2 , w R o b , = 0 . 1 2 5 7 R a n = 0 . 0 5 0 5 , w R a u = 0 . 1 3 7 3 R o b s = 0 . 0 1 7 8 , w R o b , = 0 . 0 7 5 0 R a l l = 0 . 0 1 8 0 , W R a n = 0 . 0 7 5 1 R o b s = 0 . 1 0 6 4 , w R o t , s = 0 . 2 3 0 7 R . , “ = 0 . 1 9 6 0 , w R a n = 0 . 2 5 9 0 0 . 0 0 0 9 7 ( 7 ) 0 . 0 5 0 1 a n d 0 . 6 4 0 4 4 . 3 0 a n d 4 0 5 e . A ' 3 R = 2 1 1 8 1 - 1 8 1 1 / 2 1 8 . 1 , w R = { 2 [ W ( | F o | 2 - 1 8 1 2 ) " ? l e t l F o l ‘ m ‘ ” a n d w = 1 / ( 0 2 ( I ) + 0 . 0 0 1 6 I z ) 1 7 1 T a b l e 3 . 5 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r S m T e ; a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . a L a b e l W a v e x y z c h S m 0 9 4 4 9 1 6 9 3 ( 1 ) 2 5 4 9 2 ( 1 ) s i n , 1 0 0 1 6 ( 4 ) c o s , 1 5 7 ( 1 ) 6 ( 1 ) 0 T e [ 1 ] 0 9 4 2 5 ( 4 ) 2 9 5 2 ( 1 ) 2 5 4 9 2 ( 1 ) s i n , 1 0 0 - 7 ( 4 ) c o s , 1 5 ( 1 ) 0 ( 1 ) 0 T e [ 2 ] 0 9 4 1 3 ( 4 ) 7 0 6 ( 1 ) 7 5 4 9 3 ( 1 ) s i n , 1 0 0 1 4 ( 5 ) c o s , 1 - 2 1 8 ( 2 ) 0 ( 1 ) 0 T e [ 3 ] 0 4 3 4 8 ( 4 ) 7 0 8 ( 1 ) 2 5 4 9 3 ( 1 ) s i n , 1 0 0 5 ( 4 ) c o s , 1 1 9 6 ( 2 ) 0 ( 1 ) 0 r U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 5 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r S m T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 S m 2 ( 1 ) 2 ( 1 ) 2 ( 1 ) 0 ( 1 ) 0 0 T e [ 1 ] 3 ( 1 ) 2 ( 1 ) 2 ( 1 ) - 1 0 ) 0 0 T e [ 2 ] 4 ( 1 ) 3 ( 1 ) 3 ( 1 ) 2 ( 1 ) 0 0 T e [ 3 ] 2 ( 1 ) 3 ( 1 ) 3 ( 1 ) 1 ( 1 ) 0 0 T a b l e 3 . 5 4 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r S m T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e S m - T e [ 1 ] 3 . 2 1 9 5 ( 1 2 ) 3 . 2 0 4 ( 2 ) 3 . 2 3 5 ( 2 ) S m - T e [ 1 ] x 2 3 . 1 7 6 2 ( 1 5 ) 3 . 1 6 5 3 ( 1 2 ) 3 . 1 8 7 0 ( 1 2 ) S m - T e [ 1 ] x 2 3 . 1 9 0 3 ( 1 5 ) 3 . 1 6 7 6 ( 1 5 ) 3 . 2 1 3 2 ( 1 5 ) S m - T e [ 2 ] x 2 3 . 3 2 2 0 ( 1 4 ) 3 . 3 0 7 5 ( 1 3 ) 3 . 3 3 6 9 ( 1 3 ) S m - T e [ 3 ] 3 . 3 2 6 0 ( 1 5 ) 3 . 3 0 0 ( 2 ) 3 . 3 5 3 ( 2 ) S m - T e [ 3 ] 3 . 2 9 7 5 ( 1 5 ) 3 . 2 4 6 ( 2 ) 3 . 3 4 9 ( 2 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 7 2 ( 2 ) 2 . 9 6 1 9 ( 1 8 ) 3 . 1 8 5 ( 2 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 3 3 ( 2 ) 2 . 9 1 8 9 ( 1 8 ) 3 . 1 4 8 3 ( 1 9 ) 1 7 2 T a b l e 3 . 5 5 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r S m T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - S m - T e [ 1 ] x 8 7 3 5 4 ( 3 ) 7 3 4 2 ( 3 ) 7 3 6 5 ( 3 ) T e [ 1 ] - S m - T e [ 2 ] x 2 1 3 9 . 3 5 ( 4 ) 1 3 9 . 1 4 ( 5 ) 1 3 9 . 6 1 ( 5 ) T e [ 1 ] - S m - T e [ 3 ] x 2 1 3 9 . 3 6 ( 4 ) 1 3 8 . 7 9 ( 4 ) 1 3 9 . 9 2 ( 4 ) T e [ 1 ] - S m - T e [ 1 ] x 2 8 5 8 1 ( 4 ) 8 5 3 8 ( 4 ) 8 6 2 5 ( 4 ) T e [ 1 ] - S m - T e [ 1 ] x 6 8 5 . 1 1 ( 4 ) 8 4 8 3 ( 4 ) 8 5 3 8 ( 4 ) T e [ 1 ] - S m - T e [ 1 ] x 4 1 4 6 . 8 9 ( 3 ) 1 4 6 . 3 6 ( 4 ) 1 4 7 . 4 1 ( 5 ) T e [ 1 ] - S m - T e [ 2 ] x 4 7 6 9 6 ( 4 ) 7 5 5 2 ( 4 ) 7 8 4 3 ( 4 ) T e [ 1 ] - S m - T e [ 2 ] x 2 1 3 1 . 3 8 ( 4 ) 1 2 9 . 2 4 ( 4 ) 1 3 3 . 5 5 ( 4 ) T e [ 1 ] - S m - T e [ 3 ] x 4 7 7 0 0 ( 4 ) 7 6 7 7 ( 3 ) 7 7 2 4 ( 3 ) T e [ 1 ] - S m - T e [ 3 ] x 2 1 3 0 . 8 3 ( 5 ) 1 3 0 . 5 7 ( 4 ) 1 3 l . 0 8 ( 4 ) T e [ 1 ] - S m - T e [ 2 ] x 2 1 3 0 . 9 9 ( 4 ) 1 2 9 . 2 8 ( 4 ) 1 3 2 . 6 7 ( 4 ) T e [ 1 ] - S m - T e [ 3 ] x 2 1 3 1 . 1 8 ( 5 ) l 3 0 . 4 4 ( 4 ) 1 3 1 9 2 ( 4 ) T e [ 2 ] - S m - T e [ 2 ] x 2 8 1 2 5 ( 4 ) 8 1 0 1 ( 4 ) 8 1 . 4 4 ( 4 ) T e [ 2 ] - S m - T e [ 3 ] x 2 5 5 0 3 ( 4 ) 5 2 9 8 ( 4 ) 5 7 . 1 4 ( 4 ) T e [ 2 ] - S m - T e [ 3 ] x 2 5 4 5 5 ( 4 ) 5 2 8 2 ( 4 ) 5 6 2 6 ( 4 ) T e [ 3 ] - S m - T e [ 3 ] x 2 8 1 0 8 ( 4 ) 8 0 7 2 ( 5 ) 8 1 . 4 4 ( 5 ) S m - T e [ 1 ] - S m x 8 1 0 6 . 3 9 ( 4 ) 1 0 6 . 2 4 ( 4 ) 1 0 6 . 5 3 ( 4 ) S m - T e [ 1 ] - S m x 6 8 5 . 1 1 ( 3 ) 8 4 8 3 ( 4 ) 8 5 3 8 ( 4 ) S m - T e [ 1 ] - S m x 4 1 4 6 . 8 9 ( 4 ) 1 4 6 . 4 8 ( 5 ) 1 4 7 . 2 9 ( 5 ) S m - T e [ 1 ] - S m x 2 8 5 8 2 ( 4 ) 8 5 . 7 5 ( 5 ) 8 5 8 8 ( 5 ) S m - T e [ 2 ] - S m x 2 8 1 2 3 ( 3 ) 8 1 . 1 3 ( 5 ) 8 1 2 8 ( 3 ) S m - T e [ 2 ] - T e [ 3 ] x 4 6 2 5 3 ( 3 ) 6 1 9 7 ( 3 ) 6 3 0 7 ( 3 ) S m - T e [ 2 ] - T e [ 3 ] x 4 1 1 7 . 1 3 ( 5 ) 1 1 4 . 6 0 ( 6 ) 1 1 9 . 6 4 ( 6 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 6 8 9 . 6 0 ( 6 ) 8 5 . 7 6 ( 6 ) 9 3 5 3 ( 7 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 7 . 4 9 ( 7 ) 1 7 5 3 6 ( 7 ) 1 7 9 . 8 5 ( 3 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 9 1 0 8 ( 7 ) 8 7 2 4 ( 6 ) 9 5 0 4 ( 7 ) S m - T e [ 3 ] - S m x 2 8 1 0 8 ( 2 ) 8 0 7 2 ( 4 ) 8 1 . 4 4 ( 4 ) S m - T e [ 3 ] - T e [ 2 ] x 2 6 3 1 5 ( 4 ) 6 1 . 7 6 ( 4 ) 6 4 6 1 ( 4 ) S m - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 3 4 ( 4 ) 1 1 6 . 5 4 ( 4 ) 1 1 8 . 0 8 ( 4 ) S m - T e [ 3 ] - T e [ 2 ] x 2 6 2 4 3 ( 4 ) 6 0 7 7 ( 4 ) 6 4 1 0 ( 4 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 9 1 0 5 ( 7 ) 8 7 . 4 1 ( 7 ) 9 4 8 5 ( 7 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 6 8 9 6 6 ( 5 ) 8 9 5 3 ( 4 ) 8 9 8 4 ( 6 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 7 . 5 2 ( 7 ) 1 7 5 . 4 5 ( 7 ) 1 7 9 . 8 5 ( 3 ) 1 7 3 T a b l e 3 . 5 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r S m T e 3 a t 4 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 1 8 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( 1 ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 6 ( 1 ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 “ o r d e r s a t e l l i t e s [ I > 2 0 ( 1 ) ] R l s t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m m a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e S m T e 3 5 3 3 . 2 4 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 c m ( 0 0 y ) 0 0 0 a = 4 . 3 2 6 9 ( 6 ) A , 0 1 = 9 0 ° b = 2 5 . 6 9 1 ( 4 ) A , B = 9 0 ° c = 4 . 3 3 4 1 ( 7 ) A , y = 9 0 ° 0 . 2 9 3 6 ( 4 ) o ‘ 4 8 1 . 8 0 ( 1 3 ) A 3 4 7 . 3 4 8 g / c m 3 2 9 . 7 5 9 m m " 8 7 2 0 . 1 7 x 0 . 1 1 x 0 . 0 1 m m 3 2 . 1 0 t o 2 9 . 1 8 ° ~ 5 < = h < = 5 , - 3 4 < = k < = 3 4 , - 6 < = l < = 6 , - 1 < = m < = 1 6 7 2 8 ( 2 1 1 7 m a i n + 4 6 1 1 s a t e l l i t e s ) 1 9 2 9 ( 6 6 8 m a i n + 1 2 6 1 s a t e l l i t e s ) [ R i m = 0 . 1 0 3 6 ] 9 9 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 1 9 2 9 / 0 / 3 8 1 . 4 5 R o b s = 0 . 0 4 7 2 , w R o b , = 0 . 1 0 4 6 R , “ = 0 . 0 8 2 7 , w R a u = 0 . 1 1 1 9 R o b s = 0 . 0 4 4 4 , w R o i , s = 0 . 1 0 2 2 R , “ = 0 . 0 4 5 3 , w R a u = 0 . 1 0 2 5 R o b s = 0 . 1 4 4 3 , w R o b , = 0 . 1 8 4 4 R , " = 0 . 4 7 0 9 , w a = 0 . 3 0 9 1 0 . 0 0 0 2 3 ( 6 ) 0 . 0 5 0 1 a n d 0 . 6 4 0 4 3 . 3 2 a n d - 2 . 6 1 e . A ' 3 R = E l l F o l - c h l l / 2 1 m , w R = { 2 [ w ( | F o | 2 - | F c | 2 ) 2 ] / £ [ w ( | F . , | “ ) ] } " 2 a n d w = 1 / ( o z ( l ) + 0 . 0 0 1 6 1 2 ) 1 7 4 T a b l e 3 . 5 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r S m T e 3 a t 4 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . L a b e l W a v e x y z U , q S m 0 9 2 4 9 1 6 9 5 ( 1 ) 2 5 4 9 1 0 ( 1 ) s i n , 1 0 0 2 8 ( 5 ) c o s , 1 1 9 ( 1 ) 6 ( 1 ) 0 T e [ 1 ] 0 9 2 0 9 ( 5 ) 2 9 5 3 ( 1 ) 2 5 4 9 9 ( 1 ) s i n , 1 0 0 1 0 ( 6 ) c o s , 1 0 ( 2 ) - 1 ( 1 ) 0 T e [ 2 ] 0 9 1 9 5 ( 7 ) 7 0 8 ( 1 ) 7 5 4 9 1 4 ( 1 ) s i n , 1 0 0 1 ( 6 ) c o s , 1 - 8 7 ( 3 ) 0 ( 1 ) 0 T e [ 3 ] O 9 2 2 8 ( 6 ) 4 2 9 1 ( 1 ) 7 5 4 9 1 4 ( 1 ) s i n , 1 0 0 - 3 ( 6 ) c o s , 1 6 1 ( 3 ) - 1 ( 1 ) 0 ' U , q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 5 8 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r S m T e 3 a t 4 0 0 K w i t h e . s . d ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 S m 1 0 ( 1 ) 1 1 ( 1 ) 8 ( 1 ) 1 ( 1 ) 0 0 T e [ 1 ] 9 ( 1 ) 1 0 ( 1 ) 8 ( 1 ) - 2 0 ) 0 0 T e [ 2 ] 1 5 ( 1 ) 1 5 ( 1 ) 1 2 ( 1 ) 1 0 ( 1 ) 0 0 T e [ 3 ] 1 4 ( 1 ) 1 5 ( 1 ) 1 2 ( 1 ) 1 ( 1 ) 0 o T a b l e 3 . 5 9 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r S m T e 3 a t 4 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e S m - T e [ 1 ] 3 . 2 3 2 1 ( 1 5 ) 3 . 2 1 5 ( 3 ) 3 . 2 4 9 ( 3 ) S m - T e [ 1 ] x 2 3 . 1 9 1 ( 2 ) 3 . 1 8 2 ( 2 ) 3 . 1 9 8 ( 2 ) S m - T e [ 1 ] x 2 3 . 1 9 5 ( 2 ) 3 . 1 8 6 ( 2 ) 3 . 2 0 5 ( 2 ) S m - T e [ 2 ] x 2 3 . 3 3 4 9 ( 1 9 ) 3 . 3 2 1 0 ( 1 9 ) 3 . 3 4 8 7 ( 1 9 ) S m - T e [ 3 ] 3 . 3 2 3 ( 2 ) 3 . 3 2 0 ( 3 ) 3 . 3 2 6 ( 3 ) S m - T e [ 3 ] 3 . 3 3 9 ( 2 ) 3 . 3 1 8 ( 3 ) 3 . 3 6 0 ( 3 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 5 2 ( 3 ) 3 . 0 1 2 ( 3 ) 3 . 0 9 3 ( 3 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 7 3 ( 3 ) 3 . 0 3 2 ( 3 ) 3 . 1 1 3 ( 3 ) 1 7 5 T a b l e 3 . 6 0 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r S m T e 3 a t 4 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - S m - T e [ 1 ] x 8 7 3 5 8 ( 4 ) 7 3 3 8 ( 4 ) 7 3 7 7 ( 4 ) T e [ 1 ] - S m - T e [ 2 ] x 2 l 3 9 . 4 6 ( 6 ) 1 3 9 . 1 4 ( 7 ) 1 3 9 . 8 0 ( 7 ) T e [ 1 ] - S m - T e [ 3 ] l 3 9 . 7 2 ( 5 ) 1 3 9 . 4 9 ( 6 ) 1 3 9 . 9 5 ( 6 ) T e [ 1 ] - S m - T e [ 3 ] 1 3 9 . 2 7 ( 5 ) 1 3 9 . 2 3 ( 6 ) 1 3 9 . 3 1 ( 6 ) T e [ 1 ] - S m - T e [ 1 ] x 8 8 5 5 7 ( 6 ) 8 5 5 3 ( 6 ) 8 5 6 1 ( 6 ) T e [ 1 ] - S m - T e [ 1 ] x 4 1 4 7 . 0 9 ( 5 ) 1 4 6 . 6 0 ( 6 ) 1 4 7 . 5 8 ( 6 ) T e [ 1 ] - S m - T e [ 2 ] x 4 7 6 9 1 ( 6 ) 7 6 2 1 ( 6 ) 7 7 6 2 ( 6 ) T e [ 1 ] - S m - T e [ 2 ] x 4 l 3 1 . 0 2 ( 6 ) 1 3 0 . 1 1 ( 6 ) 1 3 1 . 9 5 ( 6 ) T e [ 1 ] - S m - T e [ 3 ] x 4 7 7 . 1 6 ( 5 ) 7 7 0 5 ( 5 ) 7 7 2 8 ( 5 ) T e [ 1 ] - S m - T e [ 3 ] x 4 1 3 1 . 0 0 ( 6 ) 1 3 0 . 6 9 ( 7 ) 1 3 1 . 3 2 ( 7 ) T e [ 2 ] — S m - T e [ 2 ] x 2 8 1 0 6 ( 5 ) 8 0 7 4 ( 6 ) 8 1 3 8 ( 6 ) T e [ 2 ] - S m - T e [ 3 ] x 4 5 4 5 6 ( 6 ) 5 3 6 8 ( 6 ) 5 5 4 7 ( 6 ) T e [ 3 ] - S m - T e [ 3 ] x 2 8 1 0 0 ( 5 ) 8 0 7 4 ( 7 ) 8 1 2 7 ( 7 ) S m - T e [ 1 ] - S m x 8 1 0 6 . 3 9 ( 5 ) 1 0 6 . 3 2 ( 6 ) 1 0 6 . 4 7 ( 6 ) S m - T e [ 1 ] - S m x 8 8 5 4 1 ( 6 ) 8 4 9 7 ( 7 ) 8 5 8 3 ( 7 ) S m - T e [ 1 ] - S m x 4 1 4 7 . 0 9 ( 5 ) l 4 6 7 8 ( 7 ) 1 4 7 . 4 0 ( 7 ) S m - T e [ 2 ] - S m x 2 8 1 . 0 6 ( 5 ) 8 1 0 0 ( 6 ) 8 1 . 1 1 ( 6 ) S m - T e [ 2 ] - T e [ 3 ] x 4 6 2 5 2 ( 5 ) 6 2 3 4 ( 4 ) 6 2 6 9 ( 4 ) S m - T e [ 2 ] - T e [ 3 ] x 4 1 1 7 . 4 8 ( 8 ) l 1 6 5 4 ( 9 ) 1 1 8 4 1 ( 9 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 9 0 4 9 ( 1 0 ) 8 9 1 0 ( 1 0 ) 9 1 8 9 ( 1 1 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 6 8 9 8 9 ( 8 ) 8 9 8 6 ( 7 ) 8 9 9 4 ( 9 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 9 0 7 ( 1 1 ) 1 7 8 2 0 ( 1 0 ) 1 8 0 S m - T e [ 3 ] - S m x 2 8 1 0 0 ( 3 ) 8 0 7 4 ( 6 ) 8 1 2 7 ( 6 ) S m - T e [ 3 ] - T e [ 2 ] x 2 6 2 5 2 ( 5 ) 6 2 1 7 ( 5 ) 6 2 . 8 7 ( 6 ) S m - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 3 3 ( 6 ) 1 1 7 . 1 0 ( 6 ) 1 1 7 . 5 6 ( 6 ) S m - T e [ 3 ] - T e [ 2 ] x 2 6 2 9 1 ( 5 ) 6 2 1 9 ( 5 ) 6 3 6 3 ( 5 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 6 8 9 7 3 ( 1 0 ) 8 8 4 5 ( 1 0 ) 9 1 0 1 ( 1 0 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 9 . 1 4 ( 1 0 ) 1 7 8 . 3 2 ( 1 0 ) 1 8 0 T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 9 0 4 9 ( 1 0 ) 8 9 1 8 ( 1 0 ) 9 1 8 0 ( 1 0 ) T a b l e 3 . 6 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r S m T e ; a t 5 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 1 5 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 c r ( 1 ) ] R i n d i c e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t L a r g e s t d i f f . p e a k a n d h o l e S m T e 3 5 3 3 . 2 5 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C m c m a = 4 . 3 3 4 3 ( 1 3 ) A , 0 1 = 9 0 ° b = 2 5 . 6 7 4 ( 1 0 ) A , B = 9 0 ° c = 4 . 3 4 7 0 ( 1 5 ) A , y = 9 0 ° 4 8 3 . 7 ( 3 ) A 3 4 7 . 3 1 8 g / c m 3 2 9 . 6 3 9 m m " 8 7 2 0 . 1 7 x 0 . 1 1 x 0 . 0 1 m m 3 4 . 7 7 t o 2 9 . 1 5 ° - 5 < = h < = 5 , - 2 1 < = k < = 3 4 , - 5 < = l < = 5 1 0 4 3 3 7 4 [ R i m = 0 . 0 4 2 3 ] 9 1 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 3 7 4 / 0 / 1 8 1 . 5 5 R o b s = 0 . 0 2 6 9 , w a s = 0 . 0 6 9 8 R . , “ = 0 . 0 2 8 1 , w R a u = 0 . 0 7 0 1 0 . 0 9 7 ( 9 ) 1 . 2 4 a n d - 1 . 5 6 e . A ' 3 R = X I I F o I - I F c l l / Z l F o I . w R = { X I W G F o I 2 - I R E ) ? £ [ W ( | F o l 4 ) ] } 1 7 2 a n d W = 1 / ( 0 2 ( I ) + 0 - 0 0 1 6 1 2 ) T a b l e 3 . 6 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r S m T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . L a b e l x y 2 O c c u p a n c y U e q S m 0 1 6 9 6 ( 1 ) 2 5 4 9 1 1 3 ( 1 ) T e [ 1 ] 0 2 9 5 3 ( 1 ) 2 5 4 9 1 1 2 ( 1 ) T e [ 2 ] O 4 2 9 0 ( 1 ) 7 5 4 9 1 1 8 ( 1 ) 1 7 7 T a b l e 3 . 6 2 . ( C o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r S m T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 3 ] 0 7 0 9 ( 1 ) 7 5 4 9 1 1 8 ( 1 ) ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 6 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r S m T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 S m 1 1 ( 1 ) 1 5 ( 1 ) 1 3 ( 1 ) 0 0 0 T e [ 1 ] 1 0 ( 1 ) 1 4 ( 1 ) 1 2 ( 1 ) 0 0 0 T e [ 2 ] 1 7 ( 1 ) 1 9 ( 1 ) 1 8 ( 1 ) 0 0 0 T e [ 3 ] 1 6 ( 1 ) 1 9 ( 1 ) 1 8 ( 1 ) 0 0 0 T a b l e 3 . 6 4 . B o n d d i s t a n c e s [ A ] f o r S m T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l D i s t a n c e s L a b e l D i s t a n c e s S m - T e [ 1 ] 3 . 2 2 8 1 ( 8 ) S m - T e [ 2 ] x 2 3 . 3 3 2 2 ( 7 ) S m - T e [ 1 ] x 4 3 . 1 9 8 8 ( 2 ) S m - T e [ 3 ] x 2 3 . 3 3 7 6 ( 7 ) T a b l e 3 . 6 5 . B o n d a n g l e s [ ° ] f o r S m T e 3 a t 5 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l A n g l e s L a b e l A n g l e s T e [ 1 ] - S m - T e [ 1 ] x 8 7 3 6 4 4 ( 1 4 ) S m - T e [ 1 ] - S m x 4 8 5 . 2 9 7 ( 7 ) T e [ 1 ] - S m - T e [ 2 ] x 2 1 3 9 4 3 0 0 0 ) S m - T e [ 1 ] - S m x 4 1 4 7 . 2 9 ( 2 ) T e [ 1 ] - S m - T e [ 1 ] x 4 8 5 . 6 0 7 ( 6 ) S m - T e [ 2 ] - T e [ 3 ] x 4 6 2 . 6 9 1 ( 1 3 ) T e [ 1 ] - S m - T e [ 1 ] x 4 8 5 . 2 9 7 ( 6 ) S m - T e [ 2 ] - T e [ 3 ] x 4 1 1 7 . 3 6 ( 2 ) T e [ 1 ] - S m - T e [ 1 ] x 4 1 4 7 . 2 9 ( 2 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 9 0 . 1 6 8 T e [ 1 ] - S m - T e [ 2 ] x 4 7 6 8 9 6 ( 1 2 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 8 9 . 8 3 2 T e [ 1 ] - S m - T e [ 2 ] x 4 1 3 0 8 8 4 0 3 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 8 0 T e [ 1 ] - S m - T e [ 3 ] x 4 7 6 . 7 7 4 ( 1 2 ) S m - T e [ 3 ] - S m x 2 8 1 . 2 6 7 ( 1 8 ) T e [ 1 ] - S m — T e [ 3 ] x 4 1 3 1 . 0 1 0 ( 1 3 ) S m - T e [ 3 ] - T e [ 2 ] x 4 6 2 . 5 1 1 ( 1 4 ) T e [ 2 ] - S m - T e [ 2 ] x 2 8 1 . 1 4 0 ( 1 6 ) S m - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 4 3 ( 2 ) T e [ 2 ] - S m - T e [ 3 ] x 4 5 4 . 7 9 8 ( 1 0 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 9 0 . 1 6 8 T e [ 3 ] - S m - T e [ 3 ] x 2 8 1 . 2 6 7 ( 1 6 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 8 9 . 8 3 2 S m - T e [ 1 ] - S m x 8 1 0 6 . 3 5 6 ( 1 4 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 8 0 1 7 8 T a b l e 3 . 6 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r G d T e 3 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 1 1 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( 1 ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 “ o r d e r s a t e l l i t e s [ I > 2 0 ( 1 ) ] R 1 “ o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f f i c i e n t T m a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e G d T e 3 5 4 0 1 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 0 m ( 0 0 y ) 0 0 0 a = 4 . 2 9 5 4 ( 4 ) A , 0 1 = 9 0 ° b = 2 5 4 4 3 0 ) A , 1 3 = 9 0 ° c = 4 . 3 0 9 7 ( 5 ) A , y = 9 0 ° 0 . 2 8 8 4 ( 3 ) c ‘ 4 7 0 . 9 9 ( 8 ) A 3 4 7 . 6 1 3 5 g / c m 3 3 2 . 0 6 5 m m " 8 8 0 0 . 1 1 x 0 . 1 0 x 0 . 0 1 m m 3 2 . 1 0 t o 2 9 . 1 1 ° - 5 < = h < = 5 , - 3 4 < = k < = 3 4 , - 6 < = l < = 6 , - 1 < = m < = 1 6 7 7 5 ( 2 2 0 6 m a i n + 4 5 6 9 s a t e l l i t e s ) 1 9 0 6 ( 6 6 7 m a i n + 1 2 3 9 s a t e l l i t e s ) [ R i o t = 0 . 0 9 6 3 ] 9 9 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 1 9 0 6 / 0 / 3 9 1 . 6 8 R . , , = 0 . 0 4 3 8 , w R . . . , = 0 . 1 1 0 2 R , “ = 0 . 0 6 1 8 , w R . . . , l = 0 . 1 1 4 7 R . , , = 0 . 0 4 0 7 , w R o b , = 0 . 1 0 8 7 R , " = 0 . 0 4 0 9 , w R . u = 0 . 1 0 8 9 R o b , = 0 . 0 6 9 5 , w R o b s = 0 . 1 1 8 0 R , “ = 0 . 1 8 9 7 , w R . . . 1 = 0 . 1 4 1 6 0 . 0 0 0 3 1 ( 5 ) 0 . 0 5 9 0 a n d 0 . 8 1 8 8 3 . 1 4 a n d - 3 3 6 e . A ' 3 R = E n r o l - 1 F . “ / 2 1 F . 1 . w R = { Z [ W ( | F o | 2 - c h | 2 ) 2 ] / E [ W ( | F o l 4 ) ] } " 2 a n d w = 1 / ( c z a ) + 0 . 0 0 1 6 1 2 ) 1 7 9 T a b l e 3 . 6 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r G d T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . # L a b e l W a v e x y z U e q G d 0 9 4 4 9 1 6 9 4 ( 1 ) 2 5 4 9 5 ( 1 ) s i n , 1 0 0 1 8 ( 4 ) c o s , 1 5 8 ( 1 ) 5 ( 1 ) 0 T e [ 1 ] 0 9 3 9 7 ( 5 ) 2 9 4 8 ( 1 ) 2 5 4 9 5 ( 1 ) s i n , 1 0 0 6 ( 5 ) c o s , 1 7 ( 1 ) 0 ( 1 ) 0 T e [ 2 ] 0 9 3 2 0 ( 5 ) 7 0 9 ( 1 ) 7 5 4 9 6 ( 1 ) s i n , 1 0 0 - 3 ( 5 ) c o s , 1 - 2 1 7 ( 3 ) - 1 ( 1 ) 0 T e [ 3 ] 0 4 3 9 6 ( 5 ) 7 1 0 ( 1 ) 2 5 4 9 6 ( 1 ) s i n , 1 0 0 - 1 2 ( 6 ) c o s , 1 1 9 1 ( 3 ) 1 ( 1 ) 0 ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 6 8 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r G d T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 G d 5 ( 1 ) 1 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) 0 0 T e [ 1 ] 4 ( 1 ) 1 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 0 T e [ 2 ] 6 ( 1 ) 1 2 ( 1 ) 1 ( 1 ) 2 ( 1 ) 0 0 T e [ 3 ] 6 ( 1 ) 1 2 ( 1 ) 2 ( 1 ) 2 ( 1 ) 0 0 T a b l e 3 . 6 9 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r G d T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e G d - T e [ 1 ] 3 . 1 9 0 1 ( 1 8 ) 3 . 1 7 6 ( 3 ) 3 . 2 0 5 ( 3 ) G d - T e [ 1 ] x 4 3 . 1 7 6 5 ( 1 9 ) 3 . 1 6 2 8 ( 1 7 ) 3 . 1 9 0 1 ( 1 7 ) G d - T e [ 2 ] x 2 3 . 3 0 6 8 ( 1 9 ) 3 . 2 9 3 ( 2 ) 3 . 3 2 2 ( 2 ) G d - T e [ 3 ] x 2 3 . 3 0 0 ( 2 ) 3 . 2 7 1 ( 3 ) 3 . 3 2 9 ( 3 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 2 0 ( 3 ) 2 . 9 0 9 ( 2 ) 3 . 1 3 4 ( 3 ) T e [ 2 ] — T e [ 3 ] x 2 3 . 0 6 7 ( 3 ) 2 . 9 5 8 ( 2 ) 3 . 1 7 8 ( 3 ) 1 8 0 T a b l e 3 . 7 0 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r G d T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - G d - T e [ 1 ] x 8 7 3 3 4 ( 4 ) 7 3 2 7 ( 4 ) 7 3 4 2 ( 4 ) T e [ 1 ] - G d - T e [ 2 ] x 2 l 3 9 2 8 ( 5 ) 1 3 9 . 0 6 ( 5 ) 1 3 9 . 5 6 ( 5 ) T e [ 1 ] - G d - T e [ 3 ] x 2 1 3 9 . 3 4 ( 5 ) 1 3 8 . 8 6 ( 5 ) 1 3 9 . 8 1 ( 6 ) T e [ 1 ] - G d - T e [ 1 ] x 8 8 5 4 3 ( 5 ) 8 5 0 9 ( 5 ) 8 6 7 9 ( 5 ) T e [ 1 ] - G d - T e [ 1 ] x 4 1 4 6 . 7 1 ( 5 ) 1 4 6 . 2 6 ( 7 ) 1 4 7 . 1 5 ( 7 ) T e [ 1 ] - G d - T e [ 2 ] x 2 7 6 5 7 ( 5 ) 7 5 . 1 8 ( 6 ) 7 7 9 9 ( 6 ) T e [ 1 ] - G d - T e [ 2 ] x 2 1 3 0 . 7 1 ( 5 ) 1 2 8 . 5 9 ( 5 ) 1 3 2 . 8 5 ( 5 ) T e [ 1 ] - G d - T e [ 3 ] x 4 7 7 . 1 0 ( 5 ) 7 6 8 5 ( 4 ) 7 7 3 4 ( 4 ) T e [ 1 ] - G d - T e [ 3 ] x 4 1 3 1 . 1 3 ( 6 ) 1 3 0 . 7 9 ( 6 ) 1 3 1 . 4 5 ( 6 ) T e [ 1 ] - G d - T e [ 2 ] x 2 7 7 . 4 0 ( 5 ) 7 6 2 3 ( 6 ) 7 8 5 5 ( 6 ) T e [ 1 ] - G d - T e [ 2 ] x 2 1 3 1 . 8 2 ( 5 ) 1 3 0 . 0 7 ( 5 ) 1 3 3 . 5 3 ( 5 ) T e [ 2 ] - G d - T e [ 2 ] x 2 8 1 3 6 ( 5 ) 8 0 9 3 ( 6 ) 8 1 . 7 4 ( 6 ) T e [ 2 ] - G d - T e [ 3 ] x 2 5 4 3 9 ( 6 ) 5 2 3 3 ( 6 ) 5 6 5 2 ( 6 ) T e [ 2 ] - G d - T e [ 3 ] x 2 5 5 3 4 ( 6 ) 5 3 6 7 ( 6 ) 5 7 0 0 ( 6 ) T e [ 3 ] - G d - T e [ 3 ] x 2 8 1 2 3 ( 5 ) 8 0 9 9 ( 7 ) 8 1 . 4 6 ( 7 ) G d - T e [ 1 ] - G d x 8 1 0 6 . 6 7 ( 5 ) 1 0 6 . 4 9 ( 6 ) 1 0 6 . 8 5 ( 6 ) G d - T e [ 1 ] - G d x 8 8 5 5 1 ( 6 ) 8 5 0 0 ( 6 ) 8 6 0 1 ( 6 ) G d - T e [ 1 ] - G d x 4 1 4 6 . 7 1 ( 6 ) 1 4 6 . 3 9 ( 7 ) l 4 7 . 0 3 ( 7 ) G d - T e [ 2 ] - G d x 2 8 1 3 4 ( 5 ) 8 1 . 1 8 ( 7 ) 8 1 . 4 5 ( 7 ) G d - T e [ 2 ] - T e [ 3 ] x 2 6 2 6 7 ( 4 ) 6 2 1 9 ( 4 ) 6 3 1 2 ( 4 ) G d - T e [ 2 ] - T e [ 3 ] x 2 1 1 8 . 1 4 ( 7 ) 1 1 5 . 7 8 ( 8 ) 1 2 0 . 4 6 ( 9 ) G d - T e [ 2 ] - T e [ 3 ] x 2 6 2 1 8 ( 4 ) 6 1 5 8 ( 4 ) 6 2 7 8 ( 4 ) G d - T e [ 2 ] - T e [ 3 ] x 2 1 1 6 7 5 ( 7 ) 1 1 4 . 1 1 ( 8 ) 1 1 9 . 3 8 ( 9 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 9 1 . 1 5 ( 9 ) 8 7 . 4 1 ( 8 ) 9 4 9 9 ( 9 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 6 8 9 7 3 ( 7 ) 8 9 . 6 3 ( 6 ) 8 9 8 8 ( 8 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 7 . 5 0 ( 9 ) 1 7 5 . 2 8 ( 9 ) 1 8 0 G d - T e [ 3 ] - G d x 2 8 1 2 3 ( 4 ) 8 0 9 9 ( 7 ) 8 1 . 4 6 ( 7 ) G d - T e [ 3 ] - T e [ 2 ] x 2 6 2 4 8 ( 5 ) 6 1 2 1 ( 5 ) 6 3 8 1 ( 5 ) G d - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 1 2 ( 6 ) 1 1 6 . 5 0 ( 6 ) 1 1 7 . 6 8 ( 6 ) G d - T e [ 3 ] - T e [ 2 ] x 2 6 2 9 4 ( 5 ) 6 1 2 1 ( 5 ) 6 4 6 7 ( 5 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 6 8 9 3 7 ( 8 ) 8 3 7 5 ( 8 ) 9 3 1 4 ( 9 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 l 7 7 . 5 4 ( 9 ) l 7 5 . 4 0 ( 9 ) 1 8 0 T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 9 l . l 8 ( 8 ) 8 7 . 4 4 ( 8 ) 9 4 9 4 ( 9 ) 1 8 1 T a b l e 3 . 7 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r T b T e 3 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 2 2 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 o ( 1 ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 6 ( 1 ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 “ o r d e r s a t e l l i t e s [ I > 2 0 ’ ( 1 ) ] R 1 “ o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m a n d T m a x c o e f f i c i e n t s L a r g e s t d i f f . p e a k a n d h o l e T b T e 3 5 4 1 . 7 1 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 c m ( 0 0 y ) 0 0 0 a = 4 . 2 8 0 1 ( 7 ) A , 0 1 = 9 0 ° b = 2 5 . 3 0 7 ( 5 ) A , 1 3 = 9 0 ° c = 4 . 3 0 5 2 ( 9 ) A , y = 9 0 0 0 . 2 9 1 2 ( 5 ) e ‘ 4 6 6 . 3 2 0 6 ) A 3 4 7 . 7 1 4 g / c m 3 3 3 . 4 2 9 m m “ 8 8 4 0 . 2 8 x 0 . 2 0 x 0 . 0 3 m m “ 2 . 1 1 t o 2 9 . 2 2 ° - 5 < = h < = 5 , - 3 4 < = k < = 3 4 , - 6 < = l < = 6 , - 1 < = m < = 1 6 5 0 6 ( 2 0 7 9 m a i n + 4 4 2 7 s a t e l l i t e s ) 1 8 7 1 ( 6 5 1 m a i n + 1 2 2 0 s a t e l l i t e s ) [ R i m = 0 . 0 3 1 1 ] 9 8 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 1 8 7 1 / 0 / 3 8 1 . 6 5 R o b , = 0 . 0 2 7 0 , w R . . . , = 0 . 1 0 4 5 R . , l l = 0 . 0 4 1 2 , w R a u = 0 . 1 0 8 4 R o b s = 0 . 0 2 4 8 , w R o b , = 0 . 1 0 8 6 R a l l = 0 . 0 2 4 8 , m e = 0 . 1 0 8 6 R o b , = 0 . 0 4 7 1 , w R o b s = 0 . 0 8 2 1 R , “ = 0 . 1 5 1 6 , w R . . . , = 0 . 1 0 7 6 0 . 0 0 0 6 6 ( 5 ) 0 . 0 2 8 6 a n d 0 . 3 1 9 8 2 . 5 6 a n d - 2 7 4 e . A ‘ 3 R = £ | | F 0 | - | F c | | / 2 1 1 a ) , w R = { 2 0 0 1 1 3 0 1 2 - c h | 2 ) 2 ] / £ [ w ( | F o | 4 ) ] } " 2 a n d w = 1 / ( 0 ' 2 ( I ) + 0 0 0 1 6 1 2 ) 1 8 2 T a b l e 3 . 7 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r T b T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . L a b e l W a v e x y z U e q T h 0 9 2 4 9 1 6 9 6 ( 1 ) 2 5 4 9 2 ( 1 ) s i n , 1 0 0 - l ( 3 ) c o s , 1 4 8 ( 1 ) 1 ( 1 ) 0 T e [ 1 ] 0 9 1 6 1 ( 3 ) 2 9 4 7 ( 1 ) 2 5 4 9 2 ( 1 ) s i n , 1 0 0 - 2 ( 3 ) c o s , 1 5 ( 1 ) 0 ( 1 ) 0 T e [ 2 ] 0 9 2 5 0 ( 3 ) 7 1 2 ( 1 ) 7 5 4 9 3 ( 1 ) s i n , 1 O 0 - 5 ( 4 ) c o s , 1 - 1 7 9 ( 2 ) 7 ( 1 ) 0 T e [ 3 ] O 9 2 3 4 ( 4 ) 4 2 8 6 ( 1 ) 7 5 4 9 4 ( 1 ) s i n , 1 0 0 2 2 ( 4 ) c o s , 1 1 5 6 ( 2 ) - 1 ( 1 ) 0 “ U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 7 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r T b T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 T b 2 ( 1 ) 4 ( 1 ) 2 ( 1 ) 1 ( 1 ) 0 0 T e [ 1 ] 2 ( 1 ) 4 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 0 T e [ 2 ] 3 ( 1 ) 6 ( 1 ) 1 ( 1 ) - 5 0 ) 0 0 T e [ 3 ] 3 ( 1 ) 6 ( 1 ) 3 ( 1 ) - 3 0 ) 0 0 T a b l e 3 . 7 4 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r T b T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e T b - T e [ 1 ] 3 . 1 6 3 8 ( 1 2 ) 3 . 1 6 2 ( 2 ) 3 . 1 6 6 ( 2 ) T b - T e [ 1 ] x 2 3 . 1 7 8 5 ( 1 2 ) 3 . 1 6 6 1 ( 1 2 ) 3 . 1 9 0 6 ( 1 2 ) T b - T e [ 1 ] x 2 3 . 1 5 5 5 ( 1 2 ) 3 . 1 4 1 7 ( 1 2 ) 3 . 1 6 9 5 ( 1 2 ) T b - T e [ 2 ] x 2 3 . 2 9 2 8 ( 1 2 ) 3 . 2 7 9 4 ( 1 3 ) 3 . 3 0 7 6 ( 1 3 ) T b - T e [ 3 ] 3 . 2 7 1 1 ( 1 4 ) 3 . 2 4 1 5 ( 1 9 ) 3 . 3 0 1 4 ( 1 9 ) T b - T e [ 3 ] 3 . 2 9 0 8 ( 1 4 ) 3 . 2 6 0 6 ( 1 9 ) 3 . 3 2 0 6 ( 1 9 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 4 0 4 ( 1 8 ) 2 . 9 5 3 3 ( 1 6 ) 3 . 1 3 0 1 ( 1 7 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 3 1 7 ( 1 8 ) 2 . 9 3 8 7 ( 1 6 ) 3 . 1 2 5 1 ( 1 7 ) 1 8 3 T a b l e 3 . 7 5 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r T b T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - T b - T e [ 1 ] x 8 7 3 2 7 ( 3 ) 7 3 1 4 ( 3 ) 7 3 4 1 ( 3 ) T e [ 1 ] - T b - T e [ 2 ] x 2 1 3 9 . 1 5 ( 3 ) 1 3 8 . 9 4 ( 4 ) 1 3 9 . 3 5 ( 5 ) T e [ 1 ] - T b - T e [ 3 ] x 2 1 3 9 . 1 8 ( 3 ) 1 3 8 . 9 0 ( 4 ) l 3 9 . 4 6 ( 4 ) T e [ 1 ] - T b - T e [ 1 ] x 2 8 5 2 6 ( 3 ) 8 4 8 3 ( 3 ) 8 5 6 9 ( 3 ) T e [ 1 ] - T b - T e [ 1 ] x 4 8 5 0 2 ( 4 ) 8 5 0 0 ( 3 ) 8 5 0 5 ( 3 ) T e [ 1 ] - T b - T e [ 1 ] x 4 1 4 6 . 8 5 ( 3 ) 1 4 6 . 7 9 ( 4 ) 1 4 6 . 9 1 ( 4 ) T e [ 1 ] - T b - T e [ 2 ] x 2 7 7 0 8 ( 3 ) 7 5 8 8 ( 3 ) 7 8 3 0 ( 4 ) T e [ 1 ] - T b - T e [ 2 ] x 2 1 3 1 . 4 6 ( 3 ) 1 2 9 . 9 3 ( 3 ) 1 3 3 . 0 0 ( 3 ) T e [ 1 ] - T b - T e [ 3 ] x 4 7 7 0 1 ( 3 ) 7 6 7 4 ( 4 ) 7 7 2 8 ( 4 ) T e [ 1 ] - T b - T e [ 3 ] x 2 1 3 1 . 2 4 ( 4 ) 1 3 0 . 8 7 ( 4 ) 1 3 1 . 6 0 ( 4 ) T e [ 1 ] - T b - T e [ 1 ] x 2 8 6 0 3 ( 3 ) 8 5 5 8 ( 3 ) 8 6 4 7 ( 3 ) T e [ 1 ] - T b - T e [ 2 ] x 2 7 6 4 9 ( 3 ) 7 5 5 8 ( 3 ) 7 7 3 8 ( 4 ) T e [ 1 ] - T b - T e [ 2 ] x 2 l 3 1 . 1 7 ( 4 ) 1 2 9 . 5 2 ( 3 ) 1 3 2 . 8 1 ( 3 ) T e [ 1 ] - T b - T e [ 3 ] x 2 1 3 0 . 9 0 ( 4 ) 1 3 0 . 4 8 ( 4 ) l 3 1 3 1 ( 4 ) T e [ 2 ] - T b - T e [ 2 ] x 2 8 1 6 7 ( 3 ) 8 1 . 4 5 ( 4 ) 8 1 8 3 ( 4 ) T e [ 2 ] - T b - T e [ 3 ] x 2 5 4 8 5 ( 4 ) 5 3 1 1 ( 4 ) 5 6 5 7 ( 4 ) T e [ 3 ] - T b - T e [ 3 ] x 2 8 1 . 4 2 ( 4 ) 8 1 . 4 1 ( 5 ) 8 1 . 4 3 ( 3 ) T b - T e [ 1 ] - T b x 8 1 0 6 . 8 5 ( 3 ) 1 0 6 . 5 9 ( 4 ) 1 0 7 . 1 0 ( 4 ) T b - T e [ 1 ] - T b x 2 8 6 0 3 ( 4 ) 8 5 . 7 9 ( 4 ) 8 6 2 6 ( 4 ) T b - T e [ 1 ] - T b x 4 1 4 6 . 8 5 ( 4 ) 1 4 6 . 7 3 ( 2 ) 1 4 6 . 9 8 ( 2 ) T b - T e [ 1 ] - T b x 2 8 5 2 6 ( 4 ) 8 5 0 3 ( 4 ) 8 5 4 9 ( 4 ) T b - T e [ 2 ] - T b x 2 8 1 6 5 ( 3 ) 8 1 2 2 ( 4 ) 8 2 0 4 ( 4 ) T b - T e [ 2 ] - T e [ 3 ] x 2 l 1 7 2 2 ( 4 ) 1 1 4 . 7 2 ( 5 ) 1 1 9 . 7 2 ( 5 ) T b - T e [ 2 ] - T e [ 3 ] x 2 1 1 7 . 8 9 ( 4 ) 1 1 6 . 2 7 ( 5 ) 1 1 9 . 4 6 ( 5 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 9 0 2 1 ( 6 ) 8 6 9 1 ( 5 ) 9 3 5 6 ( 6 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 8 9 6 1 ( 5 ) 8 9 3 6 ( 4 ) 8 9 9 4 ( 5 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 7 . 9 6 ( 6 ) 1 7 6 . 5 7 ( 6 ) 1 7 9 . 9 2 ( 4 ) T b - T e [ 3 ] - T b x 2 8 1 . 4 2 ( 2 ) 8 1 . 4 1 ( 4 ) 8 1 . 4 2 8 ( 1 2 ) T b - T e [ 3 ] - T e [ 2 ] x 2 1 1 7 . 5 7 ( 4 ) 1 1 6 . 5 3 ( 3 ) 1 1 8 . 6 1 ( 3 ) T b - T e [ 3 ] - T e [ 2 ] x 2 1 1 7 . 2 6 ( 4 ) 1 1 6 . 9 6 ( 4 ) 1 1 7 . 5 3 ( 4 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 9 0 5 6 ( 6 ) 8 7 5 1 ( 6 ) 9 3 6 8 ( 6 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 8 9 6 1 ( 4 ) 8 9 3 6 ( 5 ) 8 9 9 4 ( 5 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 8 . 0 5 ( 6 ) 1 7 6 . 7 4 ( 6 ) 1 7 9 . 8 7 ( 4 ) 1 8 4 T a b l e 3 . 7 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r D y T e 3 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( l ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 0 1 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( 1 ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( 1 ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 “ o r d e r s a t e l l i t e s [ I > 2 c r ( 1 ) ] R 1 “ o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T w i n a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e D Y T C 3 5 4 5 . 3 1 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 c m ( 0 0 y ) 0 0 0 a = 4 . 2 8 3 1 ( 6 ) A , a = 9 0 ° b = 2 5 . 2 5 0 ( 5 ) A , B = 9 0 ° c = 4 . 2 8 8 7 ( 6 ) A , y = 9 0 ° 0 . 2 9 2 6 ( 3 ) e ' 4 6 3 . 8 1 0 3 ) A 3 4 7 . 8 0 7 g / c m 3 3 4 . 4 4 3 m m " 8 8 8 0 . 2 3 x 0 . 1 5 x 0 . 0 3 m m 3 2 . 1 2 t o 2 9 0 1 ° - 5 < = h < = 5 , - 3 4 < = k < = 3 4 , - 5 < = l < = 6 , - 1 < = m < = 1 5 8 9 1 ( 1 5 6 7 m a i n + 4 3 2 4 s a t e l l i t e s ) 1 8 1 9 ( 5 7 7 m a i n + 1 2 4 2 s a t e l l i t e S ) [ R i m = 0 . 0 3 9 7 ] 9 5 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 1 8 1 9 / 0 / 3 7 1 . 9 2 R o b , = 0 . 0 3 6 0 , w R o b s = 0 . 1 2 0 2 R , “ = 0 . 0 5 2 2 , m e = 0 . 1 2 7 3 R o b s = 0 . 0 2 7 8 , w R o t , s = 0 . 1 1 4 5 R , “ = 0 . 0 2 7 8 , w R a n = 0 . 1 1 4 5 R o b , = 0 . 0 8 5 6 , w R o b s = 0 . 1 3 8 9 R 3 1 1 = 0 . 1 7 0 6 , W R a u = 0 . 1 6 5 2 0 . 0 0 1 6 4 ( 1 4 ) 0 . 0 2 3 4 a n d 0 . 3 0 7 9 3 . 3 3 a n d - 4 8 2 e . A ' 3 R = l e F o I - I F c I I / 2 1 F 0 1 . w R = { Z [ W ( | F o l z - c h | 2 ) 2 ] / 2 1 w ( 1 F . 1 “ ) 1 } " 2 a n d w = 1 / ( c z ( I ) + 0 . 0 0 1 6 1 2 ) 1 8 5 T a b l e 3 . 7 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r D y T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . L a b e l W a v e x y z U e q D y 0 9 4 4 9 1 6 9 8 ( 1 ) 2 5 4 9 2 ( 1 ) s i n , 1 0 0 4 ( 3 ) c o s , 1 4 6 ( 1 ) 3 ( 1 ) 0 T e [ 1 ] 0 9 3 7 4 ( 3 ) 2 9 4 6 ( 1 ) 2 5 4 9 1 ( 1 ) s i n , 1 0 0 0 ( 3 ) c o s , 1 4 ( 1 ) - 1 ( 1 ) 0 T e [ 2 ] O 9 4 3 9 ( 4 ) 7 1 4 ( 1 ) 7 5 4 9 3 ( 1 ) s i n , 1 0 0 2 9 ( 3 ) c o s , 1 - 1 6 4 ( 2 ) - 2 ( 1 ) 0 T e [ 3 ] 0 4 4 2 0 ( 4 ) 7 1 5 ( 1 ) 2 5 4 9 3 ( 1 ) s i n , 1 0 0 - 2 ( 3 ) c o s , 1 1 4 7 ( 2 ) 0 ( 1 ) 0 ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 7 8 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r D y T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 D y 3 ( 1 ) 1 ( 1 ) 2 ( 1 ) 1 ( 1 ) 0 0 T e [ 1 ] 2 ( 1 ) 2 ( 1 ) 1 ( 1 ) - 1 0 ) 0 0 T e [ 2 ] 3 ( 1 ) 4 ( 1 ) 1 ( 1 ) - 5 0 ) 0 0 T e [ 3 ] 4 ( 1 ) 3 ( 1 ) 3 ( 1 ) 2 ( 1 ) 0 0 T a b l e 3 . 7 9 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r D y T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e D y - T e [ 1 ] x 3 3 . 1 5 1 3 ( 1 2 ) 3 . 1 4 2 ( 2 ) 3 . 1 6 0 ( 2 ) D y - T e [ 1 ] x 2 3 . 1 6 8 6 ( 1 2 ) 3 . 1 5 7 7 ( 1 2 ) 3 . 1 7 9 4 ( 1 2 ) D y - T e [ 2 ] x 2 3 . 2 8 1 8 ( 1 3 ) 3 . 2 6 7 4 ( 1 3 ) 3 . 2 9 6 0 ( 1 3 ) D y - T e [ 3 ] 3 . 2 7 1 8 ( 1 4 ) 3 . 2 4 9 7 ( 1 9 ) 3 . 2 9 4 5 ( 1 9 ) D y - T e [ 3 ] 3 . 2 8 3 5 ( 1 4 ) 3 . 2 4 9 6 ( 1 9 ) 3 . 3 1 7 0 ( 1 9 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 3 6 6 ( 1 8 ) 2 . 9 5 6 0 ( 1 6 ) 3 . 1 1 9 2 ( 1 7 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 2 6 0 ( 1 8 ) 2 . 9 3 7 9 ( 1 6 ) 3 . 1 1 3 9 ( 1 7 ) 1 8 6 T a b l e 3 . 8 0 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r D y T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - D y - T e [ 1 ] x 8 7 3 3 8 ( 3 ) 7 3 3 1 ( 3 ) 7 3 4 5 ( 3 ) T e [ 1 ] - D y - T e [ 2 ] x 2 1 3 9 . 1 8 ( 3 ) l 3 9 . 0 9 ( 4 ) 1 3 9 2 8 ( 4 ) T e [ 1 ] - D y - T e [ 3 ] x 2 1 3 9 . 1 2 ( 3 ) 1 3 8 . 7 9 ( 4 ) 1 3 9 . 4 5 ( 4 ) T e [ 1 ] - D y - T e [ 1 ] x 6 8 5 . 1 8 ( 3 ) 8 4 8 2 ( 3 ) 8 5 5 5 ( 3 ) T e [ 1 ] - D y - T e [ 1 ] x 4 1 4 6 . 9 7 ( 4 ) 1 4 6 . 7 5 ( 5 ) 1 4 7 . 1 8 ( 5 ) T e [ 1 ] - D y - T e [ 2 ] x 2 7 7 0 4 ( 3 ) 7 6 0 4 ( 3 ) 7 8 0 5 ( 3 ) T e [ 1 ] - D y - T e [ 2 ] x 2 1 3 1 . 3 2 ( 4 ) 1 2 9 . 7 3 ( 3 ) 1 3 2 . 9 3 ( 3 ) T e [ 1 ] - D y - T e [ 3 ] x 4 7 6 8 3 ( 3 ) 7 6 6 3 ( 3 ) 7 7 0 4 ( 3 ) T e [ 1 ] - D y - T e [ 3 ] x 4 l 3 1 2 4 ( 4 ) l 3 1 . 0 2 ( 4 ) 1 3 1 . 4 7 ( 4 ) T e [ 1 ] - D y - T e [ 1 ] x 2 8 5 6 9 ( 3 ) 8 5 2 1 ( 3 ) 8 6 1 7 ( 3 ) T e [ 1 ] - D y - T e [ 2 ] x 2 7 6 5 8 ( 3 ) 7 5 5 9 ( 4 ) 7 7 5 5 ( 4 ) T e [ 1 ] - D y - T e [ 2 ] x 2 l 3 1 . 0 4 ( 4 ) 1 2 9 . 6 6 ( 4 ) 1 3 2 . 4 0 ( 4 ) T e [ 2 ] - D y - T e [ 2 ] x 2 8 1 6 2 ( 3 ) 8 1 5 7 ( 4 ) 8 1 6 4 ( 3 ) T e [ 2 ] - D y - T e [ 3 ] x 2 5 5 2 0 ( 4 ) 5 3 6 7 ( 4 ) 5 6 7 7 ( 4 ) T e [ 2 ] - D y - T e [ 3 ] x 2 5 4 8 9 ( 4 ) 5 3 5 4 ( 4 ) 5 6 2 3 ( 4 ) T e [ 3 ] - D y - T e [ 3 ] x 2 8 1 5 9 ( 4 ) 8 1 . 4 2 ( 5 ) 8 1 . 7 6 ( 5 ) D y - T e [ 1 ] - D y x 8 1 0 6 . 7 0 ( 3 ) 1 0 6 . 4 8 ( 4 ) 1 0 6 . 9 1 ( 4 ) D y - T e [ 1 ] - D y x 8 8 5 2 9 ( 3 ) 8 5 2 1 ( 4 ) 8 5 3 8 ( 4 ) D y - T e [ 1 ] - D y x 4 1 4 6 . 9 7 ( 4 ) 1 4 6 . 8 2 ( 3 ) 1 4 7 . l 2 ( 3 ) D y - T e [ 2 ] - D y x 2 8 1 6 0 ( 3 ) 8 1 . 4 1 ( 5 ) 8 1 . 7 6 ( 5 ) D y - T e [ 2 ] - T e [ 3 ] x 2 6 2 2 2 ( 3 ) 6 1 . 7 7 ( 3 ) 6 2 6 9 ( 3 ) D y - T e [ 2 ] - T e [ 3 ] x 2 1 1 7 . 2 1 ( 5 ) 1 1 5 . 4 3 ( 6 ) 1 1 8 . 9 6 ( 6 ) D y - T e [ 2 ] - T e [ 3 ] x 2 6 2 5 8 ( 3 ) 6 2 1 6 ( 3 ) 6 2 9 8 ( 3 ) D y - T e [ 2 ] - T e [ 3 ] x 2 1 1 7 . 7 9 ( 5 ) 1 1 5 . 7 5 ( 6 ) 1 1 9 . 8 4 ( 6 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 6 8 9 9 1 ( 6 ) 8 7 0 6 ( 5 ) 9 2 8 0 ( 6 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 8 . 1 3 ( 6 ) 1 7 6 . 8 6 ( 6 ) 1 7 9 . 9 1 ( 4 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 9 0 3 3 ( 6 ) 8 7 4 3 ( 6 ) 9 3 3 0 ( 6 ) D y - T e [ 3 ] - D y x 2 8 1 5 9 ( 2 ) 8 1 . 4 2 ( 4 ) 8 1 . 7 6 ( 4 ) D y - T e [ 3 ] - T e [ 2 ] x 4 6 2 5 3 ( 3 ) 6 1 5 8 ( 3 ) 6 3 5 2 ( 3 ) D y - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 6 3 ( 4 ) 1 1 7 . 1 1 ( 4 ) 1 1 8 . 1 3 ( 4 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 9 0 3 1 ( 6 ) 8 7 8 0 ( 6 ) 9 2 9 3 ( 6 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 6 8 9 8 8 ( 4 ) 8 9 5 6 ( 4 ) 9 0 2 7 ( 4 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 8 . 1 8 ( 6 ) 1 7 6 . 9 4 ( 6 ) 1 7 9 . 9 1 ( 4 ) 1 8 7 T a b l e 3 . 8 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r H o T e 3 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( l ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 3 1 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( 1 ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 6 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 “ o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 “ o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m m a n d T m c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e H o T e 3 5 4 7 . 7 1 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 c m ( 0 0 y ) 0 0 0 a = 4 . 2 7 2 3 ( 8 ) A , 0 1 = 9 0 ° b = 2 5 . 2 0 3 ( 4 ) A , B = 9 0 ° c = 4 . 2 8 5 5 ( 6 ) A , y = 9 0 ° 0 . 2 9 3 5 ( 3 ) c ‘ 4 6 1 . 4 5 0 3 ) A 3 4 7 . 8 8 2 g / e m 3 3 5 . 6 1 m r n ' I 8 9 2 0 . 2 4 x 0 . 2 0 x 0 . 0 4 m m 3 2 . 1 3 t o 2 9 3 1 ° - 5 < = h < = 5 , - 3 4 < = k < = 3 4 , - 5 < = l < = 6 , - 1 < = m < = 1 6 5 3 6 ( 2 1 0 3 m a i n + 4 4 3 3 s a t e l l i t e s ) 1 9 3 2 ( 6 8 3 m a i n + 1 2 4 9 s a t e l l i t e s ) [ R i m = 0 . 0 3 9 1 ] 9 9 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 1 9 3 2 / 0 / 3 8 1 . 5 8 R o b , = 0 . 0 3 5 3 , w R o b s = 0 . 1 0 2 7 R , “ = 0 . 0 5 0 1 , m e = 0 . 1 0 6 3 R o b s = 0 . 0 3 2 7 , w R o b s = 0 . 1 0 0 4 R a n = 0 . 0 3 2 7 , W R a u = 0 . 1 0 0 4 R o b , = 0 . 0 6 8 4 , w R o b s = 0 . 1 1 5 9 R a n = 0 . 1 9 7 6 , w a = 0 . 1 3 6 5 0 . 0 0 0 2 5 ( 3 ) 0 . 0 0 9 5 a n d 0 . 2 4 2 5 3 . 4 7 a n d - 3 . 3 6 e . A ‘ 3 R = Z I I F o l - c h l l / 2 1 m , w R = { 2 [ W ( | F o | 2 - 1 1 0 9 2 1 / l e q F o l ‘ m ‘ ” a n d “ F l / ( 0 ’ 0 ) + 0 . 0 0 1 6 1 2 ) 1 8 8 T a b l e 3 . 8 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r H o T e ; a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e x y z U s q H o 0 9 2 4 9 1 6 9 9 ( 1 ) 2 5 4 9 9 ( 1 ) s i n , 1 0 0 2 ( 3 ) c o s , 1 4 3 ( 1 ) 4 ( 1 ) 0 T e [ 1 ] O 9 1 6 8 ( 4 ) 2 9 4 5 ( 1 ) 2 5 4 9 9 ( 1 ) s i n , 1 0 0 - 8 ( 4 ) c o s , 1 5 ( 1 ) - 1 ( 1 ) 0 T e [ 2 ] 0 9 2 3 2 ( 4 ) 7 1 5 ( 1 ) 7 5 4 9 1 0 ( 1 ) s i n , 1 0 0 1 7 ( 4 ) c o s , 1 - 1 4 7 ( 1 ) 1 ( 1 ) 0 T e [ 3 ] 0 9 2 2 1 ( 5 ) 4 2 8 4 ( 1 ) 7 5 4 9 1 0 ( 1 ) s i n , 1 0 0 4 ( 4 ) c o s , 1 1 3 1 ( 1 ) 0 ( 1 ) 0 ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 8 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r H o T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 H o 9 ( 1 ) 1 0 ( 1 ) 8 ( 1 ) 2 ( 1 ) 0 0 T e [ 1 ] 9 ( 1 ) 1 0 ( 1 ) 8 ( 1 ) - 1 0 ) 0 0 T e [ 2 ] 1 0 ( 1 ) 1 2 ( 1 ) 8 ( 1 ) 4 0 ) 0 0 T e [ 3 ] 1 0 ( 1 ) 1 1 ( 1 ) 9 ( 1 ) 0 ( 1 ) 0 0 T a b l e 3 . 8 4 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r H o T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e H o - T e [ 1 ] 3 . 1 4 0 4 ( 1 3 ) 3 . 1 2 9 ( 2 ) 3 . 1 5 2 ( 2 ) H o - T e [ 1 ] x 2 3 . 1 6 5 1 ( 1 5 ) 3 . 1 5 7 6 ( 1 3 ) 3 . 1 7 2 5 ( 1 3 ) H o - T e [ 1 ] x 2 3 . 1 4 6 5 ( 1 5 ) 3 . 1 3 0 4 ( 1 5 ) 3 . 1 6 2 8 ( 1 5 ) H o - T e [ 2 ] x 2 3 . 2 7 8 1 ( 1 5 ) 3 . 2 6 7 4 ( 1 4 ) 3 . 2 8 8 0 ( 1 4 ) H o - T e [ 3 ] 3 . 2 6 5 9 ( 1 7 ) 3 . 2 4 9 ( 2 ) 3 . 2 8 3 ( 2 ) H o - T e [ 3 ] 3 . 2 7 7 9 ( 1 7 ) 3 . 2 4 6 ( 2 ) 3 . 3 1 0 ( 2 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 2 9 ( 2 ) 2 . 9 5 7 4 ( 1 9 ) 3 . 1 0 3 ( 2 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 2 3 ( 2 ) 2 . 9 4 5 3 ( 1 9 ) 3 . 1 0 1 ( 2 ) 1 8 9 T a b l e 3 . 8 5 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r H o T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - H o - T e [ 1 ] x 4 7 3 3 6 ( 3 ) 7 3 2 7 ( 3 ) 7 3 4 5 ( 3 ) T e [ 1 ] - H o - T e [ 1 ] x 4 7 3 6 1 ( 3 ) 7 3 3 3 ( 3 ) 7 3 9 0 ( 3 ) T e [ 1 ] - H o - T e [ 2 ] x 2 1 3 9 . 1 6 ( 4 ) 1 3 9 . 1 0 ( 6 ) 1 3 9 . 2 4 ( 6 ) T e [ 1 ] - H o - T e [ 3 ] x 2 1 3 9 . 1 1 ( 4 ) 1 3 8 . 7 9 ( 4 ) 1 3 9 . 4 3 ( 4 ) T e [ 1 ] - H o - T e [ 1 ] x 6 8 5 2 2 ( 4 ) 8 4 8 4 ( 4 ) 8 5 6 1 ( 4 ) T e [ 1 ] - H o - T e [ 1 ] x 4 1 4 6 . 9 7 ( 4 ) 1 4 6 . 7 1 ( 5 ) 1 4 7 . 2 2 ( 5 ) T e [ 1 ] - H o - T e [ 2 ] x 2 7 6 9 7 ( 4 ) 7 6 0 4 ( 4 ) 7 7 9 2 ( 4 ) T e [ 1 ] - H o - T e [ 2 ] x 4 1 3 1 . 2 8 ( 4 ) 1 2 9 . 8 2 ( 4 ) 1 3 2 . 7 6 ( 4 ) T e [ 1 ] - H o - T e [ 3 ] x 4 7 6 8 6 ( 4 ) 7 6 7 0 ( 4 ) 7 7 0 3 ( 4 ) T e [ 1 ] - H o - T e [ 3 ] x 4 1 3 1 . 2 1 ( 5 ) 1 3 1 . 0 3 ( 4 ) 1 3 1 . 3 8 ( 4 ) T e [ 1 ] - H o - T e [ 1 ] x 2 8 5 8 4 ( 4 ) 8 5 . 4 5 ( 4 ) 8 6 2 3 ( 4 ) T e [ 1 ] - H o - T e [ 2 ] x 2 7 6 5 7 ( 4 ) 7 5 . 7 4 ( 4 ) 7 7 3 9 ( 4 ) T e [ 2 ] - H o - T e [ 2 ] x 2 8 1 6 5 ( 4 ) 8 1 6 2 ( 4 ) 8 1 6 7 ( 3 ) T e [ 2 ] - H o - T e [ 3 ] x 4 5 5 1 4 ( 4 ) 5 3 8 1 ( 4 ) 5 6 5 1 ( 4 ) T e [ 3 ] - H o - T e [ 3 ] x 2 8 1 5 2 ( 4 ) 8 1 2 9 ( 5 ) 8 1 . 7 4 ( 5 ) H o - T e [ 1 ] - H o x 4 1 0 6 . 7 4 ( 4 ) 1 0 6 . 5 6 ( 4 ) 1 0 6 . 9 1 ( 4 ) H o - T e [ 1 ] - H o x 4 1 0 6 . 2 8 ( 4 ) 1 0 5 . 9 6 ( 4 ) 1 0 6 . 6 1 ( 4 ) H o - T e [ 1 ] - H o x 2 8 5 8 4 ( 4 ) 8 5 5 8 ( 5 ) 8 6 0 9 ( 5 ) H o - T e [ 1 ] - H o x 6 8 5 2 0 ( 3 ) 8 5 0 4 ( 4 ) 8 5 3 7 ( 4 ) H o - T e [ 1 ] - H o x 4 1 4 6 . 9 7 ( 4 ) l 4 6 8 1 ( 4 ) 1 4 7 . 1 3 ( 4 ) H o - T e [ 2 ] - H o x 2 8 1 6 4 ( 4 ) 8 1 5 9 ( 5 ) 8 1 6 7 ( 3 ) H o - T e [ 2 ] - T e [ 3 ] x 2 6 2 2 2 ( 3 ) 6 1 . 7 8 ( 3 ) 6 2 6 5 ( 3 ) H o - T e [ 2 ] - T e [ 3 ] x 2 1 1 7 . 3 2 ( 5 ) 1 1 5 . 5 6 ( 6 ) 1 1 9 . 0 7 ( 6 ) H o - T e [ 2 ] - T e [ 3 ] x 2 6 2 5 3 ( 3 ) 6 2 2 2 ( 3 ) 6 2 8 3 ( 3 ) H o - T e [ 2 ] - T e [ 3 ] x 2 1 1 7 . 7 7 ( 5 ) 1 1 6 . 1 1 ( 6 ) 1 1 9 . 4 1 ( 6 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 8 9 0 0 9 ( 6 ) 8 7 4 8 ( 6 ) 9 2 7 3 ( 7 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 8 . 3 5 ( 7 ) 1 7 7 . 2 7 ( 7 ) 1 8 0 H o - T e [ 3 ] - H o x 2 8 1 5 2 ( 3 ) 8 1 2 9 ( 5 ) 8 1 . 7 4 ( 5 ) H o - T e [ 3 ] - T e [ 2 ] x 4 6 2 5 5 ( 4 ) 6 1 5 9 ( 4 ) 6 3 5 5 ( 4 ) H o - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 5 6 ( 4 ) 1 1 6 . 9 3 ( 4 ) 1 1 8 . 1 7 ( 4 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 9 0 3 4 ( 7 ) 8 7 9 9 ( 7 ) 9 2 7 4 ( 7 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 8 9 7 9 ( 5 ) 8 9 6 2 ( 4 ) 8 9 9 7 ( 5 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 8 . 4 0 ( 7 ) 1 7 7 . 3 4 ( 7 ) 1 7 9 . 9 2 ( 4 ) 1 9 0 T a b l e 3 . 8 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r E r T e 3 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 3 1 . 7 8 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ’ ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ' ( 1 ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 “ o r d e r s a t e l l i t e s [ I > 2 0 ( 1 ) ] R 1 “ o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m i n a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e E r T e 3 5 5 0 . 1 1 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 c m ( 0 0 y ) 0 0 0 a = 4 . 2 6 4 1 ( 8 ) A , a = 9 0 ° b = 2 5 . 1 6 4 ( 6 ) A , B = 9 0 0 c = 4 . 2 7 9 1 ( 8 ) A , y = 9 0 ° 0 . 2 9 9 2 ( 4 ) c ‘ 4 5 9 . 1 5 0 7 ) A 3 4 7 . 9 5 5 g / c m 3 3 6 . 8 7 4 m m " 8 9 6 0 . 5 0 x 0 . 3 2 x 0 . 0 3 m m 3 3 . 2 3 t o 3 1 . 7 8 ° - 6 < = h < = 6 , - 3 6 < = k < = 3 6 , - 6 < = l < = 6 , - 1 < = m < = 1 7 6 3 6 ( 2 3 9 1 m a i n + 5 2 4 5 s a t e l l i t e s ) 2 3 4 2 ( 8 1 1 m a i n + 1 5 3 1 s a t e l l i t e s ) [ R i m = 0 . 0 4 0 2 ] 9 8 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 2 3 4 2 / 0 / 3 7 1 . 4 9 R o b , = 0 . 0 3 0 7 , w R . . . , = 0 . 1 0 1 8 R a n = 0 . 0 6 2 8 , W R a n = 0 . 1 1 0 1 R o b , = 0 . 0 2 5 5 , w R . . . , = 0 . 0 9 9 5 R , “ = 0 . 0 2 6 2 , w R , u = 0 . 1 0 0 1 R o b s = 0 . 0 9 5 7 , w R . . . , = 0 . 1 2 4 8 R , “ = 0 . 3 1 6 9 , w R . . . = 0 . 1 8 8 8 0 . 0 0 0 4 5 ( 5 ) 0 . 0 2 1 5 a n d 0 . 6 3 5 0 3 . 4 3 a n d - 3 7 4 e . A ' 3 R = Z I I F o l - c h l l / 2 3 | F o l . w R = { 2 [ W ( I F 0 1 2 - c h l z f l / X l W ( l F o l 4 ) ] } " 2 a n d W = 1 / ( O T ( I ) + 0 - 0 0 1 6 1 2 ) 1 9 1 T a b l e 3 . 8 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r E r T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . . L a b e l W a v e x y z U e q B r 0 9 0 0 0 1 7 0 0 ( 1 ) 2 5 4 9 4 ( 1 ) s i n , 1 0 0 - 1 7 ( 5 ) c o s , 1 4 0 ( 1 ) 6 ( 1 ) 0 T e [ 1 ] 0 8 9 7 0 ( 3 ) 2 9 4 4 ( 1 ) 2 5 4 9 4 ( 1 ) s i n , 1 0 0 7 ( 7 ) c o s , 1 5 ( 1 ) 1 ( 1 ) 0 T e [ 2 ] 0 9 0 2 5 ( 3 ) 7 1 7 ( 1 ) 7 5 4 9 5 ( 1 ) s i n , 1 0 0 1 5 ( 8 ) c o s , 1 - 1 3 6 ( 2 ) 1 ( 1 ) 0 T e [ 3 ] 0 9 0 3 1 ( 4 ) 4 2 8 3 ( 1 ) 7 5 4 9 5 ( 1 ) s i n , 1 0 0 - 3 ( 7 ) c o s , 1 1 1 9 ( 2 ) 1 ( 1 ) 0 ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 8 8 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r E r T e ; a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 E r 4 ( 1 ) 5 ( 1 ) 4 ( 1 ) - 1 0 ) 0 0 T e [ 1 ] 2 ( 1 ) 5 ( 1 ) 4 ( 1 ) 1 ( 1 ) 0 0 T e [ 2 ] 4 0 ) 7 ( 1 ) 5 ( 1 ) 0 ( 1 ) 0 0 T e [ 3 ] 4 ( 1 ) 6 ( 1 ) 5 ( 1 ) 3 ( 1 ) 0 0 T a b l e 3 . 8 9 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r E r T e ; a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e E r - T e [ 1 ] 3 . 1 2 9 3 ( 1 4 ) 3 . 1 1 7 ( 3 ) 3 . 1 4 2 ( 3 ) E r - T e [ 1 ] x 2 3 . 1 5 9 1 ( 1 8 ) 3 . 1 4 8 ( 2 ) 3 . 1 7 0 ( 2 ) E r - T e [ 1 ] x 2 3 . 1 4 1 5 ( 1 8 ) 3 . 1 2 7 0 ( 1 2 ) 3 . 1 5 6 3 ( 1 3 ) E r - T e [ 2 ] x 2 3 . 2 7 2 ( 2 ) 3 . 2 5 5 ( 2 ) 3 . 2 8 8 ( 2 ) E r - T e [ 3 ] 3 . 2 5 6 8 ( 1 6 ) 3 . 2 4 7 ( 2 ) 3 . 2 6 7 ( 2 ) E r - T e [ 3 ] 3 . 2 7 4 4 ( 1 6 ) 3 . 2 4 0 ( 2 ) 3 . 3 0 9 ( 2 ) T e [ 2 ] - T e [ 3 ] x 4 3 . 0 1 9 ( 3 ) 2 . 9 5 2 2 ( 1 8 ) 3 . 0 8 6 5 ( 1 9 ) 1 9 2 T a b l e 3 . 9 0 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r H R ; a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - E r - T e [ 1 ] x 6 7 3 3 8 ( 4 ) 7 3 1 8 ( 3 ) 7 3 5 7 ( 3 ) T e [ 1 ] - E r - T e [ 1 ] x 2 7 3 6 2 ( 4 ) 7 3 1 7 ( 3 ) 7 4 0 6 ( 3 ) T e [ 1 ] - E r - T e [ 2 ] x 2 1 3 9 . 1 5 ( 7 ) 1 3 8 . 8 2 ( 9 ) 1 3 9 . 4 7 ( 1 0 ) T e [ 1 ] - E r - T e [ 3 ] x 2 1 3 9 . 1 8 ( 4 ) 1 3 8 . 8 2 ( 4 ) 1 3 9 . 5 5 ( 4 ) T e [ 1 ] - E r - T e [ 1 ] x 6 8 5 2 6 ( 5 ) 8 5 . 1 2 ( 5 ) 8 5 4 0 ( 5 ) T e [ 1 ] - E r - T e [ 1 ] x 4 1 4 6 . 9 9 ( 4 ) 1 4 6 . 4 1 ( 5 ) l 4 7 . 5 6 ( 5 ) T e [ 1 ] - E r - T e [ 2 ] x 2 7 6 9 0 ( 5 ) 7 6 0 2 ( 5 ) 7 7 8 0 ( 5 ) T e [ 1 ] - E r - T e [ 2 ] x 4 1 3 1 . 2 5 ( 4 ) 1 2 9 . 8 3 ( 4 ) l 3 2 . 6 9 ( 4 ) T e [ 1 ] - E r - T e [ 3 ] x 4 7 6 9 1 ( 5 ) 7 6 8 3 ( 5 ) 7 6 9 9 ( 5 ) T e [ 1 ] - E r - T e [ 3 ] x 4 1 3 1 . 2 2 ( 7 ) 1 3 1 . 0 6 ( 8 ) 1 3 1 . 3 8 ( 8 ) T e [ 1 ] - E r - T e [ 1 ] x 2 8 5 8 5 ( 5 ) 8 5 2 7 ( 5 ) 8 6 4 3 ( 5 ) T e [ 1 ] - E r - T e [ 2 ] x 2 7 6 5 9 ( 5 ) 7 5 7 7 ( 6 ) 7 7 3 9 ( 6 ) T e [ 2 ] - E r - T e [ 2 ] x 2 8 1 6 9 ( 6 ) 8 1 5 0 ( 6 ) 8 1 8 5 ( 6 ) T e [ 2 ] - E r - T e [ 3 ] x 4 5 5 0 7 ( 6 ) 5 3 7 7 ( 5 ) 5 6 4 2 ( 5 ) T e [ 3 ] - E r - T e [ 3 ] x 2 8 1 5 2 ( 4 ) 8 1 . 1 5 ( 5 ) 8 1 8 9 ( 5 ) E r - T e [ 1 ] - E r x 4 1 0 6 . 7 2 ( 5 ) 1 0 6 . 4 0 ( 6 ) 1 0 7 . 0 4 ( 6 ) E r - T e [ 1 ] - E r x 4 1 0 6 . 2 9 ( 5 ) 1 0 5 . 7 2 ( 4 ) 1 0 6 . 8 6 ( 4 ) E r - T e [ 1 ] - E r x 2 8 5 8 5 ( 5 ) 8 5 7 1 ( 5 ) 8 5 9 8 ( 5 ) E r - T e [ 1 ] - E r x 6 8 5 1 8 ( 5 ) 8 4 9 5 ( 4 ) 8 5 4 2 ( 4 ) E r - T e [ 1 ] — E r x 4 1 4 6 . 9 9 ( 5 ) 1 4 6 . 6 4 ( 7 ) 1 4 7 . 3 4 ( 7 ) E r - T e [ 2 ] - E r x 2 8 1 6 8 ( 5 ) 8 1 3 5 ( 6 ) 8 1 9 8 ( 6 ) E r - T e [ 2 ] - T e [ 3 ] x 2 6 2 2 0 ( 4 ) 6 1 . 7 1 ( 4 ) 6 2 6 9 ( 4 ) E r - T e [ 2 ] - T e [ 3 ] x 4 1 1 7 . 4 4 ( 5 ) 1 1 5 . 9 3 ( 7 ) 1 1 8 . 9 4 ( 7 ) E r - T e [ 2 ] - T e [ 3 ] x 2 6 2 5 3 ( 4 ) 6 2 3 3 ( 4 ) 6 2 7 3 ( 4 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 9 0 3 1 ( 7 ) 8 7 9 9 ( 7 ) 9 2 6 6 ( 7 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 8 9 7 7 ( 7 ) 8 9 5 9 ( 1 0 ) 9 O T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 8 . 4 9 ( 9 ) 1 7 7 . 5 5 ( 7 ) 1 8 0 E r - T e [ 3 ] - E r x 2 8 1 5 2 ( 3 ) 8 1 . 1 5 ( 5 ) 8 1 8 9 ( 5 ) E r - T e [ 3 ] - T e [ 2 ] x 4 6 2 4 6 ( 5 ) 6 1 . 5 9 ( 4 ) 6 3 3 6 ( 4 ) E r - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 5 4 ( 6 ) 1 1 6 . 8 9 ( 5 ) 1 1 8 . 1 7 ( 5 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 8 9 0 1 5 ( 8 ) 8 8 0 3 ( 8 ) 9 2 3 2 ( 8 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 8 . 5 5 ( 9 ) 1 7 7 . 6 4 ( 8 ) 1 8 0 1 9 3 T a b l e 3 . 9 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r T m T e 3 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 2 8 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( 1 ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 “ o r d e r s a t e l l i t e s [ I > 2 c ( I ) ] R 1 “ o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m i n a n d T m c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e T m T e 3 5 5 1 . 7 1 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c C 2 c m ( 0 0 y ) 0 0 0 a = 4 . 2 6 1 7 ( 6 ) A , 0 1 = 9 0 0 b = 2 5 . 0 9 2 0 ) A , 1 3 = 9 0 ° c = 4 . 2 7 1 4 ( 8 ) A , y = 9 0 ° 0 . 3 0 2 6 ( 4 ) o ‘ 4 5 6 . 7 6 0 3 ) A 3 4 8 . 0 2 1 g / e m 3 3 8 . 0 8 1 m m ' 1 9 0 0 0 . 4 3 x 0 . 4 0 x 0 . 0 4 m m 3 2 . 1 7 t o 2 9 . 2 8 ° - 5 < = h < = 5 , - 3 4 < = k < = 3 4 , - 6 < = 1 < = 6 , - 1 < = m < = 1 7 7 2 4 ( 2 4 7 8 m a i n + 5 2 4 6 s a t e l l i t e s ) 1 8 3 7 ( 6 4 3 m a i n + 1 1 9 4 s a t e l l i t e S ) [ R i o t = 0 . 0 7 8 6 ] 9 9 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 1 8 3 7 / 0 / 3 8 2 . 3 5 R o b , = 0 . 0 4 5 5 , w R . . . , = 0 . 1 3 1 3 R . “ = 0 . 0 6 8 1 , w R . . . = 0 . 1 7 1 2 R o b s = 0 . 0 4 3 3 , w R . . . , = 0 . 1 3 1 4 R . , l l = 0 . 0 4 4 8 , w R . . . = 0 . 1 7 0 4 R o b , = 0 . 0 9 0 3 , w R . . . , s = 0 . 1 2 8 0 R a l l = 0 . 3 0 3 6 , w R , l l = 0 . 1 8 5 9 0 . 0 0 0 3 9 ( 5 ) 0 . 0 0 4 5 a n d 0 . 1 6 4 3 4 . 2 4 a n d 5 0 4 6 A 3 R = l e F o l - c h l l / Z I F o l . w R = { 2 0 1 / ( l e - c h | 2 ) 2 ] / 2 [ W ( I F 0 | 4 ) ] } " r a n d W = 1 / ( 0 2 ( 1 ) + 0 - 0 0 1 6 1 7 ) 1 9 4 T a b l e 3 . 9 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r T m T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e x y z U , q T m 0 9 0 0 0 1 7 0 3 ( 1 ) 2 5 4 9 7 ( 1 ) s i n , 1 0 0 2 2 ( 6 ) c o s , 1 3 5 ( 2 ) 6 ( 1 ) 0 T e [ 1 ] 0 9 0 8 5 ( 6 ) 2 9 4 2 ( 1 ) 2 5 4 9 6 ( 1 ) s i n , 1 0 0 - 2 ( 8 ) c o s , 1 2 ( 3 ) 2 ( 2 ) 0 T e [ 2 ] 0 9 0 1 9 ( 6 ) 7 1 7 ( 1 ) 7 5 4 9 8 ( 1 ) s i n , 1 0 0 5 ( 9 ) c o s , 1 - 1 2 0 ( 5 ) 1 ( 2 ) 0 T e [ 3 ] 0 8 9 8 2 ( 9 ) 4 2 8 2 ( 1 ) 7 5 4 9 8 ( 1 ) s i n , 1 0 0 5 ( 9 ) c o s , 1 1 1 1 ( 5 ) 0 ( 2 ) 0 “ U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 9 3 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r T m T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 T m 6 ( 1 ) 1 1 ( 1 ) 6 ( 1 ) - 2 0 ) 0 0 T e [ 1 ] 4 ( 1 ) 1 0 ( 1 ) 5 ( 1 ) 0 ( 1 ) 0 0 T e [ 2 ] 5 ( 1 ) 1 3 ( 1 ) 5 ( 1 ) - 2 0 ) 0 0 T e [ 3 ] 6 ( 1 ) 1 3 ( 1 ) 6 ( 1 ) - 4 0 ) 0 0 T a b l e 3 . 9 4 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r T m T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e T m - T e [ 1 ] 3 . 1 0 7 ( 3 ) 3 . 0 9 6 ( 5 ) 3 . 1 1 9 ( 5 ) T m - T e [ 1 ] x 2 3 . 1 2 1 ( 3 ) 3 . 1 1 4 ( 2 ) 3 . 1 2 8 ( 2 ) T m - T e [ 1 ] x 2 3 . 1 7 1 ( 3 ) 3 . 1 5 4 ( 3 ) 3 . 1 8 7 ( 3 ) T m - T e [ 2 ] x 2 3 . 2 6 9 ( 3 ) 3 . 2 5 8 ( 3 ) 3 . 2 8 1 ( 3 ) T m - T e [ 3 ] 3 . 2 6 8 ( 3 ) 3 . 2 5 9 ( 5 ) 3 . 2 7 8 ( 5 ) T m - T e [ 3 ] 3 . 2 5 9 ( 3 ) 3 . 2 2 6 ( 5 ) 3 . 2 9 1 ( 5 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 2 8 ( 4 ) 2 . 9 6 8 ( 4 ) 3 . 0 8 9 ( 4 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 0 7 ( 4 ) 2 . 9 4 4 ( 4 ) 3 . 0 6 9 ( 4 ) 1 9 5 T a b l e 3 . 9 5 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r T m T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - T m - T e [ 1 ] x 4 7 3 8 8 ( 6 ) 7 3 7 0 ( 6 ) 7 4 0 6 ( 6 ) T e [ 1 ] - T m - T e [ 1 ] x 4 7 3 2 0 ( 6 ) 7 2 7 7 ( 6 ) 7 3 6 3 ( 6 ) T e [ 1 ] - T m - T e [ 2 ] x 2 1 3 9 . 1 9 ( 8 ) 1 3 8 . 8 5 ( 9 ) 1 3 9 . 5 5 ( 9 ) T e [ 1 ] - T m - T e [ 3 ] x 2 1 3 9 . 8 0 ( 7 ) 1 3 9 . 4 5 ( 8 ) 1 4 0 . 1 5 ( 8 ) T e [ 1 ] - T m - T e [ 1 ] x 4 8 5 2 7 ( 8 ) 8 4 9 9 ( 8 ) 8 5 5 4 ( 8 ) T e [ 1 ] - T m - T e [ 1 ] x 4 l 4 7 . 0 7 ( 7 ) 1 4 6 . 4 6 ( 9 ) 1 4 7 . 6 7 ( 9 ) T e [ 1 ] - T m - T e [ 2 ] x 4 7 6 7 4 ( 7 ) 7 5 7 6 ( 8 ) 7 7 . 7 5 ( 8 ) T e [ 1 ] - T m - T e [ 2 ] x 2 1 3 1 . 6 7 ( 7 ) 1 3 0 . 3 7 ( 7 ) l 3 2 9 8 ( 7 ) T e [ 1 ] - T m - T e [ 3 ] x 2 7 7 . 1 1 ( 8 ) 7 7 0 0 ( 7 ) 7 7 2 1 ( 7 ) T e [ 1 ] - T m - T e [ 3 ] x 4 1 3 0 . 8 3 ( 9 ) l 3 0 . 5 6 ( 1 0 ) 1 3 l . 1 2 ( 1 0 ) T e [ 1 ] - T m - T e [ 1 ] x 2 8 4 7 0 ( 7 ) 8 4 2 3 ( 7 ) 8 5 1 6 ( 7 ) T e [ 1 ] - T m - T e [ 2 ] x 2 1 3 0 . 6 3 ( 7 ) 1 2 9 . 7 2 ( 6 ) 1 3 1 . 5 4 ( 6 ) T e [ 1 ] - T m - T e [ 3 ] x 2 7 6 5 7 ( 8 ) 7 6 2 4 ( 8 ) 7 6 9 1 ( 8 ) T e [ 2 ] - T m - T e [ 2 ] x 2 8 1 5 9 ( 7 ) 8 1 3 3 ( 8 ) 8 1 8 3 ( 8 ) T e [ 3 ] - T m - T e [ 3 ] x 2 8 1 5 3 ( 9 ) 8 1 . 1 8 ( 1 0 ) 8 1 8 9 ( 1 0 ) T m - T e [ 1 ] - T m x 4 1 0 5 . 8 5 ( 7 ) 1 0 5 . 8 2 ( 8 ) 1 0 5 . 8 8 ( 8 ) T m - T e [ 1 ] - T m x 4 1 0 7 . 0 6 ( 7 ) 1 0 6 . 6 0 ( 8 ) 1 0 7 . 5 3 ( 8 ) T m - T e [ 1 ] - T m x 2 8 4 7 0 ( 7 ) 8 4 1 9 ( 8 ) 8 5 1 9 ( 8 ) T m - T e [ 1 ] - T m x 4 8 5 2 7 ( 6 ) 8 4 9 9 ( 8 ) 8 5 5 4 ( 8 ) T m - T e [ 1 ] - T m x 4 l 4 7 . 0 7 ( 8 ) 1 4 6 . 5 6 ( 1 3 ) 1 4 7 . 5 7 ( 1 3 ) T m - T e [ 1 ] - T m x 2 8 6 3 5 ( 8 ) 8 6 2 0 ( 8 ) 8 6 5 0 ( 8 ) T m - T e [ 2 ] - T m x 2 8 1 5 8 ( 7 ) 8 1 . 4 9 ( 1 0 ) 8 1 6 5 ( 1 0 ) T m - T e [ 2 ] - T e [ 3 ] x 4 6 2 3 8 ( 6 ) 6 2 0 6 ( 6 ) 6 2 6 8 ( 6 ) T m - T e [ 2 ] - T e [ 3 ] x 4 1 1 7 . 2 7 ( 9 ) 1 1 5 . 7 8 ( 1 2 ) 1 1 8 7 5 ( 1 2 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 6 8 9 . 7 4 ( 1 2 ) 8 7 6 1 ( 1 2 ) 9 1 8 9 ( 1 3 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 8 6 3 ( 1 3 ) 1 7 7 . 4 6 ( 1 3 ) 1 7 9 . 8 9 ( 6 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 9 0 5 7 ( 1 2 ) 8 8 5 1 ( 1 3 ) 9 2 6 7 ( 1 3 ) T m - T e [ 3 ] - T m x 2 8 1 5 4 ( 5 ) 8 1 . 1 8 ( 9 ) 8 1 8 9 ( 1 0 ) T m - T e [ 3 ] - T e [ 2 ] x 4 6 2 7 7 ( 8 ) 6 2 0 2 ( 8 ) 6 3 5 3 ( 8 ) T m - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 5 6 ( 8 ) 1 1 7 . 0 7 ( 8 ) 1 1 8 . 0 3 ( 8 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 9 0 5 7 ( 1 3 ) 8 8 5 6 ( 1 4 ) 9 2 6 2 ( 1 4 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 6 8 9 8 4 ( 1 0 ) 8 9 7 8 ( 8 ) 8 9 8 8 ( 9 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 8 . 6 6 ( 1 4 ) 1 7 7 5 0 ( 1 4 ) 1 7 9 . 8 8 ( 7 ) 1 9 6 T a b l e 3 . 9 6 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r Y T e 3 a t 1 0 0 K . E m p i r i c a l f o r m u l a “ F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 2 5 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ’ ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 “ o r d e r s a t e l l i t e s [ I > 2 0 ’ ( I ) ] R 1 “ o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e Y T C 3 4 7 1 . 7 1 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A O r t h o r h o m b i c c z o m ( o o y ) 0 0 0 a = 4 . 2 8 4 0 ( 7 ) A , 0 1 = 9 0 ° b = 2 5 . 3 1 2 0 ) A , 1 3 = 9 0 ° c = 4 . 2 9 3 2 ( 9 ) A , y = 9 0 ° 0 . 2 9 0 7 ( 5 ) o ‘ 4 6 5 . 5 4 0 5 ) A 3 4 6 . 7 2 8 g / o m 3 3 1 . 0 4 1 m m “ 7 8 0 0 . 2 9 x 0 . 2 7 x 0 . 0 2 m m 3 1 . 6 1 t o 2 9 . 2 5 ° - 5 < = h < = 5 , - 3 4 < = k < = 3 4 , - 6 < = 1 < = 6 , - l < = m < = 1 6 5 5 6 ( 2 1 3 8 m a i n + 4 4 1 8 s a t e l l i t e s ) 1 9 3 7 ( 6 8 2 m a i n + 1 2 5 5 s a t e l l i t e s ) [ R i m = 0 . 0 5 5 8 ] 9 8 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 1 9 3 7 / 0 / 3 9 1 . 5 3 R o b s = 0 . 0 3 6 5 , w R o b s = 0 . 0 9 7 6 R , " = 0 . 0 5 4 5 , w R . “ = 0 . 1 0 2 0 R o b s = 0 . 0 3 2 1 , w R o b , = 0 . 0 8 6 0 R , “ = 0 . 0 3 2 6 , w R . , , l = 0 . 0 8 6 2 R o b , = 0 . 0 7 0 4 , w R . . . , = 0 . 1 3 0 3 R . , “ = 0 . 1 8 6 8 , w R a u = 0 . 1 4 4 1 0 . 0 0 0 6 0 ( 8 ) 0 . 0 4 1 0 a n d 0 . 7 0 9 2 1 . 9 3 a n d - 2 2 7 e . A ' 3 R = Z I I F o l - c h l l / Z l F o l , w R = { 2 [ W ( | F o l 2 - c h I T ) 2 ] / Z [ W ( | F o l 4 ) ] } m a n d W = 1 / ( 6 2 ( 1 ) + 0 - 0 0 1 6 1 2 ) 1 9 7 T a b l e 3 . 9 7 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r Y T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . # L a b e l W a v e x y z q u Y 0 9 0 4 3 ( 4 ) 1 7 0 0 ( 1 ) 2 5 4 9 1 0 ( 1 ) s i n , 1 0 0 5 ( 7 ) c o s , 1 - 4 9 ( 1 ) 0 ( 1 ) 0 T e [ 1 ] 0 9 0 0 0 2 9 4 6 ( 1 ) 2 5 4 9 9 ( 1 ) s i n , 1 O 0 5 ( 5 ) c o s , 1 - 7 ( 1 ) - 1 ( 1 ) 0 T e [ 2 ] 0 8 9 9 3 ( 3 ) 7 1 2 ( 1 ) 7 5 4 9 1 0 ( 1 ) s i n , 1 0 0 - 1 5 ( 6 ) c o s , 1 1 8 1 ( 2 ) 0 ( 1 ) 0 T e [ 3 ] 0 3 9 8 5 ( 3 ) 7 1 4 ( 1 ) 2 5 4 9 1 0 ( 1 ) s i n , 1 0 0 - 7 ( 6 ) c o s , 1 - 1 6 5 ( 2 ) 6 ( 1 ) 0 “ U . . . q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 3 . 9 8 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r Y T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 Y 0 7 ( 1 ) 1 5 ( 1 ) 8 ( 1 ) 5 ( 1 ) 0 0 T e [ 1 ] 0 7 ( 1 ) 1 4 ( 1 ) 7 ( 1 ) - 2 0 ) 0 0 T e [ 2 ] 0 9 ( 1 ) 1 4 ( 1 ) 6 ( 1 ) - 1 0 ) 0 0 T e [ 3 ] 0 9 ( 1 ) 1 5 ( 1 ) 7 ( 1 ) 1 ( 1 ) 0 0 T a b l e 3 . 9 9 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r Y T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e Y - T e [ 1 ] 3 . 1 5 5 5 ( 1 7 ) 3 . 1 5 2 ( 3 ) 3 . 1 5 9 ( 3 ) Y - T e [ 1 ] x 2 3 . 1 7 4 ( 2 ) 3 . 1 6 2 6 ( 1 8 ) 3 . 1 8 6 7 ( 1 8 ) Y - T e [ 1 ] x 2 3 . 1 5 0 ( 2 ) 3 . 1 3 5 2 ( 1 7 ) 3 . 1 6 4 1 ( 1 7 ) Y - T e [ 2 ] x 2 3 . 2 9 6 ( 2 ) 3 . 2 9 0 ( 2 ) 3 . 2 9 9 ( 2 ) Y - T e [ 3 ] 3 . 3 0 6 ( 2 ) 3 . 2 8 4 ( 3 ) 3 . 3 2 7 ( 3 ) Y - T e [ 3 ] 3 . 2 7 2 ( 2 ) 3 . 2 3 0 ( 3 ) 3 . 3 1 6 ( 3 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 3 6 ( 2 ) 2 . 9 4 5 3 ( 1 5 ) 3 . 1 2 7 6 ( 1 5 ) T e [ 2 ] - T e [ 3 ] x 2 3 . 0 3 0 ( 2 ) 2 . 9 3 4 9 ( 1 5 ) 3 . 1 2 8 2 ( 1 5 ) 1 9 8 T a b l e 3 . 1 0 0 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r Y T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - Y - T e [ 1 ] x 4 7 3 3 7 ( 4 ) 7 3 2 0 ( 5 ) 7 3 5 3 ( 5 ) T e [ 1 ] - Y - T e [ 1 ] x 4 7 3 7 1 ( 4 ) 7 3 5 4 ( 5 ) 7 3 8 7 ( 5 ) T e [ 1 ] - Y - T e [ 2 ] x 2 1 3 9 . 3 2 ( 7 ) 1 3 9 . 2 1 ( 4 ) 1 3 9 . 4 5 ( 6 ) T e [ 1 ] - Y - T e [ 3 ] 1 3 8 . 7 0 ( 6 ) 1 3 8 . 2 3 ( 7 ) 1 3 9 . 1 8 ( 7 ) T e [ 1 ] - Y - T e [ 3 ] 1 4 0 . 0 3 ( 6 ) 1 3 9 . 8 6 ( 7 ) 1 4 0 . 2 0 ( 7 ) T e [ 1 ] - Y - T e [ 1 ] x 6 8 5 1 0 ( 5 ) 8 4 6 1 ( 6 ) 8 5 5 7 ( 6 ) T e [ 1 ] - Y - T e [ 1 ] x 4 1 4 7 . 0 8 ( 6 ) 1 4 7 . 0 6 ( 4 ) 1 4 7 . 1 0 ( 3 ) T e [ 1 ] - Y - T e [ 2 ] x 2 7 6 6 6 ( 5 ) 7 5 5 6 ( 5 ) 7 7 . 7 4 ( 5 ) T e [ 1 ] - Y - T e [ 2 ] x 2 1 3 0 . 5 6 ( 6 ) 1 2 8 . 9 4 ( 6 ) 1 3 2 . 1 6 ( 6 ) T e [ 1 ] - Y - T e [ 3 ] x 2 7 6 5 2 ( 5 ) 7 6 1 4 ( 5 ) 7 6 9 2 ( 5 ) T e [ 1 ] - Y - T e [ 3 ] x 4 1 3 0 . 9 5 ( 7 ) 1 3 0 . 6 2 ( 7 ) 1 3 1 . 2 8 ( 6 ) T e [ 1 ] - Y - T e [ 1 ] x 2 8 5 9 3 ( 5 ) 8 5 5 3 ( 6 ) 8 6 3 3 ( 6 ) T e [ 1 ] - Y - T e [ 2 ] x 2 7 7 0 6 ( 5 ) 7 6 0 0 ( 5 ) 7 8 1 4 ( 5 ) T e [ 1 ] - Y - T e [ 2 ] x 2 1 3 l . 6 1 ( 6 ) 1 3 0 . 0 0 ( 6 ) 1 3 3 . 2 4 ( 6 ) T e [ 1 ] - Y - T e [ 3 ] x 2 7 7 3 4 ( 6 ) 7 7 . 1 5 ( 5 ) 7 7 5 3 ( 5 ) T e [ 2 ] - Y - T e [ 2 ] x 2 8 1 3 1 ( 5 ) 8 1 . 1 5 ( 7 ) 8 1 . 4 2 ( 7 ) T e [ 3 ] - Y - T e [ 3 ] x 2 8 1 2 7 ( 4 ) 8 0 9 5 ( 7 ) 8 1 5 7 ( 7 ) Y - T e [ 1 ] - Y x 4 1 0 6 . 7 6 ( 5 ) 1 0 6 . 5 1 ( 4 ) 1 0 7 . 0 1 ( 4 ) Y - T e [ 1 ] - Y x 4 1 0 6 . 1 6 ( 4 ) 1 0 5 . 8 6 ( 4 ) 1 0 6 . 4 5 ( 4 ) Y - T e [ 1 ] - Y x 2 8 5 9 3 ( 6 ) 8 5 7 3 ( 6 ) 8 6 1 3 ( 6 ) Y - T e [ 1 ] - Y x 6 8 5 2 8 ( 6 ) 8 5 2 3 ( 5 ) 8 5 3 3 ( 5 ) Y - T e [ 1 ] - Y x 4 1 4 7 . 0 8 ( 5 ) 1 4 6 . 9 5 ( 3 ) 1 4 7 . 2 1 ( 3 ) Y - T e [ 2 ] - Y x 2 8 1 2 9 ( 5 ) 8 1 2 0 ( 6 ) 8 1 3 4 ( 5 ) Y - T e [ 2 ] - T e [ 3 ] x 2 1 1 7 . 6 7 ( 5 ) 1 1 5 . 4 3 ( 6 ) 1 1 9 . 9 0 ( 6 ) Y - T e [ 2 ] - T e [ 3 ] x 2 1 1 7 . 1 2 ( 5 ) 1 1 5 . 1 5 ( 6 ) 1 1 9 . 0 6 ( 6 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 8 9 0 0 8 ( 6 ) 8 6 8 4 ( 6 ) 9 3 4 1 ( 6 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 4 1 7 7 9 3 ( 7 ) 1 7 6 . 6 5 ( 6 ) 1 7 9 . 8 6 ( 4 ) Y - T e [ 3 ] - Y x 2 8 1 2 7 ( 4 ) 8 0 9 5 ( 6 ) 8 1 5 7 ( 6 ) Y - T e [ 3 ] - T e [ 2 ] x 4 1 1 7 . 2 5 ( 5 ) 1 1 6 . 3 1 ( 4 ) 1 1 8 1 3 ( 4 ) Y - T e [ 3 ] - T e [ 2 ] x 2 6 2 4 5 ( 4 ) 6 1 3 0 ( 4 ) 6 3 6 4 ( 4 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 9 0 2 9 ( 6 ) 8 7 2 7 ( 6 ) 9 3 3 2 ( 6 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 8 9 8 2 ( 6 ) 8 9 6 5 ( 4 ) 8 9 9 8 ( 6 ) T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 4 1 7 7 . 9 4 ( 7 ) 1 7 6 . 6 8 ( 6 ) 1 7 9 . 8 6 ( 6 ) 1 9 9 R e f e r e n c e s 1 H a y d e n , S . M . ; M o o k , H . A . ; D a l , P . ; P e n i n g , T . G . ; D o g a n , F . N a t u r e 2 0 0 4 , 4 2 9 , 5 3 1 . 2 G r fi n e r , G . D e n s i t y W a v e s i n S o l i d s , A d d i s o n - W e s l e y , R e a d i n g , M A , 1 9 9 4 . 3 M i l w a r d , G . C . ; G a l d e r o ' n , M . J . ; L i t t l e w o o d , P . B . N a t u r e 2 0 0 5 , 4 3 3 , 6 0 7 . 4 R u , N . ; F i s h e r , 1 . R . P h y s . R e v . B 2 0 0 6 , 7 3 , 0 3 3 1 0 1 a n d r e f e r e n c e s t h e r e i n 5 D i M a s i , E . ; A r o n s o n , M . C . ; M a n s fi e l d , J . F . ; F o r a n , B . a n d L e e S . P h y s . R e v . 1 9 9 5 , 8 5 2 , 1 4 5 1 6 . 6 K o m o d a , H . ; S a t o , T . ; S o u m a , S . ; T a k a h a s h i , T . ; I t o , Y . ; S u z u k i , K . P h y s . R e v . B 2 0 0 4 , 7 0 , 1 9 5 1 0 1 a n d r e f e r e n c e s t h e r e i n . 7 C u m m i n s , H . Z . P h y s . R e p . 1 9 9 0 , I 8 5 , 2 1 1 a n d r e f e r e n c e s t h e r e i n . 8 M o n c t o n , D . E . ; A x e , J . D . ; D i S a l v o , F . J . P h y s . R e v . L e t t . 1 9 7 5 , 3 4 , 7 3 4 . 9 D i C a r l o , D . ; T h o r n e , R . E . , S w e e t l a n d , E . ; S u t t o n , M ; B r o c k , J . D . P h y s . R e v . B 1 9 9 4 , 5 0 , 8 2 8 8 . 1 0 W i l s o n , J . A . ; D i S a l v o , F . J . ; M a h a j a n , S . A d v . P h y s . 1 9 7 5 , 2 4 , 1 1 7 . 1 1 M c M i l l a n , W . L . P h y s . R e v . B 1 9 7 5 , 1 2 , 1 1 8 7 a n d r e f e r e n c e s t h e r e i n . 1 2 M a l l i a k a s , C ; B i l l i n g e , S . J . L . ; K i m , H . J . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 5 , 1 2 7 , 6 5 1 0 a n d r e f e r e n c e s t h e r e i n . 1 3 F o k w a , B . P . T . ; D o e r t , T . S o l i d S t a t e S c i . 2 0 0 5 , 7 , 5 7 3 . 1 4 X - A R E A , I P D S S o f t w a r e , S T O E & C i e G m b H , D a r m s t a d t , 2 0 0 6 . 1 5 P e t r i c e k , V . ; D u s e k , M . I n s t i t u t e o f P h y s i c s , P r a h a , C z e c h R e p u b l i c , 2 0 0 0 . 1 6 S h e l d r i c k , G . M . S H E L fl - 9 7 : P r o g r a m f o r C r y s t a l S t r u c t u r e R e fi n e m e n t ; U n i v e r s i t y o f G fi t t i n g e n , t h t i n g e n , G e r m a n y , 1 9 9 7 . 1 7 J u n g , M . H . ; A l s m a d i , A . ; K i m , H . C . ; B a n g , Y . ; A h n , K . H . ; U m e o , K . ; L a c e r d a , A . H . ; N a k o t t e , H . ; R i , H . C . ; T a k a b a t a k e , T . P h y s . R e v . B , 2 0 0 3 , 6 7 , 2 1 2 5 0 4 . 2 0 0 1 8 D i M a s i , E . ; F o r a n , B . ; A r o n s o n , M C . a n d L e e S . C h e m . M a t e r . 1 9 9 4 , 1 8 6 7 . 1 9 K i m , H . J . ; M a l l i a k a s , C . D . ; T o m i c , A . ; T e s s m e r , S . H . ; K a n a t z i d i s M . G . ; B i l l i n g e , S . J . L . P h y s . R e v . L e t t . 2 0 0 6 , 9 6 , 2 2 6 4 0 1 . 2 0 M a l l i a k a s , C . D . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 6 , 1 2 8 , 1 2 6 1 2 2 0 1 C h a p t e r 4 E f f e c t o f t h e T h r e e D i m e n s i o n a l C h a r a c t e r o n t h e C h a r g e D e n s i t y W a v e s o f t h e S q u a r e N e t s o f T e l l u r i u m o f A M R E T e 4 ( A = K , N a ; M = C u , A g ; R E = L a , C e ) “ C h a r g e D e n s i t y W a v e s i n t h e S q u a r e N e t s o f T e l l u r i u m o f A M R E T e 4 ( A = K , N a ; M = C u , A g ; R E = L a , C e ) ” , M a l l i a k a s , C . D . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 7 , 1 2 9 , 1 0 6 7 5 - 1 0 6 7 7 . A m e r i c a n C h e m i c a l S o c i e t y ( A C S ) i s g r a t e f u l l y a c k n o w l e d g e d f o r t h e p e r m i s s i o n t o i n c l u d e t h i s r e p r i n t i n t h e T h e s i s . 2 0 2 4 . 1 . I n t r o d u c t i o n C h a r g e d e n s i t y w a v e s ( C D W s ) a r e c o o p e r a t i v e s t a t e s t h a t a r i s e f r o m t h e c o u p l i n g o f p h o n o n s a n d f r e e e l e c t r o n s i n q u a s i - o n e - a n d t w o - d i m e n s i o n a l m e t a l s . T h e m o d u l a t i o n o f t h e e l e c t r o n d e n s i t y d u e t o t h i s c o u p l i n g c r e a t e s a n e w b r o k e n s y m m e t r y g r o u n d s t a t e w i t h a l o w e r t o t a l fi ' e e e n e r g y t h r o u g h a P e i e r l s d i s t o r t i o n . C D W f o r m a t i o n i s b e l i e v e d t o b e d r i v e n b y F e r m i s u r f a c e i n s t a b i l i t i e s m a i n l y c a u s e d b y n e s t i n g e f f e c t s i n t h e e l e c t r o n i c b a n d s t r u c t u r e . S o m e t i m e s i n s t a b i l i t i e s o n t h e F e r m i s u r f a c e f a v o r a n o t h e r c o o p e r a t i v e s t a t e , i . e . s u p e r c o n d u c t i v i t y . ‘ U n d e r s t a n d i n g t h e m e c h a n i s m o f C D W d e s t a b i l i z a t i o n a n d t h e c o m p e t i t i o n b e t w e e n C D W s t a t e s a n d s u p e r c o n d u c t i v i t y i s o f fi m d a m e n t a l i m p o r t a n c e . S e v e r a l c h e m i c a l t u n i n g p a r a m e t e r s c a n b e e m p l o y e d t o m a n i p u l a t e t h e C D W s t a t e . F o r e x a m p l e , i t i s o f s i g n i fi c a n t i n t e r e s t t o b e a b l e t o s u p p r e s s a C D W a n d a c c e s s a s u p e r c o n d u c t i n g s t a t e . T h e o r e t i c a l l y , t h e C D W m o d u l a t i o n i s a f u n c t i o n o f t h e F e r m i l e v e l a n d t h e n e s t i n g p r o p e r t i e s o f t h e F e r m i s u r f a c e . 2 D o p i n g ( T a a n d T i d o p e d N b S e 3 ) 3 , i n t e r c a l a t i o n o f a t o m s ( I a n b 3 S e 4 ) 4 a n d a m i n e m o l e c u l e s ( l T - T a S 2 ' E D A o 2 5 ) 5 h a v e b e e n w i d e l y u s e d . T h i s t y p e o f t u n i n g i n v o l v e s e l e c t r o n t r a n s f e r a n d a l t e r s t h e e l e c t r o n c o u n t o n t h e C D W w h i c h c h a n g e s t h e m o d u l a t i o n b e c a u s e i t c h a n g e s t h e e n e r g y o f t h e F e r m i l e v e l . T h i s d o e s n o t a l l o w t h e s t u d y o f t h e C D W s t a t e i n a s i t u a t i o n w h e r e s t r u c t u r a l c h a n g e s a r e d e c o u p l e d f r o m c h a n g e s i n e l e c t r o n c o u n t . T o o b s e r v e s u c h a d e c o u p l i n g , i s o e l e c t r o n i c t u n i n g i s n e e d e d t o c h a n g e t h e c h a r a c t e r o f F e r m i s u r f a c e n e s t i n g b u t n o t t h e e l e c t r o n c o u n t o f t h e C D W . T h e f a m i l y o f A M R E T e 4 ( A = K , N a ; M = C u , A g ; R E = L a , C e ) c o m p o u n d s 6 m a y r e p r e s e n t s u c h a c a s e . 2 0 3 T h e s t r u c t u r e o f A M R E T e a c a n b e s e e n a s a n i n t e r g r o w t h o f e l e c t r o n i c a l l y n e u t r a l R E T e 3 7 a n d A C u T e 8 s l a b s i n 1 : 1 r a t i o . T h e l a y e r e d s t r u c t u r e o f R E T e 3 i s e s s e n t i a l l y i n t e r c a l a t e d w i t h s l a b s o f A C u T e . B e c a u s e o f t h i s t h e R E T e ; l a y e r s i n A M R E T e a a r e s i g n i fi c a n t l y s e p a r a t e d c o m p a r e d t o t h o s e i n R E T e 3 , a s s h o w n i n F i g u r e 4 . 1 . A s t h e R E T e 3 p h a s e s h a v e C D W s , 9 A M R E T e 4 t o o h a v e C D W s . B e c a u s e t h e a l t e r n a t i n g l a y e r s a r e n e u t r a l , n o e l e c t r o n t r a n s f e r b e t w e e n t h e m i s n e c e s s a r y a n d t h e A C u T e l a y e r d o e s n o t a l t e r t h e e l e c t r o n c o u n t i n t h e a d j a c e n t l a y e r s o f R E T e 3 . T h e i n s e r t i o n o f t h e A C u T e l a y e r d o e s h o w e v e r d i s r u p t t h e v a n d e r W a a l s i n t e r a c t i o n s t h a t a r e p r e s e n t i n t h e s t r u c t u r e o f t h e b i n a r i e s R E T C 3 . H e r e w e r e p o r t t h e d e t a i l s o f t h e C D W i n A M R E T e a a n d c o m p a r e t h e m t o t h o s e o f t h e p a r e n t R E T e 3 c o m p o u n d s . W e fi n d t h a t t h e C D W i n A M R E T e a , w h i c h o r i g i n a t e s fi ' o m a d i s t o r t i o n o f t h e T e n e t s i n t h e R E T e 3 s l a b i n t h e s e c o m p o u n d s , i s s t i l l p r e s e n t b u t , s u r p r i s i n g l y , t h e m o d u l a t i o n q - v e c t o r s a r e s i g n i fi c a n t l y d i f f e r e n t f r o m t h e o n e s f o u n d i n t h e R E T e 3 s e r i e s . 1 0 T h e q - v e c t o r c h a n g e s f r o m ~ 2 / 7 i n t h e b i n a r y p h a s e s t o ~ 1 / 3 i n t h e q u a t e r n a r y m o d i f y i n g t h e c h a r a c t e r o f t h e C D W . I f t h e C D W q - v e c t o r w e r e s t r i c t l y g o v e r n e d b y t h e e l e c t r o n i c s t r u c t u r e o f t h e R E T e 3 i t s e l f n o s i g n i fi c a n t c h a n g e s w o u l d b e e x p e c t e d b y s e p a r a t i n g t h e R E T e 3 s l a b s . T h e i n s e r t i o n o f t h e A C u T e l a y e r s i n t o t h e v a n d e r W a a l s g a p s o f t h e R E T e 3 s t r u c t u r e s e p a r a t e s t h e R E T e ; s l a b s , F i g u r e 4 . 1 . T h e i n t e r - s l a b i n t e r a c t i o n s i n R E T e 3 s h o u l d b e d i m i n i s h e d s o t h a t a q u a s i t h r e e - d i m e n s i o n a l s y s t e m b e c o m e s m o r e t w o - d i m e n s i o n a l i n c h a r a c t e r . T h i s o p e n s t h e p o s s i b i l i t y t h a t t h e c h a n g e s i n t h e C D W o f A W E T e a a r i s e f r o m t h e e n h a n c e d t w o - d i m e n s i o n a l i t y o f t h e R E T e 3 l a y e r . 1 1 T h i s w o u l d i m p l y t h a t t h e v a n d e r W a a l s i n t e r f a c e b e t w e e n a d j a c e n t T e s q u a r e n e t s i n R E T e 3 i s 2 0 4 i m p o r t a n t i n a f f e c t i n g t h e F e r m i s u r f a c e n e s t i n g . T h e A M R E T e a c o m p o u n d c o u l d p r e s e n t a r a r e e x a m p l e t h a t i l l u s t r a t e s t h e e f f e c t o f d i m e n s i o n a l i t y o n t h e C D W d i s t o r t i o n w i t h o u t c h a n g i n g t h e e l e c t r o n c o u n t . 4 . 2 . E x p e r i m e n t a l S e c t i o n 4 . 2 . 1 . R e a g e n t s T h e f o l l o w i n g r e a g e n t s w e r e u s e d a s o b t a i n e d P o t a s s i u m m e t a l , S p e c t r u m C h e m i c a l s M f g . C o r p . , G a r d e n a , C A ; S o d i u m m e t a l , S p e c t r u m C h e m i c a l s M f g . C o r p . , G a r d e n a , C A ; L a n t h a n u m m e t a l , 4 0 m e s h , C e r a c , M i l w a u k e e , W I ; C e r i u m m e t a l , ~ 1 m m t u r n i n g s , C e r a c , M i l w a u k e e , W I ; C o p p e r m e t a l , 4 0 m e s h , C e r a c , M i l w a u k e e , W I ; T e l l u r i u m c h u n k s , T e l l u r e x C o r p , T r a v e r s e C i t y , M I ; N , N — D i m e t h y l f o r m a m i d e ( D M F ) , A C S r e a g e n t g r a d e , S p e c t r u m C h e m i c a l s , N e w B r u n s w i c k , N J ; D i e t h y l e t h e r a n h y d r o u s , A C S r e a g e n t g r a d e , C o l u m b u s C h e m i c a l I n d u s t r i e s , C o l u m b u s , W I . A l k a l i M e t a l T e l l u r i d e , A z T e ( A = K , N a ) - 5 . 8 3 6 g ( 0 . 1 5 m o l ) K ( o r 3 . 4 4 8 g o f N a ) w a s s l i c e d i n s m a l l p i e c e s ( ~ 3 m m ) i n a N 2 fi l l e d g l o v e b o x a n d c o m b i n e d w i t h 9 . 5 2 3 g ( 0 . 0 7 5 m o l ) T e i n a 1 0 0 0 m L s i n g l e n e c k r o u n d b o t t o m fl a s k . A T e fl o n c o a t e d m a g n e t i c s t i r b a r w a s a d d e d i n t h e fl a s k a s w e l l . T h e fl a s k w a s c o n n e c t e d t o a g l a s s a d a p t e r w i t h a s t o p c o c k j o i n t a n d r e m o v e d f r o m t h e g l o v e b o x . T h e fl a s k a n d a d a p t e r w e r e t h e n c o n n e c t e d t o a d r y c o n d e n s e r a p p a r a t u s a n d c h i l l e d t o ~ 7 8 C u s i n g a d r y i c e / a c e t o n e b a t h . A p p r o x i m a t e l y 8 0 0 m L o f p u r e N H 3 w e r e c o n d e n s e d , u n d e r N 2 a t m o s p h e r e , o n t o t h e r e a g e n t s , y i e l d i n g a p u r p l e s o l u t i o n . T h e s o l u t i o n w a s k e p t u n d e r s t i r r i n g a n d m a i n t a i n e d a t - 7 8 C f o r u p t o 1 6 h o u r s . T h e d r y i c e / a c e t o n e m i x t u r e w a s r e m o v e d a n d t h e N H 3 w a s a l l o w e d t o e v a p o r a t e o f f a s t h e fl a s k w a r m e d u p t o r o o m t e m p e r a t u r e u n d e r a c o n s t a n t 2 0 5 fl o w o f N 2 f o r ~ 6 h o u r s . T h e r e s u l t i n g p o w d e r ( b r o w n c o l o r f o r K 2 T e a n d w h i t e - g r a y f o r N a 2 T e ) w a s e v a c u a t e d o n a S c h l e n c k l i n e f o r ~ 4 h o u r s a n d t a k e n i n t o a N 2 fi l l e d g l o v e b o x . T h e p r o d u c t w a s g r o u n d t o a fi n e p o w d e r w i t h a m o r t a r a n d p e s t l e a n d p l a c e d i n t o a s c r e w - c a p p e d v i a l i n t h e g l o v e b o x . 4 . 2 . 2 . S y n t h e s i s A l l fl i E T e 4 ( A = K , N a ; M = C u , A g ; R E = L a , C e ) — A 1 - x M 1 + x R E T e 4 w a s s y n t h e s i z e d fi o m a m i x t u r e o f A 2 T e ( A = K , N a ; 0 . 5 0 0 m m o l ) , M ( M = C u , A g ; 0 . 1 2 5 m m o l ) , R E ( R E = L a , C e ; 0 . 1 2 5 m m o l ) , a n d T e ( 2 . 0 m m o l ) t h a t w a s s e a l e d u n d e r v a c u u m i n a q u a r t z t u b e a n d h e a t e d t o 7 0 0 ° C f o r 5 d a y s . T h e t u b e w a s t h e n c o o l e d t o 3 0 0 ° C a t a r a t e o f 4 ° C / h , f o l l o w e d b y q u e n c h i n g t o r o o m t e m p e r a t u r e a t a r a t e o f 1 0 ° C / h . T h e e x c e s s A 2 T e y fl u x w a s w a s h e d o f f w i t h N , N - d i m e t h y l f o r m a m i d e u n d e r n i t r o g e n t o r e v e a l v e r y t h i n r e d - b r o w n p l a t e - s h a p e d c r y s t a l s . 4 . 2 . 3 . P h y s i c a l M e a s u r e m e n t s S e m i q u a n t i t a t i v e E n e r g y D i s p e r s i v e S p e c t r o s c o p y ( E D S ) — T h e a n a l y s e s w e r e p e r f o r m e d w i t h a J E O L J S M - 3 5 C s e a m i n g e l e c t r o n m i c r o s c o p e e q u i p p e d w i t h a N o r a n V a n t a g e E D S ( S i z L i ) d e t e c t o r . C r y s t a l s w e r e m o u n t e d o n a n a l u m i n u m s t a g e w i t h c a r b o n t a p e . D a t a w e r e a c q u i r e d o n s e v e r a l c r y s t a l s a n d d i f f e r e n t r e g i o n s o f e a c h c r y s t a l u s i n g a n a c c e l e r a t i n g v o l t a g e o f 2 5 k V a n d a c c u m u l a t i o n t i m e o f 4 0 8 . S i n g l e C r y s t a l X - r a y D i fl r a c t i o n — A l l t e m p e r a t u r e d e p e n d e n t m e a s u r e m e n t s w e r e p e r f o r m e d o n t h e s a m e s i n g l e c r y s t a l f o r e a c h A M R E T e a c o m p o u n d . S i n g l e c r y s t a l s w e r e q u e n c h e d f r o m r o o m t e m p e r a t u r e t o 1 0 0 K . T h e h e a t i n g r a t e f o r w a r m i n g r a m p s w a s 2 0 6 ~ 2 0 0 K / h . T y p i c a l a c q u i s i t i o n t i m e w a s a r o u n d 2 4 h . D e t a i l e d c r y s t a l l o g r a p h i c t a b l e r e p o r t s f o r e a c h i n d i v i d u a l A M R E T e 4 a n a l o g u e a n d t e m p e r a t u r e c a n b e f o u n d i n t a b l e s 4 . 4 - 4 . 5 3 . I n t e n s i t y d a t a w e r e c o l l e c t e d o n a S T O E I P D S H d i f f r a c t o m e t e r e q u i p p e d w i t h a g r a p h i t e m o n o c h r o m a t i z e d M o r a d i a t i o n ( A = 0 . 7 1 0 7 3 A ) a n d a n I m a g e P l a t e ( I P ) d e t e c t o r . T h e d a t a w e r e c o l l e c t e d w i t h a n ( l s - s c a n t e c h n i q u e f r o m 0 - 1 8 0 ° a n d a n a r b i t r a r y ( p - a n g l e . D a t a r e d u c t i o n w a s p e r f o r m e d w i t h t h e X - A r e a p a c k a g e . 1 2 T h e l e n g t h d e t e r m i n a t i o n a n d r e fi n e m e n t o f t h e q - v e c t o r s w a s p e r f o r m e d w i t h t h e P e a k l i s t 1 . 0 6 s o f t w a r e p a r t o f t h e X - A r e a s u i t e u s i n g a l e a s t s q u a r e r e fi n e m e n t a l g o r i t h m . A n a n a l y t i c a l a b s o r p t i o n c o r r e c t i o n w a s p e r f o r m e d ( X - S h a p e w i t h i n X - A r e a ) a n d a l l s t r u c t u r e s w e r e r e fi n e d w i t h J A N A 2 0 0 0 s o f t w a r e . l 3 D i r e c t m e t h o d s o f S H E L X T L s o f t w a r e l 4 w e r e u s e d t o fi n d t h e a t o m i c p o s i t i o n s i n t h e s u b c e l l . S a t e l l i t e r e fl e c t i o n s o f fi r s t o r d e r w e r e o b s e r v e d a n d u s e d f o r t h e r e fi n e m e n t . A s i n g l e m o d u l a t i o n w a v e f o r p o s i t i o n a l a n d t e m p e r a t u r e p a r a m e t e r s w a s u s e d . O n l y t h e s y m m e t r y a l l o w e d F o u r i e r t e r m s w e r e r e fi n e d . I n m o r e d e t a i l s , t h e s i n u s o i d a l c o e f fi c i e n t s i n a l l t h e d i r e c t i o n s f o r p o s i t i o n a l ( x , y a n d z ) a n d t h e r m a l p a r a m e t e r s ( U 1 1 , U 2 2 , U 3 3 , U 1 2 , U 1 3 a n d U 2 3 ) w e r e f r e e l y r e fi n e d a n d t h e c o r r e s p o n d i n g c o s i n e c o e f fi c i e n t s v a l u e s w e r e i n d u c e d b y s y m m e t r y . S o m e o f t h e q u a t e r n a r y a n a l o g u e s h a d t w i n d o m a i n s t h a t c o u l d d e s c r i b e d w i t h a t w i n l a w o f 9 0 d e g r e e s r o t a t i o n a l o n g t h e c — a x i s [ 0 - 1 0 1 0 0 0 0 1 ] . S e v e r a l c e n t r o s y m m e t l i c s u p e r s p a c e g r o u p s w e r e t e s t e d y i e l d i n g R — v a l u e s f o r t h e s a t e l l i t e s t o m o r e t h a n 5 0 % . T e m p e r a t u r e w a s c o n t r o l l e d b y a n O x f o r d C r y o s t r e a m 7 0 0 P l u s c r y o s t a t . C h a r g e t r a n s p o r t m e a s u r e m e n t s - E l e c t r i c a l r e s i s t i v i t y a n d t h e r m o p o w e r d a t a w e r e m e a s u r e d a s a f u n c t i o n o f t e m p e r a t u r e f o r s i n g l e c r y s t a l s o f K C u L a T e 4 . E l e c t r i c a l 2 0 7 c o n t a c t f o r t h e r e s i s t i v i t y m e a s u r e m e n t w a s m a d e u s i n g s i l v e r p a i n t a n d C u w i r e d i r e c t l y o n t o t h e c r y s t a l s u r f a c e . M e a s u r e m e n t s w e r e m a d e f o r a r b i t r a r y c u r r e n t d i r e c t i o n s i n t h e a b - p l a n e u s i n g a s t a n d a r d f o u r p o i n t c o n t a c t g e o m e t r y ( A C ) i n a Q u a n t u m D e s i g n P h y s i c a l P r o p e r t y M e a s u r e m e n t S y s t e m ( P P M S ) . E l e c t r i c a l c o n t a c t f o r t h e t h e r m o p o w e r m e a s u r e m e n t w a s m a d e u s i n g g o l d p a i n t o n a n a l u m i n a s t a g e o f a S B - 1 0 0 S e e b e c k M e a s u r e m e n t M M R S y s t e m . I n fi a r e d ( I R ) S p e c t r o s c o p y — — O p t i c a l d i fi u s e r e fl e c t a n c e m e a s u r e m e n t s w e r e p e r f o r m e d o n s i n g l e c r y s t a l s o f a l l A M R E T e a m e m b e r s a t r o o m t e m p e r a t u r e . T h e s p e c t r a w e r e r e c o r d e d i n t h e M i d - I R r e g i o n ( 6 0 0 0 — 4 0 0 c m “ ) w i t h a N i c o l e t 6 7 0 0 F T - I R S p e c t r o m e t e r e q u i p p e d w i t h a d i f f u s e r e fl e c t a n c e c o l l e c t o r f r o m S p e c t r a - T e c h I n c . 4 . 3 . R e s u l t s a n d D i s c u s s i o n S u b c e l l D e s c r i p t i o n o f A M E T e 4 ( A = K , N a ; M = C u , A g ; R E = L a , C e ) — T h e A M R E T e a a d o p t a l a y e r e d s t r u c t u r e c o m p o s e d o f t w o t y p e s o f l a y e r s , t h e s e m i c o n d u c t i v e [ N a C u T e ] a n d m e t a l l i c [ R E T e 3 ] , F i g u r e 4 . 1 . E a c h c o m p o n e n t i s k n o w n t o e x i s t a s a n i n d e p e n d e n t c o m p o u n d . “ 8 T h e [ R E T C 3 ] l a y e r a d o p t s t h e N d T e 3 s t r u c t u r e t y p e a n d h a s a n a n t i - P b O t y p e [ R E T e ] + s u b l a y e r s a n d w i c h e d b e t w e e n t w o s q u a r e T e n e t s . T h e [ C u T e ] l a y e r c a n b e d e s c r i b e d a s a n i d e a l a n t i - P b O s t r u c t u r e t y p e , m a d e u p o f r i b b o n t e t r a h e d r a l [ C u T e a ] u n i t s t h a t s h a r e e d g e s i n t w o d i m e n s i o n s . T h e n e u t r a l [ N a C u T e ] a n d [ R E T C 3 ] s l a b s a l t e r n a t e i n a 1 : 1 r a t i o a n d s t a c k a l o n g t h e c - a x i s s e p a r a t e d b y v a n d e r W a a l s g a p s t o b u i l d t h e s t r u c t u r e . S i n c e b o t h s l a b s h a v e n o n e t c h a r g e t h e a v e r a g e e l e c t r o n c o u n t i n t h e T e a t o m s o f t h e n e t o f t h e [ R E T e 3 ] s u b l a y e r r e m a i n s - 0 5 e ' . N o e l e c t r o n t r a n s f e r i s n e c e s s a r y b e t w e e n t h e [ N a C u T e ] a n d [ R E T C 3 ] s l a b s . A m o r e d e s c r i p t i v e f o r m u l a o f t h e 2 0 8 s t r u c t u r e c a n b e N a + [ C u T e ] ' [ R E T e ] + [ T e 2 ] ‘ . T h e s i n g l e c r y s t a l s t r u c t u r e r e fi n e m e n t i n d i c a t e d t h a t i n s o m e m e m b e r s o f t h e f a m i l y t h e r e i s s o m e i n t e r c h a n g e b e t w e e n t h e a l k a l i a t o m s a n d m o n o v a l e n t M a t o m s i n t h e i r c r y s t a l l o g r a p h i c s i t e s i n t h e f o r m A 1 - x M i t h E T e a . I n m o s t o f t h e q u a t e r n a r y s e r i e s t h e a l k a l i m e t a l s i t e i s m i x e d - o c c u p i e d w i t h t h e c o i n a g e m e t a l ( e x c e p t t h e K / C u c o m b i n a t i o n ) . T h e s i m i l a r a t o m i c r a d i i a n d s a m e s q u a r e a n t i p r i s m a t i c s i t e e n v i r o n m e n t o f t h e s e a t o m s c a n f a c i l i t a t e s u c h d i s o r d e r . ( A ) , _ ( B ) ( D ) A C u T e R E T e 3 A C u R E T e a F i g u r e 4 . 1 . ( A ) T h e l a y e r e d s t r u c t u r e o f R E T e 3 ( N d T e 3 - t y p e ) . T h e v a n d e r W a a l s g a p i s i n d i c a t e d b y t h e a r r o w . ( B ) T h e u n d i s t o r t e d s q u a r e n e t o f T e a t o m s i n R E T e 3 a n d A M R E T e a . ( C ) T h e e l e c t r o n i c a l l y n e u t r a l A C u T e l a y e r w h i c h w h e n i n s e r t e d i n t h e s t r u c t u r e o f R E T e ; g i v e s A M R E T e a . ( D ) T h e s t r u c t u r e o f A M R E T e 4 ( A = K , N a ; M = C u , A g ; R E = L a , C e ) . 2 0 9 S u p e r c e l l D e s c r i p t i o n o f A W E T e 4 ( A = K , N a ; M = C u , A g ; R E = L a , C e ) — T h e C D W i n a l l A 1 - x M . + x R E T e 4 a n a l o g s g i v e s r i s e t o m o d u l a t e d i n c o m m e n s u r a t e s u p e r s t r u c t u r e s . T h e a p p l i c a t i o n o f s u p e r s p a c e c r y s t a l l o g r a p h i c t e c h n i q u e s w a s n e c e s s a r y t o s o l v e t h e i r s t r u c t u r e . A l t h o u g h t h e u n d i s t o r t e d ( n o C D W ) s u b c e l l s t r u c t u r e h a s a t e t r a g o n a l s y m m e t r y ( T a b l e 4 . 3 ) , t h e m o d u l a t i o n q - v e c t o r i s a l w a y s a l o n g t h e b - a x i s g i v i n g o r t h o r h o m b i c s y m m e t r y . T h e d i s t o r t i o n i s l o c a t e d i n t h e p l a n a r T e n e t s o f t h e R E T e 3 s l a b s . T h e [ C u T e ] l a y e r a l s o c o n t a i n s a s q u a r e T e n e t . H o w e v e r , i t i s n o t d i s t o r t e d a s t h e f o r m a l c h a r g e o n e a c h T e a t o m i n t h i s l a y e r i s 2 - a n d T e - T e i n t e r a t o m i c d i s t a n c e s g r e a t e r t h a n 4 . 4 A . M o s t o f t h e A 1 - x M 1 + x R E T e 4 ( A = K , N a ; M = C u , A g ; R E = L a , C e ) a n a l o g s a d o p t t h e P 2 1 2 1 2 ( O B I / 2 ) 0 S 0 s u p e r s p a c e g r o u p , e x c e p t f o r N a M C e T e a ( M = A g a n d C u ) w h i c h a d o p t s P 2 1 2 1 2 ( 0 [ 3 0 ) 0 s 0 a n d K A g R E T e 4 ( R E = L a , C e ) w h i c h a d o p t s t h e l o w e r s y m m e t r y P m ( O B l / 2 ) 0 s u p e r s p a c e g r o u p . T h e q - v e c t o r v a r i e s f r o m 0 . 3 3 6 1 ( 6 ) i n K A g C e T e a t o 0 . 3 8 6 1 ( 5 ) i n K C u L a T e a , a t 1 0 0 K . T h e d i f f e r e n c e i n t h e c e l l c o n s t a n t s a l o n g t h e p l a n e o f t h e T e n e t b e t w e e n t h e s e q u a t e r n a r y p h a s e s a n d t h e c o r r e s p o n d i n g R E T e 3 b i n a r i e s i s n e g l i g i b l e ( ~ 2 % ) . S u r p r i s i n g l y , h o w e v e r , t h e d i f f e r e n c e i n q - v e c t o r s b e t w e e n q u a t e r n a r y ( 0 . 3 5 5 0 ( 8 ) f o r K C u C e T e a ) a n d b i n a r y ( 0 . 2 7 9 0 ( 3 ) f o r C e T e 3 ) c o m p o u n d s i s l a r g e ~ 3 0 % . A 2 % c h a n g e . i n t h e l a t t i c e c o n s t a n t c a n n o t a c c o u n t f o r t h e l a r g e c h a n g e i n q - v e c t o r . A d i f f e r e n c e o f ~ 2 % i n t h e c e l l p a r a m e t e r s t h e b i n a r y R E T e 3 r e s u l t s i n n o m o r e t h a n 6 % c h a n g e i n t h e q - v e c t o r s i n c e a 2 % d e c r e a s e i n t h e c - a x i s o f C e T e 3 ( q = 0 . 2 7 9 0 ( 3 ) ) g i v e s a c e l l c o n s t a n t c o m p a r a b l e w i t h t h e c e l l o f H o T e ; ( q = 0 . 2 9 3 5 ( 3 ) ) a t 1 0 0 K . G i v e n t h a t t h e R E T e 3 l a y e r s i n t h e q u a t e r n a r y a n d b i n a r y c o m p o u n d s a r e i s o e l e c t r o n i c , t h e l a r g e c h a n g e i n t h e C D W 2 1 0 c h a r a c t e r c o u l d a r i s e f r o m t h e a l t e r a t i o n o c c u r r i n g i n i n t e r l a y e r c o u p l i n g b e t w e e n a d j a c e n t T e n e t s o f R E T e 3 s l a b s u p o n i n s e r t i o n o f t h e A M T e l a y e r . T h e n e w C D W m o d u l a t i o n s f o u n d i n t h e q u a t e r n a r y c o m p o u n d s f e a t u r e s T e x o l i g o m e r s w h i c h a r e d i f f e r e n t f r o m t h o s e o b s e r v e d i n t h e R E T e 3 ( R E = L a a n d C e ) s e r i e s . T h e m a j o r i t y o f o l i g o m e r s i n t h e b i n a r y R E T e ; c o m p o u n d s a r e t e t r a m e r s a n d t r i m e r s a n d o c c a s i o n a l l y s i n g l e T e a t o m s a n d W - s h a p e d p e n t a m e r s . l s I n c o n t r a s t , e v e r y T e p a t t e r n w i t h i n t h e A l - x M 1 + x R E T e 4 s e r i e s i s u n i q u e w i t h a d i f f e r e n t s e q u e n c e o f o l i g o m e r s a l o n g t h e m o d u l a t i o n d i r e c t i o n . I n t e r e s t i n g l y , t e t r a m e r s w e r e n o t f o u n d i n m o s t o f t h e q u a t e r n a r y p h a s e s . I n s t e a d , a s e q u e n c e o f t r i m e r s a n d p e n t a m e r s w i t h o n e l i n e a r T e a t o m a n d o c c a s i o n a l l y m o n o m e r s a n d d i m e r s i s o b s e r v e d f o r t h e c o m p o u n d s t h a t h a v e a q - v e c t o r i n t h e r a n g e o f 0 3 6 ( 1 ) , F i g u r e s 4 . 2 - 4 . 5 , 4 . 7 , 4 . 9 . F o r t h e t w o c a s e s t h a t t h e q - v e c t o r d e v i a t e s s i g n i fi c a n t l y f r o m t h i s r a n g e t h e T e p a t t e r n s s t a r t t o c o n t a i n t e t r a m e r s s i m i l a r t o t h o s e f o u n d i n t h e b i n a r i e s . S p e c i fi c a l l y , t h e m a j o r i t y o f o l i g o m e r s i n t h e T e n e t o f K C u L a T e 4 ( q - v e c t o r o f 0 . 3 8 6 1 ( 5 ) ) c o n s i s t s o f d i m e r s a n d o c c a s i o n a l l y t r i m e r s , t e t r a m e r s a n d s i n g l e T e a t o m s , F i g u r e 4 . 6 . F o r K A g C e T e a ( q - v e c t o r o f 0 . 3 8 6 1 ( 5 ) ) t h e n e t i s m a i n l y c o m p o s e d b y t r i m e r s a n d a s m a l l e r f r a c t i o n o f d i m e r s a n d t e t r a m e r s , F i g u r e 4 . 9 . T h e b o n d l e n g t h d i s t r i b u t i o n b e t w e e n T e a t o m s i n t h e n e t s o f A 1 - x M 1 + x R E T e 4 i s c o m p a r a b l e w i t h t h a t i n t h e R E T e 3 b i n a r i e s , T a b l e 4 . 2 . T h e q - v e c t o r i n c r e a s e s a s t h e c e l l v o l u m e d e c r e a s e s , f o r e x a m p l e f r o m 0 . 3 3 6 1 ( 6 ) i n K A g C e T e 4 t o 0 . 3 8 6 1 ( 5 ) i n K C u L a T e a , a t 1 0 0 K . T h e s a m e t r e n d e x i s t s i n t h e R E T e 3 s e r i e s . 1 5 T h e t e m p e r a t u r e d e p e n d e n c e o f t h e q - v e c t o r b e t w e e n 1 0 0 K a n d 3 0 0 K s e e m s n e g l i g i b l e . 2 1 1 . d l o h s e r h t A 7 9 0 . 3 d n a ‘ c 2 / 1 + ‘ b ) 8 ( 0 6 6 3 . 0 = q h t i w K 0 0 1 t a 4 e T a L ) 1 ( 8 2 . 1 g A ) 0 2 7 . 0 3 N . 4 . 4 e r u g i F < < < < < < < < < < < < < < < < < < < < / / / / / / / / / / > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > ‘ 2 2 2 2 2 8 2 2 2 < < < < < < < < < < < , 8 8 8 8 8 8 8 8 8 < > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > 8 2 2 2 2 2 8 2 8 < < < < < < < < < < 8 8 8 8 8 8 8 8 9 > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > ‘ 2 8 2 8 2 2 2 8 2 < < < < < < < < < < < . 8 8 8 8 8 8 8 8 8 < > > > > > > > > > > > > > > > > > > > > 2 2 8 2 2 8 2 2 2 2 < < < < < < < < < < < < < < < < < < < < , 8 8 8 8 8 8 8 8 8 < > > > > > > > > > > > > > > > > > > > > 2 8 2 2 2 2 2 2 2 8 < < < < < < < < < < < < < < < < < < < < j § < < < < < < < < < 5 5 5 5 5 5 5 3 5 2 5 , 3 5 5 3 5 3 , 8 8 8 8 8 8 8 8 < > 8 8 8 8 8 8 8 8 8 < > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > \ > \ > \ > \ > \ > \ > \ > \ > \ > \ . < < < < < < < < < < \ 3 3 3 3 3 3 3 3 < g g g g g g g g g < < < < < < < < < < I > > > > > > > > > > 4 3 3 3 3 3 3 3 3 < > > > > > > > > > > : . 5 8 8 8 8 8 8 8 8 ’ 8 2 2 2 2 2 8 2 2 2 E > > > ) > ) ) > > > < < < < < < < < < < < < < < < < < < < < § < < < < < < < < < < g > > > > > > > > ( I C E / ' 3 “ ' 3 3 3 $ ' < E > i > \ > \ > \ > i > \ > \ > : > \ > \ ' 8 8 8 8 ; ; 9 2 , 2 2 2 , 2 2 2 . 3 ? 3 3 ? ? ? ? \ E 3 > > > > > > > > > g < < < < < < < < < < § > > > > > > > > > > z 8 < < < < < < < < < < < < < < < < < < < < 8 . 3 2 3 2 3 2 2 2 2 c 2 : 3 3 3 3 3 3 I I ; < < < < < < < < < < < < < < < < < < < < 3 2 2 2 2 2 2 2 2 2 ; ' 2 5 5 5 5 5 5 5 5 5 5 < 2 2 2 2 2 2 2 9 g 3 ) > 3 } } ? 3 ; < < < < < < < < < < 7 . . < § < < < < < < < < < < < ; , _ « ‘ f < < < < < < < < < < < : 1 9 . § 3 > > > > > > > > > § 3 > > > > > > > > 2 C 2 > > > > > > > ) > > Q > > > > > > > > > > . i 2 8 S 2 ? Z < < < < < < < < < < _ D Z < < < < < < < < < < i n 2 1 2 d l o h s e r \ \ . d l o h s e r h \ \ t \ \ A h 0 7 q h t t A 9 0 1 . 3 d n a ' o 2 / 1 + * b ) 5 ( 1 6 8 w 3 K 0 0 1 t a \ 4 e T e C ) 1 ( 1 2 . 0 q h t i w K 0 0 1 t a 4 e T a L u C K 6 4 e r u g i F > 8 8 8 8 8 8 8 8 8 ’ > > > > > > > > > > \ \ \ \ \ \ \ \ \ \ ' < < < < < < < < < < < < < < < < < < < < > 8 8 8 8 8 8 8 8 8 < > > > > > > > > > > > > > > > > > > > > 2 2 2 2 2 2 2 8 2 2 I < < < < < < < < < < < < < < < < < < < < > 8 8 8 8 8 8 8 8 8 ’ > > > > > > > > > > 2 2 8 2 2 2 2 2 2 8 < < < < < < < < < < < > 8 8 8 8 8 8 8 8 8 < > > > > > > > > > > > > > > > > > > > > 8 2 2 2 2 2 8 8 2 8 I < < < < < < < < < < < < < < < < < < < < > 8 8 8 8 8 8 8 8 8 ’ > > > > > > > > > > > 2 8 2 8 2 2 2 2 2 < < < < < < < < < < < > 8 8 8 8 8 8 8 8 8 < > > > > > > > > > > > > > > > > > > > > 2 8 2 8 8 8 2 2 2 2 ' < < < < < < < < < < < < < < < < < < < < 5 8 8 8 8 8 6 8 2 8 2 2 2 2 2 2 2 2 2 2 / / / / / / / / / / \ \ \ \ \ \ \ \ \ \ l / l / l / l / l / \ \ \ \ \ \ \ \ \ \ / / / / / / / / / / \ \ \ \ \ \ \ \ \ \ / / / / / / / / / / / / / / / / / / / / \ \ \ \ \ \ \ \ \ \ l / l / l / l / l / > > > > > > > > > > / / / / / / / / / / \ \ \ \ \ \ \ \ \ \ l / l / l / l / l / " 2 2 2 2 2 2 2 2 2 2 / / / / / / / / \ \ \ \ \ \ \ \ \ \ / / / / / / / / / / / / / / / / \ \ \ \ \ \ \ \ \ \ / / / / / / / / l / 3 2 > > > > > > 2 > > § / / / / / / / / / / , \ \ \ \ \ \ \ \ \ \ n x / x x x r x x x x § “ 2 2 2 2 2 2 2 2 2 2 e / / / / / / / / / / g \ \ \ \ \ \ \ \ \ \ ” ( ( 4 4 4 4 4 4 4 4 ' < < < < < < < < < \ / / / / / / / / I \ \ \ ’ \ \ x x \ \ \ \ \ \ \ \ \ \ \ / / / / / / / / / 2 2 2 2 2 2 2 2 l / l / l / l / l / \ \ \ \ \ \ \ \ \ \ 2 / / / / / / / / / / w . . . . . . . . . . . . . . . . . . . . § , \ \ \ \ \ \ \ \ \ \ § / / / / / / / / / / ' \ \ \ \ \ \ \ \ \ \ z / / / / / / / / / / , D . d / / / / / / / / / / A V ; \ \ \ \ \ \ \ \ \ \ A o / / / / / / / / / / E , > > > > > > > > > > E : 6 4 2 1 3 . d l o h s e r h t A 0 0 1 . 3 d n a ‘ 6 2 / 1 + ‘ b ) 7 ( 0 5 4 3 . 0 > > > > > > > > > > 2 > > > > > > > > > ' \ \ \ \ \ \ \ \ \ \ ) ) ) > > ) > > ) > < < < < < < < < < < > > > > > > > > > > < < < < < < < < < < > > > > > > > > > > “ “ “ “ “ “ “ “ “ “ > 9 9 9 3 3 3 3 8 8 3 > > > > > > > > > > ’ > > > > > > > > > 3 3 5 3 3 3 ; ? ? ? ) > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > e 2 > > > > > > > > > ) > > > > > > > > ) g > > > > > > > > > > > > > > > > > > > > g \ \ > \ > \ > \ > \ > \ > \ > \ > \ > \ > > > > > > > > > > < > > > > > > > > > > ~ < < < < < < < < < < 8 > > > > > > > > > . 8 8 8 8 8 8 8 8 8 8 8 3 2 3 3 3 3 3 3 3 ? ' g / > > > > > > > ) > ° < < < < < < < < < < : 3 > > > > > > > > > > > > > > > > > > > > < < < < < < < < < < 3 8 < t , > > > > > > > > > > 3 8 8 8 8 8 8 8 8 e > > > > > > > > > > > > > > > > > > > > R > > > > > > > > > > / > > > > > > > > > ° > > > > > > > > > > > > > > > > > > > > g ‘ > > > > > > > > > > > > > > > > > > > > s > > > > > > > > > > > > > > > > > > > > m > > > > > > > > > > > > > > > > > > > > § > > > > > > > > > > > > > > > > > > > > a > > > > > > > > > > > > > > > > > > > > g 8 > > > > > > > > > . \ > > > > > > > > > > > > > > > > > > > : 1 > > > > > > > > > > . 3 ’ 8 2 2 2 2 8 2 2 2 2 2 8 2 8 2 2 : < < < < < < < < < < < < < < < < < < < < £ < < < < < < < < < < ( ( ( < ( < < ( ( < — D h : / / / / / / / / / / ' D 8 3 8 8 3 3 2 3 3 3 2 ’ > > > > > > > > > g , > > > > > > > > > > 2 1 4 F i g u r e 4 . 8 . K o , 7 1 ( 1 ) A g 1 , 2 9 ( | ) L a T C 4 a t 3 0 0 K W i t h q . d d l l o o h h s s e e r r h h t . t A 0 8 0 . 9 0 . 3 c / = q h t i w K A 5 5 0 . 3 d n a ‘ c 2 / 1 + ‘ b ) 8 ( 0 5 5 3 . 0 q h t i w K 0 0 0 0 3 1 t a 4 e T e C g A K L 0 ( t a 4 e T e C u C K . b 1 l . 1 . 4 4 e r u g i e r u g i F F / / / / / / / / / / A fi w m w w m m » / / / / / / / / / / A w m w w m m w w » / / / / / / / / / / A m w w w w w w w r / / / / / / / / / / A w w m m w w w w » / / / / / / / / / / A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A 0 . 3 3 6 1 ( 6 ) b ‘ + 1 / 2 c ‘ ” A A A A A A A A A / A A A A A A A A A A ” A A A A A A A A A / A A A A A A A A A A ” A A A A A A A A A / A A A A A A A A A A ” A A A A A A A A A A A A A A A A A A A A ” A A A A A A A A A x A A A A A A A A A A ” A A A A A A A A A x \ \ \ \ \ \ \ \ \ \ % w w w w w m w w . . v v v v v v v v v v v v v v v v v v v v . v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v w v v v v v v v v v v m v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v w v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v m v v v v v v v v v v w i t h q = g C e T e 4 a t 1 0 0 K A A A A A A A A A ¢ h V 9 v v v v v v v v v v b A A A A A A A A A A + A A A A A A A A A A a A T v v v v v v v v v v 3 4 N ; A A A A A A A A A A A A A A A A A A A A \ \ \ \ \ \ \ \ \ \ v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v @ 8 8 8 8 , A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ . a v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v v . . , - - - - A . a A A A A A A A A A A m A A A A A A A A A A o . A A A A A A A A A A 1 \ \ \ \ \ \ \ \ \ \ + v v v v v v v v v v v v v v v v v v v v . l v v v v v v v v v v v v v v v v v v v v . _ _ . . _ _ v w w 3 8 % , A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A 4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ v v v v v v v v v v v v v v v v v v v v o v v v v v v v v v v A t h r e s h o l . ( 8 ) b . 3 3 8 A . % w w w m w . x v v v v v v v v v v w D i s o r d e r a n d p u r i t y o f A 1 . x M 1 + x R E T e 4 - A l l A 1 - x M 1 + x R E T e 4 ( A = K , N a ; M = C u , A g ; R E = L a , C e ) c o m p o u n d s w e r e s y n t h e s i z e d f r o m a n e x c e s s o f r e a c t i v e A x T e y fl u x . S i m i l a r i o n i c r a d i i a n d c o o r d i n a t i o n g e o m e t r y o f A a n d M ( e x c e p t t h e K / C u c o m b i n a t i o n ) c r e a t e d d i s o r d e r o n t h e A c r y s t a l l o g r a p h i c s i t e a n d a f r a c t i o n o f M w a s f o u n d t o o c c u p y s i t e A a s w e l l . T h e r e f o r e , t h e o c c u p a t i o n a l f r a c t i o n x c o u l d n ’ t b e c o n t r o l l e d b y t h e s e e x p e r i m e n t a l c o n d i t i o n s . N e v e r t h e l e s s , d i f f e r e n t x v a l u e s w i l l n o t a fl ‘ e c t t h e e l e c t r o n c o u n t o n t h e T e n e t o f t h e [ R E T e 3 ] l a y e r o f t h e q u a t e m a r i e s a n d t h e C D W m o d u l a t i o n . D i f f e r e n t c o n c e n t r a t i o n s o f M t h o u g h m a y c h a n g e t h e n u m b e r o f c a r r i e r s a n d r e s i s t i v i t y b u t n o t t h e m e t a l l i c c h a r a c t e r o f t h e m a t e r i a l s . T h e m a j o r p h a s e f r o m t h e fl u x r e a c t i o n s w a s t h e t a r g e t q u a t e r n a r y c o m p o u n d . M i n o r i m p u r i t i e s w e r e i n d e x e d a s R E T e 3 b i n a r i e s ( a n d A R E 3 T e 3 a n d A 2 M 5 R E 2 T e 9 i n s o m e o t h e r c a s e s ) . F i g u r e 4 . 1 2 s h o w s a r e p r e s e n t a t i v e p o w d e r x - r a y d i f f r a c t i o n p a t t e r n o f t h e a s s y n t h e s i z e d N a A g C e T e 4 p h a s e i n c o m p a r i s o n w i t h t h e c a l c u l a t e d p o w d e r p a t t e r n s o f t h e q u a t e r n a r y a n d C e T e 3 p h a s e s r e s p e c t i v e l y . S i n c e c r y s t a l m o r p h o l o g y a n d c o l o r o f q u a t e r n a r y a n d b i n a r y p h a s e s w e r e i d e n t i c a l , E n e r g y d i s p e r s i v e s p e c t r o s c o p y ( E D S ) w a s p e r f o r m e d o n t h e s i n g l e c r y s t a l s u s e d f o r t r a n s p o r t m e a s u r e m e n t s . T h e a n a l y s i s v e r i fi e d t h e p r e s e n c e o f a l l f o u r e l e m e n t s i n t h e c r y s t a l s . 2 1 6 1 . 8 I I 1 I I I I I V I V I I T L 6 - L 1 . 4 : _ , _ ‘ L 2 — q i n ) ; “ j g 0 8 L U I q N a A g C e T e 4 e x p e r i m e n t a l I M 0 . 6 - C e T e 3 c a l c u l a t e d - o , 4 . _ J _ _ _ L _ _ A J _ L _ » J L 1 . 0 . 2 _ N a A g C e T e 4 c a l c u l a t e d ; 0 . 0 L _ + . _ L + n _ m f # 1 4 4 a n i l a n t h l m n s z n m u m 1 0 2 0 3 0 5 0 6 0 7 0 8 0 2 0 0 ( d e g ) F i g u r e 4 . 1 2 . C o m p a r i s o n o f t h e e x p e r i m e n t a l X - r a y p o w d e r p a t t e r n o f N a A g C e T e 4 w i t h t h e c a l c u l a t e d p o w d e r p a t t e r n s o f t h e q u a t e r n a r y a n d C e T e 3 . B a n d s t r u c t u r e c a l c u l a t i o n o f K C u L a T e 4 — T h e c a l c u l a t i o n s w e r e p e r f o r m e d u s i n g t h e s e l f - c o n s i s t e n t f u l l - p o t e n t i a l l i n e a r i z e d a u g m e n t e d p l a n e w a v e m e t h o d ( L A P W ) 1 6 a n d t h e g e n e r a l i z e d g r a d i e n t a p p r o x i m a t i o n ( G G A ) l 7 f o r t h e e x c h a n g e a n d c o r r e l a t i o n p o t e n t i a l . T h e e x p e r i m e n t a l c e l l c o n s t a n t s ( T a b l e 4 . 2 9 ) a n d a t o m i c c o o r d i n a t e s ( T a b l e 4 . 1 ) f r o m t h e c r y s t a l s t r u c t u r e r e fi n e m e n t o f K O J L a T e 4 i n P m m n w e r e u s e d . D i r e c t i o n s i n t h e B r i l l o u i n z o n e ( B Z ) o f P m m n s p a c e g r o u p a r e s h o w n i n F i g u r e 4 . 1 5 . 1 8 I n t e r a t o m i c f o r c e s w e r e m i n i m i z e d w i t h i n 0 . 1 m R y / b o h r u s i n g a r e v e r s e - c o m m u n i c a t i o n t r u s t - r e g i o n q u a s i - N e w t o n m e t h o d f r o m t h e P o r t l i b r a r y . 1 9 S c a l a r r e l a t i v i s t i c c o r r e c t i o n s w e r e i n c l u d e d a n d a s p i n - o r b i t i n t e r a c t i o n w a s i n c o r p o r a t e d u s i n g a s e c o n d v a r i a t i o n a l p r o c e d u r e . 2 0 T h e v a l u e s o f t h e a t o m i c r a d i i w e r e t a k e n t o b e : 2 . 7 a . u . f o r K a t o m , 2 . 4 a . u . 2 1 7 f o r C u a t o m , 2 . 7 a . u . f o r L a a t o m a n d 2 . 5 a . u . f o r T e a t o m s , w h e r e a . u . i s t h e a t o m i c u n i t ( 0 . 5 2 9 A ) . C o n v e r g e n c e o f t h e s e l f - c o n s i s t e n t i t e r a t i o n s w a s p e r f o r m e d f o r 3 0 k p o i n t s i n s i d e t h e i r r e d u c i b l e B Z t o w i t h i n 0 . 0 0 0 1 R y w i t h a c u t o f f o f - 6 . 0 R y b e t w e e n t h e v a l e n c e a n d t h e c o r e s t a t e s . T h e c a l c u l a t i o n s w e r e p e r f o r m e d u s i n g W I E N Z K p r o g r a m . 2 1 E l e c t r o n i c b a n d s t r u c t u r e c a l c u l a t i o n s p e r f o r m e d o n t h e u n d i s t o r t e d s t r u c t u r e o f K C u L a T e 4 c o n fi r m t h a t t h e F e r m i s u r f a c e t o p o l o g y f a v o r s t h e f o r m a t i o n o f a n e s t i n g v e c t o r ( q - v e c t o r ) a l o n g t h e b * d i r e c t i o n w i t h a v a l u e o f ~ 0 . 3 3 , F i g u r e 4 . 1 6 . 2 2 T h e F e r m i s u r f a c e t o p o l o g y i s s i m i l a r t o t h e o n e f o r L a T e 3 ( F i g u r e 2 . 2 3 ) t h a t f o r m s a n e s t i n g v e c t o r o f 0 2 8 ( 2 ) . T h e d i f f e r e n c e i s t h e p r e s e n c e o f t h r e e e x t r a b a n d s , m a m l y C u d a n d T e p i n c h a r a c t e r f r o m t h e [ K C u T e ] l a y e r , t h a t a r e c r o s s i n g t h e F e r m i s u r f a c e a n d t h e y a r e l o c a t e d o u t s i d e t h e n e s t i n g r e g i o n o f t h e p b a n d s o f t h e T e n e t o f [ R E T e 3 ] ( s e e F i g u r e 4 . 1 4 a n d F i g u r e 4 . 1 6 ) . T a b l e 4 . 1 . A t o m i c c o o r d i n a t e s f o r K C u L a T e 4 i n P m m n u s e d f o r t h e D F T c a l c u l a t i o n . L a b e l x y 2 L a 0 . 2 5 0 . 2 5 0 . 3 9 3 2 1 0 T e [ 1 ] 0 . 2 5 0 . 7 5 0 . 2 6 3 4 4 9 T e [ 2 ] 0 . 2 5 0 . 7 5 0 . 7 3 6 2 9 8 T e [ 3 ] 0 . 2 5 0 . 2 5 0 . 0 7 8 5 0 9 T e [ 4 ] 0 . 2 5 0 . 2 5 0 . 5 6 1 3 0 4 K 0 . 2 5 0 . 7 5 0 . 0 0 0 2 8 3 C u 0 . 2 5 0 . 2 5 0 . 8 7 3 0 4 2 2 1 8 xP t I L \ ~ , 1 b — T . Q - 2 . 0 9 1 7 ' ; M ‘ D D ; / a \ i » X 1 _ ' l ’ 1 ’ 1 0 _ l 1 ' 4 ' ' _ 1 u H _ l U ‘ D . . ‘ p ‘ v . l . 1 ' 0 . 0 1 1 E F I A } : ‘ ' _ . l A - 1 . o - W 3 " : 3 - , \ ‘ 1 , i _ S a g - 2 . 0 — . \ - \ { _ § ‘ I ‘ / I v ’ : ' - 3 . o - f _ _ \ , . ‘ : v f w — * / - 4 . 0 - _ - 5 . o : - - 6 . 0 F X S Y F Z U R T Z S R F F i g u r e 4 . 1 3 . B a n d s t r u c t u r e o f K C u L a T e 4 n e a r t h e F e r m i l e v e l . C u d a n d T e [ 3 ] p b a n d s f r o m t h e [ K C u T e ] l a y e r a r e d r a w n i n o p e n c i r c l e s . T e [ 1 ] a n d T e [ 2 ] p b a n d s f r o m t h e d i s t o r t e d p l a n a r n e t a r e d r a w n i n c l o s e d c i r c l e s . T h e c o n t r i b u t i o n o f e a c h o r b i t a l i s p r o p o r t i o n a l t o t h e b r e a d t h o f t h e c i r c l e s t r a c i n g o u t t h e b a n d . O n l y t h e b a n d s t h a t c r o s s t h e F e r m i s u r f a c e a r e d r a w n i n c i r c l e s f o r c l a r i t y . 2 1 9 . = ' 2 . ~ a : . 1 " K » ) . Z i t a ” - _ y ’ 3 a 3 1 3 ' _ R M ” . 0 " - H . , ) " " " 3 2 : 4 3 : " : " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ‘ . K M a w - 5 . 2 : - . . Z Z Z Z z z - i . : 1 " « i f _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . , , : : : > A - l J , : 1 : : : Z _ _ _ _ _ _ _ _ d > 1 ' ' « : 3 " " " " 3 I c } " j ; ; f : - - - - - - - - - - - - - - - - - - - - - - : « a 3 " , " q ? " " " " " " " " " " " " " " " " " " " " " " " " 2 , » " " " " " M . . . . . . . . . . . . . . . . . 3 - 2 1 3 . . . . ” ‘ - ‘ q - . m ~ ¢ . . . . . . Z " “ " " “ " ' : : " - - - - - - - - - - - - n _ L a . - - - - - - - C u - - . . . . . , _ . . . . . . . . . . K “ M d " - - - - - - - - T e [ 1 ] ” W T C [ 2 ] ‘ - - - - - - - T e [ 3 ] T e [ 4 ] l _ 6 . 1 1 1 . J . 1 . 1 . 1 , 1 . | 4 4 . O 1 2 3 4 6 7 8 9 1 0 5 D O S F i g u r e 4 . 1 4 . T o t a l d e n s i t y o f s t a t e s ( D O S ) o f K C u L a T e 4 n e a r t h e F e r m i l e v e l . T e [ 1 ] a n d T e [ 2 ] a r e t h e t e l l u r i u m a t o m s i n t h e [ R E T e 3 ] n e t , T e [ 3 ] i s i n t h e [ C u T e ] l a y e r a n d T e [ 4 ] i s i n t h e [ R E T e 3 ] s l a b . 2 2 0 l k z A B E W I ? / T P A ( 5 O H X \ » D A k : 1 , - - x X 5 D W k y E ‘ C F i g u r e 4 . 1 6 . F e r m i s u r f a c e t o p o l o g y o f K C u L a T e 4 . P o s s i b l e n e s t i n g v e c t o r s ( q - v e c t o r s ) w i t h a n a v e r a g e l e n g t h o f 0 3 3 ( 2 ) a l o n g t h e b * - a x i s ( Y p o i n t ) a r e d r a w n i n a r r o w s . 2 2 1 7 0 0 . . . . . I . . . , ) m c 0 . “ ( y A oo t i v i t s i s e R C h a r g e t r a n s p o r t m e a s u r e m e n t s - G e n e r a l l y , t h e f o r m a t i o n o f C D W S l e a d s t o t h e a p p e a r a n c e o f e n e r g y g a p s a t t h e F e r m i l e v e l ( B f ) . I n t h e c a s e o f R E T e 3 h o w e v e r n e a r B f t h e r e i s a n e n e r g y g a p a s s o c i a t e d w i t h t h e C D W d i s t o r t i o n o f t h e T e n e t b u t s o m e e l e c t r o n i c s t a t e s s t i l l r e m a i n a t E f b e c a u s e o f b a n d s a s s o c i a t e d w i t h o t h e r p a r t s o f t h e s t r u c t u r e . T h u s , t h e C D W d i s t o r t i o n s d o n o t c r e a t e a f u l l y g a p p e d F e r m i s u r f a c e . 2 3 T h i s s i t u a t i o n c r e a t e s a p o o r m e t a l c h a r a c t e r f o r R E T e 3 a n d t h i s i s c o n fi r m e d b y e l e c t r i c a l r e s i s t i v i t y m e a s u r e m e n t s . 2 4 T h e s i t u a t i o n i n K C u L a T e 4 i s s i m i l a r a s i n d i c a t e d b y t h e t e m p e r a t u r e d e p e n d e n t r e s i s t i v i t y d a t a s h o w n i n F i g u r e 4 . 1 7 . T h e t h e r m o p O w e r v a r i e s b e t w e e n + 3 5 t o + 5 5 u V / K i n t h e r a n g e o f 3 0 0 - 5 5 0 K . T h e s e a r e r e l a t i v e l y s m a l l v a l u e s a n d a r e c o n s i s t e n t w i t h m e t a l l i c p - t y p e c h a r a c t e r f o r t h e m a t e r i a l , F i g u r e 4 . 1 8 . 6 0 0 M O O 3 0 0 2 0 0 b d 1 0 0 - - l l l I l l 0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 T e m p e r a t u r e ( K ) F i g u r e 4 . 1 7 . T e m p e r a t u r e d e p e n d e n t r e s i s t i v i t y o f K C u L a T e 4 s i n g l e c r y s t a l . 2 2 2 O \ O ' 0 p 5 5 ? “ r o w g 3 4 I 3 5 0 - i f ? . . 1 0 3 0 ' E 4 5 — a . . 0 8 4 m - g ’ . l { — 4 3 5 — f - 3 0 0 3 5 0 4 0 0 4 5 0 5 0 0 5 5 0 T e m p e r a t u r e ( K ) F i g u r e 4 . 1 8 . D e p e n d e n c e o f t h e r m o p o w e r w i t h t e m p e r a t u r e o f K C u L a T e 4 s i n g l e c r y s t a l . I n fi a r e d ( I R ) S p e c t r o s c o p y — D e s p i t e t h e p o o r m e t a l c h a r a c t e r o f A M R E T e 4 , t h e r e a r e s p e c t r o s c o p i c a l l y o b s e r v e d e l e c t r o n i c t r a n s i t i o n s w h i c h c a n b e a s s i g n e d t o t h e C D W e n e r g y g a p o f t h e T e - n e t . T h e e n e r g y v a l u e s a r e b e t w e e n 0 2 5 ( 2 ) e V f o r N a o , 6 o C u 1 , 4 o L a T e 4 a n d 0 3 3 ( 2 ) e V f o r K C u C e T e 4 a t r o o m t e m p e r a t u r e a s m e a s u r e d b y i n f r a r e d d i f f u s e r e fl e c t a n c e s p e c t r o s c o p y , T a b l e 4 . 2 . A r e p r e s e n t a t i v e p l o t o f t h e a p p a r e n t e n e r g y g a p i s s h o w n i n F i g u r e 4 . 1 9 . 2 2 3 T a b l e 4 . 2 . C o m p a r i s o n o f t h e m i n i m u m a n d m a x i m u m d i s t a n c e s o f T e - T e w i t h i n t h e n e t ( X - r a y d i f f r a c t i o n a t 1 0 0 K ) a n d r o o m t e m p e r a t u r e e n e r g y g a p v a l u e s o f a l l A l . x M 1 + x R E T e 4 ( A = K , N a ; M = C u , A g ; R E = L a , C e ) q u a t e r n a r y c o m p o u n d s w i t h t h e b i n a r y R E T e 3 a n a l o g s . M i n i m u m M a x i m u m E n e r g y g a p C o m p o u n d d i s t a n c e ( A ) d i s t a n c e ( A ) ( e V ) C e T e 3 2 . 9 2 5 ( 2 ) 3 . 2 5 5 ( 3 ) 0 2 7 ( 2 ) L a T e 3 2 . 9 2 9 ( 6 ) 3 . 2 7 2 ( 7 ) 0 2 5 ( 2 ) N a o . 6 0 ( 2 ) C u 1 , 4 o ( 2 ) L a T e 4 2 . 9 9 9 ( 4 ) 3 . 2 6 0 ( 4 ) 0 2 5 ( 2 ) N a o , 7 3 ( 1 ) C u l . 2 2 ( 1 ) C e T e 4 2 . 9 7 5 ( 3 ) 3 . 2 4 1 ( 2 ) 0 2 7 ( 2 ) N a o . 7 o m A g l . 3 0 m L a T e 4 1 0 3 7 ( 4 ) 3 2 7 3 ( 3 ) 0 2 7 ( 2 ) N a o _ 7 3 ( 1 ) A g 1 _ 2 2 ( 1 ) C e T e 4 2 . 9 8 5 ( 3 ) 3 . 2 6 4 ( 3 ) 0 2 8 ( 2 ) K C u C e T e 4 2 . 9 7 2 ( 2 ) 3 . 2 7 5 ( 2 ) 0 3 3 ( 2 ) K C u L a T e 4 2 . 9 1 0 ( 4 ) 3 . 3 9 2 ( 4 ) 0 3 0 ( 2 ) K o , 7 1 ( 2 ) A g 1 . 2 9 ( 2 ) L a T e 4 2 . 9 2 9 ( 4 ) 3 4 4 7 ( 4 ) 0 2 8 ( 2 ) K A g C e T e 4 2 . 8 9 6 ( 9 ) 3 . 4 0 6 ( 9 ) 0 . 3 0 ( 2 ) I l I 7 . 0 ~ 1 6 . 5 - - , 7 fl ( 3 . 6 . 0 " . 1 v U ) \ U 5 . 5 - - 5 . 0 - s L l l l l l 0 . 0 0 0 . 1 5 0 . 3 0 0 . 4 5 0 . 6 0 0 . 7 5 E n e r g y ( e V ) F i g u r e 4 . 1 9 . T y p i c a l r o o m t e m p e r a t u r e i n f r a r e d a b s o r p t i o n s p e c t r u m N a o , 7 3 C u 1 , 2 2 C e T e 4 s h o w i n g e n e r g y g a p a t a r o u n d 0 . 2 7 e V . 2 2 4 o f 4 . 4 . C o n c l u s i o n s T h e A M R E T e 4 t o g e t h e r w i t h t h e R E T e 3 a r e e x c e l l e n t m o d e l s y s t e m s f o r fi m d a m e n t a l s t u d i e s o f C D W d i s t o r t i o n s b e c a u s e t h e i r s t r u c t u r e s a r e s i m p l e a n d e x h i b i t a w a v e m o d u l a t i o n a l o n g a s i n g l e a x i s d i r e c t i o n . T h e r e s u l t s r e p o r t e d h e r e s u g g e s t t h a t i n t e r a c t i o n s a l o n g t h e t h i r d , c r o s s - p l a n e d i m e n s i o n i n t h e q u a s i - t w o d i m e n s i o n a l s y s t e m s o f A M R E T e 4 a n d R E T e 3 p l a y a n i m p o r t a n t r o l e o n d e fi n i n g t h e C D W m o d u l a t i o n s . 2 5 T h e v a n d e r W a a l s g a p s i n R E T e 3 i n fl u e n c e b a n d d i s p e r s i o n w h i c h a l t e r s t h e F e r m i s u r f a c e n e s t i n g t h e r e b y c h a n g i n g t h e C D W c h a r a c t e r . I n t h i s r e g a r d t h e v a n d e r W a a l s g a p s i n R E T e 3 a r e n o t s i m p l e “ i n n o c e n t ” s p a c e r s . T h u s , w e w o u l d e x p e c t t h e a p p l i c a t i o n o f p r e s s u r e t o s t r o n g l y i n fl u e n c e t h e s e g a p s a n d g r e a t l y a f f e c t a n d e v e n s u p p r e s s t h e C D W . 2 2 5 T a b l e 4 . 3 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r u n d i s t o r t e d ( n o C D W ) K C u C e T e 4 . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 0 6 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ > 2 8 i g m a ( l ) ] R i n d i c e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t L a r g e s t d i f f . p e a k a n d h o l e K C u C e T e 4 7 5 3 . 1 6 1 0 0 . 0 ( 3 ) K 0 . 7 1 0 7 3 A T e t r a g o n a l P 4 / n m m a = 4 . 4 1 4 2 ( 6 ) A , a = 9 0 . 0 0 ° b = 4 . 4 1 4 2 ( 6 ) A , a = 9 0 . 0 0 ° c = 2 1 . 0 8 6 ( 4 ) A , y = 9 0 . 0 0 ° 4 1 0 . 8 6 ( 1 1 ) A 3 2 6 . 0 8 8 g / e m 3 2 2 . 3 7 8 m m " 6 2 8 0 . 1 5 x 0 . 1 0 x 0 . 0 1 m m 3 4 . 7 2 t o 2 9 . 0 6 0 - 5 < = h < = 6 , - 5 < = k < = 5 , - 2 8 < = l < = 2 8 2 5 4 8 3 7 9 [ R i m = 0 . 0 8 3 1 ] 9 6 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 3 7 9 / 0 / 2 0 1 . 0 9 7 R . , . . . = 0 . 0 2 7 4 , w R . . . , = 0 . 0 6 0 0 R , “ = 0 . 0 2 9 4 , w k , “ = 0 . 0 6 1 0 0 . 0 0 3 1 ( 6 ) 2 . 5 3 4 a n d - 1 7 7 3 e . A ' 3 R = Z I I F O I ' I F C H / E l F O I , W R = { z l q u O I Z ' I F C | 2 ) 2 ] / 2 [ W ( I F O I K ) ] } W a n d W ' - = 1 / [ O ' 2 ( F 0 2 ) + ( 0 . 0 1 9 9 P ) 2 + 6 . 3 4 3 8 P ] w h e r e P = ( F 0 2 + 2 F c z ) / 3 2 2 6 T a b l e 4 . 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r K A g C e T e 4 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 3 0 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m m a n d T m c o e f f i c i e n t s L a r g e s t d i f f . p e a k a n d h o l e K A g C e T e 4 7 9 7 . 5 1 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A M o n o c l i n i c P m ( 0 [ 3 1 / 2 ) 0 a = 4 . 4 4 4 5 ( 9 ) A , a = 9 0 ° b = 4 . 4 8 0 0 ( 8 ) A , B = 9 0 ° c = 2 1 . 3 9 8 ( 4 ) A , y = 9 0 ° 0 . 3 3 5 8 ( 1 0 ) h ’ + 1 / 2 c ' 4 2 6 . 0 7 ( 1 4 ) A 3 2 6 . 2 1 4 g / c m 3 2 1 . 3 9 1 m m " 6 6 4 0 . 4 0 x 0 . 0 6 x 0 . 0 1 m m 3 1 . 5 9 t o 2 9 . 3 0 0 - 6 < = h < = 6 , - 6 < = k < = 5 , - 2 9 < = l < = 2 9 , - 1 < = m < = 1 9 8 8 1 ( 2 6 9 4 m a i n + 7 1 8 7 s a t e l l i t e s ) 5 3 1 2 ( 1 6 9 8 m a i n + 3 6 1 4 s a t e l l i t e s ) [ R i m = 0 . 1 0 7 2 ] 9 6 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 5 3 1 2 / 0 / 1 9 3 2 . 5 0 R . , , = 0 . 0 9 1 6 , w R o b s = 0 . 2 1 6 4 R . , l l = 0 . 1 4 6 1 , w k , “ = 0 . 2 2 6 0 R . , , = 0 . 0 8 2 4 , w R . . . , = 0 . 2 1 0 4 R , " = 0 . 0 9 2 3 , w R . . . l = 0 . 2 1 4 2 R o b , = 0 . 1 4 1 1 , w a o b , = 0 . 2 4 9 8 R . , l l = 0 . 3 1 8 3 , w k , " = 0 . 2 8 5 5 0 . 0 0 0 8 5 ( 8 ) 0 . 1 6 7 6 a n d 0 . 9 1 4 3 8 . 2 5 a n d - 7 7 4 e . A ' 3 R = Z I I F e l - I F e I I / l e . | . w R = { E l w a F o F - I F c | 2 ) 2 ] / 2 [ W ( | F o | ‘ ) ] ) 1 ” a n d w = 1 / ( o ’ ( 1 ) + 0 . 0 0 1 6 1 2 ) 2 2 7 T a b l e 4 . 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K A g C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x y 2 O c c u p a n c y U e q C e [ l ] 0 0 5 0 0 0 4 0 1 0 1 2 2 ( 1 ) s i n , 1 - 8 9 ( 8 ) - 3 ( 4 ) 2 ( 2 ) c o s , 1 - 2 8 ( 3 ) 8 ( 1 1 ) 1 ( 1 ) C e [ 2 ] 0 5 0 1 3 ( 5 ) 0 5 9 3 4 ( 1 ) 1 1 5 ( 1 ) s i n , 1 1 0 1 ( 8 ) - 2 ( 3 ) 1 ( 2 ) c o s , 1 - 3 1 ( 2 ) - 8 ( 1 0 ) 0 ( 1 ) T e [ 1 ] 0 5 2 5 0 ( 9 ) 0 9 1 6 9 ( 2 ) 1 2 7 ( 1 ) s i n , 1 - 1 3 ( 3 ) - 1 2 ( 1 2 ) 0 ( 1 ) c o s , 1 4 9 ( 1 0 ) - 3 ( 3 ) - 1 ( 3 ) T e [ 2 ] 0 2 7 2 ( 9 ) 5 0 0 0 7 8 3 ( 3 ) 1 3 2 ( 1 ) s i n , 1 1 ( 2 ) 5 ( 1 3 ) 0 ( 1 ) c o s , 1 3 ( 9 ) - 1 ( 3 ) 1 ( 3 ) T e [ 3 ] 0 5 0 1 6 ( 1 0 ) 0 4 4 0 6 ( 3 ) 1 2 1 ( 1 ) s i n , 1 - 1 0 ( 9 ) 3 ( 2 ) - 3 ( 3 ) c o s , 1 - 2 ( 2 ) - 1 3 ( 1 2 ) 0 ( 1 ) T e [ 4 ] 0 1 0 0 2 2 ( 1 0 ) 5 0 0 0 5 5 2 9 ( 2 ) 1 1 5 ( 1 ) s i n , 1 - 4 0 ( 1 0 ) 1 ( 2 ) 2 ( 3 ) c o s , 1 7 ( 2 ) 5 ( 1 2 ) 0 ( 1 ) T e [ 5 ] 0 5 1 4 4 ( 1 1 ) 5 0 0 0 2 8 3 3 ( 2 ) 1 2 5 ( 1 ) s i n , 1 - 2 1 6 ( 1 1 ) 4 4 ( 1 2 ) - 5 ( 3 ) c o s , 1 - 1 7 5 ( 9 ) - 5 5 ( 1 5 ) - 4 ( 2 ) T e [ 6 ] 0 1 1 3 ( 1 2 ) 0 2 8 2 6 ( 2 ) 1 2 7 ( 1 ) s i n , 1 2 1 7 ( 1 2 ) - 3 8 ( 1 3 ) - 1 ( 3 ) c o s , 1 1 7 7 ( 1 0 ) 4 7 ( 1 5 ) - l ( 2 ) T e [ 7 ] 0 5 1 1 7 ( 1 3 ) 5 0 0 0 7 1 1 2 ( 3 ) 1 2 4 ( 1 ) s i n , 1 - 3 8 6 ( 9 ) - 4 2 ( 1 2 ) 1 ( 3 ) c o s , 1 3 0 1 ( 7 ) - 5 4 ( 1 6 ) - 1 ( 2 ) T e [ 8 ] 0 1 5 9 ( 1 2 ) 0 7 1 1 1 ( 3 ) 1 2 1 ( 1 ) s i n , 1 2 9 7 ( 8 ) 7 8 ( 1 1 ) - 7 ( 3 ) c o s , 1 - 2 3 2 ( 7 ) 1 0 0 ( 1 4 ) 5 ( 2 ) 2 2 8 T a b l e 4 . 5 . ( C o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K A g C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . K [ l ] 0 5 3 2 5 ( 2 0 ) 0 1 4 4 1 ( 6 ) 2 4 ( 3 ) s i n , 1 5 0 ( 1 3 ) - 1 5 ( 4 0 ) 1 0 ( 4 ) c o s , 1 1 0 5 ( 3 0 ) 1 1 ( 1 7 ) 2 1 ( 8 ) K [ 2 ] 0 3 4 5 ( 2 0 ) 5 0 0 0 8 4 5 4 ( 5 ) 2 4 ( 3 ) s i n , 1 1 5 ( 2 0 ) 5 5 ( 4 0 ) 8 ( 4 ) c o s , 1 - 5 ( 4 0 ) 3 5 ( 2 0 ) - 1 5 ( 8 ) A g [ l ] 0 3 2 2 ( 1 3 ) 0 9 9 6 7 ( 3 ) 3 2 ( 1 ) s i n , 1 0 0 0 c o s , 1 0 0 0 A g [ 2 ] 0 5 3 0 6 ( 1 2 ) 5 0 0 0 9 9 6 1 ( 3 ) 3 0 ( 1 ) s i n , 1 0 0 0 c o s , 1 0 0 0 ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 4 . 6 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K A g C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 C e [ l ] 0 2 7 ( 1 ) 2 3 ( 2 ) 1 6 ( 1 ) 0 - 3 ( 1 ) 0 s i n , 1 - 1 ( 2 ) - 2 ( 3 ) 2 ( 2 ) - 1 ( 1 ) 0 ( 2 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 3 ( 1 ) 0 ( 1 ) 1 ( 2 ) C e [ 2 ] 0 5 ( 1 ) 6 ( 1 ) 3 5 ( 1 ) 0 - l ( 1 ) 0 s i n , 1 2 ( 2 ) 1 ( 2 ) - 4 ( 3 ) 1 ( 1 ) 1 ( 2 ) 0 ( 1 ) C O S , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 2 ( 1 ) 0 ( 1 ) 0 ( 2 ) T e [ 1 ] 0 2 5 ( 2 ) 2 5 ( 2 ) 3 1 ( 2 ) 0 0 ( 1 ) 0 s i n , 1 0 ( 1 ) 1 ( 1 ) - 1 ( 1 ) - 4 ( 2 ) 0 ( 1 ) 0 ( 2 ) c o s , 1 - l ( 2 ) - 3 ( 3 ) 3 ( 3 ) - 1 ( 1 ) - 1 ( 2 ) 0 ( 1 ) T e [ 2 ] 0 2 7 ( 2 ) 2 8 ( 2 ) 4 1 ( 2 ) 0 - 5 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 2 ( 2 ) 0 ( 1 ) 0 ( 3 ) C O S , 1 2 ( 2 ) - 1 ( 3 ) 3 ( 4 ) - 1 ( 1 ) - 2 ( 2 ) 0 ( 1 ) T e [ 3 ] 0 1 6 ( 1 ) 1 7 ( 2 ) 3 1 ( 2 ) 0 - 1 ( 1 ) 0 s i n , 1 1 ( 2 ) 2 ( 3 ) - 6 ( 3 ) 0 ( 1 ) - 1 ( 2 ) 1 ( 1 ) C O S , 1 0 ( 1 ) 0 ( 1 ) - l ( 1 ) - 1 ( 1 ) 0 ( 1 ) - 3 ( 2 ) 2 2 9 T a b l e 4 . 6 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K A g C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 4 ] 0 1 6 ( 1 ) 1 3 ( 2 ) 1 8 ( 1 ) 0 - 3 ( 1 ) 0 s i n , 1 - l ( 2 ) - 1 ( 3 ) 4 ( 3 ) 0 ( 1 ) - l ( 2 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) - 2 ( 2 ) 0 ( 1 ) - 1 ( 2 ) T e [ 5 ] 0 4 4 ( 2 ) 2 2 ( 2 ) 9 ( 1 ) 0 - 3 ( 1 ) 0 s i n , 1 8 ( 3 ) 0 ( 3 ) ~ 1 0 ( 2 ) - 4 ( 2 ) - 2 ( 2 ) 4 ( 2 ) c o s , 1 6 ( 2 ) 0 ( 3 ) - 8 ( 2 ) 5 ( 2 ) - 2 ( 2 ) - 4 ( 2 ) T e [ 6 ] 0 4 7 ( 2 ) 2 7 ( 2 ) 6 ( 1 ) 0 - 4 ( 1 ) 0 s i n , 1 - 6 ( 3 ) - 3 ( 4 ) - 1 ( 2 ) - 8 ( 2 ) - 4 ( 2 ) 4 ( 2 ) c o s , 1 - 5 ( 2 ) - 2 ( 3 ) - 1 ( 2 ) 1 0 ( 2 ) - 3 ( 2 ) - 4 ( 2 ) T e [ 7 ] 0 9 ( 1 ) 1 3 ( 2 ) 4 9 ( 2 ) 0 - l ( l ) 0 s i n , 1 8 ( 2 ) 1 ( 3 ) - l ( 3 ) - 3 ( 1 ) - 2 ( 2 ) 1 ( 2 ) c o s , 1 - 6 ( 2 ) 0 ( 2 ) 1 ( 2 ) — 4 ( 2 ) 2 ( 2 ) 2 ( 3 ) T e [ 8 ] 0 1 0 ( 1 ) 1 1 ( 2 ) 4 4 ( 2 ) 0 - 2 ( 1 ) 0 s i n , 1 - 4 ( 2 ) 0 ( 3 ) 8 ( 3 ) 5 ( 1 ) 1 ( 2 ) 0 ( 2 ) c o s , 1 3 ( 2 ) 0 ( 2 ) - 6 ( 2 ) 7 ( 2 ) - 1 ( 2 ) 0 ( 2 ) K [ l ] 0 1 5 ( 4 ) 1 8 ( 6 ) 3 9 ( 7 ) 0 3 ( 3 ) 0 s i n , 1 - 1 ( 2 ) 3 ( 4 ) - 1 2 ( 5 ) - l ( 4 ) 1 ( 2 ) - 2 ( 7 ) c o s , 1 - 3 ( 5 ) 5 ( 8 ) - 2 4 ( 1 0 ) 0 ( 2 ) 2 ( 5 ) 1 ( 3 ) K [ 2 ] 0 3 0 ( 5 ) 3 0 ( 6 ) 1 0 ( 4 ) 0 2 ( 3 ) 0 s i n , 1 - 4 ( 4 ) - 7 ( 5 ) 9 ( 4 ) 1 2 ( 6 ) 0 ( 3 ) 0 ( 7 ) c o s , 1 8 ( 8 ) 1 2 ( 1 0 ) - 1 8 ( 7 ) 7 ( 3 ) 0 ( 6 ) 0 ( 4 ) A g [ l ] 0 3 5 ( 2 ) 3 1 ( 3 ) 3 0 ( 2 ) 0 - 1 ( 1 ) 0 s i n , 1 0 0 0 0 0 0 c o s , 1 0 0 0 0 0 0 A g [ 2 ] 0 2 9 ( 2 ) 2 7 ( 2 ) 3 4 ( 2 ) 0 1 ( 1 ) 0 s i n , 1 0 0 0 0 0 0 c o s , 1 0 0 0 0 0 0 2 3 0 T a b l e 4 . 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K A g C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e C e [ l ] - T e [ 3 ] x 4 3 . 2 6 3 ( 6 ) 3 . 2 3 7 ( 6 ) 3 . 2 8 8 ( 6 ) C e [ l ] - T e [ 4 ] 3 . 2 5 2 ( 7 ) 3 . 2 5 0 ( 9 ) 3 . 2 5 4 ( 9 ) C e [ l ] - T e [ 5 ] 3 . 3 1 8 ( 7 ) 3 . 2 5 0 ( 8 ) 3 . 3 8 5 ( 8 ) C e [ l ] - T e [ 5 ] 3 . 4 0 2 ( 7 ) 3 . 3 6 1 ( 8 ) 3 . 4 4 4 ( 8 ) C e [ l ] - T e [ 6 ] x 2 3 . 3 8 3 ( 7 ) 3 . 3 6 8 ( 7 ) 3 . 3 9 5 ( 7 ) C e [ 2 ] - T e [ 3 ] 3 . 2 6 8 ( 8 ) 3 . 2 6 0 ( 1 0 ) 3 . 2 7 6 ( 1 0 ) C e [ 2 ] - T e [ 4 ] x 4 3 . 2 7 0 ( 6 ) 3 . 2 3 0 ( 5 ) 3 . 3 0 8 ( 5 ) C e [ 2 ] - T e [ 7 ] x 2 3 . 3 7 7 ( 8 ) 3 . 3 5 6 ( 9 ) 3 . 3 9 2 ( 8 ) C e [ 2 ] - T e [ 8 ] 3 . 3 1 6 ( 8 ) 3 . 2 2 3 ( 9 ) 3 . 4 1 2 ( 9 ) C e [ 2 ] - T e [ 8 ] 3 . 4 0 4 ( 8 ) 3 . 3 3 8 ( 9 ) 3 . 4 6 9 ( 9 ) T e [ 1 ] - K [ 2 ] x 2 3 . 4 8 1 ( 1 7 ) 3 . 4 4 3 ( 1 7 ) 3 . 5 2 0 ( 1 7 ) T e [ 1 ] - A g [ l ] 2 . 7 7 6 ( 8 ) 2 . 7 5 8 ( 9 ) 2 . 7 9 6 ( 9 ) T e [ 1 ] - A g [ l ] 2 . 8 2 7 ( 8 ) 2 . 8 1 0 ( 9 ) 2 . 8 4 4 ( 9 ) T e [ 1 ] - A g [ 2 ] x 2 2 . 8 0 8 ( 6 ) 2 . 8 0 4 ( 7 ) 2 . 8 1 3 ( 7 ) T e [ 2 ] - K [ l ] x 4 3 . 4 4 2 ( 1 5 ) 3 . 4 2 8 ( 1 5 ) 3 . 4 5 5 ( 1 5 ) T e [ 2 ] - A g [ l ] x 2 2 . 8 4 0 ( 7 ) 2 . 8 3 9 ( 7 ) 2 . 8 4 2 ( 7 ) T e [ 2 ] - A g [ 2 ] 2 . 8 2 3 ( 8 ) 2 . 8 2 1 ( 9 ) 2 . 8 2 5 ( 9 ) T e [ 2 ] - A g [ 2 ] 2 . 8 4 6 ( 8 ) 2 . 8 4 6 ( 9 ) 2 . 8 4 6 ( 9 ) T e [ 5 ] - T e [ 6 ] x 3 3 . 1 6 6 ( 9 ) 3 . 0 1 4 ( 9 ) 3 . 3 2 2 ( 9 ) T e [ 5 ] - T e [ 6 ] 3 . 1 4 7 ( 9 ) 2 . 9 9 2 ( 9 ) 3 . 3 0 5 ( 9 ) T e [ 7 ] - T e [ 8 ] x 2 3 . 1 4 5 ( 9 ) 2 . 8 9 6 ( 9 ) 3 . 4 0 2 ( 9 ) T e [ 7 ] - T e [ 8 ] x 2 3 . 1 7 6 ( 9 ) 2 . 9 4 9 ( 9 ) 3 . 4 0 6 ( 9 ) T e [ 7 ] - K [ 2 ] 3 . 5 7 3 ( 1 9 ) 3 . 4 7 ( 2 ) 3 . 6 8 ( 2 ) A g [ l ] - A g [ 2 ] x 4 3 . 1 6 0 ( 6 ) 3 . 1 6 0 ( 6 ) 3 . 1 6 0 ( 6 ) T a b l e 4 . 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K A g C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 3 ] - C e [ l ] - T e [ 3 ] x 2 8 6 . 7 3 ( 1 3 ) 8 5 . 6 4 ( l 4 ) 8 7 . 8 1 ( 1 4 ) T e [ 3 ] - C e [ l ] - T e [ 3 ] x 4 8 5 . 7 0 ( 1 4 ) 8 5 . 5 0 ( 1 6 ) 8 5 . 9 1 ( 1 6 ) T e [ 3 ] - C e [ l ] - T e [ 3 ] x 4 1 4 9 . 9 ( 2 ) 1 4 9 . 6 ( 2 ) 1 5 0 . 2 ( 2 ) T e [ 3 ] - C e [ l ] - T e [ 4 ] x 4 7 5 . 0 4 ( 1 6 ) 7 4 . 7 1 ( 1 6 ) 7 5 . 3 7 ( l 6 ) 2 3 1 T a b l e 4 . 8 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K A g C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 3 ] - C e [ l ] - T e [ 5 ] x 2 T e [ 3 ] - C e [ l ] - T e [ 5 ] x 2 T e [ 3 ] - C e [ l ] - T e [ 6 ] x 2 T e [ 3 ] - C e [ l ] - T e [ 6 ] x 2 T e [ 3 ] - C e [ l ] - T e [ 3 ] x 2 T e [ 3 ] - C e [ l ] - T e [ 5 ] x 2 T e [ 3 ] - C e [ l ] - T e [ 5 ] x 2 T e [ 3 ] - C e [ l ] - T e [ 6 ] x 2 T e [ 3 ] - C e [ l ] - T e [ 6 ] x 2 T e [ 4 ] - C e [ l ] - T e [ 5 ] T e [ 4 ] - C e [ l ] - T e [ 5 ] T e [ 4 ] - C e [ l ] - T e [ 6 ] x 2 T e [ 5 ] - C e [ l ] - T e [ 5 ] x 2 T e [ 5 ] - C e [ l ] - T e [ 6 ] x 2 T e [ 5 ] - C e [ l ] - T e [ 6 ] x 2 T e [ 6 ] - C e [ l ] - T e [ 6 ] x 2 T e [ 3 ] - C e [ 2 ] - T e [ 4 ] x 4 T e [ 3 ] - C e [ 2 ] - T e [ 7 ] x 2 T e [ 3 ] - C e [ 2 ] - T e [ 8 ] T e [ 3 ] - C e [ 2 ] - T e [ 8 ] T e [ 4 ] - C e [ 2 ] - T e [ 4 ] x 4 T e [ 4 ] - C e [ 2 ] - T e [ 4 ] x 4 T e [ 4 ] - C e [ 2 ] - T e [ 4 ] x 4 T e [ 4 ] - C e [ 2 ] - T e [ 7 ] x 2 T e [ 4 ] - C e [ 2 ] - T e [ 7 ] x 2 T e [ 4 ] - C e [ 2 ] - T e [ 8 ] x 2 T e [ 4 ] - C e [ 2 ] - T e [ 8 ] x 2 T e [ 4 ] - C e [ 2 ] - T e [ 7 ] x 2 T e [ 4 ] - C e [ 2 ] - T e [ 7 ] x 2 T e [ 4 ] - C e [ 2 ] - T e [ 8 ] x 2 T e [ 4 ] - C e [ 2 ] - T e [ 8 ] x 2 T e [ 7 ] - C e [ 2 ] - T e [ 7 ] x 2 T e [ 7 ] - C e [ 2 ] - T e [ 8 ] x 4 T e [ 8 ] - C e [ 2 ] - T e [ 8 ] x 2 7 5 . 8 7 0 7 ) 1 3 0 . 4 6 ( 1 8 ) 7 5 . 5 5 0 7 ) 1 3 1 . 2 6 0 9 ) 8 6 . 3 9 ( 1 2 ) 1 2 9 . 8 2 ( 1 8 ) 7 4 . 6 0 ( 1 6 ) 7 4 . 3 6 ( 1 7 ) 1 2 9 . 6 1 0 8 ) 1 3 9 . 5 8 0 8 ) 1 3 7 . 6 1 0 7 ) 1 3 8 . 4 6 0 7 ) 8 2 . 8 0 0 9 ) 5 6 . 0 4 0 7 ) 5 5 . 6 3 0 7 ) 8 2 . 9 7 0 7 ) 7 4 . 6 7 0 7 ) 1 3 8 . 2 5 0 7 ) 1 3 9 . 4 6 0 9 ) 1 3 7 . 7 4 0 9 ) 8 6 . 5 0 0 4 ) 8 5 . 5 6 0 4 ) 1 4 9 . 3 ( 2 ) 7 5 . 6 1 0 7 ) 1 3 1 . 4 1 0 9 ) 7 6 . 1 0 0 7 ) 1 3 0 . 6 9 0 7 ) 7 4 . 5 6 0 7 ) 1 2 9 . 9 9 0 9 ) 1 2 9 . 9 8 0 7 ) 7 4 . 8 5 0 6 ) 8 3 . 3 ( 2 ) 5 6 . 0 2 0 7 ) 8 2 . 8 ( 2 ) 7 5 . 4 0 0 5 ) 1 2 9 . 3 9 0 7 ) 7 3 . 8 1 0 7 ) 1 2 8 . 7 7 0 6 ) 8 5 . 7 2 0 4 ) 1 2 9 . 1 3 0 8 ) 7 4 . 0 4 0 7 ) 7 2 . 6 7 0 8 ) 1 2 6 . 9 2 0 7 ) 1 3 9 . 1 ( 2 ) 1 3 6 . 8 ( 2 ) 1 3 8 . 1 2 0 3 ) 8 2 . 4 ( 2 ) 5 3 . 4 1 0 7 ) 5 3 . 1 1 0 7 ) 8 2 . 1 2 0 8 ) 7 4 . 1 9 0 7 ) 1 3 7 . 9 6 0 4 ) 1 3 9 . 0 ( 2 ) 1 3 6 . 9 ( 2 ) 8 5 . 2 1 0 4 ) 8 5 . 4 8 0 4 ) 1 4 9 . 2 ( 2 ) 7 2 . 7 6 0 8 ) 1 2 7 . 5 0 0 9 ) 7 5 . 0 7 0 5 ) 1 2 9 . 2 6 0 6 ) 7 1 . 8 7 0 8 ) 1 2 5 . 8 8 0 9 ) 1 2 8 . 5 9 0 8 ) 7 3 . 9 1 0 7 ) 8 2 . 4 ( 2 ) 5 1 . 6 5 0 6 ) 8 2 . 4 ( 2 ) 7 6 . 3 6 0 6 ) 1 3 1 . 5 2 0 7 ) 7 7 . 2 4 0 7 ) 1 3 3 . 7 3 0 7 ) 8 7 . 0 7 0 4 ) 1 3 0 . 4 8 ( 1 8 ) 7 5 . 1 5 0 7 ) 7 6 . 0 9 0 8 ) 1 3 2 . 3 0 0 7 ) 1 4 0 . 0 ( 2 ) 1 3 8 . 4 ( 2 ) 1 3 8 . 8 3 0 6 ) 8 3 . 2 ( 2 ) 5 8 . 6 3 0 7 ) 5 8 . 2 0 0 7 ) 8 3 . 7 2 0 8 ) 7 5 . 1 7 0 8 ) 1 3 8 . 7 7 0 6 ) 1 3 9 . 9 ( 2 ) 1 3 8 . 6 ( 2 ) 8 7 . 8 3 0 5 ) 8 5 . 6 6 0 4 ) 1 4 9 . 4 6 0 9 ) 7 8 . 4 8 0 8 ) 1 3 5 . 3 ( 2 ) 7 7 . 1 1 0 6 ) 1 3 2 . 0 9 0 6 ) 7 7 . 2 2 0 8 ) 1 3 4 . 0 ( 2 ) 1 3 1 . 3 7 0 8 ) 7 5 . 8 2 0 7 ) 8 3 . 9 ( 2 ) 6 0 . 4 6 0 7 ) 8 3 . 1 ( 2 ) 2 3 2 T a b l e 4 . 8 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K A g C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . K [ 2 ] - T e [ 1 ] - K [ 2 ] x 2 K [ 2 ] - T e [ 1 ] - K [ 2 ] x 2 K [ 2 ] - T e [ 1 ] - K [ 2 ] x 2 K [ 2 ] - T e [ 1 ] - A g [ 1 ] x 2 K [ 2 ] - T e [ 1 ] - A g [ 1 ] x 2 K [ 2 ] - T e [ 1 ] - A g [ 2 ] x 2 K [ 2 ] - T e [ 1 ] - A g [ 2 ] x 2 A g [ 1 ] - T e [ 1 ] - A g [ 1 ] x 2 A g [ 1 ] - T e [ 1 ] - A g [ 2 ] x 2 A g [ 1 ] - T e [ 1 ] - A g [ 2 ] x 2 A g [ 2 ] - T e [ 1 ] — A g [ 2 ] x 2 K [ 1 ] - T e [ 2 ] - K [ 1 ] x 4 K [ 1 ] - T e [ 2 ] - K [ 1 ] x 4 K [ 1 ] - T e [ 2 ] - K [ l ] x 4 K [ l ] - T e [ 2 ] - A g [ 1 ] x 4 K [ 1 ] - T e [ 2 ] - A g [ l ] x 2 K [ l ] - T e [ 2 ] - A g [ 2 ] x 2 K [ l ] - T e [ 2 ] - A g [ 2 ] x 4 K [ l ] - T e [ 2 ] - A g [ 1 ] x 2 K [ l ] - T e [ 2 ] - A g [ 2 ] x 2 A g [ 1 ] - T e [ 2 ] - A g [ l ] x 2 A g [ l ] - T e [ 2 ] - A g [ 2 ] x 2 A g [ l ] - T e [ 2 ] - A g [ 2 ] x 2 A g [ 2 ] - T e [ 2 ] - A g [ 2 ] x 2 C e [ 1 ] - T e [ 3 ] - C e [ 1 ] x 2 C e [ l ] - T e [ 3 ] - C e [ 1 ] x 4 C e [ l ] - T e [ 3 ] - C e [ 1 ] x 4 C e [ l ] - T e [ 3 ] - C e [ 2 ] x 4 C e [ 1 ] - T e [ 3 ] - C e [ 1 ] x 2 C e [ l ] - T e [ 4 ] - C e [ 2 ] x 4 C e [ 2 ] - T e [ 4 ] - C e [ 2 ] x 4 C e [ 2 ] - T e [ 4 ] - C e [ 2 ] x 4 C e [ 2 ] - T e [ 4 ] - C e [ 2 ] x 4 C e [ 1 ] - T e [ 5 ] - C e [ 1 ] x 2 8 0 . 1 ( 4 ) 7 8 . 6 ( 4 ) 1 2 8 . 2 ( 4 ) 7 7 . 1 ( 3 ) 1 3 9 . 9 ( 3 ) 7 6 . 0 ( 3 ) 1 4 1 . 6 ( 3 ) 1 0 5 . 0 ( 3 ) 6 8 . 6 8 0 8 ) 6 8 . 2 2 0 8 ) 1 0 5 . 8 ( 3 ) 8 1 . 2 ( 4 ) 8 0 . 0 ( 3 ) 1 3 1 . 9 ( 5 ) 7 5 . 1 ( 3 ) 1 4 0 . 4 ( 3 ) 7 5 . 8 ( 3 ) 1 3 9 . 1 ( 3 ) 1 3 8 . 9 ( 3 ) 7 5 . 1 ( 3 ) 1 0 4 . 1 ( 3 ) 6 7 . 8 4 0 9 ) 6 7 . 2 9 0 9 ) 1 0 3 . 3 ( 3 ) 8 6 . 3 9 0 5 ) 8 5 . 7 0 0 2 ) 1 4 9 . 9 ( 3 ) 1 0 5 . 0 2 0 7 ) 8 6 . 7 3 0 5 ) 1 0 5 . 1 9 0 8 ) 8 6 . 3 5 0 5 ) 8 5 . 5 6 0 2 ) 1 4 9 . 3 ( 2 ) 8 2 . 8 0 0 8 ) 8 0 . 1 ( 4 ) 7 8 . 0 ( 4 ) 1 2 8 . 0 ( 4 ) 7 6 . 6 ( 3 ) 1 3 9 . 3 ( 3 ) 7 5 . 3 ( 3 ) 1 4 1 . 1 ( 3 ) 1 0 4 . 9 ( 3 ) 6 8 . 3 9 0 9 ) 6 7 . 9 9 0 9 ) 1 0 5 . 8 ( 3 ) 8 1 . 1 ( 4 ) 7 9 . 4 ( 3 ) 1 3 1 . 0 ( 5 ) 7 4 . 7 ( 3 ) 1 3 9 . 3 ( 3 ) 7 4 . 7 ( 3 ) 1 3 8 . 9 ( 3 ) 1 3 8 . 7 ( 3 ) 7 5 . 0 ( 3 ) 1 0 4 . 1 ( 3 ) 6 7 . 8 0 0 9 ) 6 7 . 2 6 0 8 ) 1 0 3 . 2 ( 3 ) 8 6 . 0 2 0 7 ) 8 5 . 5 0 ( 1 3 ) 1 4 9 . 5 ( 3 ) 1 0 4 . 5 0 0 6 ) 8 6 . 3 7 ( 1 7 ) 1 0 4 . 9 3 0 8 ) 8 5 . 3 2 0 7 ) 8 5 . 4 8 0 3 ) 1 4 9 . 1 ( 2 ) 8 2 . 4 2 0 8 ) 8 0 . 1 ( 4 ) 7 9 . 2 ( 4 ) 1 2 8 . 4 ( 4 ) 7 7 . 5 ( 3 ) 1 4 0 . 5 ( 3 ) 7 6 . 7 ( 3 ) 1 4 2 . 1 ( 3 ) 1 0 5 . 0 ( 3 ) 6 8 . 9 6 0 9 ) 6 8 . 4 ( 2 ) 1 0 5 . 9 ( 3 ) 8 1 . 3 ( 4 ) 8 0 . 7 ( 3 ) 1 3 2 . 8 ( 5 ) 7 5 . 6 ( 3 ) 1 4 1 . 4 ( 3 ) 7 7 . 0 ( 3 ) 1 3 9 . 3 ( 3 ) 1 3 9 . 2 ( 3 ) 7 5 . 1 ( 3 ) 1 0 4 . 2 ( 3 ) 6 7 . 8 8 0 9 ) 6 7 . 3 1 0 8 ) 1 0 3 . 3 ( 3 ) 8 6 . 7 7 0 7 ) 8 5 . 9 1 ( 1 3 ) 1 5 0 . 2 ( 3 ) 1 0 5 . 5 3 0 6 ) 8 7 . 0 7 0 7 ) 1 0 5 . 4 5 0 8 ) 8 7 . 3 7 0 7 ) 8 5 . 6 6 0 2 ) 1 4 9 . 6 ( 2 ) 8 3 . 1 6 0 8 ) 2 3 3 T a b l e 4 . 8 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K A g C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . C e [ l ] - T e [ 5 ] - T e [ 6 ] x 2 C e [ l ] - T e [ 5 ] - T e [ 6 ] x 2 C e [ l ] - T e [ 5 ] - T e [ 6 ] x 2 C e [ l ] - T e [ 5 ] - T e [ 6 ] x 2 T e [ 6 ] - T e [ 5 ] - T e [ 6 ] x 2 T e [ 6 ] - T e [ 5 ] - T e [ 6 ] x 4 T e [ 6 ] - T e [ 5 ] - T e [ 6 ] x 4 T e [ 6 ] - T e [ 5 ] - T e [ 6 ] x 2 C e [ l ] - T e [ 6 ] - C e [ 1 ] x 2 C e [ l ] - T e [ 6 ] - T e [ 5 ] x 2 C e [ l ] - T e [ 6 ] - T e [ 5 ] x 2 C e [ l ] - T e [ 6 ] - T e [ 5 ] x 2 C e [ l ] - T e [ 6 ] - T e [ 5 ] x 2 C e [ l ] - T e [ 6 ] - K [ 1 ] x 2 T e [ 5 ] - T e [ 6 ] - T e [ 5 ] x 2 T e [ 5 ] - T e [ 6 ] - T e [ 5 ] x 4 T e [ 5 ] - T e [ 6 ] - T e [ 5 ] x 4 T e [ 5 ] - T e [ 6 ] - K [ l ] x 2 T e [ 5 ] - T e [ 6 ] - T e [ 5 ] x 2 T e [ 5 ] - T e [ 6 ] - K [ l ] x 2 C e [ 2 ] - T e [ 7 ] - C e [ 2 ] x 2 C e [ 2 ] - T e [ 7 ] - T e [ 8 ] x 2 C e [ 2 ] - T e [ 7 ] - T e [ 8 ] x 2 C e [ 2 ] - T e [ 7 ] - T e [ 8 ] x 2 C e [ 2 ] - T e [ 7 ] - T e [ 8 ] x 2 C e [ 2 ] - T e [ 7 ] - K [ 2 ] x 4 T e [ 8 ] - T e [ 7 ] - T e [ 8 ] x 2 T e [ 8 ] - T e [ 7 ] - T e [ 8 ] x 4 T e [ 8 ] — T e [ 7 ] - T e [ 8 ] x 4 T e [ 8 ] - T e [ 7 ] - K [ 2 ] x 2 T e [ 8 ] - T e [ 7 ] - K [ 2 ] x 2 T e [ 8 ] - T e [ 7 ] - T e [ 8 ] x 2 T e [ 8 ] - T e [ 7 ] - K [ 2 ] x 2 T e [ 8 ] - T e [ 7 ] - K [ 2 ] x 2 6 1 . 9 1 0 8 ) 1 1 8 . 3 ( 2 ) 1 1 7 . 5 ( 2 ) 6 3 . 0 6 0 9 ) 9 0 . 2 ( 2 ) 8 9 . 4 ( 2 ) 1 7 6 . 8 ( 3 ) 9 0 . 9 ( 2 ) 8 2 . 9 2 0 7 ) 6 0 . 9 0 0 8 ) 1 1 7 . 2 ( 2 ) 6 2 . 4 7 0 8 ) 1 1 8 . 4 ( 2 ) 1 2 6 . 8 ( 3 ) 9 0 . 9 ( 2 ) 8 9 . 4 ( 2 ) 1 7 6 . 8 ( 3 ) 6 6 . 1 ( 3 ) 9 0 . 3 ( 2 ) 1 1 4 . 5 ( 3 ) 8 3 . 1 ( 2 ) 6 0 . 9 ( 2 ) 1 1 7 . 6 ( 3 ) 6 2 . 5 ( 2 ) 1 1 8 . 5 ( 3 ) 1 2 6 . 3 ( 4 ) 9 1 . 3 ( 2 ) 8 9 . 2 ( 2 ) 1 7 4 . 9 ( 3 ) 6 5 . 5 ( 3 ) 1 1 6 . 0 ( 4 ) 9 0 . 2 ( 2 ) 1 1 4 . 6 ( 4 ) 6 3 . 7 ( 3 ) 6 0 . 1 2 0 7 ) 1 1 7 . 7 ( 2 ) 1 1 5 . 9 ( 2 ) 6 0 . 8 3 0 8 ) 8 6 . 1 ( 2 ) 8 8 . 3 ( 2 ) 1 7 4 . 7 ( 3 ) 8 5 . 6 ( 2 ) 8 2 . 5 9 0 7 ) 5 9 . 7 7 0 8 ) 1 1 4 . 2 ( 2 ) 6 1 . 6 7 0 7 ) 1 1 5 . 0 ( 2 ) 1 2 4 . 2 ( 3 ) 8 6 . 9 ( 2 ) 8 8 . 3 ( 2 ) 1 7 4 . 6 ( 3 ) 6 4 . 0 ( 3 ) 8 4 . 8 ( 2 ) 1 1 3 . 9 ( 3 ) 8 2 . 9 ( 2 ) 5 9 . 2 0 0 8 ) 1 1 2 . 7 ( 3 ) 6 1 . 2 2 0 9 ) 1 1 2 . 7 ( 3 ) 1 2 1 . 3 ( 3 ) 8 4 . 9 ( 2 ) 8 7 . 6 ( 2 ) 1 7 1 . 5 ( 3 ) 6 1 . 7 ( 3 ) 1 1 4 . 3 ( 4 ) 8 1 . 5 ( 2 ) 1 1 4 . 1 ( 4 ) 6 0 . 2 ( 3 ) 6 3 . 7 2 0 9 ) 1 1 8 . 8 ( 2 ) 1 1 9 . 1 ( 2 ) 6 5 . 4 ( 2 ) 9 4 . 4 ( 3 ) 9 0 . 9 ( 2 ) 1 7 9 . 6 ( 3 ) 9 6 . 4 ( 3 ) 8 3 . l 6 ( 1 8 ) 6 2 . 1 7 0 8 ) 1 2 0 . 3 ( 3 ) 6 3 . 1 7 0 8 ) 1 2 1 . 7 ( 3 ) 1 2 9 . 3 ( 3 ) 9 5 . 1 ( 3 ) 9 0 . 9 ( 2 ) 1 7 9 . 5 ( 3 ) 6 8 . 2 ( 3 ) 9 5 . 8 ( 3 ) 1 1 5 . 0 ( 3 ) 8 3 . 3 ( 2 ) 6 2 . 9 ( 2 ) 1 2 2 . 3 ( 3 ) 6 3 . 5 ( 2 ) 1 2 4 . 3 ( 3 ) 1 3 1 . 1 ( 4 ) 9 8 . 0 ( 3 ) 9 1 . 5 ( 2 ) 1 8 0 6 9 . 3 ( 4 ) 1 1 7 . 9 ( 4 ) 9 9 . 4 ( 3 ) 1 1 4 . 9 ( 4 ) 6 7 . 4 ( 4 ) 2 3 4 T a b l e 4 . 8 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K A g C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . K [ 2 ] - T e [ 7 ] - K [ 2 ] C e [ 2 ] - T e [ 8 ] - C e [ 2 ] x 2 C e [ 2 ] - T e [ 8 ] - T e [ 7 ] x 2 C e [ 2 ] - T e [ 8 ] - T e [ 7 ] x 2 C e [ 2 ] - T e [ 8 ] - K [ 2 ] x 2 C e [ 2 ] - T e [ 8 ] - T e [ 7 ] x 2 C e [ 2 ] - T e [ 8 ] - T e [ 7 ] x 2 C e [ 2 ] - T e [ 8 ] - K [ 2 ] x 2 T e [ 7 ] - T e [ 8 ] - T e [ 7 ] x 2 T e [ 7 ] - T e [ 8 ] - T e [ 7 ] x 4 T e [ 7 ] - T e [ 8 ] - T e [ 7 ] x 4 T e [ 7 ] - T e [ 8 ] - K [ 2 ] x 2 T e [ 7 ] - T e [ 8 ] - K [ 2 ] x 2 T e [ 7 ] - T e [ 8 ] - T e [ 7 ] x 2 T e [ 7 ] - T e [ 8 ] - K [ 2 ] x 2 T e [ 7 ] - T e [ 8 ] - K [ 2 ] x 2 T e [ 2 ] - K [ l ] - T e [ 2 ] x 6 T e [ 2 ] - K [ l ] - T e [ 2 ] x 4 T e [ 2 ] - K [ l ] - T e [ 6 ] x 2 T e [ 2 ] - K [ l ] - T e [ 2 ] x 2 T e [ 2 ] - K [ l ] - T e [ 6 ] x 2 T e [ 1 ] - K [ 2 ] - T e [ 1 ] x 2 T e [ 1 ] - K [ 2 ] - T e [ 1 ] x 2 T e [ 1 ] - K [ 2 ] - T e [ 1 ] x 2 T e [ 1 ] - K [ 2 ] - T e [ 7 ] x 2 T e [ 1 ] - K [ 2 ] - T e [ 7 ] x 2 T e [ 1 ] - K [ 2 ] - T e [ 8 ] x 2 T e [ 1 ] - K [ 2 ] - T e [ 8 ] x 2 T e [ 7 ] - K [ 2 ] - T e [ 7 ] T e [ 7 ] - K [ 2 ] - T e [ 8 ] x 2 T e [ 1 ] - A g [ 1 ] - T e [ 1 ] x 2 T e [ 1 ] - A g [ 1 ] - T e [ 2 ] x 2 T e [ 1 ] - A g [ l ] - A g [ 2 ] x 2 T e [ 1 ] - A g [ l ] - A g [ 2 ] x 4 7 5 . 3 ( 4 ) 8 2 . 8 ( 2 ) 6 1 . 7 ( 2 ) 1 1 8 . 0 ( 3 ) 1 2 6 . 7 ( 3 ) 1 1 7 . 3 ( 3 ) 6 3 . 0 ( 2 ) 1 2 5 . 8 ( 3 ) 9 0 . 2 ( 2 ) 8 9 . 2 ( 2 ) 1 7 5 . 2 ( 3 ) 6 5 . 1 ( 3 ) 1 1 6 . 7 ( 4 ) 9 1 . 3 ( 2 ) 6 2 . 9 ( 3 ) 1 1 4 . 9 ( 4 ) 8 0 . 4 ( 3 ) 1 3 1 . 9 ( 6 ) 1 3 5 . 0 ( 5 ) 8 1 . 2 ( 4 ) 8 7 . 7 ( 3 ) 7 8 . 6 ( 3 ) 1 2 8 . 2 ( 5 ) 8 0 . 1 ( 4 ) 1 3 7 . 4 ( 5 ) 8 9 . 0 ( 4 ) 8 8 . 0 ( 4 ) 1 3 9 . 1 ( 5 ) 7 5 . 3 ( 4 ) 5 1 . 6 ( 3 ) 1 0 5 . 0 ( 3 ) 1 1 1 . 4 0 0 9 ) 5 5 . 6 0 0 6 ) 1 2 3 . 9 3 0 9 ) 7 4 . 4 ( 4 ) 8 2 . 4 ( 2 ) 5 9 . 1 4 ( 1 8 ) 1 1 7 . 1 ( 3 ) 1 2 3 . 6 ( 3 ) 1 1 4 . 3 ( 3 ) 5 9 . 5 1 0 8 ) 1 2 2 . 2 ( 3 ) 8 4 . 0 ( 2 ) 8 7 . 6 ( 2 ) 1 7 2 . 3 ( 3 ) 6 3 . 0 ( 3 ) 1 1 2 . 4 ( 3 ) 8 3 . 5 ( 2 ) 6 2 . 5 ( 3 ) 1 1 1 . 4 ( 3 ) 7 9 . 0 ( 4 ) 1 3 0 . 4 ( 6 ) 1 3 3 . 7 ( 4 ) 8 0 . 8 ( 4 ) 8 7 . 5 ( 3 ) 7 8 . 0 ( 3 ) 1 2 7 . 1 ( 5 ) 7 9 . 3 ( 4 ) 1 3 6 . 2 ( 5 ) 8 6 . 7 ( 4 ) 8 6 . 9 ( 4 ) 1 3 6 . 3 ( 4 ) 7 4 . 4 ( 4 ) 4 7 . 9 ( 3 ) 1 0 4 . 9 ( 3 ) 1 1 1 . 2 3 ( 1 8 ) 5 5 . 4 2 0 6 ) 1 2 3 . 7 4 0 9 ) 7 6 . 0 ( 4 ) 8 3 . 1 ( 2 ) 6 4 . 4 ( 2 ) 1 1 8 . 7 ( 3 ) 1 2 9 . 9 ( 3 ) 1 2 0 . 1 ( 3 ) 6 6 . 7 ( 2 ) 1 2 9 . 4 ( 3 ) 9 6 . 8 ( 3 ) 9 1 . 5 ( 2 ) 1 7 9 . 8 ( 3 ) 6 7 . 4 ( 3 ) 1 2 1 . 1 ( 4 ) 9 9 . 2 ( 3 ) 6 3 . 4 ( 3 ) 1 1 8 . 3 ( 4 ) 8 1 . 9 ( 4 ) 1 3 3 . 3 ( 7 ) 1 3 6 . 3 ( 4 ) 8 1 . 6 ( 4 ) 8 7 . 9 ( 3 ) 7 9 . 2 ( 3 ) 1 2 9 . 3 ( 5 ) 8 0 9 ( 4 ) 1 3 8 . 5 ( 5 ) 9 1 . 3 ( 5 ) 8 9 . 1 ( 4 ) 1 4 2 . 0 ( 5 ) 7 6 . 0 ( 4 ) 5 5 . 4 ( 3 ) 1 0 5 . 0 ( 3 ) 1 1 1 . 5 8 0 9 ) 5 5 . 7 9 0 6 ) 1 2 4 . 1 1 ( 1 9 ) T a b l e 4 . 8 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K A g C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 1 ] - A g [ 1 ] - T e [ 2 ] x 2 1 1 2 . 5 8 ( 1 9 ) 1 1 2 . 4 0 ( 1 8 ) 1 1 2 . 7 6 ( 1 8 ) T e [ 1 ] - A g [ l ] - A g [ 2 ] x 2 5 6 . 1 4 ( l 6 ) 5 5 . 9 7 ( 1 6 ) 5 6 . 3 0 ( 1 6 ) T e [ 2 ] - A g [ l ] — T e [ 2 ] x 2 1 0 4 . 1 ( 3 ) 1 0 4 . 1 ( 3 ) 1 0 4 . 1 ( 3 ) T e [ 2 ] - A g [ l ] - A g [ 2 ] x 2 5 5 . 8 1 ( 1 6 ) 5 5 . 7 8 ( 1 6 ) 5 5 . 8 5 ( 1 6 ) T e [ 2 ] - A g [ l ] - A g [ 2 ] x 2 1 2 3 . 8 ( 2 ) 1 2 3 . 8 ( 2 ) 1 2 3 . 8 ( 2 ) T e [ 2 ] - A g [ l ] - A g [ 2 ] x 2 5 6 . 4 4 ( l 6 ) 5 6 . 4 3 ( 1 6 ) 5 6 . 4 6 ( 1 6 ) T e [ 2 ] - A g [ l ] - A g [ 2 ] x 2 1 2 4 . 7 ( 3 ) 1 2 4 . 6 ( 3 ) 1 2 4 . 7 ( 3 ) A g [ 2 ] — A g [ l ] - A g [ 2 ] x 2 9 0 2 7 ( 1 8 ) 9 0 2 7 ( 1 8 ) 9 0 2 7 ( 1 8 ) A g [ 2 ] - A g [ l ] - A g [ 2 ] x 4 8 9 . 5 4 ( 1 0 ) 8 9 . 5 4 ( 1 0 ) 8 9 . 5 4 ( 1 0 ) A g [ 2 ] - A g [ l ] - A g [ 2 ] x 4 1 7 9 . 5 ( 3 ) 1 7 9 . 5 ( 3 ) 1 7 9 . 5 ( 3 ) A g [ 2 ] - A g [ l ] - A g [ 2 ] x 2 9 0 . 6 4 ( 1 8 ) 9 0 . 6 4 ( 1 8 ) 9 0 . 6 4 ( 1 8 ) T e [ 1 ] - A g [ 2 ] - T e [ 1 ] x 2 1 0 5 . 8 ( 3 ) 1 0 5 . 7 ( 3 ) 1 0 6 . 0 ( 3 ) T e [ 1 ] - A g [ 2 ] - T e [ 2 ] x 2 1 1 1 . 5 ( 2 ) 1 1 1 . 0 ( 2 ) 1 1 1 . 9 ( 2 ) T e [ 1 ] - A g [ 2 ] - T e [ 2 ] x 2 1 1 2 . 5 ( 2 ) 1 1 2 . 2 ( 2 ) 1 1 2 . 8 ( 2 ) T e [ 1 ] - A g [ 2 ] - A g [ l ] x 2 5 5 . 1 8 ( 1 6 ) 5 4 . 7 8 ( l 7 ) 5 5 . 6 0 ( 1 7 ) T e [ 1 ] - A g [ 2 ] - A g [ l ] x 2 1 2 4 . 3 ( 2 ) 1 2 3 . 9 ( 3 ) 1 2 4 . 7 ( 3 ) T e [ 1 ] - A g [ 2 ] - A g [ l ] x 2 5 6 . 1 8 ( 1 6 ) 5 5 . 8 0 ( 1 7 ) 5 6 . 5 5 ( 1 7 ) T e [ 1 ] - A g [ 2 ] - A g [ l ] x 2 1 2 5 . 0 ( 2 ) 1 2 4 . 6 ( 3 ) 1 2 5 . 4 ( 3 ) T e [ 2 ] - A g [ 2 ] - T e [ 2 ] x 2 1 0 3 . 3 ( 3 ) 1 0 3 . 2 ( 3 ) 1 0 3 . 3 ( 3 ) T e [ 2 ] - A g [ 2 ] - A g [ l ] x 4 5 6 2 7 ( 1 6 ) 5 6 2 3 ( 1 8 ) 5 6 . 3 1 ( 1 8 ) T e [ 2 ] - A g [ 2 ] - A g [ l ] x 4 1 2 3 . 5 ( 2 ) 1 2 3 . 5 ( 2 ) 1 2 3 . 5 ( 2 ) A g [ l ] - A g [ 2 ] - A g [ l ] x 2 9 0 . 6 4 ( 1 7 ) 9 0 . 6 4 ( 1 7 ) 9 0 . 6 4 ( 1 7 ) A g [ l ] - A g [ 2 ] - A g [ l ] x 4 8 9 . 5 4 ( 1 0 ) 8 9 . 5 4 ( 1 0 ) 8 9 . 5 4 ( 1 0 ) A g [ l ] - A g [ 2 ] - A g [ l ] x 4 1 7 9 . 5 ( 3 ) 1 7 9 . 5 ( 3 ) 1 7 9 . 5 ( 3 ) A g [ l ] - A g [ 2 ] - A g [ l ] x 2 9 0 2 7 ( 1 7 ) 9 0 2 7 ( 1 7 ) 9 0 2 7 ( 1 7 ) 2 3 6 T a b l e 4 . 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r K A g C e T e 4 a t 3 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f f i c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 2 4 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 o ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 s t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f f i c i e n t T m m a n d T m c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e K A g C e T e 4 7 9 7 . 5 3 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A M o n o c l i n i c P m ( O B l / 2 ) O a = 4 . 4 6 5 7 ( 9 ) A , a = 9 0 ° b = 4 . 4 9 2 7 ( 8 ) A , B = 9 0 ° c = 2 1 . 5 2 5 ( 4 ) A , y = 9 0 ° 0 . 3 3 8 1 ( 8 ) h ‘ + 1 / 2 c ‘ 4 3 1 . 8 5 0 4 ) A 3 2 6 . 1 3 1 g / c m 3 2 1 . 1 0 4 m m " ! 6 6 4 0 . 3 7 x 0 . 1 5 x 0 . 0 4 m m 3 1 . 8 9 t o 2 9 . 2 4 ° - 6 < = h < = 6 , - 6 < = k < = 5 , - 2 9 < = l < = 2 9 , - 1 < = m < = l 9 8 1 0 ( 2 5 7 7 m a i n + 7 2 3 3 s a t e l l i t e s ) 5 3 2 6 ( 1 6 5 7 m a i n + 3 6 6 9 s a t e l l i t 6 8 ) [ R i m = 0 . 0 8 9 0 ] 9 6 % F u l l — m a t r i x l e a s t - s q u a r e s o n F 2 5 3 2 6 / 0 / 1 9 3 2 . 1 3 R . , , = 0 . 0 8 0 0 , w R . . . , = 0 . 1 8 1 8 R , “ = 0 . 1 3 6 7 , w R . . . , " = 0 . 1 9 4 3 R o b , = 0 . 0 7 1 5 , w R o b , = 0 . 1 7 6 7 R , " = 0 . 0 8 1 8 , w R a n = 0 . 1 8 2 1 R o b s = 0 . 1 2 3 9 , w R o b s = 0 . 2 0 7 7 R 3 1 1 = 0 . 3 0 9 4 , w R , , u = 0 . 2 5 0 7 0 . 0 0 0 8 1 ( 8 ) 0 . 0 2 7 1 a n d 0 . 1 1 7 6 7 . 5 5 a n d 4 1 7 e . A ' 3 R = l e F o l - c h l l / 2 1 m , w R = { 2 [ w ( | F o | 2 - 0 : 4 6 2 ] / 2 0 . 7 0 0 1 6 1 ) " : a n d w = l / ( o Z ( I ) + 0 . 0 0 1 6 I Z ) 2 3 7 T a b l e 4 . 1 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K A g C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x y 2 O c c u p a n c y c h C e [ l ] 0 0 5 0 0 0 4 0 1 0 1 2 3 ( 1 ) s i n , 1 - 9 8 ( 6 ) 2 ( 3 ) 3 ( 2 ) c o s , 1 - 3 2 ( 2 ) - 7 ( 9 ) 1 ( 1 ) C e [ 2 ] 0 5 0 0 4 ( 4 ) 0 5 9 2 4 ( 1 ) 1 2 1 ( 1 ) s i n , 1 7 5 ( 7 ) - 2 ( 3 ) 4 ( 2 ) c o s , 1 - 2 2 ( 2 ) - 7 ( 8 ) - 1 ( 1 ) T e [ 1 ] 0 5 2 1 4 ( 9 ) 0 9 1 6 8 ( 3 ) 1 3 7 ( 1 ) s i n , 1 - 1 1 ( 2 ) - 7 ( 1 1 ) 0 ( 1 ) c o s , 1 4 3 ( 8 ) - 2 ( 3 ) - 2 ( 3 ) T e [ 2 ] 0 2 2 9 ( 9 ) 5 0 0 0 7 7 4 ( 3 ) 1 4 0 ( 1 ) s i n , 1 4 ( 2 ) 2 ( 1 1 ) 0 ( 1 ) c o s , 1 1 4 ( 8 ) 0 ( 3 ) 1 ( 3 ) T e [ 3 ] 0 5 0 1 5 ( 9 ) 0 4 4 1 2 ( 2 ) 1 2 3 ( 1 ) s i n , 1 1 7 ( 7 ) 0 ( 2 ) 1 ( 2 ) c o s , 1 3 ( 1 ) - 1 ( 9 ) 0 ( 1 ) T e [ 4 ] 0 1 0 0 1 4 ( 9 ) 5 0 0 0 5 5 2 9 ( 2 ) 1 2 0 ( 1 ) s i n , 1 6 ( 8 ) 0 ( 2 ) 0 ( 2 ) c o s , 1 - l ( l ) - 3 ( 1 0 ) 0 ( 1 ) T e [ 5 ] 0 5 1 1 8 ( 1 0 ) 5 0 0 0 2 8 3 9 ( 2 ) 1 3 0 ( 1 ) s i n , 1 - 2 0 6 ( 8 ) 4 2 ( 1 0 ) - 6 ( 2 ) c o s , 1 - 1 6 7 ( 7 ) - 5 2 ( 1 2 ) - 5 ( 2 ) T e [ 6 ] 0 1 1 0 ( 1 1 ) 0 2 8 3 7 ( 2 ) 1 3 1 ( 1 ) s i n , 1 1 9 6 ( 8 ) - 3 5 ( 1 0 ) - 1 ( 2 ) c o s , 1 1 5 8 ( 7 ) 4 3 ( 1 2 ) - 1 ( 2 ) T e [ 7 ] 0 5 1 0 0 ( 1 2 ) 5 0 0 0 7 1 0 8 ( 3 ) 1 2 8 ( 1 ) s i n , 1 - 4 0 9 ( 7 ) - 4 9 ( 1 1 ) - 6 ( 2 ) c o s , 1 3 1 9 ( 6 ) - 6 3 ( 1 4 ) 5 ( 2 ) T e [ 8 ] 0 1 3 3 ( 1 1 ) 0 7 1 0 1 ( 3 ) 1 2 8 ( 1 ) s i n , 1 2 9 8 ( 7 ) 6 7 ( 1 0 ) - 1 1 ( 2 ) c o s , 1 - 2 3 1 ( 6 ) 8 6 ( 1 3 ) 9 ( 2 ) 2 3 8 T a b l e 4 . 1 0 . ( C o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K A g C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . K [ l ] 0 5 2 5 5 ( 2 0 ) 0 1 4 5 8 ( 7 ) 3 7 ( 4 ) s i n , 1 - 2 4 ( 1 1 ) 2 5 ( 3 0 ) 6 ( 4 ) c o s , 1 - 4 5 ( 2 0 ) - 1 2 ( l 6 ) 1 2 ( 7 ) K [ 2 ] 0 2 7 5 ( 3 0 ) 5 0 0 0 8 4 6 2 ( 6 ) 3 5 ( 3 ) s i n , 1 - 1 1 8 ( 1 9 ) 1 5 ( 4 0 ) 4 ( 4 ) c o s , 1 2 3 5 ( 4 0 ) 1 5 ( 2 0 ) - 8 ( 7 ) A g [ l ] 0 2 8 6 ( 1 2 ) 0 9 9 6 3 ( 3 ) 4 6 ( 2 ) s i n , 1 0 0 0 c o s , 1 0 0 0 A g [ 2 ] 0 5 2 7 5 ( 1 2 ) 5 0 0 0 9 9 5 4 ( 3 ) 4 2 ( 1 ) s i n , 1 0 0 0 c o s , 1 0 0 0 ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 4 . 1 1 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K A g C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 C e [ l ] 0 2 5 ( 1 ) 2 0 ( 2 ) 2 4 ( 1 ) 0 - 1 0 ) 0 s i n , 1 - 1 0 ) - 1 ( 2 ) 4 ( 2 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 2 ) C e [ 2 ] 0 1 4 ( 1 ) 1 2 ( 1 ) 3 6 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 2 ) - 3 ( 2 ) 0 ( 1 ) 3 ( 1 ) 1 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) - 1 0 ) - 1 0 ) 2 ( 2 ) T e [ 1 ] 0 3 1 ( 1 ) 3 0 ( 2 ) 4 9 ( 2 ) 0 5 ( 1 ) 0 s i n , 1 1 ( 1 ) 0 ( 1 ) - 1 0 ) - 2 ( 2 ) 0 ( 1 ) 0 ( 2 ) c o s , 1 - 2 ( 2 ) - 1 ( 3 ) 4 ( 3 ) 0 ( 1 ) - 1 ( 2 ) 0 ( 1 ) T e [ 2 ] 0 3 6 ( 2 ) 3 5 ( 2 ) 4 9 ( 2 ) 0 - 3 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 2 ) 0 ( 1 ) 0 ( 2 ) c o s , 1 0 ( 2 ) 1 ( 3 ) 2 ( 3 ) 0 ( 1 ) - 2 ( 2 ) 0 ( 1 ) T e [ 3 ] 0 1 9 ( 1 ) 2 0 ( 2 ) 3 1 ( 2 ) 0 1 ( 1 ) 0 s i n , 1 - 1 0 ) 1 ( 2 ) - 2 ( 2 ) 0 ( 1 ) - 2 ( 2 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 0 ) 0 ( 1 ) - 1 ( 2 ) 2 3 9 T a b l e 4 . 1 1 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K A g C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 4 ] 0 2 0 ( 1 ) 1 2 ( 2 ) 2 8 ( 2 ) 0 - 1 ( 1 ) 0 s i n , 1 2 ( 1 ) 0 ( 2 ) 4 ( 2 ) 0 ( 1 ) 1 ( 2 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) - l ( 2 ) T e [ 5 ] 0 4 1 ( 2 ) 3 0 ( 2 ) 2 0 ( 1 ) 0 1 ( 1 ) 0 s i n , 1 7 ( 2 ) 5 ( 3 ) - 5 ( 2 ) 1 ( 1 ) 1 ( 2 ) 3 ( 1 ) c o s , 1 6 ( 2 ) 4 ( 2 ) - 4 ( 2 ) - 1 ( 2 ) 1 ( 1 ) - 4 ( 2 ) T e [ 6 ] 0 4 6 ( 2 ) 2 9 ( 2 ) l 7 ( 1 ) 0 - 1 ( 1 ) 0 s i n , 1 - 5 ( 2 ) 3 ( 3 ) 3 ( 2 ) - 5 ( 1 ) 2 ( 2 ) 3 ( 1 ) c o s , 1 - 4 ( 2 ) 3 ( 2 ) 2 ( 2 ) 7 ( 2 ) 1 ( 1 ) - 4 ( 2 ) T e [ 7 ] 0 1 7 ( 1 ) 1 9 ( 2 ) 4 9 ( 2 ) 0 - 1 ( 1 ) 0 s i n , 1 5 ( 2 ) - 4 ( 2 ) 7 ( 3 ) - 6 ( 1 ) - 5 ( 2 ) 3 ( 2 ) c o s , 1 - 4 ( 1 ) 3 ( 2 ) - 5 ( 2 ) - 8 ( 2 ) 4 ( 1 ) 4 ( 2 ) T e [ 8 ] 0 2 5 ( 1 ) 1 4 ( 2 ) 4 4 ( 2 ) 0 - 2 ( 1 ) 0 s i n , 1 - 6 ( 2 ) - 4 ( 2 ) 1 2 ( 3 ) 2 ( 1 ) 2 ( 2 ) 4 ( 1 ) c o s , 1 4 ( 2 ) 3 ( 2 ) - 9 ( 2 ) 3 ( 1 ) - 2 ( 1 ) 5 ( 2 ) K [ l ] 0 2 6 ( 5 ) 2 9 ( 6 ) 5 7 ( 7 ) 0 - 3 ( 4 ) 0 s i n , 1 3 ( 2 ) - 4 ( 4 ) - 5 ( 5 ) 3 ( 4 ) - 2 ( 2 ) 0 ( 7 ) c o s , 1 7 ( 5 ) - 8 ( 8 ) - 1 0 ( 9 ) - 2 ( 2 ) - 4 ( 5 ) 0 ( 3 ) K [ 2 ] 0 4 3 ( 6 ) 4 1 ( 8 ) 2 2 ( 4 ) 0 1 0 ( 4 ) 0 s i n , 1 1 0 ( 4 ) 9 ( 5 ) - l ( 4 ) - 2 ( 6 ) 6 ( 3 ) - 2 ( 6 ) c o s , 1 - l 9 ( 8 ) - l 7 ( 1 0 ) 2 ( 7 ) - 1 ( 3 ) - 1 2 ( 6 ) - l ( 3 ) A g [ l ] 0 4 5 ( 2 ) 4 7 ( 3 ) 4 7 ( 2 ) 0 6 ( 2 ) 0 s i n , 1 0 0 0 0 0 0 c o s , 1 0 0 0 0 0 0 A g [ 2 ] 0 4 0 ( 2 ) 3 6 ( 3 ) 5 2 ( 3 ) 0 - 2 ( 1 ) 0 s i n , 1 0 0 0 0 0 0 c o s , 1 0 0 0 0 0 0 2 4 0 T a b l e 4 . 1 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K A g C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e C e [ l ] - T e [ 3 ] x 4 3 . 2 7 9 ( 5 ) 3 . 2 4 4 ( 5 ) 3 . 3 1 4 ( 5 ) C e [ l ] - T e [ 4 ] 3 . 2 7 0 ( 6 ) 3 . 2 6 5 ( 8 ) 3 . 2 7 6 ( 8 ) C e [ l ] - T e [ 5 ] 3 . 3 3 2 ( 6 ) 3 . 2 6 7 ( 7 ) 3 . 3 9 8 ( 7 ) C e [ l ] - T e [ 5 ] 3 . 4 0 2 ( 6 ) 3 . 3 7 2 ( 7 ) 3 . 4 3 3 ( 7 ) C e [ l ] - T e [ 6 ] x 2 3 . 3 8 1 ( 6 ) 3 . 3 6 4 ( 6 ) 3 . 3 9 6 ( 6 ) C e [ 2 ] - T e [ 3 ] 3 . 2 5 4 ( 7 ) 3 . 2 4 7 ( 8 ) 3 . 2 6 1 ( 8 ) C e [ 2 ] - T e [ 4 ] x 4 3 . 2 7 6 ( 5 ) 3 . 2 5 0 ( 5 ) 3 . 3 0 2 ( 5 ) C e [ 2 ] - T e [ 7 ] x 2 3 . 4 0 3 ( 7 ) 3 . 3 7 8 ( 7 ) 3 . 4 2 7 ( 7 ) C e [ 2 ] - T e [ 8 ] 3 . 3 3 9 ( 7 ) 3 . 2 2 4 ( 8 ) 3 . 4 5 8 ( 8 ) C e [ 2 ] - T e [ 8 ] 3 . 4 1 8 ( 7 ) 3 . 3 5 9 ( 8 ) 3 . 4 7 8 ( 7 ) T e [ 1 ] - K [ 2 ] x 4 3 . 4 9 7 ( 1 7 ) 3 . 4 3 6 ( 1 7 ) 3 . 5 5 9 ( 1 7 ) T e [ 1 ] - A g [ l ] 2 . 7 8 8 ( 8 ) 2 . 7 7 0 ( 9 ) 2 . 8 0 6 ( 9 ) T e [ 1 ] - A g [ l ] 2 . 8 3 9 ( 8 ) 2 . 8 2 6 ( 9 ) 2 . 8 5 3 ( 9 ) T e [ 1 ] - A g [ 2 ] x 2 2 . 8 1 3 ( 7 ) 2 . 8 0 9 ( 7 ) 2 . 8 1 6 ( 7 ) T e [ 2 ] - K [ l ] x 4 3 . 4 8 7 ( 1 5 ) 3 . 4 5 5 ( 1 5 ) 3 . 5 1 8 ( 1 5 ) T e [ 2 ] - A g [ l ] x 2 2 . 8 4 5 ( 7 ) 2 . 8 4 4 ( 7 ) 2 . 8 4 5 ( 7 ) T e [ 2 ] - A g [ 2 ] 2 . 8 3 0 ( 8 ) 2 . 8 2 4 ( 9 ) 2 . 8 3 6 ( 9 ) T e [ 2 ] - A g [ 2 ] 2 . 8 6 2 ( 8 ) 2 . 8 5 8 ( 9 ) 2 . 8 6 7 ( 9 ) T e [ 5 ] - T e [ 6 ] x 4 3 . 1 7 0 ( 8 ) 3 . 0 2 9 ( 8 ) 3 . 3 1 6 ( 8 ) T e [ 7 ] - T e [ 8 ] x 2 3 . 1 6 0 ( 8 ) 2 . 9 0 7 ( 8 ) 3 . 4 2 2 ( 8 ) T e [ 7 ] - T e [ 8 ] x 2 3 . 1 8 5 ( 8 ) 2 . 9 4 6 ( 8 ) 3 . 4 2 7 ( 8 ) A g [ 1 ] - A g [ 2 ] x 4 3 . 1 7 1 ( 5 ) 3 . 1 7 1 ( 5 ) 3 . 1 7 1 ( 5 ) T a b l e 4 . 1 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K A g C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 3 ] - C e [ l ] - T e [ 3 ] x 4 8 6 . 5 0 ( 1 0 ) 8 5 . 3 3 ( 1 1 ) 8 7 . 6 7 ( 1 2 ) T e [ 3 ] - C e [ l ] - T e [ 3 ] x 4 8 5 . 6 9 ( 1 2 ) 8 5 . 6 0 ( 1 3 ) 8 5 . 7 9 ( 1 3 ) T e [ 3 ] - C e [ l ] - T e [ 3 ] x 4 l 4 9 . 4 3 ( 1 8 ) l 4 9 . 2 4 ( 1 8 ) 1 4 9 . 5 9 ( 1 7 ) T e [ 3 ] - C e [ l ] - T e [ 4 ] x 4 7 4 . 7 8 ( 1 3 ) 7 4 2 4 ( 1 3 ) 7 5 . 3 1 ( 1 3 ) T e [ 3 ] - C e [ l ] - T e [ 5 ] x 2 7 5 . 8 5 ( 1 4 ) 7 5 . 4 0 ( l 4 ) 7 6 2 8 ( 1 4 ) T e [ 3 ] - C e [ l ] - T e [ 5 ] x 4 l 3 0 . 6 6 ( l 4 ) 1 2 9 . 7 4 ( 1 4 ) 1 3 1 . 5 7 ( 1 4 ) 2 4 1 T a b l e 4 . 1 3 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K A g C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 3 ] - C e [ l ] - T e [ 6 ] x 2 T e [ 3 ] - C e [ l ] - T e [ 6 ] x 2 T e [ 3 ] - C e [ l ] - T e [ 5 ] x 2 T e [ 3 ] - C e [ l ] - T e [ 6 ] x 2 T e [ 3 ] - C e [ l ] - T e [ 6 ] x 2 T e [ 4 ] - C e [ l ] - T e [ 5 ] T e [ 4 ] - C e [ l ] - T e [ 5 ] T e [ 4 ] - C e [ l ] - T e [ 6 ] x 2 T e [ 5 ] - C e [ l ] - T e [ 5 ] x 2 T e [ 5 ] - C e [ l ] - T e [ 6 ] x 4 T e [ 6 ] - C e [ l ] - T e [ 6 ] x 2 T e [ 3 ] - C e [ 2 ] - T e [ 4 ] x 4 T e [ 3 ] - C e [ 2 ] - T e [ 7 ] x 2 T e [ 3 ] - C e [ 2 ] - T e [ 8 ] T e [ 3 ] - C e [ 2 ] - T e [ 8 ] T e [ 4 ] - C e [ 2 ] - T e [ 4 ] x 4 T e [ 4 ] - C e [ 2 ] - T e [ 4 ] x 4 T e [ 4 ] - C e [ 2 ] - T e [ 4 ] x 4 T e [ 4 ] - C e [ 2 ] - T e [ 7 ] x 2 T e [ 4 ] - C e [ 2 ] - T e [ 7 ] x 2 T e [ 4 ] - C e [ 2 ] - T e [ 8 ] x 2 T e [ 4 ] - C e [ 2 ] - T e [ 8 ] x 4 T e [ 4 ] - C e [ 2 ] - T e [ 7 ] x 2 T e [ 4 ] - C e [ 2 ] - T e [ 7 ] x 2 T e [ 4 ] - C e [ 2 ] - T e [ 8 ] x 2 T e [ 7 ] - C e [ 2 ] - T e [ 7 ] x 2 T e [ 7 ] - C e [ 2 ] - T e [ 8 ] x 4 T e [ 8 ] - C e [ 2 ] - T e [ 8 ] x 2 K [ 2 ] - T e [ 1 ] - K [ 2 ] x 8 K [ 2 ] - T e [ 1 ] - K [ 2 ] x 4 K [ 2 ] - T e [ 1 ] - A g [ l ] x 4 K [ 2 ] - T e [ 1 ] - A g [ 1 ] x 4 K [ 2 ] - T e [ 1 ] - A g [ 2 ] x 4 K [ 2 ] - T e [ 1 ] - A g [ 2 ] x 2 7 5 . 6 2 0 4 ) 1 3 1 . 4 7 0 5 ) 7 4 . 7 8 0 4 ) 7 4 . 4 7 0 4 ) 1 2 9 . 8 5 0 5 ) 1 3 9 . 2 5 0 5 ) 1 3 7 . 6 9 0 4 ) 1 3 8 . 2 7 0 3 ) 8 3 . 0 6 0 5 ) 5 6 . 3 0 0 4 ) 8 3 . 3 2 0 4 ) 7 5 . 0 4 0 5 ) 1 3 8 . 5 1 0 4 ) 1 3 9 . 4 7 0 6 ) 1 3 7 . 8 1 0 6 ) 8 6 . 5 7 0 2 ) 8 5 . 8 3 0 2 ) 1 4 9 . 9 8 0 9 ) 7 5 . 4 8 0 5 ) 1 3 0 . 9 5 ( 1 7 ) 7 5 . 7 6 0 5 ) 1 3 0 . 4 1 0 5 ) 7 4 . 5 5 0 5 ) 1 2 9 . 6 7 0 7 ) 7 4 . 6 4 0 4 ) 8 2 . 8 3 0 6 ) 5 5 . 8 5 0 5 ) 8 2 . 7 0 0 7 ) 8 0 0 ( 4 ) 1 2 8 . 7 ( 4 ) 7 6 . 6 ( 3 ) 1 3 9 . 9 ( 3 ) 7 5 . 8 ( 3 ) 1 4 1 . 4 ( 3 ) 7 4 . 0 0 0 4 ) 1 2 9 . 1 5 0 4 ) 7 4 . 3 5 0 5 ) 7 2 . 9 5 0 5 ) 1 2 7 . 1 7 0 4 ) 1 3 9 . 0 7 0 7 ) 1 3 7 . 3 8 0 6 ) 1 3 7 . 9 1 0 2 ) 8 2 . 5 6 0 6 ) 5 3 . 9 1 0 4 ) 8 2 . 4 9 0 5 ) 7 4 . 6 6 0 5 ) 1 3 7 . 9 6 ( l 3 ) 1 3 8 . 6 9 0 8 ) 1 3 6 . 2 2 0 8 ) 8 5 . 7 8 0 2 ) 8 5 . 7 1 0 2 ) 1 4 9 . 7 ( 2 ) 7 2 . 3 9 0 6 ) 1 2 7 . 1 9 0 6 ) 7 4 . 8 0 0 4 ) 1 2 8 . 9 2 0 4 ) 7 1 . 8 1 0 6 ) 1 2 5 . 3 8 0 6 ) 7 3 . 4 2 0 5 ) 8 1 . 4 3 0 7 ) 5 1 . 7 0 0 4 ) 8 1 . 8 3 0 8 ) 7 9 . 3 ( 4 ) 1 2 7 . 7 ( 4 ) 7 5 . 3 ( 3 ) 1 3 9 . 3 ( 3 ) 7 5 . 5 ( 3 ) 1 4 0 . 0 ( 3 ) 7 7 . 2 1 0 4 ) 1 3 3 . 7 7 0 4 ) 7 5 . 2 1 0 4 ) 7 6 . 0 2 0 5 ) 1 3 2 . 5 2 0 4 ) 1 3 9 . 4 4 0 6 ) 1 3 8 . 0 0 0 6 ) 1 3 8 . 7 1 0 4 ) 8 3 . 5 5 0 6 ) 5 8 . 6 4 0 4 ) 8 4 . 0 6 0 5 ) 7 5 . 4 2 0 5 ) 1 3 9 . 1 0 0 2 ) 1 4 0 . 3 0 0 8 ) 1 3 9 . 4 8 0 8 ) 8 7 . 3 8 0 3 ) 8 5 . 9 5 0 2 ) 1 5 0 . 3 ( 2 ) 7 8 . 6 1 0 6 ) 1 3 4 . 6 9 0 7 ) 7 6 . 7 4 0 4 ) 1 3 1 . 8 6 0 4 ) 7 7 . 2 9 0 6 ) 1 3 3 . 8 8 0 7 ) 7 5 . 8 9 0 5 ) 8 3 . 8 7 0 7 ) 6 0 . 0 7 ( 1 4 ) 8 3 . 4 9 0 8 ) 8 0 7 ( 4 ) 1 2 9 . 7 ( 4 ) 7 8 . 0 ( 4 ) 1 4 0 . 6 ( 3 ) 7 6 . 1 ( 3 ) 1 4 2 . 7 ( 4 ) 2 4 2 T a b l e 4 . 1 3 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K A g C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . K [ 2 ] — T e [ 1 ] - A g [ 2 ] x 2 A g [ 1 ] - T e [ 1 ] - A g [ 1 ] x 2 A g [ 1 ] - T e [ 1 ] - A g [ 2 ] x 4 A g [ 2 ] - T e [ 1 ] - A g [ 2 ] x 2 K [ 1 ] - T e [ 2 ] - K [ 1 ] x 8 K [ l ] - T e [ 2 ] - K [ l ] x 4 K [ 1 ] - T e [ 2 ] - A g [ 1 ] x 4 K [ 1 ] - T e [ 2 ] - A g [ 1 ] x 4 K [ l ] - T e [ 2 ] - A g [ 2 ] x 4 K [ l ] - T e [ 2 ] - A g [ 2 ] x 4 A g [ 1 ] - T e [ 2 ] - A g [ l ] x 2 A g [ l ] - T e [ 2 ] - A g [ 2 ] x 4 A g [ 2 ] - T e [ 2 ] - A g [ 2 ] x 2 C e [ 1 ] - T e [ 3 ] - C e [ l ] x 8 C e [ 1 ] - T e [ 3 ] - C e [ l ] x 4 C e [ l ] - T e [ 3 ] - C e [ 2 ] x 4 C e [ l ] - T e [ 4 ] - C e [ 2 ] x 4 C e [ 2 ] - T e [ 4 ] - C e [ 2 ] x 8 C e [ 2 ] - T e [ 4 ] - C e [ 2 ] x 4 C e [ 1 ] - T e [ 5 ] - C e [ 1 ] x 2 C e [ l ] - T e [ 5 ] - T e [ 6 ] x 4 C e [ l ] - T e [ 5 ] - T e [ 6 ] x 4 T e [ 6 ] - T e [ 5 ] - T e [ 6 ] x 8 T e [ 6 ] - T e [ 5 ] - T e [ 6 ] x 4 C e [ l ] - T e [ 6 ] - C e [ 1 ] x 2 C e [ l ] - T e [ 6 ] - T e [ 5 ] x 2 C e [ l ] - T e [ 6 ] - T e [ 5 ] x 2 C e [ l ] - T e [ 6 ] - T e [ 5 ] x 2 C e [ l ] - T e [ 6 ] - T e [ 5 ] x 2 T e [ 5 ] - T e [ 6 ] - T e [ 5 ] x 8 T e [ 5 ] - T e [ 6 ] - T e [ 5 ] x 4 C e [ 2 ] - T e [ 7 ] - C e [ 2 ] x 2 C e [ 2 ] - T e [ 7 ] - T e [ 8 ] x 2 C e [ 2 ] - T e [ 7 ] - T e [ 8 ] x 4 1 3 9 . 6 ( 3 ) 1 0 5 . 0 ( 3 ) 6 8 . 8 0 ( 1 9 ) 1 0 6 . 0 ( 3 ) 8 0 2 ( 3 ) 1 3 0 . 1 ( 4 ) 7 5 . 9 ( 3 ) 1 4 0 . 7 ( 3 ) 7 6 . 4 ( 3 ) 1 3 9 . 7 ( 3 ) 1 0 4 . 3 ( 3 ) 6 7 . 9 5 0 9 ) 1 0 3 . 4 ( 3 ) 8 6 . 1 9 0 2 ) 1 4 9 . 4 ( 2 ) 1 0 5 . 2 0 0 4 ) 1 0 4 . 9 1 0 5 ) 8 6 . 3 9 0 3 ) 1 5 0 . 0 ( 2 ) 8 3 . 0 6 ( 1 5 ) 6 1 . 8 1 0 5 ) 1 1 8 . 3 ( 2 ) 9 0 4 ( 2 ) 1 7 7 . 0 ( 2 ) 8 3 . 2 8 0 4 ) 6 1 . 0 6 0 5 ) 1 1 7 . 4 ( 2 ) 6 2 . 4 6 0 5 ) 1 1 8 . 7 ( 2 ) 9 0 5 ( 2 ) 1 7 7 . 1 ( 2 ) 8 2 . 6 2 0 7 ) 6 0 9 9 ( 1 7 ) 1 1 7 . 2 ( 2 ) 1 3 8 . 4 ( 3 ) 1 0 4 . 9 ( 3 ) 6 8 . 5 2 0 9 ) 1 0 5 . 9 ( 3 ) 8 0 0 ( 3 ) 1 2 9 . 8 ( 4 ) 7 5 . 5 ( 3 ) 1 4 0 . 5 ( 3 ) 7 6 . 3 ( 3 ) 1 3 9 . 3 ( 3 ) 1 0 4 . 3 ( 3 ) 6 7 . 8 6 0 9 ) 1 0 3 . 3 ( 3 ) 8 5 . 6 1 0 4 ) 1 4 9 . 2 ( 2 ) 1 0 4 . 9 1 0 4 ) 1 0 4 . 3 4 0 6 ) 8 6 . 0 2 0 4 ) 1 4 9 . 8 ( 2 ) 8 2 . 5 6 0 5 ) 6 0 . 1 7 0 4 ) 1 1 7 . 8 ( 2 ) 8 6 . 5 4 0 9 ) 1 7 5 . 3 ( 2 ) 8 3 . 1 1 0 4 ) 5 9 . 9 5 0 5 ) 1 1 4 . 6 ( 2 ) 6 1 . 6 1 0 4 ) 1 1 5 . 5 ( 2 ) 8 6 . 8 8 0 9 ) 1 7 5 . 4 ( 2 ) 8 1 . 8 6 0 7 ) 5 8 . 9 8 0 6 ) 1 1 1 . 9 ( 2 ) 1 4 0 . 7 ( 4 ) 1 0 5 . 2 ( 3 ) 6 9 . 0 7 0 9 ) 1 0 6 . 1 ( 3 ) 8 0 4 ( 3 ) 1 3 0 . 5 ( 4 ) 7 6 . 3 ( 3 ) 1 4 0 . 9 ( 3 ) 7 6 . 5 ( 3 ) 1 4 0 . 1 ( 3 ) 1 0 4 . 4 ( 3 ) 6 8 . 0 4 0 9 ) 1 0 3 . 4 ( 3 ) 8 6 . 7 8 0 4 ) 1 4 9 . 7 ( 2 ) 1 0 5 . 4 8 0 4 ) 1 0 5 . 4 8 0 6 ) 8 6 . 7 5 0 5 ) 1 5 0 . 2 ( 2 ) 8 3 . 5 5 0 6 ) 6 3 . 4 6 0 6 ) 1 1 8 . 6 ( 2 ) 9 4 . 3 ( 2 ) 1 7 9 . 9 ( 2 ) 8 3 . 3 8 0 4 ) 6 2 . 2 9 0 5 ) 1 2 0 . 2 ( 2 ) 6 3 . 2 4 0 5 ) 1 2 1 . 9 ( 2 ) 9 4 . 3 ( 2 ) 1 7 9 . 9 ( 3 ) 8 3 . 1 1 ( 1 7 ) 6 3 . 3 3 0 7 ) 1 2 2 . 5 ( 3 ) 2 4 3 T a b l e 4 . 1 3 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K A g C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . C e [ 2 ] - T e [ 7 ] - T e [ 8 ] x 2 C e [ 2 ] - T e [ 7 ] - K [ 2 ] x 4 T e [ 8 ] - T e [ 7 ] - T e [ 8 ] x 4 T e [ 8 ] - T e [ 7 ] - T e [ 8 ] x 4 T e [ 8 ] - T e [ 7 ] - T e [ 8 ] x 4 T e [ 8 ] - T e [ 7 ] - K [ 2 ] x 4 T e [ 8 ] - T e [ 7 ] - K [ 2 ] x 4 C e [ 2 ] - T e [ 8 ] - C e [ 2 ] x 2 C e [ 2 ] - T e [ 8 ] - T e [ 7 ] x 2 C e [ 2 ] - T e [ 8 ] - T e [ 7 ] x 4 C e [ 2 ] - T e [ 8 ] - K [ 2 ] x 4 C e [ 2 ] - T e [ 8 ] - T e [ 7 ] x 2 T e [ 7 ] - T e [ 8 ] - T e [ 7 ] x 8 T e [ 7 ] - T e [ 8 ] - T e [ 7 ] x 4 T e [ 7 ] - T e [ 8 ] - K [ 2 ] x 4 T e [ 7 ] - T e [ 8 ] - K [ 2 ] x 4 T e [ 2 ] - K [ l ] - T e [ 2 ] x 8 T e [ 2 ] - K [ l ] - T e [ 2 ] x 4 T e [ 1 ] - K [ 2 ] - T e [ 1 ] x 8 T e [ 1 ] - K [ 2 ] - T e [ 1 ] x 4 T e [ 1 ] - K [ 2 ] - T e [ 7 ] x 4 T e [ 1 ] - K [ 2 ] - T e [ 7 ] x 4 T e [ 1 ] - K [ 2 ] - T e [ 8 ] x 4 T e [ 1 ] - K [ 2 ] - T e [ 8 ] x 4 T e [ 1 ] - A g [ l ] - T e [ 1 ] x 2 T e [ 1 ] - A g [ 1 ] - T e [ 2 ] x 2 T e [ 1 ] - A g [ 1 ] - A g [ 2 ] x 4 T e [ 1 ] - A g [ l ] - A g [ 2 ] x 4 T e [ 1 ] - A g [ 1 ] - T e [ 2 ] x 2 T e [ 2 ] - A g [ l ] - T e [ 2 ] x 2 T e [ 2 ] - A g [ l ] - A g [ 2 ] x 4 T e [ 2 ] - A g [ l ] - A g [ 2 ] x 4 A g [ 2 ] - A g [ l l - A g [ 2 ] x 8 A g [ 2 ] - A g [ l l - A g [ 2 ] x 4 6 2 . 3 5 0 7 ) 1 2 6 . 5 ( 3 ) 9 1 . 1 ( 2 ) 8 9 . 3 1 0 9 ) 1 7 4 . 7 ( 3 ) 6 5 . 7 ( 3 ) 1 1 5 . 9 ( 3 ) 8 2 . 7 0 0 8 ) 6 1 . 9 7 0 7 ) 1 1 8 . 1 ( 2 ) 1 2 6 . 8 ( 3 ) 6 3 . 1 5 0 7 ) 9 0 2 ( 2 ) 1 7 5 . 2 ( 2 ) 6 4 . 9 ( 3 ) 1 1 6 . 0 ( 3 ) 7 9 . 9 ( 3 ) 1 3 0 . 1 ( 6 ) 7 9 . 1 ( 4 ) 1 2 8 . 7 ( 5 ) 8 6 . 6 ( 4 ) 1 3 6 . 6 ( 5 ) 8 6 . 8 ( 4 ) 1 3 5 . 8 ( 5 ) 1 0 5 . 0 ( 3 ) 1 1 1 . 2 6 0 8 ) 5 5 . 4 7 0 6 ) 1 2 3 . 9 ( 2 ) 1 1 2 . 5 7 ( 1 8 ) 1 0 4 . 3 ( 3 ) 5 5 . 8 1 ( 1 6 ) 1 2 3 . 8 ( 3 ) 9 0 2 2 ( 1 7 ) 1 7 9 . 3 ( 3 ) 6 1 . 0 7 0 6 ) 1 2 2 . 4 ( 3 ) 8 4 . 2 4 0 8 ) 8 7 . 7 7 0 8 ) 1 7 1 . 3 ( 3 ) 6 2 . 7 ( 3 ) 1 1 4 . 1 ( 4 ) 8 1 . 8 3 ( 1 8 ) 5 9 . 0 8 0 5 ) 1 1 7 . 2 ( 2 ) 1 2 2 . 8 ( 3 ) 5 9 . 6 8 0 6 ) 8 4 . 0 0 0 8 ) 1 7 2 . 2 ( 2 ) 6 3 . 4 ( 3 ) 1 1 1 . 2 ( 3 ) 7 9 . 7 ( 4 ) 1 2 9 . 3 ( 6 ) 7 7 . 0 ( 4 ) 1 2 8 . 1 ( 6 ) 8 6 2 ( 4 ) 1 3 5 . 1 ( 5 ) 8 3 . 9 ( 3 ) 1 3 1 . 6 ( 5 ) 1 0 4 . 9 ( 3 ) 1 1 1 . 0 4 0 8 ) 5 5 . 3 1 0 6 ) 1 2 3 . 8 ( 2 ) 1 1 2 . 3 5 ( 1 8 ) 1 0 4 . 3 ( 3 ) 5 5 . 6 8 0 7 ) 1 2 3 . 7 ( 3 ) 9 0 . 2 2 0 7 ) 1 7 9 . 3 ( 3 ) 6 3 . 4 2 0 8 ) 1 3 0 . 5 ( 3 ) 9 8 . 3 ( 2 ) 9 1 . 5 3 0 9 ) 1 7 9 . 4 ( 3 ) 6 8 . 7 ( 3 ) 1 1 7 . 7 ( 3 ) 8 3 . 4 9 0 8 ) 6 5 . 0 2 0 8 ) 1 1 8 . 8 ( 2 ) 1 3 0 . 8 ( 3 ) 6 6 . 8 0 0 9 ) 9 6 . 8 ( 2 ) 1 7 9 . 7 ( 3 ) 6 6 . 8 ( 3 ) 1 2 0 . 8 ( 3 ) 8 0 . 0 ( 4 ) 1 3 0 . 9 ( 6 ) 8 1 . 1 ( 4 ) 1 2 9 . 3 ( 6 ) 8 6 . 8 ( 4 ) 1 3 8 . 1 ( 5 ) 8 9 . 5 ( 3 ) 1 4 0 . 0 ( 5 ) 1 0 5 . 2 ( 3 ) 1 1 1 . 4 9 0 8 ) 5 5 . 6 4 0 6 ) 1 2 4 . 1 ( 2 ) 1 1 2 . 7 8 0 8 ) 1 0 4 . 3 ( 3 ) 5 5 . 9 3 0 7 ) 1 2 3 . 9 ( 3 ) 9 0 2 2 ( 1 7 ) 1 7 9 . 3 ( 3 ) T a b l e 4 . 1 3 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K A g C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 1 ] - A g [ 2 ] - T e [ 1 ] x 2 1 0 6 . 0 ( 3 ) 1 0 5 . 9 ( 3 ) 1 0 6 . 1 ( 3 ) T e [ 1 ] - A g [ 2 ] - T e [ 2 ] x 2 1 1 1 . 3 0 0 9 ) 1 1 0 . 9 ( 2 ) 1 1 1 . 7 ( 2 ) T e [ 1 ] — A g [ 2 ] - T e [ 2 ] x 2 1 1 2 . 5 1 0 9 ) 1 1 2 . 2 ( 2 ) 1 1 2 . 8 ( 2 ) T e [ 1 ] - A g [ 2 ] - A g [ l ] x 2 5 5 . 2 3 0 6 ) 5 4 . 8 6 0 7 ) 5 5 . 6 1 0 7 ) T e [ 1 ] — A g [ 2 ] - A g [ l ] x 4 1 2 4 . 3 ( 3 ) 1 2 4 . 0 ( 3 ) 1 2 4 . 6 ( 3 ) T e [ 1 ] - A g [ 2 ] - A g [ l ] x 2 5 6 2 8 ( 1 6 ) 5 5 . 9 6 0 7 ) 5 6 . 5 9 0 7 ) T e [ 2 ] - A g [ 2 ] - T e [ 2 ] x 2 1 0 3 . 4 ( 3 ) 1 0 3 . 3 ( 3 ) 1 0 3 . 4 ( 3 ) T e [ 2 ] - A g [ 2 ] - A g [ l ] x 4 5 6 . 0 6 0 7 ) 5 6 . 0 1 0 6 ) 5 6 . 1 2 0 6 ) T e [ 2 ] - A g [ 2 ] - A g [ l ] x 4 1 2 3 . 5 ( 2 ) 1 2 3 . 4 ( 2 ) 1 2 3 . 5 ( 2 ) A g [ l ] - A g [ 2 ] - A g [ l ] x 4 9 0 . 4 7 0 7 ) 9 0 4 7 ( 1 7 ) 9 0 4 7 ( 1 7 ) A g [ l ] - A g [ 2 ] — A g [ l ] x 4 8 9 . 6 5 0 0 ) 8 9 . 6 5 0 0 ) 8 9 . 6 5 0 0 ) A g [ l ] — A g [ 2 ] - A g [ l ] x 4 1 7 9 . 3 ( 3 ) 1 7 9 . 3 ( 3 ) 1 7 9 . 3 ( 3 ) 2 4 5 T a b l e 4 . 1 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r K o , 7 1 ( 1 ) A g 1 , 2 9 ( 1 ) L a T e 4 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 2 8 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 6 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 o ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 s t o r d e r s a t e l l i t e s [ I > 2 0 ’ ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T u m , a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e K 0 . 7 1 ( 1 ) A g 1 . 2 9 ( 1 ) L a T e 4 8 1 6 . 2 1 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A M o n o c l i n i c P m ( 0 ] 3 1 / 2 ) 0 a = 4 . 4 8 3 8 ( 5 ) A , o = 9 0 ° b = 4 . 5 0 5 7 ( 6 ) A , l 3 = 9 0 ° c = 2 0 8 7 7 0 ) A , y = 9 0 0 0 . 3 4 6 6 ( 7 ) b ‘ + 1 / 2 c ‘ 4 2 1 . 7 7 0 0 ) A 3 2 6 . 4 2 4 9 g / c m 3 2 1 . 7 1 6 m i n 1 6 7 8 0 . 0 9 x 0 . 0 5 x 0 . 0 2 m m 3 1 . 6 4 t o 2 9 . 2 8 ° - 6 < = h < = 6 , - 6 < = k < = 6 , - 2 9 < = l < = 2 9 , - 1 < = m < = 1 1 0 3 2 2 ( 2 6 8 1 m a i n + 7 6 4 1 s a t e l l i t e s ) 5 8 5 6 ( 1 8 3 0 m a i n + 4 0 2 6 s a t e l l i t e S ) [ R i m = 0 . 0 5 7 7 ] 9 8 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 5 8 5 6 / 1 6 / 2 1 2 1 . 5 4 R o b , = 0 . 0 5 1 8 , w R . . . , = 0 . 1 2 0 7 R , “ = 0 . 0 9 1 6 , w k , " = 0 . 1 3 0 6 R o b , = 0 . 0 3 2 2 , w R . . . , = 0 . 0 8 6 9 R , “ = 0 . 0 3 4 4 , w R . . . , = 0 . 0 8 7 4 R o b , = 0 . 1 4 2 9 , w R o b s = 0 . 2 5 5 1 R , " = 0 . 2 7 2 7 , w R a u = 0 . 2 8 8 3 0 . 0 0 0 7 4 0 ) 0 . 1 9 5 3 a n d 0 . 7 1 5 1 4 . 3 2 a n d - 3 . 5 1 e . A ' 3 R = l e F o l - I F C H / £ ] F o | , w R = { 2 [ w ( | 1 = . , | 2 - | F . | 2 ) 2 ] / > : [ w ( | F , | “ ) ] } ” 2 a n d w = l / ( 0 2 ( I ) + 0 . 0 0 1 6 1 2 ) 2 4 6 T a b l e 4 . 1 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) d i s p l a c e m e n t a n d e q u i v a l e n t i s o t r o p i c K o , 7 1 ( . ) A g 1 , 2 9 ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . p a r a m e t e r s ( A 2 x 1 0 4 ) A t o m W a v e x y 2 O c c u p a n c y U e q L a [ l ] 0 0 5 0 0 0 4 0 1 0 1 9 ( 1 ) s i n , 1 - l ( 3 ) 0 ( 1 ) 1 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 3 ) 0 ( 1 ) L a [ 2 ] 0 4 9 9 9 ( 3 ) 0 6 0 0 0 ( 1 ) 1 9 ( 1 ) s i n , 1 1 4 2 ( 5 ) 6 ( 1 ) 4 ( 1 ) c o s , 1 - 4 6 ( 2 ) 1 8 ( 4 ) - 1 ( 1 ) T e [ 1 ] 0 5 0 0 8 ( 4 ) 0 8 9 9 6 ( 1 ) 1 1 9 ( 1 ) s i n , 1 - 1 6 ( 2 ) - 1 0 ( 5 ) 1 ( 1 ) c o s , 1 4 8 ( 7 ) - 3 ( 2 ) - 2 ( 1 ) T e [ 2 ] 0 7 ( 3 ) 5 0 0 0 7 2 2 ( 1 ) 1 1 7 ( 1 ) s i n , 1 4 ( 1 ) - 1 ( 4 ) 0 ( 1 ) c o s , 1 1 9 ( 4 ) 0 ( 1 ) 0 ( 1 ) T e [ 3 ] 0 4 9 9 8 ( 4 ) 0 4 4 3 2 ( 1 ) 1 9 ( 1 ) s i n , 1 1 ( 3 ) 1 ( 1 ) 2 ( 1 ) c o s , 1 0 ( 1 ) - 4 ( 3 ) 0 ( 1 ) T e [ 4 ] 0 1 0 0 0 0 ( 4 ) 5 0 0 0 5 5 9 2 ( 1 ) 1 8 ( 1 ) s i n , 1 - 4 0 ( 6 ) - 2 ( 1 ) 1 ( 1 ) c o s , 1 8 ( 1 ) - 1 2 ( 4 ) 0 ( 1 ) T e [ 5 ] 0 5 0 0 7 ( 4 ) 5 0 0 0 2 7 9 6 ( 1 ) 1 1 7 ( 1 ) s i n , 1 - 1 9 ( 5 ) - 2 ( 4 ) - 2 ( 1 ) c o s , 1 - l 6 ( 4 ) 3 ( 5 ) - 2 ( 1 ) T e [ 6 ] 0 3 ( 4 ) 0 2 7 9 4 ( 1 ) 1 2 0 ( 1 ) s i n , 1 2 8 ( 6 ) - 1 5 ( 5 ) - 1 ( 1 ) c o s , 1 2 3 ( 5 ) 1 8 ( 6 ) - l ( 1 ) T e [ 7 ] 0 5 0 1 1 ( 6 ) 5 0 0 0 7 2 2 4 ( 1 ) 1 1 3 ( 1 ) s i n , 1 - 3 5 5 ( 5 ) - 8 6 ( 4 ) - 3 ( 1 ) c o s , 1 2 9 8 ( 4 ) - 1 0 2 ( 5 ) 2 ( 1 ) T e [ 8 ] 0 2 ( 5 ) 0 7 2 2 0 ( 1 ) 1 1 2 ( 1 ) s i n , 1 3 4 0 ( 4 ) 9 1 ( 4 ) 1 ( 1 ) c o s , 1 - 2 8 5 ( 4 ) 1 0 8 ( 5 ) - 1 ( 1 ) 2 4 7 T a b l e 4 . 1 5 . ( C o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K o , 7 1 ( l ) A g 1 , 2 9 ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . K [ l ] 0 4 9 8 1 ( 1 3 ) 0 1 3 9 4 ( 3 ) 1 2 3 ( 1 ) s i n , 1 1 6 ( 6 ) - 7 ( 1 4 ) 1 ( 2 ) c o s , 1 3 4 ( 1 2 ) 3 ( 6 ) 2 ( 4 ) K [ 2 ] 0 1 5 0 0 0 8 5 1 2 0 . 4 1 6 ( 1 3 ) 1 2 ( 1 ) s i n , 1 1 ( 5 ) 4 4 ( 6 ) 4 ( 1 ) c o s , 1 - 2 ( 1 0 ) 2 2 ( 3 ) - 7 ( 2 ) A g [ l ] 0 1 5 ( 5 ) 0 9 9 2 1 ( 1 ) 2 0 ( 1 ) s i n , 1 - 1 ( 1 ) - 5 ( 8 ) 0 ( 1 ) c o s , 1 3 1 ( 8 ) 0 ( 1 ) - 3 ( 2 ) A g [ 2 ] 0 5 0 1 3 ( 5 ) 5 0 0 0 9 9 1 8 ( 1 ) 2 1 ( 1 ) s i n , 1 - 1 ( 1 ) - 1 8 ( 8 ) 0 ( 1 ) c o s , 1 3 1 ( 8 ) 0 ( 1 ) - 2 ( 2 ) A g [ 3 ] 0 1 ( 5 ) 5 0 0 0 8 5 1 2 ( 1 ) 0 . 5 8 4 ( 1 3 ) 1 2 ( 1 ) s i n , 1 1 ( 5 ) 4 4 ( 6 ) 4 ( 1 ) c o s , 1 - 2 ( 1 0 ) 2 2 ( 3 ) - 7 ( 2 ) ‘ U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 4 . 1 6 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K 0 . 7 1 ( 1 ) A g 1 , 2 9 ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 L a [ l ] 0 9 ( 1 ) 9 ( 1 ) 9 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 1 ( 1 ) 0 ( 1 ) - 2 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) L a [ 2 ] 0 7 ( 1 ) 7 ( 1 ) 1 2 ( 1 ) 0 - 1 0 ) 0 s i n , 1 - 3 0 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) - 1 0 ) 0 ( 1 ) c o s , 1 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) T e [ 1 ] 0 1 8 ( 1 ) 2 1 ( 1 ) 1 7 ( 1 ) 0 - 1 0 ) 0 s i n , 1 1 ( 1 ) 0 ( 1 ) - 1 0 ) - 2 0 ) 1 ( 1 ) 1 ( 1 ) c o s , 1 - 2 0 ) 0 ( 1 ) 3 ( 1 ) 0 ( 1 ) - 2 0 ) 0 ( 1 ) T e [ 2 ] 0 1 1 ( 1 ) 1 1 ( 1 ) 2 9 ( 1 ) 0 - 1 0 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) - 2 0 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 2 4 8 T a b l e 4 . 1 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K o , 7 1 ( 1 ) A g 1 , 2 9 ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e L a [ l ] - T e [ 3 ] x 4 3 . 2 9 9 1 ( 1 9 ) 3 . 2 9 8 ( 2 ) 3 . 3 0 0 ( 2 ) L a [ l ] - T e [ 4 ] 3 . 3 0 4 ( 3 ) 3 . 3 0 3 ( 4 ) 3 . 3 0 5 ( 4 ) L a [ l ] - T e [ 5 ] x 2 3 . 3 8 1 ( 3 ) 3 . 3 6 8 ( 3 ) 3 . 3 9 4 ( 3 ) L a [ l ] - T e [ 6 ] x 2 3 . 3 9 4 ( 3 ) 3 . 3 8 8 ( 3 ) 3 . 4 0 1 ( 3 ) L a [ 2 ] - T e [ 3 ] 3 . 2 7 2 ( 3 ) 3 . 2 6 8 ( 4 ) 3 . 2 7 7 ( 4 ) L a [ 2 ] - T e [ 4 ] x 4 3 . 2 9 1 ( 3 ) 3 . 2 3 4 ( 3 ) 3 . 3 4 7 ( 3 ) L a [ 2 ] - T e [ 7 ] x 2 3 . 4 1 2 ( 3 ) 3 . 3 6 8 ( 3 ) 3 . 4 4 6 ( 3 ) L a [ 2 ] - T e [ 8 ] x 2 3 . 3 9 4 ( 4 ) 3 . 3 0 2 ( 4 ) 3 . 4 8 7 ( 4 ) T e [ 1 ] - K [ 2 ] x 4 3 . 3 3 7 ( 4 ) 3 . 3 0 7 ( 3 ) 3 . 3 6 7 ( 3 ) T e [ 1 ] - A g [ l ] x 2 2 . 9 5 7 ( 4 ) 2 . 9 5 1 ( 6 ) 2 . 9 6 2 ( 6 ) T e [ 1 ] - A g [ 2 ] x 2 2 . 9 6 3 ( 4 ) 2 . 9 5 8 ( 4 ) 2 . 9 6 8 ( 4 ) T e [ 1 ] - A g [ 3 ] x 4 3 . 3 3 7 ( 4 ) 3 . 3 0 7 ( 4 ) 3 . 3 6 7 ( 4 ) T e [ 2 ] - K [ l ] x 2 3 . 4 8 1 ( 7 ) 3 . 4 7 4 ( 7 ) 3 . 4 8 8 ( 7 ) T e [ 2 ] - K [ l ] x 2 3 . 4 6 6 ( 7 ) 3 . 4 5 4 ( 7 ) 3 . 4 7 8 ( 7 ) T e [ 2 ] - A g [ l ] x 2 2 . 8 0 6 ( 3 ) 2 . 8 0 2 ( 3 ) 2 . 8 0 9 ( 3 ) T e [ 2 ] - A g [ 2 ] x 2 2 . 7 9 9 ( 4 ) 2 . 7 9 7 ( 5 ) 2 . 8 0 1 ( 5 ) T e [ 5 ] - T e [ 6 ] x 4 3 . 1 8 0 ( 4 ) 3 . 1 5 8 ( 4 ) 3 . 2 0 1 ( 4 ) T e [ 7 ] - T e [ 8 ] x 4 3 . 1 8 5 ( 4 ) 2 . 9 3 0 ( 4 ) 3 . 4 4 7 ( 4 ) T e [ 7 ] - K [ 2 ] x 2 3 . 5 0 7 ( 4 ) 3 . 3 9 5 ( 5 ) 3 . 6 2 4 ( 5 ) T e [ 7 ] - A g [ 3 ] x 2 3 . 5 0 7 ( 5 ) 3 . 3 9 5 ( 5 ) 3 . 6 2 4 ( 5 ) T e [ 8 ] - K [ 2 ] x 2 3 . 5 1 7 ( 4 ) 3 . 4 9 1 ( 4 ) 3 . 5 3 9 ( 4 ) T e [ 8 ] - A g [ 3 ] x 2 3 . 5 1 7 ( 4 ) 3 . 4 9 1 ( 5 ) 3 . 5 3 9 ( 4 ) A g [ l ] - A g [ 2 ] x 4 3 . 1 7 9 ( 4 ) 3 . 1 7 1 ( 4 ) 3 . 1 8 7 ( 4 ) T a b l e 4 . 1 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K o , 7 1 ( 1 ) A g 1 _ 2 9 ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 3 ] - L a [ l ] - T e [ 3 ] x 4 8 6 1 4 ( 5 ) 8 6 0 8 ( 5 ) 8 6 1 9 ( 5 ) T e [ 3 ] - L a [ l ] - T e [ 3 ] x 4 8 5 . 6 4 ( 5 ) 8 5 . 6 0 ( 5 ) 8 5 . 6 8 ( 5 ) T e [ 3 ] - L a [ l ] - T e [ 3 ] x 4 l 4 8 . 9 8 ( 7 ) l 4 8 . 9 7 ( 9 ) 1 4 8 . 9 9 ( 9 ) T e [ 3 ] - L a [ l ] - T e [ 4 ] x 4 7 4 4 9 ( 6 ) 7 4 2 7 ( 6 ) 7 4 . 7 1 ( 6 ) T e [ 3 ] - L a [ l ] - T e [ 5 ] x 4 7 5 5 3 ( 6 ) 7 5 . 4 9 ( 6 ) 7 5 5 8 ( 6 ) 2 4 9 T a b l e 4 . 1 8 . ( C o n t ’ d ) . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K o , 7 1 ( 1 ) A g 1 , 2 o ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 3 ] - L a [ l ] - T e [ 5 ] x 4 T e [ 3 ] - L a [ l ] - T e [ 6 ] x 4 T e [ 3 ] - L a [ l ] - T e [ 6 ] x 4 T e [ 4 ] - L a [ l ] - T e [ 5 ] x 2 T e [ 4 ] - L a [ l ] - T e [ 6 ] x 2 T e [ 5 ] - L a [ l ] - T e [ 5 ] x 2 T e [ 5 ] - L a [ l ] - T e [ 6 ] x 4 T e [ 6 ] - L a [ l ] - T e [ 6 ] x 2 T e [ 3 ] - L a [ 2 ] - T e [ 4 ] x 4 T e [ 3 ] - L a [ 2 ] - T e [ 7 ] x 2 T e [ 3 ] - L a [ 2 ] - T e [ 8 ] x 2 T e [ 4 ] - L a [ 2 ] - T e [ 4 ] x 4 T e [ 4 ] - L a [ 2 ] - T e [ 4 ] x 4 T e [ 4 ] - L a [ 2 ] - T e [ 4 ] x 4 T e [ 4 ] - L a [ 2 ] - T e [ 7 ] x 4 T e [ 4 ] - L a [ 2 ] - T e [ 7 ] x 4 T e [ 4 ] - L a [ 2 ] - T e [ 8 ] x 4 T e [ 4 ] - L a [ 2 ] - T e [ 8 ] x 4 T e [ 7 ] - L a [ 2 ] - T e [ 7 ] x 2 T e [ 7 ] - L a [ 2 ] - T e [ 8 ] x 4 T e [ 8 ] - L a [ 2 ] - T e [ 8 ] x 2 K [ 2 ] - T e [ 1 ] - K [ 2 ] x 4 K [ 2 ] - T e [ 1 ] - K [ 2 ] x 4 K [ 2 ] - T e [ 1 ] - K [ 2 ] x 4 K [ 2 ] - T e [ 1 ] - A g [ l ] x 4 K [ 2 ] - T e [ 1 ] - A g [ 1 ] x 4 K [ 2 ] - T e [ 1 ] - A g [ 2 ] x 4 K [ 2 ] - T e [ 1 ] - A g [ 2 ] x 4 K [ 2 ] - T e [ 1 ] - A g [ 3 ] x 4 K [ 2 ] - T e [ 1 ] - A g [ 3 ] x 4 K [ 2 ] - T e [ 1 ] - A g [ 3 ] x 4 A g [ 1 ] - T e [ 1 ] - A g [ 1 ] x 2 A g [ 1 ] - T e [ 1 ] - A g [ 2 ] x 4 A g [ 1 ] - T e [ 1 ] - A g [ 3 ] x 4 1 3 0 . 6 2 ( 6 ) 7 5 3 5 ( 6 ) 1 3 0 . 8 0 ( 7 ) 1 3 8 . 5 3 ( 7 ) 1 3 8 . 4 2 ( 6 ) 8 3 0 1 ( 8 ) 5 5 9 3 ( 7 ) 8 3 . l 6 ( 7 ) 7 5 0 0 ( 7 ) 1 3 8 . 4 7 ( 6 ) 1 3 8 . 7 0 ( 9 ) 8 6 4 4 ( 7 ) 8 5 8 9 ( 6 ) 1 5 0 . 0 2 0 0 ) 7 5 0 2 ( 7 ) 1 3 0 . 3 2 ( 9 ) 7 5 2 2 ( 7 ) 1 3 0 . 1 0 ( 7 ) 8 2 8 3 ( 7 ) 5 5 7 9 ( 7 ) 8 2 6 2 ( 8 ) 8 4 9 2 ( 9 ) 8 4 4 8 ( 8 ) 1 4 4 . 7 3 0 1 ) 7 1 . 8 4 ( 9 ) 1 3 5 . 0 3 0 0 ) 7 1 5 7 ( 8 ) 1 3 5 . 2 7 0 1 ) 8 4 9 2 ( 9 ) 8 4 4 8 ( 8 ) 1 4 4 . 7 3 0 2 ) 9 8 . 5 1 0 1 ) 6 4 9 3 ( 8 ) 7 1 8 4 ( 9 ) 1 3 0 . 5 0 ( 6 ) 7 5 0 5 ( 6 ) 1 3 0 . 6 1 ( 6 ) 1 3 8 . 1 8 ( 9 ) 1 3 8 . 2 4 ( 5 ) 8 2 8 4 ( 8 ) 5 5 7 4 ( 7 ) 8 2 8 5 ( 8 ) 7 4 2 8 ( 8 ) 1 3 7 . 5 8 ( 5 ) 1 3 8 . 2 9 0 0 ) 8 4 8 4 ( 7 ) 8 5 5 9 ( 6 ) 1 4 9 . 7 5 0 1 ) 7 2 2 0 ( 7 ) 1 2 6 . 5 1 ( 9 ) 7 4 1 4 ( 7 ) 1 2 8 . 6 9 ( 7 ) 8 1 0 4 ( 8 ) 5 1 . 4 6 ( 7 ) 8 2 4 2 ( 9 ) 8 4 9 0 ( 1 0 ) 8 4 0 0 ( 7 ) 1 4 4 . 7 1 0 2 ) 7 1 5 7 ( 9 ) 1 3 4 . 6 2 0 1 ) 7 1 0 3 ( 9 ) 1 3 4 8 0 0 3 ) 8 4 . 9 0 ( 1 0 ) 8 4 0 0 ( 8 ) 1 4 4 . 7 1 0 3 ) 9 8 . 4 7 0 4 ) 6 4 5 6 ( 8 ) 7 1 5 7 ( 8 ) 1 3 0 . 7 3 ( 6 ) 7 5 6 5 ( 6 ) 1 3 0 . 9 9 ( 6 ) 1 3 8 . 8 9 ( 9 ) 1 3 8 . 5 9 ( 5 ) 8 3 1 8 ( 8 ) 5 6 1 2 ( 7 ) 8 3 4 8 ( 8 ) 7 5 7 3 ( 8 ) 1 3 9 . 5 9 ( 6 ) 1 3 9 . 1 5 0 1 ) 8 8 0 9 ( 8 ) 8 6 2 3 ( 6 ) 1 5 0 . 2 7 0 0 ) 7 7 8 6 ( 7 ) 1 3 4 . 1 4 0 0 ) 7 6 2 6 ( 7 ) 1 3 1 . 4 7 ( 7 ) 8 4 2 9 ( 8 ) 6 0 1 7 ( 7 ) 8 2 7 4 ( 9 ) 8 4 . 9 5 ( 1 0 ) 8 4 9 7 ( 7 ) 1 4 4 . 7 6 0 2 ) 7 2 . 1 1 ( 9 ) 1 3 5 . 4 3 0 1 ) 7 2 . 1 1 ( 9 ) 1 3 5 . 7 4 0 3 ) 8 4 . 9 5 ( 1 0 ) 8 4 9 7 ( 8 ) 1 4 4 . 7 6 ( 1 3 ) 9 8 5 5 ( 1 4 ) 6 5 3 0 ( 8 ) 7 2 . 1 1 ( 8 ) 2 5 0 T a b l e 4 . 1 8 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K o , 7 1 ( 1 ) A g 1 _ 2 9 ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A g [ 1 ] - T e [ 1 ] - A g [ 3 ] x 4 A g [ 2 ] - T e [ 1 ] - A g [ 2 ] x 2 A g [ 2 ] - T e [ 1 ] - A g [ 3 ] x 4 A g [ 2 ] - T e [ 1 ] - A g [ 3 ] x 4 A g [ 3 ] - T e [ 1 ] - A g [ 3 ] x 4 A g [ 3 ] - T e [ 1 ] - A g [ 3 ] x 4 A g [ 3 ] - T e [ 1 ] - A g [ 3 ] x 4 K [ 1 ] - T e [ 2 ] - K [ 1 ] x 6 K [ 1 ] - T e [ 2 ] - K [ 1 ] x 4 K [ l ] - T e [ 2 ] - A g [ l ] x 4 K [ 1 ] - T e [ 2 ] - A g [ l ] x 4 K [ l ] - T e [ 2 ] - A g [ 2 ] x 4 K [ l ] - T e [ 2 ] - A g [ 2 ] x 4 K [ 1 ] - T e [ 2 ] - K [ 1 ] x 2 A g [ l ] - T e [ 2 ] - A g [ 1 ] x 2 A g [ l ] - T e [ 2 ] - A g [ 2 ] x 4 A g [ 2 ] - T e [ 2 ] - A g [ 2 ] x 2 L a [ 1 ] - T e [ 3 ] - L a [ 1 ] x 4 L a [ 1 ] - T e [ 3 ] - L a [ 1 ] x 4 L a [ 1 ] - T e [ 3 ] - L a [ 1 ] x 4 L a [ l ] - T e [ 3 ] - L a [ 2 ] x 4 L a [ l ] - T e [ 4 ] - L a [ 2 ] x 4 L a [ 2 ] - T e [ 4 ] - L a [ 2 ] x 4 L a [ 2 ] - T e [ 4 ] - L a [ 2 ] x 4 L a [ 2 ] - T e [ 4 ] - L a [ 2 ] x 4 L a [ 1 ] - T e [ 5 ] - L a [ 1 ] x 2 L a [ l ] - T e [ 5 ] - T e [ 6 ] x 4 L a [ 1 ] - T e [ 5 ] - T e [ 6 ] x 4 T e [ 6 ] - T e [ 5 ] - T e [ 6 ] x 4 T e [ 6 ] - T e [ 5 ] - T e [ 6 ] x 4 T e [ 6 ] - T e [ 5 ] - T e [ 6 ] x 4 L a [ 1 ] - T e [ 6 ] - L a [ l ] x 2 L a [ l ] - T e [ 6 ] - T e [ 5 ] x 4 L a [ l ] - T e [ 6 ] - T e [ 5 ] x 4 1 3 4 . 9 6 ( 9 ) 9 8 9 9 ( 1 1 ) 7 1 5 7 ( 9 ) 1 3 5 . 2 7 0 2 ) 8 4 9 2 ( 9 ) 8 4 4 8 ( 9 ) 1 4 4 . 7 3 0 2 ) 8 0 6 6 ( 1 5 ) 1 3 2 . 4 0 ( 1 9 ) 7 3 . 8 1 ( 1 3 ) 1 3 9 . 5 1 ( 1 4 ) 7 3 . 9 6 0 5 ) 1 3 9 . 4 2 0 3 ) 8 1 . 0 8 ( 1 5 ) 1 0 6 . 8 3 0 2 ) 6 9 . 1 1 ( 1 1 ) 1 0 6 . 3 3 0 2 ) 8 6 1 8 ( 5 ) 8 5 6 4 ( 4 ) l 4 8 . 9 8 ( 8 ) 1 0 5 . 5 3 ( 6 ) 1 0 4 . 9 8 ( 7 ) 8 6 4 5 ( 7 ) 8 5 8 9 ( 6 ) 1 5 0 . 0 3 0 0 ) 8 3 0 1 ( 7 ) 6 2 1 8 ( 8 ) 1 1 7 . 9 6 0 0 ) 9 0 2 3 ( 9 ) 8 9 . 7 2 ( 9 ) 1 7 9 . 6 1 0 2 ) 8 3 1 6 ( 7 ) 6 1 8 2 ( 7 ) 1 1 7 . 9 7 0 1 ) 1 3 4 . 4 6 ( 9 ) 9 8 . 7 3 0 2 ) 7 1 0 3 ( 8 ) 1 3 4 . 8 0 0 1 ) 8 4 . 9 0 ( 1 0 ) 8 4 0 0 ( 8 ) 1 4 4 . 7 1 0 3 ) 8 0 . 5 2 ( 1 5 ) 1 3 2 . 2 ( 2 ) 7 3 . 5 6 ( l 3 ) 1 3 9 . 4 4 0 5 ) 7 3 . 8 0 ( l 6 ) 1 3 9 . 1 7 0 4 ) 8 0 9 8 ( 1 5 ) 1 0 6 . 7 1 ( 1 3 ) 6 8 . 9 8 0 0 ) 1 0 6 . 2 3 0 5 ) 8 6 1 3 ( 6 ) 8 5 6 0 ( 4 ) 1 4 8 . 8 5 ( 9 ) 1 0 4 . 6 2 ( 6 ) 1 0 4 . 5 0 ( 7 ) 8 5 5 5 ( 8 ) 8 5 5 9 ( 5 ) 1 4 9 . 6 6 ( 8 ) 8 2 8 4 ( 8 ) 6 1 9 4 ( 8 ) 1 1 7 . 8 2 ( 1 0 ) 8 9 . 9 9 0 0 ) 8 9 . 4 7 ( 9 ) 1 7 9 . 3 6 0 2 ) 8 3 0 5 ( 7 ) 6 1 5 2 ( 7 ) 1 1 7 . 5 5 0 1 ) 1 3 5 . 4 5 ( 9 ) 9 9 . 2 5 0 2 ) 7 2 1 1 ( 9 ) 1 3 5 . 7 4 0 1 ) 8 4 . 9 5 ( 1 0 ) 8 4 9 7 ( 8 ) 1 4 4 . 7 6 0 3 ) 8 0 7 9 ( 1 5 ) 1 3 2 . 6 ( 2 ) 7 4 . 0 5 0 3 ) 1 3 9 . 5 8 ( 1 5 ) 7 4 . 1 1 0 6 ) 1 3 9 . 6 7 0 4 ) 8 1 . 1 7 0 5 ) 1 0 6 . 9 5 0 3 ) 6 9 2 5 ( 1 0 ) 1 0 6 4 4 ( 1 5 ) 8 6 2 3 ( 6 ) 8 5 6 8 ( 4 ) 1 4 9 . 1 1 ( 9 ) 1 0 6 . 4 2 ( 6 ) 1 0 5 . 4 5 ( 7 ) 8 7 3 3 ( 8 ) 8 6 2 3 ( 5 ) 1 5 0 . 4 3 ( 8 ) 8 3 1 8 ( 8 ) 6 2 4 1 ( 8 ) 1 1 8 . 1 1 ( 1 0 ) 9 0 4 8 ( 1 0 ) 8 9 9 7 ( 9 ) 1 7 9 . 8 5 ( 1 2 ) 8 3 2 7 ( 7 ) 6 2 1 2 ( 7 ) 1 1 8 . 4 0 ( 1 1 ) 2 5 1 T a b l e 4 . 1 8 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K o . 7 1 ( 1 ) A g 1 , 2 9 ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 5 ] - T e [ 6 ] - T e [ 5 ] x 4 T e [ 5 ] - T e [ 6 ] - T e [ 5 ] x 4 T e [ 5 ] - T e [ 6 ] - T e [ 5 ] x 4 L a [ 2 ] - T e [ 7 ] - L a [ 2 ] x 2 L a [ 2 ] - T e [ 7 ] - T e [ 8 ] x 4 L a [ 2 ] - T e [ 7 ] - T e [ 8 ] x 4 L a [ 2 ] - T e [ 7 ] - K [ 2 ] x 2 L a [ 2 ] - T e [ 7 ] - K [ 2 ] x 2 L a [ 2 ] - T e [ 7 ] - A g [ 3 ] x 3 L a [ 2 ] - T e [ 7 ] - A g [ 3 ] T e [ 8 ] - T e [ 7 ] - T e [ 8 ] x 4 T e [ 8 ] - T e [ 7 ] - T e [ 8 ] x 4 T e [ 8 ] - T e [ 7 ] - T e [ 8 ] x 4 T e [ 8 ] - T e [ 7 ] - K [ 2 ] x 4 T e [ 8 ] - T e [ 7 ] - K [ 2 ] x 4 T e [ 8 ] - T e [ 7 ] - A g [ 3 ] x 4 T e [ 8 ] - T e [ 7 ] - A g [ 3 ] x 4 K [ 2 ] - T e [ 7 ] - K [ 2 ] x 2 K [ 2 ] - T e [ 7 ] - A g [ 3 ] x 2 A g [ 3 ] - T e [ 7 ] - A g [ 3 ] x 2 L a [ 2 ] - T e [ 8 ] - L a [ 2 ] x 2 L a [ 2 ] - T e [ 8 ] - T e [ 7 ] x 4 L a [ 2 ] - T e [ 8 ] - T e [ 7 ] x 4 L a [ 2 ] - T e [ 8 ] - K [ 2 ] x 4 L a [ 2 ] - T e [ 8 ] - A g [ 3 ] x 4 T e [ 7 ] - T e [ 8 ] - T e [ 7 ] x 4 T e [ 7 ] - T e [ 8 ] - T e [ 7 ] x 4 T e [ 7 ] - T e [ 8 ] - T e [ 7 ] x 4 T e [ 7 ] - T e [ 8 ] - K [ 2 ] x 4 T e [ 7 ] - T e [ 8 ] - K [ 2 ] x 4 T e [ 7 ] - T e [ 8 ] - A g [ 3 ] x 4 T e [ 7 ] - T e [ 8 ] - A g [ 3 ] x 4 K [ 2 ] - T e [ 8 ] - K [ 2 ] x 2 K [ 2 ] - T e [ 8 ] - A g [ 3 ] x 2 9 0 . 3 2 0 0 ) 8 9 . 7 2 ( 9 ) 1 7 9 5 5 0 2 ) 8 2 6 7 ( 7 ) 6 1 . 7 7 ( 7 ) 1 1 7 . 7 4 ( 1 1 ) 1 2 5 . 0 1 ( 9 ) 1 2 5 . 2 0 ( 9 ) 1 2 5 . 0 1 ( 1 0 ) 1 2 5 . 2 4 0 0 ) 9 0 5 1 ( 1 0 ) 8 9 3 9 ( 8 ) 1 7 4 . 8 7 0 2 ) 6 3 . 2 9 ( 8 ) 1 1 6 6 8 ( 1 0 ) 6 3 . 2 9 ( 9 ) 1 1 6 6 8 ( 1 0 ) 7 9 5 0 ( 9 ) 7 9 5 0 ( 9 ) 7 9 5 0 ( 1 0 ) 8 2 6 2 ( 8 ) 6 2 4 2 ( 8 ) 1 1 7 . 7 1 ( 9 ) 1 2 5 . 0 9 ( 9 ) 1 2 5 . 0 9 ( 9 ) 9 0 . 6 4 0 0 ) 8 9 3 9 ( 9 ) 1 7 4 . 9 2 0 2 ) 6 2 7 1 ( 8 ) 1 1 6 . 8 5 0 1 ) 6 2 . 7 1 ( 8 ) 1 1 6 . 8 5 0 1 ) 7 9 6 5 ( 8 ) 7 9 6 5 ( 9 ) 8 9 . 7 5 ( 1 0 ) 8 9 4 7 ( 9 ) 1 7 9 3 3 0 2 ) 8 2 4 8 ( 7 ) 5 9 6 7 ( 7 ) 1 1 2 7 3 ( 1 0 ) 1 2 0 . 1 1 ( 9 ) 1 2 0 . 1 2 ( 9 ) 1 2 0 . 1 1 ( 9 ) 1 2 0 . 1 2 ( 9 ) 8 4 4 1 ( 9 ) 8 7 0 9 ( 8 ) 1 7 1 . 8 9 0 2 ) 6 0 0 3 ( 8 ) 1 1 3 . 9 3 0 0 ) 6 0 0 3 ( 8 ) 1 1 3 9 3 ( 1 0 ) 7 8 9 1 ( 9 ) 7 8 . 9 1 0 0 ) 7 8 9 1 ( 1 1 ) 8 2 4 2 ( 9 ) 5 9 4 8 ( 7 ) 1 1 6 . 1 8 ( 1 0 ) 1 2 1 . 4 1 ( 9 ) 1 2 1 . 4 1 0 0 ) 8 4 6 3 ( 9 ) 8 7 0 9 ( 8 ) 1 7 1 . 7 6 0 2 ) 6 0 3 5 ( 7 ) 1 1 2 5 3 ( 1 0 ) 6 0 3 5 ( 8 ) 1 1 2 5 3 ( 1 0 ) 7 8 9 7 ( 8 ) 7 8 9 7 ( 9 ) 9 0 9 1 ( 1 0 ) 8 9 9 7 ( 9 ) 1 7 9 . 8 2 ( 1 3 ) 8 2 8 0 ( 7 ) 6 4 1 8 ( 7 ) 1 2 2 . 6 9 0 1 ) 1 2 9 . 8 9 ( 9 ) 1 3 0 . 4 2 0 0 ) 1 2 9 . 8 9 ( 9 ) 1 3 0 . 4 2 0 0 ) 9 6 . 9 2 0 2 ) 9 2 4 8 ( 8 ) 1 7 9 8 3 0 2 ) 6 6 5 9 ( 9 ) 1 1 9 . 6 4 ( 1 0 ) 6 6 5 9 ( 9 ) 1 1 9 . 6 4 ( 1 0 ) 7 9 9 2 ( 9 ) 7 9 9 2 ( 1 0 ) 7 9 9 2 ( 1 1 ) 8 2 7 4 ( 9 ) 6 5 5 6 ( 8 ) 1 1 8 . 9 9 0 0 ) 1 2 8 . 8 5 ( 9 ) 1 2 8 . 8 5 ( 9 ) 9 7 . 1 0 0 2 ) 9 2 4 8 ( 9 ) 1 7 9 . 7 1 0 3 ) 6 5 3 7 ( 8 ) 1 2 1 . 2 6 ( 1 1 ) 6 5 3 7 ( 8 ) 1 2 1 . 2 6 0 2 ) 8 0 2 1 ( 8 ) 8 0 2 1 ( 9 ) T a b l e 4 . 1 8 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K o , 7 1 ( . ) A g 1 , 2 9 ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A g [ 3 ] - T e [ 8 ] - A g [ 3 ] x 2 T e [ 2 ] - K [ l ] - T e [ 2 ] x 2 T e [ 2 ] - K [ l ] - T e [ 2 ] x 6 T e [ 2 ] - K [ l ] - T e [ 2 ] x 4 T e [ 1 ] - K [ 2 ] - T e [ 1 ] x 4 T e [ 1 ] - K [ 2 ] - T e [ 1 ] x 4 T e [ 1 ] - K [ 2 ] - T e [ 1 ] x 4 T e [ 1 ] - K [ 2 ] - T e [ 7 ] x 4 T e [ 1 ] - K [ 2 ] - T e [ 7 ] x 4 T e [ 1 ] - K [ 2 ] - T e [ 8 ] x 4 T e [ 1 ] - K [ 2 ] - T e [ 8 ] x 4 T e [ 7 ] - K [ 2 ] - T e [ 7 ] x 2 T e [ 7 ] - K [ 2 ] - T e [ 8 ] x 4 T e [ 8 ] - K [ 2 ] - T e [ 8 ] x 2 T e [ 1 ] - A g [ 1 ] - T e [ 1 ] x 2 T e [ 1 ] - A g [ 1 ] - T e [ 2 ] x 4 T e [ 1 ] - A g [ 1 ] - A g [ 2 ] x 4 T e [ 1 ] - A g [ l ] - A g [ 2 ] x 4 T e [ 2 ] - A g [ l ] - T e [ 2 ] x 2 T e [ 2 ] - A g [ l ] - A g [ 2 ] x 4 T e [ 2 ] - A g [ l ] - A g [ 2 ] x 4 A g [ 2 ] - A g [ l ] - A g [ 2 ] x 4 A g [ 2 ] - A g [ l l - A g [ 2 ] x 4 A g [ 2 ] - A g [ l ] - A g [ 2 ] X 4 T e [ 1 ] - A g [ 2 ] - T e [ 1 ] x 2 T e [ 1 ] - A g [ 2 ] - T e [ 2 ] x 4 T e [ 1 ] - A g [ 2 ] - A g [ 1 ] x 4 T e [ 1 ] - A g [ 2 ] - A g [ 1 ] x 4 T e [ 2 ] - A g [ 2 ] - T e [ 2 ] x 2 T e [ 2 ] - A g [ 2 ] - A g [ l ] x 4 T e [ 2 ] - A g [ 2 ] - A g [ l ] x 4 A g [ l l - A g [ 2 ] - A g [ I ] x 4 M N ] - A g [ 2 ] - A g [ l l X 4 A g [ I ] - A g [ 2 1 - A g [ l l x 4 7 9 . 6 5 ( 9 ) 8 1 0 7 ( 1 6 ) 8 0 . 3 9 0 3 ) 1 3 2 . 4 ( 3 ) 8 5 0 6 ( 9 ) 8 4 4 8 ( 7 ) 1 4 4 . 7 4 0 2 ) 7 8 . 7 0 ( 9 ) 1 3 1 . 4 9 ( 9 ) 7 8 . 4 7 ( 8 ) 1 3 1 . 7 2 0 2 ) 7 9 5 0 ( 1 0 ) 5 3 9 0 ( 8 ) 7 9 8 0 ( 9 ) 9 8 5 1 ( 1 1 ) 1 1 2 8 1 ( 1 0 ) 5 7 5 7 ( 8 ) 1 2 2 2 2 0 1 ) 1 0 6 8 3 0 2 ) 5 5 3 4 ( 8 ) 1 2 4 . 7 1 0 2 ) 9 0 2 6 ( 1 0 ) 8 9 7 2 ( 9 ) 1 7 9 . 7 0 0 3 ) 9 8 9 9 ( 1 1 ) 1 1 2 . 8 5 0 1 ) 5 7 4 4 ( 8 ) 1 2 2 . 6 8 0 2 ) 1 0 6 . 3 4 0 3 ) 5 5 5 3 ( 8 ) 1 2 4 . 3 0 0 1 ) 9 0 . 3 1 0 0 ) 8 9 . 7 2 ( 9 ) 1 7 9 . 6 9 ( 1 3 ) 7 8 9 7 ( 9 ) 8 0 . 7 7 0 8 ) 8 0 . 3 2 0 3 ) 1 3 2 . 2 ( 2 ) 8 5 0 4 ( 1 0 ) 8 4 0 0 ( 8 ) 1 4 4 . 1 8 ( l 4 ) 7 6 5 8 ( 8 ) 1 2 9 . 3 4 ( 9 ) 7 5 8 3 ( 8 ) 1 2 8 . 7 7 0 0 ) 7 8 9 1 ( 1 0 ) 4 9 8 7 ( 8 ) 7 7 . 9 4 0 0 ) 9 8 . 4 7 0 6 ) 1 1 2 . 7 0 0 0 ) 5 7 5 5 ( 7 ) 1 2 2 2 2 0 0 ) 1 0 6 6 3 0 7 ) 5 5 2 6 ( 7 ) 1 2 4 . 3 1 0 6 ) 8 9 . 8 8 0 3 ) 8 9 5 4 ( 7 ) 1 7 9 . 5 7 0 7 ) 9 8 9 3 ( 1 5 ) 1 1 2 . 3 3 0 2 ) 5 7 1 6 ( 9 ) 1 2 2 . 3 7 0 0 ) 1 0 6 . 2 3 ( l 7 ) 5 5 2 7 ( 7 ) 1 2 3 . 9 4 0 2 ) 9 0 0 7 ( 1 2 ) 8 9 . 5 4 ( 1 1 ) 1 7 9 . 6 4 0 4 ) 8 0 2 1 ( 9 ) 8 1 . 3 9 0 8 ) 8 0 . 4 6 0 3 ) 1 3 2 . 6 ( 2 ) 8 5 0 7 ( 1 0 ) 8 4 9 7 ( 8 ) 1 4 5 . 2 9 0 4 ) 8 0 9 3 ( 9 ) 1 3 3 . 6 5 ( 9 ) 8 1 0 9 ( 8 ) 1 3 4 6 9 0 0 ) 7 9 . 9 2 0 1 ) 5 7 8 5 ( 8 ) 8 1 . 4 6 0 0 ) 9 8 5 5 ( 1 6 ) 1 1 2 9 2 ( 1 0 ) 5 7 5 9 ( 7 ) 1 2 2 . 2 3 0 0 ) 1 0 7 . 0 3 0 7 ) 5 5 4 3 ( 7 ) 1 2 5 . 1 2 0 6 ) 9 0 . 6 2 0 3 ) 8 9 9 0 ( 7 ) l 7 9 . 8 1 ( l 3 ) 9 9 0 5 ( 1 5 ) 1 1 3 . 3 9 0 2 ) 5 7 7 2 ( 9 ) 1 2 2 . 9 9 0 0 ) 1 0 6 . 4 4 0 8 ) 5 5 7 9 ( 7 ) 1 2 4 . 6 8 0 2 ) 9 0 5 5 ( 1 3 ) 8 9 9 0 ( 1 1 ) 1 7 9 . 7 7 ( 1 2 ) 2 5 3 T a b l e 4 . 1 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r K C u C e T e 4 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 3 3 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 o ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 6 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 s t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R l S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e K C u C e T e 4 7 5 3 . 2 1 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A O r t h o r h o m b i c P 2 1 2 1 2 ( 0 0 1 / 2 ) 0 s 0 a = 4 . 4 0 6 5 ( 6 ) A , 0 1 = 9 0 0 b = 4 . 4 2 2 0 ( 6 ) A , [ 3 = 9 0 0 c = 2 1 . 0 8 6 ( 3 ) 1 8 1 , 7 = 9 0 ° 0 . 3 5 5 0 ( 8 ) b ‘ + 1 / 2 c ‘ 4 1 0 . 8 7 ( 1 0 ) A 3 2 6 . 0 8 5 9 g / c m 3 2 2 . 4 2 1 m m ' 1 6 2 8 0 . 1 5 x 0 . 1 0 x 0 0 1 1 1 1 1 1 1 3 1 . 7 0 t o 2 9 . 3 3 ° - 6 < = h < = 6 , - 6 < = k < = 6 , - 2 9 < = l < = 2 9 , - 1 < = m < = 1 9 8 9 0 ( 2 5 8 0 m a i n + 7 3 1 0 s a t e l l i t e s ) 3 2 0 4 ( 9 9 5 m a i n + 2 2 0 9 s a t e l l i t e S ) [ R i n t = 0 . 0 7 4 2 ] 9 6 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 3 2 0 4 / 0 / 1 0 1 1 . 5 8 R o b . = 0 . 0 4 9 3 , w R o b s = 0 . 1 2 0 9 R . " = 0 . 0 9 1 5 , w R a u = 0 . 1 2 8 1 R o b s = 0 . 0 4 2 1 , w R o b s = 0 . 1 1 3 4 R . “ = 0 . 0 4 5 6 , w k . ” = 0 . 1 1 4 4 R o b s = 0 . 0 9 4 8 , w R o b s = 0 . 1 5 3 9 R . " = 0 . 2 7 0 0 , w R a u = 0 . 1 8 2 0 0 . 0 0 1 0 4 0 1 ) 0 . 0 9 5 5 a n d 0 . 7 7 5 9 3 . 6 9 a n d - 2 . 6 3 6 1 5 : 3 R = l e F o l - c h l l / z l l F o l , w R = { E I W G F O I 2 - c h | 2 ) 2 ] / 2 “ ‘ [ W ( | F o l 4 ) ] } " 2 a n d W = 1 / ( < > 2 ( I ) + 0 - 0 0 1 6 1 2 ) 2 5 4 T a b l e 4 . 2 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K C u C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x y 2 O c c u p a n c y U e q C e 0 0 0 4 0 1 3 ( 1 ) 1 1 3 ( 1 ) s i n , 1 2 2 ( 1 ) - 7 ( 2 ) 2 ( 1 ) c o s , 1 - 6 8 ( 1 ) 2 2 ( 5 ) 1 ( 1 ) T e [ 1 ] 0 0 0 7 0 5 ( 1 ) 1 1 6 ( 1 ) s i n , 1 - 2 4 ( 2 ) - 4 ( 6 ) 0 ( 1 ) c o s , 1 5 ( 1 ) 1 ( 1 ) - l ( 2 ) T e [ 2 ] 0 0 0 5 5 6 6 ( 1 ) 1 1 2 ( 1 ) s i n , 1 0 ( 1 ) - 6 ( 1 ) 1 ( 2 ) c o s , 1 0 ( 2 ) - 3 3 ( 6 ) 0 ( 1 ) T e [ 3 ] 0 0 5 0 0 0 2 8 1 3 ( 1 ) 1 1 7 ( 1 ) s i n , 1 - 1 7 3 ( 2 ) 2 8 ( 4 ) - 2 ( 2 ) c o s , 1 2 1 1 ( 2 ) - 3 4 ( 5 ) - 1 ( 1 ) T e [ 4 ] 0 0 5 0 0 0 7 1 8 5 ( 1 ) 1 1 6 ( 1 ) s i n , 1 1 5 0 ( 2 ) 1 2 ( 4 ) 3 ( 2 ) c o s , 1 1 8 3 ( 2 ) 1 5 ( 5 ) - 2 ( 1 ) K 0 0 0 8 5 9 0 ( 1 ) 1 1 7 ( 1 ) s i n , 1 - 5 6 ( 6 ) 1 5 9 ( 1 9 ) 8 ( 2 ) c o s , 1 - 2 7 ( 3 ) 7 6 ( 9 ) - 1 7 ( 5 ) C u 0 0 5 0 0 0 - 1 ( 1 ) 1 2 1 ( 1 ) s i n , 1 - 3 2 ( 8 ) 2 8 ( 1 2 ) 0 c o s , 1 0 0 — 5 ( 3 ) ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 4 . 2 1 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K C u C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 C e 0 7 ( 1 ) 1 4 ( 1 ) 1 7 ( 1 ) 7 ( 1 ) 0 0 s i n , 1 - 2 0 ) - 1 0 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 - 1 0 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 2 5 5 T a b l e 4 . 2 1 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K C u C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 1 ] 0 9 ( 1 ) 1 7 ( 1 ) 2 2 ( 1 ) 4 ( 1 ) 0 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) c o s , 1 — 1 ( 1 ) 1 ( 1 ) 0 ( 2 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) T e [ 2 ] 0 7 ( 1 ) 1 3 ( 1 ) 1 7 ( 1 ) - 7 0 ) 0 0 s i n , 1 1 ( 1 ) 1 ( 1 ) - 3 0 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) - 1 0 ) - 2 0 ) T e [ 3 ] 0 1 3 ( 1 ) 1 9 ( 1 ) 1 8 ( 1 ) 1 2 ( 1 ) 0 0 s i n , 1 - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 2 0 ) 2 ( 1 ) 2 ( 1 ) c o s , 1 - 1 0 ) 0 ( 1 ) 0 ( 1 ) - 2 0 ) - 2 0 ) - 3 0 ) T e [ 4 ] 0 1 2 ( 1 ) 1 9 ( 1 ) 1 7 ( 1 ) . 4 0 ) 0 0 s i n , 1 - 2 0 ) 1 ( 1 ) - 3 0 ) - 1 0 ) - 1 0 ) 0 ( 1 ) c o s , 1 2 ( 1 ) - 1 0 ) 2 ( 1 ) 1 ( 1 ) - 1 0 ) 0 ( 1 ) K 0 1 4 ( 1 ) 1 9 ( 2 ) 2 0 ( 1 ) — 9 ( 2 ) 0 0 s i n , 1 5 ( 2 ) - 1 ( 2 ) 8 ( 2 ) 0 ( 1 ) - 1 0 ) 4 ( 3 ) c o s , 1 1 1 ( 4 ) 2 ( 4 ) - 1 6 ( 4 ) 1 ( 1 ) 0 ( 1 ) 2 ( 2 ) C u 0 1 7 ( 1 ) 2 5 ( 1 ) 2 0 ( 1 ) - 1 1 ( 2 ) 0 0 s i n , 1 0 0 0 0 1 ( 1 ) - 1 2 ( 2 ) c o s , 1 1 ( 3 ) 2 ( 3 ) 0 ( 3 ) 0 ( 2 ) 0 0 T a b l e 4 . 2 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K C u C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e C e - T e [ 2 ] 3 . 2 7 6 ( 3 ) 3 . 2 7 2 ( 4 ) 3 . 2 8 0 ( 4 ) C e - T e [ 2 ] x 4 3 . 2 4 5 3 ( 1 9 ) 3 . 2 3 2 9 ( 1 4 ) 3 . 2 5 7 5 ( 1 4 ) C e - T e [ 3 ] x 2 3 . 3 6 1 ( 3 ) 3 . 3 4 3 ( 3 ) 3 . 3 8 1 ( 3 ) C e - T e [ 4 ] x 2 3 . 3 5 2 ( 3 ) 3 . 3 0 3 ( 3 ) 3 . 4 0 1 ( 3 ) T e [ 1 ] - K x 4 3 . 4 5 7 ( 6 ) 3 . 3 9 0 ( 6 ) 3 . 5 2 5 ( 6 ) T e [ 1 ] - C u x 2 2 . 6 6 5 ( 4 ) 2 . 6 5 5 ( 4 ) 2 . 6 7 6 ( 4 ) T e [ 1 ] - C u x 2 2 . 6 5 7 ( 3 ) 2 . 6 5 2 ( 3 ) 2 . 6 6 3 ( 3 ) T e [ 3 ] - T e [ 4 ] x 4 3 . 1 2 3 ( 2 ) 3 . 0 0 8 ( 3 ) 3 . 2 4 2 ( 2 ) C u - C u x 4 3 . 1 2 1 ( 4 ) 3 . 1 0 3 ( 5 ) 3 . 1 4 0 ( 5 ) 2 5 6 T a b l e 4 . 2 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K C u C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 2 ] - C e - T e [ 2 ] x 8 7 4 1 2 ( 7 ) 7 3 9 9 ( 7 ) 7 4 2 6 ( 7 ) T e [ 2 ] - C e - T e [ 3 ] x 2 l 3 8 . 8 0 ( 8 ) 1 3 8 . 0 4 ( 9 ) l 3 9 . 5 3 ( 9 ) T e [ 2 ] - C e - T e [ 4 ] x 2 l 3 8 . 9 1 ( 5 ) 1 3 8 . 5 0 ( 5 ) 1 3 9 . 3 2 ( 5 ) T e [ 2 ] - C e - T e [ 2 ] x 4 8 5 9 0 ( 4 ) 8 5 0 9 ( 4 ) 8 6 7 0 ( 4 ) T e [ 2 ] - C e - T e [ 2 ] x 4 8 5 5 2 ( 5 ) 8 5 0 6 ( 6 ) 8 5 9 8 ( 6 ) T e [ 2 ] - C e - T e [ 2 ] x 4 1 4 8 . 2 4 ( 1 0 ) 1 4 7 . 9 8 ( 1 1 ) 1 4 8 . 5 3 ( l 1 ) T e [ 2 ] - C e - T e [ 3 ] x 4 7 5 9 7 ( 6 ) 7 4 8 2 ( 5 ) 7 7 0 9 ( 5 ) T e [ 2 ] - C e - T e [ 3 ] x 4 1 3 0 . 8 5 ( 5 ) 1 2 8 . 6 2 ( 6 ) 1 3 3 . 1 1 ( 7 ) T e [ 2 ] - C e - T e [ 4 ] x 4 7 6 1 1 ( 5 ) 7 5 7 7 ( 6 ) 7 6 4 6 ( 6 ) T e [ 2 ] - C e - T e [ 4 ] x 4 1 3 0 . 7 2 ( 7 ) 1 2 9 . 9 2 ( 8 ) 1 3 1 . 5 2 ( 8 ) T e [ 3 ] - C e - T e [ 3 ] x 2 8 2 3 4 ( 8 ) 8 2 0 9 ( 9 ) 8 2 6 8 ( 9 ) T e [ 3 ] - C e - T e [ 4 ] x 4 5 5 4 5 ( 5 ) 5 3 0 7 ( 5 ) 5 7 8 1 ( 5 ) T e [ 4 ] - C e - T e [ 4 ] x 2 8 2 1 8 ( 7 ) 8 1 9 1 ( 8 ) 8 2 4 9 ( 8 ) K - T e [ 1 ] - K x 4 7 9 . 4 9 ( 1 5 ) 7 7 . 8 9 ( 1 7 ) 8 1 . 1 0 ( 1 7 ) K - T e [ 1 ] - K x 4 7 9 . 2 0 ( 1 3 ) 7 7 . 7 8 ( 1 3 ) 8 0 . 6 2 ( 1 3 ) K - T e [ 1 ] - K x 4 1 2 9 . 0 7 ( 1 7 ) 1 2 8 . 5 8 ( 1 7 ) l 2 9 . 5 6 ( 1 6 ) K - T e [ 1 ] - C u x 8 7 3 . l 3 ( 1 5 ) 7 2 3 0 ( 1 4 ) 7 3 9 6 ( 1 4 ) K - T e [ 1 ] ~ C u x 8 1 4 0 . 4 0 ( 1 1 ) l 3 9 . 7 l ( 1 2 ) 1 4 1 . 0 8 ( 1 2 ) C u - T e [ 1 ] - C u x 4 1 1 2 . 1 1 ( 1 3 ) 1 1 1 . 9 2 ( 1 5 ) 1 1 2 . 2 9 ( 1 5 ) C u - T e [ 1 ] - C u x 8 7 1 . 8 1 ( l 3 ) 7 1 . 5 0 ( 1 3 ) 7 2 1 2 ( 1 3 ) C e - T e [ 2 ] - C e x 8 1 0 5 . 8 7 ( 7 ) 1 0 5 . 7 4 ( 7 ) 1 0 6 . 0 1 ( 7 ) C e - T e [ 2 ] - C e x 4 8 5 9 0 ( 4 ) 8 5 5 3 ( 3 ) 8 6 2 7 ( 3 ) C e - T e [ 2 ] - C e x 4 8 5 5 2 ( 5 ) 8 5 0 6 ( 5 ) 8 5 9 8 ( 5 ) C e - T e [ 2 ] - C e x 4 1 4 8 . 2 5 ( 1 0 ) 1 4 8 . 1 1 ( 1 2 ) l 4 8 . 3 9 ( 1 2 ) C e - T e [ 3 ] - C e x 2 8 2 2 8 ( 8 ) 8 1 9 4 ( 8 ) 8 2 7 1 ( 9 ) C e - T e [ 3 ] - T e [ 4 ] x 4 6 2 1 1 ( 7 ) 6 1 . 5 0 ( 7 ) 6 2 7 8 ( 7 ) C e - T e [ 3 ] - T e [ 4 ] x 4 1 1 7 . 7 5 ( 9 ) 1 1 4 . 8 7 ( 8 ) 1 2 0 . 5 3 ( 1 0 ) C e - T e [ 3 ] - K x 4 1 2 7 . 0 9 ( 1 3 ) 1 2 6 . 0 8 ( 1 2 ) 1 2 7 . 9 5 ( 1 3 ) T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 9 0 3 4 ( 5 ) 8 6 0 4 ( 5 ) 9 4 6 8 ( 5 ) T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 8 9 . 6 9 ( 7 ) 8 8 9 6 ( 7 ) 9 0 2 4 ( 7 ) T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 2 1 7 6 . 8 5 ( 7 ) 1 7 5 . 0 8 ( 7 ) 1 7 9 . 8 7 ( 1 2 ) T e [ 4 ] - T e [ 3 ] - K x 4 6 5 1 3 ( 1 3 ) 6 4 4 4 ( 1 2 ) 6 5 8 2 ( 1 3 ) T e [ 4 ] - T e [ 3 ] - K x 4 1 1 4 . 9 0 ( 1 5 ) 1 1 3 . 0 5 ( 1 4 ) 1 1 6 . 6 1 ( 1 4 ) 2 5 7 T a b l e 4 . 2 3 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K C u C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 2 C e - T e [ 4 ] - C e x 2 C e - T e [ 4 ] - T e [ 3 ] x 4 C e - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 2 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 2 T e [ 1 ] - K - T e [ 1 ] x 4 T e [ 1 ] - K - T e [ 1 ] x 4 T e [ 1 ] - K - T e [ 1 ] x 4 T e [ 1 ] - K - T e [ 3 ] x 4 T e [ 1 ] - K - T e [ 3 ] x 4 T e [ 1 ] - C u - T e [ 1 ] x 4 T e [ 1 ] - C u - T e [ 1 ] x 8 T e [ 1 ] - C u - C u x 4 T e [ 1 ] - C u - C u x 8 T e [ 1 ] - C u - C u x 4 C u - C u - C u x 4 C u - C u - C u x 4 C u - C u - C u x 4 1 7 7 . 6 2 ( 7 ) 8 2 1 9 ( 8 ) 6 2 4 5 ( 7 ) 1 1 7 . 6 4 ( 1 0 ) 9 0 3 4 ( 5 ) 8 9 7 0 ( 7 ) 1 7 7 . 6 5 ( 8 ) 1 7 7 . 0 9 ( 7 ) 7 9 5 1 ( 1 1 ) 7 9 . 1 9 0 5 ) 1 2 9 . 1 ( 2 ) 8 7 . 9 5 0 0 ) 1 3 6 . 5 ( 2 ) 1 1 2 1 0 ( 1 4 ) 1 0 8 . 1 9 0 1 ) 5 3 9 8 ( 9 ) 1 2 5 . 9 5 0 3 ) 5 4 2 1 ( 9 ) 9 0 . 2 0 0 1 ) 8 9 . 8 0 0 3 ) 1 7 9 5 2 0 6 ) 1 7 6 2 8 0 ) 8 1 9 1 ( 8 ) 6 0 7 8 ( 7 ) 1 1 6 . 3 8 ( 1 0 ) 8 6 2 4 ( 4 ) 8 8 9 6 ( 6 ) 1 7 6 . 3 5 ( 7 ) 1 7 5 . 4 7 ( 7 ) 7 8 . 9 2 0 0 ) 7 7 . 7 8 ( 1 4 ) 1 2 7 . 8 ( 3 ) 8 6 2 8 ( 1 1 ) 1 3 3 . 6 ( 2 ) 1 1 1 . 7 ( 2 ) 1 0 7 9 6 ( 6 ) 5 3 7 9 ( 7 ) 1 2 5 . 7 4 0 4 ) 5 4 1 5 ( 1 0 ) 8 9 . 8 4 0 2 ) 8 9 2 5 ( 1 4 ) 1 7 9 . 3 2 0 9 ) 1 7 9 . 8 9 ( 1 3 ) 8 2 4 9 ( 8 ) 6 4 1 5 ( 8 ) 1 1 8 . 8 5 ( 1 0 ) 9 4 4 5 ( 5 ) 9 0 2 4 ( 6 ) 1 7 9 . 8 9 ( 1 2 ) 1 7 9 . 8 8 ( 1 2 ) 8 0 0 9 ( 1 0 ) 8 0 . 6 2 0 5 ) 1 3 0 . 4 ( 3 ) 8 9 . 6 4 ( 1 1 ) 1 3 9 . 3 ( 2 ) 1 1 2 . 5 ( 2 ) 1 0 8 . 4 2 ( 6 ) 5 4 1 7 ( 7 ) 1 2 6 . 1 7 0 4 ) 5 4 2 8 ( 1 0 ) 9 0 5 6 ( 1 2 ) 9 0 . 3 5 0 5 ) 1 7 9 . 9 ( 2 ) 2 5 8 T a b l e 4 . 2 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r K C u C e T e 4 a t 3 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 2 2 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 o ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 6 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 s t o r d e r s a t e l l i t e s [ I > 2 o ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f f i c i e n t T w i n a n d T m c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e K C u C e T e 4 7 5 3 . 2 3 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A O r t h o r h o m b i c P 2 1 2 1 2 ( O B l / 2 ) 0 s 0 a = 4 . 4 2 2 9 ( 3 ) A , 0 1 = 9 0 ° b = 4 . 4 3 7 1 ( 3 ) A , B = 9 0 ° c = 2 1 . 1 9 7 6 ( 1 7 ) A , y = 9 0 ° 0 . 3 5 3 8 ( 4 ) b ‘ + 1 / 2 c ' 4 1 6 . 0 0 ( 5 ) A 3 2 6 . 0 1 0 8 g / c m 3 2 2 . 1 4 5 m m " 6 2 8 0 . 1 3 x 0 . 0 4 x 0 0 1 m m 3 1 . 6 9 t o 2 9 . 2 2 ° - 6 < = h < = 6 , - 6 < = k < = 5 , - 2 9 < = l < = 2 9 , - 1 < = m < = 1 1 0 3 6 4 ( 2 6 7 2 m a i n + 7 6 9 2 s a t e l l i t e s ) 3 2 7 7 ( 1 0 4 8 m a i n + 2 2 2 9 s a t e l l i t e S ) [ R i m = 0 . 0 4 0 0 ] 9 8 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 3 2 7 7 / 0 / 1 0 1 1 . 1 0 R o b s = 0 . 0 3 0 2 , w R o b s = 0 . 0 7 1 7 R . , “ = 0 . 0 6 2 4 , w R a u = 0 . 0 8 3 2 R o b s = 0 . 0 1 8 9 , w R o b s = 0 . 0 5 0 6 R a n = 0 . 0 2 1 1 , w R , n = 0 . 0 5 1 6 R o b s = 0 . 0 9 1 6 , w R o b s = 0 . 1 2 9 3 R , “ = 0 . 2 2 5 8 , w R a u = 0 . 1 6 0 2 0 . 0 0 0 1 7 0 ) 0 . 1 2 7 4 a n d 0 . 8 5 7 0 1 . 5 6 a n d - 1 5 4 e . A ' 3 R = 2 1 1 1 7 0 1 1 1 1 1 / 2 1 F 0 1 , w R = { 2 1 0 1 6 . 1 2 - c h | 2 ) 2 1 / 2 1 w < 1 F o 1 4 > 1 } ‘ ” a n d w = 1 / ( o Z ( I > + 0 . 0 0 1 6 1 2 ) 2 5 9 T a b l e 4 . 2 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K C u C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x y 2 O c c u p a n c y c h C e 0 0 0 4 0 1 8 ( 1 ) 1 1 0 ( 1 ) s i n , 1 2 8 ( 1 ) - 7 ( 1 ) 0 ( 1 ) c o s , 1 - 8 7 ( 1 ) 2 3 ( 4 ) 0 ( 1 ) T e [ 1 ] 0 0 0 7 0 5 ( 1 ) 1 2 0 ( 1 ) s i n , 1 - 2 9 ( 2 ) - 1 0 ( 5 ) 0 ( 1 ) c o s , 1 6 ( 1 ) 2 ( 1 ) - 2 ( 1 ) T e [ 2 ] 0 0 0 5 5 6 4 ( 1 ) 1 1 0 ( 1 ) s i n , 1 0 ( 1 ) 1 ( 1 ) - 2 ( 1 ) c o s , 1 1 ( 1 ) 3 ( 4 ) 0 ( 1 ) T e [ 3 ] 0 0 5 0 0 0 2 8 2 2 ( 1 ) 1 1 5 ( 1 ) s i n , 1 - 2 4 2 ( 2 ) - 1 7 ( 3 ) - 3 ( 1 ) c o s , 1 2 9 7 ( 3 ) 2 1 ( 4 ) - 2 ( 1 ) T e [ 4 ] 0 0 5 0 0 0 7 1 7 6 ( 1 ) 1 1 4 ( 1 ) s i n , 1 1 9 4 ( 2 ) 1 1 ( 3 ) 3 ( 1 ) c o s , 1 2 3 8 ( 2 ) 1 4 ( 4 ) - 2 ( 1 ) K 0 0 0 8 5 8 0 ( 1 ) 1 2 5 ( 1 ) s i n , 1 - 7 0 ( 6 ) - 3 5 ( 1 8 ) 3 ( 2 ) c o s , 1 - 3 3 ( 3 ) - 1 7 ( 8 ) - 6 ( 3 ) C u 0 0 5 0 0 0 - l ( 1 ) 1 3 2 ( 1 ) s i n , 1 - 4 0 ( 8 ) 9 4 ( 1 4 ) 0 c o s , 1 0 0 - 1 6 ( 2 ) ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 4 . 2 6 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K C u C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 C e 0 1 0 ( 1 ) 8 ( 1 ) 1 2 ( 1 ) 1 ( 1 ) 0 0 s i n , 1 - 2 0 ) - 2 0 ) 3 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 - 1 0 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) - 1 0 ) 1 ( 1 ) 2 6 0 T a b l e 4 . 2 6 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K C u C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 1 ] 0 1 8 ( 1 ) 1 7 ( 1 ) 2 5 ( 1 ) 8 ( 1 ) 0 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 - 1 0 ) 1 ( 1 ) - 1 0 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) T e [ 2 ] 0 9 ( 1 ) 9 ( 1 ) 1 1 ( 1 ) - 1 0 ) 0 0 s i n , 1 0 ( 1 ) 3 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) - 1 0 ) 0 ( 1 ) 0 ( 1 ) - 1 0 ) - 2 ( 1 ) T e [ 3 ] 0 1 8 ( 1 ) 1 3 ( 1 ) 1 4 ( 1 ) 4 ( 1 ) 0 0 s i n , 1 3 ( 1 ) - 2 0 ) - 3 0 ) 4 ( 1 ) 2 ( 1 ) 1 ( 1 ) c o s , 1 2 ( 1 ) - 2 0 ) - 2 0 ) - 3 0 ) - 2 0 ) - 1 0 ) T e [ 4 ] 0 1 8 ( 1 ) 1 1 ( 1 ) 1 3 ( 1 ) 2 ( 1 ) 0 0 s i n , 1 - 1 3 0 ) 0 ( 1 ) 2 ( 1 ) - 3 ( 1 ) 0 ( 1 ) 1 ( 1 ) c o s , 1 1 1 ( 1 ) 0 ( 1 ) - 2 0 ) 2 ( 1 ) 0 ( 1 ) 1 ( 1 ) K 0 2 8 ( 2 ) 2 2 ( 2 ) 2 5 ( 1 ) - 9 ( 3 ) 0 0 s i n , 1 5 ( 2 ) 1 ( 2 ) 1 1 ( 2 ) 0 ( 1 ) 2 ( 1 ) 9 ( 3 ) c o s , 1 1 0 ( 3 ) - 2 ( 3 ) - 2 3 ( 3 ) 0 ( 1 ) 1 ( 1 ) 4 ( 1 ) C u 0 3 4 ( 1 ) 3 5 ( 1 ) 2 6 ( 1 ) - 8 ( 2 ) 0 0 s i n , 1 0 0 0 0 0 ( 1 ) - 1 6 ( 2 ) c o s , 1 5 ( 2 ) - 5 ( 3 ) 9 ( 3 ) 2 ( 2 ) 0 0 T a b l e 4 . 2 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K C u C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e C e - T e [ 2 ] 3 . 2 7 8 2 ( 1 8 ) 3 . 2 7 3 ( 3 ) 3 . 2 8 4 ( 3 ) C e - T e [ 2 ] x 4 3 . 2 5 5 7 ( 1 3 ) 3 . 2 3 4 1 ( 1 4 ) 3 . 2 7 7 5 ( 1 4 ) C e - T e [ 3 ] x 2 3 . 3 7 1 ( 2 ) 3 . 3 6 7 ( 2 ) 3 . 3 7 9 ( 2 ) C e - T e [ 4 ] x 2 3 . 3 6 0 7 ( 1 9 ) 3 . 2 9 8 0 ( 1 7 ) 3 . 4 2 4 1 ( 1 7 ) T e [ 1 ] - K x 4 3 . 4 8 0 ( 5 ) 3 . 4 6 4 ( 5 ) 3 . 4 9 6 ( 5 ) T e [ 1 ] - C u x 2 2 . 6 7 7 ( 4 ) 2 . 6 3 8 ( 5 ) 2 . 7 1 4 ( 5 ) T e [ 1 ] - C u x 2 2 . 6 6 7 ( 3 ) 2 . 6 4 9 ( 3 ) 2 . 6 8 4 ( 3 ) T e [ 3 ] - T e [ 4 ] x 4 3 . 1 3 4 0 ( 1 9 ) 2 . 9 5 2 ( 2 ) 3 . 3 2 4 ( 2 ) C u - C u x 4 3 . 1 3 3 ( 4 ) 3 . 0 8 1 ( 5 ) 3 . 1 8 5 ( 5 ) 2 6 1 T a b l e 4 . 2 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K C u C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 2 ] - C e - T e [ 2 ] x 8 7 4 1 9 ( 5 ) 7 3 8 2 ( 5 ) 7 4 5 5 ( 5 ) T e [ 2 ] - C e - T e [ 3 ] x 2 1 3 8 . 7 4 ( 5 ) 1 3 8 . 4 2 ( 7 ) 1 3 9 . 1 6 ( 5 ) T e [ 2 ] - C e - T e [ 4 ] x 2 1 3 8 . 8 6 ( 3 ) 1 3 8 . 3 4 ( 3 ) 1 3 9 . 3 9 ( 3 ) T e [ 2 ] - C e - T e [ 2 ] x 4 8 5 9 2 ( 3 ) 8 5 0 3 ( 2 ) 8 6 8 1 ( 2 ) T e [ 2 ] - C e - T e [ 2 ] x 4 8 5 5 7 ( 3 ) 8 5 3 8 ( 4 ) 8 5 7 5 ( 4 ) T e [ 2 ] - C e - T e [ 2 ] x 4 1 4 8 . 3 7 ( 6 ) 1 4 8 . 3 1 ( 7 ) 1 4 8 . 4 6 ( 7 ) T e [ 2 ] - C e - T e [ 3 ] x 4 7 5 9 1 ( 4 ) 7 3 6 9 ( 4 ) 7 8 1 0 ( 4 ) T e [ 2 ] - C e - T e [ 3 ] x 4 1 3 0 . 7 9 ( 4 ) 1 2 7 . 6 3 ( 4 ) 1 3 3 . 9 6 ( 5 ) T e [ 2 ] - C e - T e [ 4 ] x 4 7 6 0 1 ( 4 ) 7 5 4 4 ( 4 ) 7 6 6 2 ( 4 ) T e [ 2 ] - C e - T e [ 4 ] x 4 1 3 0 . 7 0 ( 5 ) 1 2 9 . 7 5 ( 6 ) l 3 1 . 6 4 ( 5 ) T e [ 3 ] - C e - T e [ 3 ] x 2 8 2 4 2 ( 5 ) 8 2 1 6 ( 6 ) 8 2 8 7 ( 6 ) T e [ 3 ] - C e - T e [ 4 ] x 4 5 5 5 3 ( 4 ) 5 2 5 1 ( 4 ) 5 8 5 6 ( 4 ) T e [ 4 ] - C e - T e [ 4 ] x 2 8 2 2 9 ( 5 ) 8 2 1 5 ( 5 ) 8 2 4 7 ( 5 ) K - T e [ 1 ] - K x 4 7 9 . 2 1 ( 1 4 ) 7 8 . 7 9 ( 1 5 ) 7 9 . 6 3 ( 1 5 ) K - T e [ 1 ] - K x 4 7 8 9 0 ( 1 1 ) 7 8 . 4 8 ( 1 0 ) 7 9 3 3 ( 1 0 ) K - T e [ 1 ] - K x 4 1 2 8 . 3 4 ( 1 2 ) 1 2 8 . 2 6 ( 1 2 ) 1 2 8 . 4 2 ( 1 2 ) K - T e [ 1 ] - C u x 8 7 3 . 4 4 ( 1 3 ) 7 2 7 2 ( 1 3 ) 7 4 1 8 ( 1 3 ) K - T e [ 1 ] - C u x 8 l 4 0 . 5 5 ( 1 0 ) 1 4 0 . 3 5 ( 1 0 ) 1 4 0 . 7 5 ( 1 0 ) C u - T e [ l ] - C u x 4 1 1 2 . 0 1 ( 1 3 ) l l l . 5 1 ( 1 4 ) 1 1 2 . 4 9 ( 1 4 ) C u - T e [ 1 ] - C u x 8 7 1 . 7 9 ( l 4 ) 7 0 . 8 1 ( 1 3 ) 7 2 7 8 ( 1 3 ) C e - T e [ 2 ] - C e x 8 1 0 5 . 8 l ( 5 ) 1 0 5 . 4 1 ( 4 ) 1 0 6 . 2 0 ( 4 ) C e - T e [ 2 ] - C e x 4 8 5 9 2 ( 2 ) 8 5 4 3 ( 2 ) 8 6 4 0 ( 2 ) C e - T e [ 2 ] - C e x 4 8 5 5 7 ( 4 ) 8 5 3 8 ( 3 ) 8 5 7 5 ( 3 ) C e - T e [ 2 ] - C e x 4 1 4 8 . 3 7 ( 6 ) 1 4 7 . 8 9 ( 8 ) 1 4 8 . 8 6 ( 8 ) C e - T e [ 3 ] - C e x 2 8 2 3 1 ( 6 ) 8 1 9 7 ( 6 ) 8 2 8 1 ( 6 ) C e - T e [ 3 ] - T e [ 4 ] x 4 6 2 0 6 ( 5 ) 6 0 7 8 ( 5 ) 6 3 3 2 ( 5 ) C e - T e [ 3 ] - T e [ 4 ] x 4 1 1 7 . 7 3 ( 6 ) 1 1 3 . 6 6 ( 6 ) 1 2 1 . 6 3 ( 7 ) C e - T e [ 3 ] - K x 4 1 2 7 . 1 4 ( 1 1 ) 1 2 3 . 3 1 ( l l ) 1 3 0 . 8 4 ( 1 2 ) T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 2 9 0 4 3 ( 4 ) 8 4 5 3 ( 4 ) 9 6 4 5 ( 5 ) T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 8 9 6 2 ( 5 ) 8 9 2 8 ( 5 ) 9 0 0 9 ( 5 ) T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 2 1 7 6 . 3 2 ( 6 ) 1 7 4 . 2 5 ( 6 ) 1 7 9 . 8 8 ( 6 ) T e [ 4 ] - T e [ 3 ] - K x 4 6 5 2 3 ( 1 1 ) 6 2 5 2 ( 1 0 ) 6 7 9 7 ( 1 1 ) T e [ 4 ] - T e [ 3 ] - K x 4 1 1 4 . 9 0 ( 1 2 ) 1 1 4 . 1 3 ( 1 2 ) 1 1 5 8 0 ( 1 2 ) 2 6 2 T a b l e 4 . 2 8 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K C u C e T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 2 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 2 C e - T e [ 4 ] - C e x 2 C e - T e [ 4 ] - T e [ 3 ] x 4 C e - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 2 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 2 T e [ 1 ] - K - T e [ 1 ] x 4 T e [ 1 ] - K - T e [ 1 ] x 4 T e [ 1 ] - K - T e [ 1 ] x 4 T e [ 1 ] - K - T e [ 3 ] x 4 T e [ 1 ] - K - T e [ 3 ] x 4 T e [ 1 ] - C u - T e [ 1 ] x 4 T e [ 1 ] - C u - T e [ 1 ] x 8 T e [ 1 ] - C u - C u x 4 T e [ 1 ] ~ C u - C u x 8 T e [ 1 ] - C u - C u x 4 C u - C u - C u x 4 C u - C u - C u x 4 C u - C u - C u x 4 1 7 6 . 0 4 ( 6 ) 9 0 3 3 ( 4 ) 8 2 2 9 ( 5 ) 6 2 4 7 ( 5 ) 1 1 7 6 6 ( 7 ) 9 0 4 3 ( 4 ) 8 9 6 2 ( 5 ) 1 7 6 . 5 4 ( 6 ) 9 0 3 3 ( 4 ) 7 9 2 1 ( 8 ) 7 8 9 0 ( 1 2 ) 1 2 8 . 3 4 ( 1 6 ) 8 8 3 0 ( 8 ) 1 3 6 7 8 ( 1 8 ) 1 1 2 0 0 ( 1 4 ) 1 0 8 . 2 0 0 1 ) 5 3 . 9 7 0 0 ) 1 2 5 . 8 7 0 3 ) 5 4 2 3 ( 9 ) 9 0 . 1 7 0 2 ) 8 9 . 8 2 0 5 ) 1 7 8 . 6 7 0 7 ) 1 7 3 . 8 2 ( 6 ) 8 4 5 3 ( 4 ) 8 2 1 5 ( 5 ) 6 0 0 1 ( 5 ) 1 1 6 2 6 ( 7 ) 8 4 9 7 ( 4 ) 8 9 2 8 ( 5 ) 1 7 4 . 5 8 ( 6 ) 8 4 9 7 ( 4 ) 7 8 . 7 1 ( 7 ) 7 8 . 4 8 ( 1 5 ) 1 2 7 . 9 1 0 9 ) 8 7 5 0 ( 9 ) 1 3 6 . 6 ( 2 ) 1 1 0 . 8 ( 2 ) 1 0 7 . 4 3 0 6 ) 5 3 3 8 ( 8 ) 1 2 4 . 9 7 0 3 ) 5 3 . 7 8 0 0 ) 8 9 . 1 7 0 3 ) 8 8 0 1 ( 1 6 ) 1 7 8 . 2 ( 2 ) 1 7 9 . 8 8 ( 6 ) 9 6 4 5 ( 5 ) 8 2 4 7 ( 5 ) 6 5 0 0 ( 5 ) 1 1 8 9 4 ( 7 ) 9 5 9 2 ( 4 ) 9 0 0 9 ( 6 ) 1 7 9 . 8 9 ( 7 ) 9 5 9 2 ( 4 ) 7 9 7 0 ( 7 ) 7 9 . 3 3 0 5 ) 1 2 8 . 7 6 0 9 ) 8 9 . 1 2 0 0 ) 1 3 6 . 9 ( 2 ) 1 1 3 . 3 ( 2 ) 1 0 8 . 9 8 0 6 ) 5 4 5 5 ( 9 ) 1 2 6 . 7 7 0 3 ) 5 4 7 0 ( 1 0 ) 9 1 . 1 8 0 3 ) 9 1 . 6 7 0 7 ) 1 7 9 . 5 ( 2 ) 2 6 3 T a b l e 4 . 2 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r K C u L a T e 4 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 3 1 . 8 5 0 R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 6 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 s t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m m a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e K C u L a T e 4 7 5 2 1 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A O r t h o r h o m b i c P 2 1 2 1 2 ( 0 1 3 1 / 2 ) 0 s 0 a = 4 . 4 4 2 1 ( 4 ) A , o = 9 0 ° b = 4 . 4 5 1 7 ( 4 ) A , 1 3 = 9 0 ° = 1 9 . 7 5 0 7 0 8 ) A , ' y = 9 0 ° 0 . 3 8 6 1 ( 5 ) b ‘ + 1 / 2 c ‘ 3 9 0 5 7 ( 6 ) A 3 2 6 . 3 9 1 9 g / c r n 3 2 3 . 1 6 1 m m " 6 2 6 0 . 2 8 x 0 . 1 0 x 0 . 0 3 m m 3 2 . 3 4 t o 3 1 . 8 5 ° - 6 < = h < = 6 , - 6 < = k < = 6 , - 2 9 < = 1 < = 2 9 , - 1 < = m < = 1 1 2 4 7 0 ( 3 5 1 9 m a i n + 8 9 5 1 s a t e l l i t e s ) 4 0 0 3 ( 1 3 2 6 m a i n + 2 6 7 7 s a t e l l i t e s ) [ R i m = 0 . 0 8 1 4 ] 9 8 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 4 0 0 3 / 0 / 9 6 2 . 0 6 R o b , = 0 . 0 6 9 9 , w R o b s = 0 . 1 6 8 0 R . , l l = 0 . 1 1 0 5 , w k , “ = 0 . 1 7 5 3 R . , , = 0 . 0 6 1 7 , w R o b s = 0 . 1 7 1 6 R , " = 0 . 0 6 7 1 , w k , “ = 0 . 1 7 3 0 R 0 , , = 0 . 1 1 3 1 , w R o b s = 0 . 1 5 0 1 R . , l l = 0 . 2 5 5 3 , w k , " = 0 . 1 8 5 7 0 . 0 0 0 5 3 0 4 ) 0 . 0 2 0 9 a n d 0 . 1 4 6 7 8 . 0 5 a n d - 4 . 4 8 6 A 3 R = Z | | F o | - | F c | | / 2 1 6 , 1 , w R = { 2 [ w ( | F , | T - 1 1 2 1 6 2 ] / Z [ w ( | F o | 4 ) ] } ” 2 a n d w = 1 / ( o Z ( I ) + 0 . 0 0 1 6 1 2 ) 2 6 4 T a b l e 4 . 3 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K C u L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x y 2 O c c u p a n c y U , q L a 0 0 0 3 9 3 2 ( 1 ) 1 1 8 ( 1 ) s i n , 1 4 6 ( 1 ) 9 ( 3 ) 0 ( 2 ) c o s , 1 - 1 3 3 ( 3 ) - 2 6 ( 9 ) 0 ( 1 ) T e [ 1 ] 0 0 0 7 8 1 ( 1 ) 1 3 1 ( 1 ) s i n , 1 - 8 ( 5 ) 4 0 ( 1 3 ) 8 ( 1 ) c o s , 1 2 ( 1 ) - 1 0 ( 3 ) 3 1 ( 3 ) T e [ 2 ] 0 0 0 5 6 1 3 ( 1 ) 1 1 8 ( 1 ) s i n , 1 1 ( 1 ) 0 ( 2 ) 1 ( 2 ) c o s , 1 5 ( 3 ) 1 ( 1 0 ) 0 ( 1 ) T e [ 3 ] 0 0 5 0 0 0 2 6 3 6 ( 1 ) 1 1 8 ( 1 ) s i n , 1 - 3 0 9 ( 5 ) - 2 7 ( 8 ) - 1 ( 2 ) c o s , 1 3 3 7 ( 5 ) 3 0 ( 8 ) - l ( 2 ) T e [ 4 ] 0 0 5 0 0 0 7 3 6 8 ( 1 ) 1 2 3 ( 1 ) s i n , 1 2 8 0 ( 5 ) - 1 7 ( 9 ) - 2 ( 2 ) c o s , 1 3 0 4 ( 5 ) - 1 8 ( 9 ) 2 ( 2 ) K 0 0 0 8 7 2 9 ( 2 ) 1 2 5 ( 2 ) s i n , 1 - 1 1 5 ( 1 3 ) 1 4 5 ( 4 0 ) - 2 ( 3 ) c o s , 1 - 4 9 ( 5 ) 5 9 ( 1 6 ) 5 ( 8 ) C u 0 0 5 0 0 0 1 5 ( 4 ) 1 5 8 ( 2 ) s i n , 1 - 5 5 ( 3 0 ) 1 6 5 ( 3 0 ) 0 c o s , 1 0 ( 1 ) - l ( 1 ) 0 ‘ U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 4 . 3 1 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K C u L a T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 L a 0 2 3 ( 1 ) 7 ( 1 ) 2 5 ( 1 ) 4 ( 1 ) 0 0 s i n , 1 - 9 ( 2 ) - 3 ( 2 ) 6 ( 1 ) - 1 0 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 - 3 0 ) - 1 0 ) 2 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 2 6 5 T a b l e 4 . 3 1 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K C u L a T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 1 ] 0 3 4 ( 1 ) 1 3 ( 1 ) 4 6 ( 1 ) - 9 ( 1 ) 0 0 s i n , 1 1 ( 1 ) 1 ( 1 ) - 6 ( 1 ) - 1 ( 1 ) 2 ( 1 ) 0 ( 2 ) c o s , 1 4 ( 3 ) 5 ( 2 ) - 2 4 ( 2 ) - 3 ( 1 ) - 1 ( 1 ) 0 ( 1 ) T e [ 2 ] 0 2 3 ( 1 ) 6 ( 1 ) 2 5 ( 1 ) - 6 ( 1 ) 0 0 s i n , 1 - 4 ( 2 ) - 4 ( 2 ) 5 ( 2 ) 2 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 1 ( 1 ) 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) T e [ 3 ] 0 1 4 ( 1 ) 1 8 ( 1 ) 2 2 ( 1 ) 1 1 ( 1 ) 0 0 s i n , 1 - 1 ( 1 ) 0 ( 2 ) - l ( 1 ) - 5 ( 1 ) 3 ( 1 ) - 2 ( 1 ) c o s , 1 - 1 ( 1 ) 0 ( 2 ) - 1 ( 1 ) - 5 ( 1 ) - 3 ( 1 ) 2 ( 1 ) T e [ 4 ] 0 1 6 ( 1 ) 2 2 ( 1 ) 3 0 ( 1 ) - 9 ( 1 ) 0 0 s i n , 1 1 ( 2 ) - 4 ( 2 ) 2 ( 1 ) - 2 ( 1 ) 0 ( 1 ) - 2 ( 1 ) c o s , 1 0 ( 1 ) 3 ( 2 ) - 2 ( 1 ) 2 ( 1 ) 0 ( 1 ) - 2 ( 2 ) K 0 2 6 ( 3 ) 1 6 ( 3 ) 3 3 ( 1 ) 1 ( 2 ) 0 0 s i n , 1 2 ( 3 ) 1 ( 3 ) - 1 ( 3 ) 1 ( 1 ) 0 ( 3 ) - 9 ( 4 ) c o s , 1 - 4 ( 7 ) - 2 ( 7 ) 2 ( 6 ) - 1 ( 2 ) 0 ( 1 ) - 4 ( 2 ) C u 0 1 0 1 ( 4 ) 3 4 ( 2 ) 3 8 ( 1 ) - 4 ( 7 ) 0 0 s i n , 1 0 0 O 0 - 3 ( 2 ) - 2 4 ( 4 ) c o s , 1 0 0 0 0 0 ( 1 ) 0 ( 1 ) T a b l e 4 . 3 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K C u L a T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e L a - T e [ 2 ] 3 . 3 2 0 ( 4 ) 3 . 3 1 7 ( 5 ) 3 . 3 2 3 ( 5 ) L a - T e [ 2 ] x 4 3 . 2 7 0 ( 3 ) 3 . 2 2 1 ( 3 ) 3 . 3 2 0 ( 3 ) L a - T e [ 3 ] x 2 3 . 3 9 6 ( 5 ) 3 . 3 8 1 ( 5 ) 3 . 4 1 7 ( 5 ) L a - T e [ 4 ] x 2 3 . 3 9 6 ( 4 ) 3 . 3 1 8 ( 4 ) 3 . 4 7 6 ( 4 ) T e [ 1 ] - K x 4 3 . 2 8 9 ( 1 0 ) 3 . 1 8 6 ( 1 1 ) 3 . 3 9 4 ( 1 1 ) T e [ 1 ] - C u x 2 2 . 6 9 3 ( 9 ) 2 . 6 0 2 ( 1 2 ) 2 . 7 8 2 ( 1 2 ) T e [ 1 ] - C u x 2 2 . 7 2 3 ( 9 ) 2 . 6 8 2 ( 6 ) 2 . 7 6 3 ( 6 ) T e [ 3 ] - T e [ 4 ] x 4 3 . 1 4 7 ( 4 ) 2 . 9 1 0 ( 5 ) 3 . 3 9 2 ( 4 ) T e [ 3 ] - K x 2 3 . 4 9 4 ( 1 0 ) 3 . 4 0 2 ( 9 ) 3 . 5 9 0 ( 8 ) T e [ 4 ] - K x 2 3 . 4 9 3 ( 1 3 ) 3 . 4 5 1 ( 1 2 ) 3 . 5 3 4 ( 1 2 ) K - C u x 2 3 . 3 7 7 ( 1 5 ) 3 . 3 3 3 ( 1 4 ) 3 . 4 2 3 ( 1 4 ) 2 6 6 T a b l e 4 . 3 2 . ( C o n t ’ d ) B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K C u L a T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . K - C u x 2 C u - C u x 4 3 . 3 3 2 ( 1 2 ) 3 . 1 4 6 0 2 ) 3 . 3 1 1 ( 1 4 ) 3 . 0 6 1 ( 1 4 ) 3 . 3 5 4 ( 1 4 ) 3 . 2 3 1 ( 1 4 ) T a b l e 4 . 3 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K C u L a T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 2 ] — L a - T e [ 2 ] x 8 7 4 0 7 ( 1 0 ) 7 3 . 4 1 ( 1 0 ) 7 4 . 7 1 ( 1 0 ) T e [ 2 ] - L a - T e [ 3 ] x 2 1 3 8 . 8 8 ( 1 2 ) l 3 8 . 2 7 ( 1 4 ) 1 3 9 . 3 0 ( 1 4 ) T e [ 2 ] - L a - T e [ 4 ] x 2 l 3 9 . l 7 ( 7 ) 1 3 8 . 7 5 ( 8 ) l 3 9 . 6 2 ( 8 ) T e [ 2 ] — L a - T e [ 2 ] x 4 8 5 8 0 ( 6 ) 8 4 4 5 ( 5 ) 8 7 1 7 ( 5 ) T e [ 2 ] - L a - T e [ 2 ] x 4 8 5 5 6 ( 8 ) 8 5 2 9 ( 9 ) 8 5 8 0 ( 9 ) T e [ 2 ] - L a - T e [ 2 ] x 4 1 4 8 . l 3 ( 1 2 ) 1 4 8 . 0 9 ( 1 1 ) l 4 8 . 1 9 ( l 4 ) T e [ 2 ] - L a - T e [ 3 ] x 4 7 6 1 7 ( 9 ) 7 3 2 1 ( 9 ) 7 9 0 9 ( 9 ) T e [ 2 ] - L a - T e [ 3 ] x 4 l 3 0 . 7 8 ( 8 ) 1 2 6 . 7 3 ( 9 ) l 3 4 . 8 5 ( 1 0 ) T e [ 2 ] - L a - T e [ 4 ] x 4 7 6 3 3 ( 8 ) 7 5 8 1 ( 8 ) 7 6 9 0 ( 9 ) T e [ 2 ] - L a - T e [ 4 ] x 4 1 3 0 . 6 8 ( 1 2 ) l 2 9 . 8 7 ( 1 2 ) l 3 1 . 4 7 ( 1 2 ) T e [ 3 ] - L a - T e [ 3 ] x 2 8 2 0 8 ( 1 1 ) 8 1 . 7 7 ( 1 0 ) 8 2 6 7 ( 1 2 ) T e [ 3 ] - L a - T e [ 4 ] x 4 5 5 2 6 ( 9 ) 5 1 . 7 2 ( 9 ) 5 8 8 7 ( 8 ) T e [ 4 ] - L a - T e [ 4 ] x 2 8 1 . 6 6 ( 1 0 ) 8 1 . 5 6 ( 1 2 ) 8 1 . 8 4 ( 1 1 ) K - T e [ 1 ] - K x 8 8 5 1 ( 3 ) 8 4 0 ( 3 ) 8 6 3 ( 3 ) K - T e [ 1 ] - K x 4 1 4 5 . 8 ( 3 ) 1 4 4 . 7 ( 3 ) 1 4 7 . 0 ( 3 ) K - T e [ 1 ] - C u x 4 6 6 8 ( 3 ) 6 6 4 ( 3 ) 6 7 . 1 ( 3 ) K - T e [ 1 ] - C u x 8 1 3 6 . 4 ( 4 ) 1 3 5 . 4 ( 4 ) 1 3 7 . 5 ( 4 ) K - T e [ 1 ] - C u x 4 6 7 . 6 ( 3 ) 6 6 2 ( 3 ) 6 9 . 0 ( 3 ) C u - T e [ 1 ] - C u x 2 1 1 1 . 6 ( 3 ) 1 1 1 . 0 ( 3 ) 1 1 2 . 2 ( 4 ) C u - T e [ 1 ] - C u x 8 7 1 . 0 ( 3 ) 6 9 4 ( 3 ) 7 2 7 ( 3 ) C u - T e [ 1 ] - C u x 2 1 0 9 . 3 ( 3 ) 1 0 7 . 3 ( 3 ) 1 1 1 . 6 ( 3 ) L a - T e [ 2 ] - L a x 8 1 0 5 . 9 3 ( 1 0 ) 1 0 5 . 0 3 ( 1 1 ) 1 0 6 8 3 ( 1 1 ) L a - T e [ 2 ] - L a x 4 8 5 8 1 ( 6 ) 8 5 2 6 ( 5 ) 8 6 3 4 ( 5 ) L a - T e [ 2 ] - L a x 4 8 5 5 5 ( 8 ) 8 5 2 9 ( 6 ) 8 5 8 0 ( 6 ) L a - T e [ 2 ] - L a x 4 1 4 8 . l 4 ( 1 2 ) 1 4 7 . 9 2 ( 1 6 ) 1 4 8 . 3 6 ( 1 5 ) L a - T e [ 3 ] - L a x 2 8 1 9 2 ( 1 1 ) 8 1 . 7 3 ( 1 0 ) 8 2 3 0 ( 1 1 ) L a - T e [ 3 ] - T e [ 4 ] x 4 6 2 3 8 ( 1 1 ) 6 0 8 6 ( 1 0 ) 6 3 . 8 0 ( 1 1 ) 2 6 7 T a b l e 4 . 3 3 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K C u L a T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a - T e [ 3 ] - T e [ 4 ] x 4 L a - T e [ 3 ] - K x 4 T e [ 4 ] - T e [ 4 ] - T e [ 4 ] - T e [ 4 ] - T e [ 4 ] - T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 3 ] - T e [ 4 ] x 4 T e [ 3 ] - T e [ 4 ] x 2 T e [ 3 ] - K x 4 T e [ 3 ] - K x 4 T e [ 3 ] - T e [ 4 ] x 2 K - T e [ 3 ] - K x 2 L a - T e [ 4 ] - L a x 2 L a - T e [ 4 ] - T e [ 3 ] x 4 L a - T e [ 4 ] - T e [ 3 ] x 4 L a - T e [ 4 ] ~ K x 4 T e [ 3 ] - T e [ 3 ] - T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 4 ] - T e [ 3 ] x 4 T e [ 4 ] - T e [ 3 ] x 2 T e [ 3 ] - T e [ 4 ] - K x 4 T e [ 3 ] - T e [ 4 ] - K x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 2 K - T e [ 4 ] - K x 2 T e [ 1 ] - K — T e [ 1 ] x 8 T e [ 1 ] - K - T e [ 1 ] x 4 T e [ 1 ] - K - T e [ 3 ] x 4 T e [ 1 ] - K - T e [ 3 ] x 4 T e [ 1 ] - K - T e [ 4 ] x 4 T e [ 1 ] - K - T e [ 4 ] x 4 T e [ 1 ] - K - C u x 8 T e [ 1 ] - K - C u x 8 T e [ 3 ] - K - T e [ 3 ] x 2 T e [ 3 ] - K - T e [ 4 ] x 4 T e [ 3 ] - K - C u x 4 T e [ 3 ] - K - C u x 2 T e [ 3 ] - K - C u x 2 T e [ 4 ] - K - T e [ 4 ] x 2 1 1 7 8 4 ( 1 3 ) 1 2 5 . 6 ( 2 ) 9 0 . 4 8 0 0 ) 8 9 5 9 ( 1 2 ) 1 7 5 . 9 1 0 4 ) 6 3 2 ( 2 ) 1 1 6 . 4 ( 3 ) 1 7 5 . 2 0 0 4 ) 7 8 9 0 ( 1 9 ) 8 1 . 6 6 ( 1 1 ) 6 2 4 5 ( 1 0 ) 1 1 7 2 3 0 5 ) 1 2 5 . 6 1 0 8 ) 9 9 4 7 ( 9 ) 8 9 . 5 8 ( 1 3 ) 1 7 5 . 4 7 ( 1 4 ) 6 3 . 1 8 0 8 ) 1 1 7 0 ( 2 ) 1 7 6 0 3 0 4 ) 7 9 2 ( 3 ) 8 5 1 6 ( 1 7 ) 1 4 5 . 7 ( 4 ) 7 8 3 5 ( 1 8 ) 1 3 1 . 0 ( 4 ) 7 8 . 1 ( 2 ) 1 3 1 . 1 ( 2 ) 4 8 2 ( 3 ) 1 0 3 . 0 ( 4 ) 7 8 9 ( 3 ) 5 3 5 6 ( 1 8 ) 1 2 5 . 5 ( 4 ) 9 8 . 7 ( 2 ) 1 7 6 . 7 ( 4 ) 7 9 3 ( 3 ) 1 1 2 . 8 2 ( 1 2 ) 1 2 1 . 8 ( 2 ) 8 3 6 2 ( 9 ) 8 8 . 6 8 0 2 ) 1 7 3 . 6 2 0 4 ) 6 0 9 ( 2 ) 1 1 4 . 7 ( 3 ) 1 7 2 . 5 1 0 4 ) 7 8 . 7 ( 2 ) 8 1 . 5 6 ( 1 1 ) 5 9 3 9 ( 1 0 ) 1 1 5 8 6 ( 1 6 ) 1 2 2 . 2 0 0 7 ) 8 3 9 0 ( 9 ) 8 8 . 6 8 ( 1 2 ) 1 7 2 . 9 4 0 4 ) 6 2 . 1 3 ( 1 8 ) 1 1 2 6 6 ( 1 9 ) 1 7 3 . 8 3 0 4 ) 7 7 6 ( 3 ) 8 3 . 8 7 ( l 7 ) 1 4 5 . 3 ( 5 ) 7 7 9 1 ( 1 9 ) 1 2 9 . 2 ( 4 ) 7 6 5 ( 3 ) 1 2 7 . 2 ( 3 ) 4 7 0 ( 3 ) 1 0 2 . 8 ( 4 ) 7 8 . 7 ( 3 ) 4 9 9 7 ( 1 5 ) 1 2 4 . 0 ( 4 ) 9 7 2 ( 3 ) 1 7 4 . 9 ( 4 ) 7 9 0 ( 2 ) 1 2 2 . 6 2 0 4 ) 1 2 9 . 2 ( 3 ) 9 7 4 5 ( 1 1 ) 9 0 . 1 1 0 2 ) 1 7 9 . 7 9 ( 1 7 ) 6 5 7 ( 3 ) 1 1 7 . 9 ( 3 ) 1 7 9 . 7 5 0 7 ) 7 9 2 ( 2 ) 8 1 . 8 4 0 2 ) 6 5 5 9 ( 1 1 ) 1 1 8 . 4 3 0 5 ) 1 2 8 . 9 ( 2 ) 9 7 . 1 0 0 0 ) 9 0 . 1 1 0 3 ) 1 7 9 . 8 5 ( 1 5 ) 6 4 4 9 ( 1 8 ) 1 2 1 . 1 ( 2 ) 1 7 9 . 8 5 ( 1 6 ) 8 0 9 ( 3 ) 8 6 4 5 ( 1 8 ) 1 4 6 . 3 ( 5 ) 7 8 . 8 ( 2 ) 1 3 2 . 8 ( 4 ) 7 9 8 ( 2 ) 1 3 5 . 0 ( 3 ) 4 9 4 ( 3 ) 1 0 3 . 1 ( 4 ) 7 9 . 2 ( 3 ) 5 7 1 5 ( 1 6 ) 1 2 7 . 0 ( 4 ) 1 0 0 . 2 ( 3 ) 1 7 8 . 1 ( 4 ) 7 9 9 ( 3 ) 2 6 8 T a b l e 4 . 3 3 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K C u L a T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 4 ] - K - C u x 2 T e [ 4 ] - K - C u x 2 T e [ 4 ] - K - C u x 4 C u - K - C u x 2 C u - K - C u x 8 C u - K - C u x 2 T e [ 1 ] - C u - T e [ 1 ] x 2 T e [ 1 ] - C u - T e [ 1 ] x 1 0 T e [ 1 ] - C u - K x 4 T e [ 1 ] - C u - K x 2 T e [ 1 ] - C u - K x 4 T e [ 1 ] - C u - C u x 4 T e [ 1 ] - C u - C u x 4 T e [ 1 ] - C u - K x 4 T e [ 1 ] - C u - K x 2 T e [ 1 ] - C u - C u x 4 T e [ 1 ] - C u - C u x 4 K - C u - K x 2 K - C u - K x 8 K - C u - C u x 4 K - C u - C u x 4 K - C u - K x 2 K - C u - C u x 4 K - C u - C u x 4 C u - C u - C u x 8 C u - C u - C u x 4 9 9 1 ( 4 ) 1 7 6 . 6 ( 4 ) 1 2 5 . 0 ( 3 ) 8 2 4 ( 4 ) 5 5 9 ( 3 ) 8 3 . 6 ( 4 ) 1 1 1 . 6 ( 3 ) 1 0 8 . 9 ( 3 ) 8 3 0 ( 3 ) 1 6 5 . 4 ( 4 ) 6 5 2 ( 3 ) 5 4 9 ( 3 ) 1 2 6 . 5 ( 4 ) 6 4 2 ( 2 ) 1 6 6 . 8 ( 3 ) 5 4 0 ( 3 ) 1 2 4 . 4 ( 4 ) 8 2 5 ( 3 ) 1 2 4 . 0 ( 4 ) 6 1 3 ( 3 ) 1 1 6 9 ( 3 ) 8 3 . 6 ( 3 ) 6 2 8 ( 3 ) 1 1 9 0 ( 4 ) 9 0 . 1 ( 4 ) 1 7 7 . 1 ( 4 ) 9 7 5 ( 3 ) 1 7 4 . 5 ( 4 ) 1 2 2 . 7 ( 3 ) 8 0 5 ( 4 ) 5 4 4 ( 3 ) 8 3 . 4 ( 4 ) 1 1 1 . 2 ( 3 ) 1 0 7 . 9 ( 4 ) 8 2 2 ( 3 ) 1 6 4 . 3 ( 3 ) 6 3 5 ( 3 ) 5 4 2 ( 2 ) 1 2 5 . 6 ( 3 ) 6 2 0 ( 2 ) 1 6 5 . 9 ( 3 ) 5 3 0 ( 2 ) 1 2 1 . 7 ( 4 ) 8 0 . 8 ( 4 ) 1 2 1 . 6 ( 5 ) 6 0 . 1 ( 3 ) 1 1 6 3 ( 3 ) 8 3 . 4 ( 3 ) 6 1 . 4 ( 4 ) 1 1 6 6 ( 4 ) 8 8 . 3 ( 4 ) 1 7 6 . 4 ( 5 ) 1 0 0 . 8 ( 3 ) 1 7 8 . 9 ( 4 ) 1 2 7 . 3 ( 3 ) 8 4 4 ( 4 ) 5 7 5 ( 3 ) 8 3 9 ( 4 ) 1 1 1 . 9 ( 3 ) 1 0 9 . 9 ( 5 ) 8 3 . 8 ( 3 ) 1 6 6 . 5 ( 3 ) 6 7 1 ( 4 ) 5 5 7 ( 2 ) 1 2 7 . 5 ( 3 ) 6 6 5 ( 2 ) 1 6 8 . 3 ( 3 ) 5 5 1 ( 2 ) 1 2 7 . 2 ( 4 ) 8 4 2 ( 4 ) 1 2 6 . 5 ( 5 ) 6 2 5 ( 3 ) 1 1 7 . 5 ( 3 ) 8 3 9 ( 3 ) 6 4 2 ( 4 ) 1 2 1 . 3 ( 4 ) 9 1 . 8 ( 4 ) 1 7 7 . 9 ( 3 ) 2 6 9 T a b l e 4 . 3 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N a o _ 7 g ( 1 ) A g 1 _ 2 2 ( 1 ) C e T e 4 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 2 5 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 o ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 o ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m m a n d T m c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e N 3 0 . 7 8 ( 1 ) A g 1 2 2 0 ) C € T € 4 8 0 0 . 1 1 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A O r t h o r h o m b i c P 2 1 2 1 2 ( 0 0 0 ) 0 s 0 a = 4 . 4 1 3 9 ( 7 ) A , 0 1 = 9 0 " b = 4 . 4 1 8 5 ( 8 ) A , B = 9 0 ° c = 2 0 . 2 4 5 ( 3 ) A , y = 9 0 ° 0 . 3 6 8 1 ( 8 ) b ‘ 3 9 4 . 8 3 ( 1 1 ) A 3 2 6 . 7 2 7 5 g / c i n 3 2 3 . 1 2 1 m i n - 1 6 6 4 0 . 2 0 x 0 . 1 4 x 0 . 1 0 m m 3 1 . 9 7 t o 2 9 . 2 5 ° - 6 < = h < = 6 , - 6 < = k < = 6 , - 2 7 < = 1 < = 2 7 , - 1 < = m < = l 1 0 6 7 9 ( 3 1 4 0 m a i n + 7 5 3 9 s a t e l l i t e s ) 3 1 6 3 ( 1 0 3 5 m a i n + 2 1 2 8 s a t e l l i t e s ) [ R 1 m = 0 . 0 9 6 5 ] 9 9 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 3 1 6 3 / 1 5 / 1 0 1 2 . 0 9 R o b s = 0 . 0 6 3 7 , w R o b s = 0 . 1 5 8 1 R a n = 0 . 1 0 1 8 , w R a n = 0 . 1 6 7 2 R o b s = 0 . 0 5 4 4 , w R o b s = 0 . 1 5 2 9 R 3 " = 0 . 0 5 9 0 , w R , " = 0 . 1 5 5 3 R o b s = 0 . 1 2 9 6 , w R o b s = 0 . 1 9 5 5 R . , “ = 0 . 2 9 6 1 , w R o u = 0 . 2 4 1 6 0 . 0 0 1 0 3 ( l 3 ) 0 . 0 6 2 1 a n d 0 . 1 4 8 6 4 . 8 7 a n d - 3 . 4 1 e . A ' 3 R = 2 1 1 6 1 - 1 1 4 1 / 2 1 1 3 . 1 , w R = { 2 1 q u 4 2 - 1 1 7 . 1 2 1 2 ] 7 2 1 1 4 0 1 4 1 5 1 1 1 4 a n d “ F l / ( 6 2 1 1 1 0 0 0 1 6 1 2 ) 2 7 0 T a b l e 4 . 3 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) d i s p l a c e m e n t a n d e q u i v a l e n t i s o t r o p i c N a 0 _ 7 g ( 1 ) A g 1 , 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . p a r a m e t e r s ( A 2 x 1 0 4 ) A t o m W a v e x y 2 O c c u p a n c y U e q C e 0 0 0 3 9 7 3 ( 1 ) 1 1 5 ( 1 ) s i n , 1 6 1 ( 3 ) - 7 ( 6 ) 0 c o s , 1 0 0 3 ( 2 ) T e [ 1 ] 0 0 0 9 1 2 ( 1 ) 1 2 3 ( 1 ) s i n , 1 - 6 ( 3 ) 1 0 ( 8 ) 0 c o s , 1 0 0 2 ( 2 ) T e [ 2 ] 0 0 0 5 5 9 1 ( 1 ) 1 1 4 ( 1 ) s i n , 1 - 4 ( 3 ) - 3 ( 7 ) 0 c o s , 1 0 0 3 ( 2 ) T e [ 3 ] 0 0 5 0 0 0 2 7 2 2 ( 1 ) 1 1 8 ( 1 ) s i n , 1 - 2 6 6 ( 6 ) 4 9 ( 7 ) 0 c o s , 1 0 0 - 1 ( 2 ) T e [ 4 ] 0 0 5 0 0 0 7 2 7 6 ( 1 ) 1 1 9 ( 1 ) s i n , 1 2 2 1 ( 6 ) - 5 ( 7 ) 0 c o s , 1 0 0 2 ( 2 ) N a 0 0 0 8 6 0 2 0 . 7 8 1 ( 1 0 ) 3 3 ( 2 ) s i n , 1 - 4 7 ( l 2 ) 2 5 ( 3 0 ) 0 c o s , 1 0 0 - 2 3 ( 8 ) A g [ l ] 0 0 5 0 0 0 0 ( 1 ) 1 2 4 ( 1 ) s i n , 1 - 2 1 ( 1 0 ) 4 4 ( 1 0 ) 0 c o s , 1 0 0 - 4 ( 2 ) A g [ 2 ] 0 0 0 8 6 0 2 ( 3 ) 0 . 2 1 9 ( 1 0 ) 3 3 ( 2 ) s i n , 1 - 4 7 ( 1 2 ) 2 5 ( 3 0 ) 0 c o s , 1 0 0 - 2 3 ( 8 ) ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 4 . 3 6 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r N a o _ 7 3 ( 1 ) A g 1 _ 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 C e 0 1 0 ( 1 ) 1 0 ( 1 ) 2 4 ( 1 ) - 5 0 ) 0 0 s i n , 1 o 0 0 0 0 ( 1 ) 1 ( 1 ) c o s , 1 - 6 ( 1 ) - 1 0 ) 0 ( 1 ) 0 ( 1 ) 0 0 2 7 1 T a b l e 4 . 3 6 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r N a o _ 7 3 ( 1 ) A g 1 , 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 1 ] 0 1 9 ( 1 ) 1 8 ( 1 ) 3 1 ( 1 ) - 7 0 ) 0 0 s i n , 1 0 0 0 0 0 ( 1 ) 1 ( 1 ) c o s , 1 3 ( 2 ) 2 ( 2 ) 0 ( 2 ) 0 ( 1 ) 0 0 T e [ 2 ] 0 9 ( 1 ) 9 ( 1 ) 2 5 ( 1 ) 6 ( 1 ) 0 0 s i n , 1 0 0 0 0 - 1 0 ) 2 ( 1 ) c o s , 1 4 0 ) - 1 0 ) 5 ( 2 ) 0 ( 1 ) 0 0 T e [ 3 ] 0 1 5 ( 1 ) 1 5 ( 1 ) 2 5 ( 1 ) - 6 ( 1 ) 0 0 s i n , 1 0 0 0 0 2 ( 1 ) - 4 0 ) c o s , 1 1 ( 2 ) 2 ( 1 ) 2 ( 2 ) 4 ( 1 ) 0 0 T e [ 4 ] 0 1 5 ( 1 ) 1 6 ( 1 ) 2 5 ( 1 ) 1 2 ( 1 ) 0 0 s i n , 1 0 0 0 0 - 1 0 ) 2 ( 1 ) c o s , 1 2 ( 2 ) 2 ( 1 ) 1 ( 2 ) 1 ( 1 ) 0 0 N a 0 2 6 ( 2 ) 2 5 ( 2 ) 4 6 ( 3 ) - 9 ( 3 ) 0 0 s i n , 1 0 0 0 0 1 ( 2 ) 3 0 ( 5 ) c o s , 1 - 2 0 ( 6 ) 1 ( 5 ) - 2 0 ( 8 ) 2 ( 3 ) 0 0 A g [ l ] 0 2 2 ( 1 ) 2 3 ( 1 ) 2 7 ( 1 ) - 5 0 ) 0 0 s i n , 1 0 o 0 0 1 ( 1 ) 4 ( 2 ) c o s , 1 - 3 ( 2 ) 2 ( 2 ) 4 ( 2 ) 2 ( 2 ) 0 0 A g [ 2 ] 0 2 6 ( 2 ) 2 5 ( 2 ) 4 6 ( 3 ) - 9 ( 3 ) 0 0 s i n , 1 0 0 0 0 1 ( 2 ) 3 0 ( 5 ) c o s , 1 - 2 0 ( 6 ) 1 ( 5 ) 2 0 ( 8 ) 2 ( 3 ) 0 0 T a b l e 4 . 3 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N a o , 7 8 ( 1 ) A g 1 , 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e C e - T e [ 2 ] 3 . 2 7 5 ( 3 ) 3 . 2 7 5 ( 5 ) 3 . 2 7 5 4 ( 1 3 ) C e - T e [ 2 ] x 4 3 . 2 4 6 ( 2 ) 3 . 2 2 8 ( 2 ) 3 . 2 6 4 ( 2 ) C e - T e [ 3 ] x 2 3 . 3 6 2 ( 3 ) 3 . 3 4 3 ( 3 ) 3 . 3 8 3 ( 3 ) C e - T e [ 4 ] x 2 3 . 3 5 6 ( 3 ) 3 . 3 0 9 ( 2 ) 3 . 4 0 2 ( 2 ) T e [ 1 ] - N a x 4 3 . 2 7 4 ( 6 ) 3 . 2 4 7 ( 7 ) 3 . 3 0 0 ( 7 ) T e [ 1 ] - A g [ l ] x 4 2 . 8 7 9 ( 4 ) 2 . 8 6 1 ( 4 ) 2 . 8 9 7 ( 4 ) T e [ 1 ] - A g [ 2 ] x 4 3 . 2 7 4 ( 6 ) 3 . 2 4 7 ( 7 ) 3 . 3 0 0 ( 7 ) T e [ 3 ] - T e [ 4 ] x 4 3 . 1 2 4 ( 2 ) 3 . 0 1 0 ( 3 ) 3 . 2 4 1 ( 3 ) 2 7 2 T a b l e 4 . 3 7 . ( C o n t ’ d ) B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N a o , 7 3 ( 1 ) A g 1 , 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 3 ] - N a x 2 3 . 4 7 2 ( 8 ) T e [ 3 ] - A g [ 2 ] x 2 3 . 4 7 2 ( 9 ) T e [ 4 ] - N a K 2 3 . 4 7 7 ( 9 ) T e [ 4 ] - A g [ 2 ] x 2 3 . 4 7 7 ( 1 0 ) A g [ 1 ] - A g [ 1 ] x 4 3 . 1 2 3 ( 4 ) 3 . 4 0 2 ( 4 ) 3 . 4 0 2 ( 6 ) 3 . 4 3 9 0 2 ) 3 . 4 3 9 0 3 ) 3 . 0 9 9 ( 5 ) 3 . 5 4 3 ( 4 ) 3 . 5 4 3 ( 6 ) 3 5 1 7 0 2 ) 3 . 5 1 7 ( 1 3 ) 3 . 1 4 7 ( 5 ) T a b l e 4 . 3 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o , 7 g ( 1 ) A g 1 , 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 2 ] - C e - T e [ 2 ] x 8 7 4 1 8 ( 5 ) 7 3 8 2 ( 5 ) 7 4 5 5 ( 5 ) T e [ 2 ] - C e - T e [ 3 ] x 2 1 3 8 . 8 6 ( 7 ) 1 3 8 . 5 6 ( 7 ) 1 3 9 . 0 9 ( 8 ) T e [ 2 ] - C e - T e [ 4 ] x 2 1 3 8 . 8 8 ( 5 ) 1 3 8 . 4 8 ( 5 ) 1 3 9 . 2 9 ( 5 ) T e [ 2 ] - C e - T e [ 2 ] x 8 8 5 8 0 ( 6 ) 8 5 . 1 8 ( 5 ) 8 6 4 2 ( 5 ) T e [ 2 ] - C e - T e [ 2 ] x 4 1 4 8 . 3 7 ( 8 ) 1 4 8 . 2 4 ( 1 2 ) 1 4 8 . 5 0 ( 1 2 ) T e [ 2 ] - C e - T e [ 3 ] x 4 7 5 9 9 ( 7 ) 7 4 7 6 ( 6 ) 7 7 2 0 ( 6 ) T e [ 2 ] - C e - T e [ 3 ] x 4 1 3 0 . 7 4 ( 7 ) 1 2 8 . 7 l ( 7 ) 1 3 2 . 8 0 ( 7 ) T e [ 2 ] - C e - T e [ 4 ] x 4 7 6 0 1 ( 6 ) 7 5 4 7 ( 7 ) 7 6 5 6 ( 7 ) T e [ 2 ] - C e - T e [ 4 ] x 4 1 3 0 . 7 3 ( 9 ) 1 2 9 . 9 8 ( 9 ) 1 3 1 . 4 7 ( 9 ) T e [ 3 ] - C e - T e [ 3 ] x 2 8 2 2 3 ( 8 ) 8 1 9 3 ( 1 0 ) 8 2 6 2 ( 9 ) T e [ 3 ] - C e - T e [ 4 ] x 4 5 5 4 3 ( 7 ) 5 3 2 2 ( 7 ) 5 7 6 4 ( 6 ) T e [ 4 ] - C e - T e [ 4 ] x 2 8 2 2 4 ( 7 ) 8 2 1 7 ( 1 0 ) 8 2 3 3 ( 1 0 ) N a - T e [ 1 ] - N a x 8 8 4 8 8 ( 1 9 ) 8 4 7 6 ( 1 8 ) 8 5 0 1 ( 1 8 ) N a - T e [ 1 ] - N a x 4 1 4 5 0 5 ( 1 9 ) l 4 4 . 5 1 ( 1 6 ) 1 4 5 . 5 8 ( 1 7 ) N a - T e [ 1 ] - A g [ l ] x 8 7 1 . 0 2 ( 1 7 ) 7 0 . 4 ( 2 ) 7 1 . 6 ( 2 ) N a - T e [ 1 ] - A g [ 1 ] x 8 l 3 5 2 7 ( 1 6 ) 1 3 4 . 8 ( 2 ) 1 3 5 . 7 5 ( 1 9 ) N a - T e [ 1 ] - A g [ 2 ] x 8 8 4 8 8 ( 1 9 ) 8 4 7 6 ( 1 8 ) 8 5 0 1 ( 1 8 ) N a - T e [ 1 ] - A g [ 2 ] x 4 1 4 5 . 0 ( 2 ) l 4 4 . 5 1 ( 1 9 ) 1 4 5 . 5 8 ( 1 9 ) A g [ l ] - T e [ 1 ] - A g [ l ] x 4 1 0 0 . 2 3 ( 1 2 ) 9 9 9 7 ( 1 6 ) 1 0 0 . 4 8 ( 1 6 ) A g [ 1 ] - T e [ 1 ] - A g [ 1 ] x 8 6 5 6 9 ( 1 1 ) 6 5 2 3 ( 1 0 ) 6 6 1 6 ( 1 0 ) A g [ l ] - T e [ 1 ] - A g [ 2 ] x 8 7 1 . 0 2 ( 1 6 ) 7 0 4 0 ( 1 6 ) 7 1 . 6 4 ( 1 6 ) A g [ l ] - T e [ 1 ] - A g [ 2 ] x 8 l 3 5 2 6 ( 1 4 ) 1 3 4 . 8 3 ( 1 5 ) 1 3 5 7 0 ( 1 5 ) A g [ 2 ] - T e [ 1 ] — A g [ 2 ] x 8 8 4 9 ( 2 ) 8 4 7 6 ( 1 8 ) 8 5 0 1 ( 1 8 ) A g [ 2 ] - T e [ 1 ] - A g [ 2 ] x 4 1 4 5 . 0 ( 2 ) 1 4 4 . 5 ( 2 ) 1 4 5 . 6 ( 2 ) 2 7 3 T a b l e 4 . 3 8 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o , 7 g ( 1 ) A g 1 , 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . C e - T e [ 2 ] - C e x 8 C e - T e [ 2 ] - C e x 4 C e - T e [ 2 ] - C e x 4 C e - T e [ 2 ] - C e x 4 C e - T e [ 3 ] - C e x 2 C e - T e [ 3 ] - T e [ 4 ] x 4 C e - T e [ 3 ] - T e [ 4 ] x 4 C e - T e [ 3 ] - N a x 4 C e - T e [ 3 ] - A g [ 2 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 2 T e [ 4 ] - T e [ 3 ] - N a K 4 T e [ 4 ] - T e [ 3 ] - N a x 4 T e [ 4 ] - T e [ 3 ] - A g [ 2 ] x 4 T e [ 4 ] - T e [ 3 ] - A g [ 2 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 2 N a - T e [ 3 ] - N a x 2 N a - T e [ 3 ] - A g [ 2 ] x 2 A g [ 2 ] - T e [ 3 ] - A g [ 2 ] x 2 C e - T e [ 4 ] - C e x 2 C e - T e [ 4 ] - T e [ 3 ] x 4 C e - T e [ 4 ] - T e [ 3 ] x 4 C e - T e [ 4 ] - N a x 4 C e - T e [ 4 ] - A g [ 2 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 2 T e [ 3 ] - T e [ 4 ] - N a x 4 T e [ 3 ] - T e [ 4 ] - N a x 4 T e [ 3 ] - T e [ 4 ] - A g [ 2 ] x 4 T e [ 3 ] - T e [ 4 ] - A g [ 2 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 2 N a - T e [ 4 ] - N a x 2 1 0 5 . 8 1 ( 6 ) 8 5 8 0 ( 5 ) 8 5 . 6 8 ( 6 ) 1 4 8 . 3 7 ( 9 ) 8 2 1 7 ( 8 ) 6 2 1 7 ( 5 ) 1 1 7 . 6 7 ( 8 ) 1 2 5 . 5 5 0 7 ) 1 2 5 . 5 5 0 7 ) 9 9 1 9 ( 7 ) 8 9 8 4 ( 8 ) 1 7 7 . 0 4 ( 9 ) 6 3 . 4 0 0 6 ) 1 1 6 6 9 ( 1 8 ) 6 3 . 4 0 0 7 ) 1 1 6 6 9 ( 1 8 ) 1 7 7 . 7 3 ( 9 ) 7 8 9 2 ( 1 4 ) 7 8 9 2 ( 1 5 ) 7 8 9 2 ( 1 6 ) 8 2 2 4 ( 6 ) 6 2 3 8 ( 6 ) 1 1 7 . 7 2 ( 8 ) 1 2 5 5 3 0 3 ) 1 2 5 5 3 0 3 ) 9 9 1 2 ( 7 ) 8 9 8 5 ( 8 ) 1 7 7 . 6 9 ( 9 ) 6 3 . 1 7 0 3 ) 1 1 6 . 6 4 ( 1 4 ) 6 3 . 1 7 ( 1 3 ) 1 1 6 6 4 ( 1 5 ) 1 7 7 . 4 8 ( 9 ) 7 8 9 ( 2 ) 1 0 5 . 3 0 ( 6 ) 8 5 4 9 ( 5 ) 8 5 6 5 ( 6 ) 1 4 8 0 5 0 3 ) 8 2 0 3 ( 1 1 ) 6 1 . 7 4 ( 6 ) 1 1 4 . 7 8 ( 7 ) 1 2 3 . 6 5 0 7 ) 1 2 3 . 6 5 0 8 ) 8 6 1 4 ( 8 ) 8 9 2 5 ( 1 0 ) 1 7 5 . 3 9 0 2 ) 6 1 . 8 5 0 6 ) 1 1 5 . 7 7 0 7 ) 6 1 . 8 5 0 6 ) 1 1 5 . 7 7 ( 1 8 ) 1 7 6 . 4 7 ( 1 2 ) 7 8 0 ( 2 ) 7 8 . 0 ( 2 ) 7 8 . 0 ( 2 ) 8 2 1 7 ( 1 1 ) 6 9 8 8 ( 6 ) 1 1 6 . 7 5 ( 8 ) 1 2 3 . 4 2 0 4 ) 1 2 3 . 4 2 0 5 ) 8 6 3 9 ( 8 ) 8 9 2 5 ( 8 ) 1 7 6 4 0 ( 1 2 ) 6 2 3 7 ( 1 4 ) 1 1 4 . 1 3 0 3 ) 6 2 3 7 ( 1 4 ) 1 1 4 . 1 3 ( 1 4 ) 1 7 6 . 0 7 ( 1 2 ) 7 8 2 ( 2 ) 1 0 6 . 3 3 ( 6 ) 8 6 1 0 ( 5 ) 8 5 7 1 ( 6 ) 1 4 8 . 6 9 0 3 ) 8 2 3 9 ( 1 1 ) 6 2 6 3 ( 5 ) 1 2 9 4 7 0 ) 1 2 7 . 3 4 0 9 ) 1 2 7 . 3 4 0 9 ) 9 4 2 7 ( 9 ) 9 0 3 9 ( 9 ) 1 7 9 . 8 7 ( 8 ) 6 4 9 4 ( 1 7 ) 1 1 7 . 4 9 0 7 ) 6 4 9 4 ( 1 8 ) 1 1 7 . 4 9 0 7 ) 1 7 9 . 9 1 ( 9 ) 7 9 9 ( 2 ) 7 9 . 9 ( 2 ) 7 9 . 9 ( 2 ) 8 2 3 3 ( 1 1 ) 6 3 9 5 ( 6 ) 1 1 8 . 6 4 ( 9 ) 1 2 7 . 6 5 0 5 ) 1 2 7 . 6 5 0 5 ) 9 3 9 7 ( 9 ) 9 9 3 9 ( 7 ) 1 7 9 . 9 0 ( 7 ) 6 4 0 2 ( 1 4 ) 1 1 9 . 2 1 0 3 ) 6 4 0 2 ( 1 4 ) 1 1 9 2 1 ( 1 4 ) 1 7 9 . 9 1 ( 7 ) 7 9 6 ( 2 ) 2 7 4 T a b l e 4 . 3 8 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o , 7 g ( 1 ) A g 1 , 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . N a - T e [ 4 ] - A g [ 2 ] x 2 A g [ 2 ] - T e [ 4 ] - A g [ 2 ] x 2 T e [ 1 ] - N a - T e [ 1 ] x 8 T e [ 1 ] - N a - T e [ 1 ] x 4 T e [ 1 ] - N a - T e [ 3 ] x 4 T e [ 1 ] - N a - T e [ 3 ] x 4 T e [ 1 ] - N a - T e [ 4 ] x 4 T e [ 1 ] - N a - T e [ 4 ] x 4 T e [ 3 ] - N a - T e [ 3 ] x 2 T e [ 3 ] - N a - T e [ 4 ] x 4 T e [ 4 ] - N a - T e [ 4 ] x 2 T e [ 1 ] - A g [ l ] - T e [ 1 ] x 4 T e [ 1 ] - A g [ l ] - T e [ 1 ] x 8 T e [ 1 ] - A g [ 1 ] - A g [ 1 ] x 8 T e [ 1 ] - A g [ 1 ] - A g [ 1 ] x 8 A 8 1 1 ] - A 8 1 1 1 - A 8 1 1 ] x 8 A 8 1 1 1 - A 8 1 1 ] - A 8 1 1 ] x 4 T e [ 1 ] - A g [ 2 ] - T e [ 1 ] x 8 T e [ 1 ] - A g [ 2 ] - T e [ 1 ] x 4 T e [ 1 ] - A g [ 2 ] - T e [ 3 ] x 4 T e [ 1 ] - A g [ 2 ] - T e [ 3 ] x 4 T e [ 1 ] - A g [ 2 ] - T e [ 4 ] x 4 T e [ 1 ] - A g [ 2 ] - T e [ 4 ] x 4 T e [ 3 ] - A g [ 2 ] - T e [ 3 ] x 2 T e [ 3 ] - A g [ 2 ] - T e [ 4 ] x 4 T e [ 4 ] - A g [ 2 ] - T e [ 4 ] x 2 7 8 . 9 ( 2 ) 7 8 . 9 ( 2 ) 8 4 8 7 ( 1 3 ) 1 4 5 . 0 ( 3 ) 7 8 . 6 7 0 3 ) 1 3 1 . 3 ( 3 ) 7 8 . 6 3 0 6 ) 1 3 1 . 4 ( 2 ) 7 8 . 9 3 0 8 ) 5 3 . 4 1 0 4 ) 7 8 9 4 ( 1 9 ) 1 0 0 . 2 3 ( 1 1 ) 1 1 4 . 3 0 0 1 ) 5 7 1 4 ( 8 ) 1 2 2 . 8 9 ( 1 2 ) 9 9 0 6 ( 1 2 ) 1 7 9 4 3 0 5 ) 8 4 8 7 ( 1 4 ) 1 4 5 . 0 ( 4 ) 7 8 . 6 7 0 3 ) 1 3 1 . 3 ( 3 ) 7 8 . 6 3 0 6 ) 1 3 1 . 4 ( 2 ) 7 8 . 9 ( 2 ) 5 3 . 4 1 0 5 ) 7 8 . 9 ( 2 ) 7 8 . 2 ( 2 ) 7 8 . 2 ( 2 ) 8 4 1 7 ( 1 3 ) 1 4 3 . 4 ( 5 ) 7 7 6 0 ( 1 3 ) 1 2 9 . 8 ( 2 ) 7 7 . 8 9 ( 1 2 ) 1 2 8 . 9 ( 2 ) 7 8 0 ( 3 ) 5 2 0 9 ( 9 ) 7 8 . 0 ( 3 ) 1 0 0 . 0 6 ( 1 6 ) 1 1 3 9 9 ( 1 7 ) 5 6 9 7 ( 8 ) 1 2 2 . 6 1 ( 1 2 ) 8 9 . 5 8 ( 1 2 ) 1 7 9 . 1 5 0 9 ) 8 4 1 7 ( 1 4 ) 1 4 3 . 4 ( 6 ) 7 7 6 0 ( 1 4 ) 1 2 9 . 8 ( 2 ) 7 7 . 8 9 0 2 ) 1 2 8 . 9 ( 3 ) 7 8 0 ( 4 ) 5 2 0 9 ( 1 1 ) 7 8 . 0 ( 4 ) 7 9 . 6 ( 2 ) 7 9 . 6 ( 2 ) 8 5 5 9 ( 1 3 ) 1 4 6 . 7 ( 5 ) 7 9 . 7 7 0 4 ) 1 3 2 . 8 ( 2 ) 7 9 3 8 ( 1 2 ) 1 3 3 . 8 ( 2 ) 7 9 . 9 ( 3 ) 5 4 7 8 ( 9 ) 7 9 . 9 ( 3 ) 1 0 0 . 4 0 ( 1 6 ) 1 1 4 6 2 ( 1 7 ) 5 7 3 1 ( 8 ) 1 2 3 . 1 9 0 2 ) 9 0 5 4 ( 1 2 ) 1 7 9 . 8 8 ( 1 8 ) 8 5 5 9 ( 1 4 ) 1 4 6 . 7 ( 6 ) 7 9 . 7 7 0 4 ) 1 3 2 . 8 ( 2 ) 7 9 3 8 ( 1 3 ) 1 3 3 . 8 ( 3 ) 7 9 9 ( 4 ) 5 4 . 7 8 ( 1 1 ) 7 9 . 9 ( 4 ) 2 7 5 T a b l e 4 . 3 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N a o _ 7 o ( 1 ) A g 1 , 3 o ( 1 ) L a T e 4 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 1 6 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m m a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e N 3 0 . 7 0 ( 1 ) A g 1 . 3 0 0 ) L a T e 4 8 0 5 . 6 1 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A O r t h o r h o m b i c P 2 1 2 1 2 ( 0 0 1 / 2 ) 0 s 0 a = 4 . 4 4 1 5 ( 6 ) A , 0 1 = 9 0 ° b = 4 . 4 4 6 7 ( 7 ) A , 1 3 = 9 0 ° c = 2 0 . 2 3 9 ( 3 ) A , ' y = 9 0 ° 0 . 3 6 6 0 ( 8 ) b “ + 1 / 2 c ‘ 3 9 9 7 2 0 0 ) A 3 2 6 . 6 9 1 4 g / c m 3 2 2 . 6 0 5 m m " 6 6 7 0 . 2 1 x 0 . 1 2 x 0 . 0 8 m m 3 1 . 7 5 t o 2 9 . 1 6 ° - 6 < = h < = 6 , - 6 < = k < = 6 , 2 7 < = 1 < = 2 8 , - l < = m < = 1 1 0 0 4 3 ( 2 5 1 0 m a i n + 7 5 3 3 s a t e l l i t e s ) 3 1 6 2 ( 9 9 9 m a i n + 2 1 6 3 s a t e l l i t e S ) [ R i m = 0 . 0 9 8 7 ] 9 7 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 3 1 6 2 / 1 5 / 1 0 2 2 . 5 0 R o b , = 0 . 0 7 3 5 , w R . , . , s = 0 . 1 9 1 7 R 3 1 1 : 0 . 1 1 3 9 , w k , ” = 0 . 2 0 5 3 R . , . . . = 0 . 0 6 4 5 , w R o b s = 0 . 1 9 1 4 R , l l = 0 . 0 7 1 4 , w k , J l = 0 . 2 0 0 4 R 0 , , = 0 . 1 3 6 9 , w R . . . , = 0 . 1 9 3 7 R . , l l = 0 . 3 0 0 4 , w R , l l = 0 . 2 3 8 4 0 0 0 0 9 0 0 5 ) 0 . 0 5 7 3 a n d 0 . 1 5 4 4 6 . 3 2 a n d 4 7 4 6 A 3 R = 2 1 9 0 1 - 1 1 3 1 1 7 2 1 1 2 . 1 , w R = { Z i w a F o F - 1 9 1 2 1 2 1 / 2 1 w ( 1 F . 1 “ ) 1 } ‘ ” a n d “ F l / ( 0 1 0 1 0 0 0 1 6 1 2 ) 2 7 6 T a b l e 4 . 4 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t N a o _ 7 o ( 1 ) A g 1 , 3 o ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . p a r a m e t e r s ( A 2 x 1 0 4 ) A t o m W a v e x y 2 O c c u p a n c y q u L a 0 0 0 3 9 6 2 ( 1 ) 1 1 3 ( 1 ) . s i n , 1 1 9 ( 1 ) 2 ( 2 ) - 5 ( 2 ) c o s , 1 - 5 6 ( 3 ) - 6 ( 7 ) - 2 ( 1 ) T e [ 1 ] 0 0 0 9 1 3 ( 1 ) 1 1 8 ( 1 ) s i n , 1 - 7 ( 3 ) 1 ( 8 ) 1 ( 1 ) c o s , 1 2 ( 1 ) 0 ( 2 ) 4 ( 2 ) T e [ 2 ] 0 0 0 5 5 9 7 ( 1 ) 1 1 3 ( 1 ) s i n , 1 0 ( 1 ) - 2 ( 1 ) 0 ( 2 ) c o s , 1 - 1 ( 3 ) - 1 2 ( 7 ) 0 ( 1 ) T e [ 3 ] 0 0 5 0 0 0 2 7 0 0 ( 1 ) 1 1 9 ( 1 ) s i n , 1 - 1 6 3 ( 4 ) 1 4 ( 6 ) - 1 ( 2 ) c o s , 1 1 8 5 ( 5 ) - 1 6 ( 7 ) - l ( 2 ) T e [ 4 ] 0 0 5 0 0 0 7 2 9 9 ( 1 ) 1 1 9 ( 1 ) s i n , 1 1 3 3 ( 4 ) 1 2 ( 6 ) 1 ( 2 ) c o s , 1 1 5 1 ( 5 ) 1 4 ( 7 ) - 1 ( 1 ) N a 0 0 0 8 6 1 5 0 . 7 0 3 ( 1 2 ) 3 2 ( 2 ) s i n , 1 - 5 3 ( 1 1 ) - 5 5 ( 2 0 ) 7 ( 3 ) c o s , 1 - 2 5 ( 5 ) - 2 7 ( 1 1 ) - 1 6 ( 6 ) A g [ l ] 0 0 5 0 0 0 0 ( 1 ) 1 2 1 ( 1 ) s i n , 1 - 3 3 ( 1 0 ) 4 4 ( 1 1 ) 0 c o s , 1 0 0 1 ( 3 ) A g [ 2 ] 0 0 0 8 6 1 5 ( 3 ) 0 . 2 9 7 ( 1 2 ) 3 2 ( 2 ) s i n , 1 - 5 3 ( 1 1 ) - 5 5 ( 2 0 ) 7 ( 3 ) c o s , 1 - 2 5 ( 5 ) - 2 7 ( 1 1 ) - 1 6 ( 6 ) ‘ U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 4 . 4 1 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r N a o . 7 o ( 1 ) A g 1 _ 3 o ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 L a 0 1 1 ( 1 ) 1 2 ( 1 ) 1 8 ( 1 ) - 8 ( 1 ) 0 0 s i n , 1 - 1 0 ) 0 ( 1 ) - 1 0 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) - 1 0 ) 2 7 7 T a b l e 4 . 4 1 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r N a o , 7 o A g 1 , 3 o L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 1 ] 0 1 7 ( 1 ) 1 7 ( 1 ) 1 9 ( 1 ) - 7 0 ) 0 0 s i n , 1 0 ( 1 ) - 1 0 ) 1 ( 1 ) 0 ( 1 ) - 1 0 ) 2 ( 1 ) c o s , 1 - 1 0 ) — 3 ( 2 ) 4 ( 2 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) T e [ 2 ] 0 1 0 ( 1 ) 1 1 ( 1 ) 1 7 ( 1 ) 7 ( 1 ) 0 0 s i n , 1 - 1 0 ) - 3 0 ) 4 ( 2 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 1 ( 1 ) - 1 0 ) 0 ( 1 ) - 1 0 ) 0 ( 1 ) T e [ 3 ] 0 1 9 ( 1 ) 1 9 ( 1 ) 1 7 ( 1 ) - 5 0 ) 0 0 s i n , 1 - 3 0 ) 0 ( 1 ) 3 ( 1 ) 2 ( 1 ) 2 ( 1 ) 1 ( 1 ) c o s , 1 - 3 0 ) 0 ( 1 ) 3 ( 1 ) 2 ( 1 ) 2 ( 1 ) - 1 0 ) T e [ 4 ] 0 1 8 ( 1 ) 2 2 ( 1 ) 1 7 ( 1 ) 1 1 ( 1 ) 0 0 s i n , 1 1 ( 1 ) 2 ( 1 ) - 1 0 ) 1 ( 1 ) 0 ( 1 ) 2 ( 1 ) c o s , 1 - 1 0 ) 2 ( 1 ) 1 ( 1 ) - 1 0 ) 0 ( 1 ) 2 ( 1 ) N a 0 3 7 ( 4 ) 2 6 ( 3 ) 3 2 ( 3 ) - 1 1 ( 3 ) 0 0 s i n , 1 1 7 ( 3 ) 6 ( 2 ) 8 ( 3 ) - 4 0 ) - 1 ( 2 ) - 2 8 ( 4 ) c o s , 1 - 3 6 ( 6 ) - 1 4 ( 5 ) - 1 7 ( 6 ) 1 0 ( 3 ) 0 ( 1 ) - 1 3 ( 2 ) A g [ l ] 0 2 1 ( 1 ) 2 2 ( 1 ) 1 9 ( 1 ) 5 ( 2 ) 0 0 s i n , 1 0 0 0 0 0 ( 1 ) 2 ( 2 ) c o s , 1 4 ( 2 ) 4 ( 2 ) 5 ( 2 ) 0 ( 2 ) 0 0 A g [ 2 ] 0 3 7 ( 4 ) 2 6 ( 3 ) 3 2 ( 3 ) - 1 1 ( 3 ) 0 0 s i n , 1 1 7 ( 3 ) 6 ( 2 ) 8 ( 3 ) - 4 0 ) - 1 ( 2 ) - 2 8 ( 4 ) c o s , 1 - 3 6 ( 6 ) - 1 4 ( 5 ) - 1 7 ( 6 ) 1 0 ( 3 ) 0 ( 1 ) - 1 3 ( 2 ) T a b l e 4 . 4 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N a o , 7 o ( 1 ) A g 1 _ 3 o ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e L a - T e [ 2 ] 3 . 3 0 9 ( 3 ) 3 . 2 9 8 ( 5 ) 3 . 3 2 0 ( 5 ) L a - T e [ 2 ] x 4 3 . 2 6 7 ( 2 ) 3 . 2 4 8 ( 2 ) 3 . 2 8 6 ( 2 ) L a - T e [ 3 ] x 2 3 . 3 8 8 ( 4 ) 3 . 3 8 6 ( 4 ) 3 . 3 9 1 ( 4 ) L a - T e [ 4 ] x 2 3 . 3 8 2 ( 3 ) 3 . 3 4 1 ( 3 ) 3 . 4 2 5 ( 3 ) T e [ 1 ] - N a x 4 3 . 2 8 4 ( 7 ) 3 . 2 7 1 ( 6 ) 3 . 2 9 8 ( 6 ) T e [ 1 ] - A g [ 1 ] x 4 2 . 8 9 1 ( 4 ) 2 . 8 7 1 ( 5 ) 2 . 9 1 1 ( 5 ) T e [ 1 ] - A g [ 2 ] x 4 3 . 2 8 4 ( 7 ) 3 . 2 7 1 ( 6 ) 3 . 2 9 8 ( 6 ) T e [ 3 ] - T e [ 4 ] x 4 3 . 1 4 3 ( 4 ) 3 . 0 3 7 ( 4 ) 3 . 2 5 3 ( 4 ) 2 7 8 T a b l e 4 . 4 2 . ( C o n t ’ d ) B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N a o , 7 o ( 1 ) A g 1 , 3 o ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 3 ] - N a x 2 3 . 4 6 6 ( 8 ) T e [ 3 ] - A g [ 2 ] x 2 3 . 4 6 6 ( 9 ) T e [ 4 ] - N a x 2 3 . 4 7 2 ( 9 ) T e [ 4 ] - A g [ 2 ] x 2 3 . 4 7 2 ( 1 0 ) A g [ l ] - A g [ l ] x 4 3 . 1 4 2 ( 4 ) 3 . 4 0 7 ( 6 ) 3 . 4 0 7 ( 8 ) 3 . 4 4 2 ( 9 ) 3 . 4 4 2 0 0 ) 3 . 1 1 7 ( 5 ) 3 . 5 2 6 ( 6 ) 3 . 5 2 6 ( 7 ) 3 . 4 9 9 ( 9 ) 3 . 4 9 9 0 0 ) 3 . 1 6 8 ( 5 ) T a b l e 4 . 4 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o , 7 o ( 1 ) A g 1 , 3 o ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 2 ] - L a - T e [ 2 ] x 8 7 4 1 4 ( 8 ) 7 3 9 0 ( 9 ) 7 4 3 8 ( 9 ) T e [ 2 ] - L a - T e [ 3 ] x 2 1 3 8 . 9 3 ( 1 0 ) l 3 8 . 6 8 ( 9 ) 1 3 9 . 1 5 ( 8 ) T e [ 2 ] - L a - T e [ 4 ] x 2 1 3 8 . 9 6 ( 6 ) 1 3 8 . 5 9 ( 6 ) 1 3 9 . 3 4 ( 6 ) T e [ 2 ] - L a - T e [ 2 ] x 4 8 5 7 8 ( 5 ) 8 5 2 0 ( 4 ) 8 6 3 6 ( 4 ) T e [ 2 ] - L a - T e [ 2 ] x 4 8 5 6 5 ( 6 ) 8 5 4 5 ( 5 ) 8 5 8 6 ( 5 ) T e [ 2 ] - L a - T e [ 2 ] x 4 1 4 8 . 2 7 ( 1 1 ) 1 4 7 . 9 7 ( 1 3 ) 1 4 8 . 5 9 ( 1 3 ) T e [ 2 ] - L a - T e [ 3 ] x 4 7 6 0 8 ( 7 ) 7 4 7 2 ( 7 ) 7 7 4 3 ( 7 ) T e [ 2 ] - L a - T e [ 3 ] x 4 1 3 0 . 7 5 ( 7 ) 1 2 8 . 9 2 ( 8 ) 1 3 2 . 5 8 ( 8 ) T e [ 2 ] - L a - T e [ 4 ] x 4 7 6 1 1 ( 7 ) 7 5 8 7 ( 8 ) 7 6 3 5 ( 8 ) T e [ 2 ] - L a - T e [ 4 ] x 4 1 3 0 . 7 3 ( 1 0 ) 1 3 0 . 3 9 ( 1 0 ) 1 3 1 . 0 6 ( 1 0 ) T e [ 3 ] - L a - T e [ 3 ] x 2 8 2 0 9 ( 9 ) 8 1 . 7 0 ( 1 0 ) 8 2 5 6 ( 1 0 ) T e [ 3 ] - L a - T e [ 4 ] x 4 5 5 3 4 ( 7 ) 5 3 . 1 2 ( 7 ) 5 7 5 6 ( 7 ) T e [ 4 ] - L a - T e [ 4 ] x 2 8 2 0 7 ( 8 ) 8 1 9 1 ( 1 0 ) 8 2 2 5 ( 1 0 ) N a - T e [ 1 ] - N a x 8 8 5 2 2 ( 1 9 ) 8 4 3 ( 2 ) 8 6 1 ( 2 ) N a - T e [ 1 ] - N a x 4 1 4 6 . 2 ( 2 ) 1 4 5 4 0 ( l 9 ) 1 4 6 . 9 9 ( 1 9 ) N a - T e [ 1 ] - A g [ 1 ] x 8 7 0 4 3 ( 1 8 ) 6 9 . 8 1 ( 1 6 ) 7 1 . 0 6 ( 1 6 ) N a - T e [ 1 ] - A g [ 1 ] x 8 1 3 4 . 9 5 ( l 6 ) 1 3 4 . 4 1 ( 1 7 ) 1 3 5 . 4 9 ( 1 7 ) N a - T e [ 1 ] - A g [ 2 ] x 8 8 5 2 2 ( 1 9 ) 8 4 . 3 ( 2 ) 8 6 . 1 ( 2 ) N a - T e [ 1 ] - A g [ 2 ] x 4 1 4 6 . 2 ( 2 ) 1 4 5 . 4 ( 2 ) 1 4 7 . 0 ( 2 ) A g [ l ] - T e [ 1 ] - A g [ l ] x 4 1 0 0 . 5 6 ( 1 2 ) 1 0 0 . 3 5 ( 1 4 ) 1 0 0 . 7 6 ( 1 4 ) A g [ l ] - T e [ 1 ] - A g [ l ] x 8 6 5 8 8 ( 1 2 ) 6 5 4 8 ( 1 2 ) 6 6 2 8 ( 1 2 ) A g [ l ] - T e [ 1 ] - A g [ 2 ] x 8 7 0 4 3 ( 1 7 ) 6 9 . 8 1 ( 1 7 ) 7 1 . 0 6 ( 1 7 ) A g [ l ] - T e [ 1 ] - A g [ 2 ] x 8 1 3 4 . 9 5 ( 1 5 ) l 3 4 . 6 7 ( l 4 ) 1 3 5 2 3 ( 1 4 ) A g [ 2 ] - T e [ 1 ] - A g [ 2 ] x 8 8 5 . 2 2 ( 1 9 ) 8 4 . 3 ( 2 ) 8 6 . 1 ( 2 ) 2 7 9 T a b l e 4 . 4 3 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o _ 7 o ( 1 ) A g 1 , 3 o ( 1 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A g [ 2 ] - T e [ 1 ] - A g [ 2 ] x 4 L a - T e [ 2 ] - L a x 8 L a - T e [ 2 ] - L a x 4 L a - T e [ 2 ] - L a x 4 L a - T e [ 2 ] - L a x 4 L a - T e [ 3 ] - L a x 2 L a - T e [ 3 ] - T e [ 4 ] x 4 L a - T e [ 3 ] - T e [ 4 ] x 4 L a - T e [ 3 ] - N a x 4 L a - T e [ 3 ] - A g [ 2 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 2 T e [ 4 ] - T e [ 3 ] - N a x 4 T e [ 4 ] - T e [ 3 ] - N a x 4 T e [ 4 ] - T e [ 3 ] - A g [ 2 ] x 4 T e [ 4 ] - T e [ 3 ] - A g [ 2 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 2 N a - T e [ 3 ] - N a x 2 N a - T e [ 3 ] - A g [ 2 ] x 2 A g [ 2 ] - T e [ 3 ] - A g [ 2 ] x 2 L a - T e [ 4 ] - L a x 2 L a - T e [ 4 ] - T e [ 3 ] x 4 L a - T e [ 4 ] - T e [ 3 ] x 4 L a - T e [ 4 ] - N a x 4 L a - T e [ 4 ] - A g [ 2 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 2 T e [ 3 ] - T e [ 4 ] - N a x 4 T e [ 3 ] - T e [ 4 ] - N a x 4 T e [ 3 ] - T e [ 4 ] - A g [ 2 ] x 4 T e [ 3 ] - T e [ 4 ] - A g [ 2 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 2 1 4 6 . 2 ( 2 ) 1 0 5 . 8 6 ( 8 ) 8 5 7 8 ( 5 ) 8 5 6 5 ( 6 ) 1 4 8 . 2 8 0 1 ) 8 2 0 4 ( 9 ) 6 2 . 2 4 ( 8 ) 1 1 7 . 6 5 ( 1 1 ) 1 2 5 . 4 0 0 7 ) 1 2 5 . 4 0 0 7 ) 9 9 1 8 ( 8 ) 8 9 . 8 5 0 0 ) 1 7 7 . 3 7 0 1 ) 6 3 . 1 8 0 7 ) 1 1 6 . 9 2 ( 1 8 ) 6 3 . 1 8 0 7 ) l l 6 . 9 2 ( 1 9 ) 1 7 7 . 7 9 0 1 ) 7 9 . 6 7 ( 1 6 ) 7 9 6 7 ( 1 7 ) 7 9 . 6 7 ( 1 8 ) 8 2 0 7 ( 9 ) 6 2 4 4 ( 8 ) 1 1 7 . 6 6 0 2 ) 1 2 5 . 4 1 0 4 ) 1 2 5 . 4 1 0 4 ) 9 9 1 8 ( 8 ) 8 9 . 8 5 ( 1 0 ) 1 7 7 . 9 7 0 1 ) 6 2 9 8 ( 1 3 ) 1 1 6 9 3 ( 1 5 ) 6 2 9 8 ( 1 4 ) 1 1 6 . 9 3 0 5 ) 1 7 7 5 8 0 1 ) 1 4 5 . 4 ( 2 ) 1 0 5 . 4 5 ( 9 ) 8 5 5 3 ( 4 ) 8 5 . 4 5 ( 8 ) 1 4 8 . 0 1 0 4 ) 8 1 9 7 ( 9 ) 6 1 . 7 3 ( 8 ) 1 1 5 0 0 ( 1 0 ) 1 2 3 0 3 0 6 ) 1 2 3 0 3 0 7 ) 8 6 4 2 ( 8 ) 8 9 3 9 ( 1 0 ) 1 7 5 . 9 0 0 1 ) 6 1 2 5 ( 1 6 ) 1 1 6 4 7 ( 1 9 ) 6 1 2 5 ( 1 6 ) 1 1 6 . 4 7 ( 1 9 ) 1 7 6 5 5 0 1 ) 7 8 9 9 0 7 ) 7 8 9 9 ( 1 8 ) 7 8 . 9 9 0 8 ) 8 1 9 1 ( 9 ) 6 9 8 0 ( 8 ) 1 1 6 6 3 ( 1 2 ) 1 2 3 . 0 1 0 3 ) 1 2 3 . 0 1 0 4 ) 8 6 7 0 ( 8 ) 8 9 3 9 ( 9 ) l 7 6 . 8 4 ( 1 1 ) 6 2 1 1 ( 1 3 ) 1 1 4 4 7 ( 1 5 ) 6 2 1 1 ( 1 4 ) 1 1 4 4 7 ( 1 5 ) 1 7 6 . 2 2 ( 1 1 ) 1 4 7 . 0 ( 2 ) 1 0 6 . 2 7 ( 9 ) 8 6 0 3 ( 4 ) 8 5 8 6 ( 8 ) 1 4 8 . 5 5 0 3 ) 8 2 1 7 ( 1 0 ) 6 2 7 6 ( 8 ) 1 2 0 . 2 2 ( 1 1 ) 1 2 7 . 7 2 ( 1 8 ) 1 2 7 . 7 2 ( 1 8 ) 9 3 9 6 ( 9 ) 9 9 1 5 ( 1 0 ) 1 7 9 . 8 9 ( 1 4 ) 6 5 1 1 ( 1 7 ) 1 1 7 3 6 ( 1 8 ) 6 5 . 1 1 0 7 ) 1 1 7 3 6 ( 1 9 ) 1 7 9 . 9 0 ( 1 4 ) 8 9 3 9 ( 1 7 ) 8 9 3 9 ( 1 8 ) 8 9 3 9 ( 1 9 ) 8 2 2 5 ( 9 ) 6 4 1 0 ( 9 ) 1 1 8 . 6 0 0 2 ) 1 2 7 . 7 6 ( 1 4 ) 1 2 7 . 7 6 ( 1 4 ) 9 3 6 4 ( 8 ) 9 9 1 5 ( 1 0 ) 1 7 9 . 9 2 ( 1 3 ) 6 3 . 8 2 0 4 ) 1 1 9 . 3 4 0 5 ) 6 3 . 8 2 0 4 ) 1 1 9 3 4 ( 1 6 ) 1 7 9 . 9 1 ( 1 3 ) 2 8 0 T a b l e 4 . 4 3 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o , 7 o A g 1 _ 3 o L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . N a - T e [ 4 ] - N a x 2 N a - T e [ 4 ] - A g [ 2 ] x 2 A g [ 2 ] - T e [ 4 ] - A g [ 2 ] x 2 T e [ 1 ] - N a — T e [ 1 ] x 8 T e [ 1 ] - N a - T e [ 1 ] x 4 T e [ 1 ] - N a - T e [ 3 ] x 4 T e [ 1 ] - N a - T e [ 3 ] x 4 T e [ 1 ] - N a - T e [ 4 ] x 4 T e [ 1 ] - N a - T e [ 4 ] x 4 T e [ 3 ] - N a - T e [ 3 ] x 2 T e [ 3 ] - N a - T e [ 4 ] x 4 T e [ 4 ] - N a - T e [ 4 ] x 2 T e [ 1 ] - A g [ 1 ] - T e [ 1 ] x 4 T e [ 1 ] - A g [ l ] - T e [ 1 ] x 8 T e [ 1 ] - A g [ 1 ] - A g [ 1 ] x 8 T e [ 1 ] - A g [ 1 ] - A g [ 1 ] x 8 A 8 1 1 ] - A 8 1 1 ] - A 8 1 1 ] x 8 A 8 1 1 ] - A 8 1 1 ] - A 8 1 1 ] x 2 A 8 1 1 ] - A 8 1 1 ] - A 8 1 1 ] x 2 T e [ 1 ] - A g [ 2 ] - T e [ 1 ] x 8 T e [ 1 ] - A g [ 2 ] - T e [ 1 ] x 4 T e [ 1 ] - A g [ 2 ] - T e [ 3 ] x 4 T e [ 1 ] - A g [ 2 ] - T e [ 3 ] x 4 T e [ 1 ] - A g [ 2 ] - T e [ 4 ] x 4 T e [ 1 ] - A g [ 2 ] - T e [ 4 ] x 4 T e [ 3 ] - A g [ 2 ] - T e [ 3 ] x 2 T e [ 3 ] - A g [ 2 ] - T e [ 4 ] x 4 T e [ 4 ] - A g [ 2 ] - T e [ 4 ] x 2 7 9 7 ( 2 ) 7 9 . 7 ( 2 ) 7 9 . 7 ( 2 ) 8 5 2 1 ( 1 3 ) 1 4 6 . 2 ( 3 ) 7 7 8 8 ( 1 3 ) 1 3 1 . 0 ( 3 ) 7 7 8 6 ( 1 7 ) 1 3 1 . 1 ( 2 ) 7 9 . 7 ( 2 ) 5 3 8 9 ( 1 4 ) 7 9 . 7 ( 2 ) 1 0 9 5 6 0 3 ) 1 1 4 1 2 0 1 ) 5 7 0 3 ( 9 ) 1 2 2 9 7 0 2 ) 9 9 0 6 ( 1 2 ) 1 7 9 . 4 1 0 4 ) 1 7 9 . 6 9 ( 1 3 ) 8 5 2 1 ( 1 4 ) 1 4 6 . 2 ( 4 ) 7 7 8 8 ( 1 4 ) 1 3 1 . 0 ( 3 ) 7 7 . 8 6 0 8 ) 1 3 1 . 1 ( 2 ) 7 9 . 7 ( 2 ) 5 3 . 8 9 0 6 ) 7 9 . 7 ( 2 ) 7 9 3 ( 2 ) 7 9 . 3 ( 2 ) 7 9 . 3 ( 2 ) 8 4 5 6 ( 1 3 ) 1 4 4 . 9 ( 4 ) 7 7 4 3 ( 1 3 ) 1 3 0 . 4 ( 3 ) 7 6 4 ( 2 ) 1 2 8 . 7 ( 2 ) 7 9 . 0 ( 2 ) 5 2 3 3 ( 1 2 ) 7 8 . 8 ( 2 ) 1 0 0 . 5 1 0 8 ) 1 1 4 0 2 ( 1 7 ) 5 6 8 3 ( 9 ) 1 2 2 7 2 0 1 ) 8 9 . 5 6 ( 1 2 ) 1 7 9 0 7 0 9 ) 1 7 9 5 2 0 9 ) 8 4 5 6 ( 1 4 ) 1 4 4 . 9 ( 4 ) 7 7 . 4 3 0 4 ) 1 3 0 . 4 ( 3 ) 7 6 . 4 ( 2 ) 1 2 8 . 7 ( 3 ) 7 9 0 ( 3 ) 5 2 3 3 ( 1 4 ) 7 8 . 8 ( 3 ) 8 9 1 ( 2 ) 8 0 . 1 ( 2 ) 8 0 . 1 ( 2 ) 8 5 . 8 6 ( 1 3 ) 1 4 7 . 5 ( 4 ) 7 8 . 3 4 ( 1 4 ) 1 3 1 . 7 ( 3 ) 7 9 4 ( 2 ) 1 3 3 . 5 ( 2 ) 8 9 4 ( 2 ) 5 5 . 4 5 0 2 ) 8 9 6 ( 3 ) 1 0 0 . 6 1 0 8 ) 1 1 4 2 2 ( 1 7 ) 5 7 2 4 ( 9 ) 1 2 3 . 2 3 0 1 ) 9 0 5 7 ( 1 2 ) 1 8 0 1 8 0 8 5 . 8 6 ( 1 4 ) 1 4 7 . 5 ( 4 ) 7 8 3 4 ( 1 4 ) 1 3 1 . 7 ( 3 ) 7 9 . 4 ( 2 ) 1 3 3 . 5 ( 3 ) 8 9 4 ( 3 ) 5 5 4 5 ( 1 4 ) 8 0 . 6 ( 3 ) 2 8 1 T a b l e 4 . 4 4 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N a o , 7 3 ( 1 ) C u 1 , 2 2 ( 1 ) C e T e 4 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 3 0 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 0 ' ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e N 3 9 7 8 0 ) C 1 1 1 2 2 0 ) C 6 T e 4 7 4 7 . 2 1 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A O r t h o r h o m b i c P 2 1 2 1 2 ( 0 1 3 0 ) 0 s 0 a = 4 . 3 8 5 0 ( 6 ) A , 0 1 = 9 0 ° b = 4 . 3 9 7 3 ( 6 ) A , 1 3 = 9 0 0 c = 1 9 . 8 1 0 ( 3 ) A , y = 9 0 ° 0 . 3 6 2 1 ( 7 ) b ‘ 3 8 1 . 9 9 ( 9 ) A 3 2 6 . 4 8 3 6 g / c m 3 2 4 . 2 1 2 m m ' 1 6 2 0 0 . 7 0 x 0 . 1 0 x 0 0 1 m m 3 1 . 9 6 t o 2 9 . 3 0 0 - 6 < = h < = 6 , - 6 < = k < = 5 , 2 7 < = 1 < = 2 7 , - 1 < = m < = 1 9 7 4 3 ( 2 7 6 3 m a i n + 6 9 8 0 s a t e l l i t e s ) 3 0 9 0 ( 1 0 2 8 m a i n + 2 0 6 2 s a t e l l i t e s ) [ R i m = 0 . 0 4 8 2 ] 9 9 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 3 0 9 0 / 1 5 / 1 0 2 1 . 4 5 R o b , = 0 . 0 4 5 4 , w R o b s = 0 . 1 1 1 4 R . , l l = 0 . 0 9 1 7 , w k , “ = 0 . 1 2 2 5 R . , . . . = 0 . 0 3 3 7 , w R o b s = 0 . 0 9 8 0 R . , l l = 0 . 0 3 8 5 , w R a n = 0 . 1 0 0 4 R o b , = 0 . 1 2 3 7 , w R . . . , = 0 . 1 8 0 3 R . , l l = 0 . 3 0 7 3 , w k , “ = 0 . 2 2 2 8 0 . 0 0 0 1 9 0 ) 0 . 0 7 7 3 a n d 0 . 9 0 8 8 3 . 3 0 a n d - 3 . 5 6 e . A ' 3 R = 2 1 1 9 1 - 1 9 1 1 7 2 1 1 : 1 4 4 1 = { 2 9 4 1 1 2 . 1 2 - 1 1 3 . 1 2 1 2 ] / 2 1 9 1 1 3 0 1 5 1 1 “ a n d w = 1 / ( 6 ’ ( I ) + 0 . 0 0 1 6 1 2 ) 2 8 2 T a b l e 4 . 4 5 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) d i s p l a c e m e n t a n d e q u i v a l e n t i s o t r o p i c N a o . 7 3 ( 1 ) C u 1 , 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . p a r a m e t e r s ( A 2 x 1 0 4 ) A t o m W a v e x y 2 O c c u p a n c y U e q C e 0 0 0 3 9 4 3 ( 1 ) 1 9 ( 1 ) s i n , 1 6 1 ( 2 ) 1 ( 6 ) 0 c o s , 1 0 0 - 1 ( 1 ) T e [ 1 ] 0 0 0 7 8 7 ( 1 ) 1 1 6 ( 1 ) s i n , 1 - 1 4 ( 2 ) - 3 1 ( 7 ) 0 c o s , 1 0 0 2 0 ( 2 ) T e [ 2 ] 0 0 0 5 6 0 3 ( 1 ) 1 9 ( 1 ) s i n , 1 0 ( 2 ) - 2 ( 6 ) 0 c o s , 1 0 0 3 ( 2 ) T e [ 3 ] 0 0 5 0 0 0 2 6 6 3 ( 1 ) 1 1 2 ( 1 ) s i n , 1 - 2 8 6 ( 4 ) 1 1 ( 7 ) 0 c o s , 1 0 0 0 ( 2 ) T e [ 4 ] 0 0 5 0 0 0 7 3 3 6 ( 1 ) 1 1 2 ( 1 ) s i n , 1 2 2 0 ( 4 ) - l 6 ( 7 ) 0 c o s , 1 0 0 1 ( 2 ) N a 0 0 0 8 7 4 3 0 . 7 8 5 ( 1 3 ) 2 0 ( 1 ) s i n , 1 - 5 3 ( 1 0 ) - 5 5 ( 3 0 ) 0 c o s , 1 0 0 5 ( 6 ) C u [ l ] 0 0 5 0 0 0 - 1 ( 1 ) 1 2 8 ( 1 ) s i n , 1 - 5 3 ( 1 4 ) - 8 8 ( 1 7 ) 0 c o s , 1 0 0 8 ( 3 ) C u [ 2 ] 0 0 0 8 7 4 3 ( 2 ) 0 . 2 1 5 ( 1 3 ) 2 0 ( 1 ) s i n , 1 - 5 3 ( 1 0 ) - 5 5 ( 3 0 ) 0 c o s , 1 0 0 5 ( 6 ) ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 4 . 4 6 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r N a o . 7 g ( 1 ) C u 1 , 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 C e 0 6 ( 1 ) 8 ( 1 ) 1 3 ( 1 ) - 3 0 ) 0 0 s i n , 1 0 0 0 0 0 ( 1 ) 2 ( 1 ) c o s , 1 - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) 0 0 2 8 3 T a b l e 4 . 4 6 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r N a o g g C u t z z C e T e n , a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 1 ] 0 1 0 ( 1 ) 1 3 ( 1 ) 2 4 ( 1 ) 7 ( 1 ) 0 0 s i n , 1 0 0 0 0 0 ( 1 ) 2 ( 1 ) c o s , 1 8 ( 1 ) 8 ( 1 ) - 1 3 ( 1 ) 1 ( 1 ) 0 0 T e [ 2 ] 0 6 ( 1 ) 8 ( 1 ) 1 2 ( 1 ) 6 ( 1 ) 0 0 s i n , 1 0 0 0 0 0 ( 1 ) 1 ( 1 ) c o s , 1 - l ( l ) 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 0 T e [ 3 ] 0 1 1 ( 1 ) 1 2 ( 1 ) 1 3 ( 1 ) - 5 ( 1 ) 0 0 s i n , 1 0 0 0 0 0 ( 1 ) - 3 ( 1 ) c o s , 1 - 5 ( 1 ) 5 ( 1 ) 1 ( 1 ) - 2 ( 1 ) 0 0 T e [ 4 ] 0 1 0 ( 1 ) 1 3 ( 1 ) 1 3 ( 1 ) 6 ( 1 ) 0 0 s i n , 1 0 0 0 0 1 ( 1 ) 0 ( 1 ) c o s , 1 3 ( 1 ) - 2 ( 1 ) 1 ( 1 ) 3 ( 1 ) 0 0 N a 0 1 5 ( 2 ) 2 3 ( 2 ) 2 2 ( 2 ) - 9 ( 4 ) 0 0 s i n , 1 0 0 0 0 - 4 ( 2 ) - l 7 ( 5 ) c o s , 1 - 1 3 ( 5 ) 8 ( 7 ) 1 ( 6 ) 4 ( 2 ) 0 0 C u [ l ] 0 2 9 ( 1 ) 3 4 ( 1 ) 2 1 ( 1 ) 1 ( 3 ) 0 0 s i n , 1 0 0 0 0 - 1 ( 1 ) 8 ( 3 ) c o s , 1 1 6 ( 3 ) - l 9 ( 3 ) 2 ( 3 ) - 2 ( 3 ) 0 0 C u [ 2 ] 0 1 5 ( 2 ) 2 3 ( 2 ) 2 2 ( 2 ) - 9 ( 4 ) 0 0 s i n , 1 0 0 0 0 - 4 ( 2 ) - 1 7 ( 5 ) c o s , 1 - l 3 ( 5 ) 8 ( 7 ) 1 ( 6 ) 4 ( 2 ) 0 0 T a b l e 4 . 4 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N a o , 7 g ( 1 ) C u 1 _ 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e C e - T e [ 2 ] 3 . 2 8 8 ( 2 ) 3 . 2 8 0 ( 4 ) 3 . 2 9 6 ( 4 ) C e - T e [ 2 ] x 4 3 . 2 3 2 7 ( 1 7 ) 3 . 2 1 3 ( 2 ) 3 . 2 5 2 4 ( 1 9 ) C e - T e [ 3 ] x 2 3 . 3 5 7 ( 2 ) 3 . 3 5 6 ( 2 ) 3 . 3 6 0 ( 2 ) C e - T e [ 4 ] x 2 3 . 3 5 0 5 ( 1 9 ) 3 . 3 0 4 9 ( 1 4 ) 3 . 3 9 6 5 ( 1 5 ) T e [ 1 ] - N a x 4 3 . 2 4 2 ( 6 ) 3 . 2 2 8 ( 4 ) 3 . 2 5 6 ( 4 ) T e [ 1 ] - C u [ l ] x 4 2 . 6 9 6 ( 5 ) 2 . 6 8 4 ( 4 ) 2 . 7 0 7 ( 4 ) T e [ 1 ] - C u [ 2 ] x 4 3 . 2 4 2 ( 6 ) 3 . 2 2 8 ( 4 ) 3 . 2 5 6 ( 4 ) T e [ 3 ] - T e [ 4 ] x 4 3 . 1 0 6 ( 2 ) 2 . 9 7 5 ( 3 ) 3 . 2 4 1 ( 2 ) 2 8 4 T a b l e 4 . 4 7 . ( C o n t ’ d ) B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N 3 0 _ 7 3 ( 1 ) C 1 1 1 3 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 3 ] - N a x 2 3 . 5 4 5 ( 6 ) T e [ 3 ] - C u [ 2 ] x 2 3 . 5 4 5 ( 7 ) N a - C u [ l ] x 4 3 . 3 2 1 ( 9 ) C u [ l ] - C u [ 1 ] x 4 3 . 1 0 5 ( 6 ) C u [ l ] - C h l [ 2 ] x 4 3 . 3 2 1 ( 1 0 ) 3 . 4 8 2 ( 3 ) 3 . 4 8 2 ( 4 ) 3 . 2 9 6 ( 1 1 ) 3 . 0 5 6 ( 7 ) 3 . 2 9 6 ( 1 1 ) 3 . 6 1 0 ( 3 ) 3 . 6 1 0 ( 4 ) 3 . 3 4 7 ( 1 1 ) 3 . 1 5 4 ( 7 ) 3 . 3 4 7 ( 1 1 ) T a b l e 4 . 4 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o , 7 g ( 1 ) C u 1 , 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 2 ] - C e - T e [ 2 ] x 8 7 3 8 5 ( 4 ) 7 3 5 0 ( 4 ) 7 4 1 9 ( 4 ) T e [ 2 ] - C e - T e [ 3 ] x 2 1 3 9 . 0 3 ( 7 ) 1 3 8 . 9 3 ( 5 ) 1 3 9 . 1 4 ( 5 ) T e [ 2 ] - C e - T e [ 4 ] x 2 1 3 9 . 1 3 ( 4 ) 1 3 8 . 7 0 ( 4 ) 1 3 9 . 5 8 ( 4 ) T e [ 2 ] - C e - T e [ 2 ] x 4 8 5 7 1 ( 5 ) 8 5 1 2 ( 4 ) 8 6 3 1 ( 4 ) T e [ 2 ] - C e - T e [ 2 ] x 4 8 5 4 1 ( 5 ) 8 5 3 3 ( 4 ) 8 5 4 9 ( 4 ) T e [ 2 ] - C e - T e [ 2 ] x 4 1 4 7 . 6 9 ( 6 ) 1 4 7 . 5 4 ( 9 ) 1 4 7 . 8 5 ( 9 ) T e [ 2 ] - C e - T e [ 3 ] x 4 7 6 3 9 ( 6 ) 7 4 8 2 ( 5 ) 7 7 9 5 ( 5 ) T e [ 2 ] - C e - T e [ 3 ] x 4 1 3 0 . 9 6 ( 5 ) 1 2 8 . 8 0 ( 5 ) 1 3 3 . 1 3 ( 6 ) T e [ 2 ] - C e - T e [ 4 ] x 4 7 6 5 0 ( 5 ) 7 5 9 6 ( 6 ) 7 7 0 6 ( 6 ) T e [ 2 ] - C e - T e [ 4 ] x 4 l 3 0 . 8 6 ( 7 ) 1 3 0 . 1 6 ( 9 ) 1 3 1 . 5 4 ( 9 ) T e [ 3 ] - C e - T e [ 3 ] x 2 8 1 8 9 ( 6 ) 8 1 . 7 7 ( 7 ) 8 2 1 1 ( 8 ) T e [ 3 ] - C e - T e [ 4 ] x 4 5 5 1 9 ( 5 ) 5 2 9 4 ( 6 ) 5 7 4 4 ( 6 ) T e [ 4 ] - C e - T e [ 4 ] x 2 8 1 . 7 4 ( 5 ) 8 1 6 4 ( 7 ) 8 1 8 7 ( 7 ) N a - T e [ 1 ] - N a x 8 8 5 4 ( 2 ) 8 4 . 4 ( 3 ) 8 6 4 ( 3 ) N a - T e [ 1 ] - N a x 4 1 4 6 . 5 7 ( 1 6 ) l 4 5 . 3 4 ( 1 4 ) 1 4 7 . 7 9 ( 1 4 ) N a - T e [ 1 ] - C u [ l ] x 8 6 7 2 5 ( 1 9 ) 6 7 . 0 3 ( 1 9 ) 6 7 4 7 ( 1 9 ) N a - T e [ 1 ] - C u [ l ] x 8 1 3 6 . 0 0 ( 1 7 ) 1 3 5 . 4 0 ( 1 7 ) 1 3 6 . 6 0 ( 1 6 ) N a - T e [ 1 ] - C u [ 2 ] x 8 8 5 . 4 ( 2 ) 8 4 4 ( 3 ) 8 6 . 4 ( 3 ) N a - T e [ 1 ] - C u [ 2 ] x 4 1 4 6 . 5 7 ( l 7 ) l 4 5 . 3 4 ( 1 5 ) 1 4 7 . 7 9 ( 1 5 ) C u [ l ] - T e [ 1 ] - C u [ l ] x 4 1 0 9 . 2 9 ( 1 5 ) 1 0 7 . 3 2 ( 1 8 ) 1 1 1 . 2 9 ( l 7 ) C u [ l ] - T e [ 1 ] - C u [ l ] x 8 7 0 4 3 ( 1 7 ) 6 9 . 2 4 ( 1 6 ) 7 1 . 6 2 ( 1 6 ) C u [ l ] - T e [ 1 ] - C u [ 2 ] x 8 6 7 2 5 ( 1 9 ) 6 7 0 3 ( 1 8 ) 6 7 4 7 ( 1 8 ) C u [ 1 ] - T e [ 1 ] - C u [ 2 ] x 8 1 3 6 . 0 0 ( 1 6 ) 1 3 5 . 8 1 ( l 9 ) 1 3 6 . 1 9 ( l 9 ) C u [ 2 ] - T e [ 1 ] - C u [ 2 ] x 8 8 5 . 4 ( 2 ) 8 4 . 4 ( 3 ) 8 6 . 4 ( 3 ) 2 8 5 T a b l e 4 . 4 8 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o _ 7 g ( 1 ) C u 1 , 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . C u [ 2 ] - T e [ 1 ] - C u [ 2 ] x 4 C e - T e [ 2 ] - C e x 8 C e - T e [ 2 ] - C e x 4 C e - T e [ 2 ] - C e x 4 C e - T e [ 2 ] - C e x 4 C e - T e [ 3 ] - C e x 2 C e - T e [ 3 ] - T e [ 4 ] x 4 C e - T e [ 3 ] - T e [ 4 ] x 4 C e - T e [ 3 ] - N a x 4 C e - T e [ 3 ] - C u [ 2 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - N a x 4 T e [ 4 ] - T e [ 3 ] - N a x 4 T e [ 4 ] - T e [ 3 ] - C u [ 2 ] x 4 T e [ 4 ] - T e [ 3 ] - C u [ 2 ] x 4 N a - T e [ 3 ] - N a x 2 N a - T e [ 3 ] - C u [ 2 ] x 2 C u [ 2 ] - T e [ 3 ] - C u [ 2 ] x 2 C e - T e [ 4 ] - C e x 2 C e - T e [ 4 ] - T e [ 3 ] x 4 C e - T e [ 4 ] - T e [ 3 ] x 4 C e - T e [ 4 ] - N a x 4 C e - T e [ 4 ] - C u [ 2 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 2 T e [ 3 ] - T e [ 4 ] - N a x 4 T e [ 3 ] - T e [ 4 ] - N a x 4 T e [ 3 ] - T e [ 4 ] - C u [ 2 ] x 4 T e [ 3 ] - T e [ 4 ] - C u [ 2 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 2 T e [ 1 ] - N a - T e [ 1 ] x 8 1 4 6 . 5 7 ( 1 8 ) 1 0 6 . 1 5 ( 5 ) 8 5 7 1 ( 5 ) 8 5 4 1 ( 5 ) 1 4 7 7 0 0 ) 8 1 8 3 ( 6 ) 6 2 2 9 ( 5 ) 1 1 7 . 6 3 ( 6 ) 1 2 6 4 2 ( l 9 ) 1 2 6 . 4 ( 2 ) 9 9 3 0 ( 6 ) 8 9 7 3 ( 7 ) 1 7 7 2 0 ( 8 ) 6 4 1 9 ( 1 9 ) 1 1 5 . 8 7 ( 1 9 ) 6 4 1 9 ( 1 9 ) 1 1 5 . 9 ( 2 ) 7 6 3 9 ( 1 1 ) 7 6 3 9 ( 1 1 ) 7 6 3 9 ( 1 2 ) 8 1 . 7 4 ( 4 ) 6 2 5 3 ( 4 ) 1 1 7 5 0 ( 7 ) 1 2 6 . 4 0 0 3 ) 1 2 6 4 0 ( 1 3 ) 9 9 2 3 ( 6 ) 8 9 7 4 ( 7 ) 1 7 7 . 4 2 ( 8 ) 6 3 9 3 ( 1 3 ) 1 1 5 9 5 ( 1 4 ) 6 3 9 3 ( 1 4 ) 1 1 5 9 5 ( 1 4 ) 1 7 7 5 8 ( 8 ) 8 5 . 4 0 0 1 ) l 4 5 . 3 4 ( 1 6 ) 1 0 5 . 7 5 ( 5 ) 8 5 4 6 ( 4 ) 8 5 3 3 ( 4 ) 1 4 7 . 3 2 0 1 ) 8 1 . 7 8 ( 4 ) 6 1 . 6 2 ( 5 ) 1 1 4 5 2 ( 5 ) 1 2 3 . 5 6 0 9 ) 1 2 3 . 5 6 0 9 ) 8 5 9 9 ( 6 ) 8 9 5 7 ( 7 ) 1 7 5 . 6 1 0 0 ) 6 1 9 2 ( 1 8 ) 1 1 5 . 3 ( 2 ) 6 1 . 9 2 0 8 ) 1 1 5 . 3 ( 2 ) 7 6 2 0 ( 1 5 ) 7 6 2 0 ( 1 6 ) 7 6 2 0 ( 1 6 ) 8 1 6 4 ( 7 ) 6 9 8 7 ( 5 ) 1 1 6 . 6 6 ( 6 ) 1 2 4 4 7 0 3 ) 1 2 4 4 7 0 4 ) 8 6 3 9 ( 6 ) 8 9 5 7 ( 9 ) 1 7 5 . 9 7 0 0 ) 6 3 5 5 ( 1 4 ) 1 1 3 . 6 4 ( 1 3 ) 6 3 5 5 ( 1 4 ) 1 1 3 . 6 4 0 3 ) 1 7 6 2 2 ( 1 0 ) 8 4 8 8 ( 9 ) 1 4 7 . 7 9 ( 1 6 ) 1 0 6 5 5 ( 5 ) 8 5 9 6 ( 4 ) 8 5 4 9 ( 4 ) 1 4 8 . 0 7 0 1 ) 8 1 9 0 ( 8 ) 6 2 9 4 ( 5 ) 1 2 0 . 6 5 ( 5 ) 1 2 9 . 2 ( 2 ) 1 2 9 . 2 ( 2 ) 9 4 6 6 ( 7 ) 9 0 0 1 ( 5 ) 1 8 0 6 6 . 5 ( 2 ) l 1 6 5 3 ( 1 9 ) 6 6 . 5 ( 2 ) 1 1 6 . 5 ( 2 ) 7 6 6 3 ( 1 5 ) 7 6 6 3 ( 1 6 ) 7 6 6 3 ( 1 6 ) 8 1 8 7 ( 7 ) 6 4 2 5 ( 5 ) 1 1 8 . 3 0 ( 7 ) 1 2 8 . 3 4 ( 1 5 ) 1 2 8 . 3 4 ( 1 5 ) 9 4 1 9 ( 7 ) 9 9 0 1 ( 6 ) 1 8 0 6 4 3 3 ( 1 4 ) 1 1 8 2 6 ( 1 4 ) 6 4 . 3 3 0 4 ) 1 1 8 . 2 6 ( 1 4 ) 1 8 0 8 5 9 2 ( 9 ) 2 8 6 T a b l e 4 . 4 8 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o , 7 g ( 1 ) C u 1 , 2 2 ( 1 ) C e T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 1 ] - N a - T e [ 1 ] x 4 T e [ 1 ] - N a - T e [ 3 ] x 4 T e [ 1 ] - N a - T e [ 3 ] x 4 T e [ 1 ] - N a - T e [ 4 ] x 4 T e [ 1 ] - N a - T e [ 4 ] x 4 T e [ 1 ] - N a - C u [ 1 ] x 8 T e [ 1 ] - N a - C u [ 1 ] x 8 T e [ 3 ] - N a - T e [ 3 ] x 2 T e [ 3 ] - N a - T e [ 4 ] x 4 T e [ 3 ] - N a - C u [ l ] x 4 T e [ 3 ] - N a - C u [ 1 ] x 2 T e [ 3 ] - N a - C u [ l ] x 2 C u [ l ] - N a - C u [ 1 ] x 4 C u [ 1 ] - N a - C u [ 1 ] x 8 T e [ 1 ] - C u [ 1 ] - T e [ 1 ] x 1 1 T e [ 1 ] - C u [ l ] - N a x 4 T e [ 1 ] - C u [ 1 ] - N a x 4 T e [ 1 ] - C u [ 1 ] - N a x 8 T e [ 1 ] - C u [ l ] - C u [ 1 ] x 8 T e [ 1 ] - C u [ 1 ] - C u [ 1 ] x 8 T e [ 1 ] - C u [ 1 ] - C u [ 2 ] x 4 T e [ 1 ] - C u [ 1 ] - C u [ 2 ] x 4 T e [ 1 ] - C u [ 1 ] - C u [ 2 ] x 8 T e [ 1 ] - C u [ l ] - T e [ 1 ] N a - C u [ 1 ] - N a x 4 N a - C u [ 1 ] - N a x 8 N a - C u [ 1 ] - C u [ l ] x 8 N a - C u [ l ] - C u [ l ] x 8 N a - C u [ l ] - C u [ 2 ] x 4 N a - C u [ l ] - C u [ 2 ] x 8 C u [ 1 ] - C u [ 1 ] - C u [ 1 ] x 8 C u [ 1 ] - C u [ 1 ] - C u [ l ] x 4 C u [ l ] - C u [ 1 ] - C u [ 2 ] x 8 C u [ 1 ] - C u [ 1 ] - C u [ 2 ] x 8 1 4 6 . 6 ( 2 ) 7 8 9 3 ( 1 2 ) 1 3 0 . 1 ( 3 ) 7 8 . 8 1 0 7 ) 1 3 0 . 2 4 ( 1 6 ) 4 8 3 6 ( 1 6 ) 1 0 3 . 5 ( 2 ) 7 6 3 9 ( 1 4 ) 5 1 . 9 0 0 1 ) 1 2 6 . 1 ( 2 ) 1 0 0 . 4 6 ( 1 1 ) 1 7 6 . 7 ( 2 ) 8 2 9 ( 2 ) 5 5 7 5 ( 1 8 ) 1 0 9 . 3 0 0 5 ) 8 3 9 ( 2 ) 1 6 6 . 8 ( 3 ) 6 4 3 ( 2 ) 5 4 7 0 ( 1 2 ) 1 2 5 2 4 0 7 ) 8 3 . 9 ( 2 ) 1 6 6 . 8 ( 3 ) 6 4 . 3 ( 2 ) 1 0 9 . 5 9 0 4 ) 8 2 9 ( 3 ) 1 2 4 . 3 ( 3 ) 6 2 1 1 ( 1 4 ) 1 1 7 . 9 9 0 7 ) 8 2 . 9 ( 3 ) 1 2 4 . 3 ( 3 ) 9 9 1 6 ( 1 8 ) 1 7 9 . 2 ( 2 ) 6 2 1 1 ( 1 7 ) 1 1 8 . 0 ( 2 ) 1 4 6 . 4 ( 4 ) 7 8 . 6 6 ( 1 1 ) 1 2 9 . 6 ( 3 ) 7 6 9 ( 2 ) 1 2 8 . 1 1 0 3 ) 4 8 . 0 l ( 1 4 ) 1 0 2 . 8 ( 2 ) 7 6 2 ( 3 ) 4 9 7 8 ( 8 ) 1 2 5 . 4 8 0 1 ) 9 9 1 6 ( 1 4 ) 1 7 5 . 3 ( 2 ) 8 2 1 ( 3 ) 5 4 8 4 ( 1 5 ) 1 0 9 . 0 ( 2 ) 8 2 5 ( 2 ) 1 6 5 . 5 ( 3 ) 6 3 . 6 ( 2 ) 5 3 . 6 0 0 5 ) 1 2 4 . 4 8 0 9 ) 8 2 . 5 ( 2 ) 1 6 5 . 5 ( 3 ) 6 3 . 6 ( 2 ) 1 0 7 . 6 ( 2 ) 8 2 0 ( 3 ) 1 2 2 . 9 ( 3 ) 6 1 . 2 5 0 6 ) 1 1 7 7 1 ( 1 7 ) 8 2 . 0 ( 3 ) 1 2 2 . 9 ( 3 ) 8 9 1 8 ( 1 5 ) 1 7 8 . 9 ( 3 ) 6 1 2 5 ( 1 9 ) 1 1 7 5 4 ( 1 8 ) 1 4 6 . 7 ( 4 ) 7 9 . 1 7 0 1 ) 1 3 0 . 6 ( 3 ) 8 9 7 ( 2 ) 1 3 2 . 3 4 0 3 ) 4 8 . 7 0 0 4 ) 1 0 4 . 1 ( 2 ) 7 6 6 ( 3 ) 5 4 0 7 ( 8 ) 1 2 6 . 6 9 0 1 ) 1 0 1 . 7 7 0 5 ) 1 7 7 . 6 ( 3 ) 8 3 . 7 ( 3 ) 5 6 6 6 ( 1 5 ) 1 0 9 . 6 ( 2 ) 8 5 3 ( 3 ) 1 6 8 . 1 ( 3 ) 6 4 9 ( 2 ) 5 5 7 7 ( 1 6 ) 1 2 5 . 9 5 0 8 ) 8 5 . 3 ( 3 ) 1 6 8 . 1 ( 3 ) 6 4 . 9 ( 2 ) 1 1 1 . 5 ( 3 ) 8 3 8 ( 3 ) 1 2 5 . 6 ( 3 ) 6 2 9 5 ( 1 6 ) 1 1 8 2 6 ( 1 6 ) 8 3 . 8 ( 3 ) 1 2 5 . 6 ( 3 ) 9 1 . 1 3 0 4 ) 1 7 9 . 7 ( 2 ) 6 2 9 ( 2 ) 1 1 8 . 4 2 0 8 ) 2 8 7 T a b l e 4 . 4 8 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a n - , g C u L z z C e T e i i a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . C u [ 2 ] - C u [ l ] - C u [ 2 ] x 4 C u [ 2 ] - C u [ l ] - C u [ 2 ] x 8 T e [ 1 ] - C u [ 2 ] - T e [ 1 ] x 8 T e [ 1 ] - C u [ 2 ] - T e [ 1 ] x 4 T e [ 1 ] - C u [ 2 ] - T e [ 3 ] x 4 T e [ 1 ] - C u [ 2 ] - T e [ 3 ] x 4 T e [ 1 ] - C u [ 2 ] - T e [ 4 ] x 4 T e [ 1 ] - C u [ 2 ] - T e [ 4 ] x 4 T e [ 1 ] - C u [ 2 ] - C u [ 1 ] x 8 T e [ 1 ] - C u [ 2 ] - C u [ 1 ] x 8 T e [ 3 ] - C u [ 2 ] - T e [ 3 ] x 2 T e [ 3 ] - C u [ 2 ] - T e [ 4 ] x 4 T e [ 3 ] - C u [ 2 ] - C u [ 1 ] x 4 T e [ 3 ] - C u [ 2 ] - C u [ l ] x 2 T e [ 3 ] - C u [ 2 ] - C u [ 1 ] x 2 C u [ l ] - C u [ 2 ] - C u [ 1 ] x 4 C u [ 1 ] - C u [ 2 ] - C u [ 1 ] x 8 8 2 . 9 ( 3 ) 1 2 4 . 3 ( 3 ) 8 5 4 0 ( 1 1 ) 1 4 6 . 6 ( 3 ) 7 8 9 3 ( 1 2 ) 1 3 0 . 1 ( 3 ) 7 8 8 1 ( 1 7 ) 1 3 0 . 2 4 ( 1 8 ) 4 8 . 3 6 0 6 ) 1 0 3 . 5 ( 2 ) 7 6 . 3 9 0 6 ) 5 1 . 9 0 0 2 ) 1 2 6 . 1 ( 2 ) 1 0 0 . 4 6 ( 1 1 ) 1 7 6 . 7 ( 2 ) 8 2 . 9 ( 2 ) 5 5 7 5 ( 1 9 ) 8 2 . 0 ( 3 ) 1 2 2 . 9 ( 3 ) 8 4 8 8 ( 1 0 ) 1 4 6 . 4 ( 5 ) 7 8 . 6 6 0 1 ) 1 2 9 . 6 ( 3 ) 7 6 . 9 ( 2 ) 1 2 8 . 1 1 ( 1 4 ) 4 8 . 0 1 ( 1 4 ) 1 0 2 . 8 ( 2 ) 7 6 . 2 ( 3 ) 4 9 7 8 ( 9 ) 1 2 5 . 4 8 ( 1 1 ) 9 9 . 1 6 0 4 ) 1 7 5 . 3 ( 2 ) 8 2 . 1 ( 3 ) 5 4 8 4 ( 1 6 ) 8 3 . 8 ( 3 ) 1 2 5 . 6 ( 3 ) 8 5 . 9 2 0 0 ) 1 4 6 . 7 ( 5 ) 7 9 . 1 7 0 1 ) 1 3 0 . 6 ( 3 ) 8 0 . 7 ( 2 ) 1 3 2 3 4 0 5 ) 4 8 . 7 0 0 4 ) 1 0 4 . 1 ( 2 ) 7 6 . 6 ( 3 ) 5 4 0 7 ( 1 0 ) 1 2 6 . 6 9 0 1 ) 1 0 1 . 7 7 0 5 ) 1 7 7 . 6 ( 3 ) 8 3 . 7 ( 3 ) 5 6 6 6 ( 1 6 ) 2 8 8 T a b l e 4 . 4 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N a o _ 5 o ( 2 ) C u 1 , 4 o ( z ) L a T e 4 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 2 0 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 o ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e N 3 9 6 0 ( 2 ) C u 1 . 4 0 ( 2 ) L a T e 4 7 5 2 . 1 1 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A O r t h o r h o m b i c P 2 1 2 1 2 ( 0 0 1 / 2 ) 0 s 0 a = 4 . 4 1 7 8 ( 6 ) A , o = 9 0 ° b = 4 . 4 2 5 7 ( 7 ) A , 1 3 = 9 0 0 c = 1 9 7 6 0 0 ) A , y = 9 0 0 0 . 3 6 3 2 ( 8 ) b ‘ + 1 / 2 c ' 3 8 6 3 4 0 0 ) A 3 2 6 . 4 6 2 8 g / c t n 3 2 3 . 9 8 2 m m ' 1 6 2 4 0 . 1 1 x 0 . 0 5 x 9 0 1 m m 3 1 . 7 5 t o 2 9 . 2 0 0 - 5 < = h < = 6 , - 6 < = k < = 6 , 2 7 < = 1 < = 2 7 , - l < = m < = 1 9 6 9 5 ( 2 6 7 8 m a i n + 7 0 1 7 s a t e l l i t e s ) 3 0 8 2 ( 1 0 0 3 m a i n + 2 0 7 9 s a t e l l i t e s ) 1 R . m = 0 . 0 8 6 5 ] 9 9 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 3 0 8 2 / 1 5 / 1 0 2 1 . 9 9 R . , , = 0 . 0 6 9 9 , w R . . . , = 0 . 1 7 2 6 R , l l = 0 . 1 2 3 2 , w R , l l = 0 . 1 8 2 8 R o b , = 0 . 0 6 1 5 , w R . . . , = 0 . 1 7 1 8 R , “ = 0 . 0 6 7 9 , w k , " = 0 . 1 7 4 1 R . , , = 0 . 1 2 9 8 , w R . . . , = 0 . 1 8 3 3 R . , “ = 0 . 3 3 8 3 , w R . . . = 0 . 2 6 9 9 0 . 0 0 0 6 3 ( 8 ) 0 . 1 0 7 7 a n d 0 . 8 4 0 2 7 . 0 3 a n d - 6 . 2 9 e . A ' 3 R = 2 1 1 1 5 1 - 1 6 1 1 / 2 1 6 . 1 , w R = { 2 [ W ( | F o | 2 - 1 1 5 . 1 2 1 2 ] / 2 1 w < 1 1 = o 1 4 ) l } ” 2 a n d w l / ( o z a n o o o w l z ) 2 8 9 T a b l e 4 . 5 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) N a o . 6 0 ( 2 ) C u 1 , 4 o ( 2 , L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x y z O c c u p a n c y U e q L a 0 0 0 3 9 3 1 ( 1 ) 1 1 3 ( 1 ) s i n , 1 2 1 ( 2 ) - 1 ( 2 ) 0 ( 2 ) c o s , 1 - 6 0 ( 4 ) 2 ( 7 ) 0 ( 1 ) T e [ 1 ] 0 0 0 7 8 1 ( 1 ) 1 2 1 ( 1 ) s i n , 1 - 7 ( 5 ) - 4 ( 9 ) 7 ( 1 ) c o s , 1 2 ( 1 ) 1 ( 2 ) 2 9 ( 2 ) T e [ 2 ] 0 0 0 5 6 1 2 ( 1 ) 1 1 2 ( 1 ) s i n , 1 0 ( 1 ) 1 ( 2 ) 1 ( 2 ) c o s , 1 0 ( 4 ) 7 ( 9 ) 0 ( 1 ) T e [ 3 ] 0 0 5 0 0 0 2 6 3 6 ( 1 ) 1 1 7 ( 1 ) s i n , 1 — 1 8 5 ( 6 ) - 1 1 ( 6 ) - 1 ( 1 ) c o s , 1 2 0 1 ( 6 ) 1 2 ( 6 ) - l ( 1 ) T e [ 4 ] 0 0 5 0 0 0 7 3 6 4 ( 1 ) 1 1 7 ( 1 ) s i n , 1 1 4 0 ( 5 ) 2 ( 6 ) 0 ( 1 ) c o s , 1 1 5 3 ( 6 ) 2 ( 7 ) 0 ( 1 ) N a 0 0 0 8 7 6 0 0 6 0 ( 2 ) 2 4 ( 1 ) s i n , 1 - 5 4 ( l 7 ) - 2 5 ( 3 0 ) - 2 ( 3 ) c o s , 1 - 2 2 ( 7 ) - 1 2 ( 1 2 ) 6 ( 6 ) C u [ l ] 0 0 5 0 0 0 1 ( 1 ) 1 3 4 ( 1 ) s i n , 1 - 4 5 ( 3 0 ) - 2 5 ( 2 0 ) 0 c o s , 1 0 0 5 ( 4 ) C u [ 2 ] 0 0 0 8 7 6 0 ( 2 ) 0 4 0 ( 2 ) 2 4 ( 1 ) s i n , 1 - 5 4 ( 1 7 ) - 2 5 ( 3 0 ) - 2 ( 3 ) c o s , 1 - 2 2 ( 7 ) - 1 2 ( 1 2 ) 6 ( 6 ) ' U e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . T a b l e 4 . 5 1 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r N a o , 6 o ( 2 ) C u 1 , 4 o ( 2 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . L a b e l W a v e U l l U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 L a 0 1 0 ( 1 ) 1 0 ( 1 ) 1 8 ( 1 ) 5 ( 1 ) 0 0 s i n , 1 - 1 ( 2 ) - 1 0 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 2 9 0 T a b l e 4 . 5 1 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r N a o , 6 o ( 2 ) C u 1 , 4 o ( 2 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 1 ] 0 1 4 ( 1 ) 1 5 ( 1 ) 3 3 ( 1 ) - 5 0 ) 0 0 s i n , 1 3 ( 1 ) 2 ( 1 ) - 5 ( 1 ) 0 ( 1 ) 0 ( 1 ) 2 ( 2 ) c o s , 1 1 2 ( 2 ) 9 ( 2 ) - 1 8 ( 2 ) - 1 0 ) 0 ( 1 ) 0 ( 1 ) T e [ 2 ] 0 9 ( 1 ) 9 ( 1 ) 1 8 ( 1 ) - 8 ( 1 ) 0 0 s i n , 1 2 ( 2 ) 3 ( 2 ) 3 ( 2 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) - 1 0 ) 0 ( 1 ) - 1 0 ) 0 ( 1 ) T e [ 3 ] 0 1 6 ( 1 ) 1 7 ( 1 ) 1 7 ( 1 ) 8 ( 1 ) 0 0 s i n , 1 1 ( 2 ) 0 ( 1 ) 0 ( 1 ) - 1 0 ) 1 ( 1 ) 0 ( 1 ) c o s , 1 1 ( 2 ) 0 ( 1 ) 0 ( 1 ) - 1 0 ) - 1 0 ) 0 ( 1 ) T e [ 4 ] 0 1 6 ( 1 ) 1 9 ( 1 ) 1 7 ( 1 ) - 1 0 0 ) 0 0 s i n , 1 1 ( 2 ) 0 ( 1 ) 0 ( 1 ) 2 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 - 1 0 ) 0 ( 1 ) 0 ( 1 ) 2 ( 1 ) 0 ( 1 ) 0 ( 1 ) N a 0 2 5 ( 3 ) 2 5 ( 2 ) 2 1 ( 2 ) - 1 4 ( 5 ) 0 0 s i n , 1 - 3 ( 3 ) 2 ( 2 ) 0 ( 2 ) - 1 0 ) 2 ( 4 ) 0 ( 5 ) c o s , 1 7 ( 8 ) - 5 ( 6 ) 1 ( 5 ) 2 ( 3 ) 1 ( 2 ) 0 ( 2 ) C u [ l ] 0 3 8 ( 2 ) 3 8 ( 2 ) 2 5 ( 1 ) 3 ( 5 ) 0 0 s i n , 1 0 0 0 0 0 ( 2 ) 3 ( 4 ) c o s , 1 1 3 ( 6 ) - l 8 ( 5 ) 0 ( 4 ) 3 ( 6 ) 0 0 C u [ 2 ] 0 2 5 ( 3 ) 2 5 ( 2 ) 2 1 ( 2 ) - 1 4 ( 5 ) 0 0 s i n , 1 - 3 ( 3 ) 2 ( 2 ) 0 ( 2 ) - 1 0 ) 2 ( 4 ) 0 ( 5 ) c o s , 1 7 ( 8 ) - S ( 6 ) 1 ( 5 ) 2 ( 3 ) 1 ( 2 ) 0 ( 2 ) T a b l e 4 . 5 2 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N a o , 6 o ( 2 ) C u 1 , 4 o ( 2 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e L a - T e [ 2 ] 3 . 3 2 0 ( 3 ) 3 . 3 1 9 ( 4 ) 3 . 3 2 1 ( 4 ) L a - T e [ 2 ] x 4 3 . 2 5 5 ( 3 ) 3 . 2 3 6 ( 3 ) 3 . 2 7 3 ( 3 ) L a - T e [ 3 ] x 2 3 . 3 8 5 ( 4 ) 3 . 3 8 2 ( 4 ) 3 . 3 9 1 ( 4 ) L a - T e [ 4 ] x 2 3 . 3 8 1 ( 3 ) 3 . 3 3 9 ( 3 ) 3 . 4 2 3 ( 3 ) T e [ 1 ] - N a x 4 3 . 2 5 5 ( 8 ) 3 . 2 3 3 ( 1 1 ) 3 . 2 7 9 ( 1 0 ) T e [ 1 ] - C u [ 1 ] x 4 2 . 6 9 8 ( 7 ) 2 . 6 7 7 ( 8 ) 2 . 7 1 8 ( 8 ) T e [ 1 ] - C u [ 2 ] x 4 3 . 2 5 5 ( 8 ) 3 . 2 3 3 ( 1 1 ) 3 . 2 7 9 ( 1 1 ) T e [ 3 ] - T e [ 4 ] x 4 3 . 1 2 7 ( 4 ) 2 . 9 9 9 ( 4 ) 3 . 2 6 0 ( 4 ) 2 9 1 T a b l e 4 . 5 2 . ( C o n t ’ d ) B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N a o , 6 o ( 2 ) C u 1 , 4 o ( 2 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 3 ] - N a x 2 3 . 5 3 3 ( 8 ) T e [ 3 ] - C u [ 2 ] x 2 3 . 5 3 3 ( 9 ) N a - C u [ 1 ] x 4 3 . 3 0 2 ( 1 1 ) C u [ 1 ] - C u [ 1 ] x 4 3 . 1 2 6 0 0 ) C u [ l ] - C u [ 2 ] x 4 3 . 3 0 2 ( 1 2 ) 3 . 4 7 4 ( 7 ) 3 . 4 7 4 ( 8 ) 3 . 2 8 7 ( 1 1 ) 3 . 1 0 2 ( 1 1 ) 3 . 2 8 7 ( 1 2 ) 3 . 5 9 5 ( 7 ) 3 . 5 9 5 ( 8 ) 3 . 3 1 7 ( 1 1 ) 3 . 1 5 1 0 1 ) 3 . 3 1 7 ( 1 2 ) T a b l e 4 . 5 3 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o . 6 o ( 2 ) C u 1 , 4 o ( 2 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 2 ] - L a - T e [ 2 ] x 8 7 3 8 8 ( 8 ) 7 3 6 3 ( 9 ) 7 4 1 4 ( 9 ) T e [ 2 ] - L a - T e [ 3 ] x 2 1 3 9 . 1 3 ( 9 ) 1 3 9 . 0 0 ( 9 ) 1 3 9 . 2 3 ( 7 ) T e [ 2 ] - L a - T e [ 4 ] x 2 1 3 9 . 2 1 ( 7 ) 1 3 8 . 8 8 ( 8 ) 1 3 9 . 5 4 ( 8 ) T e [ 2 ] - L a - T e [ 2 ] x 4 8 5 6 8 ( 5 ) 8 5 0 6 ( 5 ) 8 6 3 0 ( 5 ) T e [ 2 ] - L a - T e [ 2 ] x 4 8 5 4 9 ( 6 ) 8 5 4 2 ( 5 ) 8 5 5 6 ( 5 ) T e [ 2 ] - L a - T e [ 2 ] x 4 1 4 7 . 7 6 ( 1 0 ) l 4 7 . 7 6 ( 1 1 ) 1 4 7 . 7 8 ( 1 2 ) T e [ 2 ] - L a - T e [ 3 ] x 4 7 6 4 5 ( 7 ) 7 4 8 1 ( 7 ) 7 8 0 6 ( 8 ) T e [ 2 ] - L a - T e [ 3 ] x 4 1 3 0 . 8 7 ( 8 ) 1 2 8 . 6 0 ( 8 ) 1 3 3 . 1 6 ( 9 ) T e [ 2 ] - L a - T e [ 4 ] x 4 7 6 5 1 ( 7 ) 7 6 2 0 ( 7 ) 7 6 8 4 ( 7 ) T e [ 2 ] - L a - T e [ 4 ] x 4 l 3 0 . 8 1 ( 9 ) 1 3 0 . 3 3 ( 1 0 ) 1 3 1 . 2 9 ( 1 0 ) T e [ 3 ] - L a - T e [ 3 ] x 2 8 1 . 6 9 ( 8 ) 8 1 . 5 6 ( 9 ) 8 1 9 2 ( 9 ) T e [ 3 ] - L a - T e [ 4 ] x 4 5 5 0 8 ( 7 ) 5 2 9 8 ( 7 ) 5 7 1 8 ( 7 ) T e [ 4 ] - L a - T e [ 4 ] x 2 8 1 5 8 ( 8 ) 8 1 5 7 ( 8 ) 8 1 5 1 ( 9 ) N a - T e [ 1 ] - N a x 8 8 5 7 ( 2 ) 8 4 8 ( 3 ) 8 6 5 ( 3 ) N a - T e [ 1 ] - N a x 4 1 4 7 . 7 ( 2 ) 1 4 5 . 9 ( 2 ) 1 4 9 . 4 ( 2 ) N a - T e [ 1 ] - C u [ l ] x 8 6 6 5 ( 3 ) 6 6 . 4 ( 3 ) 6 6 6 ( 3 ) N a - T e [ 1 ] - C u [ l ] x 8 1 3 5 . 8 ( 3 ) 1 3 4 . 9 ( 3 ) 1 3 6 . 6 ( 3 ) N a - T e [ 1 ] - C u [ 2 ] x 8 8 5 . 7 ( 2 ) 8 4 . 8 ( 3 ) 8 6 . 5 ( 3 ) N a - T e [ 1 ] - C u [ 2 ] x 4 1 4 7 . 7 ( 2 ) 1 4 5 . 9 ( 2 ) 1 4 9 . 4 ( 2 ) C u [ l ] - T e [ 1 ] - C u [ l ] x 4 1 1 0 . 2 ( 2 ) 1 0 8 . 0 ( 2 ) 1 1 2 . 5 ( 2 ) C u [ l ] - T e [ 1 ] - C u [ l ] x 8 7 0 . 9 ( 3 ) 7 0 . 1 ( 3 ) 7 1 . 6 ( 3 ) C u [ l ] - T e [ 1 ] - C u [ 2 ] x 8 6 6 . 5 ( 2 ) 6 6 4 ( 2 ) 6 6 6 ( 2 ) C u [ l ] - T e [ 1 ] - C u [ 2 ] x 8 1 3 5 . 8 ( 2 ) 1 3 5 . 2 ( 2 ) 1 3 6 . 3 ( 2 ) C u [ 2 ] - T e [ 1 ] - C u [ 2 ] x 8 8 5 . 7 ( 2 ) 8 4 . 8 ( 3 ) 8 6 . 5 ( 3 ) 2 9 2 T a b l e 4 . 5 3 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o , 6 o ( 2 ) C u 1 , a o ( 2 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . C u [ 2 ] - T e [ 1 ] - C u [ 2 ] x 4 L a - T e [ 2 ] - L a x 8 L a - T e [ 2 ] - L a x 4 L a - T e [ 2 ] - L a x 4 L a - T e [ 2 ] - L a x 4 L a - T e [ 3 ] - L a x 2 L a - T e [ 3 ] - T e [ 4 ] x 4 L a - T e [ 3 ] - T e [ 4 ] x 4 L a - T e [ 3 ] - N a x 4 L a - T e [ 3 ] - C u [ 2 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - N a x 4 T e [ 4 ] - T e [ 3 ] - N a x 4 T e [ 4 ] - T e [ 3 ] - C u [ 2 ] x 4 T e [ 4 ] - T e [ 3 ] - C u [ 2 ] x 4 N a - T e [ 3 ] - N a x 2 N a - T e [ 3 ] - C u [ 2 ] x 2 C u [ 2 ] - T e [ 3 ] - C u [ 2 ] x 2 L a - T e [ 4 ] - L a x 2 L a - T e [ 4 ] - T e [ 3 ] x 4 L a - T e [ 4 ] - T e [ 3 ] x 4 L a - T e [ 4 ] - N a x 4 L a - T e [ 4 ] - C u [ 2 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - N a x 4 T e [ 3 ] - T e [ 4 ] - N a x 4 T e [ 3 ] - T e [ 4 ] — C u [ 2 ] x 4 T e [ 3 ] - T e [ 4 ] - C u [ 2 ] x 4 T e [ 1 ] - N a - T e [ 1 ] x 8 T e [ 1 ] - N a - T e [ 1 ] x 4 1 4 7 . 7 ( 2 ) 1 0 6 . 1 2 ( 9 ) 8 5 . 6 8 ( 5 ) 8 5 4 8 ( 7 ) 1 4 7 . 7 7 0 0 ) 8 1 5 3 ( 8 ) 6 2 3 9 ( 8 ) 1 1 7 . 5 6 ( 1 0 ) 1 2 6 . 2 ( 2 ) 1 2 6 . 2 ( 2 ) 9 9 2 3 ( 1 0 ) 8 9 8 1 ( 9 ) 1 7 7 . 4 7 0 2 ) 6 3 9 ( 2 ) 1 1 6 . 2 ( 2 ) 6 3 . 9 ( 2 ) 1 1 6 . 2 ( 2 ) 7 7 . 3 6 0 7 ) 7 7 3 6 ( 1 7 ) 7 7 3 6 ( 1 8 ) 8 1 5 8 ( 8 ) 6 2 5 7 ( 8 ) 1 1 7 . 4 6 0 1 ) 1 2 6 2 1 0 7 ) 1 2 6 2 1 0 7 ) 9 9 2 3 ( 9 ) 8 9 . 8 0 0 0 ) 1 7 7 . 6 2 ( 1 2 ) 6 3 . 6 8 ( 1 6 ) 1 1 6 . 2 8 ( 1 7 ) 6 3 . 6 8 ( 1 6 ) 1 1 6 . 2 8 0 8 ) 8 5 6 6 ( 1 6 ) 1 4 7 . 7 ( 3 ) 1 4 5 . 9 ( 2 ) 1 0 5 . 7 7 0 0 ) 8 5 4 2 ( 5 ) 8 5 4 2 ( 9 ) 1 4 7 . 6 2 0 3 ) 8 1 5 8 ( 8 ) 6 1 5 3 ( 8 ) 1 1 4 6 7 ( 1 0 ) 1 2 3 . 4 ( 2 ) 1 2 3 . 4 ( 2 ) 8 6 1 2 ( 9 ) 8 9 . 5 6 ( 1 0 ) 1 7 6 . 0 4 0 2 ) 6 1 8 1 ( 1 9 ) 1 1 5 . 6 ( 2 ) 6 1 8 1 ( 1 9 ) 1 1 5 . 6 ( 2 ) 7 7 0 9 ( 1 7 ) 7 7 0 9 ( 1 8 ) 7 7 . 0 9 0 8 ) 8 1 5 7 ( 8 ) 6 9 8 9 ( 8 ) 1 1 6 5 7 0 1 ) 1 2 4 . 3 0 0 6 ) 1 2 4 . 3 0 0 6 ) 8 6 5 3 ( 9 ) 8 9 . 5 6 ( 1 0 ) 1 7 6 2 6 0 2 ) 6 3 2 4 ( 1 6 ) 1 1 4 0 4 ( 1 7 ) 6 3 2 4 ( 1 6 ) 1 1 4 0 4 ( 1 7 ) 8 5 . 1 2 0 8 ) 1 4 7 . 2 ( 4 ) 1 4 9 . 4 ( 2 ) 1 0 6 . 4 6 ( 1 0 ) 8 5 9 3 ( 5 ) 8 5 5 6 ( 9 ) 1 4 7 . 9 2 ( 1 3 ) 8 1 7 5 ( 9 ) 6 3 2 2 ( 8 ) 1 2 0 . 3 5 0 1 ) 1 2 9 . 0 ( 2 ) 1 2 9 . 0 ( 2 ) 9 4 3 8 ( 1 0 ) 9 9 0 2 ( 9 ) 1 8 0 6 5 9 ( 2 ) 1 1 6 . 9 ( 2 ) 6 5 . 9 ( 2 ) 1 1 6 . 9 ( 2 ) 7 7 . 6 7 0 7 ) 7 7 . 6 7 0 8 ) 7 7 6 7 ( 1 8 ) 8 1 5 1 ( 8 ) 6 4 2 6 ( 9 ) 1 1 8 . 2 9 0 1 ) 1 2 8 . 0 8 0 7 ) 1 2 8 . 0 8 ( l 7 ) 9 3 9 1 ( 1 0 ) 9 9 0 2 ( 1 0 ) 1 8 0 6 4 1 6 ( 1 6 ) 1 1 8 . 4 4 0 8 ) 6 4 1 6 ( 1 6 ) 1 1 8 . 4 4 0 8 ) 8 6 2 2 ( 1 8 ) 1 4 8 . 1 ( 4 ) 2 9 3 T a b l e 4 . 5 3 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o , 6 o ( 2 ) C u 1 , 4 o ( 2 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 1 ] - N a - T e [ 3 ] x 4 T e [ 1 ] - N a - T e [ 3 ] x 4 T e [ 1 ] - N a - T e [ 4 ] x 4 T e [ 1 ] - N a - T e [ 4 ] x 4 T e [ 1 ] - N a - C u [ l ] x 8 T e [ 1 ] - N a - C u [ 1 ] x 8 T e [ 3 ] - N a - T e [ 3 ] x 2 T e [ 3 ] - N a - T e [ 4 ] x 4 T e [ 3 ] - N a - C u [ 1 ] x 4 T e [ 3 ] - N a - C u [ l ] x 2 T e [ 3 ] - N a - C u [ 1 ] x 2 C u [ l ] - N a - C u [ 1 ] x 4 C u [ 1 ] - N a - C u [ 1 ] x 8 T e [ 1 ] - C u [ 1 ] - T e [ 1 ] x 4 T e [ 1 ] - C u [ l ] - T e [ 1 ] x 8 T e [ 1 ] - C u [ 1 ] - N a x 4 T e [ 1 ] - C u [ 1 ] - N a x 4 T e [ 1 ] - C u [ 1 ] - N a x 8 T e [ 1 ] - C u [ 1 ] — C u [ l ] x 8 T e [ 1 ] — C u [ 1 ] - C u [ 1 ] x 8 T e [ 1 ] - C u [ l ] - C u [ 2 ] x 4 T e [ 1 ] - C u [ 1 ] - C u [ 2 ] x 4 T e [ 1 ] - C u [ 1 ] - C u [ 2 ] x 8 N a - C u [ 1 ] - N a x 4 N a - C u [ 1 ] - N a x 8 N a - C u [ l ] - C u [ 1 ] x 8 N a - C u [ 1 ] - C u [ l ] x 8 N a - C u [ 1 ] - C u [ 2 ] x 4 N a - C u [ l ] - C u [ 2 ] x 8 C u [ 1 ] - C u [ 1 ] - C u [ 1 ] x 8 C u [ 1 ] - C u [ l ] - C u [ 1 ] x 4 C u [ 1 ] - C u [ 1 ] - C u [ 2 ] x 8 C u [ 1 ] - C u [ 1 ] - C u [ 2 ] x 8 C u [ 2 ] - C u [ l ] - C u [ 2 ] x 4 7 8 0 6 ( 1 6 ) 1 2 9 . 9 ( 3 ) 7 8 . 0 ( 2 ) 1 3 0 . 0 ( 2 ) 4 8 5 ( 3 ) 1 0 4 . 4 ( 3 ) 7 7 3 6 ( 1 9 ) 5 2 5 1 ( 1 4 ) 1 2 5 . 4 ( 3 ) 9 9 3 ( 2 ) 1 7 6 . 6 ( 3 ) 8 4 2 ( 3 ) 5 6 . 6 ( 3 ) 1 1 0 . 3 ( 2 ) 1 0 9 . 1 ( 2 ) 8 2 8 ( 2 ) 1 6 6 . 9 ( 3 ) 6 4 9 ( 3 ) 5 4 5 ( 2 ) 1 2 5 . 5 ( 3 ) 8 2 8 ( 3 ) 1 6 6 . 9 ( 3 ) 6 4 . 9 ( 3 ) 8 4 . 2 ( 3 ) 1 2 3 . 4 ( 3 ) 6 1 7 ( 2 ) 1 1 8 . 3 ( 3 ) 8 4 . 2 ( 3 ) 1 2 3 . 4 ( 3 ) 9 9 1 ( 3 ) 1 7 9 . 8 ( 3 ) 6 1 . 7 ( 2 ) 1 1 8 . 3 ( 3 ) 8 4 . 2 ( 3 ) 7 7 5 9 ( 1 5 ) 1 2 9 . 4 ( 3 ) 7 6 1 ( 2 ) 1 2 7 . 6 ( 2 ) 4 8 0 ( 3 ) 1 0 3 . 7 ( 3 ) 7 7 . 1 ( 2 ) 5 0 . 4 2 0 2 ) 1 2 5 . 0 ( 3 ) 9 8 . 1 ( 3 ) 1 7 5 . 4 ( 3 ) 8 4 . 0 ( 3 ) 5 6 0 ( 2 ) 1 0 9 . 7 ( 3 ) 1 0 7 . 7 ( 4 ) 8 1 5 ( 3 ) 1 6 5 . 8 ( 3 ) 6 4 7 ( 3 ) 5 3 . 6 ( 3 ) 1 2 5 . 2 ( 4 ) 8 1 . 6 ( 3 ) 1 6 5 . 8 ( 3 ) 6 4 . 7 ( 3 ) 8 3 . 7 ( 3 ) 1 2 2 . 7 ( 3 ) 6 1 . 3 ( 2 ) 1 1 8 . 0 ( 3 ) 8 3 7 ( 3 ) 1 2 2 . 7 ( 3 ) 8 9 . 6 ( 3 ) 1 7 9 . 7 ( 3 ) 6 1 . 3 ( 3 ) 1 1 7 . 9 ( 3 ) 8 3 . 7 ( 3 ) 7 8 5 4 ( 1 5 ) 1 3 0 . 4 ( 3 ) 7 9 8 ( 3 ) 1 3 2 . 3 ( 2 ) 4 9 1 ( 3 ) 1 0 5 . 1 ( 3 ) 7 7 7 ( 2 ) 5 4 6 1 ( 1 2 ) 1 2 5 . 8 ( 3 ) 1 0 0 . 4 ( 3 ) 1 7 7 . 7 ( 3 ) 8 4 3 ( 3 ) 5 7 1 ( 2 ) 1 1 0 . 8 ( 3 ) 1 1 0 . 5 ( 4 ) 8 4 . 0 ( 3 ) 1 6 8 . 0 ( 3 ) 6 5 0 ( 3 ) 5 5 4 ( 3 ) 1 2 5 . 8 ( 4 ) 8 4 . 0 ( 3 ) 1 6 8 . 0 ( 3 ) 6 5 . 0 ( 3 ) 8 4 . 6 ( 3 ) 1 2 4 . 2 ( 3 ) 6 2 . 0 ( 2 ) 1 1 8 . 6 ( 3 ) 8 4 . 6 ( 3 ) 1 2 4 . 2 ( 3 ) 9 0 . 6 ( 3 ) 1 7 9 . 9 ( 3 ) 6 2 0 ( 3 ) 1 1 8 . 7 ( 3 ) 8 4 . 6 ( 3 ) 2 9 4 T a b l e 4 . 5 3 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o , 6 o ( 2 ) C u 1 , 4 o ( 2 ) L a T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . C u [ 2 ] - C u [ l ] - C u [ 2 ] x 8 T e [ 1 ] - C u [ 2 ] - T e [ 1 ] x 8 T e [ 1 ] - C u [ 2 ] - T e [ 1 ] x 4 T e [ 1 ] - C u [ 2 ] - T e [ 3 ] x 4 T e [ 1 ] - C u [ 2 ] - T e [ 3 ] x 4 T e [ 1 ] - C u [ 2 ] - T e [ 4 ] x 4 T e [ 1 ] - C u [ 2 ] - T e [ 4 ] x 4 T e [ 1 ] - C u [ 2 ] - C u [ l ] x 8 T e [ 1 ] - C u [ 2 ] - C u [ 1 ] x 8 T e [ 3 ] - C u [ 2 ] - T e [ 3 ] x 2 T e [ 3 ] - C u [ 2 ] - T e [ 4 ] x 4 T e [ 3 ] - C u [ 2 ] - C u [ l ] x 4 T e [ 3 ] - C u [ 2 ] - C u [ l ] x 2 T e [ 3 ] - C u [ 2 ] - C u [ l ] x 2 C u [ 1 ] - C u [ 2 ] - C u [ 1 ] x 4 C u [ 1 ] - C u [ 2 ] - C u [ 1 ] x 8 1 2 3 . 4 ( 3 ) 8 5 6 6 ( 1 7 ) 1 4 7 . 7 ( 3 ) 7 8 0 6 ( 1 6 ) 1 2 9 . 9 ( 3 ) 7 8 . 0 ( 2 ) 1 3 0 . 0 ( 2 ) 4 8 . 5 ( 3 ) 1 0 4 . 4 ( 3 ) 7 7 4 ( 2 ) 5 2 5 1 ( 1 5 ) 1 2 5 . 4 ( 3 ) 9 9 . 3 ( 2 ) 1 7 6 . 6 ( 3 ) 8 4 . 2 ( 3 ) 5 6 . 6 ( 3 ) 1 2 2 . 7 ( 3 ) 8 5 . 1 2 ( 1 8 ) 1 4 7 . 2 ( 4 ) 7 7 5 9 ( 1 5 ) 1 2 9 . 4 ( 3 ) 7 6 . 1 ( 2 ) 1 2 7 . 6 ( 2 ) 4 8 . 0 ( 3 ) 1 0 3 . 7 ( 3 ) 7 7 1 ( 2 ) 5 9 4 2 ( 1 2 ) 1 2 5 . 0 ( 3 ) 9 8 . 1 ( 3 ) 1 7 5 . 4 ( 3 ) 8 4 . 0 ( 3 ) 5 6 . 0 ( 2 ) 1 2 4 . 2 ( 3 ) 8 6 2 2 ( 1 9 ) 1 4 8 . 1 ( 4 ) 7 8 5 4 ( 1 5 ) 1 3 0 . 4 ( 3 ) 7 9 . 8 ( 3 ) 1 3 2 . 3 ( 2 ) 4 9 . 1 ( 3 ) 1 0 5 . 1 ( 3 ) 7 7 . 7 ( 2 ) 5 4 6 1 ( 1 3 ) 1 2 5 . 8 ( 3 ) 1 0 0 . 4 ( 3 ) 1 7 7 . 7 ( 3 ) 8 4 . 3 ( 3 ) 5 7 . 1 ( 2 ) 2 9 5 R e f e r e n c e s 1 M o r o s a n , E . ; Z a n d b e r g e n , H . W . ; D e n n i s , B . 8 ; B 0 8 , J . W . G . ; O n o s e , Y . ; K l i m c z u k , T . ; R a m i r e z , A . P . ; O n g , N . P . ; C a v a , R . J . N a t . P h y s . 2 0 0 6 , 8 , 5 4 4 . 2 G r u n e r , G . D e n s i t y W a v e s i n S o l i d s , A d d i s o n - W e s l e y , R e a d i n g , M A , 1 9 9 4 . 3 F u l l e r , W . W . ; C h a i k i n , P . M . . ; O n g , N . P . P h y s . R e v . B , 1 9 8 1 , 2 4 , 1 3 3 3 . 4 S c h o l z , G . A . S o l i d S t a t e I o n i c s , 2 0 0 2 , I 4 9 , 1 3 1 . 5 M e y e r , S . F . ; H o w a r d , . R . E . ; S t e w a r d , G . R . ; A c r i v o s , J . V . ; G e b a l l e , T . H . ; J . C h e m . P h y s . 1 9 7 5 , 6 2 , 4 4 1 1 . 6 ( a ) P a t s c h k e , R ; H e i s i n g , J . ; B r a z i s , P . ; K a n n e w u r f , C . R . ; K a n a t z i d i s , M . G . C h e m . M a t e r . 1 9 9 8 , 1 0 , 6 9 5 . ( b ) P a t s c h k e , R . ; K a n a t z i d i s , M . G . P h y s . C h e m . C h e m . P h y s . 2 0 0 2 , 4 , 3 2 6 6 . 7 L i n , W . ; S t e i n fi n k , H . ; W e i s s , E . J . I n o r g . C h e m . 1 9 6 5 , 4 , 8 7 7 . 8 S a v e l s b e r g , G . ; S c h a e f e r , H . Z . N a t u r f o r s c h . B 1 9 7 8 , 3 3 B , 3 7 0 . K C u T e a d o p s a B N s t r u c t u r e t y p e w h i c h i s d i f f e r e n t f r o m t h e s t r u c t u r e o f N a C u T e . H o w e v e r , i n a l l K - c o n t a i n i n g m e m b e r s , K g o e s t o t h e N a s i t e o f t h e N a C u T e s t r u c t u r e . 9 ( a ) D i M a s i , E . ; A r o n s o n , M . C . ; M a n s fi e l d , J . F . ; F o r a n , B . a n d L e e S . P h y s . R e v . 1 9 9 5 , B 5 2 , 1 4 5 1 6 . ( b ) K i m , H . J . ; M a l l i a k a s , C . D . ; T o m i c , A . ; T e s s m e r , S . H . ; K a n a t z i d i s M . G . ; B i l l i n g e , S . J . L . P h y s . R e v . L e t t . 2 0 0 6 , 9 6 , 2 2 6 4 0 1 . ( c ) D o e r t T . ; F o k w a B . P . T . ; S i m o n P . ; L i d i n S . ; S o h n e l T . C h e m . E u r . J . 2 0 0 3 , 9 , : 5 8 6 5 . 1 0 M a l l i a k a s , C . ; B i l l i n g e , S . J . L . ; K i m , H . J . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 5 , 1 2 7 , 6 5 1 0 . 1 1 T h e e l e c t r o n i c p r o p e r t i e s o f t h e R E T e ; s e r i e s b a r e l y h a v e a t w o - d i m e n s i o n a l c h a r a c t e r a c c o r d i n g t o t h e h i d d e n o n e - d i m e n s i o n a l b e h a v i o r r e p o r t e d i n S a c c h e t t i , A . ; D e g i o r g i , L . ; G i a m a r c h i , T . ; R u , N . ; F i s h e r , 1 . R . P h y s . R e v . B 2 0 0 6 , 7 4 , 1 2 5 1 1 5 . 1 2 X - A R E A , I P D S S o f t w a r e , S T O E & C i e G m b H , D a r m s t a d t , 2 0 0 6 . 1 3 P e t r i c e k , V . ; D u s e k , M . I n s t i t u t e o f P h y s i c s , P r a h a , C z e c h R e p u b l i c , 2 0 0 0 . 1 4 S h e l d r i c k , G . M . S H E L X L - 9 7 : P r o g r a m f o r C r y s t a l S t r u c t u r e R e fi n e m e n t ; U n i v e r s i t y o f G e t t i n g e n , G e t t i n g e n , G e r m a n y , 1 9 9 7 . 2 9 6 1 5 M a l l i a k a s , C . D . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 6 , 1 2 8 , 1 2 6 1 2 . 1 6 S i n g h , D . P l a n e w a v e s , P s e u d o p o t e n t i a l s , a n d t h e L A P W m e t h o d ; K l u w e r A c a d e m i c : B o s t o n , M A , 1 9 9 4 . 1 7 P e r d e w , J . P . , B u r k e , K . , E m z e r h o f , M . P h y s . R e v . L e t t . 1 9 9 6 , 7 7 , 3 8 6 5 - 3 8 6 8 . 1 8 B i l b a o C r y s t a l l o g r a p h i c S e r v e r , ( h t t p : / / w w w . c r v s t . e h u . e s ) . 1 9 h t t p : / / w w w . b e l l - l a b s . c o m / p r o j e c t / P O R T / d o c / p o r t 3 d o c . t a r . g z , G a y 1 9 8 3 . 2 0 K o e l l i n g , D . D . , H a r m o n , B . , J . P h y s . C 1 9 7 7 , 1 0 , 3 1 0 7 . 2 1 B l a h a , P . , S c h w a r z , K . , M a d s e n , G . , K v a s n i c k a , D . , L u i t z , J . , W I E N 2 K , A n A u g m e n t e d P l a n e W a v e + L o c a l O r b i t a l s P r o g r a m f o r C a l c u l a t i n g C r y s t a l P r o p e r t i e s ; K a r l h e i n z S c h w a r z , T e c h . U n i v . , W i e n , V i e n n a , 2 0 0 1 . 2 2 W e c a l c u l a t e d t h e a v e r a g e v a l u e o f 0 3 3 ( 2 ) f r o m t h e m i n i m u m v a l u e o f t h e n e s t i n g v e c t o r o f 0 . 3 1 ( c l o s e t o t h e Y p o i n t ) a n d m a x i m u m o f 0 . 3 5 ( c l o s e t o t h e X p o i n t ) . 2 3 K o m o d a , H . ; S a t o , T . ; S o u m a , S . ; T a k a h a s h i , T . ; I t o , Y . ; S u z u k i , K . P h y s . R e v . B 2 0 0 4 , 7 0 , 1 9 5 1 0 1 . 2 4 R u , N . ; M a r g u l i s , G . Y . ; S h i n , K . Y . ; T o n e y , M . F . ; F i s h e r , 1 . R . c o n d - m a t / 0 6 1 0 3 1 9 . 2 5 M a l l i a k a s , C . D . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 7 , 1 2 8 , 1 2 6 1 2 . 2 9 7 H 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I I I I I I I I I I I I I I I I I I I I I I I I H I W L I B R A R Y M i c h i c ; m S t a t e U n i v a r s i t y P L A C E I N R E T U R N B O X t o r e m o v e t h i s c h e c k o u t f r o m y o u r r e c o r d . T o A V O I D F I N E S r e t u r n o n o r b e f o r e d a t e d u e . M A Y B E R E C A L L E D w i t h e a r l i e r d u e d a t e i f r e q u e s t e d . D A T E D U E D A T E D U E D A T E D U E 5 / 0 8 K . l P r o j / A o c & P r e s / C I R C I D a I e D u e . I n d d C H A R G E D E N S I T Y W A V E S A N D S T R U C T U R A L M O D U L A T I O N S I N P O L Y T E L L U R I D E C O M P O U N D S V O L U M E I I B y C h r i s t o s D . M a l l i a k a s A D I S S E R T A T I O N S u b m i t t e d t o M i c h i g a n S t a t e U n i v e r s i t y i n p a r t i a l f u l fi l l m e n t o f t h e r e q u i r e m e n t s f o r t h e d e g r e e o f D O C T O R O F P H I L O S O P H Y D e p a r t m e n t o f C h e m i s t r y 2 0 0 7 C h a p t e r 5 C h a r g e D e n s i t y W a v e D i s t o r t i o n s i n S q u a r e N e t s o f T e l l u r i u m i n L a y e r e d I n t e r g r o w t h P o l y t e l l u r i d e C o m p o u n d s : s z T e s a n d K z A g 4 L a 2 T e l o 2 9 8 5 . 1 . I n t r o d u c t i o n L o w - d i m e n s i o n a l s y s t e m s o f t e n e x h i b i t e l e c t r o n i c i n s t a b i l i t i e s t h a t c a n l e a d t o c h a r g e d e n s i t y w a v e s ( C D W s ) o r s u p e r c o n d u c t i v i t y . T h e C D W s h a v e a c h a r a c t e r i s t i c f r e q u e n c y q ( q — v e c t o r ) a n d t h i s v e c t o r c o r r e s p o n d s t o t h e s o - c a l l e d n e s t i n g v e c t o r o f t h e F e r m i s u r f a c e ( F S ) . N e s t i n g f a v o r s e l e c t r o n — p h o n o n c o u p l i n g a n d i s b e l i e v e d t o b e r e s p o n s i b l e f o r t h e f o r m a t i o n o f t h e C D W a n d o f t e n o v e r p o w e r s t h e c o m p e t i n g s u p e r c o n d u c t i v e s t a t e . A l t h o u g h t h e d e s c r i p t i o n o f t h e C D W b e h a v i o r f o r o n e - d i m e n s i o n a l s y s t e m s i s w e l l e s t a b l i s h e d t h e o r e t i c a l l y n o p r o p e r m o d e l s h a v e b e e n d e v e l o p e d f o r t h e t w o - d i m e n s i o n a l c a s e s . l R e c e n t s t u d i e s h a v e f o c u s e d o n t h e h i g h - t e m p e r a t u r e C D W f a m i l y o f m a t e r i a l s R E T e z a n d R E T e 3 . ( R E = r a r e e a r t h e l e m e n t ) a n d h a v e s h e d n e w i n s i g h t s a s t o t h e n a t u r e o f t h e p h e n o m e n o n i n t h e s e m a t e r i a l s . 2 ’ 3 ' 4 H o w e v e r , o n l y r e c e n t l y i t w a s r e c o g n i z e d t h r o u g h a n g l e - r e s o l v e d p h o t o e m i s s i o n s p e c t r o s c o p y ( A R P E S ) s t u d i e s t h a t L a T e z i s t h e fi r s t s e m i c o n d u c t o r t h a t i t s t w o - d i m e n s i o n a l C D W d i s t o r t i o n i s F e r m i s u r f a c e n e s t i n g d r i v e n . 5 T h e R E T e 3 f a m i l y h a s g a i n e d m o r e a t t e n t i o n t h e r e c e n t y e a r s b e c a u s e o f i t s t w o - d i m e n s i o n a l i n c o m m e n s u r a t e C D W m o d u l a t e d s t a t e s a n d t h e i r e f f e c t t o t h e e l e c t r o n i c s t r u c t u r e . E x t e n s i v e s t r u c t u r a l , 6 s p e c t r o s c o p i c 7 a n d o t h e r p h y s i c a l 8 s t u d i e s h a v e r e v e a l e d u n i q u e c h e m i c a l a n d p h y s i c a l b e h a v i o r a m o n g t h e c l a s s i c a l C D W s y s t e m s . H o w e v e r , s u r p r i s i n g l y p h y s i c a l a n d s t r u c t u r a l c h a r a c t e r i z a t i o n s t u d i e s o f t h e o t h e r m e m b e r s o f t h e f a m i l y R E z T e s r e m a i n b u t a f e w . 9 T h e s t r u c t u r e o f R E z T e s i s e s s e n t i a l l y a 1 : 1 c o m b i n a t i o n o f t h e s t r u c t u r e s o f R E T e z a n d R E T e 3 , F i g u r e 5 . 5 . I t c o n t a i n s o n e s q u a r e n e t o f T e " a t o m s f o u n d i n t h e 1 / 2 - R E T e z f a m i l y a n d t w o s q u a r e n e t s o f T e a t o m s p r e s e n t i n t h e R E T e 3 c o m p o u n d . 2 9 9 T h e r e f o r e , R E z T e s i s u n i q u e i n t h a t p o s s e s s e s s i m u l t a n e o u s l y t w o i n d i v i d u a l p l a n a r n e t s o f t e l l u r i u m e a c h w i t h i t s o w n a v e r a g e o x i d a t i o n s t a t e o f 1 - a n d 1 / 2 - r e s p e c t i v e l y . I t i s w e l l k n o w n t h a t t h e n u m b e r o f e l e c t r o n s p e r T e a t o m c o n t r o l s t h e t y p e o f C D W m o d u l a t i o n . 1 0 V a r i a t i o n s i n t h e e l e c t r o n c o u n t a l t e r s t h e e n e r g y o f t h e F e r m i l e v e l t h u s t h e n e s t i n g p r o p e r t i e s o f t h e F e r m i s u r f a c e ( q - v e c t o r ) . C D W m o d u l a t i o n s f r o m c o m b i n a t i o n o f t e l l u r i u m n e t s i n d i f f e r e n t o x i d a t i o n s t a t e s t h o u g h h a v e n o t b e e n r e p o r t e d u p t o d a t e e m d t h e i r e l e c t r o n i c b e h a v i o r i s u n k n o w n . A l t h o u g h t h e C D W R E T e z a n d R E T e 3 c o m p o u n d s a r e s u b s t r u c t u r e c o m p o n e n t s o f t h e R E z T e s p h a s e n o C D W d i s t o r t i o n s h a v e b e e n f o u n d f o r t h e c o m p o s i t e s t r u c t u r e ? H e r e , w e r e p o r t f o r t h e fi r s t t i m e t h e e x i s t e n c e a n d c r y s t a l l o g r a p h i c s o l u t i o n o f t h e i n c o m m e n s u r a t e C D W m o d u l a t i o n s i n s z T e s . W e fi n d t h a t e a c h o f t h e t w o t y p e s o f p l a n a r T e n e t s h a s i t s o w n C D W d i s t o r t i o n . T h i s i s m a n i f e s t e d b y t h e e x i s t e n c e o f t w o i n d i v i d u a l q - v e c t o r s i n t h e s t r u c t u r e . W e h a v e v e r i fi e d t h e t w o C D W m o d u l a t i o n s b y d i r e c t v i s u a l i z a t i o n o f t h e d i s t o r t i o n s w i t h S c a n n i n g T u n n e l i n g M i c r o s c o p y ( S T M ) . T h e i n d e p e n d e n t c h a r a c t e r o f t h e t w o q - v e c t o r s w a s e x a m i n e d w i t h h i g h t e m p e r a t u r e s i n g l e c r y s t a l X - r a y d i f f r a c t i o n e x p e r i m e n t s g o i n g a b o v e t h e C D W t r a n s i t i o n . A d d i t i o n a l l y , t h e S m T e z . x p a r e n t s u b s t r u c t u r e w a s r e e x a m i n e d u s i n g t h e s u p e r s p a c e c r y s t a l l o g r a p h i c a p p r o a c h i n o r d e r t o p r o p e r l y c o m p a r e i t s C D W d i s t o r t i o n s t o t h e o n e s o b s e r v e d i n t h e c o m p o s i t e s z T e 5 - x . F u r t h e r m o r e , t w o i n d i v i d u a l q - v e c t o r s w e r e f o u n d i n t h e r e c e n t l y r e p o r t e d 1 / 2 - 1 0 , 1 1 i n t e r g r o w t h K z A g a L a z T e l o . x c o m p o u n d t h a t p o s s e s s e s t w o T e a n d T e " n e t s t o o . T h e l a y e r e d s t r u c t u r e i s c o m p o s e d b y t h e t w o s u b s t r u c t u r e s o f L a T e 3 a n d K 2 A g 4 T e 4 ‘ 2 . t h a t a l t e r n a t e i n a 1 : 1 r a t i o a n d s t a c k a l o n g t h e c - a x i s . O n e v e c t o r i s c o m m e n s u r a t e a n d 3 0 0 c o r r e s p o n d s t o t h e C D W d i s t o r t i o n i n t h e T e l / 2 ' n e t o f L a T e g . T h e s e c o n d i n c o m m e n s u r a t e q - v e c t o r i s c r e a t e d f r o m l o n g r a n g e o r d e r e d v a c a n c i e s i n t h e T e l ' n e t o f t h e K z A g 4 T e 4 . x s u b s t r u c t u r e . 5 . 2 . E x p e r i m e n t a l S e c t i o n 5 . 2 . 1 . R e a g e n t s T h e f o l l o w i n g r e a g e n t s w e r e u s e d a s o b t a i n e d . P o t a s s i u m m e t a l , a n a l y t i c a l r e a g e n t , A l d r i c h C h e m i c a l C o . , M i l w a u k e e , W I ; L a n t h a n u m m e t a l , 4 0 m e s h , C e r a c , M i l w a u k e e , W I ; S a m a r i u m m e t a l , 4 0 m e s h , C e r a c , M i l w a u k e e , W I ; T e l l u r i u m c h u n k s , T e l l u r e x C o r p , T r a v e r s e C i t y , M I ; R u b i d i u m C h l o r i d e , 9 9 . 8 % p u r e , 2 0 m e s h , C e r a c S p e c i a l t y I n o r g a n i c s , M i l w a u k e e , W I ; L i t h i u m C h l o r i d e , 9 9 . 8 % p u r e , 2 0 m e s h , C e r a c S p e c i a l t y I n o r g a n i c s , M i l w a u k e e , W I ; N , N — D i m e t h y l f o r m a m i d e ( D M F ) , A C S r e a g e n t g r a d e , S p e c t r u m C h e m i c a l s , N e w B r u n s w i c k , N J ; D i e t h y l e t h e r a n h y d r o u s , A C S r e a g e n t g r a d e , C o l u m b u s C h e m i c a l I n d u s t r i e s , C o l u m b u s , W I . S i l v e r p o w d e r — A s i l v e r c o i n ( 9 9 . 9 % p u r i t y o f ~ 3 1 g ) w a s d i s s o l v e d i n 2 5 0 m L o f a q u a r e g i a ( 3 p a r t s o f c o n c e n t r a t e d H C l a n d o n e p a r t o f H N O 3 ) u n d e r s t i r r i n g . T h e s o l u t i o n w a s n e u t r a l i z e d w i t h N a B H 4 a n d t h e p a l e g r a y p r e c i p i t a t e w a s fi l t e r e d , w a s h e d w i t h c o p i o u s a m o u n t s o f d i s t i l l e d w a t e r , a c e t o n e a n d d r i e d i n a v a c u u m o v e n . P o t a s s i u m T e l l u r i d e , K z T e — 5 . 8 3 6 g ( 0 . 1 5 m o l ) K w a s s l i c e d i n s m a l l p i e c e s ( ~ 3 m m ) i n a N 2 fi l l e d g l o v e b o x a n d c o m b i n e d w i t h 9 . 5 2 3 g ( 0 . 0 7 5 m o l ) T e i n a 1 0 0 0 m L s i n g l e n e c k r o u n d b o t t o m fl a s k . A T e fl o n c o a t e d m a g n e t i c s t i r b a r w a s a d d e d i n t h e fl a s k a s w e l l . T h e fl a s k w a s c o n n e c t e d t o a g l a s s a d a p t e r w i t h a s t o p c o c k j o i n t a n d r e m o v e d f r o m t h e g l o v e b o x . T h e fl a s k a n d a d a p t e r w e r e t h e n c o n n e c t e d t o a d r y c o n d e n s e r 3 0 1 a p p a r a t u s a n d c h i l l e d t o - 7 8 C u s i n g a d r y i c e / a c e t o n e b a t h . A p p r o x i m a t e l y 8 0 0 m L o f p u r e N H 3 w e r e c o n d e n s e d , u n d e r N 2 a t m o s p h e r e , o n t o t h e r e a g e n t s , y i e l d i n g a p u r p l e s o l u t i o n . T h e s o l u t i o n w a s k e p t u n d e r s t i r r i n g a n d m a i n t a i n e d a t - 7 8 C f o r u p t o 1 6 h o u r s . T h e d r y i c e / a c e t o n e m i x t u r e w a s r e m o v e d a n d t h e N H 3 w a s a l l o w e d t o e v a p o r a t e o f f a s t h e fl a s k w a r m e d u p t o r o o m t e m p e r a t u r e u n d e r a c o n s t a n t fl o w o f N 2 f o r ~ 6 h o u r s . T h e r e s u l t i n g b r o w n c o l o r e d p o w d e r w a s e v a c u a t e d o n a S c h l e n c k l i n e f o r ~ 4 h o u r s a n d t a k e n i n t o a N 2 fi l l e d g l o v e b o x . T h e p r o d u c t w a s g r o u n d t o a fi n e p o w d e r w i t h a m o r t a r a n d p e s t l e a n d p l a c e d i n t o a s c r e w - c a p p e d v i a l i n t h e g l o v e b o x . 5 . 2 . 2 . S y n t h e s i s S m 2 T e 5 — A l l m a n i p u l a t i o n s w e r e c a r r i e d o u t u n d e r d r y n i t r o g e n a t m o s p h e r e i n a V a c u u m A t m o s p h e r e s D r i - L a b g l o v e b o x . S t o i c h i o m e t r i c a m o u n t s o f S m ( 2 m m o l ) a n d T e ( 5 m m o l ) w e r e l o a d e d i n t o a q u a r t z t u b e t o g e t h e r w i t h a d o u b l e a m o u n t ( ~ 2 g ) o f h a l i d e fl u x ( 0 . 4 2 : 0 . 5 8 m o l a r m i x t u r e s o f R b C l a n d L i C l ) . T h e t u b e w a s s e a l e d u n d e r v a c u u m ( < 1 0 4 t o r r ) , h e a t e d t o 6 5 0 ° C a t 1 2 h o u r s f o r 6 d a y s a n d c o o l e d d o w n t o r o o m t e m p e r a t u r e a t a r a t e o f 4 ° C ' m i n " . T h e h a l i d e fl u x w a s d i s s o l v e d i n w a t e r a n d t h e c r y s t a l s w e r e w a s h e d w i t h a c e t o n e a n d d r i e d u n d e r n i t r o g e n e n v i r o n m e n t . T h e m o r p h o l o g y o f t h e c r y s t a l s i s t h a t o f t h i c k p l a t e s ( F i g u r e 5 . 1 ) w i t h a d a r k c o p p e r - l i k e c o l o r . T h e c o m p o u n d f o u n d t o c o n t a i n s i g n i fi c a n t S m T e 3 i m p u r i t i e s o f ~ 5 0 % ( P X R D ) , F i g u r e 5 . 2 . S m T e 2 — A l l m a n i p u l a t i o n s w e r e c a r r i e d o u t u n d e r d r y n i t r o g e n a t m o s p h e r e i n 3 V a c u u m A t m o s p h e r e s D r i - L a b g l o v e b o x . S t o i c h i o m e t r i c a m o u n t s o f S m ( 1 m m o l ) a n d T e ( 2 m m o l ) w e r e l o a d e d i n t o a q u a r t z t u b e t o g e t h e r w i t h a d o u b l e a m o u n t ( ~ 2 g ) o f h a l i d e fl u x ( 0 . 4 2 : 0 . 5 8 m o l a r m i x t u r e s o f R b C l a n d L i C l ) . T h e t u b e w a s s e a l e d u n d e r 3 0 2 v a c u u m ( < 1 0 4 t o r r ) , h e a t e d t o 7 0 0 ° C a t 1 2 h o u r s f o r 6 d a y s a n d c o o l e d d o w n t o r o o m t e m p e r a t u r e a t a r a t e o f 4 ° C ' m i n ' l . T h e h a l i d e fl u x w a s d i s s o l v e d i n w a t e r a n d t h e c r y s t a l s w e r e w a s h e d w i t h a c e t o n e a n d d r i e d u n d e r n i t r o g e n e n v i r o n m e n t . T h e m o r p h o l o g y o f t h e c r y s t a l s i s t h a t o f t h i n b l a c k p l a t e s . T h e c o m p o u n d f o u n d t o b e ~ 1 0 0 % p u r e ( P X R D ) . 1 0 0 u m F i g u r e 5 . 1 . S E M i m a g e o f a t h i c k p l a t e - l i k e S m 2 T e 5 s i n g l e c r y s t a l . K 2 A g 4 L a 2 T e 1 0 . x — K 2 A g 4 L a 2 T e m . x w a s s y n t h e s i z e d fi o m a m i x t u r e o f 0 . 2 4 7 g K 2 T e ( 1 . 2 0 m m o l ) , 0 . 1 4 6 A g ( 1 . 3 5 m m o l ) , 0 . 0 8 4 g L a ( 0 . 6 0 m m o l ) , a n d 0 . 6 1 2 g T e ( 4 . 8 0 m m o l ) t h a t w a s s e a l e d u n d e r v a c u u m i n a q u a r t z t u b e a n d h e a t e d t o 8 0 0 ° C f o r 5 d a y s . T h e t u b e w a s t h e n c o o l e d t o 3 0 0 ° C a t a r a t e o f 4 ° C / h , f o l l o w e d b y q u e n c h i n g t o r o o m t e m p e r a t u r e a t a r a t e o f 1 0 ° C / h . T h e e x c e s s K 2 T e , fl u x w a s w a s h e d o f f w i t h N , N - d i m e t h y l f o r m a m i d e u n d e r n i t r o g e n t o r e v e a l v e r y t h i n r e d - b r o w n p l a t e - s h a p e d c r y s t a l s . T h e c o m p o u n d f o u n d t o c o n t a i n K A g L a T e 4 i m p u r i t i e s o f ~ 3 0 % ( P X R D , F i g u r e 5 . 4 ) o f t h e s a m e c r y s t a l h a b i t 3 0 3 S r n Z T e 5 e x p e r i m e n t a l I n t e n s i t y ( a . u ) S m T e 3 c a l c u l a t e d 0 2 M a n . ) _ s z T e s c a l c u l a t e d 0 ' 0 I L I I I l I I I I I l I 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5 2 0 ( d e g ) F i g u r e 5 . 2 . C o m p a r i s o n o f t h e e x p e r i m e n t a l p o w d e r d i f f r a c t i o n p a t t e r n o f t h e a s p r e p a r e d S m 2 T e 5 c o m p o u n d w i t h t h e c a l c u l a t e d p a t t e r n s o f S m T e ; a n d S m 2 T e 5 . R e l a t i v e i n t e n s i t y o f t h e e x p e r i m e n t a l p a t t e r n i s d i f f e r e n t f r o m t h e c a l c u l a t e d o n e d u e t o p r e f e r e n t i a l o r i e n t a t i o n o f t h e p l a t e - l i k e c r y s t a l s . 5 0 0 u m \ I F i g u r e 5 . 3 . S E M i m a g e o f a p l a t e - l i k e K 2 A g 4 L a 2 T e m s i n g l e c r y s t a l . 3 0 4 1 . 0 - K 2 A g 4 L a 2 T e 1 0 e x p e r i m e n t a l ‘ 1 . 2 I I I I l I l U T T T r I l I I I r 7 I I I I I l l r 1 D . 0 . 8 - _ K A g L a T e 4 c a l c u l a t e d 0 4 L l J i l l " K z A g 4 L a 2 T e l 0 c a l c u l a t e d _ I n t e n s i t y ( a . u ) 9 O N T 0 . 2 - 0 . 0 b r i m . 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5 7 0 7 5 8 0 2 0 ( d e g ) F i g u r e 5 . 4 . C o m p a r i s o n o f t h e e x p e r i m e n t a l p o w d e r d i f f r a c t i o n p a t t e r n o f t h e a s p r e p a r e d K 2 A g 4 L a 2 T e m c o m p o u n d w i t h t h e c a l c u l a t e d p a t t e r n s o f K A g L a T e 4 a n d K 2 A g 4 L a 2 T e l o . R e l a t i v e i n t e n s i t y o f t h e e x p e r i m e n t a l p a t t e r n i s d i f f e r e n t f r o m t h e c a l c u l a t e d o n e d u e t o p r e f e r e n t i a l o r i e n t a t i o n o f t h e p l a t e - l i k e c r y s t a l s . 5 . 3 . P h y s i c a l M e a s u r e m e n t s S e m i q u a n t i t a t i v e E n e r g y D i s p e r s i v e S p e c t r o s c o p y ( E D S ) — T h e a n a l y s e s w e r e p e r f o r m e d w i t h a J E O L I S M - 3 5 C s c a n n i n g e l e c t r o n m i c r o s c o p e e q u i p p e d w i t h a N o r a n V a n t a g e E D S ( S i z L i ) d e t e c t o r . C r y s t a l s w e r e m o u n t e d o n a n a l u m i n u m s t a g e w i t h c a r b o n t a p e . D a t a w e r e a c q u i r e d o n s e v e r a l c r y s t a l s a n d d i f f e r e n t r e g i o n s o f e a c h c r y s t a l u s i n g a n a c c e l e r a t i n g v o l t a g e o f 2 5 k V a n d a c c u m u l a t i o n t i m e o f 4 0 s . S i n g l e C r y s t a l X - r a y D z fi i a c t i o n — A S T O E I P D S H d i f f r a c t o m e t e r w a s u s e d t o c o l l e c t i n t e n s i t y d a t a ( M o K o r r a d i a t i o n ) . A n a n a l y t i c a l a b s o r p t i o n c o r r e c t i o n w a s 3 0 5 p e r f o r m e d , a n d a l l s t r u c t u r e s w e r e r e fi n e d w i t h J A N A 2 0 0 0 s o f t w a r e ( P e t r i c e k , V . ; D u s e k , M . I n s t i t u t e o f P h y s i c s ; P r a h a , C z e c h R e p u b l i c , 2 0 0 0 ) . T h e l e n g t h d e t e r m i n a t i o n a n d r e fi n e m e n t o f t h e q - v e c t o r s w a s p e r f o r m e d w i t h t h e P e a k l i s t 1 . 0 6 s o f t w a r e p a r t o f t h e X - A r e a 1 . 3 9 s u i t e ( X - A R E A , I P D S S o f t w a r e , S T O E & C i e G m b H , D a r m s t a d t , 2 0 0 6 ) u s i n g a l e a s t s q u a r e r e fi n e m e n t a l g o r i t h m . S a t e l l i t e r e fl e c t i o n s o f fi r s t o r d e r f o r b o t h q - v e c t o r s a n d m i x e d o r d e r r e fl e c t i o n s ( q 1 + q 2 , q r — q 2 ) w e r e o b s e r v e d a t 1 0 0 K a n d u s e d f o r t h e r e fi n e m e n t f o r S m 2 T e 5 , S m T e 2 a n d K 2 A g 4 L a 2 T e 1 0 . F o u r m o d u l a t i o n w a v e s ( q 1 , q 2 , q 1 + q 2 , q 1 — q 2 ) f o r p o s i t i o n a l , t e m p e r a t u r e p a r a m e t e r s a n d o c c u p a t i o n a l ( f o r t h e a t o m s i n t h e T e " n e t ) d i s t o r t i o n s w e r e u s e d . F o u r i e r t e r m s w e r e fi ' e e l y r e fi n e d . T h e c e n t r o s y m m e t r i c P - l s u p e r s p a c e g r o u p g a v e R - v a l u e s f o r t h e s a t e l l i t e s t o m o r e t h a n 3 0 % f o r S m 2 T e 5 a n d K 2 A g 4 L a 2 T e l o . O n e o r d e r o f s a t e l l i t e r e fl e c t i o n s o f a s i n g l e q - v e c t o r w a s o b s e r v e d a t 5 0 0 K f o r S m 2 T e 5 . O n e m o d u l a t i o n w a v e f o r p o s i t i o n a l , t e m p e r a t u r e p a r a m e t e r s a n d o c c u p a t i o n a l d i s t o r t i o n s w a s u s e d a n d t h e F o u r i e r t e r m s w e r e f r e e l y r e fi n e d . S i n c e t h e o n l y a c c e p t a b l e s o l u t i o n s w a s b a s e d o n a t r i c l i n i c c e l l f o r S m 2 T e 5 , t h e o r i g i n a l o r t h o r h o m b i c s y s t e m w a s t r a n s f o r m e d t o a t r i c l i n i c c e l l a c c o r d i n g t o t h e t r a n s f o r m a t i o n m a t r i x [ - 1 0 0 , 0 0 - 1 , 0 . 5 - 0 . 5 0 ] t o a v o i d c o r r e l a t i o n s d u r i n g r e fi n e m e n t . T h u s , t h e o r t h o r h o m b i c c * - a x i s b e c a m e a t r i c l i n i c b * - a x i s . T h e l e n g t h o f t h e q - v e c t o r s a l o n g t h e p l a i n t h a t c o n t a i n s t h e T e n e t d i d n o t c h a n g e . T h e c o m p o n e n t o f t h e q - v e c t o r s a l o n g t h e s h o r t e s t c * - a x i s w a s r e d u c e d b y 0 . 5 a c c o r d i n g t o t h e t r a n s f o r m a t i o n m a t r i x . S i m i l a r t r a n s f o r m a t i o n p r o c e d u r e w a s a p p l i e d o n K 2 A g 4 L a 2 T e l o w i t h a t r a n s f o r m a t i o n m a t r i x [ 1 1 0 , 0 0 4 , 4 0 0 ] . 3 0 6 T w o c r y s t a l s o f S m 2 T e 5 a n d S m T e 2 f r o m t w o d i f f e r e n t r e a c t i o n b a t c h e s w e r e a n a l y z e d w i t h s i n g l e c r y s t a l X - r a y d i f f r a c t i o n s t u d i e s . B o t h c o m p o u n d s w e r e f o u n d t o h a v e t h e s a m e s t o i c h i o m e t r y ( e . g . c o n c e n t r a t i o n o f v a c a n c i e s ) a n d s u p e r c e l l p a r a m e t e r s w i t h i n t h e e s t i m a t e d s t a t i s t i c a l s t a n d a r d d e v i a t i o n s . I n f r a r e d ( I R ) S p e c t r o s c o p y — O p t i c a l d i f f u s e r e fl e c t a n c e m e a s u r e m e n t s w e r e p e r f o r m e d o n s i n g l e c r y s t a l s o f S m 2 T e 5 a t r o o m t e m p e r a t u r e . T h e s p e c t r a w e r e r e c o r d e d i n t h e M i d - I R r e g i o n ( 6 0 0 0 — 4 0 0 c m ' l ) w i t h a N i c o l e t 6 7 0 0 F T - I R S p e c t r o m e t e r e q u i p p e d w i t h a d i f f u s e r e fl e c t a n c e c o l l e c t o r f r o m S p e c t r a - T e c h I n c . S c a n n i n g T u n n e l i n g M i c r o s c o p y ( S T W o f S m 2 T e 5 — T h e S T M m e a s u r e m e n t s w e r e c o n d u c t e d i n c o l l a b o r a t i o n w i t h M a r i a I a v a r o n e a t t h e M a t e r i a l s S c i e n c e D i v i s i o n ( M S D ) a t A r g o n n e N a t i o n a l L a b o r a t o r y ( A N L ) . S T M m e a s u r e m e n t s w e r e p e r f o r m e d w i t h a l o w t e m p e r a t u r e h o m e m a d e S T M a t 4 . 2 K . T h e s a m p l e s w e r e c l e a v e d u n d e r i n e r t a t m o s p h e r e a n d q u i c k l y c o o l e d d o w n a t 4 . 2 K . C o n s i d e r i n g t h a t t h e c l e a v a g e o c c u r s b e t w e e n t h e v a n d e r W a a l s g a p w e e x p e c t e d t h e t o p m o s t l a y e r , o b s e r v a b l e w i t h t h e S T M , t o b e t h e T e l / 2 ’ n e t . T o p o g r a p h y i m a g e s w e r e a c q u i r e d i n c o n s t a n t c u r r e n t m o d e a s w e l l a s i n c o n s t a n t h e i g h t m o d e a n d a t d i f f e r e n t v o l t a g e t i p - s a m p l e . 5 . 4 . R e s u l t s a n d D i s c u s s i o n S u b c e l l D e s c r i p t i o n o f R E T e 2 a n d R E 2 T e 5 — T h e a v e r a g e s t r u c t u r e o f R E 2 T e 5 i s a n i n t e r g r o w t h o f t h e t w o p a r e n t s u b s t r u c t u r e s R E T e 2 a n d R E T C 3 , F i g u r e 5 . 5 . T h e R E T e 2 f a m i l y a d o p t s t h e C u 2 S b s t r u c t u r e t y p e a n d h a s a r o c k s a l t t y p e [ R E T e ] + s u b l a y e r s a n d w i c h e d b e t w e e n t w o s q u a r e T e " n e t s , F i g u r e 5 . 5 A . T h e R E T e 3 f a m i l y a d o p t s t h e N d T e 3 s t r u c t u r e t y p e a n d h a s a [ R E T e ] + s u b l a y e r s a n d w i c h e d b e t w e e n t w o s q u a r e T e l / 2 ‘ 3 0 7 n e t s m a k i n g R E T e 3 s l a b s w h i c h s t a c k a l o n g t h e b - a x i s c r e a t i n g v a n d e r W a a l s g a p s , F i g u r e 5 . 5 B . T h e a v e r a g e R E 2 T e 5 s y s t e m a d o p t s t h e s p a c e g r o u p C m c m ( N d 2 T e 5 s t r u c t u r e t y p e ) a n d i t c o n s i s t s o f t w o p u c k e r e d d o u b l e l a y e r s o f [ R E T e ] + s e p a r a t e d b y a s q u a r e n e t o f T e " a t o m s f o r m i n g R E 2 T e 3 u n i t s . E a c h R E 2 T e 3 u n i t i s s a n d w i c h e d b y t h e p l a n a r n e t s o f T e l / 2 ‘ m a k i n g a R E 2 T e 5 s l a b . T h e s l a b s t h e n s t a c k a l o n g t h e b - a x i s c r e a t i n g v a n d e r W a a l s g a p s , F i g u r e 5 . 5 C . T h e f o r m u l a c a n b e e x p r e s s l y w r i t t e n a s ( [ R E T e ] + ) 2 ( [ T e ] ” 2 ' ) 2 [ T e ] 1 ‘ . T h e R E a t o m i s s u r r o u n d e d b y n i n e T e a t o m s i n a m o n o c a p p e d t e t r a g o n a l a n t i p r i s m g e o m e t r y . T h e T e - T e d i s t a n c e i n t h e s q u a r e n e t s o f S m 2 T e 5 i s 3 . 0 7 1 5 ( 4 ) A f o r b o t h T e l / 2 ' a n d r e " n e t s a t 1 0 0 K . H y p o s t r o i c h i o m e t r y i s v e r y c o m m o n i n t h e R E Q 2 . x ( Q = S , S e , T e ) f a m i l y . I t o r i g i n a t e s f r o m v a c a n c i e s i n t h e p l a n a r n e t s o f Q t h a t a r e m o s t l y o r d e r e d f o r t h e s u l fi d e 1 3 a n d s e l e n i d e ” a n d d i s o r d e r e d f o r t h e t e l l u r i d e f a m i l y . ” A l o t o f d i f f e r e n t p h a s e s h a v e b e e n c h a r a c t e r i z e d t h e r m o d y n a m i c a l l y w i t h s m a l l c h a n g e s i n t h e x v a l u e , e . g . S m S 2 . , , 1 5 a n d P r S e 2 . , , . 1 6 W e f o u n d t h a t t h e T e l ' n e t ( S m T e 2 . x s u b s t r u c t u r e ) i n t h e S m 2 T e 5 s y s t e m h a s v a c a n c i e s t h a t a c t u a l l y a r e o r d e r e d m a k i n g S m 2 T e 4 _ 9 o ( 1 ) t h e fi r s t r a r e - e a r t h p o l y t e l l u r i d e c o m p o u n d w i t h o r d e r e d v a c a n c i e s . 3 0 8 ( A ) ( B ) a R E 2 T e 5 F i g u r e 5 . 5 . ( A ) T h e a v e r a g e s t r u c t u r e o f R E T e 2 ( C u 2 S b - t y p e ) w i t h s q u a r e n e t s o f T e l ' . ( B ) T h e a v e r a g e l a y e r e d s t r u c t u r e o f R E T e 3 ( N d T e ; - t y p e ) w i t h s q u a r e n e t s o f T e l / 2 ' . ( C ) T h e h y b r i d a v e r a g e l a y e r e d s t r u c t u r e o f R E 2 T e 5 ( N d 2 T e 5 - t y p e ) w i t h s q u a r e n e t s o f b o t h T e " a n d T e l / 2 ' . T h e v a n d e r W a a l s ( v d W ) g a p s a r e i n d i c a t e d . 3 0 9 S u b c e l l D e s c r i p t i o n o f K 2 A g 4 L a 2 T e 1 0 . x — A n o t h e r i n t e r e s t i n g e x a m p l e o f i n t e r g r o w t h c o m p o u n d w i t h t w o s q u a r e T e n e t s o f d i f f e r e n t e l e c t r o n c o u n t i s K 2 A g 4 L a 2 T e m x . T h e a v e r a g e l a y e r e d s t r u c t u r e o f t h e q u a t e r n a r y a d o p t s t h e o r t h o r h o m b i c s p a c e g r o u p I m m m w i t h c e l l p a r a m e t e r a = 4 . 4 5 9 9 ( 2 ) A , b = 4 . 4 8 4 9 ( 2 ) A , a n d c = 5 0 . 3 5 3 ( 2 ) A a t 1 0 0 K . I t i s c o m p o s e d b y t w o d i s t i n c t l a y e r s o f t w o d i f f e r e n t s u b s t r u c t u r e s o f [ L a T e 3 ] a n d [ K 2 A g 4 T e 4 ] , F i g u r e 5 . 5 . T h e t w o d i f f e r e n t l a y e r s a l t e r n a t e i n a 1 : 1 r a t i o a l o n g t h e c - a x i s s e p a r a t e d b y a v a n d e r W a a l s g a p . T h e a v e r a g e o x i d a t i o n s t a t e o f t h e T e n e t a t o m s i n t h e fi r s t s u b s t r u c t u r e o f [ L a T e 3 ] r e m a i n s - 0 . 5 w i t h a n a v e r a g e T e - T e d i s t a n c e o f 3 . 1 7 7 0 ( 5 ) A a t 1 0 0 K . T h e s e c o n d s u b s t r u c t u r e , [ K 2 A g 4 T e 4 ] , i s s i m i l a r t o t h e s t r u c t u r e f o u n d i n K C u 4 8 3 . l 7 I t i s c o m p o s e d b y t w o p u c k e r e d [ A g T e ] ' l a y e r s t h a t a r e f u s e d t o g e t h e r s h a r i n g a c o m m o n p l a n e o f T e a t o m s . E a c h [ A g T e ] - l a y e r i s m a d e u p o f r i b b o n t e t r a h e d r a l [ A g T e 4 ] u n i t s t h a t s h a r e e d g e s i n t w o d i m e n s i o n s . T h e d i f f e r e n c e , h o w e v e r , i s t h a t i n K 2 A g 4 T e 4 , a n e x t r a T e a t o m e x i s t s i n b e t w e e n t h e s e d o u b l e l a y e r s . I n t e r e s t i n g l y , t h e a d d i t i o n a l T e a t o m c r e a t e s a s e c o n d p l a n a r n e t o f T e a t o m s i n t h e [ K 2 A g 4 T e 4 ] l a y e r w i t h a n a p p a r e n t d i s t a n c e o f 3 . 1 7 7 0 ( 4 ) A a t 1 0 0 K . T h e a v e r a g e o x i d a t i o n s t a t e o f t h e T e a t o m s i n t h e s h a r e d T e n e t i s 1 - . F u r t h e r m o r e , t h i s T e n e t w a s f o u n d t o h a v e v a c a n c i e s t h a t a r e a c t u a l l y l o n g r a n g e o r d e r e d . T h e l a y e r s b e t w e e n t h e [ L a T e g ] s l a b s i n K 2 A g 4 L a 2 T e m a r e t h i c k e r i n r e s p e c t t o t h e s t r u c t u r a l l y s i m i l a r A M L a T e 4 ( A = N a , K ; M = A g , C u ) f a m i l y . 1 8 3 1 0 F i g u r e 5 . 6 . T h e a v e r a g e s t r u c t u r e o f K 2 A g 4 L a 2 T e 1 0 w i t h s q u a r e n e t s o f T e l / ” a n d T e " . 3 1 1 S u p e r c e l l D e s c r i p t i o n o f S m 2 T e 5 B a s e d o n a M o d u l a t i o n q - v e c t o r — T h e h y b r i d C D W s i n S m 2 T e 5 c r e a t e a ( 3 + 2 ) - d i m e n s i o n a l m o d u l a t e d i n c o m m e n s u r a t e s u p e r s t r u c t u r e w i t h t w o q - v e c t o r s a t 1 0 0 K . A s u p e r s p a c e c r y s t a l l o g r a p h i c a p p r o a c h w a s n e c e s s a r y i n o r d e r t o s o l v e t h e s t r u c t u r e . A t r i c l i n i c c r y s t a l s y s t e m w a s t h e o n l y p o s s i b l e o p t i o n c o n s i s t e n t w i t h t h e n u m b e r a n d o r i e n t a t i o n o f t h e o b s e r v e d q - v e c t o r s . A s t a b l e r e fi n e m e n t w a s a c h i e v e d w i t h P 1 ( a l l 3 1 7 1 , a 2 [ 3 2 y 2 ) 0 s u p e r s p a c e g r o u p . T h e t w o v e c t o r s a r e q 1 = 0 . 3 1 2 4 ( 3 ) b * + l / 2 c * a n d t h e w e a k e r q 2 = 0 . 3 3 0 3 ( 3 ) a * + 0 . 3 3 1 5 ( 3 ) b * + 0 . 3 4 9 ( 1 ) c * . T h e l a b e l i n g s c h e m e i s s h o w n i n F i g u r e 5 . 7 A . T h e C D W d i s t o r t e d p a t t e r n s o f T e a t o m s i n S m 2 T e 5 f e a t u r e T e x o l i g o m e r s o f d i fl ‘ e r e n t l e n g t h , g e o m e t r y a n d s e q u e n c e f r o m t h e o n e s o b s e r v e d s o f a r i n t h e r a r e - e a r t h p o l y t e l l u r i d e f a m i l y . S o m e s i m i l a r i t i e s m a y b e f o u n d i n t h e p a r e n t s u b s t r u c t u r e s S m T e 3 6 c a n d S m T e 2 l 9 b u t t h e c o m b i n a t i o n o f t h e t w o q - v e c t o r s a n d t h e p r e s e n c e o f o c c u p a t i o n a l 1 / 2 - n e t w a v e s o f v a c a n c i e s c r e a t e u n i q u e T e p a t t e r n s . T h e m a j o r i t y o f o l i g o m e r s i n t h e T e a t 1 0 0 K a r e V - s h a p e d t r i m e r s a n d o c c a s i o n a l l y N — s h a p e d t e t r a m e r s , F i g u r e 5 . 8 . T h e m a i n d i f f e r e n c e f r o m R E T e ; t h o u g h i s t h e d i s c o n t i n u a t i o n o f t h e s a m e t y p e o f o l i g o m e r s a l o n g t h e a - a x i s . S p e c i fi c a l l y , t h e s e q u e n c e o f t r i m e r s a l o n g a - a x i s n o w c o n t a i n s t e t r a m e r s , d i m e r s a n d s o m e t i m e s e v e n s i n g l e T e a t o m s ( s h o w n w i t h a r r o w s i n F i g u r e 5 . 8 ) . T h e T e - T e l e n g t h d i s t r i b u t i o n i n T e m ' a t 1 0 0 K v a r i e s f r o m a m i n i m u m o f 2 . 9 3 3 ( 1 0 ) A a n d m a x i m u m 3 . 2 0 8 ( 1 0 ) A w i t h a n a v e r a g e o f 3 . 0 8 9 ( 1 0 ) A . T h e T e l " n e t a t 1 0 0 K c o n t a i n s s q u a r e - l i k e o c t a m e r s w i t h a v a c a n c y i n t h e c e n t e r . F u r t h e r m o r e , d i f f e r e n t s e q u e n c e o f d i m e r s , V - s h a p e d a n d l i n e a r t r i m e r s , L - a n d T - s h a p e d t e t r a m e r s , V - s h a p e d p e n t a m e r s , F - s h a p e d h e x a m e r s , a n d d e f e c t e d s q u a r e - l i k e h e p t a m e r s i s o b s e r v e d d u e t o v a c a n c y o r d e r i n g , F i g u r e 5 . 9 . T h e m i n i m u m T e - T e b o n d i n t h e T e l ' n e t a t 1 0 0 K i s 3 1 2 s e q u e n c e o f o l i g o m e r s . A t 5 0 0 K t h e T e l / 2 - 2 . 8 0 5 ( 1 9 ) A a n d i t i s t h e s h o r t e s t T e - T e b o n d o b s e r v e d i n t h e r a r e - e a r t h p o l y t e l l u r i d e f a m i l y . T h e m a x i m u m d i s t a n c e i s 3 . 3 5 1 ( 1 9 ) A w i t h a n a v e r a g e o f 3 . 0 8 3 ( 1 9 ) A . B o t h T e n e t s r e m a i n d i s t o r t e d e v e n a b o v e t h e fi r s t C D W t r a n s i t i o n t e m p e r a t u r e . T h e e x i s t e n c e o f t h e d i a g o n a l m o d u l a t i o n v e c t o r c r e a t e s d i s t o r t e d p a t t e r n s w i t h d i f f e r e n t p a t t e r n c o n s i s t s m a i n l y o f a l t e r n a t i n g N - s h a p e d t e t r a m e r s a n d d i m e r s , F i g u r e 5 . 1 0 . T h e m a j o r i t y o f d i m e r s a r e a l i g n e d d i a g o n a l l y i n s i n g l e c h a i n s a n d o c c a s i o n a l l y i n d o u b l e c h a i n s . T h e b o n d l e n g t h d i s t r i b u t i o n b e c o m e s v e r y n a r r o w w i t h a m i n i m u m o f 3 . 0 6 3 ( 5 ) A , m a x i m u m 3 . 0 9 8 ( 5 ) A a n d a n a v e r a g e o f 3 . 0 9 5 ( 5 ) A . T h e T e " n e t a t 5 0 0 K d o e s n o t s h o w a n y o f t h e s q u a r e - l i k e o c t a m e r s b u t i t c o n t a i n s s e q u e n c e o f m o n o m e r s , d i m e r s , V - s h a p e d t r i m e r s , Z — a n d C - s h a p e d p e n t a m e r s w i t h a l i n e a r T e a t o m , F i g u r e 5 . 1 1 . T h e m i n i m u m T e - T e b o n d i s 2 . 9 5 3 ( 1 0 ) A , t h e m a x i m u m 3 . 2 1 1 ( 1 1 ) A w i t h a n a v e r a g e d i s t a n c e o f 3 . 0 8 5 ( 1 1 ) A . T h e t e m p e r a t u r e d e p e n d e n c e o f t h e q - v e c t o r s o f S m 2 T e 5 . x s u r p r i s i n g l y s h o w s a n o p p o s i t e t r e n d f r o m t h e o n e o b s e r v e d f o r S m T e g . 6 c T h e l e n g t h o f t h e q l - v e c t o r i n c r e a s e s t o 0 . 3 2 3 3 ( 8 ) a t 4 5 0 K a n d t h e d i a g o n a l q 2 - v e c t o r d e c r e a s e s t o 0 . 3 1 0 0 ( 8 ) a * + 0 . 3 2 6 8 ( 8 ) b * + 0 . 2 8 1 ( 4 ) c * . A t 5 0 0 K t h e q l - v e c t o r d i s a p p e a r s a n d q 2 b e c o m e s s h o r t e r 0 . 3 1 5 ( 1 ) a * + O . 3 1 5 ( l ) b * + 3 5 1 ( 6 ) c * . T h e q - v e c t o r t e m p e r a t u r e d e p e n d e n c e f o r t h e S m T e 2 . x s u b s t r u c t u r e i s n e g l i g i b l e ( s e e t h e s u p e r c e l l d e s c r i p t i o n o f S m T e 2 b a s e d o n a m o d u l a t i o n q - v e c t o r s e c t i o n f o r m o r e d e t a i l s ) . 3 1 3 F i g u r e 5 . 7 . ( A ) T r a n s f o r m e d c e l l o f S m 2 T e 5 a n d l a b e l i n g s c h e m e u s e d i n t h e s u p e r s p a c e r e fi n e m e n t . ( B ) C e l l l a b e l i n g s c h e m e i n S m T e 2 s u p e r c e l l . 3 1 4 ” i n . , 0 } , V \ A V V 3 W Q v \ A V v v v v x A V A A A A V V A \ A A A A N N V V V \ V W A A V A A A A A N N V A V a A A A A N W V V V V W A A V v a V A A V . ” V A Q Q Q Q Q Q Q Q Q Q Q Q Q M A H c o c o o o o o o o o o o o o c w w w w v V “ < / § ’ \ < > < > § > § > § > fl > § > § > \ > \ > \ > \ \ > \ \ > \ \ . \ ° / W W W W W \ V \ V \ V \ V \ V \ V < / < / < / ( / < / < > \ > \ > \ > \ > \ > ’ \ / \ " " " " / \ / \ / \ / \ / \ / \ / \ / \ V \ V \ V < ' / I < > I < ° / I \ ° ' / I \ ' I / I \ " / . \ ° / . x / . < / . x ' / . > > ’ . > > ’ . > I I ' I I ° I I ° I \ 3 2 { 2 ‘ 9 : V Y / \ W / \ / \ / \ / \ / \ / \ / \ / \ / \ \ ' \ A \ A \ / < \ / ( \ / \ / \ / \ / \ / \ / \ / . > < \ < \ < \ / \ / \ / > / > / > / > / > / > / > \ A A A A A A A / A / A . A . A > . 0 0 0 0 0 0 0 0 0 0 0 ; 6 3 ( 2 3 6 3 6 3 6 3 6 3 6 3 6 3 6 3 6 3 6 3 6 3 6 3 6 3 6 5 6 F i g u r e 5 . 9 . T e " n e t o f S m 2 T e 5 a t 1 0 0 K w i t h 3 . 1 1 0 A b o n d i n g t h r e s h o l d a n d 8 0 % o c c u p a t i o n a l c u t o f f . 3 1 5 2 : \ i 2 t : s : 3g 3g 3z g ; . 2 ; . 3 2 2 ‘ 2 2 ; : s \ \ 3 . 2 2 * 3 i C s 2 z \ \ \ . z 2 3 z z \ 2 . > 3 3 2 ? I I \ I ° “ < 2 \ . \ I ' I . - . < \ £ I . - € . £ \ I ( : \ \ . ( : ( I o : § 2 2 < I . . . E s s s s 3 g s s 2 A J / A J / fl J / fi / A J / A J / A J / A J / A J / / fl J / A J / A ¢ l fi ¢ / / V / / V / / / V / f V / / V / / V / l / fi J / fi ¢ / fi ¢ / fi l / / A ¢ / A ¢ / fi ¢ / A V / A J / A / / / A ¢ / A / / A J / fl / / / a F i g u r e 5 . 1 0 . T e l / 2 ' n e t o f 3 m m 5 a t 5 0 0 K w i t h 3 . 0 7 4 A b o n d i n g t h r e s h o l d . ' < 2 ' < ' I s ; 2 % ; a w e v a 3 : i i ; 5 3 2 % . " " " \ 2 < < \ . . \ . / \ ( \ 2 2 < . . \ . / \ 2 2 ( 2 8 3 2 ? ? ? " \ ' 3 0 0 2 3 3 2 3 2 ; ‘ A A ? ? ? 2 3 2 . \ . \ \ < < I E ; ' § < é i ' f “ 2 ’ 2 " - ' . . \ \ O O . . \ . . \ \ ( A x . \ . A \ < . \ ( I ( I . \ : . \ . / \ ( \ < . . . \ . A < « i f ? 2 ? < < ° ‘ . < : ‘ . < 0 f ? ? ? 2 < < ° f < z f < 2 . 2 2 ? . \ . . \ < . \ . . \ . A < . \ . . \ . A . . \ . . \ < . \ . . \ . A < . \ . . \ . A \ . . \ . . \ < . \ . . \ . / \ < . \ . . \ . A . \ . . \ . . \ < . \ . . \ . / \ < . \ . . \ . A . < ' \ ° : ‘ . < : X Q Q 3 3 % " . < : ‘ . < 3 Q } ? 3 3 % ° ‘ . < : ‘ . < 5 ‘ , ' 3 ‘ \ " . < \ : ‘ . \ ( ‘ < \ 3 3 3 " ‘ . < 3 . 0 3 3 3 < < ' \ ‘ \ : ‘ . < . ( < I . \ 3 < < 2 ? \ I . . \ . A ( \ ( \ . \ . . \ \ . / \ A ( \ 2 < “ X : ‘ . \ Q ‘ 3 2 2 3 2 % ” . 2 2 < < I \ \ . \ < ( I \ . \ I . 3 3 2 2 ; . 2 2 f . 2 < < - . - . . 3 2 2 9 2 * ; ' A 9 3 2 3 3 ‘ - : ‘ I < . A 3 3 2 3 3 < < I < § § : ‘ I i : E S I C X Q Q X Q X : ‘ . < 5 3 9 2 ? ? ? ? 3 . 3 3 % : < 8 i 3 € ¢ 7 2 € o 3 2 3 3 2 3 < ' * < Z i a - " a w b x . . \ . . \ . / \ 2 2 2 2 2 < . . . \ \ \ . . \ \ ( \ ( \ 2 2 . . \ . A ( \ < \ < I \ ‘ \ . . \ . . \ . A < . \ . ( I . \ . . \ . A I ? \ { g k g k f n ) \ ? ) < \ < , ‘ i j ‘ . < . : ‘ . { . I ( ‘ / { ? ) { ? ) < \ < ; \ g \ f é F i g u r e 5 . 1 1 . T e l ' n e t o f s z T e s a t 5 0 0 K w i t h 3 . 0 8 0 A b o n d i n g t h r e s h o l d a n d 8 0 % o c c u p a t i o n a l c u t o f f . O c c u p a t i o n a l m o d u l a t i o n w a v e s o f v a c a n c i e s i n t h e T e 1 ' n e t o f s z T 2 4 9 0 ( 1 ) — I n t h e s t r u c t u r e o f s z T e 5 - x t h e r e a r e t w o d i f f e r e n t c r y s t a l l o g r a p h i c s i t e s , T e [ 3 a ] a n d T e [ 3 b ] , f o r t h e T e a t o m s i n t h e T e " n e t . I n t e r e s t i n g l y , o n l y o n e s i t e , T e [ 3 a ] , i s o c c u p a t i o n a l l y 3 1 6 d i s t o r t e d . T h e o t h e r s i t e i s f u l l y o c c u p i e d . T h e o c c u p a n c y o f T e [ 3 a ] a t o m m o d u l a t e s a l o n g t h e 4 t h a n d 5 t h d i m e n s i o n a t 1 0 0 K c r e a t i n g a r a t h e r c o m p l i c a t e d p a t t e r n o f v a c a n c i e s . F i g u r e 5 . 1 2 s h o w s a n e x a m p l e o f t h e p r o fi l e o f t h e o c c u p a n c y o f T e [ 3 a ] a l o n g t h e t - d i r e c t i o n a t a fi x e d u = 0 . 5 s e c t i o n i n w h i c h t h e o c c u p a n c y b e c o m e s m i n i m u m . T h e c o o r d i n a t e s t a n d u c h a r a c t e r i z e t h e r e a l t h r e e d i m e n s i o n a l s t r u c t u r e c o n s t r u c t e d a s a p e r p e n d i c u l a r i n t e r s e c t i o n w i t h t h e s u p e r s p a c e a x i s A ” ( n = 4 f o r t a n d n = 5 f o r u ) t h e r e f o r e t = x 4 — q ' r w h e r e r i s a p o s i t i o n a l v e c t o r i n t h e t h r e e d i m e n s i o n a l s p a c e . ( s e e s e c t i o n 1 . 7 . 2 f o r m o r e d e t a i l s ) . A c o n t o u r p l o t o f t h e o c c u p a n c y a l o n g t a n d u d i r e c t i o n s c a n b e f o u n d i n F i g u r e 5 . 1 3 . T h e o c c u p a t i o n a l m o d u l a t i o n w a v e o f T e [ 3 a ] i s m o r e s i m p l e a t 5 0 0 K s i n c e t h e r e i s o n l y o n e q - v e c t o r . T h e p r o fi l e o f t h e o c c u p a n c y a l o n g t i s s h o w n i n F i g u r e 5 . 1 4 . T h e e x p e r i m e n t a l F o u r i e r m a p o f s z T e s a t 1 0 0 K p l o t t e d a l o n g t h e m o d u l a t i o n d i r e c t i o n ( t ) i n c o m p a r i s o n w i t h t h e c a l c u l a t e d ( fi t t e d ) p o s i t i o n o f T e [ 3 a ] i s s h o w n i n F i g u r e 5 . 1 5 . 1 . 0 0 _ - , . . . , . , . . . , . . . , . , 0 . 9 5 - T e [ 3 a ] o c c u p a n c y a t 1 0 0 K , u = 0 . 5 0 . 9 0 I 0 . 8 5 0 . 8 0 I 0 . 7 5 I > . 0 . 7 0 - i 0 6 5 - 3 0 . 6 0 I 5 0 . 5 5 I 0 . 5 0 I 0 . 4 5 I 0 . 4 0 I r - I 0 . 3 5 I + - I 0 3 0 4 L 1 l . 1 L I I [ 4 l + l L l . ' 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 t - d i r e c t i o n F i g u r e 5 . 1 2 . P r o fi l e o f t h e o c c u p a n c y o f T e [ 3 a ] i n s z T e 4 , 9 o ( 1 ) a t 1 0 0 K a l o n g t h e t - d i r e c t i o n a t a fi x e d u = 0 . 5 s e c t i o n . 3 1 7 - y c n a p u c O / L O O N 7 / , . 7 0 . 0 0 . 0 0 I 2 I 0 . 4 I 0 : 6 I o I e t : 1 . 0 F i g u r e 5 . 1 3 . C o n t o u r p l o t o f t h e o c c u p a n c y o f T e [ 3 a ] i n s z T e 4 . 9 o ( 1 ) a l o n g t h e t - u s p a c e . O n e c o n t o u r l i n e p e r 0 . 1 ( o c c u p a t i o n a l f r a c t i o n ) . l - O O ' I ' I ' I V I ' I ' I ' I fi i f I f T e [ 3 a ] o c c u p a n c y a t 5 0 0 K - 9 \ O U . l 0 . 9 0 I . I 0 . 8 5 I 0 . 8 0 I 0 . 7 5 I o 0 . 7 0 0 . 6 5 - - 0 . 6 0 - - W 0 . 5 5 L - 0 . 5 0 4 l n l n 1 J L A L r I I 1 1 l L l l 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 t - d i r e c t i o n F i g u r e 5 . 1 4 . P r o fi l e o f t h e o c c u p a n c y o f T e [ 3 a ] i n s z T e 4 . 9 o ( 1 ) a t 5 0 0 K a l o n g t h e t - d i r e c t i o n . 3 1 8 / p : . H 0 . o o . c 2 . 0 \ \ J . O o g . o . o \ . 0 . 0 0 0 . 1 0 0 . 2 0 0 . 3 0 0 . 4 0 x 1 0 . 5 0 F i g u r e 5 . 1 5 . E x p e r i m e n t a l F o u r i e r m a p o f s z T e 4 _ 9 o ( 1 ) a t 1 0 0 K p l o t t e d a l o n g t h e m o d u l a t i o n d i r e c t i o n ( t ) . T h e c e n t r a l b l u e l i n e r e p r e s e n t s t h e c a l c u l a t e d ( fi t t e d ) p o s i t i o n o f T e [ 3 a ] . O n e c o n t o u r l i n e p e r 0 . 7 5 e ' A ' 3 . S u m m a t i o n o f x 2 a l o n g 0 . 5 - 1 . 0 a n d x 5 = 0 . 5 . S c a n n i n g T u n n e l i n g M i c r o s c o p y ( S T A / 0 S t u a j z o f s z T e 5 — S T M h a s b e e n u s e d w i d e l y t o o b s e r v e C D W m o d u l a t i o n s f r o m a t o m i c r e s o l u t i o n i m a g e s i n d i r e c t s p a c e . 2 0 I n o r d e r t o v e r i f y t h e h y b r i d c h a r a c t e r o f t h e C D W d i s t o r t i o n i n t h e T e l / 2 ' n e t o f s z T e s w e p e r f o r m e d a l o w t e m p e r a t u r e S T M ( L T - S T M ) s t u d y . T h e S T M e x p e r i m e n t u n d e r t a k e n a t 4 . 2 K c l e a r l y s h o w a n i n c o m m e n s u r a t e C D W w i t h w a v e v e c t o r i n t h e T e l / 2 ' p l a n e a l o n g t h e d i a g o n a l o f t h e T e — T e s q u a r e n e t . T h e w a v e v e c t o r m e a s u r e d b y F o u r i e r t r a n s f o r m o f t h e S T M t o p o g r a p h y i m a g e s i s i n a g r e e m e n t w i t h d i f f r a c t i o n d a t a . T h e C D W p a t t e r n r e v e a l e d i n s z T e s i s s i m i l a r t o t h e o n e o b s e r v e d i n R E T e 3 . 6 b ’ 2 ' H o w e v e r , a n a d d i t i o n a l w a v e v e c t o r h a s b e e n o b s e r v e d i n t h i s m a t e r i a l t h a t w a s n o t p r e s e n t i n t h e t r i t e l l u r i d e . T h i s w a v e v e c t o r i s i n t h e d i r e c t i o n o f t h e T e - T e b o n d . T h e S T M i m a g e o f t h e s z T e s s u r f a c e i s s h o w n i n F i g u r e 5 . 1 6 A , e v i d e n c i n g t h e d i s t o r t e d T e n e t w i t h i n - p l a n e l a t t i c e p a r a m e t e r a = 3 . 1 ( 2 ) A . T h e f a s t F o u r i e r t r a n s f o r m a n a l y s i s ( F F T ) o f t h e S T M i m a g e i s 3 1 9 r e p o r t e d i n F i g u r e 5 . 1 6 B . T h e p e a k s L c o r r e s p o n d t o t h e T e s q u a r e l a t t i c e . T h e l i n e c u t fi ' o m O t o A , a l o n g t h e d i a g o n a l o f t h e T e s q u a r e n e t , i s s h o w n i n F i g u r e 5 . 1 6 0 T h i s l i n e o u t s h o w s fi v e p e a k s , o n e c o r r e s p o n d i n g t o t h e s u p e r l a t t i c e 2 1 t / a a n d f o u r i n t e r m e d i a t e p e a k s a t 0 . 3 1 , 0 . 3 8 , 0 . 6 2 , a n d 0 . 6 9 . W e i d e n t i f y q ] = 0 . 3 1 a s t h e C D W w a v e v e c t o r a n d t h e o t h e r p e a k s a s t h e 1 - 2 q 1 , 2 q 1 , 1 - q 1 h a r m o n i c s r e s p e c t i v e l y . T h e l i n e c u t O L s h o w s t w o a d d i t i o n a l p e a k s c o r r e s p o n d i n g t o q 2 = 0 . 3 3 a n d 2 q 2 = 0 . 6 6 , F i g u r e 5 . 1 6 D . ( D ) . . 0 » c ? : I : 0 8 0 8 a : . — . . . . . z E . . . . 6 0 0 6 - ~ “ ’ 0 6 - - . 5 a i — 3 0 . 4 ~ - . 2 0 4 — - i s S 0 0 — ! o q z I 5 0 . 2 7 L L 0 . 2 . 0 3 3 2 C 1 2 ~ r 2 0 . 6 6 0 . 0 | . - 0 . 0 . . - 0 . 2 1 . 0 0 . 0 0 . 2 . 8 0 : 4 0 I 6 0 8 0 4 0 . 6 0 k ( 2 7 t / a ) k ( 2 1 t / a ) F i g u r e 5 . 1 6 . ( A ) S T M i m a g e o f t h e s z T e s s u r f a c e o f T e ' m . ( B ) F F T o f t h e S T M i m a g e . T h e p e a k s L c o r r e s p o n d t o t h e T e s q u a r e l a t t i c e . ( C ) L i n e c u t p l o t f r o m O t o A , a l o n g t h e d i a g o n a l o f t h e T e s q u a r e n e t . ( D ) L i n e c u t p l o t f r o m O t o L . 3 2 0 I n fi a r e d ( I R ) S p e c t r o s c o p y o f s z T e ; — T h e h y b r i d s z T e s , l i k e S m T e 3 , s h o w s a m e t a l l i c b e h a v i o r s i n c e t h e C D W d o e s n o t r e m o v e a l l t h e s t a t e s f r o m t h e F e r m i l e v e l . 9 b D e s p i t e t h i s p o o r m e t a l l i c c h a r a c t e r t h e r e a r e s p e c t r o s c o p i c a l l y o b s e r v e d e l e c t r o n i c t r a n s i t i o n . T h e e n e r g y g a p w a s m e a s u r e d b y i n f r a r e d d i f fi i s e r e fl e c t a n c e s p e c t r o s c o p y o n s i n g l e c r y s t a l s o f s z T e s . T h e d a t a s h o w e d a g a p a r o u n d 0 . 2 5 e V w i t h a s m a l l d i s c o n t i n u i t y , F i g u r e 5 . 1 7 . T h i s e n e r g y t r a n s i t i o n s c a n b e a t t r i b u t e d t o t h e t w o C D W d i s t o r t e d T e n e t s w i t h a v e r a g e c h a r g e o f 0 . 5 - a n d 1 - . l ' I ' l ' I Y I ' I ' l 0 . 1 ‘ 0 . 2 ‘ 0 . 3 ‘ 0 . 4 ' 0 . 5 A 0 . 6 ‘ 0 . 7 l 0 . 8 E n e r g y ( e V ) F i g u r e 5 . 1 7 . R o o m t e m p e r a t u r e i n f r a r e d a b s o r p t i o n s p e c t r u m o f s z T e s s i n g l e c r y s t a l s . E n e r g y g a p a t ~ 0 . 2 5 e V c o r r e s p o n d s t o t h e C D W d i s t o r t e d T e n e t s . 3 2 1 S u p e r c e l l D e s c r i p t i o n o f S m T e 1 3 6 0 ) B a s e d o n a M o d u l a t i o n q - v e c t o r — T h e d i s t o r t i o n s f o u n d i n t h e s z T e s c o m p o u n d r e v e a l e d a m o d u l a t i o n i n t h e T e " n e t t h a t b e l o n g s t o t h e S m T e 2 s u b s t r u c t u r e . l 7 T h i s l e d u s t o t h e r e e x a m i n a t i o n o f t h e m o d u l a t e d s t r u c t u r e o f S m T e 2 u s i n g a s u p e r s p a c e c r y s t a l l o g r a p h i c a p p r o a c h . T h e i n c o m m e n s u r a t e s u p e r s t r u c t u r e o f S m T e m m ) w a s s o l v e d i n t h e t e t r a g o n a l P 4 ( a B ‘ / z ) ( B - a ‘ / 2 ) 0 s u p e r s p a c e g r o u p w i t h t w o q - v e c t o r n o r m a l t o e a c h o t h e r w i t h q 1 = 0 . 2 9 6 5 ( 3 ) a * + 0 . 2 9 6 5 ( 3 ) b * + U 2 6 “ a n d q ; = 0 . 2 9 6 5 ( 3 ) a * - 0 . 2 9 6 5 ( 3 ) b * + 1 / 2 c * a t 1 0 0 K . A d o u b l i n g o f t h e s u b c e l l a l o n g t h e c - a x i s w a s n e c e s s a r y t o a v o i d n o n - l i n e a r c o r r e l a t i o n s b e t w e e n t h e r a t i o n a l a n d i r r a t i o n a l c o m p o n e n t s o f t h e t w o q - v e c t o r s . T h e r e f o r e , a c e n t e r i n g v e c t o r o f ( 0 0 1 / 2 1 / 2 1 / 2 ) w a s u s e d w i t h t h e c o r r e s p o n d i n g s u p e r s p a c e g r o u p n o t a t i o n o f X 4 ( a B O ) ( | 3 — a 0 ) 0 . T h e l a b e l i n g s c h e m e i s s h o w n i n F i g u r e 5 . 7 3 . T h e C D W d i s t o r t e d T e n e t s i n S m T e 2 p o s s e s s t w o t y p e s o f m o d u l a t i o n s . P o s i t i o n a l a n d o c c u p a t i o n a l d i s t o r t i o n s c r e a t e a r a t h e r c o m p l i c a t e d p a t t e r n o f T e x z ' o l i g o m e r s a s c a n b e s e e n i n F i g u r e 5 . 1 8 . T h e b o n d i n g t h r e s h o l d w a s s e t t o 3 . 1 1 0 A i n o r d e r t o m a k e a f a r e c o m p a r i s o n w i t h t h e c o r r e s p o n d i n g p a t t e r n o b s e r v e d f o r T e " i n t h e s z T e s p h a s e . T h e m a j o r i t y o f o l i g o m e r s f o u n d i n S m T e 2 h a v e a l i n e a r s h a p e o f d i m e r s a n d t r i m e r s . O c c a s i o n a l l y s i n g l e T e a t o m s , L - s h a p e d t e t r a m e r s a n d d e f e c t e d s q u a r e - l i k e o l i g o m e r s ( s i m i l a r s h a p e w i t h t h e o n e s o b s e r v e d i n s z T e s ) w i t h m o r e t h a n s i x T e a t o m s i s f o u n d . T h e m i n i m u m T e - T e d i s t a n c e i n t h e d i s t o r t e d n e t i s 2 . 7 3 0 ( 1 1 ) A , t h e m a x i m u m 3 . 5 4 7 ( 1 1 ) A a n d t h e a v e r a g e v a l u e s i s 3 . 1 2 8 ( 1 0 ) A . T h e v a l u e o f t h e o c c u p a t i o n a l c u t o f f w a s t a k e n e q u a l t o t h e a v e r a g e o c c u p a n c y i n o r d e r t o o b t a i n r e a s o n a b l e b o n d d i s t a n c e s b e t w e e n a t o m s . T h e d i s t r i b u t i o n o f a t o m s / v a c a n c i e s a l o n g t h e t - u p l a n e i s s h o w n i n t h e c o n t o u r p l o t i n F i g u r e 5 . 1 9 . 3 2 2 / \ > / T h e q - v e c t o r d e p e n d e n c e a t h i g h t e m p e r a t u r e ( 5 0 0 K ) i s n e g l i g i b l e w i t h c e l l p a r a m e t e r s a — = 4 . 3 7 8 7 ( 4 ) A , c — = 8 . 9 9 7 6 ( 7 ) A a n d q l = 0 . 2 9 7 4 ( 3 ) a * + 0 . 2 9 7 4 ( 3 ) b * + 1 / 2 c a n d q 2 = 0 . 2 9 7 4 ( 3 ) a - . * 0 2 9 7 4 ( 3 ) b + 1 / 2 c * . / \ \ / \ . ’ / \ / / \ \ / ' \ I J K / \ / \ I \ ' \ / / \ < \ / / \ \ / > / \ \ . I \ K / / K / K / \ K / Q / 3 0 1 / w e \ ’ / > . . . . . . . \ / . \ / < / \ > \ / < / \ \ . ’ \ / \ > \ . ° / \ ° / \ \ ’ / \ ° / ° \ \ / ° \ ’ / \ ° / \ \ / ' \ ’ / \ > . / / / $ < ° \ / . K - ) $ < / \ / \ \ / . \ . - I \ / / \ . \ / \ / ~ / ' . \ / ° \ f / ° \ \ / \ \ ’ < \ : / ° \ \ / ° \ . ’ / \ ' / \ \ / . $ \ \ / > . / \ / / . 0 ( \ ~ / > / \ / , \ \ A / K K / \ A / V \ . ° / \ . / \ \ ’ / \ ’ / ' \ ' . / \ \ ’ / \ . / \ \ / ° \ . ’ / \ . \ I \ / \ v \ I \ / \ \ / \ / / \ / \ . ’ \ \ / / \ / \ / \ / \ / L f / \ / \ / \ \ / \ / \ / ° \ / \ \ / \ \ / \ / \ . / \ / \ / \ . / \ / . \ / . \ F i g u r e 5 . 1 8 . T e n e t o f S m T e 2 a t 1 0 0 K w i t h 3 . 1 1 0 A b o n d i n g t h r e s h o l d a n d 8 6 % o c c u p a t i o n a l c u t o f f . 3 2 3 ” I W “ - 1 0 . 8 0 0 6 ‘ 0 . 4 . 0 . 2 . l / o . o . . . . . . . . . Z 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 t 1 . 0 F i g u r e 5 . 1 9 . C o n t o u r p l o t o f t h e o c c u p a n c y o f T e [ 2 ] i n S m T e 1 , 3 5 ( 1 ) a l o n g t h e t - u s p a c e . O n e c o n t o u r l i n e p e r 0 . 0 5 ( o c c u p a t i o n a l f r a c t i o n ) . S u p e r c e l l D e s c r i p t i o n o f K z A g 4 L a 2 T e 9 , 6 1 ( 1 ) B a s e d o n a M o d u l a t i o n q - v e c t o r — T h e e x i s t e n c e o f t w o T e n e t s w i t h d i f f e r e n t o x i d a t i o n s t a t e s c r e a t e d a n i n c o m m e n s u r a t e s u p e r s t r u c t u r e w i t h t w o q - v e c t o r s a t 1 0 0 K . T h e r e i s o n e c o m m e n s u r a t e v e c t o r q ] = 1 / 3 b * a n d a n o t h e r i n c o m m e n s u r a t e o n e q 2 = 0 . 2 4 8 ( 2 ) a ’ + 0 . 1 6 6 ( 2 ) ] ; + 0 . 0 8 3 ( 3 ) c ‘ f o r t h e o r t h o r h o m b i c ( I m m m ) s u b c e l l . T h e i n t e n s i t y o f t h e s a t e l l i t e r e fl e c t i o n s o f q z - v e c t o r i s ~ 2 0 t i m e s w e a k e r t h a n t h e i n t e n s i t y o f t h e r e fl e c t i o n s o f q l - v e c t o r . T w o d i f f e r e n t a p p r o a c h e s w e r e u s e d t o s o l v e t h e s u p e r s t r u c t u r e . I n t h e fi r s t a t t e m p t , a t h r e e - f o l d s u b c e l l w a s u s e d t o c l e a r t h e c o m m e n s u r a t e q - v e c t o r . A ( 3 + 1 ) - d i m e n s i o n a l m o d u l a t i o n w i t h o n e p o s i t i o n a l a n d o n e o c c u p a t i o n a l w a v e w e r e t h e n a p p l i e d o n t h e n e w m o n o c l i n i c s u b c e l l ( P Z / m ) . A l l o f t h e a c c e p t a b l e m o n o c l i n i c s u p e r s p a c e g r o u p s ( P 2 , P m , P 2 / m g r o u p s ) g a v e a n R — v a l u e f o r t h e o b s e r v e d s a t e l l i t e r e fl e c t i o n s t o m o r e t h a n 3 0 % . A t r i c l i n i c P 1 3 2 4 s u p e r s p a c e g r o u p w a s t h e o n l y a c c e p t a b l e s o l u t i o n w i t h a n a g r e e m e n t f a c t o r f o r a l l t h e o b s e r v e d r e fl e c t i o n s ( m a i n a n d s a t e l l i t e s ) o f ~ 6 % . T h e t o t a l n u m b e r o f r e fi n e d p a r a m e t e r s w a s 2 8 5 9 . I n t h e s e c o n d a p p r o a c h , a ( 3 + 2 ) - d i m e n s i o n a 1 s u p e r c e l l w a s u s e d i n C 1 ( a 1 1 3 1 7 1 ) ( a 2 [ 3 2 7 2 ) 0 s u p e r s p a c e g r o u p . T h e s u b c e l l i n t h a t c a s e w a s t r a n s f o r m e d t o a v o i d a l a r g e n u m b e r o f c o r r e l a t i o n s a c c o r d i n g t o t h e t r a n s f o r m a t i o n m a t r i x [ 1 1 0 0 0 - 1 - 1 O 0 ] y i e l d i n g c e l l p a r a m e t e r s o f a = 6 . 3 5 2 1 ( 4 ) A , b = 6 . 3 5 3 1 ( 4 ) A , c = 2 5 . 4 0 3 6 ( 1 9 ) A , , 6 = 9 7 . 1 7 7 ( 6 ) ° , q ] = 0 . 3 3 2 7 ( 4 ) a * + 0 . 3 3 2 7 ( 4 ) b m + 0 . 3 3 4 ( 2 ) c ' , a n d q ; = 0 . 4 0 0 ( 2 ) a ' - 0 . 0 7 2 ( 2 ) b ‘ + 0 . 3 4 5 ( 6 ) c ' . T h e c o r r e s p o n d i n g R — v a l u e w a s a g a i n ~ 6 % w i t h 1 4 6 6 r e fi n e d p a r a m e t e r s . T h e s e c o n d a p p r o a c h e d w a s c h o s e n t o b e a m o r e a p p r o p r i a t e o n e s i n c e t h e s a m e c r y s t a l l o g r a p h i c s o l u t i o n w a s o b t a i n e d w i t h m u c h l e s s p a r a m e t e r s , F i g u r e 5 . 2 0 . F r o m t h e o b s e r v e d d i s t o r t i o n s i n t h e p l a n a r n e t s i t s e e m s t h a t t h e fi r s t q l - v e c t o r a f f e c t s m a i n l y t h e p o s i t i o n o f t h e a t o m s i n t h e T e l / 2 ' n e t a n d t h e s e c o n d q z - v e c t o r i s r e s p o n s i b l e f o r t h e l o n g r a n g e o r d e r i n g o f v a c a n c i e s i n t h e T e l ' n e t . T h e C D W d i s t o r t e d p a t t e r n o f T e l / 2 ' c a n b e s e e n a s a w e l l o r d e r e d s e q u e n c e o f V - s h a p e d t r i m e r s , F i g u r e 5 . 2 1 . T h e i d e a l p a t t e r n o f i d e n t i c a l o l i g o m e r s c o m e s f r o m t h e f a c t t h a t t h e m o d u l a t i o n i s c o m m e n s u r a t e . T h e m i n i m u m l e n g t h i n t h e T e - T e d i s t a n c e d i s t r i b u t i o n i s 2 . 8 7 ( 4 ) A a n d t h e m a x i m u m 3 . 4 9 ( 6 ) A . T h e m a i n d i f f e r e n c e o f t h e T e " p a t t e r n f r o m t h e T e l / 2 ' o n e i s t h e p r e s e n c e o f o r d e r e d v a c a n c i e s , F i g u r e 5 . 2 2 . T h e T e - T e l e n g t h d i s t r i b u t i o n i n t h e T e " n e t 1 / 2 - i s m u c h n a r r o w e r t h a n t h e o n e f o u n d i n t h e T e n e t w i t h a m i n i m u m d i s t a n c e o f 3 . 0 7 ( 4 ) A , m a x i m u m 3 2 4 ( 4 ) A a n d a v e r a g e v a l u e o f 3 . 1 6 ( 4 ) A . T h e d i s t r i b u t i o n o f a t o m s / v a c a n c i e s a l o n g t h e t - u p l a n e i s s h o w n i n t h e c o n t o u r p l o t i n F i g u r e 5 . 2 3 . 3 2 5 F i g u r e 5 . 2 0 . T r a n s f o r m e d c e l l o f K z A g 4 L a 2 T e o 6 m ) a n d l a b e l s u s e d i n t h e s u p e r s p a c e r e fi n e m e n t a t 1 0 0 K . r . r . r . r . r . r . r . r . r . r . r ' r r r r r r r r r r r r r r r r r r r r r . r ‘ r r r ‘ r r ‘ r r r r : r r r r r r r r ‘ r r r r r r r r r r r ‘ r r I r . . . a r ‘ _ . r ‘ . . . r ‘ . . . I " . . . r ‘ . r 1 . r ‘ _ . r ‘ . . . r ‘ . . . r . F i g u r e 5 . 2 1 . T e l / 2 ' n e t o f K z A g 4 L a 2 T e 9 , 5 1 ( 1 ) a t 1 0 0 K w i t h 3 . 0 1 7 A b o n d i n g t h r e s h o l d s h o w i n g t r i m e r s . 3 2 6 L . . F i g u r e 5 . 2 2 . T o " n e t o f K z A g 4 L a 2 T e o 6 m ) a t 1 0 0 K w i t h 3 . 1 1 0 A b o n d i n g t h r e s h o l d a n d 6 0 % o c c u p a t i o n a l c u t o f f . 3 2 7 u n o \ \ i s 0 . 0 . . . . . . . 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 t 1 . 0 F i g u r e 5 . 2 3 . C o n t o u r p l o t o f t h e o c c u p a n c y o f T e [ 2 ] i n S m T e L g m ) a l o n g t h e t - u s p a c e . O n e c o n t o u r l i n e p e r 0 . 0 5 ( o c c u p a t i o n a l fi a c t i o n ) . B a n d s t r u c t u r e c a l c u l a t i o n o f L a z T e 5 — T h e c a l c u l a t i o n s w e r e p e r f o r m e d u s i n g t h e s e l f - c o n s i s t e n t f u l l - p o t e n t i a l l i n e a r i z e d a u g m e n t e d p l a n e w a v e m e t h o d ( L A P W ) 2 2 a n d t h e g e n e r a l i z e d g r a d i e n t a p p r o x i m a t i o n ( G G A ) 2 3 f o r t h e e x c h a n g e a n d c o r r e l a t i o n p o t e n t i a l . T h e e x p e r i m e n t a l c e l l c o n s t a n t s a n d a t o m i c c o o r d i n a t e s fi ' o m t h e c r y s t a l s t r u c t u r e r e fi n e m e n t o f t h e a v e r a g e s z T e s a t 1 0 0 K w e r e u s e d a s s t a r t i n g v a l u e s . V o l u m e o p t i m i z a t i o n w a s u s e d i n o r d e r t o fi n d t h e m i n i m u m e n e r g y o f t h e l a r g e r L a z T e s c e l l t h r o u g h a M u r n a g h a n t y p e fi t t i n g o f t h e E q u a t i o n o f S t a t e s . 2 4 S c a l a r r e l a t i v i s t i c c o r r e c t i o n s w e r e i n c l u d e d a n d a s p i n - o r b i t i n t e r a c t i o n w a s i n c o r p o r a t e d u s i n g a s e c o n d v a r i a t i o n a l p r o c e d u r e . 2 5 D i r e c t i o n s i n t h e B r i l l o u i n z o n e ( 3 2 ) o f C m c m s p a c e g r o u p a r e s h o w n i n F i g u r e 5 . 2 9 . 2 6 I n t e r a t o m i c f o r c e s w e r e m i n i m i z e d w i t h i n 0 . 1 m R y / b o h r u s i n g a r e v e r s e - c o m m u n i c a t i o n t r u s t - r e g i o n q u a s i - N e w t o n m e t h o d f r o m t h e P o r t l i b r a r y . 2 7 T h e 3 2 8 v a l u e s o f t h e a t o m i c r a d i i w e r e t a k e n t o b e 2 . 7 a . u . f o r L a a t o m a n d 2 . 5 a . u . f o r T e a t o m s , w h e r e a n . i s t h e a t o m i c u n i t ( 0 . 5 2 9 A ) . C o n v e r g e n c e o f t h e s e l f - c o n s i s t e n t i t e r a t i o n s w a s p e r f o r m e d f o r 1 5 0 k p o i n t s i n s i d e t h e i r r e d u c i b l e B r i l l o u i n z o n e t o w i t h i n 0 . 0 0 0 1 R y w i t h a c u t o f f o f - 6 . 0 R y b e t w e e n t h e v a l e n c e a n d t h e c o r e s t a t e s . T h e c a l c u l a t i o n s w e r e p e r f o r m e d u s i n g W I E N Z K p r o g r a m . 2 8 E l e c t r o n i c b a n d s t r u c t u r e c a l c u l a t i o n s p e r f o r m e d o n t h e u n d i s t o r t e d ( n o C D W a n d v a c a n c y o r d e r i n g ) s t r u c t u r e o f L a z T e s . T h e m o s t i m p o r t a n t f e a t u r e o f t h e F e r m i S u r f a c e ( F S ) o f L a z T e s i s t h e s e p a r a t i o n b e t w e e n t h e t w o b a n d s l o c a t e d i n t h e c e n t e r o f t h e F S ( F p o i n t ) , F i g u r e 5 . 2 8 . T h e s e a r e T e p b a n d s i n c h a r a c t e r c o m i n g f r o m t h e t w o T e n e t s w i t h d i f f e r e n t o x i d a t i o n s t a t e s . T h e s e p a r a t i o n o f t h e b a n d s i s s u c h t h a t t h e t o p o l o g y o f t h e F S f a v o r s t h e f o r m a t i o n o f t w o n e s t i n g v e c t o r s . O n e v e c t o r a l o n g t h e b * d i r e c t o r w i t h a l e n g t h o f 0 3 2 ( 2 ) a n d a s e c o n d v e c t o r a l o n g t h e d i a g o n a l o f a * - b * p l a n e a t 0 3 5 ( 2 ) . 2 9 A w e a k e r s p l i t t i n g o f b a n d s w a s f o u n d f o r t h e R E T e 3 i n r e s p e c t t o t h e R E T e 2 d u e t o t h e i n t e r a c t i o n s b e t w e e n t h e T e l a y e r s s e p a r a t e d b y t h e v a n d e r W a a l s g a p . 3 0 A l t h o u g h t h e d i s t a n c e o f t h e T e b i l a y e r s s e p a r a t e d b y t h e v a n d e r W a a l s g a p i s e s s e n t i a l l y t h e s a m e i n b o t h S m T e 3 a n d s z T e s t h e p r e s e n c e o f t h e a d d i t i o n a l T e " l a y e r s e e m s s t r o n g l y t o a f f e c t t h e n e s t i n g p r o p e r t i e s o f t h e P S . T h e n e s t i n g v e c t o r f r o m 0 2 8 ( 2 ) f o r L a T e 3 i n c r e a s e s s i g n i fi c a n t l y t o 0 3 2 ( 2 ) f o r L a z T e s i n a s i m i l a r f a s h i o n o b s e r v e d f o r K C u L a T e 4 . 1 6 B a n d s t r u c t u r e c a l c u l a t i o n o f K z A g 4 L a 2 T e 1 0 — T h e s a m e c a l c u l a t i o n m e t h o d a n d p r o c e d u r e t h a t w a s u s e d f o r L a z T e s w e r e p e r f o r m e d o n t h e a v e r a g e I m m m s t r u c t u r e o f K z A g a L a z T e t o ( n o C D W a n d v a c a n c i e s ) . D i r e c t i o n s i n t h e B r i l l o u i n z o n e ( B 2 ) o f I m m n s p a c e g r o u p a r e s h o w n i n F i g u r e 5 . 3 3 . 2 6 T h e b a n d s t h a t c r o s s t h e F e r m i s u r f a c e a r e p r o n o m i n a l l y T e p i n c h a r a c t e r . A d d i t i o n a l l y , s o m e b a n d s a s s o c i a t e d w i t h t h e [ K z A g 4 T e 4 ] 3 2 9 l a y e r c r o s s t h e F e r m i l e v e l b u t r e m a i n o u t s i d e t h e n e s t i n g r e g i o n o f t h e b a n d s o f t h e d i s t o r t e d T e a t o m s , F i g u r e 5 . 3 1 . S i m i l a r b e h a v i o r w a s o b s e r v e d f o r t h e l a y e r s o f K C u L a T e 4 p h a s e . T h e r e a r e s e v e n b a n d s t h a t c r o s s t h e F e r m i l e v e l ( F i g u r e 5 3 2 A - G ) a n d c r e a t e t h e F e r m i s u r f a c e t o p o l o g y s h o w n i n F i g u r e 5 . 3 2 H . T h e c a l c u l a t e d n e s t i n g v e c t o r ( s h o w n i n a r r o w s i n F i g u r e 5 . 3 2 H ) i s 0 3 5 ( 2 ) . T h e a p p a r e n t d i f f e r e n c e o f t h e F S o f K z A g 4 L a z T e t o i n r e s p e c t w i t h t h e s u r f a c e c a l c u l a t e d f o r L a T e 3 , K C u L a T e 4 , a n d L a z T e s i s t h e e x i s t e n c e o f t h e b a n d a r o u n d t h e F p o i n t ( F i g u r e 5 . 3 2 A ) . T h i s b a n d i s l o c a t e d o u t s i d e t h e n e s t i n g r e g i o n a n d i t i s m a i n l y T e p i n c h a r a c t e r ( T e a t o m s i n t h e [ K z A g 4 T e 4 ] l a y e r ) . 5 . 5 . C o n c l u s i o n s T h e C D W d i s t o r t i o n s i n t h e i n t e r g r o w t h s z T e 5 , . x c o m p o u n d h a v e s h o w n a u n i q u e h y b r i d c h a r a c t e r c o m i n g f r o m t h e c o u p l i n g o f t w o i n d i v i d u a l q - v e c t o r s . T h e R E z T e s f a m i l y r e p r e s e n t s a r a r e e x a m p l e o f c o m p o s i t e s t r u c t u r e t h a t p o s s e s t w o T e n e t s w i t h d i f f e r e n t o x i d a t i o n s t a t e s , T e l / 2 ' a n d T e " . I n c o m b i n a t i o n w i t h o c c u p a t i o n a l m o d u l a t i o n w a v e s o f v a c a n c i e s t h e n e w d i s t o r t e d T e p a t t e r n s s u r p r i s i n g l y a r e v e r y d i f f e r e n t f r o m t h e o n e s f o u n d i n t h e t w o p a r e n t s u b s t r u c t u r e s . A s i m i l a r b e h a v i o r o f s i m u l t a n e o u s p r e s e n c e a n d c o u p l i n g o f t w o d i s t i n c t C D W w a s f o u n d i n t h e i n t e r g r o w t h K 2 A g 4 L a z T e m . x c o m p o u n d a s w e l l . T h e n e w r e s u l t s r e p o r t e d h e r e p r o v i d e m o r e i n f o r m a t i o n t o t h e d e v e l o p i n g t h e o r y o f t w o - d i m e n s i o n a l C D W s y s t e m s w i t h a p a r t i a l l y g a p p e d F e r m i s u r f a c e . 3 3 0 3 . 0 1 : ! ” w a n 2 . 0 - _ f ' j i [ W 1 . 0 0 . 0 - 1 . 0 I A ” S . 3 . . x . . ‘ v I ” a t ? — ‘ w . V . . a . . 1 6 ) . ‘ ' _ \ - 4 . 0 I “ f ' \ i - - 5 . o - 6 . 0 F Z T Y F " I R S Y R Z S F F i g u r e 5 . 2 4 . B a n d s t r u c t u r e o f L a z T e s n e a r t h e F e r m i l e v e l . T e [ 3 ] p b a n d s f r o m t h e T e " n e t a r e d r a w n i n o p e n c i r c l e s . T h e c o n t r i b u t i o n o f e a c h o r b i t a l i s p r o p o r t i o n a l t o t h e b r e a d t h o f t h e c i r c l e s t r a c i n g o u t t h e b a n d . O n l y t h e b a n d s t h a t c r o s s t h e F e r m i s u r f a c e a r e d r a w n i n c i r c l e s f o r c l a r i t y . 3 3 1 _ _ . - ; _ " 1 1 2 0 8 6 1 . 2 . . ? . 7 " - " . f , I $ I g 3 H ) V e ( y . : g 4 r e n E - " - - - - - - " - - " - - - - - - " - - " - - - - - - - - - - - - - - " - - - - " - - - - - M T T T L L 4 [ [ [ [ [ e e e a a ] 3 2 l 2 l ] ] ] ] ] - . , — ‘ d l 6 ‘ d — 1 - t i — q _ d g — d A I t ‘ W p . ) ( D l - _ I K I ] | — — t | l n 2 0 - 2 . 4 _ 6 r l l I 1 . 0 l 2 3 4 5 6 D O S F i g u r e 5 . 2 5 . T o t a l d e n s i t y o f s t a t e s ( D O S ) o f L a z T e s n e a r t h e F e r m i l e v e l . T e [ l ] a n d T e [ 2 ] a r e t h e t e l l u r i u m a t o m s i n t h e [ R E T e ] p u c k e r e d l a y e r s , T e [ 3 ] i s i n t h e T e " n e t a n d T e [ 4 ] , T e [ 5 ] a r e i n t h e T e l / 2 ' n e t . 3 3 2 5 " ' \ I 1 I l I l - - - - - - - - - - - - - T e [ 5 ] - 4 ' t - - - - - - - - - - T e [ 4 ] ‘ 3 ' - - - - - - - - - - T e [ 3 ] ‘ ' ‘ 3 - - - - - - T e [ 2 ] ‘ 2 - 1 4 3 . T e [ l ] _ - - - - - N f . 1 ” f « 5 . 2 2 : : - - 9 . g s . Q ) \ > ‘ 0 - - - . - - - - - . - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - g 0 . c : - 1 n m - t - 2 s - 3 _ - 4 _ - 5 ‘ - - 0 . 0 0 . 5 1 0 1 . 5 2 . 0 P a r t i a l . D O S F i g u r e 5 . 2 6 . P a r t i a l d e n s i t y o f s t a t e s ( D O S ) o f a l l T e p b a n d s i n L a z T e s n e a r t h e F e r m i l e v e l . T e [ l ] a n d T e [ 2 ] a r e t h e t e l l u r i u m a t o m s i n t h e [ R E T e ] p u c k e r e d l a y e r s , T e [ 3 ] i s i n t h e T e " n e t a n d T e [ 4 ] , T e [ 5 ] a r e i n t h e T o m “ n e t . 3 3 3 x \ V \ / \ / ‘ C / \ “ W / ( E ) \ / ( F ) \ / > > < / \ / \ F i g u r e 5 . 2 7 . ( A - F ) F e r m i s u r f a c e t o p o l o g y o f t h e s i x i n d i v i d u a l b a n d s t h a t c r o s s t h e F e r m i l e v e l o f L a z T e s . S u p e r p o s i t i o n o f a l l s i x b a n d s w i l l g i v e t h e t o t a l F e r m i s u r f a c e s h o w n i n F i g u r e 5 . 2 8 . 3 3 4 F i g u r e 5 . 2 8 . C a l c u l a t e d F e r m i s u r f a c e t o p o l o g y o f L a z T e s . P o s s i b l e n e s t i n g v e c t o r s w i t h a n a v e r a g e l e n g t h o f q t = 0 3 2 ( 2 ) a l o n g t h e b * a x i s ( Y p o i n t ) a n d q ; = 0 3 5 ( 2 ) a l o n g t h e d i a g o n a l a r e d r a w n i n a r r o w s . B E T 2 J 4 1 5 0 A H F i g u r e 5 . 2 9 . B r i l l o u i n z o n e o f C m c m s p a c e g r o u p . 2 6 3 3 5 l l l l i l l l l l ) V l e ( l y l g r l e n E i l l l l l l l l I 3 . 0 2 . 0 0 . 0 - 6 . 0 F i g u r e 5 . 3 0 . B a n d s t r u c t u r e o f K z A g 4 L a 2 T e l o n e a r t h e F e r m i l e v e l . P R U W F S F B Q r s M x 3 3 6 I I I I I I F 1 0 A ; ' " " " " " T e [ 4 ] _ ) V e ( y g N r e n E 1 4 ' I ' I ' I ' I ¢ 1 ' 1 2 I v “ , ( D l — ' l p — A I — l 1 _ 8 r I . I . l . I . 0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 D O S F i g u r e 5 . 3 1 . P a r t i a l d e n s i t y o f s t a t e s ( D O S ) o f a l l T e p b a n d s K z A g 4 L a 2 T e m n e a r t h e F e r m i l e v e l . T e [ l ] a n d T e [ 2 ] a r e t h e t e l l u r i u m a t o m s i n t h e [ R E T e ] p u c k e r e d l a y e r s , T e [ 3 ] a n d T e [ 4 ] a r e i n t h e T e l / 2 ' n e t a n d T e [ 5 ] , T e [ 6 ] a r e i n t h e r e " n e t . 3 3 7 w a \ \ ( D ) / V \ \ \ / \ / ( E ) V ( F ) \ / F i g u r e 5 . 3 2 . ( A - G ) F e r m i s u r f a c e t o p o l o g y o f t h e s e v e n i n d i v i d u a l b a n d s t h a t c r o s s t h e F e r m i l e v e l o f K 2 A g 4 L a z T e m . S u p e r p o s i t i o n o f a l l s e v e n b a n d s w i l l g i v e t h e F e r m i s u r f a c e ( H ) . 3 3 8 ( G ) \ / / \ / / F i g u r e 5 . 3 2 . ( C o n t ’ d ) ( A - G ) F e r m i s u r f a c e t o p o l o g y o f t h e s e v e n i n d i v i d u a l b a n d s t h a t c r o s s t h e F e r m i l e v e l o f K z A g r L a z T e t o . S u p e r p o s i t i o n o f a l l s e v e n b a n d s w i l l g i v e t h e F e r m i s u r f a c e ( H ) . F i g u r e 5 . 3 3 . B r i l l o u i n z o n e o f 1 m m s p a c e g r o u p . 2 6 3 3 9 T a b l e 5 . 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r s z T e 4 . 9 o ( . ) a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) q - v e c t o r ( 2 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f f i c i e n t C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 3 0 . 1 9 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 3 o ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 3 o ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 3 o ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) F i n a l R 2 n d o r d e r s a t e l l i t e s [ I > 3 o ( I ) ] R 2 ‘ “ ‘ 1 o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f f i c i e n t T m . . . a n d T m . . . c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e S m 2 T € 4 . 9 0 ( l ) 9 3 8 . 7 1 0 0 . 0 ( 3 ) K T r i c l i n i c P 1 0 1 1 1 3 1 7 0 0 1 2 1 3 2 1 0 ) a = 4 . 3 3 9 2 ( 2 ) A , a = 9 0 ° b = 4 . 3 4 8 3 ( 2 ) A , 0 = 9 5 . 6 7 9 ( 4 ) ° c = 2 1 . 8 4 3 8 ( 1 3 ) A , y = 9 0 ° 0 . 3 1 2 4 ( 3 ) h ‘ + l / 2 c " 0 . 3 3 0 3 ( 3 ) a ' + 0 . 3 3 1 5 ( 3 ) b ’ + 0 . 3 4 9 ( l ) o " 4 1 0 . 1 3 ( 4 ) A 3 2 7 . 5 9 8 9 g / o r n 3 3 1 . 4 7 4 m m " 0 . 3 3 x 0 . 2 1 x 0 . 0 2 m m 3 1 . 8 0 t o 3 0 . 1 9 ° - 6 < = h < = 6 , - 6 < = k < = 6 , - 3 1 < = l < = 3 0 , - 1 < = m , n < = 1 7 3 6 3 9 ( 7 4 2 7 m a i n + 6 6 2 1 2 s a t e l l i t e s ) 3 4 3 7 5 ( 3 9 6 9 m a i n + 3 0 4 0 6 s a t e l l i t e s ) [ R i m = 0 . 0 7 0 3 ] 9 5 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 3 4 3 7 5 / 4 2 / 1 1 0 0 1 . 4 3 R o b s = 0 . 0 5 8 7 , W R o b s = 0 . 1 9 8 1 R . . . = 0 . 1 6 5 8 , w R . . . = 0 . 2 4 2 1 R . . . = 0 . 0 4 9 0 , w R . . . = 0 . 1 7 9 8 R . . . = 0 . 0 5 2 1 , w R . . . = 0 . 1 9 0 9 R . . . = 0 . 0 8 7 2 , w R . . . = 0 . 1 9 8 7 R . . . = 0 . 2 8 6 4 , w R . . . = 0 . 2 6 3 3 R . . . = 0 . 1 4 1 0 , w R . . . = 0 . 3 0 8 5 R . . . = 0 . 4 9 8 1 , w R . . . = 0 . 4 3 0 8 0 . 0 0 0 5 1 ( 3 ) 0 . 0 0 9 5 a n d 0 . 5 1 4 7 6 . 0 4 a n d - 6 . 7 5 e . A ' 3 R = 2 | | F . | - | F . | | / 2 | F . | , w R = { 2 : [ w ( | F . | 2 - | 1 = . | 2 ) 2 ] / z : [ w ( | l = . | “ ) ] } ” 2 a n d w = l / ( 0 2 ( I ) + 0 . 0 0 3 6 1 2 ) 3 4 0 T a b l e 5 . 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r s z T e a o o m a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x y 2 O c c u p a n c y U . q S m [ l a ] 0 9 8 9 2 4 9 9 1 9 7 6 1 4 ( 1 ) s i n , 1 - 1 5 ( 4 ) 1 ( 2 ) 0 ( 1 ) c o s , 1 - 5 1 ( 2 ) - 2 ( 2 ) 0 ( 1 ) s i n , 2 3 ( 2 ) - 5 ( 2 ) 0 ( 1 ) c o s , 2 0 ( 2 ) 2 ( 2 ) 0 ( 1 ) s i n , 3 2 ( 2 ) - 1 ( 2 ) 0 ( 1 ) c o s , 3 5 ( 2 ) - 3 ( 2 ) 1 ( 1 ) s i n , 4 2 ( 4 ) 1 ( 3 ) 1 ( 1 ) c o s , 4 5 ( 4 ) 0 ( 3 ) 0 ( 1 ) S m [ 1 b ] 0 - 9 8 7 ( 1 ) - 2 4 9 7 ( 1 ) - 1 9 7 6 ( 1 ) 1 4 ( 1 ) s i n , 1 4 9 ( 3 ) 0 ( 2 ) 0 ( 1 ) c o s , 1 - 3 4 ( 3 ) 2 ( 2 ) 0 ( 1 ) s i n , 2 2 ( 2 ) 0 ( 2 ) 1 ( 1 ) c o s , 2 - 2 ( 2 ) 3 ( 2 ) 1 ( 1 ) s i n , 3 - 3 ( 2 ) - l ( 2 ) - l ( l ) c o s , 3 4 ( 2 ) - 6 ( 2 ) - l ( 1 ) s i n , 4 - 4 ( 4 ) - 1 ( 3 ) - 1 ( 1 ) c o s , 4 4 ( 4 ) - l ( 3 ) - l ( 1 ) S m [ 2 b ] 0 3 0 7 9 ( 2 ) 2 4 9 9 ( 2 ) 6 1 3 5 ( 1 ) 1 6 ( 1 ) s i n , 1 - 2 ( 2 ) 2 ( 2 ) 1 ( 1 ) c o s , 1 2 ( 2 ) 1 ( 2 ) 0 ( 1 ) s i n , 2 - l 3 ( 2 ) - 1 3 ( 2 ) 0 ( 1 ) c o s , 2 - 3 ( 2 ) - 9 ( 2 ) 1 1 ( 1 ) s i n , 3 - 1 5 ( 2 ) 2 0 ( 2 ) — 3 ( 1 ) c o s , 3 9 ( 3 ) 9 ( 2 ) 9 ( 1 ) s i n , 4 - 1 ( 4 ) - 4 ( 3 ) - 2 ( 1 ) c o s , 4 2 ( 4 ) 4 ( 3 ) 1 ( 1 ) 3 4 1 T a b l e 5 . 2 . ( C o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r s z T e 4 _ 9 o ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . S m [ 2 a ] 0 - 3 0 5 4 ( 2 ) - 2 5 0 8 ( 2 ) - 6 1 2 7 ( 1 ) 1 6 ( 1 ) s i n , 1 0 ( 2 ) 2 ( 2 ) 0 ( 1 ) c o s , 1 - 1 ( 2 ) - 2 ( 2 ) 1 ( 1 ) s i n , 2 - 7 ( 3 ) 2 ( 2 ) 7 ( 1 ) c o s , 2 - 2 1 ( 2 ) - 1 7 ( 2 ) - 8 ( 1 ) s i n , 3 3 ( 3 ) 0 ( 2 ) - 8 ( 1 ) c o s , 3 1 6 ( 2 ) - 6 ( 2 ) - 2 ( 1 ) s i n , 4 0 ( 4 ) - 2 ( 3 ) 1 ( 1 ) c o s , 4 3 ( 4 ) 6 ( 3 ) 1 ( 1 ) T e [ l b ] 0 3 8 2 3 ( 3 ) 2 4 9 3 ( 3 ) 7 6 0 6 ( 1 ) 1 4 ( 1 ) s i n , 1 - 4 ( 3 ) - 1 ( 2 ) - 1 ( 1 ) c o s , 1 - 6 ( 3 ) 5 ( 2 ) 0 ( 1 ) s i n , 2 0 ( 3 ) 6 ( 3 ) 3 ( 1 ) c o s , 2 0 ( 3 ) - 4 ( 3 ) 5 ( 1 ) s i n , 3 1 ( 3 ) 0 ( 3 ) 2 ( 1 ) c o s , 3 - 3 ( 3 ) 4 ( 3 ) 3 ( 1 ) s i n , 4 1 ( 5 ) 1 ( 4 ) 0 ( 1 ) c o s , 4 - 1 ( 5 ) 2 ( 4 ) - 3 ( 1 ) T e [ l a ] 0 - 3 7 7 7 ( 3 ) - 2 5 1 2 ( 3 ) - 7 5 9 0 ( 1 ) 1 4 ( 1 ) s i n , 1 - 8 ( 3 ) 6 ( 2 ) 0 ( 1 ) c o s , 1 - l ( 3 ) - 4 ( 2 ) - 1 ( 1 ) s i n , 2 7 ( 3 ) 0 ( 3 ) 4 ( 1 ) c o s , 2 - 2 ( 3 ) - 5 ( 3 ) - 1 ( 1 ) s i n , 3 0 ( 3 ) 0 ( 3 ) - 2 ( 1 ) c o s , 3 - 5 ( 3 ) 0 ( 3 ) - 3 ( 1 ) s i n , 4 6 ( 5 ) 7 ( 4 ) - 1 ( 1 ) c o s , 4 3 ( 5 ) - 3 ( 4 ) 1 ( 1 ) 3 4 2 T a b l e 5 . 2 . ( C o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r s z T e 4 . 9 0 ( 1 ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 2 a ] 0 1 7 6 0 ( 3 ) 2 4 8 8 ( 3 ) 3 4 7 4 ( 1 ) 1 4 ( 1 ) s i n , 1 6 ( 3 ) - 5 ( 2 ) 1 ( 1 ) c o s , 1 3 ( 3 ) - 2 ( 2 ) 1 ( 1 ) s i n , 2 - 1 ( 3 ) - 3 ( 3 ) 2 ( 1 ) c o s , 2 - 1 5 ( 3 ) - 8 ( 3 ) - 1 ( 1 ) s i n , 3 - 3 ( 3 ) - 3 ( 3 ) 2 ( 1 ) c o s , 3 - 9 ( 3 ) - 1 2 ( 3 ) 2 ( 1 ) s i n , 4 1 4 ( 5 ) 0 ( 4 ) - 1 ( 1 ) c o s , 4 - 2 ( 5 ) 9 ( 4 ) 0 ( 1 ) T e [ 2 b ] 0 - l 7 0 7 ( 3 ) - 2 5 1 5 ( 3 ) - 3 4 6 9 ( 1 ) 1 4 ( 1 ) s i n , 1 6 ( 3 ) - 7 ( 2 ) 0 ( 1 ) c o s , 1 1 ( 3 ) - 1 ( 2 ) - 1 ( 1 ) s i n , 2 - 1 0 ( 3 ) - 5 ( 3 ) - 1 ( 1 ) c o s , 2 - l 4 ( 3 ) 8 ( 3 ) 3 ( 1 ) s i n , 3 7 ( 3 ) - 1 4 ( 3 ) 0 ( 1 ) c o s , 3 - 3 ( 3 ) - 7 ( 3 ) - 3 ( 1 ) s i n , 4 6 ( 5 ) - l 3 ( 4 ) - 1 ( 1 ) c o s , 4 1 ( 5 ) 0 ( 5 ) 3 ( 1 ) T e [ 3 a ] 0 2 5 3 4 ( 5 ) 7 6 0 2 ( 4 ) 5 0 0 3 ( 1 ) 0 . 8 0 4 ( 3 ) 1 7 ( 1 ) s i n , 1 - 1 0 ( 5 ) - 3 6 ( 6 ) 3 ( 1 ) c o s , 1 1 1 ( 7 ) 6 8 ( 7 ) 5 ( 1 ) s i n , 2 - 2 1 6 ( 5 ) - 1 7 6 ( 1 0 ) 1 ( 1 ) c o s , 2 1 1 ( 1 3 ) - 1 6 4 ( l l ) 0 ( 1 ) s i n , 3 3 3 ( 1 3 ) - 2 1 6 ( 8 ) - 1 ( 1 ) c o s , 3 2 1 1 ( 5 ) - 9 1 ( l 3 ) 2 ( 1 ) s i n , 4 - 5 ( 1 0 ) 4 3 ( 7 ) - 2 ( 2 ) c o s , 4 - 3 4 ( 9 ) - 1 5 ( 1 0 ) 0 ( 1 ) 3 4 3 T a b l e 5 . 2 . ( C o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r s z T e 4 . 9 o ( I ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 3 b ] 0 - 2 4 7 0 ( 4 ) - 7 4 1 2 ( 4 ) — 4 9 9 9 ( 1 ) 1 1 8 ( 1 ) s i n , 1 - 5 ( 4 ) 5 2 ( 4 ) 4 ( 1 ) c o s , 1 - 1 0 ( 5 ) - 4 7 ( 5 ) 1 ( 1 ) s i n , 2 - 1 7 0 ( 3 ) - l 3 8 ( 7 ) - 2 ( 1 ) c o s , 2 5 ( 1 0 ) - 1 2 4 ( 8 ) 0 ( 1 ) s i n , 3 - 4 8 ( 9 ) 1 4 7 ( 6 ) 2 ( 1 ) c o s , 3 - 1 4 9 ( 4 ) 7 8 ( 9 ) 0 ( 1 ) s i n , 4 7 ( 7 ) - 1 0 ( 6 ) 4 ( 1 ) c o s , 4 1 4 ( 7 ) - l 6 ( 6 ) 1 ( 1 ) T e [ 4 a ] 0 4 7 1 ( 4 ) 7 4 9 2 ( 3 ) 8 3 8 ( 1 ) 1 5 ( 1 ) s i n , 1 2 ( 1 1 ) - 8 ( 3 ) 0 ( 1 ) c o s , 1 2 4 8 ( 3 ) 1 9 ( 3 ) - 2 ( 1 ) s i n , 2 6 ( 4 ) - 1 ( 3 ) 0 ( 1 ) c o s , 2 6 ( 4 ) 5 ( 3 ) 0 ( 1 ) s i n , 3 6 ( 4 ) - 5 ( 3 ) 1 ( 1 ) c o s , 3 4 ( 4 ) - 4 ( 3 ) - 1 ( 1 ) s i n , 4 - 1 0 ( 5 ) - 4 ( 5 ) 2 ( 1 ) c o s , 4 1 ( 5 ) - 6 ( 4 ) - 3 ( 1 ) T e [ 4 b ] 0 - 3 5 7 ( 4 ) - 7 5 1 4 ( 3 ) - 8 2 0 ( 1 ) 1 5 ( 1 ) s i n , 1 - 1 0 1 ( 8 ) 2 ( 3 ) - 1 ( 1 ) c o s , 1 1 8 0 ( 5 ) - 9 ( 3 ) 2 ( 1 ) s i n , 2 - 4 ( 3 ) - l ( 3 ) 0 ( 1 ) c o s , 2 - 3 ( 4 ) - 2 ( 3 ) 2 ( 1 ) s i n , 3 1 ( 4 ) - 2 ( 3 ) 1 ( 1 ) c o s , 3 - 5 ( 4 ) 2 ( 3 ) 0 ( 1 ) s i n , 4 - 5 ( 5 ) - 8 ( 5 ) - 5 ( 1 ) c o s , 4 - 7 ( 5 ) - 9 ( 5 ) - 2 ( 1 ) 3 4 4 T a b l e 5 . 2 . ( C o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r s z T e 4 . 9 0 ( 1 ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 5 a ] 0 5 4 5 2 ( 3 ) 2 5 0 9 ( 3 ) 8 4 0 ( 1 ) 1 6 ( 1 ) s i n , 1 1 ( 8 ) - 1 1 ( 3 ) 0 ( 1 ) c o s , 1 - 1 8 0 ( 3 ) 1 2 ( 3 ) 0 ( 1 ) s i n , 2 - 3 ( 3 ) 6 ( 3 ) 1 ( 1 ) c o s , 2 - 2 ( 3 ) 3 ( 3 ) 1 ( 1 ) s i n , 3 6 ( 4 ) - 4 ( 3 ) - 1 ( 1 ) c o s , 3 2 ( 4 ) 0 ( 3 ) 0 ( 1 ) s i n , 4 5 ( 5 ) - 1 ( 4 ) 2 ( 1 ) c o s , 4 - 3 ( 5 ) 7 ( 4 ) 3 ( 1 ) T e [ S b ] 0 - 5 3 7 3 ( 3 ) - 2 4 8 8 ( 3 ) - 8 2 3 ( 1 ) 1 6 ( 1 ) s i n , 1 1 0 5 ( 8 ) 0 ( 3 ) 1 ( 1 ) c o s , 1 - 1 8 1 ( 6 ) 2 ( 3 ) 0 ( 1 ) s i n , 2 4 ( 3 ) 0 ( 3 ) 1 ( 1 ) c o s , 2 - 2 ( 3 ) 2 ( 3 ) 0 ( 1 ) s i n , 3 - 5 ( 4 ) 0 ( 3 ) - l ( 1 ) c o s , 3 - 3 ( 4 ) 1 ( 3 ) 0 ( 1 ) s i n , 4 - 1 2 ( 5 ) 2 ( 4 ) - 5 ( 1 ) ' c o s , 4 - 7 ( 6 ) 2 ( 4 ) 0 ( 1 ) T a b l e 5 . 3 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r s z T e 4 , o o ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 S m [ l a ] 0 4 ( 1 ) 3 ( 1 ) 5 ( 1 ) 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) s i n , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) c o s , 1 - 3 ( 1 ) 1 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) s i n , 2 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 2 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) s i n , 3 0 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 3 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) s i n , 4 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) c o s , 4 - l ( l ) 1 ( 1 ) - l ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 3 4 5 T a b l e 5 . 3 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r s z T e 4 _ 9 o ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . S m [ 1 b ] 0 4 ( 1 ) 3 ( 1 ) 5 ( 1 ) 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) s i n , 1 2 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 - 2 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) s i n , 2 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 2 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) s i n , 3 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 3 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) s i n , 4 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) - l ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 4 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) S m [ 2 b ] 0 5 ( 1 ) 5 ( 1 ) 8 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) s i n , 1 0 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) c o s , 1 - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) s i n , 2 0 ( 1 ) - l ( l ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 2 0 ( 1 ) - 2 ( 1 ) 2 ( 1 ) 1 ( 1 ) 1 ( 1 ) 4 ( 1 ) s i n , 3 0 ( 1 ) 2 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 2 0 ) c o s , 3 - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 2 ( 1 ) 1 ( 1 ) 3 ( 1 ) s i n , 4 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 1 ( 1 ) c o s , 4 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) S m [ 2 a ] 0 5 ( 1 ) 5 ( 1 ) 8 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) s i n , 1 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) c o s , 1 - l ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) s i n , 2 - l ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) 2 ( 1 ) c o s , 2 0 ( 1 ) - 1 ( 1 ) - l ( 1 ) - 1 ( 1 ) - 1 ( 1 ) - 3 ( 1 ) s i n , 3 2 ( 1 ) 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 3 ( 1 ) c o s , 3 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) - 2 ( 1 ) s i n , 4 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 0 ( 1 ) c o s , 4 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 3 4 6 T a b l e 5 . 3 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r s z T e 4 _ 9 o ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ l b ] 0 4 ( 1 ) 4 ( 1 ) 5 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) s i n , l 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) c o s , 1 - 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) s i n , 2 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) c o s , 2 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 2 ( 1 ) s i n , 3 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) c o s , 3 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) s i n , 4 0 ( 1 ) - 1 ( 1 ) 0 ( 1 ) - 1 ( 1 ) - l ( l ) 0 ( 1 ) c o s , 4 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) T e [ l a ] 0 4 ( 1 ) 4 ( 1 ) 5 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) s i n , 1 - 1 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 - l ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) s i n , 2 1 ( 1 ) - 1 ( 1 ) 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) c o s , 2 - 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) s i n , 3 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 3 1 ( 1 ) 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 2 ( 1 ) s i n , 4 0 ( 1 ) - 1 ( 1 ) 1 ( 1 ) 1 ( 1 ) 1 ( 1 ) 1 ( 1 ) c o s , 4 0 ( 1 ) - 2 ( 1 ) - 1 ( 1 ) 1 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) T e [ 2 a ] 0 4 ( 1 ) 4 ( 1 ) 5 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) s i n , 1 - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) c o s , 1 - 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) s i n , 2 - 1 ( 1 ) - 1 ( 1 ) 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) c o s , 2 - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) s i n , 3 - 2 ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) 1 ( 1 ) - 1 ( 1 ) c o s , 3 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) s i n , 4 2 ( 1 ) - l ( l ) - 2 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 1 ( 1 ) c o s , 4 0 ( 1 ) - 2 ( 1 ) 2 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 3 4 7 T a b l e 5 . 3 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r s z T e 4 _ o o ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 2 b ] 0 4 ( 1 ) 4 ( 1 ) 5 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) s i n , 1 2 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) s i n , 2 - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 2 0 ( 1 ) - 1 ( 1 ) - 2 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 2 ( 1 ) s i n , 3 - 3 ( 1 ) - 3 ( 1 ) 2 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) c o s , 3 2 ( 1 ) 0 ( 1 ) 1 ( 1 ) - 2 ( 1 ) 0 ( 1 ) - 1 ( 1 ) s i n , 4 - 1 ( 1 ) 3 ( 1 ) 1 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 0 ( 1 ) c o s , 4 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) - 2 ( 1 ) 1 ( 1 ) - 1 ( 1 ) T e [ 3 a ] 0 2 1 ( 1 ) 2 5 ( 1 ) 7 ( 1 ) - 2 ( 1 ) 0 ( 1 ) 0 ( 1 ) s i n , 1 - 1 5 ( 1 ) 1 ( 2 ) 1 3 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) c o s , 1 6 ( 1 ) - 7 ( 1 ) 1 1 ( 1 ) - 6 ( 1 ) 1 ( 1 ) - 3 ( 1 ) s i n , 2 9 ( 1 ) - 1 3 ( 1 ) 6 ( 1 ) - 1 ( 1 ) 1 ( 1 ) 2 ( 1 ) c o s , 2 - 4 ( 1 ) - 8 ( 1 ) 0 ( 1 ) - 1 6 ( 1 ) 1 ( 1 ) 0 ( 1 ) s i n , 3 - l ( l ) - 1 1 ( 1 ) - 2 ( 1 ) 1 8 ( 1 ) - 1 ( 1 ) 1 ( 1 ) c o s , 3 8 ( 1 ) - 9 ( 1 ) 9 ( 1 ) 4 ( 1 ) 3 ( 1 ) 0 ( 1 ) s i n , 4 - 1 ( 2 ) - 2 ( 2 ) 6 ( 1 ) 4 ( 1 ) 1 ( 1 ) 4 0 ) c o s , 4 - 2 ( 2 ) 1 ( 2 ) 3 ( 2 ) - 7 ( 1 ) 1 ( 1 ) 0 ( 1 ) T e [ 3 b ] 0 2 1 ( 1 ) 2 5 ( 1 ) 7 ( 1 ) - 2 ( 1 ) 0 ( 1 ) 0 ( 1 ) s i n , 1 6 ( 1 ) 4 ( 1 ) - 3 ( 1 ) 0 ( 1 ) 0 ( 1 ) 5 ( 1 ) c o s , 1 3 ( 1 ) 9 ( 1 ) 2 ( 1 ) - 4 ( 1 ) 0 ( 1 ) - 1 ( 1 ) s i n , 2 - 2 ( 1 ) - 1 9 ( 1 ) 3 ( 1 ) - 3 ( 1 ) - 1 ( 1 ) 2 0 ) c o s , 2 1 0 ( 1 ) 6 ( 1 ) 1 ( 1 ) - 1 5 ( 1 ) - 2 ( 1 ) 0 ( 1 ) s i n , 3 - 1 0 ( 1 ) 4 ( 2 ) 0 ( 1 ) - 1 2 ( 1 ) - 2 ( 1 ) 2 ( 1 ) c o s , 3 6 ( 1 ) 2 2 ( 1 ) - 3 ( 1 ) - 3 ( 1 ) 0 ( 1 ) 1 ( 1 ) s i n , 4 2 ( 1 ) 4 ( 1 ) - 5 ( 1 ) - 1 ( 1 ) - 3 ( 1 ) 2 ( 1 ) c o s , 4 4 ( 1 ) 2 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) - 2 ( 1 ) 3 4 8 T a b l e 5 . 3 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r s z T e 4 . 9 0 ( I ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 4 a ] 0 5 ( 1 ) 4 ( 1 ) 6 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) s i n , 1 - 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) - l ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 4 ( 1 ) 1 ( 1 ) - 1 ( 1 ) 4 ( 1 ) 0 ( 1 ) 1 ( 1 ) s i n , 2 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 2 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) s i n , 3 - 2 ( 1 ) 0 ( 1 ) 2 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 3 - 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) s i n , 4 - 1 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) c o s , 4 - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) - 2 ( 1 ) 1 ( 1 ) T e [ 4 b ] 0 5 ( 1 ) 4 ( 1 ) 6 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) s i n , 1 0 ( 1 ) - 2 ( 1 ) 1 ( 1 ) - 2 ( 1 ) 0 ( 1 ) - 1 ( 1 ) c o s , 1 2 ( 1 ) 3 ( 1 ) 0 ( 1 ) 2 ( 1 ) 1 ( 1 ) 0 ( 1 ) s i n , 2 0 ( 1 ) - 1 ( 1 ) 1 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) c o s , 2 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) - l ( 1 ) 1 ( 1 ) s i n , 3 3 ( 1 ) - 1 ( 1 ) 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 3 1 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) - l ( 1 ) s i n , 4 2 ( 1 ) 3 ( 1 ) 1 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 3 ( 1 ) c o s , 4 - 1 ( 1 ) 2 ( 1 ) - 1 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 0 ( 1 ) T e [ 5 a ] 0 6 ( 1 ) 5 ( 1 ) 6 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) s i n , 1 0 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) 1 ( 1 ) 1 ( 1 ) - 2 ( 1 ) c o s , 1 - 6 ( 1 ) 1 ( 1 ) 0 ( 1 ) - 3 ( 1 ) 0 ( 1 ) 1 ( 1 ) s i n , 2 - 3 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) c o s , 2 - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) s i n , 3 - 2 ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 3 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) s i n , 4 - 2 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 1 ( 1 ) - 1 ( 1 ) 1 ( 1 ) c o s , 4 0 ( 1 ) 3 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 4 ( 1 ) - 1 ( 1 ) 3 4 9 T a b l e 5 . 3 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r s z T e 4 , 9 o ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ S b ] 0 s i n , 1 c o s , 1 s i n , 2 c o s , 2 s i n , 3 c o s , 3 s i n , 4 c o s , 4 6 ( 1 ) 4 ( 1 ) - 7 ( 1 ) 1 ( 1 ) 0 ( 1 ) 2 ( 1 ) 1 ( 1 ) 1 ( 1 ) - 2 ( 1 ) 5 ( 1 ) - 2 ( 1 ) 2 ( 1 ) 0 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) - 2 ( 1 ) - 2 ( 1 ) 2 ( 1 ) 6 ( 1 ) 1 ( 1 ) 2 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) 2 ( 1 ) 0 ( 1 ) 3 ( 1 ) - 2 ( 1 ) 0 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) - 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) 2 ( 1 ) 0 ( 1 ) T a b l e 5 . 4 . F o u r i e r c o m p o n e n t s o f t h e o c c u p a t i o n a l m o d u l a t i o n f o r s z T e a o o m a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e O c c u p a t i o n a l c o m p o n e n t T e [ 3 a ] s i n , 1 0 . 0 4 7 ( 9 ) c o s , 1 0 . 0 0 9 ( 5 ) T e [ 3 a ] s i n , 2 0 . 0 8 2 ( 1 3 ) c o s , 2 - 0 . 1 9 7 ( 6 ) T e [ 3 a ] s i n , 3 - 0 . 1 5 3 ( 1 0 ) c o s , 3 0 . 1 4 7 ( 1 2 ) T e [ 3 a ] s i n , 4 0 . 0 1 1 ( 1 3 ) c o s , 4 - 0 . 0 0 4 ( l 3 ) T a b l e 5 . 5 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r s z T e 4 _ 9 o ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e S m [ l a ] - T e [ l a ] x 4 3 . 2 1 1 ( 7 ) 3 . 1 9 2 ( 7 ) 3 . 2 3 0 ( 7 ) S m [ l a ] - T e [ 2 a ] 3 . 2 5 7 ( 8 ) 3 . 2 4 7 ( 8 ) 3 . 2 6 7 ( 8 ) S m [ l a ] - T e [ 4 a ] x 2 3 . 2 9 6 ( 8 ) 3 . 2 8 6 ( 8 ) 3 . 3 1 0 ( 8 ) S m [ l a ] - T e [ 5 a ] x 2 3 . 2 8 0 ( 8 ) 3 . 2 3 6 ( 8 ) 3 . 3 1 9 ( 8 ) S m [ 1 b ] - T e [ l b ] x 4 3 . 2 0 0 ( 7 ) 3 . 1 7 4 ( 7 ) 3 . 2 2 1 ( 7 ) S m [ 1 b ] - T e [ 2 b ] 3 . 2 4 6 ( 8 ) 3 . 2 3 1 ( 8 ) 3 . 2 6 4 ( 8 ) S m [ 1 b ] - T e [ 4 b ] x 2 3 . 3 2 8 ( 8 ) 3 . 3 1 6 ( 8 ) 3 . 3 4 2 ( 8 ) 3 5 0 T a b l e 5 . 5 . ( C o n t ’ d ) B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r s z T e 4 , 9 o ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . S m [ 1 b ] - T e [ 5 b ] S m [ l b ] — T e [ 5 b ] S m [ 2 b ] - T e [ l b ] S m [ 2 b ] - T e [ 2 b ] x 4 S m [ 2 b ] - T e [ 3 a ] S m [ 2 b ] - T e [ 3 a ] S m [ 2 b ] - T e [ 3 b ] x 2 S m [ 2 a ] - T e [ l a ] S m [ 2 a ] - T e [ 2 a ] x 4 S m [ 2 a ] - T e [ 3 a ] x 2 S m [ 2 a ] - T e [ 3 b ] S m [ 2 a ] - T e [ 3 b ] T e [ 3 a ] - T e [ 3 b ] x 4 T e [ 4 a ] - T e [ 5 a ] x 4 T e [ 4 b ] - T e [ 5 b ] x 3 T e [ 4 b ] - T e [ 5 b ] 3 . 3 0 6 ( 9 ) 3 . 3 2 5 ( 9 ) 3 . 1 9 9 ( 8 ) 3 . 1 9 0 ( 8 ) 3 . 2 5 8 ( 1 4 ) 3 . 3 1 6 ( 1 4 ) 3 . 2 8 2 ( 1 0 ) 3 . 1 8 0 ( 8 ) 3 . 1 9 0 ( 7 ) 3 . 2 7 3 ( 1 4 ) 3 . 2 4 8 ( 1 1 ) 3 . 3 0 5 ( 1 1 ) 3 . 0 8 3 ( 1 9 ) 3 . 0 7 5 ( 1 0 ) 3 . 0 6 8 ( 1 0 ) 3 . 0 8 9 ( 1 0 ) 3 . 2 5 4 ( 9 ) 3 . 2 7 6 ( 8 ) 3 . 1 6 6 ( 8 ) 3 . 1 7 0 ( 8 ) 3 . 1 1 4 ( 1 3 ) 3 . 2 0 8 ( 1 3 ) 3 . 2 1 5 ( 9 ) 3 . 1 5 4 ( 8 ) 3 . 1 6 3 ( 7 ) 3 . 1 8 0 ( 1 2 ) 3 . 1 6 4 ( 1 1 ) 3 . 2 2 6 ( 1 0 ) 2 . 8 3 3 ( 1 8 ) 2 . 9 5 2 ( 1 0 ) 2 . 9 5 7 ( 1 0 ) 2 . 9 7 0 ( 1 0 ) 3 . 3 5 1 ( 9 ) 3 . 3 7 4 ( 8 ) 3 . 2 3 4 ( 8 ) 3 . 2 1 2 ( 8 ) 3 . 3 6 2 ( 1 4 ) 3 . 4 4 5 ( 1 4 ) 3 . 3 5 4 ( 9 ) 3 . 2 0 0 ( 8 ) 3 . 2 1 5 ( 7 ) 3 . 3 8 7 ( 1 2 ) 3 . 3 2 3 ( 1 1 ) 3 . 3 9 5 ( 1 1 ) 3 . 3 5 1 ( 1 9 ) 3 . 1 9 6 ( 1 0 ) 3 . 1 8 4 ( 1 0 ) 3 . 2 0 7 ( 1 0 ) T a b l e 5 . 6 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r s z T e 4 , 9 o ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ l a ] - S m [ 1 a ] - T e [ l a ] x 8 8 5 3 5 ( 1 9 ) 8 4 . 6 7 ( 1 8 ) 8 5 . 9 9 ( 1 9 ) T e [ l a ] - S m [ 1 a ] - T e [ l a ] x 4 1 4 5 . 9 ( 2 ) 1 4 5 . 4 ( 2 ) 1 4 6 . 3 ( 2 ) T e [ l a ] - S m [ 1 a ] - T e [ 2 a ] x 4 7 3 . 0 0 ( 1 8 ) 7 2 3 8 ( 1 7 ) 7 3 . 5 3 ( 1 8 ) T e [ l a ] - S m [ 1 a ] - T e [ 4 a ] x 4 7 7 . 2 ( 2 ) 7 5 . 5 ( 2 ) 7 8 . 8 ( 2 ) T e [ l a ] - S m [ 1 a ] - T e [ 4 a ] x 4 1 3 2 . 3 ( 2 ) 1 2 9 . 7 ( 2 ) 1 3 4 . 5 ( 2 ) T e [ l a ] - S m [ 1 a ] - T e [ 5 a ] x 4 7 7 . 2 3 ( 1 9 ) 7 6 . 7 0 ( 1 9 ) 7 7 . 6 7 ( 1 9 ) T e [ l a ] - S m [ 1 a ] - T e [ 5 a ] x 4 1 3 1 . 8 ( 2 ) 1 3 1 . 3 ( 2 ) 1 3 2 . 4 ( 2 ) T e [ 2 a ] - S m [ 1 a ] - T e [ 4 a ] x 2 1 3 8 . 5 ( 2 ) 1 3 8 . 2 ( 2 ) 1 3 8 . 9 ( 2 ) T e [ 2 a ] - S m [ 1 a ] - T e [ 5 a ] x 2 1 3 9 . 0 ( 2 ) 1 3 8 . 4 ( 2 ) 1 3 9 . 5 ( 2 ) T e [ 4 a ] - S m [ 1 a ] - T e [ 4 a ] x 2 8 2 . 6 3 ( l 9 ) 8 2 . 2 4 ( l 9 ) 8 2 . 9 7 ( 1 9 ) T e [ 4 a ] - S m [ 1 a ] - T e [ 5 a ] x 4 5 6 . 0 4 ( 1 9 ) 5 4 . 0 0 ( 1 8 ) 5 8 . 1 2 ( 1 8 ) T e [ 5 a ] - S m [ 1 a ] - T e [ S a ] x 2 8 2 . 6 ( 2 ) 8 2 . 5 ( 2 ) 8 2 . 7 ( 2 ) T e [ l b ] - S m [ 1 b ] - T e [ l b ] x 8 8 5 . 6 9 ( 1 8 ) 8 4 . 9 4 ( 1 8 ) 8 6 . 4 6 ( 1 8 ) 3 5 1 T a b l e 5 . 6 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r s z T e a o o u ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ l b ] - S m [ 1 b ] - T e [ l b ] x 4 T e [ l b ] - S m [ 1 b ] - T e [ 2 b ] x 4 T e [ l b ] - S m [ 1 b ] - T e [ 4 b ] x 4 T e [ l b ] - S m [ 1 b ] - T e [ 4 b ] x 4 T e [ l b ] - S m [ 1 b ] - T e [ 5 b ] x 4 T e [ l b ] - S m [ 1 b ] - T e [ 5 b ] x 4 T e [ 2 b ] - S m [ 1 b ] - T e [ 4 b ] x 2 T e [ 2 b ] - S m [ 1 b ] - T e [ 5 b ] x 2 T e [ 4 b ] - S m [ l b ] - T e [ 4 b ] x 2 T e [ 4 b ] - S m [ 1 b ] - T e [ 5 b ] x 4 T e [ 5 b ] - S m [ 1 b ] - T e [ 5 b ] x 2 T e [ l b ] - S m [ 2 b ] - T e [ 2 b ] x 4 T e [ l b ] - S m [ 2 b ] - T e [ 3 a ] x 2 T e [ l b ] - S m [ 2 b ] - T e [ 3 b ] x 2 T e [ 2 b ] - S m [ 2 b ] - T e [ 2 b ] x 8 T e [ 2 b ] - S m [ 2 b ] - T e [ 2 b ] x 4 T e [ 2 b ] - S m [ 2 b ] - T e [ 3 a ] x 4 T e [ 2 b ] - S m [ 2 b ] - T e [ 3 a ] x 4 T e [ 2 b ] - S m [ 2 b ] - T e [ 3 b ] x 3 T e [ 2 b ] - S m [ 2 b ] - T e [ 3 b ] x 4 T e [ 2 b ] - S m [ 2 b ] - T e [ 3 b ] T e [ 3 a ] - S m [ 2 b ] - T e [ 3 a ] x 2 T e [ 3 a ] - S m [ 2 b ] - T e [ 3 b ] x 4 T e [ 3 b ] - S m [ 2 b ] - T e [ 3 b ] x 2 T e [ l a ] - S m [ 2 a ] - T e [ 2 a ] x 4 T e [ l a ] - S m [ 2 a ] - T e [ 3 a ] x 2 T e [ l a ] - S m [ 2 a ] - T e [ 3 b ] x 2 T e [ 2 a ] - S m [ 2 a ] - T e [ 2 a ] x 8 T e [ Z a ] - S m [ Z a ] - T e [ 2 a ] x 4 T e [ 2 a ] - S m [ 2 a ] - T e [ 3 a ] x 4 T e [ 2 a ] - S m [ 2 a ] - T e [ 3 a ] x 4 T e [ 2 a ] - S m [ 2 a ] - T e [ 3 b ] x 4 T e [ 2 a ] - S m [ Z a ] - T e [ 3 b ] x 4 T e [ 3 a ] - S m [ 2 a ] - T e [ 3 a ] x 2 1 4 7 . 0 ( 2 ) 7 3 . 5 4 ( 1 8 ) 7 6 . 9 1 ( 1 9 ) 1 3 1 . 7 ( 2 ) 7 7 . 1 ( 2 ) 1 3 1 . 2 ( 2 ) 1 3 8 . 9 ( 2 ) 1 3 9 . 5 ( 2 ) 8 1 . 7 4 ( l 9 ) 5 5 5 0 ( 1 9 ) 8 1 . 7 ( 2 ) 7 4 . 3 4 ( l 9 ) 1 3 9 . 0 ( 3 ) 1 3 8 . 8 ( 3 ) 8 6 . 1 ( 2 ) 1 4 8 . 6 ( 2 ) 7 6 . 0 ( 3 ) 1 3 1 . 3 ( 3 ) 7 6 . 3 ( 2 ) 1 3 1 . 3 ( 3 ) 7 5 . 1 ( 2 ) 8 3 . 1 ( 3 ) 5 6 . 0 ( 3 ) 8 2 . 8 ( 3 ) 7 4 . 2 3 ( 1 8 ) 1 3 8 . 7 ( 3 ) 1 3 9 . 0 ( 2 ) 8 6 0 0 ( 1 8 ) 1 4 8 . 5 ( 2 ) 7 6 . 5 ( 3 ) 1 3 1 . 6 ( 3 ) 7 6 . 1 ( 2 ) 1 3 1 . 4 ( 3 ) 8 3 . 0 ( 3 ) 1 4 6 . 4 ( 2 ) 7 3 . 0 9 ( 1 8 ) 7 5 . 2 9 ( 1 9 ) 1 2 9 . 5 ( 2 ) 7 6 . 4 2 ( 1 9 ) 1 3 0 . 5 ( 2 ) 1 3 8 . 5 ( 2 ) 1 3 8 . 7 ( 2 ) 8 1 . 4 2 ( l 9 ) 5 3 . 4 7 ( l 9 ) 8 1 . 5 ( 2 ) 7 3 . 6 7 ( 1 9 ) 1 3 6 . 4 ( 3 ) 1 3 6 . 6 ( 3 ) 8 5 . 6 3 ( 1 9 ) 1 4 7 . 1 ( 2 ) 7 2 . 8 ( 3 ) 1 2 7 . 7 ( 3 ) 7 4 . 4 ( 2 ) 1 2 8 . 4 ( 3 ) 7 3 . 3 ( 2 ) 7 6 . 6 ( 3 ) 5 2 . 1 ( 3 ) 7 8 . 0 ( 3 ) 7 3 . 5 7 ( 1 8 ) 1 3 5 . 9 ( 3 ) 1 3 6 . 9 ( 2 ) 8 5 5 5 ( 1 8 ) 1 4 7 . 2 ( 2 ) 7 3 . 5 ( 3 ) 1 2 7 . 9 ( 3 ) 7 3 . 9 ( 2 ) 1 2 9 . 0 ( 3 ) 7 7 . 4 ( 3 ) 1 4 7 . 6 ( 2 ) 7 4 . 1 5 ( 1 8 ) 7 8 3 0 ( 1 9 ) 1 3 3 . 7 ( 2 ) 7 7 . 8 ( 2 ) 1 3 2 . 0 ( 2 ) 1 3 9 . 3 ( 2 ) 1 4 0 . 3 ( 2 ) 8 2 . 1 5 ( 1 9 ) 5 7 . 5 ( 2 ) 8 1 . 9 ( 2 ) 7 5 0 4 ( 1 9 ) 1 4 2 . 6 ( 3 ) 1 4 1 . 1 ( 3 ) 8 6 . 5 ( 2 ) 1 5 0 . 2 ( 2 ) 7 9 . 2 ( 3 ) 1 3 4 . 6 ( 3 ) 7 8 . 9 ( 2 ) 1 3 3 . 9 ( 3 ) 7 7 . 0 ( 2 ) 8 8 . 4 ( 3 ) 6 0 . 9 ( 3 ) 8 7 . 1 ( 3 ) 7 4 . 9 8 ( 1 8 ) 1 4 1 . 6 ( 3 ) 1 4 1 . 9 ( 2 ) 8 6 5 5 ( 1 8 ) 1 4 9 . 9 ( 2 ) 8 0 . 2 ( 3 ) 1 3 5 . 8 ( 3 ) 7 8 . 2 ( 2 ) 1 3 3 . 6 ( 3 ) 8 7 . 9 ( 3 ) 3 5 2 T a b l e 5 . 6 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r s z T e 4 _ 9 o ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 3 a ] - S m [ 2 a ] - T e [ 3 b ] x 4 T e [ 3 b ] - S m [ 2 a ] - T e [ 3 b ] x 2 S m [ 1 b ] - T e [ l b ] - S m [ 1 b ] x 8 S m [ 1 b ] - T e [ l b ] - S m [ 1 b ] x 4 S m [ 1 b ] - T e [ l b ] - S m [ 2 b ] x 4 S m [ 1 a ] - T e [ l a ] - S m [ 1 a ] x 8 S m [ 1 a ] - T e [ l a ] - S m [ 1 a ] x 4 S m [ 1 a ] - T e [ l a ] - S m [ 2 a ] x 4 S m [ 1 a ] - T e [ 2 a ] - S m [ 2 a ] x 4 S m [ 2 a ] - T e [ 2 a ] - S m [ 2 a ] x 8 S m [ 2 a ] — T e [ 2 a ] - S m [ 2 a ] x 4 S m [ 1 b ] - T e [ 2 b ] - S m [ 2 b ] x 4 S m [ 2 b ] - T e [ 2 b ] - S m [ 2 b ] x 8 S m [ 2 b ] - T e [ 2 b ] - S m [ 2 b ] x 4 S m [ 2 b ] - T e [ 3 a ] - S m [ 2 b ] x 2 S m [ 2 b ] - T e [ 3 a ] - S m [ 2 a ] x 4 S m [ 2 b ] - T e [ 3 a ] - T e [ 3 b ] x 4 S m [ 2 b ] - T e [ 3 a ] - T e [ 3 b ] x 4 S m [ 2 a ] - T e [ 3 a ] - S m [ 2 a ] x 2 S m [ 2 a ] - T e [ 3 a ] - T e [ 3 b ] x 4 S m [ 2 a ] - T e [ 3 a ] - T e [ 3 b ] x 4 T e [ 3 b ] - T e [ 3 a ] - T e [ 3 b ] x 8 T e [ 3 b ] - T e [ 3 a ] - T e [ 3 b ] x 4 S m [ 2 b ] - T e [ 3 b ] - S m [ 2 b ] x 2 S m [ 2 b ] - T e [ 3 b ] - S m [ 2 a ] x 4 S m [ 2 b ] - T e [ 3 b ] - T e [ 3 a ] x 4 S m [ 2 b ] - T e [ 3 b ] - T e [ 3 a ] x 4 S m [ 2 a ] - T e [ 3 b ] - S m [ 2 a ] x 2 S m [ 2 a ] - T e [ 3 b ] - T e [ 3 a ] x 4 S m [ Z a ] - T e [ 3 b ] - T e [ 3 a ] x 4 T e [ 3 a ] - T e [ 3 b ] - T e [ 3 a ] x 8 T e [ B a ] - T e [ 3 b ] - T e [ 3 a ] x 4 S m [ 1 a ] - T e [ 4 a ] - S m [ 1 a ] x 2 S m [ 1 a ] - T e [ 4 a ] - T e [ 5 a ] x 4 5 6 . 3 ( 3 ) 8 3 . 1 ( 3 ) 8 5 . 3 2 0 9 ) 1 4 7 . 0 ( 2 ) 1 0 6 . 5 ( 2 ) 8 5 . 0 1 0 8 ) 1 4 5 . 8 ( 2 ) 1 0 7 . 1 ( 2 ) 1 0 5 . 6 ( 2 ) 8 5 . 7 7 ( 1 9 ) 1 4 8 . 5 ( 2 ) 1 0 5 . 6 ( 2 ) 8 5 . 7 7 ( 1 8 ) 1 4 8 . 7 ( 3 ) 8 2 . 9 ( 3 ) 1 2 2 . 8 ( 5 ) 6 1 . 6 ( 3 ) 1 1 8 . 2 ( 4 ) 8 2 . 8 ( 3 ) 6 1 . 3 ( 3 ) 1 1 7 . 1 ( 4 ) 9 0 . 1 ( 5 ) 1 7 7 . 9 ( 6 ) 8 2 . 7 ( 2 ) 1 2 3 . 0 ( 4 ) 6 1 . 5 ( 3 ) 1 1 7 . 2 ( 4 ) 8 3 . 1 ( 2 ) 6 1 . 6 ( 3 ) 1 1 8 . 3 ( 4 ) 9 0 . 2 ( 5 ) 1 7 8 . 2 ( 5 ) 8 2 . 6 0 0 9 ) 6 1 . 9 ( 2 ) 5 2 . 3 ( 3 ) 7 8 . 2 ( 3 ) 8 4 . 8 0 ( 1 9 ) 1 4 6 . 4 ( 2 ) 1 0 5 . 9 ( 2 ) 8 4 . 6 4 0 8 ) 1 4 5 . 3 ( 2 ) 1 0 6 . 5 ( 2 ) 1 0 4 . 8 ( 2 ) 8 5 . 3 7 0 9 ) 1 4 7 . 4 ( 2 ) 1 0 4 . 5 ( 2 ) 8 5 . 5 4 ( 1 8 ) 1 4 7 . 3 ( 3 ) 8 1 . 7 ( 3 ) l 1 6 . 0 ( 4 ) 5 8 . 6 ( 3 ) 1 1 5 . 7 ( 4 ) 8 2 . 2 ( 3 ) 5 7 . 5 ( 3 ) 1 1 3 . 0 ( 4 ) 8 7 . 1 ( 6 ) 1 7 5 . 5 ( 6 ) 8 1 . 5 ( 2 ) 1 1 8 . 8 ( 3 ) 5 8 . 7 ( 3 ) 1 1 5 . 2 ( 4 ) 8 2 . 3 ( 2 ) 5 9 . 8 ( 3 ) 1 1 6 . 4 ( 4 ) 8 6 . 0 ( 5 ) 1 7 5 . 0 ( 6 ) 8 2 . 2 3 0 9 ) 6 0 . 8 6 0 9 ) 6 1 . 4 ( 3 ) 8 7 . 0 ( 3 ) 8 5 . 7 9 0 9 ) 1 4 7 . 7 ( 2 ) 1 0 6 . 9 ( 2 ) 8 5 . 4 9 0 8 ) 1 4 6 . 7 ( 2 ) 1 0 7 . 5 ( 2 ) 1 0 6 . 7 ( 2 ) 8 6 . 1 9 0 9 ) 1 4 9 . 6 ( 2 ) 1 0 6 . 7 ( 2 ) 8 6 . 1 5 0 8 ) 1 5 0 . 1 ( 3 ) 8 3 . 7 ( 3 ) 1 2 9 . 9 ( 5 ) 6 4 . 6 ( 3 ) 1 2 1 . 7 ( 4 ) 8 4 . 0 ( 3 ) 6 5 . 3 ( 3 ) 1 2 0 . 5 ( 4 ) 9 4 . 3 ( 5 ) 1 8 0 8 3 . 6 ( 2 ) 1 2 7 . 8 ( 4 ) 6 4 . 4 ( 3 ) 1 1 9 . 9 ( 4 ) 8 3 . 9 ( 2 ) 6 4 . 4 ( 3 ) 1 2 0 . 4 ( 3 ) 9 3 . 3 ( 5 ) 1 8 0 8 2 . 9 0 0 9 ) 6 2 . 8 ( 2 ) 3 5 3 T a b l e 5 . 6 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r s z T e a o o m a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . S m [ 1 a ] - T e [ 4 a ] - T e [ 5 a ] x 4 T e [ 5 a ] - T e [ 4 a ] - T e [ 5 a ] x 8 T e [ 5 a ] - T e [ 4 a ] - T e [ S a ] x 4 S m [ 1 b ] - T e [ 4 b ] - S m [ 1 b ] x 2 S m [ 1 b ] - T e [ 4 b ] - T e [ 5 b ] x 4 S m [ 1 b ] - T e [ 4 b ] - T e [ 5 b ] x 4 T e [ 5 b ] - T e [ 4 b ] - T e [ 5 b ] x 8 T e [ 5 b ] - T e [ 4 b ] - T e [ 5 b ] x 4 S m [ 1 a ] - T e [ 5 a ] - S m [ 1 a ] x 2 S m [ l a ] - T e [ 5 a ] - T e [ 4 a ] x 4 S m [ l a ] - T e [ 5 a ] - T e [ 4 a ] x 4 T e [ 4 a ] - T e [ 5 a ] - T e [ 4 a ] x 8 T e [ 4 a ] - T e [ 5 a ] - T e [ 4 a ] x 4 S m [ 1 b ] - T e [ 5 b ] - S m [ 1 b ] x 2 S m [ 1 b ] - T e [ 5 b ] - T e [ 4 b ] x 4 S m [ 1 b ] - T e [ 5 b ] - T e [ 4 b ] x 4 T e [ 4 b ] - T e [ 5 b ] - T e [ 4 b ] x 8 T e [ 4 b ] - T e [ 5 b ] - T e [ 4 b ] x 4 1 1 7 . 5 ( 3 ) 9 0 . 0 ( 3 ) 1 7 7 . 6 ( 3 ) 8 1 . 7 2 0 9 ) 6 2 . 1 ( 2 ) 1 1 7 . 1 ( 3 ) 9 0 . 0 ( 3 ) 1 7 7 . 6 ( 3 ) 8 2 . 6 ( 2 ) 6 2 . 3 ( 2 ) 1 1 7 . 9 ( 3 ) 9 0 . 6 ( 3 ) 1 7 7 . 6 ( 3 ) 8 1 . 7 ( 2 ) 6 2 . 6 ( 2 ) 1 1 7 . 6 ( 2 ) 9 0 . 5 ( 3 ) 1 7 7 . 5 ( 3 ) 1 1 4 . 2 ( 3 ) 8 5 . 7 ( 3 ) 1 7 5 . 3 ( 3 ) 8 1 . 3 1 0 8 ) 6 1 . 4 9 0 9 ) 1 1 4 . 5 ( 3 ) 8 6 . 3 ( 3 ) 1 7 5 . 5 ( 3 ) 8 2 . 3 ( 2 ) 6 0 . 6 ( 2 ) 1 1 6 . 7 ( 3 ) 8 6 . 7 ( 3 ) 1 7 5 . 8 ( 3 ) 8 1 . 3 7 0 9 ) 6 0 . 7 7 0 9 ) 1 1 6 . 8 ( 3 ) 8 6 . 7 ( 3 ) 1 7 5 . 5 ( 3 ) 1 2 0 . 6 ( 3 ) 9 4 . 3 ( 3 ) 1 8 0 8 2 . 0 3 0 9 ) 6 2 . 8 ( 2 ) 1 1 9 . 8 ( 3 ) 9 3 . 8 ( 3 ) 1 7 9 . 6 ( 3 ) 8 2 . 9 ( 2 ) 6 3 . 9 ( 2 ) 1 1 9 . 1 ( 3 ) 9 4 . 1 ( 3 ) 1 8 0 8 2 . 0 7 0 9 ) 6 4 . 3 ( 2 ) 1 1 8 . 4 ( 3 ) 9 4 . 2 ( 3 ) 1 8 0 3 5 4 T a b l e 5 . 7 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r s z T e 4 . 9 0 ( . ) a t 5 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e fi i c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 1 8 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 3 o ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 3 o ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 3 ‘ o r d e r s a t e l l i t e s [ I > 3 o ( I ) ] R 1 3 t o r d e r s a t e l l i t e s ( a l l d a t a ) T . . . a n d T m . . . c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e S m 2 T 6 4 9 0 0 ) 9 2 6 5 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A T r i c l i n i c P 1 ( a B y ) 0 a = 4 . 3 5 0 6 ( 9 ) A , o = 9 0 ° b = 4 . 3 6 1 7 ( 9 ) A , 1 3 = 9 5 . 5 6 0 ( l 7 ) ° c = 2 2 . 0 0 8 ( 5 ) A , y = 9 0 ° 0 . 3 1 5 0 ) a ‘ + 0 . 3 1 5 0 ) h ‘ + 0 . 3 5 1 ( 6 ) c ‘ 4 1 5 . 6 6 0 5 ) A 3 2 7 . 3 9 6 g / c m 3 3 0 . 7 1 2 n n r n ' l 7 5 8 0 . 3 3 x 0 . 2 1 x 0 . 0 2 m m 3 1 . 8 6 t o 2 9 . 1 8 ° - 6 < = h < = 6 , - 6 < = k < = 6 , - 3 0 < = l < = 3 0 , - 1 < = m < = l 1 1 2 9 3 ( 3 2 8 2 m a i n + 8 0 1 1 s a t e l l i t e s ) 9 5 6 6 ( 2 7 8 8 m a i n + 6 8 0 4 s a t e l l i t e s ) [ R i m = 0 . 0 5 1 7 ] 9 4 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 9 5 6 6 / 4 2 / 3 3 5 2 . 3 9 R . . . = 0 . 0 4 5 9 , w R . . . = 0 . 1 6 6 3 R . . . = 0 . 0 9 2 0 , w R . . . = 0 . 2 0 1 7 R . . . = 0 . 0 4 2 8 , w R . . . = 0 . 1 6 2 1 R . . . = 0 . 0 4 6 7 , w R . . . = 0 . 1 9 1 2 R . . . = 0 . 1 1 2 7 , w R . . . = 0 . 2 4 9 2 R . . . = 0 . 4 0 9 3 , w R . . . = 0 . 3 6 1 6 0 . 0 0 9 5 a n d 0 . 5 1 4 7 2 . 8 2 a n d - 3 4 3 e . A ' 3 R = E I I F o l - I F c l l / 2 1 F . | . w R = { z l w t l F o F - 1 1 0 2 ) : ] / 2 1 w ( I F . l ‘ ) l } ” 2 a n d w = 1 / ( o z ( 1 ) + 0 . 0 0 1 6 1 2 ) 3 5 5 T a b l e 5 . 8 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r s z T e 4 . 9 o ( 1 ) a t 5 0 0 K w i t h e s t i m a t e d s t a n d a r d d e v i a t i o n s i n p a r e n t h e s e s . A t o m W a v e x y 2 O c c u p a n c y U . q S m [ 1 a ] 0 9 8 9 2 4 9 9 1 9 7 6 1 1 4 ( 1 ) s i n , 1 1 5 - 8 ( 4 ) - 1 ( 1 ) c o s , 1 - 3 ( 4 ) 0 ( 4 ) 1 ( 1 ) S m [ 1 b ] 0 - 9 9 3 ( 2 ) - 2 4 9 1 ( 2 ) - 1 9 7 9 ( 1 ) 1 1 4 ( 1 ) s i n , 1 - 1 ( 4 ) - 4 ( 4 ) 1 ( 1 ) c o s , 1 2 ( 4 ) - 6 ( 4 ) 0 ( 1 ) S m [ 2 b ] 0 3 0 9 6 ( 3 ) 2 5 0 5 ( 3 ) 6 1 3 6 ( 1 ) 1 1 6 ( 1 ) s i n , 1 - 6 ( 5 ) - 4 ( 5 ) 7 ( 1 ) c o s , 1 1 0 ( 4 ) 1 1 ( 4 ) 2 ( 2 ) S m [ 2 a ] 0 - 3 0 4 1 ( 3 ) — 2 4 9 l ( 3 ) - 6 1 3 4 ( l ) 1 1 6 ( 1 ) s i n , 1 - 8 ( 4 ) - 9 ( 4 ) - 6 ( 1 ) c o s , 1 4 ( 4 ) 8 ( 4 ) - 4 ( 2 ) T e [ l b ] 0 3 8 1 5 ( 4 ) 2 4 9 5 ( 4 ) 7 6 0 7 ( 1 ) 1 1 3 ( 1 ) s i n , 1 - 4 ( 5 ) - 6 ( 5 ) 3 ( 1 ) c o s , 1 5 ( 5 ) 1 ( 5 ) 1 ( 1 ) T e [ l a ] O - 3 7 9 8 ( 4 ) - 2 5 0 3 ( 4 ) - 7 5 9 3 ( 1 ) 1 1 3 ( 1 ) s i n , 1 - 5 ( 5 ) - 4 ( 5 ) - 3 ( 1 ) c o s , 1 - 1 ( 5 ) 1 ( 5 ) - 3 ( 1 ) T e [ Z a ] 0 1 7 7 4 ( 4 ) 2 5 3 2 ( 4 ) 3 4 7 1 ( 1 ) 1 1 4 ( 1 ) s i n , 1 - 3 ( 5 ) 4 ( 5 ) - l ( 1 ) c o s , 1 - 4 ( 5 ) 0 ( 5 ) - 1 ( 1 ) T e [ 2 b ] 0 - l 6 9 4 ( 4 ) - 2 4 6 2 ( 4 ) - 3 4 7 3 ( 1 ) 1 1 4 ( 1 ) s i n , 1 1 ( 5 ) - 2 ( 5 ) 3 ( 1 ) c o s , 1 3 ( 5 ) 3 ( 5 ) 2 ( 1 ) T e [ 3 a ] 0 2 5 6 1 ( 7 ) 7 5 4 0 ( 6 ) 4 9 8 4 ( 2 ) 0 . 8 0 4 ( 3 ) 3 5 ( 1 ) s i n , 1 - 6 5 ( 2 0 ) - 5 5 ( 2 0 ) - 2 ( 3 ) c o s , 1 1 1 0 ( 1 6 ) 1 3 2 ( 1 4 ) - 3 ( 2 ) T e [ 3 b ] 0 - 2 4 5 2 ( 5 ) - 7 4 6 5 ( 5 ) - 5 0 1 4 ( 1 ) 1 3 5 ( 1 ) s i n , 1 - 5 5 ( 1 7 ) - 3 3 ( 1 9 ) 1 ( 2 ) c o s , 1 8 5 ( 1 2 ) 9 7 ( 9 ) 2 ( 2 ) 3 5 6 T a b l e 5 . 8 . ( C o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r s z T e a o o m a t 5 0 0 K w i t h e s t i m a t e d s t a n d a r d d e v i a t i o n s i n p a r e n t h e s e s . T e [ 4 a ] 0 4 3 4 ( 5 ) 7 4 8 9 ( 4 ) 8 2 7 ( 1 ) 1 9 ( 1 ) s i n , 1 2 ( 7 ) 2 ( 6 ) - 2 ( 2 ) c o s , 1 - 2 ( 7 ) 0 ( 6 ) 0 ( 2 ) T e [ 4 b ] 0 - 3 8 3 ( 5 ) - 7 5 1 7 ( 5 ) - 8 3 9 ( 1 ) 1 9 ( 1 ) s i n , 1 - 8 ( 7 ) - 2 ( 7 ) 0 ( 2 ) c o s , 1 - 7 ( 7 ) 4 ( 7 ) - 1 ( 2 ) T e [ 5 a ] 0 5 4 1 2 ( 4 ) 2 4 8 0 ( 4 ) 8 2 8 ( 1 ) 2 0 ( 1 ) s i n , 1 - 1 0 ( 7 ) - 1 ( 7 ) - 2 ( 2 ) c o s , 1 - 4 ( 7 ) - 3 ( 7 ) - 1 ( 2 ) T e [ 5 b ] 0 - 5 4 2 5 ( 4 ) - 2 5 2 0 ( 4 ) - 8 3 7 ( 1 ) 2 0 ( 1 ) s i n , 1 - l ( 6 ) - 2 ( 7 ) 0 ( 2 ) c o s , 1 - l ( 7 ) - 4 ( 6 ) - 2 ( 2 ) T a b l e 5 . 9 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r s z T e 4 , 9 o ( . ) a t 5 0 0 K w i t h e s t i m a t e d s t a n d a r d d e v i a t i o n s i n p a r e n t h e s e s . A t o m W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 S m [ l a ] 0 1 3 ( 1 ) 1 2 ( 1 ) 1 7 ( 1 ) 0 ( 1 ) 2 ( 1 ) 2 ( 1 ) s i n , 1 0 ( 1 ) - 1 0 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 0 ) c o s , 1 - 1 0 ) 1 ( 1 ) - 1 0 ) - 1 0 ) - 1 0 ) 0 ( 1 ) S m [ 1 b ] 0 1 3 ( 1 ) 1 2 ( 1 ) 1 7 ( 1 ) 0 ( 1 ) 2 ( 1 ) 2 ( 1 ) s i n , 1 1 ( 1 ) — 1 0 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) c o s , 1 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) S m [ 2 b ] 0 1 4 ( 1 ) 1 4 ( 1 ) 2 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) s i n , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 2 ( 1 ) c o s , 1 1 ( 1 ) 0 ( 1 ) - 1 0 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) S m [ 2 a ] 0 1 4 ( 1 ) 1 4 ( 1 ) 2 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) s i n , 1 - 1 0 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) - 2 0 ) - 1 0 ) c o s , 1 0 ( 1 ) 1 ( 1 ) - 1 0 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) T e [ l b ] 0 1 3 ( 1 ) 1 2 ( 1 ) 1 6 ( 1 ) 0 ( 1 ) 2 ( 1 ) 1 ( 1 ) s i n , 1 0 ( 1 ) - 1 0 ) 1 ( 1 ) _ 1 ( 1 ) 1 ( 1 ) 1 ( 1 ) c o s , 1 0 ( 1 ) - 1 0 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 3 5 7 T a b l e 5 . 9 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r s z T e 4 , 9 o ( . ) a t 5 0 0 K w i t h e s t i m a t e d s t a n d a r d d e v i a t i o n s i n p a r e n t h e s e s . T e [ l a ] 0 1 3 ( 1 ) 1 2 ( 1 ) 1 6 ( 1 ) 0 ( 1 ) 2 ( 1 ) 1 ( 1 ) s i n , 1 0 ( 1 ) 1 ( 1 ) - 1 0 ) 0 ( 1 ) - 1 0 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) - 1 0 ) - 1 0 ) 0 ( 1 ) 0 ( 1 ) T e [ 2 a ] 0 1 3 ( 1 ) 1 2 ( 1 ) 1 8 ( 1 ) 0 ( 1 ) 1 ( 1 ) 2 ( 1 ) s i n , 1 - l ( 1 ) 0 ( 1 ) - 2 ( 1 ) 0 ( 1 ) - 2 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) - 1 0 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) T e [ 2 b ] 0 1 3 ( 1 ) 1 2 ( 1 ) 1 8 ( 1 ) 0 ( 1 ) 1 ( 1 ) 2 ( 1 ) s i n , 1 0 ( 1 ) 0 ( 1 ) - 1 0 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) c o s , 1 1 ( 1 ) 1 ( 1 ) - 1 0 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) T e [ 3 a ] 0 4 3 ( 1 ) 4 3 ( 1 ) 1 9 ( 1 ) - 3 0 ) 1 ( 1 ) 2 ( 1 ) s i n , 1 - 8 ( 3 ) - 6 ( 3 ) 1 ( 2 ) - 9 ( 2 ) 1 ( 2 ) . 1 0 ) c o s , 1 1 0 ( 3 ) 8 ( 3 ) - 6 ( 2 ) - 1 ( 2 ) 3 ( 2 ) - 3 ( 2 ) T e [ 3 b ] 0 4 3 ( 1 ) 4 3 ( 1 ) 1 9 ( 1 ) - 3 0 ) 1 ( 1 ) 2 ( 1 ) s i n , 1 8 ( 3 ) 1 2 ( 3 ) 1 ( 2 ) - 1 2 ( 2 ) - 2 0 ) 1 ( 1 ) c o s , 1 1 5 ( 2 ) 1 6 ( 3 ) - 2 ( 2 ) - 1 ( 3 ) - 3 0 ) 3 ( 1 ) T e [ 4 a ] 0 2 0 ( 1 ) 1 8 ( 1 ) 2 0 ( 1 ) 1 ( 1 ) 3 ( 1 ) 1 ( 1 ) s i n , 1 0 ( 1 ) 0 ( 1 ) - 2 0 ) - 1 0 ) - 1 0 ) - 2 0 ) c o s , 1 - 1 0 ) - 1 0 ) - 1 0 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) T e [ 4 b ] 0 2 0 ( 1 ) 1 8 ( 1 ) 2 0 ( 1 ) 1 ( 1 ) 3 ( 1 ) 1 ( 1 ) s i n , 1 0 ( 1 ) 0 ( 1 ) 2 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) T e [ 5 a ] 0 2 0 ( 1 ) 1 9 ( 1 ) 2 1 ( 1 ) 1 ( 1 ) 2 ( 1 ) 2 ( 1 ) s i n , 1 - 1 0 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) c o s , 1 1 ( 1 ) 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 0 ) T e [ 5 b ] 0 2 0 ( 1 ) 1 9 ( 1 ) 2 1 ( 1 ) 1 ( 1 ) 2 ( 1 ) 2 ( 1 ) s i n , 1 - 1 0 ) 0 ( 1 ) - 1 0 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 - 1 0 ) 0 ( 1 ) 1 ( 1 ) — 1 0 ) 0 ( 1 ) - 1 0 ) T a b l e 5 . 1 0 . F o u r i e r c o m p o n e n t s o f t h e o c c u p a t i o n a l m o d u l a t i o n f o r s z T e a o o m a t 5 0 0 K w i t h e s t i m a t e d s t a n d a r d d e v i a t i o n s i n p a r e n t h e s e s . A t o m W a v e O c c u p a t i o n a l c o m p o n e n t T e [ 3 a ] s i n , 1 - 0 . 1 1 4 ( 1 4 ) c o s , 1 - 0 . 0 6 ( 3 ) 3 5 8 T a b l e 5 . 1 1 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r s z T e 4 , 9 o ( . ) a t 5 0 0 K w i t h e s t i m a t e d s t a n d a r d d e v i a t i o n s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e S m [ l a ] - T e [ 1 a ] x 4 3 . 2 2 2 ( 3 ) 3 . 2 2 1 ( 3 ) 3 . 2 2 3 ( 3 ) S m [ l a ] - T e [ 2 a ] 3 . 2 7 4 ( 4 ) 3 . 2 7 0 ( 4 ) 3 . 2 7 9 ( 4 ) S m [ l a ] - T e [ 4 a ] x 2 3 . 3 3 3 ( 4 ) 3 . 3 3 0 ( 4 ) 3 . 3 3 6 ( 4 ) S m [ l a ] - T e [ 5 a ] 3 . 3 2 9 ( 4 ) 3 . 3 2 2 ( 4 ) 3 . 3 3 6 ( 4 ) S m [ 1 a ] - T e [ 5 a ] 3 . 3 2 1 ( 4 ) 3 . 3 1 6 ( 4 ) 3 . 3 2 6 ( 4 ) S m [ 1 b ] - T e [ l b ] x 2 3 . 2 1 1 ( 3 ) 3 . 2 0 7 ( 3 ) 3 . 2 1 6 ( 3 ) S m [ 1 b ] - T e [ l b ] 3 . 2 0 4 ( 3 ) 3 . 2 0 3 ( 3 ) 3 . 2 0 5 ( 3 ) S m [ 1 b ] - T e [ l b ] 3 . 2 1 8 ( 3 ) 3 . 2 1 5 ( 3 ) 3 . 2 2 1 ( 3 ) S m [ 1 b ] - T e [ 2 b ] 3 . 2 7 3 ( 4 ) 3 . 2 6 7 ( 4 ) 3 . 2 7 9 ( 4 ) S m [ 1 b ] - T e [ 4 b ] 3 . 3 2 2 ( 4 ) 3 . 3 1 7 ( 4 ) 3 . 3 2 8 ( 4 ) S m [ 1 b ] - T e [ 4 b ] 3 . 3 0 8 ( 4 ) 3 . 3 0 7 ( 4 ) 3 . 3 0 9 ( 4 ) S m [ 1 b ] - T e [ 5 b ] x 2 3 . 3 1 3 ( 4 ) 3 . 3 0 9 ( 4 ) 3 . 3 1 7 ( 4 ) S m [ 2 b ] - T e [ l b ] 3 . 2 2 3 ( 5 ) 3 . 2 1 3 ( 4 ) 3 . 2 3 3 ( 4 ) S m [ 2 b ] - T e [ 2 b ] 3 . 1 8 2 ( 4 ) 3 . 1 7 2 ( 4 ) 3 . 1 9 3 ( 4 ) S m [ 2 b ] - T e [ 2 b ] 3 . 2 0 2 ( 4 ) 3 . 1 9 7 ( 4 ) 3 . 2 0 6 ( 4 ) S m [ 2 b ] - T e [ 2 b ] 3 . 1 9 3 ( 4 ) 3 . 1 9 2 ( 4 ) 3 . 1 9 4 ( 4 ) S m [ 2 b ] - T e [ 2 b ] 3 . 2 1 2 ( 4 ) 3 . 2 0 4 ( 4 ) 3 . 2 2 0 ( 4 ) S m [ 2 b ] - T e [ 3 a ] 3 . 3 2 5 ( 8 ) 3 . 2 9 9 ( 8 ) 3 . 3 5 3 ( 8 ) S m [ 2 b ] - T e [ 3 a ] 3 . 3 4 5 ( 8 ) 3 . 3 1 3 ( 7 ) 3 . 3 7 8 ( 7 ) S m [ 2 b ] - T e [ 3 b ] x 2 3 . 3 2 4 ( 6 ) 3 . 3 0 3 ( 6 ) 3 . 3 4 5 ( 6 ) S m [ 2 a ] - T e [ l a ] 3 . 1 9 6 ( 5 ) 3 . 1 8 8 ( 5 ) 3 . 2 0 3 ( 5 ) S m [ 2 a ] - T e [ 2 a ] x 2 3 . 1 9 0 ( 4 ) 3 . 1 8 4 ( 4 ) 3 . 1 9 7 ( 4 ) S m [ 2 a ] - T e [ 2 a ] x 2 3 . 2 0 4 ( 4 ) 3 . 2 0 3 ( 4 ) 3 . 2 0 5 ( 4 ) S m [ Z a ] - T e [ 3 a ] 3 . 2 6 0 ( 8 ) 3 . 2 3 0 ( 8 ) 3 . 2 9 0 ( 8 ) S m [ 2 a ] - T e [ 3 a ] 3 . 2 9 1 ( 8 ) 3 . 2 6 7 ( 7 ) 3 . 3 1 6 ( 8 ) S m [ 2 a ] - T e [ 3 b ] 3 . 2 7 4 ( 6 ) 3 . 2 5 7 ( 6 ) 3 . 2 9 1 ( 6 ) S m [ 2 a ] - T e [ 3 b ] 3 . 2 8 9 ( 6 ) 3 . 2 6 8 ( 5 ) 3 . 3 1 0 ( 5 ) T e [ 3 a ] - T e [ 3 b ] x 4 3 . 0 8 5 ( 1 1 ) 2 . 9 6 1 ( 1 1 ) 3 . 2 1 1 ( 1 1 ) T e [ 4 a ] - T e [ 5 a ] x 2 3 . 0 9 0 ( 5 ) 3 . 0 8 5 ( 5 ) 3 . 0 9 5 ( 5 ) T e [ 4 a ] - T e [ 5 a ] x 2 3 . 0 7 6 ( 5 ) 3 . 0 7 3 ( 5 ) 3 . 0 7 9 ( 5 ) T e [ 4 b ] - T e [ 5 b ] x 2 3 . 0 9 5 ( 5 ) 3 . 0 9 2 ( 5 ) 3 . 0 9 8 ( 5 ) T e [ 4 b ] - T e [ 5 b ] x 2 3 . 0 6 8 ( 5 ) 3 . 0 6 3 ( 5 ) 3 . 0 7 3 ( 5 ) 3 5 9 T a b l e 5 . 1 2 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r s z T e 4 _ 9 o ( . ) a t 5 0 0 K w i t h e s t i m a t e d s t a n d a r d d e v i a t i o n s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ l a ] - S m [ 1 a ] - T e [ l a ] x 8 8 5 2 2 ( 8 ) 8 5 0 9 ( 7 ) 8 5 3 4 ( 7 ) T e [ l a ] - S m [ l a ] - T e [ l a ] x 4 1 4 5 9 0 ( 1 1 ) l 4 5 7 3 ( l l ) 1 4 6 0 7 ( 1 1 ) T e [ l a ] - S m [ 1 a ] - T e [ 2 a ] x 2 7 3 4 1 ( 9 ) 7 3 2 7 ( 9 ) 7 3 5 5 ( 9 ) T e [ l a ] - S m [ 1 a ] - T e [ 4 a ] x 4 7 7 . 1 8 ( 9 ) 7 7 . 1 1 ( 9 ) 7 7 2 6 ( 9 ) T e [ l a ] - S m [ 1 a ] - T e [ 4 a ] x 4 1 3 1 . 7 1 ( 9 ) 1 3 1 . 5 6 ( 9 ) 1 3 1 . 8 7 ( 9 ) T e [ l a ] - S m [ l a ] - T e [ 5 a ] x 4 7 7 . 1 4 ( 9 ) 7 6 9 7 ( 9 ) 7 7 3 1 ( 9 ) T e [ l a ] - S m [ 1 a ] - T e [ 5 a ] x 4 l 3 1 . 3 9 ( 1 0 ) 1 3 1 . 2 9 ( 1 0 ) l 3 l . 4 9 ( 1 0 ) T e [ l a ] - S m [ 1 a ] - T e [ 2 a ] x 2 7 2 8 6 ( 9 ) 7 2 6 3 ( 9 ) 7 3 0 8 ( 9 ) T e [ Z a ] - S m [ 1 a ] - T e [ 4 a ] x 2 1 3 9 . 2 9 ( 1 0 ) 1 3 9 . 1 2 ( 1 0 ) 1 3 9 . 4 5 ( 1 0 ) T e [ 2 a ] - S m [ 1 a ] - T e [ 5 a ] 1 3 9 . 4 5 ( 1 0 ) 1 3 9 . 2 7 ( 9 ) 1 3 9 . 6 3 ( 9 ) T e [ 2 a ] - S m [ 1 a ] - T e [ 5 a ] 1 3 8 . 8 3 ( 9 ) 1 3 8 . 6 2 ( 8 ) 1 3 9 . 0 3 ( 8 ) T e [ 4 a ] - S m [ 1 a ] - T e [ 4 a ] x 2 8 1 . 8 2 ( 1 0 ) 8 1 . 8 0 ( 1 0 ) 8 1 . 8 4 ( 1 0 ) T e [ 4 a ] - S m [ 1 a ] - T e [ 5 a ] x 4 5 5 1 6 ( 9 ) 5 5 1 3 ( 9 ) 5 5 1 8 ( 9 ) T e [ 5 a ] - S m [ l a ] - T e [ 5 a ] x 2 8 1 . 7 3 ( 1 0 ) 8 1 . 6 0 ( 1 0 ) 8 1 . 8 6 ( 1 0 ) T e [ l b ] - S m [ 1 b ] - T e [ l b ] x 6 8 5 6 7 ( 8 ) 8 5 6 4 ( 8 ) 8 5 7 1 ( 8 ) T e [ l b ] - S m [ 1 b ] - T e [ l b ] x 2 8 5 1 7 ( 8 ) 8 5 0 9 ( 8 ) 8 5 2 5 ( 8 ) T e [ l b ] - S m [ 1 b ] - T e [ l b ] x 4 1 4 7 . 2 1 ( 1 1 ) 1 4 7 . 0 2 ( 1 1 ) 1 4 7 . 4 0 ( 1 1 ) T e [ l b ] - S m [ 1 b ] - T e [ 2 b ] x 3 7 3 9 3 ( 9 ) 7 3 8 3 ( 9 ) 7 4 0 4 ( 9 ) T e [ l b ] - S m [ 1 b ] - T e [ 4 b ] x 4 7 6 5 6 ( 9 ) 7 6 3 8 ( 9 ) 7 6 7 3 ( 9 ) T e [ l b ] - S m [ 1 b ] - T e [ 4 b ] x 2 l 3 1 . 6 2 ( 1 1 ) 1 3 1 . 5 2 ( 1 1 ) l 3 l . 7 2 ( 1 1 ) T e [ l b ] - S m [ 1 b ] - T e [ 5 b ] x 4 7 6 5 5 ( 9 ) 7 6 4 5 ( 9 ) 7 6 6 5 ( 9 ) T e [ l b ] - S m [ 1 b ] - T e [ 5 b ] x 4 1 3 0 . 8 5 ( 1 0 ) 1 3 0 . 6 7 ( 1 0 ) 1 3 1 . 0 3 ( 1 0 ) T e [ l b ] - S m [ 1 b ] - T e [ 4 b ] x 2 l 3 0 . 8 2 ( 1 0 ) 1 3 0 . 7 4 ( 1 0 ) 1 3 0 9 0 ( 1 0 ) T e [ l b ] - S m [ 1 b ] - T e [ 2 b ] 7 3 2 8 ( 9 ) 7 5 1 5 ( 9 ) 7 3 4 0 ( 9 ) T e [ 2 b ] - S m [ 1 b ] - T e [ 4 b ] x 2 1 3 8 . 9 5 ( 1 0 ) 1 3 8 . 8 3 ( 1 0 ) 1 3 9 . 0 6 ( 1 0 ) T e [ 2 b ] - S m [ 1 b ] - T e [ 5 b ] x 2 l 3 9 . 2 7 ( 1 0 ) 1 3 9 2 2 ( 1 0 ) 1 3 9 . 3 2 ( 1 0 ) T e [ 4 b ] - S m [ 1 b ] - T e [ 4 b ] x 2 8 2 2 7 ( 1 1 ) 8 2 2 5 ( 1 1 ) 8 2 2 9 ( 1 1 ) T e [ 4 b ] - S m [ 1 b ] - T e [ 5 b ] x 3 5 5 5 6 ( 1 0 ) 5 5 5 3 ( 1 0 ) 5 5 5 8 ( 1 0 ) T e [ 4 b ] - S m [ 1 b ] - T e [ 5 b ] 5 4 9 9 ( 9 ) 5 4 9 0 ( 9 ) 5 5 0 9 ( 9 ) T e [ 5 b ] - S m [ 1 b ] - T e [ 5 b ] x 2 8 2 . 0 2 ( 1 0 ) 8 1 9 6 ( 1 0 ) 8 2 . 0 7 ( 1 0 ) T e [ l b ] - S m [ 2 b ] - T e [ 2 b ] x 4 7 4 3 1 ( 1 0 ) 7 4 . 0 3 ( 1 0 ) 7 4 5 9 ( 1 0 ) T e [ l b ] - S m [ 2 b ] - T e [ 3 a ] x 2 1 3 9 2 8 ( 1 9 ) 1 3 8 . 3 3 ( 1 9 ) l 4 0 . 2 2 ( 1 9 ) T e [ l b ] - S m [ 2 b ] - T e [ 3 b ] x 2 1 3 9 . 2 6 0 6 ) 1 3 8 . 6 0 ( 1 5 ) 1 3 9 9 2 ( 1 6 ) 3 6 0 T a b l e 5 . 1 2 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r s z T e 4 . 9 o ( 1 ) a t 5 0 0 K w i t h e s t i m a t e d s t a n d a r d d e v i a t i o n s i n p a r e n t h e s e s . T e [ 2 b ] - S m [ 2 b ] - T e [ 2 b ] x 6 T e [ 2 b ] - S m [ 2 b ] - T e [ 2 b ] x 4 T e [ 2 b ] - S m [ 2 b ] - T e [ 3 a ] x 4 T e [ 2 b ] - S m [ 2 b ] - T e [ 3 a ] x 4 T e [ 2 b ] - S m [ 2 b ] - T e [ 3 b ] x 4 T e [ 2 b ] - S m [ 2 b ] - T e [ 3 b ] x 4 T e [ 2 b ] - S m [ 2 b ] - T e [ 2 b ] x 2 T e [ 3 a ] - S m [ 2 b ] - T e [ 3 a ] x 2 T e [ 3 a ] - S m [ 2 b ] - T e [ 3 b ] x 4 T e [ 3 b ] - S m [ 2 b ] - T e [ 3 b ] x 2 T e [ l a ] - S m [ 2 a ] - T e [ 2 a ] x 3 T e [ l a ] - S m [ 2 a ] - T e [ 2 a ] T e [ l a ] - S m [ 2 a ] - T e [ 3 a ] x 2 T e [ l a ] - S m [ 2 a ] - T e [ 3 b ] x 2 T e [ 2 a ] - S m [ 2 a ] - T e [ 2 a ] x 6 T e [ 2 a ] - S m [ 2 a ] - T e [ 2 a ] x 4 T e [ 2 a ] - S m [ 2 a ] - T e [ 3 a ] x 4 T e [ 2 a ] - S m [ 2 a ] - T e [ 3 a ] x 4 T e [ 2 a ] - S m [ 2 a ] - T e [ 3 b ] x 4 T e [ 2 a ] - S m [ 2 a ] - T e [ 3 b ] x 4 T e [ 2 a ] - S m [ 2 a ] - T e [ 2 a ] x 2 T e [ 3 a ] - S m [ Z a ] - T e [ 3 a ] x 2 T e [ 3 a ] - S m [ 2 a ] - T e [ 3 b ] x 4 T e [ 3 b ] - S m [ 2 a ] - T e [ 3 b ] x 2 S m [ 1 b ] - T e [ l b ] - S m [ 1 b ] x 8 S m [ 1 b ] - T e [ l b ] - S m [ 1 b ] x 4 S m [ 1 b ] - T e [ l b ] - S m [ 2 b ] x 4 S m [ 1 a ] - T e [ l a ] - S m [ 1 a ] x 8 S m [ 1 a ] - T e [ l a ] - S m [ 1 a ] x 4 S m [ 1 a ] - T e [ l a ] - S m [ 2 a ] x 4 S m [ l a ] - T e [ 2 a ] - S m [ 2 a ] x 3 S m [ 1 a ] - T e [ 2 a ] - S m [ Z a ] S m [ 2 a ] - T e [ 2 a ] - S m [ 2 a ] x 8 S m [ 2 a ] - T e [ Z a ] - S m [ 2 a ] x 4 8 6 1 9 ( 1 0 ) 1 4 8 . 9 1 0 4 ) 7 6 . 3 3 0 9 ) 1 3 0 . 7 3 0 9 ) 7 6 . 2 6 0 5 ) 1 3 0 . 6 9 0 7 ) 8 5 4 2 ( 9 ) 8 1 . 7 ( 2 ) 5 5 . 3 ( 2 ) 8 1 . 6 1 0 7 ) 7 3 . 9 5 0 0 ) 7 4 . 6 4 0 0 ) 1 3 8 . 3 6 0 7 ) 1 3 8 . 4 0 0 6 ) 8 6 0 2 ( 9 ) 1 4 8 . 5 9 0 4 ) 7 5 . 9 6 0 9 ) 1 3 1 . 3 ( 2 ) 7 5 . 8 8 0 5 ) 1 3 1 . 2 7 0 7 ) 8 5 . 4 3 0 0 ) 8 3 . 3 ( 2 ) 5 6 . 2 ( 2 ) 8 3 . 3 2 0 8 ) 8 5 4 6 ( 9 ) 1 4 7 . 2 1 0 2 ) 1 0 6 . 4 6 0 0 ) 8 5 1 9 ( 7 ) 1 4 5 . 9 0 0 2 ) 1 0 7 . 3 5 0 0 ) 1 0 5 . 2 0 0 0 ) 1 0 6 . 2 1 0 1 ) 8 5 . 8 5 0 0 ) 1 4 8 5 9 ( l 4 ) 8 6 . 0 1 0 0 ) 1 4 8 . 2 4 0 3 ) 7 5 . 2 4 0 9 ) 1 2 9 . 3 3 0 9 ) 7 5 . 5 4 0 5 ) 1 2 9 . 5 7 0 7 ) 8 5 2 9 ( 9 ) 7 9 . 9 ( 2 ) 5 4 . 9 ( 2 ) 8 0 . 3 5 0 6 ) 7 3 . 6 8 0 0 ) 7 4 . 3 1 0 0 ) 1 3 7 . 5 5 0 7 ) 1 3 7 . 6 0 0 5 ) 8 5 8 5 ( 9 ) 1 4 7 . 9 9 0 4 ) 7 4 . 8 3 0 9 ) 1 2 9 . 8 ( 2 ) 7 5 0 8 ( 1 5 ) 1 3 0 . 1 2 0 7 ) 8 5 2 8 ( 1 0 ) 8 1 . 7 ( 2 ) 5 5 7 ( 2 ) 8 1 . 9 3 0 7 ) 8 5 3 3 ( 9 ) 1 4 6 . 9 4 0 2 ) 1 0 6 . 3 6 0 0 ) 8 5 1 4 ( 7 ) 1 4 5 . 5 8 0 2 ) 1 0 7 . 1 4 0 0 ) 1 0 4 . 8 5 0 0 ) 1 0 5 . 9 3 0 1 ) 8 5 8 1 ( 1 0 ) 1 4 8 . 2 2 0 4 ) 8 6 . 3 7 0 0 ) 1 4 9 . 5 6 0 3 ) 7 7 . 4 1 0 9 ) 1 3 2 . 1 4 0 9 ) 7 6 . 9 8 0 5 ) 1 3 1 . 8 3 0 7 ) 8 5 5 6 ( 9 ) 8 3 . 5 ( 2 ) 5 5 6 ( 2 ) 8 2 . 9 0 0 6 ) 7 4 . 2 3 0 0 ) 7 4 . 9 7 0 0 ) 1 3 9 . 1 7 0 8 ) 1 3 9 . 2 0 0 6 ) 8 6 1 9 ( 9 ) 1 4 9 . 2 0 0 4 ) 7 7 . 1 1 0 9 ) 1 3 2 . 7 ( 2 ) 7 6 . 6 9 0 5 ) 1 3 2 . 4 0 0 7 ) 8 5 5 8 ( 1 0 ) 8 4 . 8 ( 2 ) 5 6 . 7 ( 2 ) 8 4 . 6 9 0 6 ) 8 5 5 9 ( 9 ) 1 4 7 . 4 8 0 2 ) 1 0 6 . 5 7 0 0 ) 8 5 2 4 ( 8 ) 1 4 6 . 2 2 0 2 ) 1 0 7 . 5 5 0 0 ) 1 0 5 . 5 4 0 0 ) 1 0 6 . 4 9 ( 1 1 ) 8 5 8 8 ( 1 0 ) 1 4 8 . 9 6 0 4 ) 3 6 1 T a b l e 5 . 1 2 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r s z T e 4 . 9 0 0 ) a t 5 0 0 K w i t h e s t i m a t e d s t a n d a r d d e v i a t i o n s i n p a r e n t h e s e s . S m [ 1 b ] - T e [ 2 b ] - S m [ 2 b ] x 3 S m [ 1 b ] - T e [ 2 b ] - S m [ 2 b ] S m [ 2 b ] - T e [ 2 b ] - S m [ 2 b ] x 8 S m [ 2 b ] - T e [ 2 b ] - S m [ 2 b ] x 4 S m [ 2 b ] - T e [ 3 a ] - S m [ 2 b ] x 2 S m [ 2 b ] - T e [ 3 a ] - S m [ 2 a ] x 4 S m [ 2 b ] - T e [ 3 a ] - T e [ 3 b ] x 4 S m [ 2 b ] - T e [ 3 a ] - T e [ 3 b ] x 4 S m [ 2 a ] - T e [ 3 a ] - S m [ 2 a ] x 2 S m [ 2 a ] - T e [ 3 a ] - T e [ 3 b ] x 4 S m [ 2 a ] - T e [ 3 a ] - T e [ 3 b ] x 4 T e [ 3 b ] - T e [ 3 a ] - T e [ 3 b ] x 8 T e [ 3 b ] - T e [ 3 a ] - T e [ 3 b ] x 4 S m [ 2 b ] - T e [ 3 b ] - S m [ 2 b ] x 2 S m [ 2 b ] - T e [ 3 b ] - S m [ 2 a ] x 4 S m [ 2 b ] - T e [ 3 b ] - T e [ 3 a ] x 4 S m [ 2 b ] - T e [ 3 b ] - T e [ 3 a ] x 4 S m [ 2 a ] - T e [ 3 b ] - S m [ 2 a ] x 2 S m [ Z a ] - T e [ 3 b ] - T e [ 3 a ] x 4 S m [ 2 a ] - T e [ 3 b ] - T e [ 3 a ] x 4 T e [ 3 a ] - T e [ 3 b ] - T e [ 3 a ] x 8 T e [ 3 a ] - T e [ 3 b ] - T e [ 3 a ] x 4 S m [ l a ] - T e [ 4 a ] - S m [ 1 a ] x 2 S m [ 1 a ] - T e [ 4 a ] - T e [ 5 a ] x 4 S m [ 1 a ] - T e [ 4 a ] - T e [ 5 a ] x 4 T e [ 5 a ] - T e [ 4 a ] - T e [ 5 a ] x 8 T e [ 5 a ] - T e [ 4 a ] - T e [ 5 a ] x 4 S m [ 1 b ] - T e [ 4 b ] - S m [ 1 b ] x 2 S m [ 1 b ] - T e [ 4 b ] - T e [ 5 b ] x 4 S m [ 1 b ] - T e [ 4 b ] - T e [ 5 b ] x 2 S m [ 1 b ] - T e [ 4 b ] - T e [ 5 b ] x 2 T e [ 5 b ] - T e [ 4 b ] - T e [ 5 b ] x 6 T e [ 5 b ] - T e [ 4 b ] - T e [ 5 b ] x 4 \ T e [ 5 b ] - T e [ 4 b ] - T e [ 5 b ] x 2 1 0 5 . 1 5 0 1 ) 1 0 5 . 9 5 0 0 ) 8 5 8 4 ( 9 ) 1 4 8 . 9 0 0 4 ) 8 1 . 6 7 0 5 ) 1 2 3 . 8 ( 3 ) 6 2 . 1 1 0 9 ) 1 1 7 . 4 ( 3 ) 8 3 . 2 3 0 6 ) 6 1 . 7 0 0 9 ) 1 1 8 . 0 ( 3 ) 9 0 . 0 ( 3 ) 1 7 9 . 6 ( 3 ) 8 1 . 6 2 0 2 ) 1 2 3 . 9 ( 2 ) 6 2 . 4 ( 2 ) 1 1 7 . 5 ( 2 ) 8 3 . 3 1 0 3 ) 6 1 . 5 1 0 9 ) 1 1 7 . 9 ( 2 ) 9 0 . 3 ( 3 ) 1 7 9 . 7 ( 3 ) 8 1 . 8 2 ( 1 0 ) 6 2 . 3 7 0 0 ) 1 1 7 . 4 1 0 4 ) 8 9 . 8 9 0 3 ) 1 7 9 . 7 5 0 7 ) 8 2 . 2 6 0 0 ) 6 2 . 2 1 0 0 ) 1 1 7 . 2 9 0 4 ) 1 1 8 . 1 7 ( 1 5 ) 8 9 . 6 5 0 3 ) 1 7 9 . 5 0 0 7 ) 9 0 . 6 5 0 3 ) 1 0 4 . 8 0 0 1 ) 1 0 5 . 6 2 0 0 ) 8 5 7 6 ( 9 ) 1 4 8 . 3 3 0 4 ) 8 1 . 2 1 0 5 ) 1 2 1 . 2 ( 2 ) 6 0 . 7 5 0 7 ) 1 1 6 . 9 ( 2 ) 8 3 . 0 9 0 6 ) 6 0 . 4 0 0 8 ) 1 1 7 . 6 ( 2 ) 8 9 . 7 ( 3 ) 1 7 9 . 5 ( 4 ) 8 1 . 3 7 0 3 ) 1 2 1 . 9 1 0 9 ) 6 1 . 3 6 0 9 ) 1 1 7 . 3 ( 2 ) 8 2 . 9 2 0 3 ) 6 0 . 5 4 0 8 ) 1 1 7 . 8 ( 2 ) 8 9 . 7 ( 3 ) 1 7 9 . 4 ( 4 ) 8 1 . 6 9 0 0 ) 6 2 . 2 3 0 0 ) 1 1 7 . 3 1 0 5 ) 8 9 . 8 1 0 3 ) 1 7 9 . 6 2 0 8 ) 8 2 . 1 7 0 0 ) 6 2 . 1 4 0 0 ) 1 1 7 . 1 7 0 4 ) 1 1 8 . 1 4 0 5 ) 8 9 . 5 5 0 3 ) 1 7 9 . 4 1 0 6 ) 9 0 . 5 7 0 3 ) 1 0 5 . 5 0 0 1 ) 1 0 6 . 2 8 0 0 ) 8 5 9 2 ( 9 ) 1 4 9 . 4 7 0 4 ) 8 2 . 1 6 0 6 ) 1 2 6 . 4 ( 3 ) 6 3 . 4 8 0 8 ) 1 1 7 . 9 ( 2 ) 8 3 . 3 9 0 7 ) 6 3 . 0 ( 2 ) 1 1 8 . 4 ( 3 ) 9 0 . 3 ( 3 ) 1 7 9 . 9 ( 3 ) 8 1 . 8 7 0 3 ) 1 2 5 . 9 ( 2 ) 6 3 . 4 ( 2 ) 1 1 7 . 7 ( 2 ) 8 3 . 7 0 0 3 ) 6 2 . 4 8 0 9 ) 1 1 8 . 1 ( 2 ) 9 0 . 9 ( 3 ) 1 7 9 . 9 ( 2 ) 8 1 . 9 5 0 0 ) 6 2 . 5 0 0 0 ) 1 1 7 . 5 1 0 5 ) 8 9 . 9 7 0 3 ) 1 7 9 . 8 7 0 6 ) 8 2 . 3 6 0 0 ) 6 2 . 2 9 0 0 ) 1 1 7 . 4 2 0 4 ) 1 1 8 . 2 1 0 5 ) 8 9 . 7 5 0 3 ) 1 7 9 . 5 9 0 8 ) 9 0 . 7 2 0 3 ) 3 6 2 T a b l e 5 . 1 2 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r s z T e 4 _ 9 o ( . ) a t 5 0 0 K w i t h e s t i m a t e d s t a n d a r d d e v i a t i o n s i n p a r e n t h e s e s . S m [ l a ] - T e [ 5 a ] - S m [ 1 a ] x 2 8 1 . 7 3 ( 1 0 ) 8 1 . 6 5 ( 1 0 ) 8 1 . 8 1 ( 1 0 ) S m [ l a ] - T e [ 5 a ] - T e [ 4 a ] x 4 6 2 . 7 2 ( 1 0 ) 6 2 . 6 6 ( 1 1 ) 6 2 . 7 8 ( 1 1 ) S m [ 1 a ] - T e [ 5 a ] - T e [ 4 a ] x 4 1 1 7 . 7 1 ( 1 4 ) 1 1 7 . 6 5 ( 1 4 ) 1 1 7 . 7 8 ( 1 4 ) T e [ 4 a ] - T e [ S a ] - T e [ 4 a ] x 8 9 0 . 4 1 ( 1 3 ) 9 0 2 9 ( 1 3 ) 9 0 5 2 ( 1 3 ) T e [ 4 a ] - T e [ S a ] - T e [ 4 a ] x 4 1 7 9 . 7 5 ( 1 7 ) 1 7 9 . 6 5 ( 1 8 ) 1 7 9 . 8 4 ( l 7 ) S m [ 1 b ] - T e [ 5 b ] - S m [ 1 b ] x 2 8 2 . 0 2 ( 1 0 ) 8 1 9 5 ( 1 0 ) 8 2 . 0 8 ( 1 0 ) S m [ l b ] - T e [ 5 b ] - T e [ 4 b ] x 4 6 2 5 9 ( 1 0 ) 6 2 . 4 4 ( 1 0 ) 6 2 . 7 3 ( 1 0 ) S m [ 1 b ] - T e [ 5 b ] - T e [ 4 b ] x 4 1 1 7 . 8 7 ( 1 4 ) 1 1 7 . 7 8 ( 1 4 ) 1 1 7 9 7 ( 1 4 ) T e [ 4 b ] - T e [ 5 b ] - T e [ 4 b ] x 4 9 0 . 6 5 ( l 3 ) 9 0 5 5 ( 1 3 ) 9 0 . 7 4 ( l 3 ) T e [ 4 b ] - T e [ 5 b ] - T e [ 4 b ] x 4 1 7 9 5 0 ( 1 6 ) 1 7 9 . 4 5 ( 1 7 ) 1 7 9 . 5 5 ( 1 6 ) T e [ 4 b ] - T e [ 5 b ] - T e [ 4 b ] x 4 8 9 . 8 1 ( 1 3 ) 8 9 . 7 0 ( 1 3 ) 8 9 9 2 ( 1 3 ) 3 6 3 T a b l e 5 . 1 3 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r S m T e L g . . . ) a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e C r y s t a l s y s t e m S p a c e g r o u p C e n t e r i n g v e c t o r U n i t c e l l d i m e n s i o n s q - v e c t o r ( l ) q - v e c t o r ( 2 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 1 4 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 o ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 8 ‘ o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) F i n a l R 2 ' “ l o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 2 “ d o r d e r s a t e l l i t e s ( a l l d a t a ) T . . . a n d T m . . . c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e S m T e L g . . . ) 3 8 0 1 0 0 . 0 ( 3 ) K T e t r a g o n a l X 4 ( a B O ) ( B - 0 1 0 ) 0 ( 0 0 1 / 2 % V 2 ) a = 4 . 3 5 2 0 ( 3 ) A , a = 9 0 ° b = 4 . 3 5 2 0 ( 3 ) A , 1 3 = 9 0 ° c = 1 7 . 8 9 0 2 ( 7 ) A , y = 9 0 ° 0 . 2 9 6 5 ( 3 ) a ‘ + 0 . 2 9 6 5 ( 3 ) h ' 0 . 2 9 6 5 ( 3 ) a ‘ + - 0 . 2 9 6 5 ( 3 ) h " 3 3 8 . 8 4 ( 4 ) A 3 4 7 . 4 4 7 4 g / c m 3 3 2 . 1 9 1 m m " 0 . 1 2 x 0 . 0 8 x 0 . 0 1 n n n 3 1 . 8 6 t o 2 9 . 1 4 ° - 6 < = h < = 6 , - 6 < = k < = 6 , - 2 4 < = l < = 2 4 , - 1 < = m , n < = 1 3 8 8 3 0 ( 1 2 5 9 m a i n + 3 7 5 7 1 s a t e l l i t e s ) 4 0 9 9 ( 4 5 4 m a i n + 3 6 4 5 s a t e l l i t e s ) 1 R . . . t = 0 . 0 7 3 6 ] 1 0 0 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 4 0 9 9 / 0 / 1 3 3 1 . 2 9 R . . . = 0 . 0 4 1 9 , w R . . . = 0 . 1 0 0 6 R . . . = 0 . 0 9 4 9 , w R . . . = 0 . 1 2 3 3 R . . . = 0 . 0 2 1 2 , w R . . . = 0 . 0 6 3 3 R . . . = 0 . 0 2 2 8 , w R . . . = 0 . 0 6 6 4 R . . . = 0 . 0 6 2 8 , w R . . . = 0 . 1 2 1 4 R . . . = 0 . 1 0 6 0 , w R . . . = 0 . 1 3 6 2 R . . . = 0 . 1 5 3 5 , w R . . . = 0 . 2 7 1 9 R . . . = 0 . 4 0 5 6 , w R . . . = 0 . 4 6 4 4 0 . 0 4 8 2 a n d 0 . 7 2 2 7 3 . 1 9 a n d - 1 . 9 7 e . A ' 3 R = Z I I F o l - c h l l / 2 1 1 : 4 , w R = { 2 [ w ( | F . | 2 - 1 1 3 . 1 5 2 ] / 2 1 w ( | F . 1 4 ) ] } " 2 a n d w = 1 / ( 0 2 ( I ) + 0 . 0 0 1 6 1 2 ) 3 6 4 T a b l e 5 . 1 4 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r S m T e . _ 3 . ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x y 2 O c c u p a n c y U . . . S m [ 1 a ] 0 2 5 4 9 2 5 4 9 1 3 5 6 1 7 ( 1 ) s i n , 1 - 3 8 ( 4 ) - 4 2 ( 5 ) 0 c o s , 1 0 0 3 1 ( 1 ) s i n , 2 - 4 2 ( 5 ) 3 8 ( 4 ) 0 c o s , 2 0 0 3 1 ( 1 ) s i n , 3 1 7 ( 3 ) 1 6 ( 5 ) 0 c o s , 3 0 0 9 ( 1 ) s i n , 4 - 1 6 ( 5 ) 1 7 ( 3 ) 0 c o s , 4 0 0 9 ( 1 ) S m [ 1 b ] 0 - 2 4 5 1 - 2 4 5 1 - 1 3 5 6 ( 1 ) 1 7 ( 1 ) s i n , 1 - 2 4 ( 4 ) - 2 8 ( 5 ) 0 c o s , 1 0 0 - 3 1 ( 1 ) s i n , 2 - 2 8 ( 5 ) 2 4 ( 4 ) 0 c o s , 2 O 0 - 3 1 ( 1 ) s i n , 3 8 ( 3 ) 0 ( 5 ) 0 c o s , 3 0 0 - 7 ( 1 ) s i n , 4 0 ( 5 ) 8 ( 3 ) 0 c o s , 4 O 0 - 7 ( 1 ) T e [ 1 a ] 0 2 5 4 9 2 5 4 9 3 1 4 9 ( 2 ) 1 7 ( 1 ) s i n , 1 - 2 ( 6 ) 7 ( 6 ) 0 c o s , 1 0 0 2 6 ( 1 ) s i n , 2 7 ( 6 ) 2 ( 6 ) 0 c o s , 2 0 0 2 6 ( 1 ) s i n , 3 - 1 1 ( 3 ) 4 ( 6 ) 0 c o s , 3 0 0 0 ( 1 ) s i n , 4 - 4 ( 6 ) - 1 1 ( 3 ) 0 c o s , 4 0 0 0 ( 1 ) 3 6 5 T a b l e 5 . 1 4 . ( C o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r S m T e L g . . . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ l b ] 0 - 2 4 5 1 - 2 4 5 1 - 3 1 5 7 ( 1 ) 1 2 ( 1 ) s i n , 1 1 5 ( 5 ) 2 3 ( 5 ) 0 c o s , 1 0 0 - 2 2 ( 1 ) s i n , 2 2 3 ( 5 ) - 1 5 ( 5 ) 0 c o s , 2 0 0 - 2 2 ( 1 ) s i n , 3 - 2 ( 3 ) 7 ( 6 ) 0 c o s , 3 0 0 - 2 ( 1 ) s i n , 4 - 7 ( 6 ) - 2 ( 3 ) 0 c o s , 4 O 0 - 2 ( 1 ) T e [ 2 ] 0 2 5 4 9 7 5 4 9 - 1 6 ( 1 ) 1 2 4 ( 1 ) s i n , 1 - 2 0 9 ( 6 ) - 4 7 2 ( 8 ) 0 c o s , 1 0 0 - 2 ( 2 ) s i n , 2 - 2 6 0 ( 6 ) 2 3 7 ( 8 ) 0 c o s , 2 0 0 — 1 2 ( 2 ) s i n , 3 - 1 2 4 ( 4 ) - 2 5 ( 1 4 ) 0 c o s , 3 0 0 1 ( 2 ) s i n , 4 - 1 6 ( 1 1 ) - 2 3 5 ( 6 ) 0 c o s , 4 0 0 - 2 ( 2 ) T a b l e 5 . 1 5 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r S m T e . _ 8 6 ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 S m [ l a ] 0 5 ( 1 ) 5 ( 1 ) 1 1 ( 1 ) 0 0 0 S i n , 1 O 0 0 0 - 2 ( 1 ) 2 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 3 ( 1 ) 0 ( 1 ) 0 0 S i n , 2 O 0 0 0 2 ( 1 ) 2 ( 1 ) c o s , 2 0 ( 1 ) 0 ( 1 ) 3 ( 1 ) 0 ( 1 ) 0 0 s i n , 3 O 0 O 0 1 ( 1 ) - 1 ( 1 ) c o s , 3 0 ( 1 ) - l ( l ) 4 ( 1 ) - 4 ( 1 ) 0 0 S i n , 4 0 O O 0 1 ( 1 ) 1 ( 1 ) c o s , 4 - 1 ( 1 ) 0 ( 1 ) 4 ( 1 ) 4 ( 1 ) 0 0 3 6 6 T a b l e 5 . 1 5 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r S m T e . , 3 6 ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . S m [ 1 b ] 0 7 ( 1 ) 7 ( 1 ) 8 ( 1 ) 0 0 0 s i n , 1 0 O 0 0 1 ( 1 ) - 3 ( 1 ) c o s , 1 - 1 ( 1 ) 2 ( 1 ) - 2 ( 1 ) 0 ( 1 ) 0 0 s i n , 2 0 0 0 0 - 3 ( 1 ) 0 ( 1 ) c o s , 2 2 ( 1 ) - 1 ( 1 ) - 2 ( 1 ) 0 ( 1 ) 0 0 s i n , 3 0 0 0 0 1 ( 1 ) - 1 ( 1 ) c o s , 3 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 0 s i n , 4 O 0 0 0 1 ( 1 ) 1 ( 1 ) c o s , 4 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 0 T e [ l a ] 0 6 ( 1 ) 6 ( 1 ) 1 1 ( 1 ) 0 0 0 s i n , 1 0 0 0 0 - 2 ( 1 ) 1 ( 1 ) c o s , 1 1 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 0 s i n , 2 0 0 0 0 1 ( 1 ) 2 ( 1 ) c o s , 2 - 1 ( 1 ) 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 0 s i n , 3 O 0 0 0 0 ( 1 ) 0 ( 1 ) c o s , 3 1 ( 1 ) 1 ( 1 ) 3 ( 1 ) - 1 ( 1 ) 0 0 s i n , 4 0 0 0 0 0 ( 1 ) 0 ( 1 ) c o s , 4 1 ( 1 ) 1 ( 1 ) 3 ( 1 ) 1 ( 1 ) 0 0 T e [ l b ] 0 1 ( 1 ) 1 ( 1 ) 4 ( 1 ) 0 0 0 s i n , 1 0 0 0 0 1 ( 1 ) - 2 ( 1 ) c o s , 1 1 ( 1 ) 1 ( 1 ) - 3 ( 1 ) 0 ( 1 ) 0 0 s i n , 2 0 0 0 0 - 2 ( 1 ) - 1 ( 1 ) c o s , 2 1 ( 1 ) 1 ( 1 ) - 3 ( 1 ) 0 ( 1 ) 0 0 s i n , 3 0 0 0 0 0 ( 1 ) - 1 ( 1 ) c o s , 3 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) - 1 ( 1 ) 0 0 s i n , 4 0 0 0 0 1 ( 1 ) 0 ( 1 ) c o s , 4 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) 0 O 3 6 7 T a b l e 5 . 1 5 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r S m T e . , g 6 ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s T e [ 2 ] 0 s i n , 1 c o s , 1 s i n , 2 c o s , 2 s i n , 3 c o s , 3 s i n , 4 c o s , 4 1 4 ( 1 ) 0 - 6 ( 2 ) 0 - 1 1 ( 2 ) 0 - 1 1 ( 1 ) 0 - 1 6 ( 1 ) 4 9 ( 1 ) 0 3 2 ( 2 ) 0 1 7 ( 2 ) 0 3 1 ( 1 ) 0 8 ( 1 ) 8 ( 1 ) 0 - 2 ( 1 ) 0 5 ( 1 ) 0 - 1 ( 1 ) 0 2 ( 1 ) 2 ( 1 ) 0 - 9 0 ) 0 1 4 ( 1 ) 0 1 9 ( 2 ) 0 - 1 2 0 ) 0 5 ( 1 ) 0 0 ( 1 ) 0 3 ( 1 ) 0 2 ( 1 ) 0 0 1 6 ( 1 ) 0 - 1 ( 2 ) 0 9 ( 2 ) 0 1 0 ( 1 ) 0 T a b l e 5 . 1 6 . F o u r i e r c o m p o n e n t s o f t h e o c c u p a t i o n a l m o d u l a t i o n f o r S m l T e l . 8 a t 1 0 0 . 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e O c c u p a t i o n a l c o m p o n e n t T e [ 2 ] s i n , 1 0 c o s , 1 - 0 . 1 5 5 ( 1 2 ) T e [ 2 ] s i n , 2 0 c o s , 2 - 0 . 1 8 2 ( 1 2 ) T e [ 2 ] s i n , 3 0 c o s , 3 - 0 . 0 2 3 ( 7 ) T e [ 2 ] s i n , 4 0 c o s , 4 - 0 . 1 4 0 ( 7 ) T a b l e 5 . 1 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r S m T e . , 3 . ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e S m [ 1 a ] - T e [ l a ] 3 . 2 0 8 ( 5 ) 3 . 1 6 2 ( 8 ) 3 . 2 3 8 ( 8 ) S m [ 1 a ] - T e [ l b ] x 4 3 . 1 9 7 ( 6 ) 3 . 1 5 2 ( 6 ) 3 . 2 3 9 ( 6 ) S m [ 1 a ] - T e [ 2 ] x 4 3 . 2 6 8 ( 8 ) 3 . 1 6 6 ( 8 ) 3 . 4 6 4 ( 9 ) S m [ 1 b ] - T e [ l a ] x 4 3 . 2 0 2 ( 6 ) 3 . 1 6 7 ( 6 ) 3 . 2 3 4 ( 6 ) S m [ 1 b ] - T e [ l b ] 3 . 2 2 1 ( 4 ) 3 . 1 7 4 ( 7 ) 3 . 2 3 9 ( 7 ) S m [ 1 b ] - T e [ 2 ] x 4 3 . 2 3 5 ( 7 ) 3 . 1 8 7 ( 8 ) 3 . 3 0 3 ( 8 ) T e [ 2 ] - T e [ 2 ] x 3 3 . 1 2 8 ( 1 0 ) 2 . 7 3 0 ( 1 1 ) 3 . 5 4 7 ( 1 1 ) 3 6 8 T a b l e 5 . 1 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r S m T e . . 3 6 ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ l a ] - S m [ l a ] - T e [ l b ] x 4 7 4 . 2 3 ( 1 2 ) 7 2 . 8 0 ( 1 0 ) 7 6 1 1 ( 1 0 ) T e [ l a ] - S m [ l a ] - T e [ 2 ] x 4 1 3 8 . 0 ( 3 ) 1 3 4 . 6 ( 2 ) 1 4 4 . 3 ( 2 ) T e [ l b ] - S m [ 1 a ] - T e [ l b ] x 8 8 5 . 7 7 ( 1 8 ) 8 5 0 7 ( 1 9 ) 8 6 7 1 ( 1 7 ) T e [ l b ] - S m [ 1 a ] - T e [ l b ] x 4 1 4 8 . 4 9 ( 1 2 ) 1 4 5 . 8 1 ( 1 8 ) 1 5 2 . 1 0 ( 1 9 ) T e [ l b ] - S m [ 1 a ] - T e [ 2 ] x 8 7 5 5 ( 2 ) 7 2 . 8 ( 2 ) 7 9 2 ( 3 ) T e [ l b ] - S m [ 1 a ] - T e [ 2 ] x 8 1 3 1 . 2 ( 2 ) 1 2 7 . 2 ( 2 ) 1 3 5 . 7 ( 2 ) T e [ 2 ] - S m [ l a ] - T e [ 2 ] x 4 8 7 . 1 ( 2 ) 8 0 . 4 ( 3 ) 8 9 . 4 ( 2 ) T e [ 2 ] - S m [ 1 a ] - T e [ 2 ] x 8 5 6 9 ( 2 ) 5 0 9 ( 3 ) 6 3 2 ( 2 ) T e [ l a ] - S m [ 1 b ] - T e [ l a ] x 8 8 5 6 ( 2 ) 8 5 0 4 ( 1 9 ) 8 6 5 1 ( 1 9 ) T e [ l a ] - S m [ 1 b ] - T e [ l a ] x 4 1 4 8 . 0 1 ( l 3 ) 1 4 5 . 0 9 ( 1 8 ) 1 5 1 . 4 4 ( 1 8 ) T e [ l a ] - S m [ 1 b ] - T e [ l b ] x 4 7 4 . 0 2 ( 1 7 ) 7 2 . 4 9 ( 1 7 ) 7 5 7 9 ( 1 8 ) T e [ l a ] - S m [ 1 b ] - T e [ 2 ] x 8 7 5 3 ( 3 ) 7 1 9 ( 2 ) 7 9 . 2 ( 3 ) T e [ l a ] — S m [ 1 b ] - T e [ 2 ] x 8 1 3 1 . 8 ( 3 ) 1 2 6 . 0 ( 3 ) 1 3 8 . 1 ( 3 ) T e [ l b ] - S m [ 1 b ] - T e [ 2 ] x 4 1 3 7 . 3 ( 2 ) 1 3 5 . 1 1 ( 1 7 ) 1 4 0 . 5 ( 3 ) T e [ 2 ] - S m [ 1 b ] - T e [ 2 ] x 4 8 5 9 ( 2 ) 8 0 . 7 ( 2 ) 8 9 . 1 ( 2 ) T e [ 2 ] - S m [ 1 b ] - T e [ 2 ] x 8 5 8 . 0 ( 3 ) 4 9 . 4 ( 3 ) 6 5 4 ( 3 ) S m [ 1 a ] - T e [ l a ] - S m [ 1 b ] x 4 1 0 6 0 3 ( 1 5 ) 1 0 4 . 5 3 ( 1 2 ) 1 0 7 . 4 6 ( 1 7 ) S m [ 1 b ] - T e [ l a ] - S m [ 1 b ] x 8 8 5 6 5 ( 1 8 ) 8 4 9 6 ( 1 5 ) 8 6 3 0 ( 1 7 ) S m [ 1 b ] - T e [ l a ] - S m [ 1 b ] x 4 l 4 7 . 9 8 ( 1 6 ) 1 4 5 . 5 ( 2 ) 1 5 0 . 7 ( 2 ) S m [ l a ] - T e [ l b ] - S m [ 1 a ] x 8 8 5 . 7 7 ( 1 7 ) 8 5 2 3 ( 1 7 ) 8 6 3 8 ( 1 6 ) S m [ 1 a ] - T e [ l b ] - S m [ 1 a ] x 4 1 4 8 . 4 4 ( 1 3 ) 1 4 5 . 6 2 ( 1 9 ) 1 5 0 9 7 ( 1 9 ) S m [ 1 a ] - T e [ l b ] - S m [ 1 b ] x 4 1 0 5 . 7 7 ( 1 8 ) 1 0 4 . 2 4 ( 1 7 ) 1 0 7 . 1 9 ( 1 6 ) S m [ l a ] - T e [ 2 ] - S m [ l a ] x 2 8 3 . 8 ( 2 ) 8 1 . 4 8 ( 1 7 ) 8 5 9 ( 3 ) S m [ 1 a ] - T e [ 2 ] - S m [ 1 b ] x 4 1 2 3 . 4 ( 3 ) 1 1 4 . 4 ( 3 ) 1 3 1 . 9 ( 3 ) S m [ l a ] - T e [ 2 ] - T e [ 2 ] x 4 6 1 . 7 ( 2 ) 5 6 . 9 ( 2 ) 6 6 5 ( 2 ) S m [ 1 a ] - T e [ 2 ] - T e [ 2 ] x 4 1 1 7 . 4 ( 3 ) 1 1 4 . 2 ( 2 ) 1 2 1 . 2 ( 3 ) S m [ 1 b ] - T e [ 2 ] - S m [ 1 b ] x 2 8 4 . 8 ( 2 ) 8 3 . 7 0 ( 1 9 ) 8 5 8 ( 3 ) S m [ 1 b ] - T e [ 2 ] - T e [ 2 ] x 4 6 1 . 0 ( 2 ) 5 7 5 6 ( 1 8 ) 6 5 3 ( 2 ) S m [ 1 b ] - T e [ 2 ] - T e [ 2 ] x 4 1 1 8 . 2 ( 3 ) 1 1 1 . 9 ( 3 ) 1 2 2 . 6 ( 3 ) T e [ 2 ] - T e [ 2 ] - T e [ 2 ] x 8 8 9 . 1 ( 3 ) 8 4 . 1 ( 3 ) 9 2 5 ( 4 ) T e [ 2 ] - T e [ 2 ] - T e [ 2 ] x 4 1 7 7 . 7 ( 4 ) 1 7 3 . 7 ( 4 ) 1 7 9 . 7 ( 3 ) 3 6 9 T a b l e 5 . 1 9 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r K z A g a L a z T e o . . . ” a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) q - v e c t o r ( 2 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f f i c i e n t C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 1 8 . 0 1 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 3 o ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 3 o ( 1 ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 s t o r d e r s a t e l l i t e s [ I > 3 o ( I ) ] R l S t o r d e r s a t e l l i t e s ( a l l d a t a ) F i n a l R 2 " d o r d e r s a t e l l i t e s [ I > 3 o ( I ) ] R 2 “ d o r d e r s a t e l l i t e s ( a l l d a t a ) T . . . a n d T m . . . c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e K z A g 4 L 3 2 T C 9 6 1 0 ) 2 0 1 2 . 4 1 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A T r i c l i n i c C 1 ( a t B 1 7 1 ) ( 9 2 B 2 7 2 ) 0 a = 6 . 3 5 2 1 ( 4 ) A , 0 1 = 9 0 ° b = 6 . 3 5 3 1 ( 4 ) A , 1 3 = 9 7 . 1 7 7 ( 6 ) ° c = 2 5 . 4 0 3 6 ( 1 9 ) A , y = 9 0 ° 0 . 3 3 2 7 ( 4 ) a ’ + 0 . 3 3 2 7 ( 4 ) h ‘ + 0 . 3 3 4 ( 2 ) c ‘ 0 . 4 0 0 ( 2 ) a ’ - 0 . 0 7 2 ( 2 ) h ‘ + 0 . 3 4 5 ( 6 ) c " 1 0 1 7 . 1 4 ( 1 2 ) A 3 2 6 . 5 6 8 7 g / c r n 3 2 1 . 6 9 m m " ' 0 . 1 9 x 0 . 1 6 x 0 . 0 8 m m 3 1 . 5 6 t o 2 9 . 2 3 ° - 9 < = h < = 9 , - 9 < = k < = 8 , - 3 5 < = 1 < = 3 5 , - l < = m , n < = 1 3 7 8 3 8 ( 4 2 7 1 m a i n + 3 3 5 6 7 s a t e l l i t e s ) 3 2 6 8 7 ( 3 7 4 5 m a i n + 2 8 9 9 3 s a t e l l i t e S ) [ R i m = 0 . 0 9 8 2 ] 9 5 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 3 2 6 8 7 / 0 / 1 4 6 6 1 . 2 9 R . . . = 0 . 0 6 3 3 , w R . . . = 0 . 1 4 7 6 R . . . = 0 . 2 1 5 1 , w R . . . = 0 . 1 7 8 7 R . . . = 0 . 0 5 6 9 , w R . . . = 0 . 1 4 0 2 R . . . = 0 . 0 6 5 1 , w R . . . = 0 . 1 4 2 7 R . . . = 0 . 0 8 1 1 , w R . . . = 0 . 1 6 9 2 R . . . = 0 . 2 7 5 8 , w R . . . = 0 . 2 2 2 5 R . . . = 0 . 1 4 2 8 , w R . . . = 0 . 2 9 2 6 R . . . = 0 . 6 8 6 2 , w R . . . = 0 . 7 7 1 1 0 . 1 1 0 0 a n d 0 . 8 8 4 3 5 . 0 5 a n d - 3 5 6 6 A 3 R = £ | | F . | - | F . | | / 2 1 m , w R = { z [ w ( | 1 = . | 2 - | F . | 2 ) 2 ] / z [ w ( 1 1 ~ ‘ . | “ ) ] } ” 2 a n d w = l / ( o 2 0 ) + 0 . 0 0 1 6 1 2 ) 3 7 0 T a b l e 5 . 2 0 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K z A g 4 L a 2 T e 9 , 6 . ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x 2 O c c u p a n c y U . . . L a [ 1 ] 0 2 9 1 3 1 5 8 2 6 1 9 ( 1 ) s i n , 1 4 3 ( 1 3 ) - 3 2 ( 1 7 ) - 8 ( 3 ) c o s , 1 - 4 6 ( l 3 ) 6 0 ( 1 0 ) 1 1 ( 2 ) s i n , 2 1 ( 4 ) 5 ( 5 ) - - 1 ( 1 ) c o s , 2 - 3 ( 3 ) 1 ( 4 ) 0 ( 1 ) s i n , 3 - 3 ( 5 ) 0 ( 6 ) - 2 ( 1 ) c o s , 3 3 ( 4 ) 9 ( 5 ) 0 ( 2 ) s i n , 4 - 5 ( 4 ) 1 ( 4 ) 1 ( 1 ) c o s , 4 4 ( 4 ) 4 ( 5 ) 0 ( 1 ) L a [ 2 ] 0 - 2 9 1 3 ( 1 ) 1 6 ( 1 ) - 8 2 3 ( 1 ) 1 8 ( 1 ) s i n , 1 - 6 8 ( 5 ) 5 2 ( 1 0 ) - 1 2 ( 1 ) c o s , 1 2 5 ( 2 0 ) - 3 4 ( 1 5 ) 4 ( 3 ) s i n , 2 0 ( 3 ) 1 ( 5 ) - 1 ( 1 ) c o s , 2 - 2 ( 3 ) 4 ( 4 ) 0 ( 1 ) s i n , 3 - 5 ( 5 ) 6 ( 7 ) 0 ( 1 ) c o s , 3 4 ( 5 ) - 1 0 ( 6 ) 1 ( 1 ) s i n , 4 - 3 ( 4 ) 4 ( 5 ) 0 ( 1 ) c o s , 4 2 ( 4 ) - 7 ( 5 ) 1 ( 1 ) T e [ l ] 0 7 7 3 9 ( 3 ) 1 2 ( 3 ) 4 8 2 ( 1 ) 1 1 1 ( 1 ) s i n , 1 - 2 ( 2 ) - 6 ( 2 ) - 7 ( 3 ) c o s , 1 4 ( 2 ) - 2 ( 3 ) 9 ( 2 ) s i n , 2 4 ( 4 ) 0 ( 5 ) 2 ( 1 ) c o s , 2 4 ( 4 ) - 6 ( 5 ) - 1 ( 1 ) s i n , 3 - 4 ( 5 ) 9 ( 6 ) 1 ( 2 ) c o s , 3 4 ( 5 ) - 5 ( 7 ) 1 ( 2 ) s i n , 4 - 9 ( 5 ) - l ( 5 ) - 1 ( 1 ) c o s , 4 6 ( 6 ) 2 ( 5 ) 0 ( 2 ) 3 7 1 T a b l e 5 . 2 0 . ( C o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K z A g a L a z T e o s m ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 2 ] 0 - 7 7 3 9 ( 3 ) 1 3 ( 3 ) - 4 7 9 ( 1 ) 1 7 ( 1 ) s i n , 1 - 1 2 ( 3 ) 9 ( 3 ) - 7 ( 1 ) c o s , 1 1 0 ( 4 ) 3 ( 4 ) 3 ( 2 ) s i n , 2 0 ( 4 ) - 1 ( 5 ) 1 ( 1 ) c o s , 2 - 2 ( 3 ) 1 ( 5 ) - 1 ( 1 ) s i n , 3 2 ( 5 ) 5 ( 6 ) 0 ( 1 ) c o s , 3 - 2 ( 5 ) - 4 ( 6 ) - 1 ( 1 ) s i n , 4 0 ( 4 ) 6 ( 5 ) 0 ( 1 ) c o s , 4 1 ( 4 ) 0 ( 5 ) 0 ( 1 ) T e [ 3 ] 0 9 3 4 ( 3 ) 2 5 1 5 ( 3 ) 1 8 3 3 ( 1 ) 1 1 0 ( 1 ) s i n , 1 2 5 ( 6 0 ) - 9 5 ( 5 0 ) - 1 ( 1 ) c o s , 1 - 2 1 4 ( 6 ) 1 9 5 ( 3 0 ) 3 ( 1 ) s i n , 2 5 ( 4 ) 8 ( 5 ) 1 ( 1 ) c o s , 2 - 1 ( 5 ) 0 ( 6 ) - 1 ( 1 ) s i n , 3 9 ( 6 ) - 2 ( 6 ) 0 ( 1 ) c o s , 3 4 ( 6 ) - 4 ( 7 ) 1 ( 1 ) s i n , 4 - 1 ( 5 ) 4 ( 7 ) 0 ( 1 ) c o s , 4 5 ( 5 ) - 1 2 ( 6 ) 0 ( 1 ) T e [ 4 ] 0 9 3 7 ( 4 ) - 2 5 0 3 ( 4 ) 1 8 3 1 ( 1 ) 1 1 3 ( 1 ) s i n , 1 - 5 ( 8 0 ) 1 6 5 ( 7 0 ) - 3 ( 3 ) c o s , 1 2 9 1 ( 5 ) - 2 3 5 ( 5 0 ) 1 1 ( 1 ) s i n , 2 2 ( 5 ) - 1 4 ( 6 ) 0 ( 1 ) c o s , 2 1 0 ( 5 ) - 1 1 ( 7 ) - 1 ( 1 ) s i n , 3 2 ( 7 ) 6 ( 8 ) 0 ( 2 ) c o s , 3 8 ( 6 ) - 9 ( 7 ) - 1 ( 2 ) s i n , 4 - 5 ( 5 ) 5 ( 6 ) 0 ( 1 ) c o s , 4 3 ( 5 ) - 3 ( 6 ) - 1 ( 1 ) 3 7 2 T a b l e 5 . 2 0 . ( C o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K z A g a L a z T e 9 _ . . ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 5 ] 0 - 9 0 1 ( 4 ) 2 4 9 6 ( 4 ) - 1 8 4 4 ( 1 ) 1 1 2 ( 1 ) s i n , 1 2 5 5 ( 3 0 ) - 2 7 5 ( 1 6 ) - l 3 ( 1 ) c o s , 1 - 1 0 5 ( 7 0 ) - 4 5 ( 8 0 ) 2 ( 4 ) s i n , 2 - 6 ( 5 ) - 1 ( 6 ) 0 ( 1 ) c o s , 2 - 7 ( 5 ) - 7 ( 5 ) - 2 ( 1 ) s i n , 3 5 ( 6 ) 2 ( 7 ) 0 ( 2 ) c o s , 3 - 7 ( 6 ) 4 ( 7 ) 1 ( 2 ) s i n , 4 - 1 ( 5 ) 2 ( 6 ) - 1 ( 1 ) c o s , 4 - l ( 5 ) 3 ( 6 ) 0 ( 1 ) T e [ 6 ] 0 - 8 9 7 ( 4 ) - 2 4 8 6 ( 4 ) - 1 8 3 2 ( 1 ) 1 1 4 ( 1 ) s i n , 1 - 2 2 5 ( 2 0 ) 2 3 8 ( 5 ) - 4 ( 1 ) c o s , 1 8 5 ( 7 0 ) 1 5 ( 7 0 ) 2 ( 2 ) s i n , 2 7 ( 5 ) - 4 ( 7 ) 1 ( 1 ) c o s , 2 - 1 ( 5 ) 1 8 ( 6 ) 1 ( 1 ) s i n , 3 - 3 ( 6 ) 7 ( 8 ) 0 ( 2 ) c o s , 3 - 4 ( 6 ) 1 0 ( 7 ) - 1 ( 2 ) s i n , 4 3 ( 5 ) 9 ( 6 ) 0 ( 1 ) c o s , 4 - 1 ( 5 ) 7 ( 7 ) 1 ( 1 ) T e [ 7 ] 0 1 3 ( 5 ) 3 3 ( 5 ) 5 0 0 7 ( 1 ) 1 2 3 ( 1 ) s i n , 1 6 7 ( 3 ) 1 5 ( 1 8 ) 2 ( 1 ) c o s , 1 5 ( 2 0 ) - 6 1 ( 6 ) 3 ( 1 ) s i n , 2 - 5 4 ( 1 6 ) - 1 6 ( 1 0 ) 0 ( 2 ) c o s , 2 5 4 ( 1 6 ) 2 3 ( 8 ) 0 ( 2 ) s i n , 3 - 1 2 ( 8 ) 1 3 ( 9 ) - 1 ( 2 ) c o s , 3 9 ( 8 ) 8 ( 9 ) - 1 ( 2 ) s i n , 4 - 1 8 ( 6 ) - 7 5 ( 6 ) 0 ( 2 ) c o s , 4 1 ( 9 ) 5 ( 3 0 ) - 3 ( 2 ) 3 7 3 T a b l e 5 . 2 0 . ( C o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K z A g a L a z T e 9 _ . . ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 8 ] O 5 0 3 2 ( 5 ) 2 6 ( 5 ) 5 0 0 8 ( 1 ) 0 . 6 0 7 ( 4 ) 2 3 ( 1 ) s i n , 1 1 9 ( 1 1 ) 0 ( 1 2 ) 3 ( 2 ) c o s , 1 3 4 ( 8 ) - 3 6 ( 5 ) 7 ( 2 ) s i n , 2 1 ( 1 0 ) 1 2 ( 1 1 ) 1 ( 3 ) c o s , 2 1 7 ( 9 ) 1 3 ( 1 0 ) - 4 ( 2 ) s i n , 3 1 ( 1 2 ) 7 ( 1 3 ) 3 ( 3 ) c o s , 3 8 ( 9 ) 1 1 ( 1 1 ) - 3 ( 3 ) s i n , 4 - 1 7 ( 9 ) - l 9 ( l 1 ) 3 ( 2 ) c o s , 4 - 1 0 ( 1 1 ) - 1 5 ( 1 4 ) - 3 ( 3 ) T e [ 9 ] 0 4 2 7 2 ( 3 ) 4 5 ( 3 ) 3 5 3 0 ( 1 ) 1 1 1 ( 1 ) s i n , 1 1 3 ( 1 0 ) 2 ( 9 ) 1 ( 2 ) c o s , 1 3 3 ( 4 ) - 2 9 ( 3 ) 8 ( 1 ) s i n , 2 - 1 ( 5 ) - 2 ( 5 ) 2 ( 2 ) c o s , 2 - 7 ( 4 ) 0 ( 5 ) - 4 ( 1 ) s i n , 3 5 ( 5 ) - 7 ( 6 ) 2 ( 2 ) c o s , 3 - 1 ( 5 ) - 1 ( 6 ) - 1 ( 2 ) s i n , 4 - 8 ( 5 ) - 2 ( 6 ) - 2 ( 2 ) c o s , 4 - 3 ( 5 ) - 6 ( 5 ) - 2 ( 2 ) T e [ l O ] 0 - 4 2 7 7 ( 3 ) 4 7 ( 3 ) - 3 5 6 6 ( 1 ) 1 3 3 ( 1 ) s i n , 1 1 7 ( 3 ) - 2 6 ( 7 ) - 2 7 ( 4 ) c o s , 1 0 ( 6 ) - 2 0 ( 8 ) - 1 3 ( 8 ) s i n , 2 6 ( 1 0 ) - 1 3 ( 6 ) 2 4 ( 4 ) c o s , 2 3 3 ( 5 ) 2 ( 7 ) 1 1 ( 7 ) s i n , 3 - 3 ( 6 ) 3 ( 8 ) 2 ( 2 ) c o s , 3 1 ( 6 ) - 1 1 ( 7 ) 0 ( 2 ) s i n , 4 - 7 ( 1 2 ) - 3 5 ( 1 2 ) - 3 ( l 3 ) c o s , 4 2 8 ( 6 ) - 2 5 ( 1 5 ) 3 4 ( 2 ) 3 7 4 T a b l e 5 . 2 0 . ( C o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K z A g a L a z T e 9 _ 6 . ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A g [ l ] 0 2 0 9 9 ( 4 ) 2 5 5 6 ( 4 ) 4 2 0 3 ( 1 ) 1 1 9 ( 1 ) s i n , 1 3 5 ( 4 ) 1 5 ( 6 ) 7 ( 5 ) c o s , 1 1 ( 1 1 ) - 1 6 ( 6 ) 1 6 ( 2 ) s i n , 2 - 1 7 ( 1 2 ) - 3 2 ( 1 0 ) - 5 ( 2 ) c o s , 2 3 8 ( 7 ) - 2 6 ( 1 1 ) - 2 ( 2 ) s i n , 3 1 0 ( 1 0 ) - l 3 ( 9 ) - 2 ( 2 ) c o s , 3 1 9 ( 8 ) - 1 0 ( 1 0 ) 1 ( 2 ) s i n , 4 - 2 3 ( 8 ) - 3 8 ( 1 2 ) 2 ( 3 ) c o s , 4 1 4 ( 1 1 ) ~ 2 4 ( 1 6 ) - 7 ( 2 ) A g [ 2 ] 0 2 1 3 0 ( 4 ) - 2 4 4 8 ( 4 ) 4 2 0 3 ( 1 ) 1 2 3 ( 1 ) s i n , 1 8 6 ( 1 4 ) 1 5 ( 2 0 ) 9 ( 1 ) c o s , 1 4 5 ( 2 0 ) - 7 7 ( 5 ) 3 ( 3 ) s i n , 2 - 5 8 ( 1 0 ) - 1 5 ( 1 0 ) - 1 0 ( 2 ) c o s , 2 3 0 ( 1 6 ) - 2 3 ( 8 ) - 6 ( 3 ) s i n , 3 - 1 5 ( 1 8 ) 4 ( 1 6 ) - 6 ( 5 ) c o s , 3 4 2 ( 1 0 ) 3 3 ( 8 ) 1 3 ( 3 ) s i n , 4 1 ( 8 ) - 3 7 ( 8 ) - 1 ( 4 ) c o s , 4 - 1 3 ( 6 ) - 6 ( 1 6 ) - 1 0 ( 2 ) A g [ 3 ] 0 - 2 0 7 6 ( 4 ) 2 5 6 8 ( 5 ) - 4 2 2 9 ( l ) 1 3 6 ( 1 ) s i n , 1 6 5 ( 1 1 ) 1 5 ( 1 8 ) - 1 4 ( 4 ) c o s , 1 - 3 5 ( 1 9 ) - 5 9 ( 7 ) - 1 2 ( 4 ) s i n , 2 - 1 5 ( 2 0 ) - 3 3 ( l 3 ) 3 1 ( 3 ) c o s , 2 8 3 ( 9 ) 3 4 ( 1 2 ) 6 ( 9 ) s i n , 3 1 5 ( 2 0 ) 1 5 ( 3 0 ) 9 ( 8 ) c o s , 3 5 2 ( 1 0 ) 6 9 ( 1 0 ) - 1 9 ( 5 ) s i n , 4 - 3 0 ( 8 ) - 8 2 ( 1 1 ) - 1 ( 7 ) c o s , 4 - 7 ( 1 4 ) - 1 5 ( 3 0 ) 1 9 ( 2 ) 3 7 5 T a b l e 5 . 2 0 . ( C o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K z A g a L a z T e o . . . ” a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A g [ 4 ] 0 - 2 1 2 1 ( 5 ) 2 4 3 7 ( 5 ) . 4 2 4 4 0 ) 1 4 2 ( 1 ) s i n , 1 7 4 ( 8 ) 4 5 ( 2 0 ) - 2 8 ( 7 ) c o s , 1 . 1 5 0 0 ) - 6 6 ( 8 ) - 2 3 ( 8 ) s i n , 2 . 2 5 0 0 ) 8 ( 1 1 ) 2 4 ( 3 ) c o s , 2 1 3 5 ( 1 1 ) - 2 0 0 0 ) 6 ( 7 ) s i n , 3 4 9 0 1 ) 5 3 0 3 ) . 5 0 ) c o s , 3 1 5 ( 2 0 ) - 1 5 ( 2 0 ) 0 ( 4 ) s i n , 4 4 4 0 1 ) — 1 2 1 ( 1 1 ) - 7 ( 8 ) c o s , 4 1 9 0 9 ) 4 5 0 0 ) 2 0 ( 4 ) K [ l ] 0 8 9 7 9 ( 9 ) 5 3 ( 9 ) 2 9 5 3 ( 2 ) 1 1 2 ( 1 ) s i n , 1 - 3 7 ( 1 8 ) 3 1 0 5 ) 2 0 ) c o s , 1 5 6 0 4 ) - 4 0 0 3 ) 9 ( 2 ) s i n , 2 0 0 3 ) 5 0 6 ) 0 ( 3 ) c o s , 2 8 0 3 ) 1 ( 1 6 ) - 3 ( 3 ) s i n , 3 1 5 ( 2 0 ) 2 5 0 0 ) 2 ( 4 ) c o s , 3 3 6 0 6 ) 5 ( 2 0 ) 0 ( 4 ) s i n , 4 7 0 8 ) 1 5 ( 1 8 ) 2 ( 4 ) c o s , 4 - 2 8 ( 1 5 ) - 2 2 0 7 ) - 6 ( 4 ) K [ 2 ] 0 1 0 0 8 ( 9 ) 3 4 0 1 ) 6 9 7 8 ( 2 ) 1 1 9 ( 1 ) s i n , 1 7 2 0 6 ) - 9 1 0 1 ) - 1 5 ( 4 ) c o s , 1 , 5 5 ( 2 0 ) - 5 ( 3 0 ) - 1 0 ( 5 ) s i n , 2 1 8 0 5 ) - 6 ( 1 8 ) 4 ( 4 ) c o s , 2 - 2 8 ( 1 4 ) - 6 ( 1 8 ) 1 ( 4 ) s i n , 3 5 ( 2 0 ) . 5 0 0 ) — 1 ( 5 ) c o s , 3 - 3 3 0 7 ) . 3 5 0 0 ) 1 ( 5 ) s i n , 4 - 2 7 0 7 ) 3 8 0 9 ) 1 ( 4 ) c o s , 4 - 1 8 ( 1 8 ) 1 5 ( 2 0 ) 2 ( 4 ) 3 7 6 T a b l e 5 . 2 1 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K 2 A g 4 L a 2 T e 9 _ . . ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e U . 1 U 2 2 U 3 3 U 1 2 U . 3 U 2 3 L a [ 1 ] 0 6 ( 1 ) 5 ( 1 ) 1 7 ( 1 ) - 2 ( 1 ) 2 ( 1 ) 0 ( 1 ) s i n , 1 - 1 ( 1 ) - 1 ( 1 ) 2 ( 1 ) 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) c o s , 1 2 ( 1 ) 4 ( 1 ) - l ( l ) - 2 ( 1 ) 0 ( 1 ) - 1 ( 1 ) s i n , 2 - 1 ( 1 ) 1 ( 1 ) - 1 ( 1 ) — 1 ( 1 ) 2 ( 1 ) 0 ( 1 ) c o s , 2 1 ( 1 ) - 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) - l ( 1 ) 0 ( 1 ) s i n , 3 0 ( 1 ) - 1 ( 1 ) 0 ( 2 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 3 - 2 ( 1 ) 0 ( 1 ) 1 ( 2 ) - 1 ( 1 ) - l ( 1 ) 1 ( 1 ) s i n , 4 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 2 ( 1 ) c o s , 4 0 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) - 1 ( 1 ) - l ( 1 ) L a [ 2 ] 0 8 ( 1 ) 9 ( 1 ) 8 ( 1 ) 0 ( 1 ) 1 ( 1 ) ' 0 ( 1 ) s i n , 1 4 ( 1 ) 4 ( 1 ) - 1 ( 1 ) - 3 ( 1 ) 1 ( 1 ) 0 ( 1 ) c o s , 1 - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) s i n , 2 - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) c o s , 2 1 ( 1 ) 1 ( 1 ) 3 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) s i n , 3 - 1 ( 1 ) 3 ( 2 ) 1 ( 1 ) - 3 ( 1 ) 0 ( 1 ) - 1 ( 1 ) c o s , 3 - 1 ( 1 ) 2 ( 2 ) - 1 ( 1 ) - 2 ( 2 ) 0 ( 1 ) 2 ( 1 ) s i n , 4 1 ( 1 ) - 3 ( 1 ) 2 ( 1 ) 1 ( 1 ) 1 ( 1 ) 1 ( 1 ) c o s , 4 0 ( 1 ) 1 ( 2 ) 1 ( 1 ) 2 ( 1 ) 1 ( 1 ) 1 ( 1 ) T e [ l ] 0 8 ( 1 ) 4 ( 1 ) 2 1 ( 1 ) 3 ( 1 ) 3 ( 1 ) 1 ( 1 ) s i n , 1 0 ( 1 ) 0 ( 1 ) 2 ( 1 ) 0 ( 1 ) 1 ( 1 ) - 1 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) - 2 ( 1 ) 1 ( 1 ) - 1 ( 1 ) 1 ( 1 ) s i n , 2 - 1 ( 1 ) 0 ( 2 ) 2 ( 2 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) c o s , 2 0 ( 1 ) - 2 ( 1 ) 1 ( 2 ) 2 ( 1 ) - 3 ( 1 ) 0 ( 1 ) s i n , 3 3 ( 1 ) 3 ( 2 ) - 1 ( 2 ) - 1 ( 1 ) 2 ( 1 ) - l ( 1 ) c o s , 3 0 ( 2 ) - 2 ( 2 ) 1 ( 2 ) 1 ( 1 ) - 1 ( 1 ) 0 ( 2 ) s i n , 4 2 ( 1 ) 0 ( 1 ) - 1 ( 2 ) 2 ( 1 ) - l ( 1 ) 0 ( 1 ) c o s , 4 2 ( 1 ) 1 ( 1 ) - l ( 2 ) 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) 3 7 7 T a b l e 5 . 2 1 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K 2 A g 4 L a 2 T e 9 . . . ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 2 ] 0 6 ( 1 ) 1 0 ( 1 ) 4 ( 1 ) 4 ( 1 ) 0 ( 1 ) 1 ( 1 ) s i n , 1 - 1 0 ) - 2 0 ) 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) - 1 0 ) c o s , 1 0 ( 1 ) - 1 0 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) s i n , 2 - 1 0 ) 1 ( 1 ) 0 ( 1 ) - 1 0 ) 0 ( 1 ) 0 ( 1 ) c o s , 2 1 ( 1 ) 0 ( 1 ) - 1 0 ) 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) s i n , 3 0 ( 1 ) - 2 ( 2 ) 0 ( 2 ) 1 ( 1 ) 0 ( 1 ) - 1 0 ) c o s , 3 - 1 ( 1 ) - 2 ( 2 ) 2 ( 1 ) 2 ( 1 ) 1 ( 1 ) - 1 0 ) s i n , 4 - 1 0 ) 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 4 0 ( 1 ) 0 ( 1 ) - 1 0 ) - 2 0 ) 0 ( 1 ) 0 ( 1 ) T e [ 3 ] 0 1 1 ( 1 ) 1 2 ( 1 ) 7 ( 1 ) 4 ( 1 ) 1 ( 1 ) - 1 0 ) s i n , 1 7 ( 1 ) - 3 ( 2 ) - 1 0 ) 4 ( 2 ) 1 ( 1 ) 2 ( 1 ) c o s , 1 - 2 ( 2 ) - 5 0 ) - 1 0 ) 5 ( 1 ) 1 ( 1 ) - 3 0 ) s i n , 2 1 ( 1 ) 0 ( 2 ) 0 ( 1 ) - 2 0 ) 1 ( 1 ) 0 ( 1 ) c o s , 2 0 ( 1 ) - 1 ( 2 ) — 1 ( 1 ) - 2 0 ) - 1 0 ) 1 ( 1 ) s i n , 3 - 1 0 ) 1 ( 2 ) - 1 ( 2 ) 2 ( 1 ) 0 ( 1 ) 1 ( 2 ) c o s , 3 - 1 0 ) 0 ( 2 ) 0 ( 2 ) 1 ( 2 ) 0 ( 1 ) - 1 0 ) s i n , 4 0 ( 1 ) 1 ( 2 ) - 1 0 ) 1 ( 1 ) - 1 0 ) 1 ( 1 ) c o s , 4 0 ( 1 ) 1 ( 2 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) T e [ 4 ] 0 1 3 ( 1 ) 1 4 ( 1 ) 1 3 ( 1 ) - 2 0 ) 2 ( 1 ) - 1 0 ) s i n , 1 - 1 4 0 ) 9 ( 3 ) - 1 0 ) 1 ( 3 ) - 1 0 ) 1 ( 1 ) c o s , 1 4 ( 4 ) 1 2 ( 3 ) - 1 ( 1 ) - 1 0 0 ) 2 ( 1 ) - 4 ( 1 ) s i n , 2 1 ( 1 ) - 2 ( 2 ) 1 ( 2 ) 1 ( 2 ) 0 ( 1 ) 0 ( 1 ) c o s , 2 - 1 0 ) - 1 ( 2 ) 1 ( 2 ) 5 ( 1 ) - 1 0 ) 1 ( 1 ) s i n , 3 0 ( 2 ) 1 ( 2 ) 1 ( 2 ) - 1 ( 3 ) 2 ( 1 ) 1 ( 2 ) c o s , 3 0 ( 2 ) - 1 ( 2 ) 3 ( 2 ) 7 ( 1 ) - 1 0 ) - 1 ( 2 ) s i n , 4 0 ( 2 ) 1 ( 2 ) - 1 0 ) - 1 0 ) 1 ( 1 ) 0 ( 2 ) c o s , 4 - 2 0 ) 0 ( 2 ) 0 ( 2 ) - 1 0 ) - 1 0 ) 1 ( 1 ) 3 7 8 T a b l e 5 . 2 1 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K 2 A g 4 L a 2 T e 9 , 6 . ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 5 ] 0 1 3 ( 1 ) 1 2 ( 1 ) 1 1 ( 1 ) — 3 ( 1 ) 2 ( 1 ) 0 ( 1 ) s i n , 1 8 ( 4 ) 5 ( 3 ) 1 ( 1 ) - 9 0 ) - 3 0 ) 4 ( 1 ) c o s , 1 1 3 ( 2 ) - 9 ( 2 ) 0 ( 1 ) 1 ( 3 ) 0 ( 1 ) - 1 0 ) s i n , 2 0 ( 1 ) — 1 ( 2 ) - 1 0 ) 0 ( 1 ) - 1 0 ) 0 ( 1 ) c o s , 2 2 ( 1 ) - 1 ( 2 ) - 1 0 ) 3 ( 1 ) 0 ( 1 ) 0 ( 1 ) s i n , 3 - 2 ( 2 ) - 1 ( 2 ) 0 ( 2 ) 2 ( 2 ) - 1 0 ) 1 ( 2 ) c o s , 3 1 ( 2 ) 1 ( 2 ) 0 ( 2 ) 3 ( 2 ) - 1 0 ) - 1 ( 2 ) s i n , 4 0 ( 1 ) - 1 ( 2 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) c o s , 4 1 ( 1 ) 0 ( 2 ) - 1 0 ) 2 ( 1 ) 1 ( 1 ) 0 ( 1 ) T e [ 6 ] 0 1 0 ( 1 ) 1 0 ( 1 ) 2 1 ( 1 ) - 1 0 ) 2 ( 1 ) 1 ( 1 ) s i n , 1 - 5 ( 2 ) - 5 ( 2 ) 2 ( 1 ) 6 ( 1 ) 2 ( 1 ) - 1 0 ) c o s , 1 - 5 ( 2 ) 6 ( 2 ) 2 ( 1 ) 1 ( 2 ) 0 ( 1 ) 0 ( 1 ) s i n , 2 1 ( 1 ) 0 ( 2 ) - 1 ( 2 ) 0 ( 2 ) 1 ( 1 ) 0 ( 1 ) c o s , 2 - 3 0 ) 1 ( 2 ) 2 ( 2 ) 4 ( 1 ) 1 ( 1 ) 0 ( 1 ) s i n , 3 - 1 ( 1 ) - 1 ( 2 ) 3 ( 2 ) 3 ( 2 ) 0 ( 1 ) - 1 ( 2 ) c o s , 3 0 ( 2 ) 1 ( 2 ) 0 ( 2 ) 2 ( 2 ) 1 ( 1 ) - 1 ( 2 ) s i n , 4 0 ( 1 ) 1 ( 2 ) 0 ( 2 ) 1 ( 2 ) - 1 0 ) 1 ( 1 ) c o s , 4 0 ( 1 ) 1 ( 2 ) - 1 ( 2 ) - 3 0 ) 0 ( 1 ) 0 ( 1 ) T e [ 7 ] 0 2 6 ( 1 ) 2 8 ( 1 ) 1 5 ( 1 ) 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) s i n , 1 0 ( 1 ) 2 ( 1 ) - 1 0 ) 0 ( 1 ) - 1 0 ) - 2 0 ) c o s , 1 2 ( 1 ) 0 ( 2 ) 0 ( 1 ) 3 ( 1 ) 1 ( 1 ) - 1 0 ) s i n , 2 2 ( 3 ) - 3 ( 3 ) - 4 ( 2 ) - 1 ( 2 ) 0 ( 1 ) 2 0 ) c o s , 2 - 8 ( 2 ) - 6 ( 2 ) 5 ( 2 ) - 2 ( 2 ) 0 ( 1 ) - 1 ( 2 ) s i n , 3 1 ( 3 ) 3 ( 3 ) - 4 ( 2 ) - 2 ( 2 ) 1 ( 1 ) . 1 0 ) c o s , 3 5 ( 2 ) 4 ( 3 ) - 2 ( 3 ) - 1 ( 2 ) 0 ( 2 ) 0 ( 2 ) s i n , 4 0 ( 4 ) — 7 ( 2 ) 2 ( 2 ) 0 ( 2 ) 0 ( 1 ) 1 ( 2 ) c o s , 4 - 1 1 ( 2 ) - 1 ( 3 ) 3 ( 2 ) - 1 0 ) 0 ( 1 ) - 1 ( 2 ) 3 7 9 T a b l e 5 . 2 1 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K 2 A g 4 L a 2 T e 9 , 6 . ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 8 ] 0 1 5 ( 1 ) 1 6 ( 1 ) 2 1 ( 1 ) 0 ( 1 ) 2 ( 1 ) 1 ( 1 ) s i n , 1 - 3 ( 2 ) - 3 ( 2 ) 0 ( 2 ) 1 ( 2 ) - 4 0 ) 0 ( 1 ) c o s , 1 4 ( 2 ) 4 ( 2 ) 5 ( 2 ) 4 ( 1 ) - 2 ( 2 ) 2 ( 2 ) s i n , 2 4 ( 4 ) 5 ( 3 ) 6 ( 3 ) - 3 ( 2 ) 1 ( 2 ) 2 ( 3 ) c o s , 2 1 0 ( 3 ) 2 ( 4 ) 0 ( 3 ) 0 ( 2 ) 0 ( 2 ) - 5 ( 3 ) s i n , 3 - 5 ( 3 ) - 1 ( 4 ) 1 ( 6 ) 3 ( 2 ) - 1 ( 3 ) 1 ( 3 ) c o s , 3 3 ( 4 ) - 1 ( 4 ) - 9 ( 4 ) 1 ( 3 ) - 3 ( 3 ) 1 ( 3 ) s i n , 4 - 8 ( 3 ) 6 ( 4 ) 0 ( 4 ) 0 ( 2 ) 0 ( 3 ) 1 ( 3 ) c o s , 4 5 ( 4 ) 5 ( 4 ) 6 ( 3 ) - 2 ( 2 ) 4 ( 2 ) - 6 ( 2 ) T e [ 9 ] 0 1 0 ( 1 ) 8 ( 1 ) 1 6 ( 1 ) - 2 0 ) 3 ( 1 ) - 2 0 ) s i n , 1 1 ( 1 ) - 1 0 ) 2 ( 2 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) c o s , 1 1 ( 1 ) 1 ( 1 ) 7 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) s i n , 2 - 3 0 ) - 4 ( 2 ) 9 ( 2 ) 2 ( 1 ) 1 ( 1 ) - 1 0 ) c o s , 2 - 2 0 ) - 1 ( 2 ) 4 ( 3 ) - 1 ( 1 ) - 1 0 ) 0 ( 1 ) s i n , 3 - 1 ( 2 ) - 2 ( 2 ) 4 ( 3 ) 0 ( 1 ) 0 ( 2 ) 0 ( 2 ) c o s , 3 2 ( 1 ) 0 ( 2 ) — 7 ( 2 ) - 1 0 ) - 2 0 ) 1 ( 1 ) s i n , 4 0 ( 1 ) 1 ( 2 ) — 5 ( 2 ) - 1 0 ) — 3 0 ) - 1 0 ) c o s , 4 1 ( 1 ) 4 ( 2 ) 0 ( 2 ) 1 ( 1 ) 1 ( 2 ) 0 ( 1 ) T e [ 1 0 ] 0 1 0 ( 1 ) 1 2 ( 1 ) 7 8 ( 2 ) 1 ( 1 ) 8 ( 1 ) 6 ( 1 ) s i n , 1 2 ( 1 ) 1 ( 1 ) 3 2 ( 7 ) 1 ( 1 ) 6 ( 1 ) 1 ( 1 ) c o s , 1 0 ( 1 ) - 2 ( 1 ) 2 1 ( 9 ) 0 ( 1 ) 2 ( 2 ) 0 ( 1 ) s i n , 2 2 ( 1 ) 6 ( 2 ) - 5 5 ( 8 ) 1 ( 1 ) - 7 ( 2 ) - 1 ( 2 ) c o s , 2 1 ( 1 ) 4 0 ) - 2 6 ( 1 5 ) 0 ( 1 ) - 2 ( 2 ) 1 ( 2 ) s i n , 3 2 ( 2 ) - 2 ( 3 ) - 8 ( 3 ) 0 ( 2 ) 0 ( 2 ) - 1 ( 2 ) c o s , 3 - 1 ( 2 ) 4 ( 2 ) - 1 ( 4 ) - 2 0 ) 0 ( 2 ) 2 ( 2 ) s i n , 4 0 ( 2 ) - 1 ( 3 ) 5 ( 3 0 ) 0 ( 2 ) - 2 ( 5 ) . 1 0 ) c o s , 4 3 ( 1 ) 5 ( 2 ) - 7 3 ( 3 ) 2 ( 1 ) - 1 2 ( 2 ) 2 ( 2 ) 3 8 0 T a b l e 5 . 2 1 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K 2 A g 4 L a 2 T e 9 , 6 . ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A g [ l ] 0 1 9 ( 1 ) 2 0 ( 1 ) 1 7 ( 1 ) 3 ( 1 ) - 1 0 ) 4 ( 1 ) s i n , 1 0 ( 2 ) 4 ( 2 ) 6 ( 2 ) - 1 ( 2 ) 1 ( 1 ) 0 ( 1 ) c o s , 1 5 ( 1 ) 6 ( 2 ) 4 ( 2 ) - 5 0 ) - 1 0 ) 2 ( 1 ) s i n , 2 2 ( 2 ) - 2 ( 2 ) - 4 ( 2 ) - 2 0 ) 3 ( 2 ) . 2 0 ) c o s , 2 4 ( 2 ) - 4 ( 2 ) 2 ( 2 ) 0 ( 2 ) 4 ( 2 ) - 8 ( 2 ) s i n , 3 2 ( 2 ) 0 ( 3 ) 1 ( 3 ) - 4 ( 2 ) 6 ( 3 ) . 4 0 ) c o s , 3 - 1 ( 2 ) - 4 ( 2 ) 6 ( 2 ) - 4 ( 2 ) 6 ( 3 ) - 7 ( 2 ) s i n , 4 2 ( 2 ) - 2 ( 2 ) 1 ( 2 ) 3 ( 2 ) 1 ( 2 ) 0 ( 3 ) c o s , 4 - 4 ( 2 ) - 3 ( 2 ) - 3 ( 2 ) 2 ( 2 ) 2 ( 1 ) - 5 ( 2 ) A g [ 2 ] 0 2 4 ( 1 ) 2 2 ( 1 ) 2 5 ( 1 ) - 8 ( 1 ) 7 ( 1 ) 6 ( 1 ) s i n , 1 - 2 ( 2 ) 2 ( 2 ) 8 ( 1 ) 5 ( 1 ) 6 ( 1 ) 8 ( 1 ) c o s , 1 5 ( 1 ) 4 ( 2 ) - 1 ( 2 ) - 3 ( 2 ) 0 ( 2 ) - 1 ( 2 ) s i n , 2 - 1 ( 2 ) - 6 ( 2 ) - 1 0 ( 2 ) - 7 ( 2 ) - 7 ( 2 ) . 7 0 ) c o s , 2 - 1 ( 2 ) - 3 ( 3 ) 4 ( 3 ) - 4 ( 3 ) 1 ( 2 ) - 1 ( 3 ) s i n , 3 - 3 ( 3 ) 0 ( 3 ) - 8 ( 7 ) - 1 ( 4 ) - 4 ( 5 ) 3 0 ) c o s , 3 3 ( 2 ) - 3 ( 2 ) 1 6 ( 4 ) 8 ( 2 ) 1 2 ( 2 ) 7 ( 2 ) s i n , 4 6 ( 2 ) - 1 ( 3 ) - 2 ( 3 ) - 3 ( 4 ) - 3 ( 2 ) - 1 ( 3 ) c o s , 4 - 1 ( 3 ) - 5 ( 2 ) - 5 ( 2 ) - 8 ( 2 ) 0 ( 2 ) - 5 ( 2 ) A g [ 3 ] 0 2 5 ( 1 ) 3 1 ( 1 ) 5 2 ( 2 ) 4 ( 1 ) 0 ( 1 ) - 8 ( 1 ) s i n , 1 2 ( 2 ) 5 ( 2 ) 1 4 ( 3 ) 2 ( 2 ) - 5 ( 3 ) - 7 ( 3 ) c o s , 1 5 ( 1 ) 2 ( 2 ) 3 ( 5 ) 6 ( 1 ) 9 ( 2 ) 8 ( 3 ) s i n , 2 - 9 ( 2 ) 4 ( 3 ) - 2 7 ( 3 ) - 6 ( 2 ) 0 ( 4 ) 7 ( 5 ) c o s , 2 - 4 ( 3 ) 2 ( 3 ) - 5 ( 8 ) - 5 ( 2 ) - 1 2 ( 2 ) - 1 7 ( 3 ) s i n , 3 - 2 ( 3 ) 0 ( 3 ) - 1 3 0 1 ) - 6 ( 2 ) - 5 ( 9 ) - 2 ( 6 ) c o s , 3 - 3 ( 2 ) - 2 ( 3 ) 2 6 ( 6 ) 3 ( 3 ) - 2 0 ( 3 ) - 1 3 ( 2 ) s i n , 4 5 ( 3 ) 4 ( 5 ) - 3 ( 6 ) 2 ( 4 ) 6 ( 2 ) 9 ( 2 ) c o s , 4 - 6 ( 3 ) - 1 2 ( 3 ) - 1 5 ( 3 ) - 1 1 ( 2 ) - 1 ( 3 ) 2 ( 4 ) 3 8 1 T a b l e 5 . 2 1 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K 2 A g 4 L a 2 T e o , 6 . ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A g [ 4 ] 0 3 3 ( 1 ) 3 6 ( 2 ) 5 9 ( 2 ) 0 ( 1 ) 1 1 ( 1 ) - 3 ( 2 ) s i n , 1 5 ( 2 ) 7 ( 3 ) 1 8 ( 3 ) - 9 ( 3 ) 0 ( 2 ) 7 ( 2 ) c o s , 1 5 ( 2 ) 1 0 ( 3 ) 6 ( 6 ) - 8 ( 3 ) 2 ( 2 ) - 3 ( 3 ) s i n , 2 - 1 0 ( 4 ) — 2 ( 3 ) - 1 2 ( 3 ) 1 2 ( 4 ) 5 ( 4 ) . 7 0 ) c o s , 2 - 1 2 ( 3 ) - 2 ( 3 ) 3 ( 5 ) 1 3 ( 4 ) - 1 5 ( 2 ) 2 4 ( 3 ) s i n , 3 1 ( 4 ) 5 ( 3 ) 9 ( 4 ) - 5 ( 2 ) 1 3 ( 3 ) - 1 5 ( 4 ) c o s , 3 - 7 ( 3 ) 3 ( 4 ) - 1 ( 5 ) 3 ( 3 ) - 3 ( 6 ) 6 ( 7 ) s i n , 4 - 3 ( 3 ) 4 ( 5 ) 5 ( 5 ) 4 ( 6 ) - 1 9 ( 2 ) 1 4 ( 3 ) c o s , 4 - 5 ( 2 ) - 1 0 ( 3 ) - 9 ( 4 ) 1 5 ( 3 ) 2 ( 7 ) 4 ( 6 ) K [ l ] 0 1 6 ( 2 ) 1 3 ( 2 ) 7 ( 2 ) 0 ( 1 ) 2 ( 1 ) - 2 ( 2 ) s i n , 1 7 ( 3 ) - 6 ( 3 ) 1 ( 2 ) 1 ( 2 ) 0 ( 2 ) - 6 ( 2 ) c o s , 1 7 ( 3 ) 7 ( 3 ) 1 ( 2 ) - 4 ( 2 ) 1 ( 2 ) 1 ( 3 ) s i n , 2 1 ( 4 ) 6 ( 6 ) - 2 ( 4 ) 4 ( 3 ) - 2 ( 3 ) 4 ( 4 ) c o s , 2 - 8 ( 3 ) 1 3 ( 5 ) - 2 ( 4 ) - 3 ( 3 ) 1 ( 3 ) 4 ( 4 ) s i n , 3 — 1 ( 6 ) - 2 0 0 ) 0 ( 5 ) 0 ( 4 ) 2 ( 4 ) 2 ( 8 ) c o s , 3 - 9 ( 4 ) 2 2 ( 5 ) 2 ( 4 ) 0 ( 4 ) 0 ( 4 ) 1 5 ( 4 ) s i n , 4 - 5 ( 4 ) - 2 ( 5 ) 2 ( 4 ) 0 ( 4 ) 3 ( 3 ) - 5 ( 4 ) c o s , 4 1 ( 4 ) - 6 ( 5 ) - 2 ( 4 ) 0 ( 3 ) 0 ( 3 ) - 5 ( 4 ) K [ 2 ] 0 1 1 ( 2 ) 2 6 ( 3 ) 1 9 ( 2 ) - 7 ( 2 ) 1 ( 1 ) 4 ( 2 ) s i n , 1 4 ( 2 ) 8 ( 3 ) - 5 ( 3 ) - 6 ( 2 ) 1 ( 2 ) - 1 ( 2 ) c o s , 1 3 ( 2 ) 0 ( 4 ) - 2 ( 3 ) - 3 ( 3 ) 5 ( 2 ) - 2 ( 3 ) s i n , 2 - 1 ( 4 ) - 8 ( 6 ) 4 ( 5 ) 2 ( 4 ) 1 ( 4 ) 1 ( 5 ) c o s , 2 2 ( 3 ) - 5 ( 6 ) - 3 ( 5 ) 0 ( 4 ) - 6 ( 3 ) 6 ( 4 ) s i n , 3 - 4 ( 5 ) 1 1 0 2 ) 9 ( 6 ) - 1 ( 5 ) - 1 ( 5 ) 6 ( 7 ) c o s , 3 - 7 ( 4 ) 2 4 ( 7 ) 3 ( 7 ) 0 ( 4 ) - 6 ( 4 ) 9 ( 5 ) s i n , 4 4 ( 4 ) - 5 ( 6 ) - 5 ( 5 ) 0 ( 4 ) - 1 ( 4 ) . 7 0 ) c o s , 4 - 1 ( 4 ) 4 ( 6 ) 0 ( 5 ) 0 ( 4 ) - 2 ( 4 ) - 1 ( 5 ) 3 8 2 T a b l e 5 . 2 2 . F o u r i e r c o m p o n e n t s o f t h e o c c u p a t i o n a l m o d u l a t i o n f o r K 2 A g 4 L a 2 T e 9 , 6 . ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e O c c u p a t i o n a l c o m p o n e n t T e [ 8 ] s i n , 1 - 0 0 1 7 ( 1 0 ) c o s , 1 - 0 . 0 2 2 ( 1 0 ) T e [ 8 ] s i n , 2 0 1 2 ( 2 ) c o s , 2 0 0 4 ( 4 ) T e [ 8 ] s i n , 3 0 0 1 ( 2 ) c o s , 3 0 0 2 ( 3 ) T e [ 8 ] s i n , 4 - 0 . 0 1 ( 5 ) c o s , 4 0 . 1 0 7 ( 1 6 ) T a b l e 5 . 2 3 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K 2 A g 4 L a 2 T e 9 , 6 1 ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e L a [ 1 ] - T e [ 1 ] x 4 3 . 2 9 3 ( 1 9 ) 3 . 2 4 7 ( 1 9 ) 3 . 3 3 5 ( 1 9 ) L a [ 1 ] - T e [ 2 ] 3 2 9 ( 2 ) 3 . 2 7 3 ( 2 0 ) 3 . 3 1 2 ( 2 0 ) L a [ 1 ] - T e [ 3 ] x 2 3 3 8 ( 3 ) 3 3 2 ( 2 ) 3 4 6 ( 2 ) L a [ 1 ] - T e [ 4 ] x 2 3 3 9 ( 4 ) 3 3 5 ( 5 ) 3 4 3 ( 4 ) L a [ 2 ] - T e [ l ] 3 2 9 ( 2 ) 3 2 7 ( 2 ) 3 3 0 ( 2 ) L a [ 2 ] - T e [ 2 ] x 4 3 . 2 9 2 ( 2 0 ) 3 . 2 5 3 ( 1 6 ) 3 . 3 2 8 ( 1 6 ) L a [ 2 ] - T e [ 5 ] x 2 3 . 4 2 ( 4 ) 3 3 8 ( 4 ) 5 4 6 ( 4 ) L a [ 2 ] - T e [ 6 ] x 2 3 4 1 ( 3 ) 3 2 8 ( 2 ) 3 5 3 ( 2 ) T e [ 3 ] - T e [ 4 ] x 4 3 2 0 ( 6 ) 2 9 0 ( 6 ) 3 . 4 9 ( 6 ) T e [ 4 ] - K [ l ] x 2 5 6 4 ( 5 ) 3 . 4 9 ( 4 ) 3 . 7 8 ( 5 ) T e [ 5 ] - T e [ 6 ] x 4 3 . 1 8 ( 6 ) 2 8 7 ( 4 ) 3 4 5 ( 4 ) T e [ 7 ] - T e [ 8 ] x 4 3 1 6 ( 4 ) 3 0 7 ( 4 ) 3 2 4 ( 4 ) T e [ 7 ] - A g [ l ] x 2 3 0 3 ( 4 ) 2 9 9 ( 3 ) 3 0 7 ( 4 ) T e [ 7 ] - A g [ 2 ] x 2 3 0 3 ( 4 ) 2 9 7 ( 4 ) 3 0 7 ( 4 ) T e [ 7 ] - A g [ 3 ] x 2 2 9 6 ( 5 ) 2 8 6 ( 5 ) 3 0 3 ( 5 ) T e [ 7 ] - A g [ 4 ] x 2 2 9 3 ( 6 ) 2 8 4 ( 6 ) 2 9 9 ( 6 ) T e [ 8 ] - T e [ l O ] 3 5 9 ( 6 ) 3 3 4 ( 4 ) 3 . 7 4 ( 7 ) T e [ 8 ] - A g [ l ] x 2 3 0 5 ( 3 ) 3 0 0 ( 4 ) 3 1 0 ( 3 ) T e [ 8 ] - A g [ 2 ] x 2 3 0 2 ( 4 ) 2 8 7 ( 4 ) 3 0 9 ( 4 ) T e [ 8 ] - A g [ 3 ] x 2 2 9 8 ( 5 ) 2 8 2 ( 5 ) 3 0 5 ( 5 ) 3 8 3 T a b l e 5 . 2 3 . ( C o n t ’ d ) B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K 2 A g 4 L a z T e 9 , . . ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 8 ] - A g [ 4 ] x 2 2 9 1 ( 5 ) 2 7 3 ( 6 ) 3 0 6 ( 5 ) T e [ 9 ] - A g [ l ] x 2 2 8 2 ( 3 ) 2 7 8 ( 3 ) 2 9 2 ( 3 ) T e [ 9 ] - A g [ 2 ] x 2 2 8 1 ( 4 ) 2 7 7 ( 4 ) 2 8 5 ( 4 ) T e [ 9 ] - K [ l ] x 4 3 5 0 ( 4 ) 3 4 4 ( 4 ) 3 5 5 ( 4 ) T e [ l O ] - A g [ 3 ] x 2 2 8 2 ( 6 ) 2 7 2 ( 5 ) 2 9 4 ( 6 ) T e [ 1 0 ] - A g [ 4 ] x 2 2 8 1 ( 7 ) 2 7 4 ( 7 ) 2 9 3 ( 6 ) T e [ l O ] - K [ 2 ] x 4 3 4 6 ( 6 ) 3 3 5 ( 5 ) 3 5 2 ( 6 ) A g [ l ] - A g [ 2 ] x 4 3 . 1 8 ( 4 ) 3 0 6 ( 3 ) 3 3 0 ( 3 ) A g [ 3 ] - A g [ 4 ] x 4 3 . 1 8 ( 6 ) 2 9 8 ( 6 ) 3 . 4 2 ( 6 ) T a b l e 5 . 2 4 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K 2 A g 4 L a 2 T e 9 , 6 . ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ l ] - L a [ 1 ] - T e [ l ] x 4 1 4 9 . 4 ( 7 ) 1 4 8 . 5 ( 7 ) 1 5 0 . 2 ( 7 ) T e [ l ] - L a [ 1 ] - T e [ l ] x 8 8 6 0 ( 5 ) 8 5 6 ( 5 ) 8 6 2 ( 5 ) T e [ l ] - L a [ 1 ] - T e [ 2 ] x 4 7 4 . 7 ( 5 ) 7 4 0 ( 5 ) 7 5 . 5 ( 5 ) T e [ l ] - L a [ 1 ] - T e [ 3 ] x 4 7 5 4 ( 9 ) 7 4 . 1 ( 8 ) 7 6 7 ( 9 ) T e [ l ] - L a [ 1 ] - T e [ 3 ] x 4 1 3 0 . 6 ( 1 0 ) 1 2 9 . 0 ( 1 0 ) 1 3 2 . 1 ( 1 0 ) T e [ 1 ] - L a [ 1 ] - T e [ 4 ] x 4 7 5 . 6 ( 1 1 ) 7 2 . 3 ( 1 0 ) 7 8 . 6 ( 1 1 ) T e [ l ] - L a [ 1 ] - T e [ 4 ] x 4 1 3 0 . 7 ( 1 2 ) 1 2 5 . 3 ( 1 2 ) 1 3 6 . 3 ( 1 2 ) T e [ 2 ] - L a [ 1 ] - T e [ 3 ] x 2 1 3 8 . 6 ( 8 ) 1 3 7 . 6 ( 8 ) 1 3 9 . 6 ( 8 ) T e [ 2 ] - L a [ 1 ] - T e [ 4 ] x 2 1 3 8 . 3 ( 1 0 ) 1 3 6 . 7 ( 9 ) 1 3 9 . 9 ( 1 0 ) T e [ 3 ] - L a [ 1 ] - T e [ 3 ] x 2 8 3 . 0 ( 9 ) 8 2 . 1 ( 8 ) 8 3 9 ( 8 ) T e [ 3 ] - L a [ 1 ] - T e [ 4 ] x 4 5 6 . 4 ( 1 1 ) 5 1 . 3 ( 1 1 ) 6 1 . 1 ( 1 0 ) T e [ 4 ] - L a [ 1 ] - T e [ 4 ] x 2 8 3 . 2 ( 1 1 ) 8 0 . 9 ( 1 2 ) 8 5 . 1 ( 1 1 ) T e [ l ] - L a [ 2 ] - T e [ 2 ] x 4 7 4 . 7 ( 4 ) 7 4 . 3 ( 5 ) 7 5 . 1 ( 5 ) T e [ l ] - L a [ 2 ] - T e [ 5 ] x 2 1 3 8 . 8 ( 7 ) 1 3 7 . 4 ( 7 ) 1 4 0 . 1 ( 7 ) T e [ l ] - L a [ 2 ] - T e [ 6 ] x 2 1 3 8 . 4 ( 6 ) 1 3 7 . 5 ( 7 ) 1 3 9 . 8 ( 6 ) T e [ 2 ] - L a [ 2 ] - T e [ 2 ] x 4 1 4 9 . 5 ( 6 ) 1 4 8 . 6 ( 5 ) 1 5 0 . 3 ( 5 ) T e [ 2 ] - L a [ 2 ] - T e [ 2 ] x 8 8 6 . 0 ( 5 ) 8 5 7 ( 5 ) 8 6 4 ( 6 ) T e [ 2 ] - L a [ 2 ] - T e [ 5 ] x 4 1 3 0 . 5 ( 7 ) 1 2 5 . 4 ( 7 ) 1 3 5 . 7 ( 6 ) T e [ 2 ] - L a [ 2 ] - T e [ 5 ] x 4 7 5 6 ( 6 ) 7 2 5 ( 6 ) 7 8 8 ( 7 ) T e [ 2 ] - L a [ 2 ] - T e [ 6 ] x 4 1 3 0 . 6 ( 6 ) 1 2 9 . 1 ( 7 ) 1 3 2 . 1 ( 7 ) 3 8 4 T a b l e 5 . 2 4 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K 2 A g 4 L a 2 T e o . . ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 2 ] - L a [ 2 ] - T e [ 6 ] x 4 T e [ 5 ] - L a [ 2 ] - T e [ 5 ] x 2 T e [ 5 ] - L a [ 2 ] - T e [ 6 ] x 4 T e [ 6 ] - L a [ 2 ] - T e [ 6 ] x 2 L a [ 1 ] - T e [ 1 ] - L a [ 1 ] x 4 L a [ 1 ] - T e [ 1 ] - L a [ 1 ] x 8 L a [ 1 ] - T e [ 1 ] - L a [ 2 ] x 4 L a [ 1 ] - T e [ 2 ] - L a [ 2 ] x 4 L a [ 2 ] - T e [ 2 ] - L a [ 2 ] x 4 L a [ 2 ] - T e [ 2 ] - L a [ 2 ] x 8 L a [ 1 ] - T e [ 3 ] - L a [ 1 ] x 2 L a [ 1 ] - T e [ 3 ] - T e [ 4 ] x 4 L a [ 1 ] - T e [ 3 ] - T e [ 4 ] x 4 L a [ 1 ] - T e [ 3 ] - K [ 1 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 8 T e [ 4 ] - T e [ 3 ] - K [ l ] x 4 T e [ 4 ] - T e [ 3 ] - K [ l ] x 4 L a [ 1 ] - T e [ 4 ] - L a [ 1 ] x 2 L a [ 1 ] - T e [ 4 ] - T e [ 3 ] x 4 L a [ 1 ] - T e [ 4 ] - T e [ 3 ] x 4 L a [ 1 ] - T e [ 4 ] - K [ 1 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 8 T e [ 3 ] - T e [ 4 ] - K [ l ] x 4 T e [ 3 ] - T e [ 4 ] - K [ l ] x 4 K [ l ] - T e [ 4 ] - K [ 1 ] x 2 L a [ 2 ] - T e [ 5 ] - L a [ 2 ] x 2 L a [ 2 ] - T e [ 5 ] - T e [ 6 ] x 4 L a [ 2 ] - T e [ 5 ] - T e [ 6 ] x 4 L a [ 2 ] - T e [ 5 ] - K [ 2 ] x 4 T e [ 6 ] - T e [ 5 ] - T e [ 6 ] x 4 T e [ 6 ] - T e [ 5 ] - T e [ 6 ] x 8 T e [ 6 ] - T e [ 5 ] - K [ 2 ] x 4 7 5 6 ( 5 ) 8 2 . 2 ( 8 ) 5 5 4 ( 8 ) 8 2 . 8 ( 7 ) 1 4 9 . 4 ( 7 ) 8 6 . 1 ( 5 ) 1 0 5 . 3 ( 5 ) 1 0 5 . 2 ( 5 ) 1 4 9 . 5 ( 5 ) 8 6 . 0 ( 4 ) 8 3 . 0 ( 5 ) 6 1 . 9 ( 1 0 ) 1 1 7 . 7 0 1 ) 1 2 6 . 1 0 4 ) 1 7 4 . 8 ( 1 8 ) 8 9 . 5 0 6 ) 6 4 . 3 0 0 ) 1 1 6 . 4 ( 1 1 ) 8 2 . 9 ( 5 ) 1 1 8 . 4 ( 1 1 ) 6 1 . 7 0 0 ) 1 2 4 . 9 ( 1 6 ) 1 7 4 . 0 0 8 ) 8 9 . 8 ( 1 6 ) 1 1 6 . 2 0 2 ) 6 4 . 6 ( 1 1 ) 7 6 . 8 ( 1 0 ) 8 2 . 1 ( 5 ) 6 2 . 0 ( 8 ) 1 1 7 . 0 0 0 ) 1 2 7 . 4 0 5 ) 1 7 4 . 0 ( 1 7 ) 8 9 . 9 ( 1 4 ) 6 5 . 6 ( 1 1 ) 7 4 . 2 ( 6 ) 7 9 9 ( 9 ) 5 0 . 2 ( 5 ) 8 2 . 2 ( 5 ) 1 4 8 . 7 ( 7 ) 8 5 9 ( 5 ) 1 0 4 . 7 ( 5 ) 1 0 4 . 3 ( 5 ) 1 4 9 . 0 ( 5 ) 8 5 6 ( 4 ) 8 2 . 3 ( 5 ) 5 9 . 0 ( 8 ) 1 1 5 . 7 ( 1 1 ) 1 2 2 . 1 0 2 ) 1 7 1 . 4 0 5 ) 8 6 . 8 ( 1 7 ) 6 2 . 5 ( 1 1 ) 1 1 1 . 6 0 0 ) 8 2 . 3 ( 5 ) 1 1 2 . 4 ( 9 ) 5 9 . 5 ( 9 ) 1 1 8 . 6 0 6 ) 1 7 0 . 2 ( 1 2 ) 8 7 . 6 0 7 ) 1 1 3 . 2 0 3 ) 6 0 . 1 0 0 ) 7 6 . 1 ( 1 0 ) 8 1 . 7 ( 4 ) 5 9 . 7 ( 9 ) 1 1 0 . 3 ( 8 ) 1 2 2 . 3 0 0 ) 1 7 0 . 1 0 6 ) 8 7 . 1 0 6 ) 6 1 . 5 ( 9 ) 7 6 9 ( 6 ) 8 4 . 1 ( 7 ) 6 0 . 2 ( 5 ) 8 3 8 ( 6 ) 1 5 0 . 4 ( 7 ) 8 6 . 3 ( 5 ) 1 0 5 . 9 ( 5 ) 1 0 6 . 3 ( 5 ) 1 4 9 . 9 ( 5 ) 8 6 . 4 ( 4 ) 8 3 . 7 ( 5 ) 6 5 . 3 ( 1 0 ) 1 1 9 . 1 ( 9 ) 1 3 0 . 2 0 3 ) 1 7 9 . 8 ( 1 5 ) 9 2 . 5 0 8 ) 6 6 . 3 ( 1 1 ) 1 2 1 . 4 0 0 ) 8 3 . 3 ( 6 ) 1 2 4 . 3 ( 9 ) 6 3 . 6 0 0 ) 1 3 1 . 6 0 6 ) 1 8 0 ( 2 ) 9 3 . 1 0 9 ) 1 1 9 . 6 0 3 ) 6 8 . 7 ( 1 1 ) 7 7 . 7 0 0 ) 8 2 . 4 ( 5 ) 6 4 . 4 ( 9 ) 1 2 3 . 8 ( 7 ) 1 3 2 . 5 ( 1 1 ) 1 7 9 . 0 0 6 ) 9 3 . 1 0 6 ) 6 9 . 9 ( 1 0 ) 3 8 5 T a b l e 5 . 2 4 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K 2 A g a L a 2 T e 9 . . . ” a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 6 ] - T e [ 5 ] - K [ 2 ] x 4 L a [ 2 ] - T e [ 6 ] - L a [ 2 ] x 2 L a [ 2 ] - T e [ 6 ] - T e [ 5 ] x 4 L a [ 2 ] - T e [ 6 ] - T e [ 5 ] x 4 L a [ 2 ] - T e [ 6 ] - K [ 2 ] x 4 T e [ 5 ] - T e [ 6 ] - T e [ 5 ] x 4 T e [ 5 ] - T e [ 6 ] - T e [ 5 ] x 8 T e [ 5 ] - T e [ 6 ] - K [ 2 ] x 4 T e [ 5 ] - T e [ 6 ] - K [ 2 ] x 4 T e [ 8 ] - T e [ 7 ] - T e [ 8 ] x 4 T e [ 8 ] - T e [ 7 ] - T e [ 8 ] x 8 T e [ 8 ] - T e [ 7 ] - A g [ l ] x 4 T e [ 8 ] - T e [ 7 ] - A g [ l ] x 4 T e [ 8 ] - T e [ 7 ] - A g [ 2 ] x 4 T e [ 8 ] - T e [ 7 ] - A g [ 2 ] x 4 T e [ 8 ] - T e [ 7 ] - A g [ 3 ] x 4 T e [ 8 ] - T e [ 7 ] - A g [ 3 ] x 4 T e [ 8 ] - T e [ 7 ] - A g [ 4 ] x 4 T e [ 8 ] - T e [ 7 ] - A g [ 4 ] x 4 A g [ 1 ] - T e [ 7 ] - A g [ 1 ] x 2 A g [ l ] - T e [ 7 ] - A g [ 2 ] x 4 A g [ l ] - T e [ 7 ] - A g [ 3 ] x 4 A g [ l ] - T e [ 7 ] - A g [ 4 ] x 2 A g [ l ] - T e [ 7 ] - A g [ 4 ] x 2 A g [ 2 ] - T e [ 7 ] - A g [ 2 ] x 2 A g [ 2 ] - T e [ 7 ] - A g [ 3 ] x 2 A g [ 2 ] - T e [ 7 ] - A g [ 3 ] x 2 A g [ 2 ] - T e [ 7 ] - A g [ 4 ] x 4 A g [ 3 ] - T e [ 7 ] - A g [ 3 ] x 2 A g [ 3 ] - T e [ 7 ] - A g [ 4 ] x 4 A g [ 4 ] - T e [ 7 ] - A g [ 4 ] x 2 T e [ 7 ] - T e [ 8 ] - T e [ 7 ] x 4 T e [ 7 ] - T e [ 8 ] - T e [ 7 ] x 8 T e [ 7 ] - T e [ 8 ] - T e [ l O ] x 4 1 1 5 . 9 ( 1 2 ) 8 2 8 ( 5 ) 1 1 8 . 0 ( 9 ) 6 2 . 6 ( 8 ) 1 2 6 . 5 0 3 ) 1 7 4 . 1 0 6 ) 8 9 . 4 ( 1 3 ) 1 1 5 . 0 ( 1 1 ) 6 4 . 5 0 0 ) 1 7 8 . 9 ( 1 2 ) 9 0 . 2 ( 1 0 ) 1 2 1 . 5 0 0 ) 5 8 . 1 ( 8 ) 1 2 1 . 9 ( 1 1 ) 5 8 . 7 ( 9 ) 5 8 . 1 ( 1 1 ) 1 2 2 . 8 ( 1 3 ) 5 7 . 0 ( 1 1 ) 1 2 2 . 5 0 3 ) 9 5 . 9 ( 8 ) 6 3 . 4 ( 9 ) 1 1 5 . 0 ( 1 4 ) 1 7 7 . 1 0 3 ) 8 2 . 0 0 3 ) 9 5 . 9 ( 1 0 ) 1 7 7 . 8 ( 1 5 ) 8 2 . 7 0 4 ) 1 1 6 . 1 0 4 ) 9 8 . 8 ( 1 4 ) 6 5 . 5 ( 1 3 ) 9 9 . 9 ( 1 4 ) 1 7 8 . 9 ( 1 2 ) 8 9 . 8 ( 1 0 ) 8 9 8 ( 8 ) 1 1 2 . 2 0 4 ) 8 2 . 1 ( 4 ) 1 1 4 . 6 0 3 ) 5 8 . 4 ( 6 ) 1 2 1 . 3 ( 9 ) 1 7 0 . 8 ( 1 4 ) 8 6 . 7 ( 1 2 ) 1 0 9 . 6 0 0 ) 6 2 . 6 0 0 ) 1 7 6 . 7 ( 1 1 ) 8 7 . 7 0 0 ) 1 2 0 . 3 0 0 ) 5 5 3 ( 8 ) 1 1 9 . 5 0 0 ) 5 7 . 6 ( 9 ) 5 4 . 7 ( 1 1 ) 1 2 0 . 1 0 2 ) 5 3 . 5 0 0 ) 1 2 0 . 0 ( 1 3 ) 9 4 . 8 ( 8 ) 6 1 . 4 0 0 ) 1 1 0 . 3 0 5 ) 1 7 3 . 1 0 4 ) 7 5 . 5 ( 1 3 ) 9 4 . 0 ( 9 ) 1 7 4 . 6 0 5 ) 7 7 . 2 0 4 ) 1 1 1 . 0 0 7 ) 9 5 . 2 ( 1 4 ) 6 0 . 1 0 2 ) 9 6 . 1 0 4 ) 1 7 7 . 8 ( 1 2 ) 8 8 . 1 0 0 ) 8 9 . 0 ( 8 ) 1 1 9 . 4 0 4 ) 8 3 . 7 ( 4 ) 1 2 1 . 4 0 2 ) 6 7 . 7 ( 7 ) 1 3 2 . 2 ( 9 ) 1 7 9 . 2 ( 9 ) 9 2 . 8 ( 1 5 ) 1 2 0 . 0 ( 1 0 ) 6 6 . 6 ( 1 1 ) 1 8 0 9 3 . 0 ( 1 0 ) 1 2 2 . 5 ( 9 ) 6 0 . 2 ( 8 ) 1 2 4 . 0 ( 1 1 ) 5 9 . 7 ( 9 ) 6 0 . 1 ( 1 1 ) 1 2 6 . 2 ( 1 4 ) 6 0 . 6 0 0 ) 1 2 6 . 1 0 3 ) 9 7 . 8 ( 8 ) 6 5 . 5 ( 1 0 ) 1 1 8 . 3 0 4 ) 1 7 9 . 9 ( 1 4 ) 8 5 . 6 ( 1 3 ) 9 8 9 ( 9 ) 1 8 0 8 5 . 6 ( 1 3 ) 1 1 9 . 8 ( 1 5 ) 1 0 5 . 2 ( 1 5 ) 7 3 . 2 0 3 ) 1 0 6 . 9 ( 1 5 ) 1 8 0 9 2 . 4 ( 9 ) 9 0 . 6 ( 8 ) 3 8 6 T a b l e 5 . 2 4 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K 2 A g 4 L a 2 T e o , . . ( 1 ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 7 ] - T e [ 8 ] - A g [ l ] x 4 T e [ 7 ] - T e [ 8 ] - A g [ l ] x 4 T e [ 7 ] - T e [ 8 ] - A g [ 2 ] x 4 T e [ 7 ] - T e [ 8 ] - A g [ 2 ] x 4 T e [ 7 ] - T e [ 8 ] - A g [ 3 ] x 4 T e [ 7 ] - T e [ 8 ] - A g [ 3 ] x 4 T e [ 7 ] - T e [ 8 ] - A g [ 4 ] x 4 T e [ 7 ] - T e [ 8 ] - A g [ 4 ] x 4 T e [ 1 0 ] - T e [ 8 ] - A g [ 1 ] x 2 T e [ l O ] - T e [ 8 ] - A g [ 2 ] x 2 T e [ l O ] - T e [ 8 ] - A g [ 3 ] x 2 T e [ 1 0 ] - T e [ 8 ] - A g [ 4 ] x 2 A g [ l ] - T e [ 8 ] - A g [ l ] x 2 A g [ l ] - T e [ 8 ] - A g [ 2 ] x 4 A g [ l ] - T e [ 8 ] - A g [ 3 ] x 4 A g [ l ] - T e [ 8 ] - A g [ 4 ] x 2 A g [ l ] - T e [ 8 ] - A g [ 4 ] x 2 A g [ 2 ] - T e [ 8 ] - A g [ 2 ] x 2 A g [ 2 ] - T e [ 8 ] - A g [ 3 ] x 2 A g [ 2 ] - T e [ 8 ] - A g [ 3 ] x 2 A g [ 2 ] - T e [ 8 ] - A g [ 4 ] x 4 A g [ 3 ] - T e [ 8 ] - A g [ 3 ] x 2 A g [ 3 ] - T e [ 8 ] - A g [ 4 ] x 4 A g [ 4 ] - T e [ 8 ] - A g [ 4 ] x 2 A g [ l ] - T e [ 9 ] - A g [ 1 ] x 2 A g [ l ] - T e [ 9 ] - A g [ 2 ] x 4 A g [ 1 ] - T e [ 9 ] - K [ 1 ] x 4 A g [ l ] - T e [ 9 ] - K [ l ] x 4 A g [ 2 ] - T e [ 9 ] - A g [ 2 ] x 2 A g [ 2 ] - T e [ 9 ] - K [ l ] x 4 A g [ 2 ] - T e [ 9 ] - K [ l ] x 4 K [ l ] - T e [ 9 ] - K [ 1 ] x 4 K [ 1 ] - T e [ 9 ] - K [ 1 ] x 8 T e [ 8 ] - T e [ 1 0 ] - A g [ 3 ] x 2 5 8 . 1 ( 8 ) 1 2 1 . 4 ( 1 0 ) 5 8 . 3 ( 9 ) 1 2 1 . 4 ( 1 1 ) 1 2 2 . 3 0 4 ) 5 7 . 5 0 0 ) 1 2 2 . 7 0 4 ) 5 7 . 1 0 0 ) 1 3 1 . 5 ( 1 1 ) 1 3 2 . 2 0 2 ) 4 9 . 7 ( 1 1 ) 4 9 . 9 ( 1 1 ) 9 5 . 8 ( 1 0 ) 6 3 . 3 ( 9 ) 1 1 5 . 3 ( 1 3 ) 1 7 7 . 8 ( 1 5 ) 8 1 . 5 0 2 ) 9 5 . 8 ( 1 1 ) 1 7 7 . 6 0 5 ) 8 3 . 1 0 3 ) 1 1 6 . 0 ( 1 3 ) 9 8 . 8 ( 1 6 ) 6 5 . 4 ( 1 2 ) 9 9 . 9 ( 1 6 ) 1 0 5 . 9 ( 9 ) 6 8 . 9 ( 1 0 ) 7 4 . 7 ( 9 ) 1 3 9 . 8 ( 1 0 ) 1 0 5 . 9 ( 1 1 ) 7 5 . 1 ( 1 0 ) 1 3 9 . 7 ( 1 1 ) 1 3 0 . 7 0 0 ) 8 0 . 0 0 0 ) 5 3 . 6 0 4 ) 5 7 . 1 ( 8 ) 1 1 9 . 9 ( 1 0 ) 5 6 . 6 ( 9 ) 1 1 9 . 9 ( 1 0 ) 1 2 0 . 3 ( 1 3 ) 5 5 . 0 ( 1 0 ) 1 1 9 . 9 ( 1 4 ) 5 4 . 9 ( 1 0 ) 1 2 9 . 5 ( 1 1 ) 1 3 1 . 1 0 2 ) 4 7 . 1 ( 1 1 ) 4 7 . 1 0 1 ) 9 4 . 6 0 0 ) 6 1 . 2 ( 9 ) 1 1 1 . 1 0 3 ) 1 7 4 . 6 ( 1 5 ) 7 6 . 5 0 2 ) 9 4 . 0 ( 1 1 ) 1 7 2 . 1 0 6 ) 7 8 . 7 0 4 ) 1 1 3 . 1 0 4 ) 9 4 . 9 ( 1 4 ) 6 1 . 5 ( 1 2 ) 9 4 . 6 0 6 ) 1 0 5 . 1 ( 9 ) 6 6 . 6 0 0 ) 7 3 . 4 ( 9 ) 1 3 8 . 0 0 0 ) 1 0 3 . 0 ( 1 0 ) 7 3 . 7 ( 9 ) 1 3 7 . 7 ( 1 1 ) 1 2 8 . 9 ( 1 0 ) 7 8 . 8 ( 1 0 ) 5 0 . 6 0 4 ) 5 9 . 1 ( 8 ) 1 2 2 . 9 ( 1 0 ) 6 0 . 1 ( 1 0 ) 1 2 4 . 1 0 0 ) 1 2 5 . 8 ( 1 3 ) 5 9 . 4 ( 1 1 ) 1 2 5 . 4 ( 1 4 ) 5 9 . 4 0 0 ) 1 3 2 . 8 0 1 ) 1 3 3 . 7 0 2 ) 5 5 . 0 0 2 ) 5 5 . 3 ( 1 2 ) 9 8 . 5 ( 1 0 ) 6 6 . 3 ( 1 0 ) 1 1 7 . 8 ( 1 3 ) 1 7 9 . 9 ( 1 5 ) 8 5 . 3 ( 1 2 ) 9 9 . 1 0 1 ) 1 8 0 8 5 . 4 ( 1 4 ) 1 1 9 . 7 0 4 ) 1 0 7 . 4 0 4 ) 7 1 . 6 0 3 ) 1 0 8 . 6 0 6 ) 1 0 6 . 9 ( 9 ) 7 0 . 2 0 0 ) 7 5 5 ( 9 ) 1 4 0 . 7 0 0 ) 1 0 8 . 0 0 1 ) 7 7 . 8 ( 1 0 ) 1 4 1 . 5 0 1 ) 1 3 2 . 2 0 0 ) 8 1 . 0 ( 1 1 ) 5 7 . 3 0 3 ) 3 8 7 T a b l e 5 . 2 4 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K 2 A g 4 L a 2 T e 9 . . . ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 8 ] - T e [ l O ] - A g [ 4 ] x 2 T e [ 8 ] - T e [ l O ] - K [ 2 ] x 4 A g [ 3 ] - T e [ l O ] - A g [ 3 ] x 2 A g [ 3 ] - T e [ l O ] - A g [ 4 ] x 4 A g [ 3 ] - T e [ 1 0 ] - K [ 2 ] x 4 A g [ 3 ] - T e [ 1 0 ] - K [ 2 ] x 4 A g [ 4 ] - T e [ l O ] - A g [ 4 ] x 2 A g [ 4 ] - T e [ l O ] - K [ 2 ] x 4 A g [ 4 ] - T e [ l O ] - K [ 2 ] x 4 K [ 2 ] - T e [ l O ] - K [ 2 ] x 4 K [ 2 ] - T e [ l O ] - K [ 2 ] x 8 T e [ 7 ] - A g [ l ] - T e [ 7 ] x 2 T e [ 7 ] - A g [ l ] - T e [ 8 ] x 4 T e [ 7 ] - A g [ l ] - T e [ 9 ] x 4 T e [ 7 ] - A g [ l ] - A g [ 2 ] x 4 T e [ 7 ] - A g [ l ] - A g [ 2 ] x 4 T e [ 8 ] - A g [ l ] - T e [ 8 ] x 2 T e [ 8 ] - A g [ l ] - T e [ 9 ] x 2 T e [ 8 ] - A g [ l ] - T e [ 9 ] x 2 T e [ 8 ] - A g [ l ] - A g [ 2 ] x 4 T e [ 8 ] - A g [ l ] - A g [ 2 ] x 4 T e [ 9 ] - A g [ l ] - T e [ 9 ] x 2 T e [ 9 ] - A g [ l ] - A g [ 2 ] x 4 T e [ 9 ] - A g [ l ] - A g [ 2 ] x 4 A g [ 2 ] - A 3 1 1 ] - A g [ 2 ] X 4 A 8 1 2 ] - A 8 1 1 ] - A g [ 2 ] x 8 T e [ 7 ] - A g [ 2 ] - T e [ 7 ] x 2 T e [ 7 ] - A g [ 2 ] - T e [ 8 ] x 4 T e [ 7 ] - A g [ 2 ] - T e [ 9 ] x 4 T e [ 7 ] - A g [ 2 ] - A g [ l ] x 4 T e [ 7 ] - A g [ 2 ] - A g [ l ] x 4 T e [ 8 ] - A g [ 2 ] - T e [ 8 ] x 2 T e [ 8 ] - A g [ 2 ] - T e [ 9 ] x 2 T e [ 8 ] - A g [ 2 ] - T e [ 9 ] x 2 5 2 . 3 0 3 ) 1 1 3 . 6 ( 1 1 ) 1 0 7 ( 2 ) 6 8 . 7 0 6 ) 1 3 9 . 5 0 4 ) 7 3 . 3 0 2 ) 1 0 6 ( 2 ) 1 3 9 . 1 0 4 ) 7 3 . 8 ( 1 3 ) 1 3 3 . 3 0 9 ) 8 0 . 9 0 4 ) 9 5 8 ( 9 ) 6 3 . 3 ( 9 ) 1 1 3 . 5 ( 1 1 ) 5 8 . 3 ( 9 ) 1 2 2 . 1 ( 1 2 ) 9 5 . 8 ( 1 0 ) 7 8 . 7 ( 9 ) 1 7 5 . 3 ( 1 2 ) 5 8 . 0 ( 9 ) 1 2 1 . 6 ( 1 1 ) 1 0 5 . 9 ( 9 ) 5 5 . 4 ( 8 ) 1 2 4 . 2 ( 1 1 ) 1 7 8 . 6 0 2 ) 9 0 . 3 ( 1 1 ) 9 5 . 9 ( 1 0 ) 6 3 . 6 ( 9 ) 1 1 4 . 0 0 2 ) 1 2 1 . 1 0 3 ) 5 8 . 4 ( 9 ) 9 5 . 8 ( 1 1 ) 7 9 . 4 ( 1 0 ) 1 7 4 . 4 0 4 ) 4 8 . 9 ( 1 4 ) 1 1 1 . 6 ( 1 0 ) 1 0 1 . 0 0 8 ) 6 5 . 5 ( 1 4 ) 1 3 7 . 5 0 3 ) 7 1 . 3 0 2 ) 9 9 . 3 0 9 ) 1 3 7 . 3 0 5 ) 7 1 . 2 ( 1 1 ) 1 2 6 . 8 ( 1 4 ) 7 8 . 3 0 2 ) 9 3 . 5 ( 9 ) 6 1 . 6 ( 8 ) 1 1 0 . 9 ( 1 1 ) 5 6 . 8 ( 1 0 ) 1 1 9 . 8 ( 1 1 ) 9 4 . 8 ( 1 0 ) 7 6 . 6 ( 9 ) 1 7 3 . 7 ( 1 1 ) 5 4 9 ( 8 ) 1 1 9 . 7 0 0 ) 1 0 3 . 8 ( 8 ) 5 4 . 1 ( 8 ) 1 2 2 . 4 ( 1 1 ) 1 7 6 . 4 ( 1 3 ) 8 8 . 8 ( 1 1 ) 9 3 . 6 ( 8 ) 6 1 . 1 ( 9 ) 1 1 2 . 1 0 2 ) 1 2 0 . 0 ( 1 3 ) 5 7 . 4 0 0 ) 9 3 . 6 0 0 ) 7 7 . 4 0 0 ) 1 7 2 . 8 ( 1 5 ) 5 5 . 2 ( 1 4 ) 1 1 7 . 2 0 0 ) 1 1 4 . 1 0 8 ) 7 1 . 6 ( 1 3 ) 1 4 2 . 1 0 3 ) 7 4 . 8 ( 1 2 ) 1 1 0 ( 2 ) 1 4 1 . 7 0 4 ) 7 5 . 3 ( 1 3 ) 1 3 8 ( 2 ) 8 3 . 6 0 3 ) 1 0 0 . 0 ( 8 ) 6 4 . 5 ( 9 ) 1 1 4 . 7 ( 1 1 ) 5 9 . 2 0 0 ) 1 2 5 . 6 ( 1 1 ) 9 7 . 6 0 0 ) 8 0 . 1 ( 8 ) 1 7 9 . 0 ( 1 1 ) 5 9 . 5 ( 9 ) 1 2 3 . 3 0 0 ) 1 0 7 . 1 ( 8 ) 5 6 . 6 ( 8 ) 1 2 6 . 3 ( 1 1 ) 1 8 0 9 1 . 8 ( 1 1 ) 9 9 . 4 ( 9 ) 6 5 6 ( 9 ) 1 1 7 . 2 ( 1 0 ) 1 2 2 . 7 0 3 ) 6 0 . 5 ( 9 ) 9 9 . 3 0 0 ) 8 2 . 2 0 0 ) 1 7 5 . 9 ( 1 5 ) 3 8 8 T a b l e 5 . 2 4 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K 2 A g 4 L a 2 T e 9 , . . ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 8 ] - A g [ 2 ] - A g [ l ] x 4 T e [ 8 ] - A g [ 2 ] - A g [ l ] x 4 T e [ 9 ] - A g [ 2 ] - T e [ 9 ] x 2 T e [ 9 ] - A g [ 2 ] - A g [ l ] x 4 T e [ 9 ] - A g [ 2 ] - A g [ l ] x 4 A 8 1 1 ] - A g [ 2 ] - A 8 1 1 ] x 4 A 8 1 1 ] - A g [ 2 ] - A 8 1 1 ] x 8 T e [ 7 ] - A g [ 3 ] - T e [ 7 ] x 2 T e [ 7 ] - A g [ 3 ] - T e [ 8 ] x 4 T e [ 7 ] - A g [ 3 ] - T e [ 1 0 ] x 4 T e [ 7 ] - A g [ 3 ] - A g [ 4 ] x 4 T e [ 7 ] - A g [ 3 ] - A g [ 4 ] x 4 T e [ 7 ] - A g [ 3 ] - K [ 2 ] x 2 T e [ 7 ] - A g [ 3 ] - K [ 2 ] x 2 T e [ 8 ] - A g [ 3 ] - T e [ 8 ] x 2 T e [ 8 ] - A g [ 3 ] - T e [ l O ] x 2 T e [ 8 ] - A g [ 3 ] - T e [ 1 0 ] x 2 T e [ 8 ] - A g [ 3 ] - A g [ 4 ] x 4 T e [ 8 ] - A g [ 3 ] - A g [ 4 ] x 4 T e [ 8 ] - A g [ 3 ] - K [ 2 ] x 4 T e [ 1 0 ] - A g [ 3 ] - T e [ 1 0 ] x 2 T e [ l O ] - A g [ 3 ] - A g [ 4 ] x 4 T e [ l O ] - A g [ 3 ] - A g [ 4 ] x 4 T e [ l O ] - A g [ 3 ] - K [ 2 ] x 4 A g [ 4 ] - A g [ 3 ] - A g [ 4 ] x 4 A g [ 4 ] - A g [ 3 ] - A g [ 4 ] X 8 A g [ 4 ] - A g [ 3 ] - K [ 2 ] x 4 A g [ 4 ] - A g [ 3 ] - K [ 2 ] X 4 T e [ 7 ] - A g [ 4 ] - T e [ 7 ] x 2 T e [ 7 ] - A g [ 4 ] - T e [ 8 ] x 4 T e [ 7 ] - A g [ 4 ] - T e [ l O ] x 4 T e [ 7 ] - A g [ 4 ] - A g [ 3 ] x 4 T e [ 7 ] - A g [ 4 ] - A g [ 3 ] x 4 T e [ 7 ] - A g [ 4 ] - K [ 2 ] x 2 1 2 1 . 7 0 2 ) 5 8 8 ( 9 ) 1 0 5 . 9 ( 1 1 ) 1 2 4 . 7 0 3 ) 5 5 8 ( 8 ) 1 7 8 . 2 ( 1 3 ) 8 9 . 6 0 0 ) 9 8 . 9 ( 1 6 ) 6 4 . 5 0 2 ) 1 1 2 . 3 0 7 ) 5 6 . 8 ( 1 3 ) 1 2 2 . 6 0 9 ) 9 4 . 0 0 3 ) 1 6 6 . 6 0 7 ) 9 8 . 9 ( 1 7 ) 7 6 . 7 ( 1 4 ) 1 7 5 ( 2 ) 5 6 . 4 0 2 ) 1 2 2 . 0 0 7 ) 1 2 0 . 8 ( 1 6 ) 1 0 7 ( 2 ) 5 5 . 6 0 4 ) 1 2 5 ( 2 ) 6 1 . 3 0 3 ) 1 7 7 ( 2 ) 8 9 . 5 0 5 ) 6 5 . 6 ( 1 4 ) 1 1 4 . 9 ( 1 9 ) 9 9 . 8 ( 1 7 ) 6 5 . 6 ( 1 3 ) 1 1 3 . 4 0 8 ) 1 2 3 ( 2 ) 5 7 . 8 ( 1 4 ) 9 4 . 1 0 4 ) 1 1 8 . 6 0 2 ) 5 7 . 5 ( 8 ) 1 0 2 . 6 ( 9 ) 1 2 1 . 9 ( 1 2 ) 5 4 . 9 ( 8 ) 1 7 4 . 9 ( 1 1 ) 8 7 . 4 0 0 ) 9 4 . 1 0 2 ) 6 2 . 0 0 2 ) 1 0 7 . 4 0 7 ) 5 3 . 3 0 4 ) 1 1 7 . 0 0 8 ) 9 0 . 6 0 4 ) 1 5 9 . 7 0 6 ) 9 4 . 4 0 3 ) 6 8 . 7 0 4 ) 1 6 9 ( 3 ) 5 2 . 3 0 0 ) 1 1 8 . 4 0 9 ) 1 1 4 . 3 0 4 ) 1 0 3 ( 2 ) 5 4 . 0 ( 1 2 ) 1 2 1 . 7 0 8 ) 5 9 . 2 0 2 ) 1 7 4 . 7 0 9 ) 8 6 . 4 ( 1 5 ) 6 2 . 7 0 4 ) 1 1 0 . 7 ( 1 6 ) 9 5 . 0 ( 1 7 ) 6 1 . 8 ( 1 2 ) 1 0 7 . 5 0 6 ) 1 1 6 ( 2 ) 5 3 . 2 0 2 ) 9 0 . 5 0 4 ) 1 2 5 . 9 ( 1 2 ) 6 1 . 5 ( 9 ) 1 0 8 . 2 ( 1 1 ) 1 2 7 . 0 ( 1 3 ) 5 7 . 3 ( 9 ) 1 8 0 9 1 . 3 0 0 ) 1 0 6 . 7 0 4 ) 6 8 . 6 ( 1 4 ) 1 1 6 . 6 0 6 ) 5 9 . 3 0 4 ) 1 3 0 . 5 0 8 ) 9 6 . 3 0 3 ) 1 7 1 . 0 0 6 ) 1 0 6 . 8 ( 1 5 ) 8 1 . 9 ( 1 3 ) 1 7 9 . 8 ( 1 6 ) 5 9 . 4 0 2 ) 1 2 6 . 1 ( 1 6 ) 1 2 6 . 1 0 5 ) 1 1 0 ( 2 ) 5 7 . 3 ( 1 3 ) 1 2 7 . 3 0 9 ) 6 4 . 2 0 3 ) 1 7 9 . 8 ( 1 5 ) 9 2 . 2 0 4 ) 6 8 . 2 0 4 ) 1 1 9 . 0 0 7 ) 1 0 8 . 5 0 6 ) 6 8 . 9 ( 1 4 ) 1 1 8 . 0 0 5 ) 1 3 0 ( 2 ) 6 0 . 9 ( 1 4 ) 9 7 . 0 0 4 ) 3 8 9 T a b l e 5 . 2 4 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K 2 A g 4 L a 2 T e 9 _ . . ( . ) a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 7 ] - A g [ 4 ] - K [ 2 ] x 2 T e [ 8 ] - A g [ 4 ] - T e [ 8 ] x 2 T e [ 8 ] - A g [ 4 ] - T e [ l O ] x 2 T e [ 8 ] - A g [ 4 ] - T e [ l O ] T e [ 8 ] - A g [ 4 ] - A g [ 3 ] x 4 T e [ 8 ] - A g [ 4 ] - A g [ 3 ] x 4 T e [ 8 ] - A g [ 4 ] - K [ 2 ] x 4 T e [ 8 ] - A g [ 4 ] - T e [ l O ] T e [ 1 0 ] - A g [ 4 ] - T e [ l O ] x 2 T e [ 1 0 ] - A g [ 4 ] - A g [ 3 ] x 4 T e [ l O ] - A g [ 4 ] - A g [ 3 ] x 4 T e [ 1 0 ] - A g [ 4 ] - K [ 2 ] x 4 A g [ 3 ] - A g [ 4 ] - A g [ 3 ] X 4 A g [ 3 ] - A g [ 4 ] - A g [ 3 ] X 8 A g [ 3 ] - A g [ 4 ] - K [ 2 ] x 4 A g [ 3 ] - A g [ 4 ] - K [ 2 ] x 4 T e [ 4 ] - K [ l ] - T e [ 4 ] x 2 T e [ 4 ] - K [ l ] - T e [ 9 ] x 4 T e [ 4 ] - K [ l ] - T e [ 9 ] x 4 T e [ 9 ] - K [ l ] - T e [ 9 ] x 4 T e [ 9 ] - K [ l ] - T e [ 9 ] x 8 T e [ 1 0 ] - K [ 2 ] - T e [ 1 0 ] x 4 T e [ 1 0 ] - K [ 2 ] - T e [ 1 0 ] x 8 T e [ l O ] - K [ 2 ] - A g [ 3 ] x 4 T e [ l O ] - K [ 2 ] - A g [ 3 ] x 4 T e [ 1 0 ] - K [ 2 ] - A g [ 4 ] x 4 T e [ 1 0 ] - K [ 2 ] - A g [ 4 ] x 4 1 6 6 . 1 0 8 ) 9 9 . 9 ( 1 8 ) 7 7 . 8 ( 1 6 ) 1 7 5 ( 2 ) 1 2 3 . 2 0 9 ) 5 8 . 2 0 3 ) 1 2 1 . 9 ( 1 7 ) 1 7 6 ( 2 ) 1 0 5 ( 2 ) 1 2 4 ( 2 ) 5 5 . 7 ( 1 4 ) 6 1 . 0 ( 1 3 ) 1 7 7 ( 2 ) 9 0 . 5 ( 1 6 ) 1 1 3 . 5 0 8 ) 6 4 . 8 ( 1 5 ) 7 6 . 8 ( 1 2 ) 1 3 6 . 4 0 4 ) 8 5 . 6 ( 1 1 ) 1 3 0 . 7 ( 1 2 ) 8 0 . 0 ( 1 0 ) 1 3 3 . 3 0 8 ) 8 0 . 9 ( 1 2 ) 4 5 . 5 ( 1 1 ) 9 4 . 1 ( 1 4 ) 4 5 . 2 ( 1 1 ) 9 3 . 4 0 4 ) 1 5 9 . 3 0 8 ) 9 5 . 7 ( 1 9 ) 6 9 . 9 ( 1 5 ) 1 7 1 ( 2 ) 1 2 0 . 2 0 8 ) 5 4 . 4 ( 1 1 ) 1 1 6 . 5 0 5 ) 1 7 2 ( 2 ) 1 0 3 ( 2 ) 1 2 2 ( 2 ) 5 3 . 2 0 3 ) 5 9 . 8 ( 1 3 ) 1 7 4 ( 2 ) 8 8 . 0 ( 1 6 ) 1 0 9 . 3 0 7 ) 6 2 . 0 0 5 ) 7 5 . 9 ( 1 2 ) 1 3 2 . 9 0 4 ) 8 3 . 1 ( 9 ) 1 2 9 . 6 0 2 ) 7 9 . 0 ( 9 ) 1 3 0 . 4 0 7 ) 7 9 . 7 ( 1 1 ) 4 3 . 1 0 0 ) 9 1 . 8 ( 1 3 ) 4 3 . 0 ( 1 1 ) 9 0 . 7 ( 1 4 ) 1 7 0 . 0 0 7 ) 1 0 6 . 9 ( 1 7 ) 8 3 . 0 ( 1 6 ) 1 8 0 ( 2 ) 1 2 7 . 7 0 9 ) 6 1 . 6 0 2 ) 1 2 5 . 8 ( 1 4 ) 1 8 0 ( 2 ) 1 0 7 ( 2 ) 1 2 7 ( 2 ) 5 8 . 1 ( 1 4 ) 6 2 . 8 ( 1 4 ) 1 8 0 ( 2 ) 9 2 . 7 0 7 ) 1 1 7 . 3 0 8 ) 6 7 . 1 0 6 ) 7 7 . 6 0 3 ) 1 3 9 . 6 0 4 ) 8 8 . 2 0 1 ) 1 3 2 . 0 0 2 ) 8 0 . 7 ( 1 0 ) 1 3 6 . 4 ( 1 7 ) 8 2 . 9 ( 1 2 ) 4 7 . 4 ( 1 1 ) 9 6 . 9 ( 1 4 ) 4 6 . 9 ( 1 1 ) 9 6 . 6 0 3 ) 3 9 0 R e f e r e n c e s 1 G r fi n e r , G . D e n s i t y W a v e s i n S o l i d s , A d d i s o n - W e s l e y , R e a d i n g , M A , 1 9 9 4 . 2 M i n , B . H . ; C h o , J . H . ; L e e , H . J . ; H a n , C . W . ; K i m , D . L . ; K w o n , Y . S . P h y s i c a B 2 0 0 0 , 2 8 1 , 1 1 8 3 K w o n , Y . 8 . ; M i n , B . H . P h y s i c a B 2 0 0 0 , 2 8 1 , 1 2 0 4 S h i n , Y . 8 . ; H a n , C . W . ; M i n , B . H . ; L e e , H . J . ; C h o i , C . H . ; K i m , Y . S . ; K i m , D . L . ; K w o n , Y . S . P h y s i c a B 2 0 0 0 , 2 9 1 , 2 2 5 5 G a r c i a , D . R . ; G w e o n , G . - H . ; Z h o u , S . Y . ; G r a f , J . ; J o z w i a k , C . M . ; J u n g , M . H . ; K w o n , Y . S . ; L a n z a r a , A . P h y s . R e v . L e t t . 2 0 0 7 , 9 8 , 1 6 6 4 0 3 . 6 ( a ) M a l l i a k a s , C . ; B i l l i n g e , S . J . L . ; K i m , H . J . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 5 , 1 2 7 , 6 5 1 0 . ( b ) K i m , H . J . ; M a l l i a k a s , C . D . ; T o m i c , A . ; T e s s m e r , S . H . ; K a n a t z i d i s M . G . ; B i l l i n g e , S . J . L . P h y s . R e v . L e t t . 2 0 0 6 , 9 6 , 2 2 6 4 0 1 . ( c ) M a l l i a k a s , C . D . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 6 , 1 2 8 , 1 2 6 1 2 . 7 G w e o n , G . - H . ; D e n l i n g e r , J . D . ; C l a c k , J . A . ; A l l e n , J . W . ; O l s o n , C . G . ; D i M a s i , E . D . ; A r o n s o n , M . C . ; F o r a n , B . ; L e e , S . P h y s . R e v . L e t t . 1 9 9 8 , 8 1 , 8 8 6 . 8 ( a ) I y e i r i , Y . ; O k u m u r a , T . ; M i c h i o k a , C . ; S u z u k i , K . P h y s . R e v . B 2 0 0 3 , 6 7 , 1 4 4 4 1 7 . ( b ) R u , N . ; F i s h e r , 1 . R . P h y s . R e v . B 2 0 0 6 , 7 3 , 0 3 3 1 0 1 9 ( a ) P a r d o , M . P . ; F l a h a u t , J . B u l l . S o c . C h i m . 1 9 6 7 , 1 0 , 3 6 5 8 . ( b ) D i M a s i , E . ; F o r a n , B ; A r o n s o n , M . C . ; L e e S . C h e m . M a t e r . 1 9 9 4 , 6 , 1 8 6 7 . 1 0 P a t s c h k e , R . ; K a n a t z i d i s , M . G . P h y s . C h e m . C h e m . P h y s . 2 0 0 2 , 4 , 3 2 6 6 . 1 1 R h o n d a R e n e é P a t s c h k e ’ s D i s s e r t a t i o n , M i c h i g a n S t a t e U n i v e r s i t y , 1 9 9 9 . 1 2 O r i g i n a l l y , t h i s p h a s e w a s r e p o r t e d a s K 2 , 5 A g 4 _ 5 L a 2 T e 9 w i t h a d i s o r d e r e d K / A g s i t e i n t h e K 2 A g 4 T e 3 l a y e r . R e e x a m i n a t i o n o f t h i s d i s o r d e r e d s i t e s u g g e s t e d t h a t K o r A g a t o m s a r e t o o b i g f o r t h i s p o s i t i o n . T h e r e f o r e , t h e n e w s u p e r c e l l r e fi n e m e n t w a s p e r f o r m e d w i t h T e a t o m s i n s t e a d . T h e r e s u l t e d K 2 A g 4 T e 4 l a y e r i s s t r u c t u r a l l y s i m i l a r t o t h e K 2 C u 4 S 3 s t r u c t u r e - t y p e . 1 3 P l a m b e c k - F i s c h e r , P . ; A b r i e l , W . ; U r l a n d , W . J . S o l i d S t a t e C h e m . 1 9 8 9 , 7 8 , 1 6 4 . 1 4 G r u p e , M . ; U r l a n d , W . J . L e s s - C o m m o n M e t . 1 9 9 1 , 1 7 0 , 2 7 1 . 3 9 1 1 5 V a s i l y e v a , I . G . ; B a l y a e v a , E . I . J . S o l i d S t a t e C h e m . 1 9 9 9 , I 4 2 , 2 6 1 . 1 6 D o e r t , T . ; G r a f , C . ; S c h m i d t , P . ; V a s i l i e v a , I . G . ; S i m o n , P . ; C a r r i l l o - C a b r e r a , W . J . S o l i d S t a t e C h e m . 2 0 0 7 , 1 8 0 , 5 0 1 . 1 7 B r o w n , D . B . ; Z u b i e t a , J . A . ; V e l l a , P . A . ; W r o b l e s k i , J . T . ; W a t t , T . ; H a t fi e l d , W . E . ; D a y , P . I n o r g . C h e m . 1 9 8 0 , 1 9 , 1 9 4 5 . 1 8 M a l l i a k a s , C . D . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 7 , 1 2 9 , 1 0 6 7 7 . 1 9 ( a ) P a r k , S . - M . ; P a r k , S . - J . ; K i m , S . — J . J . S o l i d S t a t e C h e m . 1 9 9 8 , I 4 0 , 3 0 0 . ( b ) I j j a a l i , 1 . ; I b e r s , J . A . J . S o l i d S t a t e C h e m . 2 0 0 6 , 1 7 9 , 3 4 5 6 . 2 0 C o l e m a n , R . V . ; D a i , Z . ; M c N a i r y , W . W . ; S l o u g h , C . G . ; W a n g , C . I n S c a n n i n g T u n n e l i n g M i c r o s c o p y ; J . A . S t r o s c i o a n d W . J . K a i s e r , E d s ; A c a d e m i c , S a n D i e g o , 1 9 9 3 . 2 1 F a n g , A . ; R u , N . ; F i s h e r , 1 . R . ; K a p i t u l n i k , A . P h y s . R e v . L e t t . 2 0 0 7 , 9 9 , 0 4 6 4 0 1 . 2 2 S i n g h , D . P l a n e w a v e s , P s e u d o p o t e n t i a l s , a n d t h e L A P W m e t h o d ; K l u w e r A c a d e m i c : B o s t o n , M A , 1 9 9 4 . 2 3 P e r d e w , J . P . , B u r k e , K . , E m z e r h o f , M . P h y s . R e v . L e t t . 1 9 9 6 , 7 7 , 3 8 6 5 - 3 8 6 8 . 2 4 M u r n a g h a n F . D . P r o c . N a t l . A c a d . S c i . U S A 1 9 9 4 , 3 0 , 2 4 4 2 5 K o e l l i n g , D . D . , H a r m o n , B . J . P h y s . C 1 9 7 7 , 1 0 , 3 1 0 7 2 6 B i l b a o C r y s t a l l o g r a p h i c S e r v e r , ( h t t p : / / w w w . c r y s t . e h u . e s ) . 2 7 h t t p : / / w w w . b e l l - l a b s . c o m / p r o j e c t / P O R T / d o c / p o r t 3 d o c . t a r . g z , G a y 1 9 8 3 . 2 8 B l a h a , P . , S c h w a r z , K . , M a d s e n , G . , K v a s n i c k a , D . , L u i t z , J . , W T E N Z K , A n A u g m e n t e d P l a n e W a v e + L o c a l O r b i t a l s P r o g r a m f o r C a l c u l a t i n g C r y s t a l P r o p e r t i e s ; K a r l h e i n z S c h w a r z , T e c h . U n i v . , W i e n , V i e n n a , 2 0 0 1 . 2 9 W e c a l c u l a t e d t h e a v e r a g e v a l u e o f 0 3 2 ( 2 ) f r o m t h e m i n i m u m v a l u e o f t h e n e s t i n g v e c t o r o f 0 . 3 0 ( c l o s e t o t h e Y p o i n t ) a n d m a x i m u m o f 0 . 3 4 ( c l o s e t o t h e Z p o i n t ) . 3 0 L a v e r o c k , J . ; D u g d a l e , S . 8 . ; M a j o r , Z s . ; A l a m , M . A ; R u , N ; F i s h e r , 1 . R . ; S a n t i , G . ; B r u n o , E . P h y s . R e v B 1 9 9 5 , 5 2 , 1 4 5 1 6 . 3 9 2 C h a p t e r 6 R e a c t i o n s o f E u r o p i u m M e t a l ( E u ) w i t h C o i n a g e M e t a l s ( C u a n d A g ) i n P o l y c h a l c o g e n i d e F l u x : D i s t o r t e d T e l l u r i u m N e t s o f E u 2 + c o m p o u n d s 3 9 3 6 . 1 . I n t r o d u c t i o n R a r e - e a r t h m e t a l s ( R E ) u s u a l l y f o r m i s o s t r u c t u r a l c o m p o u n d s d u e t o s i m i l a r c h e m i c a l n a t u r e . I n t h e p o l y c h a l c o g e n i d e c h e m i s t r y m o s t o f t h e R E a t o m s s t a b i l i z e i n t h e 3 + s t a t e . I n g e n e r a l , o n l y a f e w R E a t o m s a r e k n o w n t o e x i s t i n t h e 2 + o x i d a t i o n s t a t e i n c l u d i n g S m , E u , T m a n d Y b w i t h E u 2 + b e i n g t h e m o s t s t a b l e c a t i o n . A l t h o u g h e u r o p i u m i s s t a b l e i n t h e 3 + o x i d a t i o n s t a t e m a i n l y i n o x i d e s ( E U 2 O 3 1 ) w h e n c o m b i n e d w i t h a c h a l c o g e n a t o m i t u s u a l l y a d o p t s a 2 + v a l e n c e . T h e r e a s o n i s t h a t t h e e n e r g y l e v e l o f t h e f - o r b i t a l s o f e u r o p i u m i s l o w e r w i t h r e s p e c t t o t h e e n e r g y o f t h e p - o r b i t a l s o f t h e c h a l c o g e n ( e s p e c i a l l y S e o r T e ) s o t h a t E u 3 + a l w a y s g e t s r e d u c e d b y t h e c h a l c o g e n a t o m t o E u ” . I n t h e c a s e o f t h e s u l fi d e a n a l o g u e s , t h e e n e r g y l e v e l o f S p - o r b i t a l s i s c o m p a r a b l e t o t h e e n e r g y o f E u “ a n d t h e r e f o r e s o m e t i m e s t h e 2 + o x i d a t i o n s t a t e c a n b e s t a b i l i z e d . A f e w e x a m p l e s o f c o m p o u n d s w i t h m i x e d v a l e n t E u z ‘ L / E u 3 + a n d S i n c l u d e t h e m i s fi t l a y e r e d p h a s e [ ( E u S ) . , 5 ] . , . 5 N b S 2 2 a n d c u b i c E u 3 S 4 . 3 R e c e n t l y , w e h a v e s h o w n t h a t a c h a n g e i n t h e r a d i u s o f R E 3 + ( f r o m L a t o T m ) h a s a n e f f e c t o n t h e l e n g t h o f t h e p e r i o d i c i t y ( q — v e c t o r ) o f t h e C D W m o d u l a t i o n i n t h e s q u a r e n e t s o f t e l l u r i u m i n t h e R E T e 3 s e r i e s . 4 T h e c h e m i c a l p r e s s u r e a p p l i e d o n t h e n e t s d u e t o t h i s l a n t h a n i d e c o n t r a c t i o n i s i n c r e a s e d a s t h e R E 3 + r a d i u s g e t s s m a l l e r . I n t h i s s i t u a t i o n , t h e a v e r a g e T e - T e d i s t a n c e s b e c o m e s h o r t e r a n d t h e o v e r l a p o f t h e T e p - o r b i t a l s i n c r e a s e s . T h e r e f o r e , t h e s h a p e a n d w i d t h o f t h e p - b a n d s t h a t a r e r e s p o n s i b l e f o r t h e C D W d i s t o r t i o n a r e a f f e c t e d a n d a n o v e r a l l c h a n g e i n t h e n e s t i n g p r o p e r t i e s o f t h e F e r m i s u r f a c e o c c u r s . E u 2 + i s g e n e r a l l y b i g g e r t h a n L a “ , t h e fi r s t a n d l a r g e r m e m b e r o f t h e R E ” s e r i e s . 5 T h u s , c o m p o u n d s w i t h s q u a r e n e t s o f T e c o o r d i n a t e d w i t h E u ” w i l l r e p r e s e n t t h e e x t r e m e c a s e o f m i n i m u m c h e m i c a l p r e s s u r e a m o n g t h e r a r e - e a r t h p o l y t e l l u r i d e s . T h e 3 9 4 s h o r t l i s t o f E u - c o n t a i n i n g p o l y t e l l u r i d e c o m p o u n d s w i t h s q u a r e n e t s o f T e i n c l u d e s C u t ) , . . 5 E u T e 2 , 6 K C u 2 E u T e 4 , 6 N a o _ 2 A g 2 _ g E u T e 4 6 a n d K 6 6 5 A g 2 E u 1 3 5 T e 4 7 . A l t h o u g h t h e s u p e r c e l l o f t h e l a t e r p h a s e o n l y w a s c h a r a c t e r i z e d w i t h c o n v e n t i o n a l c r y s t a l l o g r a p h i c t e c h n i q u e s , r e e x a m i n a t i o n o f t h e A M 2 E u T e 4 ( A = N a , K , R b , C s ; M = C u , A g ) s e r i e s a n d C h o , . . E u T e 2 w i t h t h e a p p l i c a t i o n o f m u l t i d i m e n s i o n a l c r y s t a l l o g r a p h i c a p p r o a c h i s i m p o r t a n t t o r e v e a l a n d u n d e r s t a n d t h e d e t a i l s b e h i n d t h e i r C D W d i s t o r t i o n . 4 T h e s t r u c t u r e o f A M 2 E u T e 4 c o n s i s t s o f s q u a r e n e t s o f T e a t t a c h e d o n t h e o n e s i d e o f t e t r a g o n a l a n t i p r i s m a t i c c o o r d i n a t e d e u r o p i u m a t o m s . T h e o t h e r t e t r a g o n a l s i d e o f t h e a n t i p r i s m i s c o m p o s e d b y p u c k e r e d [ M T e ] ' l a y e r s m a k i n g a p o l a r [ M 2 E u T e 4 ] ' s l a b . T h e s l a b s s t a c k a l o n g t h e c - a x i s a n d t h e y a r e s e p a r a t e d b y A + a t o m s a n d v a n d e r W a a l s g a p s . W e f o u n d t h a t t h e q - v e c t o r c h a n g e s t r e m e n d o u s l y b y c h a n g i n g t h e s i z e o f t h e a l k a l i m e t a l c a t i o n A + . T h e c o m p o n e n t o f t h e q - v e c t o r f o r t h e s m a l l e r N a - c o n t a i n i n g a n a l o g s i s ~ 0 . 3 1 a n d f o r t h e b i g g e r C s p h a s e s i s ~ 0 2 6 . T h e p l a n a r T e n e t l a y e r - l a y e r s e p a r a t i o n i n c r e a s e s w i t h t h e s i z e o f t h e A + . A s i m i l a r b e h a v i o r o f t h e e f f e c t o f t h e C D W d i s t o r t i o n w i t h t h e c h a n g e o f t h e c r o s s - p l a n e d i m e n s i o n a l i t y o f t h e c o m p o u n d w a s r e c e n t l y r e p o r t e d f o r t h e A M R E T e a ( A = N a , K ; M = C u , A g ; R E = L a , C e ) f a m i l y . 8 T h e A M 2 E u T e 4 c o m p o u n d s n o t o n l y r e p r e s e n t a n o t h e r i n t e r e s t i n g e x a m p l e o f t h i s b e h a v i o r b u t t h e y a l s o g i v e t h e p o s s i b i l i t y o f e x a m i n a t i o n o f h o w s m a l l s t e p s i n c h a n g e i n d i m e n s i o n a l i t y a f f e c t t h e C D W d i s t o r t i o n s . S u r p r i s i n g l y , t h e b e h a v i o r f o u n d i n t h e q u a t e r n a r y a n d C u x E u T e 2 p h a s e s s u g g e s t s t h a t t h e r e i s a c o m p e t i t i o n b e t w e e n d i m e n s i o n a l i t y ( c r o s s - p l a n e i n t e r a c t i o n s ) a n d c h e m i c a l p r e s s u r e ( i n p l a n e i n t e r a c t i o n s ) w i t h o p p o s i t e t r e n d s i n t h e l e n g t h o f t h e C D W m o d u l a t i o n s . 3 9 5 6 . 2 . E x p e r i m e n t a l S e c t i o n 6 . 2 . 1 . R e a g e n t s T h e f o l l o w i n g r e a g e n t s w e r e u s e d a s o b t a i n e d . P o t a s s i u m m e t a l , a n a l y t i c a l r e a g e n t , A l d r i c h C h e m i c a l C o . , M i l w a u k e e , W I ; S o d i u m m e t a l , a n a l y t i c a l r e a g e n t , A l d r i c h C h e m i c a l C o . , M i l w a u k e e , W I ; R u b i d i u m m e t a l , a n a l y t i c a l r e a g e n t , J o h n s o n M a t t h e y / A E S A R G r o u p , S e a b r o o k , N H ; C e s i u m m e t a l , a n a l y t i c a l r e a g e n t , J o h n s o n M a t t h e y / A E S A R G r o u p , S e a b r o o k , N H ; E u r o p i u m m e t a l , 9 9 . 9 % p u r e , ~ 2 m m t u r n i n g s , C h i n e s e R a r e E a r t h I n f o r m a t i o n C e n t e r , I n n e r M o n g o l i a , C h i n a ; T e l l u r i u m c h u n k s , T e l l u r e x C o r p , T r a v e r s e C i t y , M I ; N , N — D i m e t h y l f o r m a m i d e ( D M F ) , A C S r e a g e n t g r a d e , S p e c t r u m C h e m i c a l s , N e w B r u n s w i c k , N J ; D i e t h y l e t h e r a n h y d r o u s , A C S r e a g e n t g r a d e , C o l u m b u s C h e m i c a l I n d u s t r i e s , C o l u m b u s , W I . A c t i v a t e d C o p p e r — C o p p e r m e t a l ( 4 0 m e s h , C e r a c , M i l w a u k e e , W I ) w a s fi r s t a c t i v a t e d b y w a s h i n g i t w i t h c o p i o u s a m o u n t s o f d i l u t e h y d r o c h l o r i c a c i d . T h i s s t e p w a s n e c e s s a r y t o r e m o v e t h e o x i d e l a y e r f r o m t h e fi n e p a r t i c l e s ( p o w d e r ) a n d t o e n s u r e s t o i c h i o m e t r i c r e a c t i o n o f C u . P o t a s s i u m T e l l u r i d e , K 2 T e — 5 . 8 3 6 g ( 0 . 1 5 m o l ) K w a s s l i c e d i n s m a l l p i e c e s ( ~ 3 m m ) i n a N 2 fi l l e d g l o v e b o x a n d c o m b i n e d w i t h 9 . 5 2 3 g ( 0 . 0 7 5 m o l ) T e i n a 1 0 0 0 m L s i n g l e n e c k r o u n d b o t t o m fl a s k . A T e fl o n c o a t e d m a g n e t i c s t i r b a r w a s a d d e d i n t h e fl a s k a s w e l l . T h e fl a s k w e r e c o n n e c t e d t o a g l a s s a d a p t e r w i t h a s t o p c o c k j o i n t a n d r e m o v e d fi ' o r n t h e g l o v e b o x . T h e fl a s k a n d a d a p t e r w a s t h e n c o n n e c t e d t o a d r y c o n d e n s e r a p p a r a t u s a n d c h i l l e d t o - 7 8 C u s i n g a d r y i c e / a c e t o n e b a t h . A p p r o x i m a t e l y 8 0 0 m L o f p u r e N H 3 w e r e c o n d e n s e d , u n d e r N 2 a t m o s p h e r e , o n t o t h e r e a g e n t s , y i e l d i n g a p u r p l e s o l u t i o n . T h e s o l u t i o n w a s k e p t u n d e r s t i r r i n g a n d m a i n t a i n e d a t - 7 8 C f o r u p t o 1 6 h o u r s . 3 9 6 T h e d r y i c e / a c e t o n e m i x t u r e w a s r e m o v e d a n d t h e N H 3 w a s a l l o w e d t o e v a p o r a t e o f f a s t h e fl a s k w a r m e d u p t o r o o m t e m p e r a t u r e u n d e r a c o n s t a n t fl o w o f N 2 f o r ~ 6 h o u r s . T h e r e s u l t i n g b r o w n p o w d e r ( K 2 T e ) w a s e v a c u a t e d o n a S c h l e n c k l i n e f o r ~ 4 h o u r s a n d t a k e n i n t o a N 2 fi l l e d g l o v e b o x . T h e p r o d u c t w a s g r o u n d t o a fi n e p o w d e r w i t h a m o r t a r a n d p e s t l e a n d p l a c e d i n t o a s c r e w - c a p p e d v i a l i n t h e g l o v e b o x . S o d i u m T e l l u r i d e , N a 2 T e — T h e p r o c e d u r e w a s t h e s a m e a s d e s c r i b e d a b o v e f o r K 2 T e . 3 . 4 4 8 g ( 0 . 1 5 m o l ) N a w a s s l i c e d i n s m a l l p i e c e s ( ~ 3 m m ) a n d c o m b i n e d w i t h 9 . 5 2 3 g ( 0 . 0 7 5 m o l ) T e . T h e p r o d u c t h a d a w h i t e - l i g h t g r a y c o l o r a n d w a s s t o r e d i n t h e s a m e m a n n e r a s f o r K 2 T e . R u b i d i u m T e l l u r i d e , R b 2 T e - 8 . 5 8 9 g ( 0 . 1 0 m o l ) o f l i q u i d R b w a s t r a n s f e r r e d i n a 1 0 0 0 m L t r i p l e n e c k r o u n d b o t t o m fl a s k i n a N 2 fi l l e d g l o v e b o x . T h e R b m e t a l w a s k e p t i n l i q u i d s t a t e b y p l a c i n g t h e i n g o t / a m p o u l e o f R b o n a h o t p l a t e . A h o t g l a s s p i p e t t e w a s u s e d f o r t r a n s f e r r i n g t h e l i q u i d R b i n t o t h e fl a s k . T h e m i d d l e n e c k o f t h e fl a s k w a s c o n n e c t e d t o a g l a s s a d a p t e r w i t h a s t o p c o c k j o i n t . T h e o t h e r t w o n e c k s w e r e c l o s e d u s i n g a g l a s s s t o p j o i n t a n d t h e fl a s k w a s r e m o v e d f r o m t h e g l o v e b o x . T h e fl a s k a n d a d a p t e r w a s t h e n c o n n e c t e d t o a d r y c o n d e n s e r a p p a r a t u s a n d c h i l l e d t o - 7 8 C u s i n g a d r y i c e / a c e t o n e b a t h . A p p r o x i m a t e l y 4 0 0 m L o f p u r e N H 3 w e r e c o n d e n s e d , u n d e r N 2 a t m o s p h e r e , o n t o t h e a l k a l i m e t a l , y i e l d i n g a p u r p l e s o l u t i o n . 6 . 4 1 1 g ( 0 . 0 5 m o l ) o f T e a n d a T e fl o n c o a t e d m a g n e t i c s t i r b a r w e r e a d d e d . A n o t h e r ~ 4 0 0 m L o f p u r e N H 3 w e r e a d d e d i n t h e m i x t u r e . T h e s o l u t i o n w a s k e p t u n d e r s t i r r i n g a n d m a i n t a i n e d a t - 7 8 C f o r u p t o 1 6 h o u r s . T h e d r y i c e / a c e t o n e m i x t u r e w a s r e m o v e d a n d t h e N H 3 w a s a l l o w e d t o e v a p o r a t e o f f a s t h e fl a s k w a r m e d u p t o r o o m t e m p e r a t u r e u n d e r a c o n s t a n t fl o w o f N 2 f o r ~ 6 h o u r s . T h e r e s u l t i n g d a r k g r e e n p o w d e r ( R b 2 T e ) w a s e v a c u a t e d o n a S c h l e n c k l i n e f o r 3 9 7 ~ 4 h o u r s a n d t a k e n i n t o a N 2 fi l l e d g l o v e b o x . T h e p r o d u c t w a s g r o u n d t o a fi n e p o w d e r w i t h a m o r t a r a n d p e s t l e a n d p l a c e d i n t o a s c r e w - c a p p e d v i a l i n t h e g l o v e b o x . C e s i u m T e l l u r i d e , C s 2 T e — T h e p r o c e d u r e w a s t h e s a m e a s d e s c r i b e d a b o v e f o r R b 2 T e . 1 0 . 1 3 5 g ( 0 . 0 7 6 m o l ) C s w a s u s e d w i t h 4 . 8 6 5 g ( 0 . 0 4 8 m o l ) T e . T h e p r o d u c t h a d a l i g h t g r e e n / y e l l o w c o l o r a n d w a s s t o r e d i n t h e s a m e m a n n e r a s f o r R b 2 T e . 6 . 2 . 2 . S y n t h e s i s A M 2 E u T e 4 ( A = K , N a , R b , C s ; M = C u , A g ) — A . - , . M 2 E u . + , . T e 4 w a s s y n t h e s i z e d f r o m a m i x t u r e o f A 2 T e ( A = K , N a , R b , C s ; 0 . 5 0 0 m m o l ) , M ( M = C u , A g ; 0 . 1 2 5 m m o l ) , E u ( 0 . 1 2 5 m m o l ) , a n d T e ( 2 . 0 m m o l ) t h a t w a s s e a l e d u n d e r v a c u u m i n a q u a r t z t u b e a n d h e a t e d t o 7 0 0 ° C f o r 5 d a y s . T h e t u b e w a s t h e n c o o l e d t o 3 0 0 ° C a t a r a t e o f 4 ° C / h , f o l l o w e d b y q u e n c h i n g t o r o o m t e m p e r a t u r e a t a r a t e o f 1 0 ° C / h . T h e e x c e s s A 2 T e y fl u x w a s w a s h e d o f f w i t h N , N - d i m e t h y l f o r m a m i d e u n d e r n i t r o g e n t o r e v e a l v e r y t h i n r e d - p u r p l e p l a t e - s h a p e d c r y s t a l s . C u o , 6 3 E u T e 2 - C u o , 6 3 E u T e 2 w a s s y n t h e s i z e d f r o m a m i x t u r e o f 0 . 2 9 8 g R b 2 T e ( 1 . 0 m m o l ) 0 . 0 3 2 g C u ( 0 . 5 m m o l ) , 0 . 0 3 8 g E u ( 0 . 2 5 m m o l ) a n d 0 . 5 1 0 g T e ( 4 . 0 m m o l ) t h a t w a s s e a l e d u n d e r h i g h v a c u u m i n a 1 3 m m q u a r t z a m p o u l e . T h e a m p o u l e w a s h e a t e d t o 4 0 0 ° C f o r 1 2 h , k e p t a t t h a t t e m p e r a t u r e f o r 1 2 h , h e a t e d t o 8 5 0 ° C i n 2 4 h , a n d k e p t a t t h a t t e m p e r a t u r e f o r 6 d a y s . T h e t u b e w a s t h e n c o o l e d t o 4 0 0 ° C a t a r a t e o f 4 ° C ' h " , a n d t h e n q u e n c h e d t o r o o m t e m p e r a t u r e i n 4 h . T h e e x c e s s R b 2 T e . . fl u x w a s r e m o v e d u n d e r n i t r o g e n t o r e v e a l r e d - b r o w n s q u a r e p l a t e - l i k e c r y s t a l s . T h e c r y s t a l s w e r e a i r a n d w a t e r s t a b l e . E D S a n a l y s i s o n s e v e r a l c r y s t a l s c o n fi r m e d t h e a b s e n c e o f R b f r o m t h e fl u x a n d t h e h y p o s t r o i c h i o m e t r y o f C u . T h e a v e r a g e c o m p o s i t i o n o b t a i n e d f r o m t h e 3 9 8 s e m i q u a n t i t a t i v e a n a l y s i s w a s C u o . . ( . ) E u . , o ( . ) T e 2 , o ( . ) . S e v e r a l t r i e s u s i n g d i r e c t c o m b i n a t i o n o r h a l i d e fl u x g a v e a m i x t u r e o f t h e t e r n a r y p h a s e a n d b i n a r y E u T e . 6 . 2 . 3 . P h y s i c a l M e a s u r e m e n t s S e m i q u a n t i t a t i v e E n e r g y D i s p e r s i v e S p e c t r o s c o p y ( E D S ) — T h e a n a l y s e s w e r e p e r f o r m e d w i t h a J E O L J S M - 3 5 C s c a n n i n g e l e c t r o n m i c r o s c o p e e q u i p p e d w i t h a N o r a n V a n t a g e E D S ( S i z L i ) d e t e c t o r . C r y s t a l s w e r e m o u n t e d o n a n a l u m i n u m s t a g e w i t h c a r b o n t a p e . D a t a w e r e a c q u i r e d o n s e v e r a l c r y s t a l s a n d d i f f e r e n t r e g i o n s o f e a c h c r y s t a l u s i n g a n a c c e l e r a t i n g v o l t a g e o f 2 5 k V a n d a c c u m u l a t i o n t i m e o f 4 0 s . S i n g l e C r y s t a l X - r a y D i fi ‘ r a c t i o n — A l l t h e t e m p e r a t u r e d e p e n d e n t m e a s u r e m e n t s w e r e p e r f o r m e d o n t h e s a m e s i n g l e c r y s t a l f o r s o m e o f t h e A M 2 E u T e 4 c o m p o u n d s ( A = K , N a , R b , C s ; M = C u , A g ) . S i n g l e c r y s t a l s w e r e q u e n c h e d f r o m r o o m t e m p e r a t u r e t o 1 0 0 K T h e h e a t i n g r a t e f o r w a r m i n g r a m p s w a s ~ 2 0 0 K / h . T y p i c a l a c q u i s i t i o n t i m e w a s ~ 2 4 h . S u m m a r y t a b l e o f c r y s t a l d a t a a n d d e t a i l e d c r y s t a l l o g r a p h i c t a b l e r e p o r t s f o r e a c h i n d i v i d u a l A M 2 E u T e 4 a n a l o g u e a n d t e m p e r a t u r e c a n b e f o u n d i n t a b l e s 6 2 - 6 4 6 D e t a i l e d t a b l e s f o r C u o , 6 3 E u T e 2 a r e r e p o r t e d i n t a b l e s 6 . 4 7 - 6 . 5 2 . I n t e n s i t y d a t a w e r e c o l l e c t e d o n a S T O E I P D S I I d i f f r a c t o m e t e r e q u i p p e d w i t h a g r a p h i t e m o n o c h r o m a t i z e d M o r a d i a t i o n ( A = 0 . 7 1 0 7 3 A ) a n d a n I m a g e P l a t e ( I P ) d e t e c t o r . T h e d a t a w e r e c o l l e c t e d w i t h a n ( l a - s c a n t e c h n i q u e f r o m 0 - 1 8 0 ° a n d a n a r b i t r a r y ( p - a n g l e . D a t a r e d u c t i o n w a s p e r f o r m e d w i t h t h e X - A r e a p a c k a g e . 9 T h e l e n g t h d e t e r m i n a t i o n a n d r e fi n e m e n t o f t h e q - v e c t o r s w a s p e r f o r m e d w i t h t h e P e a k l i s t 1 . 0 6 s o f t w a r e p a r t o f t h e X - A r e a s u i t e u s i n g a l e a s t s q u a r e r e fi n e m e n t a l g o r i t h m . A n a n a l y t i c a l a b s o r p t i o n c o r r e c t i o n w a s p e r f o r m e d ( X - S h a p e w i t h i n X - A r e a ) a n d a l l s t r u c t u r e s w e r e r e fi n e d w i t h J A N A 2 0 0 0 s o f t w a r e . 1 0 D i r e c t 3 9 9 m e t h o d s o f S H E L X T L s o f t w a r e ” w e r e u s e d t o fi n d t h e a t o m i c p o s i t i o n s i n t h e s u b c e l l . T e m p e r a t u r e w a s c o n t r o l l e d b y a n O x f o r d C r y o s t r e a m 7 0 0 P l u s c r y o s t a t . S a t e l l i t e r e fl e c t i o n s o f fi r s t o r d e r w e r e o b s e r v e d a n d u s e d f o r t h e r e fi n e m e n t o f t h e q u a t e r n a r y A M 2 E u T e 4 c o m p o u n d s ( A = K , N a , R b , C s ; M = C u , A g ) . A s i n g l e m o d u l a t i o n w a v e f o r p o s i t i o n a l a n d t h e r m a l p a r a m e t e r s w a s u s e d . O n l y t h e s y m m e t r y a l l o w e d F o u r i e r t e r m s w e r e r e fi n e d . S a t e l l i t e r e fl e c t i o n s o f fi r s t o r d e r f o r b o t h q - v e c t o r s a n d m i x e d o r d e r r e fl e c t i o n s ( q . + q 2 , q . — q 2 ) w e r e o b s e r v e d a t 1 0 0 K a n d u s e d f o r t h e r e fi n e m e n t o f t h e t e r n a r y C u o , . 3 E u T e 2 . F o u r m o d u l a t i o n w a v e s ( q 1 , q 2 , q . + q 2 , q . — q 2 ) f o r p o s i t i o n a l a n d t e m p e r a t u r e p a r a m e t e r s w e r e u s e d . F o u r i e r t e r m s w e r e f r e e l y r e fi n e d b a s e d o n t h e s y m m e t r y e l e m e n t s o f t h e s u p e r s p a c e g r o u p . A l l t h e e x a m i n e d s u p e r s p a c e g r o u p s ( c e n t r o s y m m e t r i c a n d n o n c e n t r o s y m m e t r i c o r t h o r h o m b i c a n d c e n t r o s y m m e t r i c m o n o c l i n i c o n e s ) g a v e R — v a l u e s f o r t h e s a t e l l i t e s t o m o r e t h a n 4 0 % . I n f r a r e d ( I R ) S p e c t r o s c o p y — O p t i c a l d i f f u s e r e fl e c t a n c e m e a s u r e m e n t s w e r e p e r f o r m e d o n s i n g l e c r y s t a l s o f a l l A M 2 E u T e 4 m e m b e r s a t r o o m t e m p e r a t u r e . T h e s p e c t r a w e r e r e c o r d e d i n t h e M i d - I R r e g i o n ( 6 0 0 0 — 4 0 0 c m " ) w i t h a N i c o l e t 6 7 0 0 F T - I R S p e c t r o m e t e r e q u i p p e d w i t h a d i f f u s e r e fl e c t a n c e c o l l e c t o r f r o m S p e c t r a - T e c h I n c . M a g n e t i c S u s c e p t i b i l i t y M e a s u r e m e n t s — A M P M S Q u a n t u m D e s i g n S Q U I D m a g n e t o m e t e r w a s u s e d t o m e a s u r e t h e m a g n e t i c r e s p o n s e o f s o m e o f t h e A M 2 E u T e 4 c o m p o u n d s o v e r t h e r a n g e o f 2 - 3 0 0 K . S i n g l e c r y s t a l s o f e a c h s a m p l e w e r e m e a s u r e d p a r a l l e l a n d p e r p e n d i c u l a r t o t h e a p p l i e d m a g n e t i c fi e l d i n r e s p e c t t o t h e p l a t e g e o m e t r y o f t h e c r y s t a l s . A p e r p e n d i c u l a r fi e l d c o r r e s p o n d s t o a m a g n e t i z a t i o n d i r e c t i o n a l o n g t h e c - a x i s . A p a r a l l e l m a g n e t i c fi e l d c o r r e s p o n d s t o a r a n d o m d i r e c t i o n a l o n g t h e a b - p l a n e . A 4 0 0 fi e l d d e p e n d e n t m a g n e t i c s u s c e p t i b i l i t y a t 3 0 0 K w a s fi r s t i n v e s t i g a t e d i n t h e r a n g e o f 0 — 1 T t o e n s u r e a l i n e a r r e s p o n s e o f t h e m a g n e t i z a t i o n . S u b s e q u e n t t e m p e r a t u r e d e p e n d e n t s t u d i e s w e r e t h e n p e r f o r m e d a t a c o n s t a n t fi e l d o f 3 , 0 0 0 G . T h e e f f e c t i v e m a g n e t i c m o m e n t , 1 1 . 2 , w a s c a l c u l a t e d f r o m t h e f o l l o w i n g f o r m u l a : H e f f = 2 . 8 1 8 X " 1 . . - T w h e r e 2 ’ 1 4 i s t h e i n v e r s e o f t h e s l o p e t a k e n f r o m t h e l i n e a r r e g i o n o f t h e 1 / 2 M v s T p l o t ( 2 . , i s t h e m o l a r m a g n e t i c s u s c e p t i b i l i t y ) . 6 . 3 . R e s u l t s a n d D i s c u s s i o n S u b c e l l D e s c r i p t i o n o f A M 2 E u T e 4 — T h e a v e r a g e s t r u c t u r e o f A M 2 E u T e 4 a d o p t s t h e p o l a r s p a c e g r o u p P 4 m m i n a g r e e m e n t w i t h p r e v i o u s w o r k . 6 I t c o n s i s t s o f s q u a r e a n t i p r i s m a t i c e u r o p i u m a t o m s s a n d w i c h e d b e t w e e n a p u c k e r e d a n t i - P b O t y p e l a y e r o f [ M T e ] ' a n d a s q u a r e n e t o f t e l l u r i u m a t o m s m a k i n g a p o l a r [ M 2 E u T e 4 ] ' s l a b , F i g u r e 6 . 1 . T h e s l a b s t h e n s t a c k a l o n g t h e c - a x i s , c h a r g e b a l a n c e d w i t h A + c a t i o n s , c r e a t i n g v a n d e r W a a l s g a p s . T h e f o r m u l a c a n b e m o r e e x p r e s s l y w r i t t e n a s A + ( [ M T e ] ' ) 2 ( E u ) 2 + [ T e 2 ] ' t h a t g i v e s a n a v e r a g e e l e c t r o n c o u n t o n t h e T e a t o m s o f t h e s q u a r e n e t o f - 0 . 5 . T h e E u - T e d i s t a n c e s i n t h e a n t i p r i s m a r e 3 . 3 2 2 ( 3 ) A a n d 3 . 4 4 0 ( 8 ) A f o r N a A g 2 E u T e 4 , F i g u r e 6 2 A . T h e A + s i t e h a s a s q u a r e a n t i p r i s m a t i c g e o m e t r y w i t h A — T e d i s t a n c e s 3 . 3 4 7 ( 3 ) A a n d 3 . 4 6 6 ( 8 ) A , F i g u r e 6 2 3 . T h e T e - T e d i s t a n c e s i n t h e s q u a r e n e t a r e 3 . 1 5 3 8 ( 4 ) A , F i g u r e 6 2 C . I n t h e q u a t e r n a r y A M 2 E u T e 4 s e r i e s f o r A = N a a n d K , t h e a l k a l i m e t a l s i t e w a s f o u n d t o b e m i x e d - o c c u p i e d w i t h t h e E u m e t a l b y s i n g l e c r y s t a l d i f f r a c t i o n a n a l y s i s . T h e s i m i l a r a t o m i c r a d i i a n d s a m e s q u a r e a n t i p r i s m a t i c s i t e e n v i r o n m e n t o f t h e s e a t o m s c a n f a c i l i t a t e s u c h d i s o r d e r . 4 0 1 F i g u r e 6 . 1 . U n d i s t o r t e d s t r u c t u r e o f A M 2 E u T e 4 . T h e i n t e r p l a n a r s e p a r a t i o n d c h a n g e s f r o m ~ 3 . 7 A i n t h e N a + , t o ~ 4 . 2 A i n t h e K + , t o ~ 4 . 7 A i n t h e R b + , a n d t o ~ 5 1 A i n t h e C s + a n a l o g u e s . 4 0 2 ( C ) F i g u r e 6 . 2 . ( A ) C o o r d i n a t i o n g e o m e t r y a n d e n v i r o n m e n t o f E u i n N a A g 2 E u T e 4 . ( B ) C o o r d i n a t i o n g e o m e t r y a n d e n v i r o n m e n t o f N a i n N a A g 2 E u T e 4 . ( C ) S q u a r e n e t o f T e a t o m s i n t h e s u b c e l l o f N a A g 2 E u T e 4 . 4 0 3 S u b c e l l D e s c r i p t i o n o f C u o . 6 3 E u T e 2 - T h e u n d i s t o r t e d s t r u c t u r e o f C u o , 6 3 E u T e 2 c r y s t a l l i z e s i n t h e s p a c e g r o u p P 4 / n m m a n d a d o p t s t h e C a M n B i 2 s t r u c t u r e t y p e . I t c o n s i s t s o f e u r o p i u m a t o m s s u r r o u n d e d b y e i g h t t e l l u r i u m a t o m s i n a s q u a r e a n t i p r i s m a t i c g e o m e t r y . T h e e u r o p i u m a t o m s a r e s a n d w i c h e d b e t w e e n a n a n t i - P b O t y p e l a y e r o f [ C u T e ] a n d a s q u a r e n e t o f t e l l u r i u m a t o m s , F i g u r e 6 . 3 . T h e s t r u c t u r e i s v e r y s i m i l a r t o t h e q u a t e r n a r y A M 2 E u T e 4 p h a s e s i f t h e a l k a l i m e t a l i s r e p l a c e d b y a e u r o p i u m a t o m . I n t e r e s t i n g l y , t h e c o p p e r s i t e f o u n d t o b e p a r t i a l l y o c c u p i e d w i t h a r e fi n e d f r a c t i o n o f 0 6 3 ( 2 ) . A l t h o u g h p a r t i a l o c c u p a n c y o n t h i s c o p p e r s i t e i s u n u s u a l i n t h e p o l y t e l l u r i d e f a m i l y i t h a s b e e n o b s e r v e d i n t h e i s o s t r u c t u r a l f a m i l y o f a n t i m o n i d e s M x L a S b 2 ( M = Z n , C o , M n a n d C u w i t h x = 0 . 5 2 — 0 . 8 7 ) . 1 2 T h e f o r m u l a c a n b e m o r e e x p r e s s l y w r i t t e n a s [ 1 \ / I , . T e ] ( 2 " ‘ ) ' E u 2 + [ T e ] " ' w i t h a n a v e r a g e e l e c t r o n c o u n t o n t h e T e a t o m s o f t h e s q u a r e n e t o f - 0 . 6 3 ( 2 ) . T h e E u - T e d i s t a n c e s i n t h e a n t i p r i s m a r e 3 . 3 1 9 3 ( 6 ) A a n d 3 . 4 7 0 5 ( 8 ) A a n d t h e T e - T e d i s t a n c e s i n t h e s q u a r e n e t a r e 3 . 1 6 4 8 ( 4 ) A a t 1 0 0 K . 4 0 4 F i g u r e 6 . 3 . U n d i s t o r t e d s t r u c t u r e o f C u x E u T e 2 4 0 5 S u p e r c e l l D e s c r i p t i o n o f A M 2 E u T e 4 B a s e d o n a M o d u l a t i o n q - v e c t o r — T h e A M 2 E u T e 4 s e r i e s ( A = N a , K , R b , C s ; M = C u , A g ) a d o p t t h e P m ( O B I / 2 ) 0 s u p e r s p a c e g r o u p . T h e t e t r a g o n a l s y m m e t r y o f t h e s u b c e l l ( P 4 m m ) i s l o s t n o w d u e t o t h e d i s t o r t i o n . T h e q - v e c t o r p o s s e s a n i n c o m m e n s u r a t e c o m p o n e n t a l o n g b * a n d a c o m m e n s u r a t e o n e a l o n g c " i n t h e f o r m q = B b " + 1 / 2 c * . T h e i r r a t i o n a l c o m p o n e n t i s a l w a y s a l o n g t h e l o n g e r b - a x i s o f t h e a b - p l a n e t h a t c o n t a i n s t h e p l a n a r T e n e t f o r a l l t h e a n a l o g u e s . T h e d i s t o r t i o n i s m a i n l y l o c a t e d i n t h e p l a n a r T e l / 2 ' n e t c r e a t i n g a w i d e d i s t r i b u t i o n o f T e - T e d i s t a n c e s a s c a n b e s e e n i n F i g u r e 6 . 4 ( d i s t a n c e s f o r C s A g 2 E u T e 4 a t 1 0 0 K ) . T h e a t o m i c d i s p l a c e m e n t o f t h e T e a t o m s ( T e [ 3 ] a n d T e [ 4 ] ) i n t h e p l a n a r n e t a l o n g t h e a - a x i s ( x d i r e c t i o n ) i s a t l e a s t t w o o r d e r s o f m a g n i t u d e l a r g e r t h a n t h e d i s p l a c e m e n t s f o u n d a l o n g t h e o t h e r t w o d i r e c t i o n s , F i g u r e 6 . 5 . T h e a t o m i c d i s p l a c e m e n t s a l o n g t h e b a n d c - a x i s ( y a n d 2 d i r e c t i o n s ) , a r e s h o w n i n F i g u r e 6 . 6 a n d F i g u r e 6 . 7 r e s p e c t i v e l y . I n t e r e s t i n g l y , t h e l e n g t h o f t h e q - v e c t o r c h a n g e s s i g n i fi c a n t l y a s a f u n c t i o n o f a l k a l i m e t a l , a n d a p p e a r s t o b e l e s s s e n s i t i v e t o t h e n a t u r e o f t h e c o i n a g e m e t a l . T h e q - v e c t o r i s ~ 0 . 3 1 f o r a l l t h e N a — a n a l o g u e s , 0 . 2 8 f o r t h e K - p h a s e s a n d 0 . 2 6 f o r R b - a n d C s - m e m b e r s . S p e c i fi c a l l y , f o r N a C u 2 E u T e 4 t h e q - v e c t o r i s 0 . 3 1 2 2 ( 7 ) a n d f o r N a A g 2 E u T e 4 i s 0 . 3 1 3 4 ( 6 ) a t 1 0 0 K . F o r K C u 2 E u T e 4 a n d K A g 2 E u T e 4 t h e q - v e c t o r s a r e 0 . 2 8 2 2 ( 6 ) a n d 0 . 2 8 5 3 ( 5 ) r e s p e c t i v e l y . F i n a l l y , R b C u 2 E u T e 4 h a s a q - v e c t o r o f 0 . 2 6 5 6 ( 8 ) , f o r R b A g 2 E u T e 4 i s 0 . 2 6 2 5 ( 7 ) a n d f o r C s A g 2 E u T e 4 i s 0 . 2 6 3 1 ( 6 ) . T h e d i f f e r e n c e i n t h e c e l l p a r a m e t e r s c o n t a i n i n g t h e p l a n a r T e n e t ( a b - p l a n e ) b e t w e e n t h e m e m b e r s w i t h d i f f e r e n t a l k a l i m e t a l i s s m a l l e r t h a n 3 % ( a = 4 . 3 6 9 2 ( 7 ) A , b = 4 . 3 7 9 0 ( 6 ) A f o r N a C u 2 E u T e 4 a n d a = 4 . 4 9 1 1 ( 6 ) A , b = 4 . 5 0 6 8 ( 7 ) A f o r C s A g 2 E u T e 4 ) . S i m i l a r l y , t h e d i f f e r e n c e i n a a n d b c e l l p a r a m e t e r s b e t w e e n t h e a n a l o g u e s w i t h d i f f e r e n t c o i n a g e m e t a l ( f r o m t h e s m a l l e r C u t o 4 0 6 t h e l a r g e r A g ) i s n e g l i g i b l e . T h e E u — T e m ' d i s t a n c e s ( 3 . 4 1 - 3 . 4 4 A ) r e m a i n p r a c t i c a l l y u n c h a n g e d w i t h i n t h e A M 2 E u T e 4 f a m i l y . T h e d i s t a n c e s t h a t a r e a f f e c t e d t h e m o s t f r o m t h e o c c u p a t i o n o f t h e A s i t e ( A = N a , K , R b a n d C s ) a r e r e l a t e d t o t h e s e p a r a t i o n b e t w e e n t h e p o l a r [ M 2 E u T e 4 ] ' s l a b s . I n m o r e d e t a i l s , t h e s e p a r a t i o n o f t h e T e l / 2 ' a n d T e z ' ( fi o m t h e [ M T e ] ' l a y e r ) p l a n a r n e t s i n t h e N a - a n a l o g u e s i s ~ 3 . 7 A . T h i s d i s t a n c e i n c r e a s e s t o ~ 4 . 2 A i n t h e K - s u b s t i t u t e d m e m b e r s , a n d b e c o m e s ~ 4 . 7 A a n d ~ 5 . 1 A i n R b - a n d C s - c o n t a i n i n g p h a s e s r e s p e c t i v e l y , F i g u r e 6 . 1 . T h e d e p e n d e n c e o f t h e C D W m o d u l a t i o n s t o t h e t h i r d c r o s s p l a n e d i m e n s i o n w a s fi r s t o b s e r v e d ( p r e s e n t e d i n C h a p t e r 4 ) i n t h e A M R E T e 4 ( A = N a , K ; M = C u , A g ; R E = L a , C e ) f a m i l y . T h e A M 2 E u T e 4 f a m i l y s h o w s s i m i l a r b e h a v i o r a n d f u r t h e r m o r e i l l u s t r a t e s h o w C D W d i s t o r t i o n s a r e a f f e c t e d b y g r a d u a l l y c h a n g i n g t h e c r o s s p l a n e i n t e r a c t i o n s . T h e d i s t o r t e d T e p a t t e r n s i n t h e A M 2 E u T e 4 f a m i l y h a v e t h e s a m e t y p e o f o l i g o m e r s ( m o s t l y t r i m e r s a n d t e t r a m e r s ) w i t h t h e o n e s o b s e r v e d i n t h e R E T e 3 s e r i e s . ” I n N a o _ g o ( 2 ) C u 2 E u 1 . 2 o ( 2 ) T e 4 a t 1 0 0 K t h e m i n i m u m T e - T e d i s t a n c e i n t h e n e t i s 2 . 9 6 1 ( 3 ) A a n d t h e m a x i m u m 3 . 2 3 4 ( 4 ) A w i t h a n a v e r a g e o f 3 . 0 9 4 ( 4 ) A . B y t a k i n g 3 . 0 2 4 A t o b e t h e T e - T e b o n d i n g t h r e s h o l d , t h e n e t c a n b e c o n v e n i e n t l y v i e w e d a s a s e q u e n c e o f t r i m e r s a n d t e t r a m e r s , F i g u r e 6 . . I n N a o , 3 . ( 2 ) A g 2 E u . , 1 9 ( 2 ) T e 4 , t h e m i n i m u m a n d m a x i m u m T e - T e d i s t a n c e i s 2 . 9 8 4 ( 5 ) A a n d 3 . 2 8 4 ( 5 ) A a t 1 0 0 K a n d t h e T e p a t t e r n l o o k s s i m i l a r w i t h t h e o n e i n t h e C u - a n a l o g u e s h o w i n g t h e s a m e o l i g o m e r s i n a s l i g h t l y d i f f e r e n t s e q u e n c e , F i g u r e 6 . . T h e d i s t o r t e d T e n e t i n t h e K - m e m b e r s s h o w s a l a r g e r n u m b e r o f t e t r a m e r s o v e r t r i m e r s i n r e s p e c t w i t h t h e N a - m e m b e r s a n d o c c a s i o n a l l y s i n g l e T e a t o m s , F i g u r e s 6 . 1 5 - 6 . 1 6 . T h e T e — T e b o n d d i s t r i b u t i o n f o r K C u 2 E u T e 4 h a s a m i n i m u m d i s t a n c e o f 2 . 9 3 4 ( 4 ) A a n d m a x i m u m 3 . 2 8 4 ( 4 ) A . I n K o _ 9 7 ( 2 ) A g 2 E u . , 0 3 ( 2 ) T e 4 t h e s e d i s t a n c e s a r e 4 0 7 2 . 9 4 0 ( 5 ) A a n d 3 . 3 9 8 ( 6 ) A r e s p e c t i v e l y . T h e T e p a t t e r n s o f t h e R b - a n d C s - m e m b e r s c o n t a i n a m o r e f r e q u e n t n u m b e r o f c o l u m n s o f s i n g l e T e a t o m s fi o m t h e p a t t e r n s o f t h e K - a n a l o g u e s , F i g u r e s 6 . 1 7 - 6 . 1 9 . T h e m i n i m u m T e - T e d i s t a n c e f o r R b C u 2 E u T e 4 a t 1 0 0 K i s 2 . 9 3 2 ( 5 ) A a n d t h e m a x i m u m i s 3 . 3 2 0 ( 5 ) A . I n R b A g 2 E u T e 4 t h e m i n i m u m i s 3 . 1 6 7 ( 3 ) A a n d m a x i m u m 3 . 1 8 1 ( 3 ) A . F i n a l l y , f o r C s A g 2 E u T e 4 , t h e s h o r t e r T e - T e d i s t a n c e s a r e 2 . 9 3 7 ( 2 ) A a n d t h e l o n g e r o n e s 3 . 4 4 2 ( 3 ) A a t 1 0 0 K . T h e t e m p e r a t u r e d e p e n d e n c e o f t h e q - v e c t o r s e e m s n e g l i g i b l e f r o m 1 0 0 K t o 3 0 0 K a s m e a s u r e d f o r t h e t w o e n d m e m b e r s , N a o . 3 0 ( 2 ) C u 2 E u . _ 2 o ( 2 ) T e 4 a n d C s A g 2 E u T e 4 . S p e c i fi c a l l y , t h e q - v e c t o r o f N a o , 3 o ( 2 ) C u 2 E u 1 . 2 0 ( 2 ) T 6 4 f r o m 0 . 3 1 3 4 ( 6 ) b * + 1 / 2 0 * a t 1 0 0 K b e c o m e s 0 . 3 1 1 8 ( 5 ) b * + 1 / 2 c * a t 3 0 0 K . T h e q - v e c t o r o f C s A g 2 E u T e 4 i s 0 . 2 6 3 1 ( 6 ) b * + 1 / 2 c * a t 1 0 0 K a n d 0 . 2 6 5 0 ( 6 ) + 1 / 2 c * a t 3 0 0 K . T h e c h a n g e s i n t h e d i s t o r t e d T e p a t t e r n s w i t h t e m p e r a t u r e a r e s m a l l w i t h m i n o r d i f f e r e n c e s i n t h e s e q u e n c e o f t h e o l i g o m e r s . T h e m o d u l a t e d T e p a t t e r n o f N a o , g o ( 2 ) A g 2 E u . . 2 o ( 2 ) T e 4 a t 3 0 0 K i s s h o w n i n F i g u r e 6 . a n d f o r C s A g 2 E u T e 4 i n F i g u r e 6 . 2 0 . T h e T e - T e b o n d d i s t r i b u t i o n b e c o m e s b r o a d e r w i t h a m i n i m u m o f 2 . 9 7 3 ( 3 ) A a n d m a x i m u m o f 3 . 3 2 9 ( 4 ) A f o r N a o , 3 0 ( 2 ) C u 2 E u . , 2 o ( 2 ) T e 4 a t 3 0 0 K a n d 2 . 9 5 1 ( 2 ) A a n d 3 . 4 5 3 ( 2 ) A f o r C s A g 2 E u T e 4 r e s p e c t i v e l y . 4 0 8 3 0 5 0 fi T V I U U 1 fi T T l V I 1 ' 3 , 4 5 - T e [ 3 ] - T e [ 4 ] d i s t a n c e s . 3 . 0 0 h 3 . 4 0 3 . 3 5 2 . 9 5 . 2 . 9 0 - - 3 . 3 0 A 3 2 5 ° < 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 t — d i r e c t i o n 3 3 . 2 0 0 g 3 . 1 5 m . " d 3 . 1 0 F i g u r e 6 . 4 . R e p r e s e n t a t i v e p l o t o f t h e T e [ 3 ] - T e [ 4 ] d i s t a n c e s f o u n d i n t h e d i s t o r t e d n e t o f C s A g 2 E u T e 4 fi ' o r n t h e s u p e r s p a c e a n a l y s i s b a s e d o n a q - v e c t o r a s a f u n c t i o n o f t - d i r e c t i o n . D a s h e d l i n e s r e p r e s e n t t h e a v e r a g e ( u n d i s t o r t e d ) T e - T e d i s t a n c e s . 3 . 0 5 ’ ' I I I r I ' I ' f ' I f I ' fi ' I r 0 . 2 5 L . 0 . 2 0 - T e 4 T e 3 . 0 . 1 5 - - A 0 . 1 0 r q 3 ' E u * 5 0 . 0 5 C s 8 . . . / l o 1 - A g T 1 1 £ 0 0 5 L e T 6 2 . . a E - 0 . 1 0 4 . 0 1 5 b - - 0 . 2 0 - - - 0 2 5 - - l i 1 1 1 1 l 1 I l 1 l I l l r l 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 t - d i r e c t i o n F i g u r e 6 . 5 . P l o t o f t h e p o s i t i o n a l d i s p l a c e m e n t ( A ) a l o n g x - a x i s o f a l l t h e a t o m s i n t h e C s A g 2 E u T e 4 s u p e r c e l l a s a f u n c t i o n o f t — d i r e c t i o n . 4 0 9 ) A ( t n a l e m e c a 0 0 3 . . . . . . 0 . 0 2 , 3 : 0 . 0 1 E “ 8 ’ o 0 . 0 0 O . 2 a . m 3 8 - 0 . 0 1 > . " O - 0 . 0 2 _ O . 0 3 . 1 . 1 . 1 . i . 1 1 1 1 1 . 1 . 1 . 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 t - d i r e c t i o n F i g u r e 6 . 6 . P l o t o f t h e p o s i t i o n a l d i s p l a c e m e n t ( A ) a l o n g y - a x i s o f a l l t h e a t o m s i n t h e C s A g 2 E u T e 4 s u p e r c e l l a s a f u n c t i o n o f t - d i r e c t i o n . 0 . 0 0 8 I l I l ' I 0 . 0 0 6 0 . 0 0 4 9 § 3 . . 2 2 4 8 a - 0 . 0 0 6 _ 0 . 0 0 8 1 1 1 1 m 1 1 1 r 1 1 1 1 1 1 1 1 1 4 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 t - d i r e c t i o n F i g u r e 6 . 7 . P l o t o f t h e p o s i t i o n a l d i s p l a c e m e n t ( A ) a l o n g z - a x i s o f a l l t h e a t o m s i n t h e C s A g 2 E u T e 4 s u p e r c e l l a s a f u n c t i o n o f t - d i r e c t i o n . 4 1 0 h q t i W K 0 0 1 t a 4 e T ) 2 ( 9 1 1 ( h t i W K 0 0 3 t a 4 6 T ) 2 ( 9 1 _ 1 1 U E 2 r A U E 2 g A ) 2 ( 1 3 . o a N . b 0 1 . 6 e r u g i F . v v v v v v v v v v v v v v v v v v . . N N N N N N N N N A A A A A A A A A . . A A A A A A A A A A A A A A A A A A . . A A A A A A A A A V V V V V V V V V . . V V V V V V V V V V V V V V V V V V . . V V V V V V V V V A N N N N N N N N . A A A A A A A A A A A A A A A A A A . . A A A A A A A A A A A A A A A A A A . . V V V V V V V V V V V V V V V V V V . . V V V V V V V V V V V V V V V V V V . . V V V V V V V V V A N N N N N N N N . . A A A A A A A A A A A A A A A A A A . A A A A A A A A A A A A A A A A A A . . V V V V V V V V V V V V V V V V V V . . V V V V V V V V V V V V V V V V V V . . V V V V V V V V V A N N N N N N N N . . A A A A A A A A A A A A A A A A A A . . A A A A A A A A A b A A A A A A A A A . V V V V V V V V V 3 A » b F r g u r e 6 . 8 . N 3 0 3 0 ( 2 ) C l l e u 1 2 0 ( 2 ) T C 4 a t 1 0 0 K W l t h q A A A X A A X X A . . X A A A A X A A A W A A X X A A A A . . A A A A A A A A A V V V V V V V V V . . V V V V V V V V V V V V V V V V V V . . N N N N N N N N N A A A A A A A A A . . A A A A A A A A A A A A A A A A A A . . A A A A A A A A A . A A A A A A A A A . v v v v v v v v v v v v v v v v v v n . v v v v v v v v v . N N N N N N N N N . A X A A A A A A X W A A X A A A A A . . A A A X X X A A X 0 0 . 3 1 2 2 ( 7 ) b * + 1 / 2 0 * a n d 3 . 0 2 4 A b o n d i n g t h r e s h o l d . . A A A A A A A A A V V V V V V V V V A . V V V V V V V V V V V V V V V V V . N N N N N N N N N A A A A A A A A A . . A A A A A A A A A A A A A A A A A A . A A A A A A A A A . A A A A A A A A A . b v v v v v v v . a f W A A A X A X A A . v v v v v v v v v n v v v v v v v v v u A X A X A A A A A . W A A X X A X A A . A : v v v v v v v v v n . v v v v v v v v v N N N N N N N N N . . A A A A A A A A A A A A A A A A A A . . A A A A A A A A A V V V V V V V V V . . V V V V V V V V V V V V V V V V V V . . V V V V V V V V V V V V V V V V V V . . N N N N N N N N N A A A A A A A A A . . A A A A A A A A A A A A A A A A A A . A A A A A A A A A V V V V V V V V V . . V V V V V V V V V V V V V V V V V V . . V V V V V V V V V V V V V V V V V V . . N N N N N N N N N A A A A A A A A A . . A A A A A A A A A A A A A A A A A A . V A V V V V V V V V V V V V V V V V . . V V V V V V V V V V V V V V V V V V . . V V V V V V V V V 0 . 3 1 3 4 ( 6 ) b * + 1 / 2 0 * a n d 3 . 0 4 8 A b o n d i n g t h r e s h o l d . . 1 1 e X X A A A A A A s W A A A A X A X A . N X A X A A A A A X b . . . V A V V A A A A A A A A H + 6 . A A A A A A A A A . > w . v v v v v v v v v n “ G A . . N N N N N N N N N . = 0 . 3 1 1 8 ( 5 ) b * + 1 / 2 c * a n d 3 . 0 5 8 A b o n d i n g t h r e s h o l d . 2 2 2 2 2 2 2 2 2 > A A A A A A A A B 3 § § § § § § § § § 2 2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 5 5 ( : é é é é é é é é i € 3 § § § § § § § < < < < < < < < < 2 2 2 2 2 2 2 2 2 > $ > 5 > $ > $ > 5 > $ > $ > $ > 5 < < < < < < < < < . . 5 2 2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 5 5 3 2 2 2 2 2 2 2 3 5 5 5 5 5 5 5 5 5 . 2 5 5 5 5 5 5 5 5 5 2 9 > > 2 > > > > > > > > < < < < < < < < < ‘ é 2 2 2 2 2 2 2 2 2 5 5 5 5 5 5 $ 5 5 § < < < < < < < < < < é § § § § § § § § 2 5 5 5 5 2 5 5 2 2 2 3 > > > > > > > > > 2 2 5 5 5 5 5 5 5 5 2 2 2 2 2 2 2 2 2 > > > > > > > > > : g < < < < < < < < 2 2 2 2 2 2 2 2 2 " 5 5 5 5 5 5 5 5 5 < < < < < < < < < . ; ‘ 5 " “ “ 5 $ 3 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 § < < < < < < < < < < : § § § § § § § § § g g g § § § § § § 5 5 5 5 5 5 5 5 5 5 5 5 2 2 2 2 2 2 2 2 2 2 : < < < < < < < < < i < < < < < < < < < 5 > 5 > 5 > 5 > 5 W 5 5 5 5 E € 2 5 > § > 5 > 5 > § > § > 5 > § > € 2 2 2 2 2 2 2 2 2 § : 2 2 2 2 2 2 2 2 2 2 < < < < < < < < < _ g i < < < < < < < < < , 9 5 5 5 5 5 5 5 5 5 ' 2 ? 5 5 5 5 5 5 5 5 5 A > > > > > > > > > § > > > > > > > > > 2 : 3 4 6 3 * 4 1 2 = 0 . 2 8 5 3 ( 5 ) b * + l / 2 c * a n d 3 . 0 6 9 A b o n d i n g t h r e s h o l d . F i g u r e 6 . 1 2 . K o , 9 7 ( 2 ) A g 2 E u l , o 3 ( 2 ) T e 4 a t 1 0 0 K W i t h ( 1 A \ A A A A \ ( V \ \ W \ \ V \ V . 0 0 1 t a 4 e T u E . d l o h s e r h t g n i d n o b A 7 6 1 . 3 q h t i w K 0 0 1 t a 4 e T u E 2 g A b R . b 4 1 . 6 e r u g i F > > > > > > > > > : : 2 2 2 2 2 2 2 2 2 > > > > > > > > > I > > > > > > > > > . . . . . . . . . . > > > > > > > > > 2 2 2 2 2 2 2 2 2 3 5 5 5 5 5 5 5 5 5 > > > > > > > > > : 2 2 2 2 2 2 2 2 2 2 > > > > > > > > > I > > > > > > > > > 5 5 5 5 5 5 5 5 5 : > > > > > > > > > 2 2 2 2 2 2 2 2 2 3 > > > > > > > > > > > > > > > > > > I 3 5 5 5 5 5 5 5 5 5 > > > > > > > > > z 2 2 2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 5 5 : 3 > > > > > > > > > O O O O O O O O O O > > > > > > > > > > > > > > > > > > I 3 5 5 5 5 5 5 5 5 5 > > > > > > > > > : t h r e s h o l d . O . 2 6 5 6 ( 8 ) b * + 1 / 2 c * a n d 3 . 0 2 3 A b o n d i n > 4 I < < < < < < < < < > > > > > > > > > I ° > > > > > > > > > 0 0 0 0 0 0 0 0 0 0 ° > > > > > > > > > > > > > > > > > > I 0 0 0 0 0 0 0 0 0 5 5 5 5 5 5 5 5 5 : ~ > > > > > > > > > > > > > > > > > > : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I < < < < < < < < < g ? s s s x s s x i n S o I n m > > > > > > > > 2 > p . 9 ; 2 2 2 2 2 2 2 2 2 : 2 2 2 2 2 2 2 2 2 5 5 5 5 5 5 5 5 5 . | ° I < < < < < < < < < 0 . 2 6 2 5 ( 7 ) b * + 1 / 2 0 * a n d e r h t g n i d n o b A 8 1 1 . 3 d n a ‘ b ) 3 ( 7 5 5 3 . 0 . V V V V V V V V V N N N N N N N N N . . V V V V V V V V V V V V V V V V V V . . N N N N N N N N N V V V V V V V V V . N N N N N N N N N W V V V V V V V V . . V V V V V V V V V 0 0 0 0 0 0 0 0 0 0 . V V V V V V V V V N N N N N N N N N . . V V V V V V W V V V V V V V V V V V . . N N N N N N N N N V V V V V V V V V . . N N N N N N N N N W V V V V V V V V . . V V V V V V V V V . V V V V V V V V V N N N N N N N N N . . V V V V V V V V V V V V V V V V V Y . N N N N N N N N N V V V V V V V V Y . N N N N N N N N N W V V V V V V V Y b . V V V V V V V V V H W A A A A A A A A h m d 3 0 6 0 A . b o n d i n m : + ) 6 ( I x 6 . m . V V V V V V V V V N N N N N N N N N . . m e w m w w w w N N N N N N N N N . . N N N N N N N N N w w w w w w m e . N N N N N N N N N d W V V V V V V V Y . V V V V V V V V V M A N N N N N N N N . . V V V V V V V V V m N N N N N N N N N . . V V V V V V V V V V V V V V V V V Y . N N N N N N N N N W V V V V V V V Y @ N N N N N N N N N N A N N N N N N N . V V V V V V V V V O N N N N N N N N N . V : V V V V V V V _ _ N N N N N N N N N . . N N N N N N N N N w a w w w w m e . N N N N N N N N N M W V V V V V V V Y g . v v v v v v v v v C A A A A A A A A A . m . N N N N N N N N N : m w m m m w L A A A A A A A A A A A A A A A A A A A . A A A A A A A A A . A A A A A A A A A A . \ \ \ \ \ \ \ \ \ . \ \ \ \ \ \ \ \ \ \ . v v v v v v v v v . v v v v v v v v v v . / / / / / / / / / . . / / / / / / / / / / A A A A A A A A A . n A A A A A A A A A A m A A A A A A A A A g \ \ \ \ \ \ \ \ \ \ c m . . . . . . . . . . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A . . \ \ \ \ \ \ \ \ \ . . u v v v v v v v v v v 3 . v v v v v v v v v . m / / / / / / / / / / 0 0 0 0 0 0 0 0 0 0 2 . l / / / / / / / / / / + A A A A A A A A A . b A A A A A A A A A A ( . \ \ \ \ \ \ \ \ \ . . 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 M l / / / / / / / / / / M . A A A A A A A A A . v a v v v v v v v v § _ . . s h o l d . S u p e r c e l l D e s c r i p t i o n o f C u 0 _ 6 3 E u T e 2 B a s e d o n 0 M o d u l a t i o n q - v e c t o r — A l t h o u g h t h e a v e r a g e s t r u c t u r e o f C u o . 6 3 E u T e 2 a n d A M z E u T e 4 a r e s i m i l a r , t h e d i s t o r t i o n s a n d s u p e r c e l l o f t h e f o r m e r c o m p o u n d a r e v e r y d i f f e r e n t f r o m t h e o n e s o b s e r v e d i n t h e l a t t e r p h a s e s . C u o , 6 3 E u T e 2 p o s s e s t w o i n c o m m e n s u r a t e m o d u l a t i o n q - v e c t o r s w i t h q ; = 0 . 2 9 1 0 ( 2 ) b ' + 1 / 2 c * a n d q ; = 0 . 3 5 5 7 ( 3 ) b ' a n d i t c r y s t a l l i z e s i n P m ( 0 [ 3 1 1 / 2 ) ( 0 1 3 2 0 ) 0 s u p e r s p a c e g r o u p . I n o r d e r t o o b t a i n a s t a b l e r e fi n e m e n t a n d a v o i d n o n - l i n e a r c o r r e l a t i o n s b e t w e e n t h e r a t i o n a l a n d i r r a t i o n a l c o m p o n e n t s o f t h e m o d u l a t i o n v e c t o r s a d o u b l i n g o f t h e c e l l a l o n g t h e c - a x i s w a s p e r f o r m e d t o c l e a r t h e r a t i o n a l p a r t . T h e r e f o r e a c e n t e r i n g v e c t o r o f ( 0 0 1 / 2 1 / 2 0 ) a n d a c o r r e s p o n d i n g s u p e r s p a c e g r o u p n o t a t i o n o f X m ( 0 [ 3 1 0 ) ( 0 0 2 0 ) 0 w e r e u s e d . T h e d i s t o r t i o n i s m a i n l y l o c a t e d i n t h e p l a n a r n e t s o f T e . T h e d i s t r i b u t i o n o f T e - T e d i s t a n c e s h a s a m i n i m u m o f 2 . 9 3 4 ( 5 ) A , m a x i m u m 3 . 2 8 0 ( 6 ) A a n d a n a v e r a g e v a l u e o f 3 . 1 5 8 ( 6 ) A , F i g u r e 6 . 8 . T h e a t o m i c d i s p l a c e m e n t s o f t h e T e a t o m s ( T e [ 2 a ] a n d T e [ 2 b ] ) i n t h e n e t a l o n g t h e a - a x i s ( x d i r e c t i o n ) a r e c o m p a r a b l e t o t h e d i s p l a c e m e n t s f o u n d a l o n g t h e o t h e r t w o d i r e c t i o n s , F i g u r e 6 . 9 . T h e a t o m i c d i s p l a c e m e n t s a l o n g t h e b a n d c - a x i s ( y a n d 2 d i r e c t i o n s ) , a r e s h o w n i n F i g u r e 6 . 1 0 a n d F i g u r e 6 . 1 1 r e s p e c t i v e l y f o r u = 0 . 5 . T h e s e q u e n c e o f o l i g o m e r s o f t h e d i s t o r t e d T e n e t s o f C u o , 6 3 E u T e 2 i s v e r y d i f f e r e n t f r o m t h e o n e s o b s e r v e d i n t h e q u a t e r n a r y A M z E u T e 4 s e r i e s . T h e p a t t e r n c a n b e s e e n c o n v e n t i o n a l l y a s a s e q u e n c e o f m a i n l y t r i m e r s , d i m e r s , a n d s i n g l e T e a t o m s . T h e n o t i c e a b l e d i f f e r e n c e s o f t h i s p a t t e r n a r e t h e a b s e n c e o f t e t r a m e r s a n d m o s t i m p o r t a n t l y t h e p r e s e n c e o f i n fi n i t e z i g z a g T e c h a i n s r u n n i n g a l o n g t h e a - a x i s . T h e m i n i m u m T e - T e d i s t a n c e i n t h e z i g z a g c h a i n s i s 3 . 0 7 0 ( 5 ) A a n d t h e m a x i m u m 3 . 1 1 6 ( 5 ) A . T h e c h a i n s t h a t a r e o r i e n t e d p e r p e n d i c u l a r t o t h e d i r e c t i o n o f t h e m o d u l a t i o n v e c t o r s r e s u l t f r o m t h e 4 1 5 s i m i l a r m a g n i t u d e o f d i s t o r t i o n s o c c u r r e d a l o n g t h e t w o d i r e c t i o n s i n t h e a b - p l a n e . T h i s i s a r a r e f e a t u r e t a k i n g i n t o a c c o u n t t h a t t h i s i n t e r c o n n e c t i o n b e t w e e n o l i g o m e r s ( m o n o m e r s t o f o r m c h a i n s ) i n a n o r m a l d i r e c t i o n t o t h e m o d u l a t i o n w a v e o c c u r s a t a t e m p e r a t u r e ( 1 0 0 K ) f a r a w a y f r o m t h e C D W t r a n s i t i o n t e m p e r a t u r e ( > 3 0 0 K ) . S i m i l a r t y p e o f i n t e r c o n n e c t e d a t o m s w a s o b s e r v e d f o r t h e R E T e 3 f a m i l y c l o s e t o t h e C D W t r a n s i t i o n t e m p e r a t u r e . 4 I t i s s u r p r i s i n g t h a t t h e C u o , 6 3 ( 2 ) E u T e 2 p h a s e h a s t w o q - v e c t o r s i n r e s p e c t t o t h e q u a t e r n a r y c o m p o u n d s g i v e n t h e f a c t t h a t b o t h s u b c e l l s a r e s t r u c t u r a l l y a l m o s t t h e s a m e . F u r t h e r m o r e , t h e r e i s o n l y o n e t y p e o f d i s t o r t e d T e n e t w i t h a n a v e r a g e o x i d a t i o n s t a t e o f - 0 . 6 3 ( 2 ) e / T e i n t h e s t r u c t u r e w i t h n o a p p a r e n t d i f f e r e n c e i n t h e e l e c t r o n c o u n t b e t w e e n t h e d i s t o r t e d T e n e t s . D i f f e r e n t a v e r a g e o x i d a t i o n s t a t e s o n d i s t o r t e d T e n e t s i n a c o m p o u n d a r e k n o w n t o c r e a t e m u l t i p l e h y b r i d q - v e c t o r s l i k e i n s z T e s ( C h a p t e r 5 ) . A c t u a l l y , t h e t e r n a r y p h a s e i s p a c k e d e v e n m o r e s y m m e t r i c a l l y a l o n g t h e l o n g c - a x i s s i n c e t h e r e i s o n l y o n e t y p e o f a t o m s ( E u ) i n b e t w e e n t h e l a y e r s . T h e r e f o r e , a u n i f o r m d i s t r i b u t i o n o f c h a r g e o n t h e T e n e t s i s e x p e c t e d . O n t h e o t h e r h a n d , t h e p o s s i b l e w e a k o r d e r i n g o f C u v a c a n c i e s c a n n o t b e r e s p o n s i b l e f o r t h e a p p e a r a n c e o f t h e s e c o n d q - v e c t o r . T h e s u p e r c e l l s t r u c t u r e r e fi n e s w i t h n o p r o b l e m s w i t h o u t t h e a p p l i c a t i o n o f o c c u p a t i o n a l w a v e s o n t h e C u - s i t e a n d t h e c h a n g e i n t h e r e s i d u a l i n t e n s i t i e s i s n e g l i g i b l e . T h e a g r e e m e n t f a c t o r o f a l l t h e o b s e r v e d r e fl e c t i o n s ( m a i n a n d s a t e l l i t e s ) d e c r e a s e s o n l y b y ~ 0 . 0 2 % w h e n o r d e r i n g o f C u - v a c a n c i e s i s a s s u m e d . T h e e x i s t e n c e a n d l e n g t h o f t h e t w o v e c t o r s c a n b e r a t i o n a l i z e d f r o m t h e c o m p a r i s o n o f t h e c e l l p a r a m e t e r s a n d d i s t a n c e s f o u n d i n C u o _ 6 3 ( 2 ) E u T e 2 a n d q u a t e r n a r y A C q u u T e 4 p h a s e s . T h e v a l u e o f t h e a t o m i c r a d i u s o f E u ( 1 . 2 5 A ) i s b e t w e e n t h e o n e s f o r 4 1 6 N a ( 1 . 1 8 A ) a n d K ( 1 . 5 1 A ) . F o l l o w i n g t h e t r e n d o f t h e l e n g t h o f t h e q - v e c t o r w i t h c h e m i c a l p r e s s u r e w e e x p e c t t h e v a l u e o f t h e q - v e c t o r c o m p o n e n t f o r C u o , 6 3 ( 2 ) E u T e 2 t o b e b e t w e e n t h e c o r r e s p o n d i n g v a l u e s f o r N a C q u u T e 4 a n d K C q u u T e 4 . I n d e e d , t h e t e r n a r y p h a s e h a s a v e c t o r o f q ] = O . 2 9 1 0 ( 2 ) b t w h o s e l e n g t h l i e s b e t w e e n 0 . 3 1 2 2 ( 7 ) b * ( N a o _ 3 o ( 2 ) C u 2 E u 1 _ z o ( 2 ) T e 4 ) a n d 0 . 2 8 2 2 ( 6 ) b * ( K C q u u T e 4 ) . T h e s e c o n d v e c t o r o f C u o _ 6 3 ( 2 ) E u T e 2 c a n b e s e e n a s a r e s u l t o f t h e c h a n g e i n s e p a r a t i o n d i s t a n c e o f t h e p l a n a r d i s t o r t e d T e l / 2 ' n e t s . F r o m t h e R b q u a t e r n a r y a n a l o g u e t o N a t h e s e p a r a t i o n b e t w e e n t h e T e n e t s d e c r e a s e s w h i l e t h e l e n g t h o f t h e q - v e c t o r i n c r e a s e s . S p e c i fi c a l l y , t h e s e p a r a t i o n l e n g t h i n R b C q u u T e 4 i s ~ 1 1 . 5 A , f o r K C q u u T e 4 i s ~ 1 1 . 2 A , a n d i n N a C q u u T e 4 b e c o m e s ~ 1 0 . 6 A . T h e i r q - v e c t o r s a r e ~ 0 . 2 6 , 0 . 2 8 , a n d 0 . 3 1 r e s p e c t i v e l y . I n t e r e s t i n g l y , C u o _ 5 3 ( 2 ) E u T e 2 h a s t h e s h o r t e s t c - a x i s a m o n g t h e q u a t e m a r i e s w i t h a v a l u e o f ~ 1 0 . 1 A a l t h o u g h E u 2 + i s b i g g e r t h a n N a + . T h i s i s b e c a u s e o f t h e s t r o n g e r E u — T e i n t e r a c t i o n s c o m p a r e d w i t h t h e N a - T e o n e s t h a t m a k e t h e l e n g t h o f t h e b o n d s i n t h e f o r m e r c a s e s h o r t e r . T h u s w e e x p e c t t h e l e n g t h o f t h e q - v e c t o r c o m p o n e n t t o b e a t l e a s t l o n g e r t h a n 0 . 3 1 . F a c t u a l l y , t h e s e c o n d v e c t o r o f t h e t e r n a r y p h a s e i s q z = O . 3 5 5 7 ( 3 ) b . . T h e i n t e r a c t i o n s a l o n g t h e t h i r d - d i m e n s i o n ( c - a x i s ) i n c r e a s e a s t h e s e p a r a t i o n d i s t a n c e o f t h e p l a n a r T e n e t s d e c r e a s e s m o v i n g f r o m t h e b i g g e r C s + t o t h e s m a l l e r N a + . W h e n t h e a l k a l i m e t a l i s r e p l a c e d b y E u 2 + a t o m s t h e c r o s s - p l a n e i n t e r a c t i o n s a r e e v e n s t r o n g e r s i n c e t h e E u - T e o v e r l a p o f o r b i t a l s i s g r e a t e r t h a n t h e o v e r l a p i n t h e A - T e ( A = a l k a l i m e t a l ) c a s e . I n t h a t s e n s e t h e C u o m E u T e z m e m b e r h a s a n e n h a n c e d t h r e e - d i m e n s i o n a l c h a r a c t e r i n r e s p e c t t o t h e q u a t e r n a r y p h a s e s w i t h n o a p p a r e n t v a n d e r W a a l s g a p . T h e r e f o r e , t h e g r a d u a l c h a n g e i n t h e d i m e n s i o n a l i t y w i l l h a v e a n e f f e c t o n t h e s h a p e o f t h e b a n d s a n d t h e t o p o l o g y o f t h e F e r m i s u r f a c e . 4 1 7 T e [ 2 a ] - T e [ 2 b ] d i s t a n c e s “ 3 . 3 0 — 8 ) A ( t n e m e c O8 a l p s i d x d I ' I ' l ' l ' l ' I ' l ‘ I f l 3 . 2 5 3 . 2 0 S ” g — n M D i s t a n c e ( A ) . w 3 . 0 5 3 . 0 0 2 . 9 5 - - r 1 2 . 9 0 l l l l 1 I 1 l 1 1 m l 1 l 1 l L l 1 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 t - d i r e c t i o n F i g u r e 6 . 8 . T h e T e [ 3 ] - T e [ 4 ] d i s t a n c e s f o u n d i n t h e d i s t o r t e d n e t o f C u o , 6 3 ( 2 ) E u T e 2 f r o m t h e s u p e r s p a c e a n a l y s i s b a s e d o n a q - v e c t o r a s a f u n c t i o n o f t - d i r e c t i o n . D a s h e d l i n e s r e p r e s e n t t h e a v e r a g e ( u n d i s t o r t e d ) T e - T e d i s t a n c e s . 0 . 1 5 b 0 . 1 0 - - 0 . 0 5 - 0 . 1 0 T e 2 a _ 0 . 1 5 # 1 r i m n m m l i . i . i i i . i i 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 . 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 t - d i r e c t i o n F i g u r e 6 . 9 . P l o t o f t h e p o s i t i o n a l d i s p l a c e m e n t ( A ) a l o n g x - a x i s o f a l l t h e a t o m s i n t h e C U o _ 5 3 ( 2 ) E U T e z s u p e r c e l l a s a fi m c t i o n o f t - d i r e c t i o n f o r u = 0 . 5 . 4 1 8 o . 2 o ) . 8 A ( t n e m c . 8 i 0 . S e c a l p s d z d i 0 0 8 . . . , ' I I I I I I I r T e 2 b 0 . 0 6 - - . J 0 . 0 4 — - A r T e 2 a , ’ 3 0 0 2 - \ A v , 0 > 7 fl - ” 4 ‘ a : ' ‘ 4 ‘ a » \ 1 . . ’ m ' 0 0 2 ‘ C u l a ' ' 8 T e l b T e l a > 3 " 3 - 0 . 0 4 - - - 0 . 0 6 - - _ 0 . 0 8 1 I 1 l 1 l 1 I 1 I 1 l 1 l 1 I 1 l 1 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 t - d i r e c t i o n F i g u r e 6 . 1 0 . P l o t o f t h e p o s i t i o n a l d i s p l a c e m e n t ( A ) a l o n g y - a x i s o f a l l t h e a t o m s i n t h e C u o , 6 3 ( 2 ) E u T e 2 s u p e r c e l l a s a f u n c t i o n o f t - d i r e c t i o n f o r u = 0 . 5 . 0 . 0 6 1 r . . fi T T C u l a , 5 _ 0 . 0 6 1 I 1 I 1 I 1 I L 1 4 J 4 I 4 A 1 I 1 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 t - d i r e c t i o n F i g u r e 6 . 1 1 . P l o t o f t h e p o s i t i o n a l d i s p l a c e m e n t ( A ) a l o n g z - a x i s o f a l l t h e a t o m s i n t h e C u o , 6 3 ( 2 ) E u T e 2 s u p e r c e l l a s a f u n c t i o n o f t - d i r e c t i o n f o r u = 0 . 5 . 4 1 9 3 2 5 _ C u [ 1 a ] - T e [ l b ] d i s t a n c e s _ ) A ( e c n a t s i D I r I I I ‘ I I I f I f I ' I ' I 3 . 2 0 3 . 1 0 A \ ’ - 3 . 0 5 - - U ) H L I I I I 1 I 1 l 1 J 1 I I I 1 I 1 I J 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 t - d i r e c t i o n F i g u r e 6 . 1 2 . T h e C u [ 1 a ] - C u [ 1 b ] d i s t a n c e s f o u n d i n t h e d i s t o r t e d n e t o f C U O . 6 3 ( 2 ) E U T 6 2 f r o m t h e s u p e r s p a c e a n a l y s i s b a s e d o n a q - v e c t o r a s a f u n c t i o n o f t - d i r e c t i o n . D a s h e d l i n e s r e p r e s e n t t h e a v e r a g e ( u n d i s t o r t e d ) C u - C u d i s t a n c e s . M a g n e t i c S u s c e p t i b i l i t y M e a s u r e m e n t s o f A M z E u T e 4 — V a r i a b l e t e m p e r a t u r e m a g n e t i c s u s c e p t i b i l i t y d a t a f o r m o s t o f t h e A M z E u T e 4 a n a l o g u e s w a s m e a s u r e d i n t h e r a n g e o f 2 4 3 0 0 K a t 3 0 0 0 G . T h e m a t e r i a l e x h i b i t C u r i e - W e i s s b e h a v i o r . A r e p r e s e n t a t i v e s u s c e p t i b i l i t y p l o t f o r N a A n g u T e 4 i s s h o w n i n F i g u r e 6 . 1 3 . A p e g v a l u e o f 7 . 6 4 p a a n d a W e i s s c o n s t a n t o f - 1 K w e r e e s t i m a t e d b y l i n e a r fi t t i n g o f t h e l / x M v s T d a t a . T h i s v a l u e i s c o n s i s t e n t w i t h a n f 7 c o n fi g u r a t i o n o r E u 2 + ( 7 . 9 — 8 . 0 u s ) a n d i s v e r y d i f f e r e n t f r o m t h a t e x p e c t e d f o r E u 3 + ( 3 . 3 - 3 . 5 u s ) . 4 2 0 A " 2 3 o a 0 ‘ 2 1 4 . 0 3 3 2 1 0 0 . . . . - . . 5 0 5 5 . 0 - 0 ’ 0 ? 1 b . . - 5 - 0 . 0 o ' 0 Z F C P a r I . ' - [ ® 9 1 9 9 8 0 2 0 0 I . ' I 9 4 0 0 1 9 1 6 . 0 ' 2 . _ l . . l 7 0 6 7 0 8 3 0 1 ? 0 1 . 0 . H 2 0 - . O 1 0 4 a 2 7 — _ - . 1 9 0 2 4 A m = 2 6 4 1 1 . B K 9 0 9 0 2 6 w 8 0 2 0 0 3 0 1 ' e t ' n ' t I o T e . . l l e l I ' 4 - q 3 2 1 0 0 0 £ 3 V T I ' I I I ‘ I ' I r T ' I ' I ' I fi I ' I ' I ' I r j ‘ I w T e m p e r a t u r e ( K F i g u r e 6 . 1 3 . T e m p e r a t u r e d e p e n d e n t m a g n e t i c s u s c e p t i b i l i t y f o r N a A n g u T e 4 . I n f r a r e d ( I R ) S p e c t r o s c o p y — E l e c t r o n i c t r a n s i t i o n s w h i c h c a n b e a s s i g n e d t o t h e C D W e n e r g y g a p o f t h e T e - n e t w e r e o b s e r v e d b y I R d i f fi i s e r e fl e c t a n c e m e a s u r e m e n t s . T h e e n e r g y v a l u e s a r e b e t w e e n 0 . 2 8 ( 2 ) e V f o r N a o _ 3 1 ( 2 ) A g 2 E u 1 . 1 9 ( 2 ) T e 4 a n d 0 . 0 8 ( 2 ) e V f o r C s A n g u T e 4 a t r o o m t e m p e r a t u r e , T a b l e 6 . 1 . T h e c o r r e s p o n d i n g e n e r g y g a p f o r C u o , 5 3 ( 2 ) E u T e 2 i s 0 1 6 ( 2 ) e V . A r e p r e s e n t a t i v e p l o t o f t h e a p p a r e n t g a p f o r N a o , 3 1 ( 2 ) A g 2 E u 1 , 1 9 ( 2 ) T e 4 i s s h o w n i n F i g u r e 6 . 1 4 . 4 2 1 T a b l e 6 . 1 . M i n i m u m a n d m a x i m u m d i s t a n c e s o f T e - T e w i t h i n t h e n e t ( X — r a y d i f f r a c t i o n a t 1 0 0 K ) a n d r o o m t e m p e r a t u r e e n e r g y g a p v a l u e s o f a l l A 1 - X M 2 E u 1 + x T e 4 ( A = K , N a , R b , C s ; M = C u , A g ) q u a t e r n a r y c o m p o u n d s a n d C u o m m E u T e z . M i n i m u m M a x i m u m E n e r g y g a p C ° m p ° u n d d i s t a n c e ( A ) d i s t a n c e ( A ) ( e V ) N a o _ 3 0 ( 2 ) C 1 1 2 E u 1 . 2 0 ( 2 ) T e 4 2 . 9 6 l ( 3 ) 3 2 3 4 ( 4 ) 0 2 6 ( 2 ) N a o _ 3 1 ( 2 ) A g 2 E u 1 , 1 9 ( z ) T e 4 2 . 9 8 4 ( 5 ) 3 . 2 8 4 ( 5 ) 0 2 8 ( 2 ) s z E u m 2 . 9 3 4 ( 4 ) 3 . 2 8 4 ( 4 ) 0 2 1 ( 2 ) K o . 9 7 ( 2 ) A g 2 E u 1 _ 0 3 ( 2 ) T e 4 2 . 9 4 0 ( 5 ) 3 . 3 9 8 ( 6 ) 0 2 3 ( 2 ) R b C q u u T e 4 2 . 9 3 2 ( 5 ) 3 . 3 2 0 ( 5 ) 0 . 1 1 ( 2 ) R b A g 2 E u T e 4 3 . 1 6 7 ( 3 ) 3 . 1 8 1 ( 3 ) 0 . 0 9 ( 2 ) C s A n g u T e 4 2 . 9 3 7 ( 2 ) 3 . 4 4 2 ( 3 ) 0 . 0 8 ( 2 ) C 1 1 0 . 6 3 ( 2 ) E U T 6 2 2 . 9 3 4 ( 5 ) 3 . 2 8 0 ( 6 ) 0 1 6 ( 2 ) 2 4 L - 2 2 - - 4 : 5 _ . 5 : . 2 0 m 1 B 1 8 - . 1 6 - - 1 4 . 1 . 1 . 1 1 1 1 0 . 0 0 0 . 1 5 0 . 3 0 0 . 4 5 0 . 6 0 0 . 7 5 E n e r g y ( e V ) F i g u r e 6 . 1 4 . T y p i c a l r o o m t e m p e r a t u r e i n f r a r e d a b s o r p t i o n s p e c t r u m o f N a o . 3 1 ( 2 ) A g 2 E u 1 , 1 9 ( 2 ) T e 4 s h o w i n g e n e r g y g a p a t a r o u n d 0 . 2 8 e V . B a n d s t r u c t u r e c a l c u l a t i o n o f A C u z L u T e 4 - T h e c a l c u l a t i o n s w e r e p e r f o r m e d u s i n g t h e s e l f - c o n s i s t e n t f u l l - p o t e n t i a l l i n e a r i z e d a u g m e n t e d p l a n e w a v e m e t h o d 4 2 2 ( L A P W ) l 4 a n d t h e g e n e r a l i z e d g r a d i e n t a p p r o x i m a t i o n ( G G A ) 1 5 f o r t h e e x c h a n g e a n d c o r r e l a t i o n p o t e n t i a l . T h e e x p e r i m e n t a l c e l l c o n s t a n t s a n d a t o m i c c o o r d i n a t e s fi o m t h e c r y s t a l s t r u c t u r e r e fi n e m e n t o f t h e a v e r a g e u n d i s t o r t e d A C q u u T e 4 ( A = N a , K , a n d R h ) c o m p o u n d s i n P m m 2 w e r e u s e d . T h e v o l u m e o p t i m i z a t i o n f o r K C u z L u T e 4 g a v e a m i n i m u m e n e r g y a t a v o l u m e d i f f e r e n c e o f ~ 3 % . T h i s d i f f e r e n c e w a s a s s u m e d t o b e n e g l i g i b l e s i n c e t h e n e s t i n g v e c t o r o f t h e F e r m i s u r f a c e r a n g e s i 0 . 0 2 i n l e n g t h a n d a m o r e e n e r g e t i c a l l y a c c u r a t e c a l c u l a t i o n w o u l d n o t g i v e e x t r a d e t a i l s . F u r t h e r m o r e , t h e F e r m i e n e r g y l e v e l w a s s h i f t e d b y o n e e l e c t r o n i n o r d e r t o c o m p e n s a t e t h e d i f f e r e n c e b e t w e e n t h e c h a r g e s o f E u 2 + a n d E u “ . D i r e c t i o n s i n t h e B r i l l o u i n z o n e ( B Z ) o f P m m 2 s p a c e g r o u p a r e s h o w n i n F i g u r e 6 . 1 9 . 1 6 I n t e r a t o m i c f o r c e s w e r e m i n i m i z e d w i t h i n 0 . 1 m R y / b o h r u s i n g a r e v e r s e - c o m m u n i c a t i o n t r u s t - r e g i o n q u a s i - N e w t o n m e t h o d f r o m t h e P o r t l i b r a r y . l 7 S c a l a r r e l a t i v i s t i c c o r r e c t i o n s w e r e i n c l u d e d a n d a s p i n - o r b i t i n t e r a c t i o n w a s i n c o r p o r a t e d u s i n g a s e c o n d v a r i a t i o n a l p r o c e d u r e . 1 8 T h e v a l u e s o f t h e a t o m i c r a d i i w e r e t a k e n t o b e : 2 . 5 a . u . f o r a l k a l i m e t a l a t o m , 2 . 3 a . u . f o r C u a t o m , 2 . 5 a . u . f o r L u a t o m a n d 2 . 4 a . u . f o r T e a t o m s , w h e r e a . u . i s t h e a t o m i c u n i t ( 0 . 5 2 9 A ) . C o n v e r g e n c e o f t h e s e l f - c o n s i s t e n t i t e r a t i o n s w a s p e r f o r m e d f o r 5 0 k p o i n t s i n s i d e t h e i r r e d u c i b l e B Z t o w i t h i n 0 . 0 0 0 1 R y w i t h a c u t o f f o f - 6 . 0 R y b e t w e e n t h e v a l e n c e a n d t h e c o r e s t a t e s . T h e c a l c u l a t i o n s w e r e p e r f o r m e d u s i n g W I E N Z K p r o g r a m . 1 9 T h e b a n d s t r u c t u r e o f N a C u z L u T e 4 s h o w e d t h a t t w o T e p b a n d s n e a r l y p a r a l l e l t o e a c h o t h e r c r o s s t h e F e r m i l e v e l , F i g u r e 6 . 1 5 . T h i s i n d i c a t e d t h a t a s m a l l p e r t u r b a t i o n o f t h e F e r m i l e v e l i n n o t g o i n g t o c h a n g e s i g n i fi c a n t l y t h e F e r m i s u r f a c e t o p o l o g y f o r N a M z L u T e 4 . I n d e e d , t h e m o d u l a t i o n s f o u n d i n t h e N a / E u d i s o r d e r e d N a o _ 3 o ( 2 ) C u 2 E u L 2 o ( 2 ) T e 4 p h a s e t h a t c o n t a i n s a d i s t o r t e d T e n e t w i t h a n a v e r a g e o x i d a t i o n 4 2 3 s t a t e o f 0 . 6 0 ( 4 ) ( d i f f e r e n t f r o m t h e a v e r a g e e l e c t r o n c o u n t o f 0 . 5 f o u n d i n t h e o t h e r q u a t e r n a r y a n a l o g u e s ) p o s s e s a q - v e c t o r t h a t f o l l o w s t h e e x p e c t e d t r e n d . T h e t h e o r e t i c a l c a l c u l a t i o n o n A C u z L u T e 4 ( A = N a , K , a n d R b ) v e r i fi e d t h a t t h e F e r m i s u r f a c e t o p o l o g y i n t h e s e c o m p o u n d s f a v o r s t h e f o r m a t i o n o f a n e s t i n g v e c t o r ( q - v e c t o r ) a l o n g t h e b - a x i s . T h e l e n g t h o f t h e v e c t o r d e c r e a s e s f r o m 0 . 3 0 ( l ) t o 0 . 2 6 ( 1 ) f o r N a C u z L u T e 4 t o R b C u z L u T e 4 r e s p e c t i v e l y a n d t h i s i s c o n s i s t e n t w i t h t h e e x p e r i m e n t a l r e s u l t s . T h e r e p r e s e n t a t i v e s h a p e o f t h e F e r m i s u r f a c e t o p o l o g y o f t h e t w o b a n d s o f N a C u z L u T e 4 t h a t c r o s s t h e F e r m i l e v e l i s s h o w n i n F i g u r e 6 . 1 6 A - B a n d t h e o v e r a l l F e r m i s u r f a c e i s s h o w n i n F i g u r e 6 . 1 6 C . B a n d s t r u c t u r e c a l c u l a t i o n o f C u x L u T e z — T h e s a m e c a l c u l a t i o n m e t h o d a n d p r o c e d u r e t h a t w a s u s e d f o r A C u z L u T e 4 w e r e p e r f o r m e d o n t h e a v e r a g e s t r u c t u r e o f C u L u T e z ( n o C D W a n d v a c a n c i e s ) . D i r e c t i o n s i n t h e B r i l l o u i n z o n e ( B Z ) o f P m m n s p a c e g r o u p a r e s h o w n i n F i g u r e 6 . 2 0 . 1 6 T h e b a n d s a r o u n d t h e F e r m i l e v e l t h a t a r e s t i l l T e p i n c h a r a c t e r a r e m o r e d i s p e r s e d f r o m t h e o n e s f o u n d i n t h e q u a t e r n a r y p h a s e s , F i g u r e 6 . 1 7 . T h i s m a k e s t h e F e r m i s u r f a c e m o r e c o m p l e x a n d s e n s i t i v e t o s m a l l c h a n g e s i n t h e F e r m i l e v e l . T h i s i s a p p a r e n t f r o m t h e c a l c u l a t e d F e r m i t o p o l o g i e s a t t r e e d i f f e r e n t F e r m i l e v e l s t h a t c o r r e s p o n d t o t h r e e d i f f e r e n t c o n c e n t r a t i o n s o f x f o r C u a t o m s , n a m e l y x = 0 , 1 / 3 , a n d 2 / 3 . T h e F e r m i l e v e l f o r x = 0 w a s c a l c u l a t e d fi ' o m t h e C u L u T e z s u b s t r u c t u r e ( n o v a c a n c i e s , x = 1 ) a f t e r r e m o v i n g o n e e l e c t r o n f r o m t h e s y s t e m ( c h a r g e d c e l l ) . T h e i n t e r m e d i a t e F e r m i l e v e l e n e r g i e s w e r e c a l c u l a t e d b y l i n e a r i n t e r p o l a t i o n b e t w e e n t h e t w o v a l u e s o f x = 0 a n d x = 1 . I n t e r e s t i n g l y , t h e F e r m i s u r f a c e o f C u L u T e z ( x = 1 ) d o e s n o t f a v o r s p a n n i n g o f t h e b a n d s s i n c e t h e t o p o l o g y d o e s n o t h a v e p a r a l l e l r e g i o n s i n w h i c h n e s t i n g c a n o c c u r , F i g u r e 6 . 1 8 A . A n e l e c t r o n d e fi c i e n t s i t u a t i o n l i k e i n C u 2 / 3 L u T e 2 t h e 4 2 4 F e r m i l e v e l i s l o w e r e d s i n c e t h e r e a r e l e s s e l e c t r o n s ( x < 1 ) i n t h e s y s t e m . T h i s s m a l l s h i f t i n e n e r g y g i v e s a d i f f e r e n t F e r m i s u r f a c e t o p o l o g y t h a t s t a r t s t o h a v e b a n d s t h a t a r e a l m o s t p a r a l l e l t o e a c h , F i g u r e 6 . 1 8 B . T h i s c r e a t e s a m o r e f a v o r a b l e g e o m e t r y i n w h i c h n e s t i n g m a y d e v e l o p . T h i s i s m o r e a p p a r e n t w h e n t h e F e r m i l e v e l i s s h i f t e d e v e n m o r e i n t h e c a s e o f C u l / z L u T e z t h a t c l e a r l y p o s s e s t w o b a n d s w i t h a n e s t i n g v e c t o r o f 0 3 8 ( 2 ) , F i g u r e 6 . 1 8 C . F i n a l l y , i n t h e h y p o t h e t i c a l s i t u a t i o n o f o n e e l e c t r o n e n e r g y s h i f t o f t h e F e r m i l e v e l t h e r e a r e t w o b a n d s t h a t c r o s s t h e F e r m i s u r f a c e . O n e h a n d i s l o c a t e d i n t h e c e n t e r ( a r o u n d t h e F p o i n t ) o f t h e F e r m i s u r f a c e ( F i g u r e 6 . 1 8 D ) a n d t h e o t h e r b a n d t h a t c r o s s e s t h e s u r f a c e m o r e t h a n o n c e i s l o c a t e d a t t h e e d g e s ( F i g u r e 6 . 1 8 E ) . T h e o v e r a l l t o p o l o g y g i v e s t w o p o s s i b l e p a r a l l e l n e s t i n g v e c t o r s w i t h l e n g t h s o f 0 3 9 ( 2 ) a n d 0 . 4 4 ( 2 ) , F i g u r e 6 . 1 8 F t h a t i s q u a l i t a t i v e l y i n g o o d a g r e e m e n t w i t h t h e e x p e r i m e n t a l o b s e r v a t i o n . T h e s e r e s u l t s q u a l i t a t i v e l y d e s c r i b e t h e e x p e r i m e n t a l o b s e r v a t i o n s a n d g i v e s o m e i n s i g h t f o r t h e s t a b i l i t y o f t h e C u d e fi c i e n t c o m p o u n d s v s t h e f u l l y o c c u p i e d o n e . I t s e e m s t h a t i s n e c e s s a r y t o r e m o v e e l e c t r o n s fi o m t h e C u L u T e z s y s t e m i n o r d e r t o h a v e t h e F e r m i l e v e l i n s u c h p o s i t i o n t h a t n e s t i n g i s f a v o r a b l e . T h e o n l y fl e x i b l e w a y f o r t h e s y s t e m t o a d o p t t h i s r e q u i r e d c o n fi g u r a t i o n i s t o c r e a t e v a c a n c i e s i n t h e C u p l a n e . T h i s g i v e s a r e a s o n a b l e a n s w e r t o t h e h y p o s t o i c h i o m e t r y t h a t i s a l w a y s f o u n d i n t h e C u x L u T e z f a m i l y a n d m a y b e e v e n i n t h e M x L a s z ( M = Z n , C o , M n a n d C u w i t h x = 0 . 5 2 — 0 . 8 7 ) s e r i e s . 1 2 4 2 5 3 . 0 2 . 0 0 . 0 - 2 . 0 E n e r g y ( e V ) - 3 . 0 - 4 . 0 - 5 . 0 - 6 . 0 3 V / \ H A \ ' / / e 7 / P 1 i ? _ / f \ ; Q : S t : § 5 % \ g - E / \ _ F i g u r e 6 . 1 5 . B a n d s t r u c t u r e o f N a C u z L u T e 4 n e a r t h e F e r m i l e v e l . 4 2 6 ( A ) ( B ) \ / ( C ) F i g u r e 6 . 1 6 . F e r m i s u r f a c e t o p o l o g y o f t h e t w o i n d i v i d u a l b a n d s ( A a n d B ) t h a t c r o s s t h e F e r m i l e v e l o f N a C u z L u T e 4 . ( C ) S u p e r p o s i t i o n o f t h e s e b a n d s w i l l g i v e t h e t o t a l F e r m i s u r f a c e . P o s s i b l e n e s t i n g v e c t o r s a r e d r a w n i n a r r o w s . 5 1 x 5 1 k p o i n t s w e r e u s e d f o r t h e c a l c u l a t i o n o f t h e F e r m i s u r f a c e . 4 2 7 3 o . _ 2 o . _ _ _ _ _ 1 o . _ 0 0 _ _ _ _ _ _ _ _ 0 _ o . _ _ _ 0 _ _ o . _ _ 0 _ _ _ o . _ 0 _ _ _ _ o . _ 0 _ _ _ _ 0 o . _ _ _ _ 0 o . e W \ / ( A ) ( B ) ( C ) ( D ) ( E ) ( F ) F i g u r e 6 . 1 8 . F e r m i s u r f a c e t o p o l o g y f o r C u x L u T e z . ( A ) x = 1 . ( B ) x = 2 / 3 . ( C ) x = 1 / 3 . ( D ) T h e fi r s t b a n d t h e c r o s s e s t h e F e r m i s u r f a c e f o r x = 0 . ( E ) T h e s e c o n d b a n d t h a t c r o s s e s t h e F e r m i s u r f a c e f o r x = 0 . ( F ) S u p e r p o s i t i o n o f b a n d s ( D a n d E ) t h a t g i v e s t h e t o t a l F e r m i s u r f a c e t o p o l o g y f o r x = 0 w i t h p o s s i b l e n e s t i n g v e c t o r s d r a w n i n a r r o w s . 5 1 x 5 1 k p o i n t s w e r e u s e d f o r t h e c a l c u l a t i o n o f t h e F e r m i s u r f a c e . 4 2 9 V ” R T A G O H [ 1 4 ‘ . k X / é V X _ € a s 7 q 3 Y ~ 7 y G A 5 L 5 Q A H A 2 1 g 5 , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 ’ 1 R 1 ‘ F i g u r e 6 . 1 9 . B r i l l o u i n z o n e o f P m m 2 s p a c e g r o u p . 1 6 l i k z A / B E U _ l / P W A G O H 2 D A k " X i D S ' Y k y C I J . - - " - - . . . . . . . . . . . . . . . . . . . . a a 1 4 ‘ F i g u r e 6 . 2 0 . B r i l l o u i n z o n e o f P m m n s p a c e g r o u p . 1 6 4 3 0 6 . 4 . C o n c l u s i o n s T h e A M z E u T e 4 s e r i e s ( A = N a , K , R b , C s ; M = C u , A g ) s e e m s t o b e t h e m i s s i n g l i n k b e t w e e n t h e R E T e 3 a n d A M R E T e 4 ( R E = R a r e e a r t h ; A = N a , K ; M = C u , A g ) c o m p o u n d s . A c o n t i n u o u s v a r i a t i o n o f i n c r e a s i n g d i m e n s i o n a l i t y f r o m R s z E u T e 4 t o N a M z E u T e 4 s e e m s t o h a v e a n o p p o s i t e t r e n d f r o m t h e c h e m i c a l p r e s s u r e e f f e c t . T h e q - v e c t o r i n c r e a s e s ( f r o m ~ 0 . 2 6 t o ~ 0 . 3 1 ) w i t h t h e c r o s s - p l a n e i n t e r a c t i o n s b e t w e e n t h e d i s t o r t e d T e n e t s . A t t h e s a m e t i m e t h e l e n g t h o f t h e q - v e c t o r d e c r e a s e s w i t h i n c r e a s i n g t h e s i z e o f t h e a t o m s . T h i s s u g g e s t s t h a t t h e t w o t y p e s o f d i m e n s i o n a l i t y c h a n g e s , c r o s s p l a n e ( t h i r d - d i m e n s i o n ) a n d i n p l a n e ( c h e m i c a l p r e s s u r e ) h a v e c o m p e t i n g e f f e c t s o n t h e C D W d i s t o r t i o n s . I n t h e c a s e o f R E T e 3 , A M R E T e 4 , a n d A M z E u T e 4 w h e r e a w e l l d e fi n e d v a n d e r W a a l s i s p r e s e n t , t h e s y s t e m s e e m s t o d i s t o r t w i t h a n i n t e r m e d i a t e q - v e c t o r t h a t r e s u l t s f r o m t h e t w o c o m p e t i n g p h e n o m e n a . T h e e n e r g e t i c c o s t fi ' o m t h e t w o p o s s i b l e d i f f e r e n t q — v e c t o r l e n g t h s c a n b e r e l i e v e d t h r o u g h t h e v a n d e r W a a l s g a p t h a t d e c r e a s e s t h e s t r a i n t h a t i s c r e a t e d f r o m t h e t w o d i f f e r e n t p e r i o d i c i t i e s i n t h e s y s t e m . T h e e x t e n d e d t h r e e - d i m e n s i o n a l i n t e r a c t i o n s i n C u x E u T e z f o r c e t h e s y s t e m t o p r e s e r v e t h e t w o d i f f e r e n t m o d u l a t i o n v e c t o r s c o m i n g f r o m t h e t w o c o m p e t i n g e f f e c t s s i n c e t h e r e i n n o v a n d e r W a a l s g a p . T h e r e f o r e , o n e v e c t o r i s c r e a t e d d u e t o c h e m i c a l p r e s s u r e ( s i z e o f E u ) a n d a n o t h e r v e c t o r f r o m t h e c r o s s - p l a n e i n t e r a c t i o n s . T h e n e w r e s u l t s r e p o r t e d h e r e a d d m o r e i n f o r m a t i o n t o t h e u n d e r s t a n d i n g o f C D W d i s t o r t i o n s a n d t h e e f f e c t o f t h e s t r u c t u r e o n t h e C D W m o d u l a t i o n s . T h i s g i v e s s o m e c l u e s o n t h e a n o m a l o u s b e h a v i o r o f t e m p e r a t u r e a n d R E s i z e t h a t w a s o b s e r v e d i n t h e R E T e ; f a m i l y . A t e m p e r a t u r e d i f f e r e n c e w o u l d m o s t l i k e l y a f f e c t t h e v a n d e r W a a l s g a p ( c r o s s - p l a n e i n t e r a c t i o n b e t w e e n t h e T e n e t s ) m o r e t h a t t h e s i z e o f t h e R E a t o m . 4 3 1 S i m i l a r l y , a c h a n g e i n t h e s i z e o f t h e R E ( c h e m i c a l p r e s s u r e ) f r o m L a T e 3 t o T m T e 3 w o u l d n o t a f f e c t s i g n i fi c a n t l y t h e s p a c i n g o f t h e d i s t o r t e d T e n e t s . T h e r e f o r e t h e a v e r a g e q - v e c t o r r e s u l t i n g f r o m t h e t w o d i f f e r e n t e f f e c t s ( c h e m i c a l p r e s s u r e a n d d i m e n s i o n a l i t y ) s h o u l d h a v e a d i v e r g i n g t r e n d d e p e n d e d o n t h e m o s t f a v o r a b l e i n t e r a c t i o n . I n t h i s e x t e n t , a m o r e c o n c l u s i v e e x p e r i m e n t w o u l d b e t h e a p p l i c a t i o n o f p h y s i c a l p r e s s u r e t h a t m o s t p r o b a b l y w i l l a f f e c t t h e v a n d e r W a a l s g a p e v e n m o r e a n d c o n t r a s t t h e t w o c o m p e t i n g t r e n d s . 4 3 2 T a b l e 6 . 2 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N a o . g o ( 2 ) C u 2 E u 1 , z o ( 2 ) T e 4 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f f i c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 0 1 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 o ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 o ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) T m a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e N 3 0 . 8 0 ( 2 ) C 1 1 2 E 1 1 1 2 0 ( 2 ) T 6 4 8 3 8 . 2 1 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A M o n o c l i n i c P m ( 0 [ 3 1 / 2 ) 0 a = 4 . 3 6 9 2 ( 7 ) A , a = 9 0 ° b = 4 . 3 7 9 0 ( 6 ) A , B = 9 0 ° c = 1 0 . 5 8 7 7 ( 1 8 ) A , y = 9 0 ° 0 . 3 1 2 2 ( 7 ) b ‘ + 1 / 2 c “ 2 0 2 . 5 7 ( 5 ) A 3 1 6 . 8 6 9 0 g / c m 3 2 8 . 3 8 5 m m ' 1 3 5 0 0 . 2 1 x 0 . 1 0 x 0 0 1 1 1 1 1 1 1 3 1 . 7 4 t o 2 9 . 0 1 ° - 5 < = h < = 5 , - 5 < = k < = 5 , - 1 4 < = l < = 1 4 , - 1 < = m < = 1 5 4 0 6 ( 1 7 5 6 m a i n + 3 6 5 0 s a t e l l i t e s ) 2 7 4 4 ( 9 7 9 m a i n + 1 7 6 5 s a t e l l i t e S ) [ R i m = 0 . 0 3 4 8 ] 9 6 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 2 7 4 4 / 2 8 / 1 2 3 1 . 2 1 R o b , = 0 . 0 2 7 1 , w R o b s = 0 . 0 7 6 4 R , “ = 0 . 0 5 1 3 , w R a u = 0 . 0 8 4 7 R o b s = 0 . 0 2 1 5 , w R . , b s = 0 . 0 6 8 5 R , “ = 0 . 0 2 4 9 , w R a u = 0 . 0 7 1 3 R o b , = 0 . 0 6 7 5 , w R o b s = 0 . 1 0 1 0 R , “ = 0 . 1 9 1 2 , w R a u = 0 . 1 2 3 0 0 . 0 4 5 1 a n d 0 . 7 8 8 3 1 . 8 8 a n d - 1 . 1 8 e . A ' 3 R = Z I I F o l - c h l l / 2 1 F . I , w R = { d e 1 0 2 - 1 8 W ] / 2 [ w ( I F . I ‘ ) 1 } " 2 a n d “ = 1 / ( ? ( I ) + 0 . 0 0 1 6 1 2 ) 4 3 3 T a b l e 6 . 3 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) , o c c u p a n c i e s a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r N a o , g o ( 2 ) C u 2 E u . _ 2 o ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x y 2 O c c u p a n c y U e q E u [ l ] 0 0 0 2 7 4 9 0 . 5 6 6 ( 9 ) 7 ( 1 ) s i n , 1 7 ( 6 ) 4 ( 3 ) 0 ( 2 ) c o s , 1 6 ( 5 ) - 5 ( 4 ) 0 ( 2 ) E u [ 2 ] 0 5 0 0 1 ( 2 ) 5 0 0 0 7 7 3 7 ( 1 ) 0 . 6 2 9 ( 1 0 ) 1 1 ( 1 ) s i n , 1 - 7 7 ( 2 ) - 2 1 ( 7 ) 0 ( 1 ) c o s , 1 9 0 ( 3 ) - 1 8 ( 6 ) 0 ( 1 ) T e [ l ] 0 5 0 0 0 ( 5 ) 5 0 0 0 3 7 4 7 ( 2 ) 1 8 ( 1 ) s i n , 1 - 3 4 ( 2 ) 2 ( 1 ) 1 ( 1 ) c o s , 1 - l 4 ( 1 ) - 6 ( 3 ) 0 ( 1 ) T e [ 2 ] 0 1 0 0 0 4 ( 5 ) 0 6 6 8 1 ( 2 ) 1 1 1 ( 1 ) s i n , 1 - 3 2 ( 2 ) - 1 ( 2 ) 0 ( 1 ) c o s , 1 1 9 ( 1 ) - 2 ( 3 ) 0 ( 1 ) T e [ 3 ] 0 4 9 9 5 ( 6 ) 0 2 3 5 ( 2 ) 1 9 ( 1 ) s i n , 1 - 1 8 ( 1 ) 1 9 ( 8 ) - 1 ( 1 ) c o s , 1 — 2 4 9 ( 6 ) - 1 ( 1 ) - 1 2 ( 2 ) T e [ 4 ] 0 9 9 9 2 ( 6 ) 5 0 0 0 2 2 1 ( 2 ) 1 8 ( 1 ) s i n , 1 1 8 ( 1 ) - 1 4 ( 8 ) - 1 ( 1 ) c o s , 1 2 5 3 ( 5 ) 1 ( 1 ) - 1 1 ( 2 ) C u [ l ] 0 1 0 0 1 0 ( 9 ) 5 0 0 0 5 2 2 2 ( 4 ) 1 1 1 ( 1 ) s i n , 1 - 2 8 6 ( 1 5 ) - 2 ( 1 ) - 2 7 ( 4 ) c o s , 1 2 0 ( 1 ) - 3 1 ( 1 1 ) 2 ( 1 ) C u [ 2 ] 0 4 9 9 4 ( 1 0 ) 0 5 2 1 1 ( 4 ) 1 2 3 ( 1 ) s i n , 1 2 2 4 ( 1 6 ) 0 ( 1 ) - 2 6 ( 5 ) c o s , 1 - 1 5 ( 1 ) 2 ( 1 3 ) 2 ( 1 ) N a [ l ] 0 0 0 2 7 4 9 0 . 4 3 4 ( 9 ) 7 ( 1 ) s i n , 1 7 ( 6 ) 4 ( 3 ) 0 ( 2 ) c o s , 1 6 ( 5 ) - 5 ( 4 ) 0 ( 2 ) N a [ 2 ] 0 5 0 0 1 5 0 0 0 7 7 3 7 0 . 3 7 1 ( 1 0 ) 1 1 ( 1 ) s i n , 1 - 7 7 ( 2 ) - 2 1 ( 7 ) 0 ( 1 ) c o s , 1 9 0 ( 3 ) - 1 8 ( 6 ) 0 ( 1 ) T l e q i s d e fi n e d a s o n e t h i r d o f t h e t r a c e o f t h e o r t h o g o n a l i z e d U i j t e n s o r . 4 3 4 T a b l e 6 . 4 . A n i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 3 ) f o r N a o , g o ( 2 ) C u 2 E u L 2 0 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 E u [ l ] 0 2 ( 1 ) 8 ( 1 ) 1 2 ( 1 ) 0 1 ( 1 ) 0 s i n , 1 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) - 1 ( 1 ) c o s , 1 0 ( 1 ) — 1 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 1 ( 1 ) 1 ( 1 ) E u [ 2 ] 0 9 ( 1 ) 1 1 ( 1 ) 1 3 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 - 3 ( 1 ) - 2 ( 1 ) 1 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 4 0 ) c o s , 1 4 ( 1 ) 3 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) - 1 ( 1 ) T e [ l ] 0 3 ( 1 ) 8 ( 1 ) 1 4 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 - 1 ( 1 ) 0 ( 1 ) — 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) T e [ 2 ] 0 7 ( 1 ) 8 ( 1 ) 1 7 ( 1 ) 0 1 ( 1 ) 0 s i n , 1 - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) T e [ 3 ] 0 9 ( 1 ) 5 ( 1 ) 1 2 ( 1 ) 0 1 ( 1 ) 0 s i n , 1 - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 2 ( 1 ) c o s , 1 - 1 1 ( 1 ) - 1 ( 1 ) 6 ( 1 ) 0 ( 1 ) - 2 ( 1 ) 0 ( 1 ) T e [ 4 ] 0 1 0 ( 1 ) 5 ( 1 ) 8 ( 1 ) 0 - 1 ( 1 ) 0 s i n , 1 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 3 ( 1 ) 0 ( 1 ) 1 ( 1 ) c o s , 1 1 2 ( 1 ) 0 ( 1 ) - 6 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) C u [ l ] 0 1 2 ( 2 ) 1 1 ( 2 ) 1 1 ( 1 ) 0 6 ( 1 ) 0 s i n , 1 - 1 2 ( 2 ) 0 ( 2 ) 2 ( 2 ) 0 ( 1 ) - 5 ( 1 ) 0 ( 1 ) c o s , 1 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 2 ( 2 ) 0 ( 1 ) 1 ( 2 ) C u [ 2 ] 0 1 9 ( 2 ) 3 3 ( 2 ) 1 5 ( 1 ) 0 - 8 ( 1 ) 0 s i n , 1 9 ( 2 ) 1 ( 3 ) - 9 ( 2 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) c o s , 1 - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 6 ( 2 ) 0 ( 1 ) - 2 ( 2 ) N a [ l ] 0 2 ( 1 ) 8 ( 1 ) 1 2 ( 1 ) 0 1 ( 1 ) 0 s i n , 1 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) 4 0 ) c o s , 1 0 ( 1 ) - 1 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 1 ( 1 ) 1 ( 1 ) N a [ 2 ] 0 9 ( 1 ) 1 1 ( 1 ) 1 3 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 - 3 ( 1 ) - 2 ( 1 ) 1 ( 1 ) 0 ( 1 ) - 1 ( 1 ) . 1 0 ) c o s , 1 4 ( 1 ) 3 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) - 1 ( 1 ) 4 3 5 T a b l e 6 . 5 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N a 0 _ 3 0 ( 2 ) C q u u . , 2 o ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e E u [ l ] - T e [ l ] x 4 3 . 2 8 6 ( 3 ) 3 . 2 7 2 ( 3 ) 3 . 3 0 0 ( 3 ) E u [ l ] - T e [ 3 ] x 2 3 . 4 0 6 ( 4 ) 3 . 3 2 3 ( 4 ) 3 . 4 8 9 ( 4 ) E u [ l ] - T e [ 4 ] x 2 3 . 4 1 9 ( 3 ) 3 . 4 0 8 ( 3 ) 3 . 4 3 1 ( 3 ) E u [ l ] - C u [ 1 ] x 2 3 . 4 5 4 ( 5 ) 3 . 4 3 3 ( 5 ) 3 . 4 7 7 ( 5 ) E u [ l ] - C u [ 2 ] x 2 3 . 4 4 2 ( 6 ) 3 . 3 6 1 ( 8 ) 3 . 5 2 5 ( 8 ) T e [ l ] - C u [ 1 ] x 2 2 . 6 8 3 ( 6 ) 2 . 6 1 2 ( 7 ) 2 . 7 5 5 ( 7 ) T e [ l ] - C u [ 2 ] x 2 2 . 6 8 4 ( 5 ) 2 . 6 7 0 ( 4 ) 2 . 7 0 0 ( 4 ) T e [ 2 ] - C u [ 1 ] x 2 2 . 6 8 1 ( 4 ) 2 . 6 6 1 ( 4 ) 2 . 7 0 1 ( 4 ) T e [ 2 ] - C u [ 2 ] x 2 2 . 6 8 5 ( 6 ) 2 . 6 0 9 ( 8 ) 2 . 7 6 4 ( 8 ) T e [ 2 ] - E u [ 2 ] x 4 3 . 2 9 0 ( 3 ) 3 . 2 6 1 ( 3 ) 3 . 3 1 9 ( 3 ) T e [ 3 ] - T e [ 4 ] x 4 3 . 0 9 4 ( 4 ) 2 . 9 6 1 ( 3 ) 3 . 2 3 4 ( 4 ) T e [ 3 ] - E u [ 2 ] x 2 3 . 4 3 5 ( 3 ) 3 . 4 1 5 ( 3 ) 3 . 4 5 4 ( 3 ) T e [ 4 ] - E u [ 2 ] x 2 3 . 4 1 7 ( 3 ) 3 . 3 8 8 ( 4 ) 3 . 4 4 6 ( 4 ) C u [ 1 ] - C u [ 2 ] x 4 3 . 0 9 8 ( 7 ) 2 . 9 6 5 ( 7 ) 3 . 2 3 7 ( 7 ) C u [ 1 ] - E u [ 2 ] x 2 3 . 4 4 7 ( 5 ) 3 . 4 2 3 ( 7 ) 3 . 4 7 2 ( 7 ) C u [ 2 ] - E u [ 2 ] x 2 3 . 4 5 8 ( 5 ) 3 . 4 3 0 ( 6 ) 3 . 4 8 7 ( 6 ) T a b l e 6 . 6 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o _ g o ( 2 ) C u 2 E u 1 _ 2 0 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ l ] - E u [ l ] - T e [ l ] x 8 8 3 5 8 ( 7 ) 8 3 3 7 ( 7 ) 8 3 . 7 8 ( 7 ) T e [ l ] - E u [ l ] - T e [ l ] x 4 1 4 0 . 5 6 ( 9 ) 1 4 0 . 4 4 ( 9 ) 1 4 0 . 6 7 ( 9 ) T e [ l ] - E u [ l ] - T e [ 3 ] x 4 8 0 3 1 ( 8 ) 7 9 2 5 ( 8 ) 8 1 . 4 2 ( 8 ) T e [ l ] - E u [ l ] - T e [ 3 ] x 4 1 3 3 . 2 4 ( 9 ) 1 3 2 . 6 0 ( 9 ) l 3 3 . 8 6 ( 8 ) T e [ l ] - E u [ l ] - T e [ 4 ] x 4 8 0 3 1 ( 7 ) 7 8 9 8 ( 7 ) 8 1 . 6 2 ( 7 ) T e [ l ] - E u [ l ] - T e [ 4 ] x 4 1 3 3 . 2 6 ( 9 ) 1 3 1 . 5 6 ( 9 ) l 3 4 . 9 3 ( 9 ) T e [ l ] - E u [ l ] - C u [ 1 ] x 4 4 6 . 9 3 ( 1 2 ) 4 5 . 0 5 ( 1 2 ) 4 8 . 8 2 ( 1 2 ) T e [ 1 ] - E u [ 1 ] - C u [ 1 ] x 4 9 9 3 4 ( 1 2 ) 9 8 . 1 8 ( 1 1 ) 1 0 0 . 5 0 ( 1 1 ) T e [ l ] - E u [ l ] - C u [ 2 ] x 4 4 6 9 4 ( 7 ) 4 6 5 8 ( 7 ) 4 7 3 0 ( 7 ) T e [ l ] - E u [ 1 ] - C u [ 2 ] x 4 9 9 2 7 ( 1 1 ) 9 8 . 0 1 ( 1 1 ) 1 0 0 . 4 9 ( 1 1 ) T e [ 3 ] - E u [ l ] - T e [ 3 ] x 2 7 9 8 2 ( 8 ) 7 9 5 0 ( 8 ) 8 0 0 9 ( 9 ) T e [ 3 ] - E u [ l ] - T e [ 4 ] x 4 5 3 9 1 ( 7 ) 5 1 9 5 ( 7 ) 5 5 8 7 ( 7 ) 4 3 6 T a b l e 6 . 6 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o , 3 0 ( 2 ) C u 2 E u 1 . 2 o ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 3 ] - E u [ 1 ] - C u [ 1 ] x 4 T e [ 3 ] - E u [ l ] - C u [ 2 ] x 2 T e [ 3 ] - E u [ l ] - C u [ 2 ] x 2 T e [ 4 ] - E u [ l ] - T e [ 4 ] x 2 T e [ 4 ] - E u [ 1 ] - C u [ 1 ] x 2 T e [ 4 ] - E u [ 1 ] - C u [ 1 ] x 2 T e [ 4 ] - E u [ l ] - C u [ 2 ] x 4 C u [ 1 ] - E u [ 1 ] - C u [ 1 ] x 2 C u [ 1 ] - E u [ 1 ] - C u [ 2 ] x 4 C u [ 2 ] - E u [ l ] - C u [ 2 ] x 2 E u [ l ] - T e [ l ] - E u [ 1 ] x 8 E u [ 1 ] - T e [ l ] - E u [ 1 ] x 4 E u [ 1 ] - T e [ 1 ] - C u [ 1 ] x 4 E u [ 1 ] - T e [ 1 ] - C u [ 1 ] x 4 E u [ 1 ] - T e [ 1 ] - C u [ 2 ] x 4 E u [ 1 ] - T e [ 1 ] - C u [ 2 ] x 4 C u [ 1 ] - T e [ 1 ] - C u [ 1 ] x 2 C u [ 1 ] - T e [ 1 ] - C u [ 2 ] x 4 C u [ 2 ] - T e [ l ] - C u [ 2 ] x 2 C u [ 1 ] - T e [ 2 ] - C u [ 1 ] x 2 C u [ 1 ] - T e [ 2 ] - C u [ 2 ] x 4 C u [ 1 ] - T e [ 2 ] - E u [ 2 ] x 4 C u [ 1 ] - T e [ 2 ] - E u [ 2 ] x 4 C u [ 2 ] - T e [ 2 ] - C u [ 2 ] x 2 C u [ 2 ] - T e [ 2 ] - E u [ 2 ] x 4 C u [ 2 ] - T e [ 2 ] - E u [ 2 ] x 4 E u [ 2 ] - T e [ 2 ] - E u [ 2 ] x 8 E u [ 2 ] - T e [ 2 ] - E u [ 2 ] x 4 E u [ l ] - T e [ 3 ] - E u [ 1 ] x 2 E u [ l ] - T e [ 3 ] - T e [ 4 ] x 4 E u [ l ] - T e [ 3 ] - T e [ 4 ] x 4 E u [ l ] - T e [ 3 ] - E u [ 2 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 8 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 1 2 6 . 3 8 0 3 ) 1 0 0 . 6 3 ( 1 5 ) 1 7 9 . 4 3 0 6 ) 7 9 6 9 ( 8 ) 1 0 0 . 8 3 ( 8 ) 1 7 7 . 8 1 0 5 ) 1 2 6 . 3 3 0 1 ) 7 8 . 7 3 0 0 ) 5 3 . 3 8 0 2 ) 7 8 . 8 0 0 7 ) 8 3 5 8 ( 7 ) 1 4 0 . 5 6 ( 9 ) 6 9 . 8 9 0 1 ) 1 3 7 . 4 9 ( 6 ) 6 9 . 5 6 0 6 ) 1 3 7 . 6 ( 2 ) 1 0 8 . 8 6 0 9 ) 7 0 . 3 3 0 9 ) 1 0 9 . 4 1 0 8 ) 1 0 9 . 6 2 0 6 ) 7 0 . 5 2 0 4 ) 6 9 . 6 7 0 2 ) l 3 7 . 7 6 ( 1 4 ) 1 0 9 . 0 ( 2 ) 6 9 8 8 ( 1 1 ) 1 3 7 . 5 6 0 0 ) 8 3 4 5 ( 8 ) 1 4 0 . 2 4 ( 9 ) 7 9 8 2 ( 8 ) 6 3 3 2 ( 8 ) 1 1 7 . 0 8 ( 9 ) 1 2 6 . 2 6 ( 9 ) 9 0 . 2 5 0 1 ) 1 7 7 . 0 4 0 3 ) 1 2 3 . 9 6 0 3 ) 1 0 0 . 2 6 0 6 ) 1 7 9 . 2 3 ( 1 6 ) 7 9 3 9 ( 8 ) 1 0 0 . 6 1 ( 8 ) 1 7 6 . 6 5 0 5 ) 1 2 4 . 4 7 0 1 ) 7 8 . 0 5 0 0 ) 5 1 . 5 5 0 3 ) 7 8 . 1 8 0 8 ) 8 3 . l 4 ( 7 ) 1 4 0 . 5 3 ( 9 ) 6 8 . 7 9 0 1 ) 1 3 7 . 1 2 ( 6 ) 6 8 . 3 7 0 6 ) 1 3 5 . 1 0 0 9 ) 1 0 7 . 8 ( 2 ) 6 7 . 2 6 0 8 ) 1 0 8 . 8 0 0 7 ) 1 0 9 3 2 ( 1 6 ) 6 7 . 5 8 0 7 ) 6 8 . 4 4 0 4 ) 1 3 5 . 7 0 0 8 ) 1 0 8 . 1 ( 2 ) 6 8 . 5 2 ( 1 1 ) 1 3 6 . 9 4 ( 8 ) 8 3 4 4 ( 8 ) 1 3 9 . 8 7 ( 9 ) 7 9 5 0 ( 9 ) 6 1 . 1 9 ( 8 ) 1 1 6 . 4 9 ( 1 1 ) 1 2 3 . 3 9 ( 9 ) 8 5 . 9 1 0 2 ) 1 7 5 . 4 1 0 3 ) 1 2 8 . 8 1 0 2 ) 1 0 1 . 0 5 0 5 ) 1 7 9 . 6 4 0 6 ) 7 9 9 4 ( 8 ) 1 0 1 0 ( 8 ) 1 8 o 1 2 8 . 1 4 ( 1 1 ) 7 9 . 3 2 0 0 ) 5 5 . 2 6 0 4 ) 7 9 . 3 8 0 9 ) 8 4 0 1 ( 7 ) 1 4 0 . 5 8 ( 9 ) 7 1 . 0 4 0 2 ) 1 3 7 . 8 5 ( 6 ) 7 0 . 7 4 0 6 ) 1 4 0 . 1 ( 2 ) 1 0 9 . 8 ( 2 ) 7 3 . 3 7 0 9 ) 1 0 9 . 9 1 0 7 ) 1 0 9 . 8 3 0 6 ) 7 3 . 5 4 ( 1 8 ) 7 0 . 9 3 0 4 ) 1 3 9 . 8 6 0 8 ) 1 0 9 . 9 ( 2 ) 7 1 . 2 3 0 2 ) 1 3 8 . 1 9 ( 8 ) 8 3 4 6 ( 8 ) 1 4 0 . 6 0 ( 8 ) 8 0 0 9 ( 9 ) 6 5 4 5 ( 8 ) 1 1 7 . 7 5 0 1 ) 1 2 9 . 0 5 ( 9 ) 9 4 . 6 2 0 3 ) 1 7 9 . 5 0 0 1 ) 4 3 7 T a b l e 6 . 6 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o , g o ( 2 ) C u 2 E u 1 , z o ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 4 ] - T e [ 3 ] - E u [ 2 ] x 4 T e [ 4 ] - T e [ 3 ] - E u [ 2 ] x 4 E u [ 2 ] - T e [ 3 ] - E u [ 2 ] x 2 E u [ l ] - T e [ 4 ] - E u [ l ] x 2 E u [ l ] - T e [ 4 ] - T e [ 3 ] x 4 E u [ l ] - T e [ 4 ] - T e [ 3 ] x 4 E u [ l ] - T e [ 4 ] - E u [ 2 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 8 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - E u [ 2 ] x 4 T e [ 3 ] - T e [ 4 ] - E u [ 2 ] x 4 E u [ 2 ] - T e [ 4 ] - E u [ 2 ] x 2 E u [ 1 ] - C u [ 1 ] - E u [ 1 ] x 2 E u [ 1 ] - C u [ 1 ] - T e [ 1 ] x 4 E u [ l ] - C u [ 1 ] - T e [ 2 ] x 2 E u [ 1 ] - C u [ 1 ] - T e [ 2 ] x 2 E u [ 1 ] - C u [ 1 ] - C u [ 2 ] x 4 E u [ 1 ] - C u [ 1 ] - C u [ 2 ] x 4 E u [ 1 ] - C u [ 1 ] - E u [ 2 ] x 4 T e [ 1 ] - C u [ 1 ] - T e [ 1 ] x 2 T e [ l ] - C u [ 1 ] - T e [ 2 ] x 4 T e [ 1 ] - C u [ 1 ] - C u [ 2 ] x 4 T e [ 1 ] - C u [ 1 ] - C u [ 2 ] x 4 T e [ 1 ] - C u [ 1 ] - E u [ 2 ] x 2 T e [ 1 ] - C u [ 1 ] - E u [ 2 ] x 2 T e [ 2 ] - C u [ 1 ] - T e [ 2 ] x 2 T e [ 2 ] - C u [ 1 ] - C u [ 2 ] x 4 T e [ 2 ] - C u [ 1 ] - C u [ 2 ] x 4 T e [ 2 ] - C u [ 1 ] - E u [ 2 ] x 4 C u [ 2 ] - C u [ 1 ] — C u [ 2 ] x 8 C u [ 2 ] - C u [ 1 ] - C u [ 2 ] x 4 C u [ 2 ] - C u [ 1 ] - E u [ 2 ] x 4 C u [ 2 ] - C u [ 1 ] - E u [ 2 ] x 4 E u [ 2 ] - C u [ 1 ] - E u [ 2 ] x 2 6 2 9 5 ( 7 ) 1 1 6 . 6 6 0 1 ) 7 9 2 1 ( 8 ) 7 9 6 5 ( 7 ) 6 2 8 1 ( 8 ) 1 1 6 . 7 9 0 1 ) 1 2 6 . 2 6 ( 1 0 ) 9 0 . 2 5 0 2 ) 1 7 7 . 0 5 0 3 ) 6 3 4 6 ( 9 ) 1 1 7 . 0 3 0 0 ) 7 9 4 1 ( 7 ) 7 8 . 6 8 0 1 ) 6 3 . 2 5 0 1 ) 8 5 . 8 0 0 0 ) 1 6 4 . 2 2 0 7 ) 6 3 . 0 9 0 5 ) 1 1 6 . 4 ( 2 ) 1 2 6 . 6 2 0 4 ) 1 0 8 . 8 6 0 8 ) 1 0 9 . 5 2 0 6 ) 5 4 . 7 6 0 5 ) 1 2 4 . 8 3 0 8 ) 8 6 . 1 2 0 5 ) 1 6 4 . 8 ( 2 ) 1 0 9 5 2 0 8 ) 5 4 . 7 7 0 5 ) 1 2 5 . 4 ( 2 ) 6 3 . 5 1 0 2 ) 9 0 1 ( 2 ) 1 7 6 . 9 ( 2 ) 6 3 . 5 3 0 4 ) 1 1 6 . 7 4 ( 1 6 ) 7 8 . 7 2 0 1 ) 6 2 0 5 ( 7 ) 1 1 3 . 6 1 0 1 ) 7 9 1 6 ( 9 ) 7 9 4 4 ( 8 ) 6 1 8 3 ( 8 ) 1 1 4 . 1 1 0 1 ) 1 2 4 . 3 5 0 0 ) 8 6 . 0 1 0 2 ) 1 7 5 . 4 2 0 2 ) 6 1 . 6 7 ( 8 ) 1 1 6 . 1 0 0 0 ) 7 9 1 7 ( 7 ) 7 7 . 9 7 0 3 ) 6 1 . 7 7 0 2 ) 8 5 4 6 ( 9 ) 1 6 3 . 0 3 0 8 ) 6 1 . 9 8 0 4 ) 1 1 3 . 2 ( 2 ) 1 2 4 . 3 6 0 7 ) 1 0 7 . 8 ( 2 ) 1 0 6 . 6 4 0 9 ) 5 2 . 5 1 0 5 ) 1 2 3 . 3 1 0 8 ) 8 4 . 0 4 0 9 ) 1 6 3 . 4 ( 3 ) 1 0 8 . 5 ( 2 ) 5 3 . 7 4 0 4 ) 1 2 1 . 7 ( 3 ) 6 2 . 5 7 0 4 ) 8 5 . 5 ( 2 ) 1 7 5 . 0 ( 2 ) 6 1 . 5 5 0 5 ) 1 1 5 . 6 7 0 7 ) 7 8 . 1 0 0 3 ) 6 3 8 7 ( 7 ) 1 1 9 6 3 ( 1 2 ) 7 9 2 5 ( 8 ) 7 9 8 1 ( 8 ) 6 3 8 7 ( 8 ) 1 1 9 4 8 ( 1 2 ) 1 2 8 . 1 8 ( 9 ) 9 4 . 6 7 0 3 ) 1 7 9 . 4 9 0 1 ) 6 5 3 3 ( 9 ) 0 7 8 5 ( 9 ) 7 9 6 4 ( 7 ) 7 9 . 3 2 0 4 ) 6 4 . 7 1 0 3 ) 8 6 . 1 9 0 2 ) 1 6 5 . 0 4 0 6 ) 6 4 . 3 1 0 5 ) 1 1 9 . 6 ( 2 ) 1 2 8 . 8 2 0 6 ) 1 0 9 . 8 ( 2 ) 1 1 2 . 3 6 0 9 ) 5 7 . 0 5 0 7 ) 1 2 6 . 1 9 0 8 ) 8 8 . 2 ( 2 ) 1 6 6 . 3 ( 3 ) 1 1 0 . 4 ( 2 ) 5 5 . 9 0 0 4 ) 1 2 9 . 0 ( 3 ) 6 4 . 4 0 0 4 ) 9 4 . 8 ( 3 ) 1 7 9 . 6 ( 2 ) 6 5 . 5 4 0 6 ) 1 1 7 . 7 2 0 7 ) 7 9 3 2 ( 1 3 ) 4 3 8 T a b l e 6 . 6 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o _ 3 o ( 2 ) C u 2 E u 1 , z o ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . E u [ l ] - C u [ 2 ] - E u [ 1 ] x 2 E u [ 1 ] - C u [ 2 ] - T e [ 1 ] x 4 E u [ l ] - C u [ 2 ] - T e [ 2 ] x 2 E u [ l ] - C u [ 2 ] - T e [ 2 ] x 2 E u [ 1 ] - C u [ 2 ] - C u [ 1 ] x 4 E u [ l ] - C u [ 2 ] - C u [ 1 ] x 4 E u [ l ] - C u [ 2 ] - E u [ 2 ] x 4 T e [ 1 ] - C u [ 2 ] - T e [ 1 ] x 2 T e [ l ] - C u [ 2 ] - T e [ 2 ] x 4 T e [ 1 ] - C u [ 2 ] - C u [ 1 ] x 4 T e [ 1 ] - C u [ 2 ] - C u [ 1 ] x 4 T e [ l ] - C u [ 2 ] - E u [ 2 ] x 2 T e [ l ] - C u [ 2 ] - E u [ 2 ] x 2 T e [ 2 ] - C u [ 2 ] - T e [ 2 ] x 2 T e [ 2 ] - C u [ 2 ] - C u [ 1 ] x 4 T e [ 2 ] - C u [ 2 ] - C u [ 1 ] x 4 T e [ 2 ] - C u [ 2 ] - E u [ 2 ] x 4 C u [ 1 ] - C u [ 2 ] - C u [ 1 ] x 8 C u [ 1 ] - C u [ 2 ] - C u [ 1 ] x 4 C u [ 1 ] - C u [ 2 ] - E u [ 2 ] x 4 C u [ 1 ] - C u [ 2 ] - E u [ 2 ] x 4 E u [ 2 ] - C u [ 2 ] - E u [ 2 ] x 2 T e [ 2 ] - E u [ 2 ] - T e [ 2 ] x 8 T e [ 2 ] - E u [ 2 ] - T e [ 2 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 3 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 3 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 4 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 4 ] x 4 T e [ 2 ] - E u [ 2 ] - C u [ 1 ] x 4 T e [ 2 ] - E u [ 2 ] - C u [ 1 ] x 4 T e [ 2 ] - E u [ 2 ] - C u [ 2 ] x 4 T e [ 2 ] - E u [ 2 ] - C u [ 2 ] x 4 T e [ 3 ] - E u [ 2 ] - T e [ 3 ] x 2 T e [ 3 ] - E u [ 2 ] - T e [ 4 ] x 4 7 8 . 8 0 0 3 ) 6 3 . 4 8 ( 1 2 ) 8 6 . 1 3 0 7 ) 1 6 4 . 8 ( 2 ) 6 3 6 1 ( 1 6 ) 1 1 6 . 7 7 0 8 ) 1 2 6 . 7 3 0 6 ) 1 0 9 . 4 ( 2 ) 1 0 9 . 6 3 0 9 ) 5 4 . 7 9 0 4 ) 1 2 5 . 5 ( 2 ) 8 5 . 9 4 0 1 ) 1 6 4 . 2 8 0 9 ) 1 0 9 . 0 ( 2 ) 5 4 . 8 5 0 5 ) 1 2 4 . 9 2 0 9 ) 6 3 3 1 ( 1 1 ) 9 0 . 4 ( 2 ) 1 7 7 . 1 ( 2 ) 6 3 1 2 ( 1 3 ) 1 1 6 . 5 2 0 9 ) 7 8 . 5 9 0 3 ) 8 3 5 1 ( 5 ) 1 4 0 . 2 3 0 ) 8 0 6 2 ( 8 ) 1 3 3 . 3 2 ( 8 ) 8 0 6 1 ( 8 ) 1 3 3 . 2 8 ( 1 0 ) 4 6 8 6 ( 6 ) 9 9 1 3 ( 1 1 ) 4 6 . 7 3 ( 1 4 ) 9 9 . 0 8 0 2 ) 7 9 2 4 ( 7 ) 5 3 6 9 ( 8 ) 7 8 . 1 8 0 5 ) 6 2 . 8 2 0 4 ) 8 3 7 ( 2 ) 1 6 1 . 4 ( 3 ) 6 1 . 5 7 0 5 ) 1 1 5 . 8 5 0 9 ) 1 2 4 . 2 0 0 8 ) 1 0 8 . 2 ( 2 ) 1 0 6 . 9 ( 2 ) 5 4 . 0 1 0 4 ) 1 2 2 . 3 ( 3 ) 8 5 5 5 ( 8 ) 1 6 3 . 3 ( 2 ) 1 0 8 . 1 ( 2 ) 5 2 . 7 2 0 5 ) 1 2 3 . 4 3 ( 1 8 ) 6 1 . 8 5 0 1 ) 8 6 . 3 ( 2 ) 1 7 5 . 4 ( 2 ) 6 2 . 2 2 ( 1 1 ) 1 1 3 6 ( 2 ) 7 8 . 2 3 0 5 ) 8 2 6 0 ( 5 ) 1 4 0 . 1 2 ( 7 ) 7 9 0 3 ( 8 ) 1 3 0 . 7 0 ( 8 ) 8 0 4 3 ( 8 ) 1 3 2 . 7 2 0 0 ) 4 6 7 5 ( 6 ) 9 7 . 7 9 0 1 ) 4 4 . 8 9 0 4 ) 9 7 . 6 9 0 2 ) 7 8 8 7 ( 7 ) 5 1 . 5 5 ( 8 ) 7 9 . 3 8 0 5 ) 6 4 . 1 2 0 4 ) 8 8 . 6 ( 2 ) 1 6 8 . 2 ( 3 ) 6 5 7 3 ( 1 7 ) 1 1 7 . 7 7 0 8 ) 1 2 9 . 2 6 0 7 ) 1 1 0 . 3 ( 2 ) 1 1 2 . 4 ( 2 ) 5 5 . 6 2 ( l 4 ) 1 2 8 . 7 ( 3 ) 8 6 3 1 ( 8 ) 1 6 4 . 8 2 0 8 ) 1 0 9 . 9 ( 2 ) 5 7 . 0 9 0 7 ) 1 2 6 . 2 9 0 8 ) 6 4 . 7 9 0 2 ) 9 4 . 6 ( 3 ) 1 7 9 . 6 ( 2 ) 6 4 . 1 2 0 1 ) 1 1 9 . 5 ( 2 ) 7 8 8 8 ( 1 5 ) 8 4 4 1 ( 5 ) 1 4 0 . 3 5 ( 7 ) 8 2 1 6 ( 8 ) 1 3 5 . 9 2 ( 8 ) 8 0 7 9 ( 8 ) 1 3 3 . 8 5 0 0 ) 4 6 9 8 ( 6 ) 1 0 0 . 4 7 0 1 ) 4 8 . 5 1 0 4 ) 1 0 0 . 4 4 0 2 ) 7 9 5 1 ( 7 ) 5 5 8 2 ( 8 ) 4 3 9 T a b l e 6 . 7 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N a o _ 8 1 ( 2 ) A g 2 E u 1 , 1 9 ( 2 ) T e 4 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 8 . 9 4 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ’ ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 c r ( I ) ] R 1 " o r d e r s a t e l l i t e s ( a l l d a t a ) T m i n a n d T m a m c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e N a o . 8 1 ( 2 ) A n g u 1 . 1 9 ( 2 ) T e 4 9 2 6 . 9 1 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A M o n o c l i n i c P m ( 0 [ 3 1 / 2 ) 0 a = 4 . 4 1 8 5 ( 6 ) A , a = 9 0 ° b = 4 . 4 4 3 5 ( 7 ) A , B = 9 0 ° c = 1 1 . 0 7 6 7 ( l 7 ) A , y = 9 0 ° 0 . 3 1 3 4 ( 6 ) b ’ + 1 / 2 c ‘ 2 1 7 . 4 8 ( 6 ) A 3 1 7 . 0 7 4 9 g / c m 3 2 5 . 9 8 7 m m " 3 8 5 0 . 1 6 x 0 . 0 9 x 0 . 0 1 m m 3 3 . 1 0 t o 2 8 . 9 4 ° - 5 < = h < = 5 , - 6 < = k < = 6 , - 1 5 < = l < = 1 5 , - 1 < = m < = 1 5 4 7 0 ( 1 7 2 5 m a i n + 3 7 4 5 s a t e l l i t e s ) 3 1 7 5 ( 1 0 7 1 m a i n + 2 1 0 4 s a t e l l i t e s ) [ R i m = 0 . 0 2 9 3 ] 9 7 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 3 1 7 5 / 2 8 / 1 2 2 2 . 4 3 R o b , = 0 . 0 5 7 7 , w R o b s = 0 . 1 4 3 1 R , “ = 0 . 0 8 5 4 , w R a u = 0 . 1 7 4 7 R o b s = 0 . 0 5 1 2 , w R o b , = 0 . 1 4 3 6 R 1 1 1 = 0 . 0 5 5 0 , w R , " = 0 . 1 7 3 2 R o b , = 0 . 0 8 8 0 , w R o b s = 0 . 1 4 1 1 R a n = 0 . 1 9 8 6 , w R a n = 0 . 1 8 0 0 0 . 0 8 9 7 a n d 0 . 8 0 6 2 5 . 8 9 a n d - 7 . 4 8 e . A ' 3 R = l e F o l - c h l l / 2 I F o I , w R = { 2 3 [ W ( | F o l 2 - I F c 1 9 2 ] / z 3 [ W ( | F o | 4 ) ] } W a n d W = 1 / ( 0 2 ( I ) + 0 - 0 0 1 6 1 2 ) 4 4 0 T a b l e 6 . 8 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) , o c c u p a n c i e s a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r N a o , 3 1 ( 2 ) A g 2 E u 1 , 1 9 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x y 2 O c c u p a n c y U m 1 E u [ l ] 0 0 0 2 7 4 9 0 . 5 7 7 ( 1 4 ) 1 4 ( 1 ) s i n , 1 3 7 ( 9 ) 0 ( 3 ) - 6 ( 3 ) c o s , 1 3 3 ( 8 ) 1 ( 3 ) - 5 ( 2 ) E u [ 2 ] 0 5 0 2 1 ( 4 ) 5 0 0 0 8 0 2 1 ( 2 ) 0 . 6 0 5 ( 1 4 ) 1 1 ( 1 ) s i n , 1 6 8 ( 3 ) 3 ( 5 ) - 1 ( 2 ) c o s , 1 - 9 5 ( 4 ) 2 ( 4 ) 1 ( 3 ) T e [ l ] 0 5 0 3 9 ( 8 ) 5 0 0 0 3 6 8 8 ( 3 ) 1 1 2 ( 1 ) s i n , 1 3 8 ( 3 ) 1 ( 1 ) 0 ( 2 ) c o s , 1 1 7 ( 1 ) - 2 ( 3 ) 0 ( 1 ) T e [ 2 ] 0 2 0 ( 8 ) 0 7 0 2 3 ( 3 ) 1 1 1 ( 1 ) s i n , 1 3 0 ( 3 ) 0 ( 2 ) 0 ( 2 ) c o s , 1 - 2 2 ( 2 ) 0 ( 3 ) 0 ( 1 ) T e [ 3 ] 0 4 9 9 8 ( 8 ) 0 3 9 3 ( 4 ) 1 1 5 ( 1 ) s i n , 1 3 1 ( 1 ) 3 2 ( 6 ) - l ( 1 ) c o s , 1 2 5 0 ( 1 1 ) - 4 ( 1 ) - 8 ( 3 ) T e [ 4 ] 0 7 ( 8 ) 5 0 0 0 3 8 7 ( 4 ) 1 1 3 ( 1 ) s i n , 1 - 3 5 ( 1 ) - 2 6 ( 6 ) - 1 ( 1 ) c o s , 1 - 2 8 5 ( 1 0 ) 3 ( 1 ) - 9 ( 3 ) A g [ l ] 0 9 9 1 1 ( 7 ) 5 0 0 0 5 3 7 1 ( 4 ) 1 9 ( 1 ) s i n , 1 2 2 8 ( 1 3 ) - 3 ( 1 ) - 1 6 ( 3 ) c o s , 1 - 2 7 ( 2 ) - 2 5 ( 7 ) 2 ( 1 ) A g [ 2 ] 0 4 9 5 3 ( 7 ) 0 5 3 6 3 ( 5 ) 1 1 5 ( 1 ) s i n , 1 - 2 1 2 ( 1 5 ) 2 ( 1 ) - 2 6 ( 4 ) c o s , 1 2 4 ( 2 ) 2 1 ( 7 ) 3 ( 1 ) N a [ l ] 0 0 0 2 7 4 9 0 . 4 2 3 ( 1 4 ) 1 4 ( 1 ) s i n , 1 3 7 ( 9 ) 0 ( 3 ) - 6 ( 3 ) c o s , 1 3 3 ( 8 ) 1 ( 3 ) - 5 ( 2 ) N a [ 2 ] 0 5 0 2 1 5 0 0 0 8 0 2 1 0 . 3 9 5 ( 1 4 ) 1 1 ( 1 ) s i n , 1 6 8 ( 3 ) 3 ( 5 ) - 1 ( 2 ) c o s , 1 - 9 5 ( 4 ) 2 ( 4 ) 1 ( 3 ) 4 4 1 T a b l e 6 . 9 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r N a o _ 3 . ( 2 ) A g 2 E u 1 _ 1 9 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 E u [ l ] 0 1 3 ( 1 ) 1 5 ( 1 ) 1 4 ( 1 ) 0 6 ( 1 ) 0 s i n , 1 - 2 0 ) 0 0 ) 4 0 ) - 1 0 ) - 5 0 ) - 1 0 ) c o s , 1 - 2 0 ) 0 ( 1 ) - 3 0 ) 2 ( 1 ) . 4 0 ) 1 ( 1 ) E u [ 2 ] 0 1 5 ( 1 ) 1 ( 1 ) 1 7 ( 1 ) 0 2 ( 1 ) 0 s i n , 1 - 5 0 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 0 ) - 1 ( 1 ) c o s , 1 7 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 2 ( 1 ) - 1 0 ) T e [ l ] 0 1 2 ( 1 ) 9 ( 1 ) 1 5 ( 1 ) 0 6 ( 1 ) 0 s i n , 1 - 3 0 ) 0 ( 1 ) 2 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 - 1 0 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) T e [ 2 ] 0 1 5 ( 1 ) 1 ( 1 ) 1 6 ( 1 ) 0 4 ( 1 ) 0 s i n , 1 - 2 0 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) - 1 0 ) 0 ( 1 ) c o s , 1 2 ( 1 ) 0 ( 1 ) - 1 0 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) T e [ 3 ] 0 3 0 ( 1 ) 7 ( 1 ) 9 ( 1 ) 0 2 ( 1 ) 0 s i n , 1 - 1 0 ) 0 ( 1 ) 1 ( 1 ) - 3 0 ) 0 ( 1 ) - 1 0 ) c o s , 1 - 9 ( 2 ) - 3 0 ) 4 ( 1 ) 0 ( 1 ) 3 ( 1 ) 0 ( 1 ) T e [ 4 ] 0 1 3 ( 1 ) 8 ( 1 ) 1 8 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 3 ( 1 ) 0 ( 1 ) 0 ( 1 ) 2 ( 1 ) 1 ( 1 ) 0 ( 1 ) c o s , 1 2 2 ( 2 ) - 1 0 ) - 3 0 ) 0 ( 1 ) 9 ( 1 ) 0 ( 1 ) A g [ l ] 0 6 ( 1 ) 1 1 ( 1 ) 1 1 ( 1 ) 0 - 6 ( 1 ) 0 s i n , 1 - 1 ( 2 ) - 5 0 ) - 1 0 ) 1 ( 1 ) 5 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 5 ( 1 ) - 1 0 ) 0 ( 1 ) A g [ 2 ] 0 1 1 ( 1 ) 9 ( 1 ) 2 6 ( 1 ) 0 7 ( 1 ) 0 s i n , 1 9 ( 2 ) - 5 0 ) - 5 ( 2 ) 0 ( 1 ) 6 ( 1 ) 0 ( 1 ) c o s , 1 - 1 0 ) 1 ( 1 ) 1 ( 1 ) - 3 0 ) - 1 0 ) 0 ( 1 ) N a [ l ] 0 1 3 ( 1 ) 1 5 ( 1 ) 1 4 ( 1 ) 0 6 ( 1 ) 0 s i n , 1 - 2 0 ) 0 ( 1 ) - 4 0 ) - 1 0 ) - 5 0 ) - 1 0 ) c o s , 1 - 2 0 ) 0 ( 1 ) - 3 0 ) 2 ( 1 ) 4 0 ) 1 ( 1 ) N a [ 2 ] 0 1 5 ( 1 ) 1 ( 1 ) 1 7 ( 1 ) 0 2 ( 1 ) 0 s i n , 1 - 5 0 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 0 ) - 1 0 ) c o s , 1 7 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 2 ( 1 ) - 1 0 ) 4 4 2 T a b l e 6 . 1 0 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N a 0 _ 3 . ( 2 ) A g 2 E u . , 1 9 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e E u [ l ] - T e [ l ] x 2 3 . 3 0 7 ( 4 ) 3 . 2 9 2 ( 4 ) 3 . 3 2 3 ( 4 ) E u [ l ] - T e [ 1 ] x 2 3 . 3 3 0 ( 4 ) 3 . 3 1 9 ( 4 ) 3 . 3 4 1 ( 4 ) E u [ l ] — T e [ 3 ] x 2 3 . 3 7 9 ( 6 ) 3 . 3 2 2 ( 7 ) 3 . 4 3 8 ( 7 ) E u [ l ] - T e [ 4 ] x 2 3 . 3 9 2 ( 5 ) 3 . 3 7 8 ( 5 ) 3 . 4 0 4 ( 5 ) E u [ 2 ] - T e [ 2 ] x 4 3 . 3 2 3 ( 4 ) 3 . 2 9 3 ( 4 ) 3 . 3 5 2 ( 4 ) E u [ 2 ] - T e [ 3 ] x 2 3 . 4 4 2 ( 5 ) 3 . 4 3 0 ( 5 ) 3 . 4 5 2 ( 5 ) E u [ 2 ] - T e [ 4 ] x 2 3 . 4 3 2 ( 6 ) 3 . 3 9 2 ( 6 ) 3 . 4 7 2 ( 6 ) T e [ l ] - A g [ l ] 2 . 9 3 4 ( 6 ) 2 . 8 5 9 ( 7 ) 3 . 0 1 1 ( 7 ) T e [ l ] - A g [ l ] 2 . 8 4 9 ( 6 ) 2 . 7 9 8 ( 7 ) 2 . 8 9 9 ( 7 ) T e [ l ] - A g [ 2 ] x 2 2 . 8 9 6 ( 5 ) 2 . 8 7 8 ( 5 ) 2 . 9 1 5 ( 5 ) T e [ l ] - N a [ l ] x 2 3 . 3 3 0 ( 4 ) 3 . 3 1 9 ( 4 ) 3 . 3 4 1 ( 4 ) T e [ l ] - N a [ l ] x 2 3 . 3 0 7 ( 4 ) 3 . 2 9 2 ( 4 ) 3 . 3 2 3 ( 4 ) T e [ 2 ] - A g [ l ] x 2 2 . 8 8 0 ( 4 ) 2 . 8 6 6 ( 4 ) 2 . 8 9 3 ( 4 ) T e [ 2 ] - A g [ 2 ] 2 . 8 9 9 ( 7 ) 2 . 7 9 4 ( 8 ) 3 . 0 0 2 ( 8 ) T e [ 2 ] - A g [ 2 ] 2 . 8 5 2 ( 7 ) 2 . 7 8 8 ( 8 ) 2 . 9 1 9 ( 8 ) T e [ 2 ] - N a [ 2 ] x 4 3 . 3 2 2 ( 4 ) 3 . 2 9 2 ( 3 ) 3 . 3 5 3 ( 4 ) T e [ 3 ] - T e [ 4 ] x 4 3 . 1 3 3 ( 5 ) 2 . 9 8 4 ( 5 ) 3 . 2 8 4 ( 5 ) T e [ 3 ] - N a [ l ] x 2 3 . 3 7 9 ( 6 ) 3 . 3 1 9 ( 7 ) 3 . 4 3 7 ( 7 ) T e [ 3 ] - N a [ 2 ] x 2 3 . 4 4 2 ( 5 ) 3 . 4 3 0 ( 5 ) 3 . 4 5 2 ( 5 ) T e [ 4 ] - N a [ l ] x 2 3 . 3 9 2 ( 5 ) 3 . 3 7 8 ( 5 ) 3 . 4 0 4 ( 5 ) T e [ 4 ] - N a [ 2 ] x 2 3 . 4 2 4 ( 5 ) 3 . 3 6 7 ( 6 ) 3 . 4 8 1 ( 6 ) A g [ l ] - A g [ 2 ] x 2 3 . 1 2 2 ( 5 ) 3 . 0 0 0 ( 6 ) 3 . 2 4 4 ( 6 ) A g [ l ] - A g [ 2 ] x 2 3 . 1 4 7 ( 5 ) 3 . 0 2 6 ( 6 ) 3 . 2 7 1 ( 6 ) T a b l e 6 . 1 1 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o , 3 1 ( 2 ) 1 ° 1 g 2 E u 1 , 1 9 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - E u [ l ] - T e [ l ] x 2 8 4 . 4 1 ( 1 0 ) 8 4 . 1 0 ( 1 0 ) 8 4 . 7 2 ( 1 1 ) T e [ l ] - E u [ l ] - T e [ l ] x 6 8 3 4 7 ( 9 ) 8 3 3 7 ( 9 ) 8 3 5 7 ( 9 ) T e [ 1 ] - E u [ l ] - T e [ 1 ] x 4 l 4 1 . 5 0 ( 1 3 ) 1 4 1 . 2 1 ( 1 3 ) l 4 1 . 8 0 ( 1 3 ) T e [ l ] - E u [ l ] - T e [ 3 ] x 4 7 9 4 5 ( 1 1 ) 7 8 . 5 4 ( 1 1 ) 8 0 3 6 ( 1 1 ) T e [ l ] - E u [ l ] - T e [ 3 ] x 4 1 3 3 . 1 2 ( 1 0 ) l 3 2 . 4 9 ( 1 0 ) 1 3 3 . 7 3 ( 9 ) 4 4 3 T a b l e 6 . 1 1 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o _ g l ( 2 ) A g 2 E u 1 _ 1 9 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ l ] - E u [ 1 ] - T e [ 4 ] x 4 T e [ 1 ] - E u [ 1 ] - T e [ 4 ] x 4 T e [ 3 ] - E u [ l ] - T e [ 3 ] x 2 T e [ 3 ] - E u [ l ] - T e [ 4 ] x 4 T e [ 4 ] - E u [ l ] - T e [ 4 ] x 2 T e [ 2 ] - E u [ 2 ] - T e [ 2 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 2 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 2 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 3 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 3 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 4 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 4 ] x 4 T e [ 2 ] - E u [ 2 ] - A g [ l ] x 2 T e [ 2 ] - E u [ 2 ] - A g [ l ] x 2 T e [ 3 ] - E u [ 2 ] - T e [ 3 ] x 2 T e [ 3 ] - E u [ 2 ] - T e [ 4 ] x 4 T e [ 3 ] - E u [ 2 ] - A g [ l ] x 2 T e [ 4 ] - E u [ 2 ] - T e [ 4 ] x 2 T e [ 4 ] - E u [ 2 ] - A g [ l ] T e [ 4 ] - E u [ 2 ] - A g [ l ] E u [ 1 ] - T e [ 1 ] - E u [ 1 ] x 6 E u [ 1 ] - T e [ 1 ] - E u [ l ] x 4 E u [ 1 ] - T e [ 1 ] - A g [ l ] x 2 E u [ 1 ] - T e [ l ] - A g [ 1 ] x 4 E u [ 1 ] - T e [ 1 ] - A g [ 2 ] x 2 E u [ 1 ] - T e [ 1 ] - A g [ 2 ] x 2 E u [ l ] — T e [ 1 ] - E u [ 1 ] x 2 E u [ 1 ] - T e [ 1 ] - A g [ l ] x 2 E u [ 1 ] - T e [ 1 ] - A g [ 2 ] x 2 E u [ l ] - T e [ 1 ] - A g [ 2 ] x 2 A g [ l ] - T e [ 1 ] - A g [ l ] x 2 A g [ 1 ] - T e [ l ] - A g [ 2 ] x 4 A g [ 2 ] - T e [ l ] - A g [ 2 ] x 2 E u [ 2 ] - T e [ 2 ] - E u [ 2 ] x 4 7 9 0 6 ( 9 ) 1 3 3 . 6 6 ( 1 4 ) 8 1 . 6 6 0 2 ) 5 5 1 9 ( 9 ) 8 1 8 8 ( 1 1 ) 8 3 9 3 ( 9 ) 8 3 3 5 ( 9 ) 1 4 1 . 1 3 0 3 ) 7 9 6 2 ( 9 ) 1 3 3 . 1 4 0 2 ) 7 9 . 9 2 0 0 ) 1 3 3 . 0 4 0 0 ) 9 7 . 2 6 0 2 ) 4 8 5 5 ( 8 ) 8 0 . 4 5 0 0 ) 5 4 . 1 9 0 0 ) 1 2 8 . 0 9 0 1 ) 8 0 2 4 ( 1 2 ) l 7 6 . 1 5 ( 1 5 ) 1 0 3 . 5 9 0 4 ) 8 3 . 7 0 ( 1 1 ) 1 4 1 . 5 0 0 4 ) 7 2 1 1 ( 1 3 ) 1 3 6 . 0 8 ( 8 ) 7 1 . 9 1 0 4 ) 1 3 5 . 5 ( 2 ) 8 4 . 4 1 ( 1 1 ) 7 3 . 4 8 ( 1 3 ) 7 2 . 8 8 ( 1 4 ) 1 3 7 . 4 ( 2 ) 9 9 6 3 ( 1 9 ) 6 5 3 1 ( 1 6 ) 1 0 0 . 2 5 ( 1 8 ) 8 3 . 9 5 ( 1 0 ) 7 7 . 5 9 0 0 ) 1 3 1 . 3 4 0 3 ) 8 1 . 6 2 0 4 ) 5 2 8 8 ( 9 ) 8 1 . 6 6 0 1 ) 8 3 0 8 ( 9 ) 8 3 3 1 ( 9 ) 1 4 1 . 0 0 0 2 ) 7 8 1 5 ( 9 ) 1 3 0 3 7 0 1 ) 7 9 4 6 ( 1 0 ) 1 3 2 . 5 1 0 0 ) 9 6 . 4 9 ( 1 2 ) 4 8 4 2 ( 8 ) 7 9 . 9 4 0 0 ) 5 1 . 7 2 0 0 ) 1 2 6 . 2 1 0 2 ) 7 9 . 9 9 0 3 ) 1 7 4 . 6 0 0 6 ) 1 0 2 . 3 0 0 5 ) 8 3 . 5 1 ( 1 1 ) 1 4 1 . 2 8 0 5 ) 7 1 . 4 2 0 2 ) 1 3 5 . 5 7 ( 9 ) 7 0 . 2 2 0 4 ) 1 3 3 . 4 ( 2 ) 8 4 . 3 4 0 1 ) 7 2 . 6 4 0 3 ) 7 1 . 5 8 0 4 ) 1 3 5 . 1 ( 2 ) 9 9 0 ( 2 ) 6 3 5 9 ( 1 6 ) 9 9 . 9 4 0 8 ) 8 3 . 7 1 0 0 ) 8 0 5 6 ( 9 ) l 3 6 . 0 1 ( 1 3 ) 8 1 . 6 8 0 1 ) 5 7 5 6 ( 9 ) 8 2 . 0 1 ( 1 1 ) 8 4 7 9 ( 9 ) 8 3 4 0 ( 9 ) 1 4 1 . 2 6 0 2 ) 8 1 . 1 2 ( 9 ) 1 3 5 . 9 1 0 1 ) 8 0 . 3 8 0 0 ) 1 3 3 . 5 7 0 0 ) 9 8 . 0 1 0 2 ) 4 8 6 7 ( 8 ) 8 0 . 8 6 0 0 ) 5 6 7 5 ( 1 1 ) 1 2 9 . 9 1 0 2 ) 8 0 . 4 8 0 3 ) 1 7 7 . 7 1 0 6 ) 1 0 4 . 9 2 0 5 ) 8 3 . 8 8 0 1 ) 1 4 1 . 7 2 0 5 ) 7 2 7 9 ( 1 3 ) 1 3 6 . 5 6 ( 8 ) 7 3 . 6 3 ( 1 4 ) 1 3 7 . 7 ( 2 ) 8 4 . 4 8 ( 1 1 ) 7 4 . 3 5 0 3 ) 7 4 . 1 6 0 4 ) 1 3 9 . 7 ( 2 ) 1 0 0 . 2 ( 2 ) 6 7 . 0 8 0 6 ) 1 0 0 . 4 7 0 8 ) 8 4 . 1 7 0 1 ) T a b l e 6 . 1 1 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o , 3 1 ( 2 ) A g 2 E u 1 , 1 9 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . E u [ 2 ] - T e [ 2 ] - E u [ 2 ] x 4 E u [ 2 ] - T e [ 2 ] - E u [ 2 ] x 4 E u [ 2 ] - T e [ 2 ] - A g [ l ] x 2 E u [ 2 ] - T e [ 2 ] - A g [ l ] x 2 E u [ 2 ] - T e [ 2 ] - A g [ 2 ] x 4 E u [ 2 ] - T e [ 2 ] - A g [ 2 ] x 4 E u [ 2 ] - T e [ 2 ] - A g [ l ] x 2 E u [ 2 ] - T e [ 2 ] - A g [ l ] x 2 A g [ 1 ] - T e [ 2 ] - A g [ 1 ] x 2 A g [ l ] - T e [ 2 ] - A g [ 2 ] x 2 A g [ l ] - T e [ 2 ] - A g [ 2 ] x 2 A g [ 2 ] - T e [ 2 ] - A g [ 2 ] x 2 E u [ 1 ] - T e [ 3 ] - E u [ 1 ] x 2 E u [ l ] - T e [ 3 ] - E u [ 2 ] x 4 E u [ l ] - T e [ 3 ] - T e [ 4 ] x 4 E u [ l ] - T e [ 3 ] - T e [ 4 ] x 4 E u [ 2 ] - T e [ 3 ] - E u [ 2 ] x 2 E u [ 2 ] - T e [ 3 ] - T e [ 4 ] x 4 E u [ 2 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 E u [ 1 ] - T e [ 4 ] - E u [ l ] x 2 E u [ l ] - T e [ 4 ] - E u [ 2 ] x 4 E u [ l ] - T e [ 4 ] - T e [ 3 ] x 4 E u [ l ] - T e [ 4 ] - T e [ 3 ] x 4 E u [ 2 ] - T e [ 4 ] - E u [ 2 ] x 2 E u [ 2 ] - T e [ 4 ] - T e [ 3 ] x 4 E u [ 2 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] — T e [ 3 ] x 4 T e [ 1 ] - A g [ l ] - T e [ 1 ] x 2 T e [ l ] - A g [ 1 ] - T e [ 2 ] x 2 8 3 3 5 ( 7 ) 1 4 1 . 1 4 0 4 ) 7 1 . 5 9 0 3 ) 1 3 5 . 7 7 0 9 ) 7 2 3 9 ( 1 3 ) 1 3 6 . 2 5 ( 8 ) 7 2 9 3 ( 1 3 ) 1 3 7 . 6 1 0 9 ) 1 0 1 . 0 3 0 7 ) 6 5 4 0 ( 1 4 ) 6 6 5 8 ( 1 4 ) 1 0 0 . 4 ( 2 ) 8 1 . 6 6 0 4 ) 1 2 5 . 3 9 0 2 ) 6 2 . 6 8 0 2 ) 1 1 7 4 9 ( 1 4 ) 8 0 . 4 2 ( 1 2 ) 6 2 . 7 1 0 1 ) 1 1 7 . 2 8 0 7 ) 9 0 . 5 1 0 5 ) 8 9 5 5 ( 9 ) 1 7 6 . 9 5 0 6 ) 8 1 . 8 3 ( 1 3 ) 1 2 5 . 2 9 0 2 ) 6 2 . 1 7 0 1 ) 1 1 7 . 5 2 0 7 ) 8 0 2 5 ( 1 3 ) 6 3 . 1 3 ( 1 2 ) 1 1 6 . 9 9 ( 1 5 ) 9 0 . 3 7 0 4 ) 8 9 5 5 ( 1 0 ) 1 7 6 . 8 6 0 6 ) 9 9 . 6 3 0 9 ) 1 1 5 3 7 ( 1 5 ) 8 3 3 1 ( 7 ) 1 4 0 . 7 9 0 4 ) 7 0 . 2 6 ( 1 3 ) 1 3 4 . 3 9 0 9 ) 7 1 . 7 6 0 3 ) 1 3 5 5 1 ( 9 ) 7 1 . 9 8 0 3 ) 1 3 6 . 1 2 0 9 ) 1 0 0 . 9 6 0 6 ) 6 3 . 8 2 ( 1 5 ) 6 4 . 1 8 0 6 ) 9 9 4 ( 2 ) 8 1 . 6 2 0 5 ) 1 2 2 . 6 3 0 3 ) 6 0 . 5 9 0 2 ) 1 1 6 . 3 9 ( 1 4 ) 8 0 . 1 1 0 3 ) 6 2 . 0 4 ( 1 0 ) 1 1 4 . 3 1 0 9 ) 8 5 . 6 6 0 6 ) 8 9 . 0 8 0 0 ) 1 7 5 . 1 6 0 8 ) 8 1 . 6 8 0 4 ) 1 2 2 . 8 3 0 3 ) 6 1 . 6 5 0 1 ) 1 1 4 . 3 5 0 9 ) 7 9 . 9 9 0 4 ) 6 1 . 1 6 0 2 ) 1 1 5 . 8 4 ( 1 4 ) 8 5 . 2 3 ( l 6 ) 8 9 0 8 ( 9 ) 1 7 4 . 9 5 0 7 ) 9 9 . 0 ( 2 ) 1 1 3 . 3 0 ( 1 8 ) 8 3 4 0 ( 7 ) 1 4 1 . 4 9 0 4 ) 7 2 9 1 ( 1 3 ) 1 3 7 . 1 2 0 9 ) 7 3 . 0 4 0 3 ) 1 3 7 . 0 2 ( 8 ) 7 3 8 8 ( 1 3 ) 1 3 9 . 1 3 0 9 ) 1 0 1 . 0 7 0 7 ) 6 6 9 7 ( 1 6 ) 6 9 . 0 5 0 6 ) 1 0 1 . 3 ( 2 ) 8 1 . 6 8 0 3 ) 1 2 8 . 1 7 0 3 ) 6 4 . 8 8 0 3 ) 1 1 8 . 5 5 0 4 ) 8 0 . 6 4 0 3 ) 6 3 . 2 9 0 1 ) 1 2 0 . 2 ( 2 ) 9 5 5 9 ( 1 9 ) 9 0 2 7 ( 9 ) 1 7 9 8 0 0 9 ) 8 1 . 9 1 0 2 ) 1 2 7 . 6 9 0 3 ) 6 2 . 6 4 ( 1 1 ) 1 2 0 . 6 ( 2 ) 8 0 . 4 8 ( 1 4 ) 6 5 . 1 4 0 3 ) 1 1 8 . 0 3 0 4 ) 9 5 . 6 1 0 8 ) 9 0 . 2 7 0 0 ) 1 7 9 . 8 ( 2 ) 1 0 0 . 2 ( 2 ) 1 1 7 4 5 ( 1 7 ) 4 4 5 T a b l e 6 . 1 1 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o _ 8 1 ( 2 ) A g 2 E u L 1 9 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 1 ] - A g [ 1 ] - A g [ 2 ] x 2 T e [ 1 ] - A g [ l ] - A g [ 2 ] x 4 T e [ l ] — A g [ 1 ] - T e [ 2 ] x 2 T e [ 1 ] - A g [ 1 ] - A g [ 2 ] x 2 T e [ 2 ] - A g [ l ] - T e [ 2 ] x 2 T e [ 2 ] - A g [ l ] - A g [ 2 ] x 2 T e [ 2 ] - A g [ l ] - A g [ 2 ] x 2 T e [ 2 ] - A g [ l ] - A g [ 2 ] x 2 T e [ 2 ] - A g [ l ] - A g [ 2 ] x 2 A 8 1 2 ] - A 8 1 1 ] - A g [ 2 ] x 4 A g [ 2 ] - A 8 1 1 ] - A g [ 2 ] X 4 A g [ 2 ] - A g [ l l - A g [ 2 ] X 4 T e [ 1 ] - A g [ 2 ] - T e [ 1 ] x 2 T e [ l ] - A g [ 2 ] - T e [ 2 ] x 2 T e [ l ] - A g [ 2 ] - T e [ 2 ] x 2 T e [ 1 ] - A g [ 2 ] - A g [ l ] x 2 T e [ 1 ] - A g [ 2 ] - A g [ 1 ] x 4 T e [ 1 ] - A g [ 2 ] - A g [ 1 ] x 2 T e [ 2 ] - A g [ 2 ] - T e [ 2 ] x 2 T e [ 2 ] - A g [ 2 ] - A g [ l ] x 4 T e [ 2 ] - A g [ 2 ] - A g [ l ] x 4 A 8 1 1 ] - A g [ 2 ] - A g [ l l X 8 A 8 1 1 ] - A g [ 2 1 - A 8 1 1 ] x 4 5 7 . 8 3 ( 1 5 ) 1 2 2 . 1 5 0 7 ) 1 1 3 0 2 ( 1 5 ) 5 6 . 7 8 0 4 ) 1 0 0 . 9 8 0 8 ) 5 7 . 5 7 0 4 ) 1 2 4 . 3 ( 2 ) 5 6 . 2 6 ( 1 4 ) 1 2 2 . 3 ( 2 ) 9 0 . 8 7 0 7 ) 8 9 5 8 ( 1 3 ) 1 7 7 . 4 1 0 9 ) 1 0 0 . 2 1 0 9 ) 1 1 5 . 0 6 ( 1 6 ) 1 1 3 . 3 5 ( 1 6 ) 5 7 . 9 1 0 4 ) 1 2 3 . 6 ( 2 ) 5 6 3 3 ( 1 4 ) 1 0 0 . 4 ( 2 ) 5 7 . 1 6 0 4 ) 1 2 2 . 2 4 ( 1 8 ) 8 9 9 7 ( 1 7 ) 1 7 7 . 3 9 0 9 ) 5 5 . 5 8 ( 1 4 ) 1 2 0 . 8 2 0 7 ) 1 1 0 . 8 5 0 8 ) 5 5 1 1 ( 1 5 ) 1 0 0 . 5 ( 2 ) 5 6 5 5 ( 1 5 ) 1 2 1 . 2 ( 2 ) 5 5 4 1 ( 1 4 ) 1 1 9 . 4 ( 2 ) 8 6 . 7 3 0 9 ) 8 9 2 0 ( 1 2 ) 1 7 5 . 5 ( 2 ) 9 9 3 ( 2 ) 1 1 2 . 5 0 ( 1 8 ) 1 1 0 8 6 ( 1 9 ) 5 7 . 3 0 0 3 ) 1 2 0 . 0 ( 3 ) 5 5 6 6 ( 1 4 ) 9 9 . 4 ( 2 ) 5 4 . 8 9 ( 1 4 ) 1 2 1 . 0 9 0 8 ) 8 5 . 9 ( 2 ) 1 7 5 . 6 ( 2 ) 6 0 . 1 8 0 6 ) 1 2 3 . 5 3 0 7 ) 1 1 5 1 8 ( 1 7 ) 5 8 . 4 6 ( 1 6 ) 1 0 1 . 4 ( 2 ) 5 8 . 6 1 0 4 ) 1 2 7 . 4 ( 3 ) 5 7 . 1 7 0 4 ) 1 2 5 . 3 ( 2 ) 9 5 2 ( 2 ) 9 0 . 1 4 0 2 ) 1 7 9 . 7 ( 2 ) 1 0 1 . 0 ( 2 ) 1 1 7 . 5 4 0 8 ) 1 1 5 8 7 ( 1 9 ) 5 8 . 5 7 ( 1 3 ) 1 2 7 . 2 ( 3 ) 5 7 . 0 4 0 4 ) 1 0 1 . 3 ( 2 ) 5 9 4 3 ( 1 5 ) 1 2 3 . 5 3 0 7 ) 9 4 . 1 ( 2 ) 1 7 9 . 7 ( 2 ) 4 4 6 T a b l e 6 . 1 2 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r N a o , 3 1 ( 2 ) A g 2 E u 1 . 1 9 ( 2 ) T e 4 a t 3 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 0 2 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ' ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m a n d T m c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e N 3 0 . 8 1 ( 2 ) A n g u 1 . 1 9 ( 2 ) T € 4 9 2 6 . 9 3 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A M o n o c l i n i c P m ( 0 [ 3 1 / 2 ) 0 a = 4 . 4 3 7 6 ( 5 ) A , a = 9 0 ° b = 4 . 4 5 9 9 ( 7 ) A , B = 9 0 ° c = 1 1 . 1 2 5 8 ( 1 4 ) A , y = 9 0 ° 0 . 3 1 1 8 ( 5 ) b ‘ + 1 / 2 c " 2 2 0 . 1 9 ( 5 ) A 3 1 6 . 9 8 7 6 g / c m 3 2 5 . 6 6 6 m m " 3 8 6 0 . 1 6 x 0 . 0 9 x 0 . 0 1 m m 3 1 . 6 9 t o 2 9 0 2 ° - 5 < = h < = 5 , - 6 < = k < = 6 , - 1 5 < = l < = 1 5 , - 1 < = m < = l 5 5 5 9 ( 1 7 5 4 m a i n + 3 8 0 5 s a t e l l i t e s ) 3 1 8 7 ( 1 0 7 3 m a i n + 2 1 1 4 s a t e l l i t e S ) [ R i m = 0 . 0 3 2 8 ] 9 5 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 3 1 8 7 / 2 6 / 1 2 1 1 . 3 2 R o b s = 0 . 0 3 4 2 , w R o b s = 0 . 0 8 0 1 R , “ = 0 . 0 6 0 9 , w R , “ = 0 . 1 0 0 0 R o b s = 0 . 0 2 2 4 , w R o b s = 0 . 0 6 5 1 R , “ = 0 . 0 2 5 1 , w R a u = 0 . 0 6 8 2 R o b s = 0 . 0 8 2 9 , w R o b s = 0 . 1 2 4 0 R a n = 0 . 1 8 0 7 , w R a n = 0 . 1 7 7 9 0 . 0 0 0 1 0 ( 7 ) 0 . 0 8 9 7 a n d 0 . 8 0 6 2 1 . 6 5 a n d - 1 . 6 7 e . A ' 3 R = E I I F o l - I F c l l / 2 1 F . I , w R = { E [ W ( | F o | 2 - 1 1 3 1 2 ) ? / 2 1 0 1 1 1 0 1 0 1 1 “ a n d w = 1 / ( o z a ) + 0 . 0 0 1 6 1 2 ) 4 4 7 T a b l e 6 . 1 3 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) , o c c u p a n c i e s a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r N a o , 3 1 ( 2 ) A g 2 E u 1 , 1 9 ( 2 ) T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x y 2 O c c u p a n c y U e q E u [ l ] 0 0 0 2 7 4 9 0 . 5 8 5 4 2 1 ( 1 ) s i n , 1 6 1 ( 7 ) - 7 ( 2 ) 6 ( 2 ) c o s , 1 5 4 ( 7 ) 8 ( 3 ) 6 ( 2 ) E u [ 2 ] 0 5 0 0 0 ( 2 ) 5 0 0 0 8 0 1 7 ( 1 ) 0 . 6 0 5 ( 1 4 ) 1 5 ( 1 ) s i n , 1 5 9 ( 3 ) 8 ( 3 ) - 1 ( 1 ) c o s , 1 - 8 2 ( 4 ) 5 ( 2 ) 1 ( 2 ) T e [ l ] 0 4 9 9 5 ( 6 ) 5 0 0 0 3 6 9 0 ( 2 ) 1 1 4 ( 1 ) s i n , 1 3 7 ( 3 ) - 1 ( 1 ) 1 ( 1 ) c o s , 1 1 6 ( 1 ) 1 ( 2 ) 0 ( 1 ) T e [ 2 ] 0 - 4 ( 6 ) 0 7 0 1 8 ( 2 ) 1 1 5 ( 1 ) s i n , 1 2 2 ( 3 ) 1 ( 2 ) 1 ( 1 ) c o s , 1 - 1 6 ( 2 ) 1 ( 2 ) 0 ( 1 ) T e [ 3 ] 0 4 9 8 2 ( 6 ) 0 3 4 0 ( 3 ) 1 1 8 ( 1 ) s i n , 1 3 1 ( 1 ) - 4 1 ( 4 ) - 2 ( 1 ) c o s , 1 2 9 3 ( 7 ) 4 ( 1 ) - 1 5 ( 2 ) T e [ 4 ] 0 9 9 8 2 ( 6 ) 5 0 0 0 3 3 1 ( 3 ) 1 1 6 ( 1 ) s i n , 1 - 3 6 ( 1 ) 3 8 ( 4 ) - 2 ( 1 ) c o s , 1 - 3 4 9 ( 7 ) - 4 ( 1 ) - 1 5 ( 2 ) A g [ l ] 0 9 9 5 9 ( 6 ) 5 0 0 0 5 3 2 5 ( 3 ) 1 2 2 ( 1 ) s i n , 1 1 8 0 ( 1 4 ) 0 ( 1 ) - 1 1 ( 3 ) c o s , 1 - 1 8 ( 2 ) 3 ( 5 ) 1 ( 1 ) A g [ 2 ] 0 4 9 5 5 ( 6 ) 0 5 3 1 0 ( 3 ) 1 2 7 ( 1 ) s i n , 1 - 8 8 ( 1 7 ) - 2 ( 1 ) - 1 1 ( 3 ) c o s , 1 9 ( 2 ) - 2 5 ( 5 ) 1 ( 1 ) N a [ l ] 0 0 0 2 7 4 9 0 . 4 1 4 6 2 1 ( 1 ) s i n , 1 6 1 ( 7 ) - 7 ( 2 ) 6 ( 2 ) c o s , 1 5 4 ( 7 ) 8 ( 3 ) 6 ( 2 ) N a [ 2 ] 0 5 0 0 0 5 0 0 0 8 0 1 7 0 . 3 9 5 ( 1 4 ) 1 5 ( 1 ) s i n , 1 5 9 ( 3 ) 8 ( 3 ) - 1 ( 1 ) c o s , 1 - 8 2 ( 4 ) 5 ( 2 ) 1 ( 2 ) 4 4 8 T a b l e 6 . 1 4 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r N a o , 3 1 ( 2 ) A g 2 E u 1 _ 1 9 ( 2 ) T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 E u [ l ] 0 2 4 ( 1 ) 2 6 ( 1 ) 1 4 ( 1 ) 0 - 2 0 ) 0 s i n , 1 5 ( 1 ) - 2 0 ) 1 ( 1 ) 4 0 ) - 3 ( 1 ) 2 ( 1 ) c o s , 1 4 ( 1 ) - 2 0 ) 1 ( 1 ) 5 ( 1 ) - 3 0 ) - 3 0 ) E u [ 2 ] 0 1 1 ( 1 ) 8 ( 1 ) 2 4 ( 1 ) 0 1 ( 1 ) 0 s i n , 1 5 ( 1 ) 0 ( 1 ) - 1 0 ) - 1 0 ) - 1 0 ) 2 ( 1 ) c o s , 1 - 6 ( 1 ) 1 ( 1 ) 1 ( 1 ) - 1 0 ) 1 ( 1 ) , 1 ( 1 ) T e [ l ] 0 1 5 ( 1 ) 1 6 ( 1 ) 1 1 ( 1 ) 0 1 ( 1 ) 0 s i n , 1 2 ( 1 ) - 1 0 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) c o s , 1 1 ( 1 ) - 1 0 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) T e [ 2 ] 0 1 1 ( 1 ) 9 ( 1 ) 2 5 ( 1 ) 0 - 1 0 ) 0 s i n , 1 - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 0 ) 0 ( 1 ) c o s , 1 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) T e [ 3 ] 0 1 9 ( 1 ) 1 7 ( 1 ) 1 8 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 4 0 ) 0 ( 1 ) 1 ( 1 ) c o s , 1 2 ( 2 ) 2 ( 1 ) 4 0 ) 0 ( 1 ) - 1 0 ) 0 ( 1 ) T e [ 4 ] 0 2 1 ( 1 ) 1 3 ( 1 ) 1 4 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 5 ( 1 ) 0 ( 1 ) - 1 0 ) c o s , 1 - 3 0 ) 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) A g [ l ] 0 1 9 ( 1 ) 2 8 ( 1 ) 2 0 ( 1 ) 0 - 1 0 ) 0 s i n , 1 1 ( 1 ) - 1 0 ) - 2 0 ) 1 ( 1 ) 4 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 7 ( 1 ) 0 ( 1 ) 1 ( 1 ) A g [ 2 ] 0 3 1 ( 1 ) 2 4 ( 1 ) 2 6 ( 1 ) 0 2 ( 1 ) 0 s i n , 1 - 2 ( 2 ) 1 ( 1 ) 0 ( 1 ) - 1 0 ) 3 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 8 ( 1 ) 0 ( 1 ) . 4 0 ) N a [ l ] 0 2 4 ( 1 ) 2 6 ( 1 ) 1 4 ( 1 ) 0 - 2 0 ) 0 s i n , 1 5 ( 1 ) - 2 0 ) 1 ( 1 ) 4 0 ) - 3 0 ) 2 ( 1 ) c o s , 1 4 ( 1 ) - 2 ( 1 ) 1 ( 1 ) 5 ( 1 ) - 3 ( 1 ) - 3 ( 1 ) N a [ 2 ] 0 1 1 ( 1 ) 8 ( 1 ) 2 4 ( 1 ) 0 1 ( 1 ) 0 s i n , 1 5 ( 1 ) 0 ( 1 ) - 1 0 ) - 1 0 ) - 1 0 ) 2 ( 1 ) c o s , 1 - 6 ( 1 ) 1 ( 1 ) 1 ( 1 ) - 1 0 ) 1 ( 1 ) 1 ( 1 ) 4 4 9 T a b l e 6 . 1 5 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r N a 0 , 3 1 ( 2 ) A g 2 E u 1 , 1 9 ( 2 ) T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e E u [ l ] - T e [ l ] x 4 3 . 3 3 5 ( 3 ) 3 . 3 1 6 ( 3 ) 3 . 3 5 4 ( 3 ) E u [ l ] - T e [ 3 ] 3 . 4 4 3 ( 4 ) 3 . 4 0 3 ( 4 ) 3 . 4 8 5 ( 4 ) E u [ l ] - T e [ 3 ] 3 . 4 3 3 ( 4 ) 3 . 3 5 2 ( 4 ) 3 . 5 1 4 ( 4 ) E u [ l ] - T e [ 4 ] x 2 3 . 4 5 5 ( 3 ) 3 . 4 3 1 ( 3 ) 3 . 4 7 9 ( 3 ) E u [ 2 ] - T e [ 2 ] x 4 3 . 3 3 8 ( 3 ) 3 . 3 1 1 ( 3 ) 3 . 3 6 4 ( 3 ) ' E u [ 2 ] - T e [ 3 ] x 2 3 . 4 1 6 ( 3 ) 3 . 3 9 7 ( 3 ) 3 . 4 3 5 ( 3 ) E u [ 2 ] - T e [ 4 ] 3 . 4 0 4 ( 4 ) 3 . 3 4 7 ( 4 ) 3 . 4 6 4 ( 4 ) E u [ 2 ] - T e [ 4 ] 3 . 3 9 5 ( 4 ) 3 . 3 0 8 ( 4 ) 3 . 4 8 1 ( 4 ) T e [ l ] - A g [ l ] 2 . 8 8 1 ( 5 ) 2 . 8 2 5 ( 7 ) 2 . 9 3 8 ( 7 ) T e [ l ] - A g [ l ] 2 . 8 5 7 ( 5 ) 2 . 8 1 7 ( 7 ) 2 . 8 9 7 ( 7 ) T e [ l ] - A g [ 2 ] x 2 2 . 8 6 7 ( 3 ) 2 . 8 5 5 ( 3 ) 2 . 8 7 9 ( 3 ) T e [ l ] - N a [ l ] x 4 3 . 3 3 2 ( 3 ) 3 . 3 1 0 ( 3 ) 3 . 3 5 4 ( 3 ) T e [ 2 ] - A g [ l ] x 2 2 . 9 2 0 ( 3 ) 2 . 9 1 3 ( 4 ) 2 . 9 2 7 ( 4 ) T e [ 2 ] - A g [ 2 ] 2 . 9 3 6 ( 6 ) 2 . 8 8 8 ( 7 ) 2 . 9 8 2 ( 7 ) T e [ 2 ] - A g [ 2 ] 2 . 9 0 7 ( 6 ) 2 . 8 7 8 ( 7 ) 2 . 9 3 8 ( 7 ) T e [ 2 ] - N a [ 2 ] x 4 3 . 3 3 5 ( 3 ) 3 . 3 0 9 ( 3 ) 3 . 3 6 2 ( 3 ) T e [ 3 ] - T e [ 4 ] x 4 3 . 1 5 0 ( 3 ) 2 . 9 7 3 ( 3 ) 3 . 3 2 9 ( 4 ) T e [ 3 ] - N a [ l ] 3 . 4 3 3 ( 4 ) 3 . 3 5 2 ( 4 ) 3 . 5 1 4 ( 4 ) T e [ 3 ] — N a [ l ] 3 . 4 4 3 ( 4 ) 3 . 4 0 3 ( 4 ) 3 . 4 8 5 ( 4 ) T e [ 3 ] - N a [ 2 ] x 2 3 . 4 1 6 ( 3 ) 3 . 3 9 7 ( 3 ) 3 . 4 3 5 ( 3 ) T e [ 4 ] - N a [ l ] x 2 3 . 4 5 5 ( 3 ) 3 . 4 3 1 ( 3 ) 3 . 4 7 9 ( 3 ) T e [ 4 ] - N a [ 2 ] 3 . 3 9 4 ( 4 ) 3 . 3 0 8 ( 4 ) 3 . 4 8 1 ( 4 ) T e [ 4 ] - N a [ 2 ] 3 . 4 0 5 ( 4 ) 3 . 3 4 7 ( 4 ) 3 . 4 6 4 ( 4 ) A g [ l ] - A g [ 2 ] x 4 3 . 1 4 8 ( 5 ) 3 . 0 6 7 ( 6 ) 3 . 2 2 8 ( 6 ) T a b l e 6 . 1 6 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a 0 , 3 1 ( 2 y 4 g 2 E u . _ 1 9 ( 2 ) T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ l ] - E u [ l ] - T e [ l ] x 4 8 3 9 4 ( 8 ) 8 3 . 4 7 ( 8 ) 8 4 . 4 1 ( 8 ) T e [ l ] - E u [ l ] - T e [ l ] x 4 8 3 . 4 7 ( 6 ) 8 3 3 4 ( 6 ) 8 3 . 6 0 ( 6 ) T e [ l ] - E u [ l ] - T e [ l ] x 4 1 4 1 . 4 0 ( 8 ) 1 4 1 . 0 9 ( 8 ) 1 4 1 . 7 0 ( 8 ) T e [ l ] - E u [ l ] - T e [ 3 ] x 4 7 9 7 1 ( 8 ) 7 9 0 0 ( 8 ) 8 0 4 3 ( 8 ) 4 5 0 T a b l e 6 . 1 6 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o , 3 1 ( 2 ) A g 2 E u 1 , . 9 ( 2 ) T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 1 ] - E u [ 1 ] - T e [ 3 ] x 4 T e [ 1 ] - E u [ 1 ] — T e [ 4 ] x 4 T e [ l ] - E u [ 1 ] - T e [ 4 ] x 4 T e [ 3 ] - E u [ l ] - T e [ 3 ] x 2 T e [ 3 ] - E u [ l ] - T e [ 4 ] x 4 T e [ 4 ] - E u [ l ] - T e [ 4 ] x 2 T e [ 2 ] - E u [ 2 ] - T e [ 2 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 2 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 2 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 3 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 3 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 4 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 4 ] x 4 T e [ 3 ] - E u [ 2 ] - T e [ 3 ] x 2 T e [ 3 ] - E u [ 2 ] - T e [ 4 ] x 4 T e [ 4 ] - E u [ 2 ] - T e [ 4 ] x 2 E u [ l ] - T e [ 1 ] - E u [ l ] x 4 E u [ 1 ] - T e [ l ] - E u [ 1 ] x 4 E u [ 1 ] - T e [ l ] - E u [ 1 ] x 4 E u [ l ] - T e [ 1 ] - A g [ 1 ] x 4 E u [ 1 ] - T e [ 1 ] - A g [ 1 ] x 4 E u [ l ] - T e [ 1 ] - A g [ 2 ] x 4 E u [ 1 ] - T e [ l ] - A g [ 2 ] x 4 E u [ 1 ] - T e [ l ] - N a [ 1 ] x 4 A g [ 1 ] - T e [ l ] - A g [ 1 ] x 2 A g [ l ] - T e [ 1 ] - A g [ 2 ] x 4 A g [ 2 ] - T e [ l ] - A g [ 2 ] x 2 E u [ 2 ] - T e [ 2 ] - E u [ 2 ] x 4 E u [ 2 ] - T e [ 2 ] - E u [ 2 ] x 4 E u [ 2 ] - T e [ 2 ] - E u [ 2 ] x 4 E u [ 2 ] - T e [ 2 ] - A g [ l ] x 4 E u [ 2 ] - T e [ 2 ] - A g [ l ] x 4 E u [ 2 ] - T e [ 2 ] - A g [ 2 ] x 4 E u [ 2 ] - T e [ 2 ] - A g [ 2 ] x 4 1 3 2 . 9 8 ( 6 ) 7 9 5 5 ( 7 ) 1 3 3 . 0 3 0 0 ) 8 0 3 7 ( 8 ) 5 4 2 9 ( 6 ) 8 0 4 8 ( 7 ) 8 3 8 5 ( 6 ) 8 3 3 7 ( 6 ) 1 4 1 . 0 7 ( 8 ) 7 9 2 8 ( 6 ) 1 3 3 . 4 1 ( 9 ) 7 9 4 6 ( 7 ) 1 3 3 . 3 2 ( 7 ) 8 1 5 8 ( 7 ) 5 4 9 5 ( 7 ) 8 1 4 8 ( 8 ) 8 4 0 3 ( 8 ) 8 3 4 7 ( 7 ) 1 4 1 . 4 0 ( 9 ) 7 2 1 1 ( 1 0 ) 1 3 6 . 3 4 ( 6 ) 7 1 . 5 2 0 3 ) 1 3 6 . 4 1 ( 1 8 ) 8 4 0 3 ( 8 ) 1 0 1 . 3 1 0 6 ) 6 6 3 2 ( 1 6 ) 1 0 2 . 1 1 0 3 ) 8 3 9 2 ( 7 ) 8 3 3 7 ( 5 ) 1 4 1 . 0 8 ( 9 ) 7 2 . 5 8 ( 1 1 ) l 3 6 . 2 3 ( 1 6 ) 7 3 0 9 ( 1 1 ) 1 3 6 . 1 3 ( 6 ) 1 3 2 . 5 3 ( 6 ) 7 7 7 0 ( 7 ) 1 2 9 8 6 ( 1 0 ) 7 9 8 0 ( 9 ) 5 1 0 6 ( 6 ) 8 0 3 6 ( 6 ) 8 3 0 8 ( 6 ) 8 3 2 8 ( 6 ) 1 4 0 . 9 7 ( 8 ) 7 7 . 6 4 ( 6 ) 1 3 0 . 4 8 ( 8 ) 7 8 6 7 ( 7 ) l 3 2 . 6 4 ( 7 ) 8 1 3 8 ( 7 ) 5 1 9 0 ( 7 ) 8 1 0 5 ( 9 ) 8 4 0 2 ( 8 ) 8 3 3 4 ( 7 ) 1 4 1 . 1 3 ( 9 ) 7 1 . 6 8 ( 1 0 ) 1 3 5 . 9 4 ( 6 ) 7 0 4 7 ( 1 3 ) 1 3 5 . 2 1 0 8 ) 8 4 0 2 ( 8 ) 1 0 0 . 8 9 0 8 ) 6 5 3 3 ( 1 6 ) 1 0 1 . 6 4 ( 1 3 ) 8 3 7 2 ( 7 ) 8 3 2 8 ( 5 ) 1 4 0 . 7 8 ( 9 ) 7 1 . 5 9 0 2 ) 1 3 5 . 1 7 ( 1 6 ) 7 2 5 2 ( 1 1 ) 1 3 5 . 8 3 ( 6 ) 1 3 3 . 4 1 ( 6 ) 8 1 4 3 ( 7 ) 1 3 6 . 2 5 ( 1 0 ) 8 0 9 3 ( 9 ) 5 7 6 2 ( 6 ) 8 0 5 7 ( 6 ) 8 4 6 3 ( 7 ) 8 3 4 6 ( 6 ) 1 4 l . 1 8 ( 8 ) 8 0 9 4 ( 6 ) 1 3 6 . 3 3 ( 8 ) 8 0 2 7 ( 7 ) 1 3 3 . 9 8 ( 6 ) 8 1 6 7 ( 7 ) 5 8 1 1 ( 8 ) 8 1 8 5 ( 9 ) 8 4 0 4 ( 8 ) 8 3 6 0 ( 7 ) 1 4 1 . 6 6 ( 9 ) 7 2 5 3 ( 1 1 ) 1 3 6 . 7 5 ( 6 ) 7 2 . 5 8 0 3 ) 1 3 7 . 6 0 ( 1 8 ) 8 4 0 4 ( 8 ) 1 0 1 . 7 1 0 8 ) 6 7 . 3 3 0 6 ) 1 0 2 . 5 5 0 3 ) 8 4 . 1 2 ( 7 ) 8 3 4 6 ( 5 ) 1 4 1 . 3 8 ( 9 ) 7 3 5 5 ( 1 1 ) 1 3 7 . 2 8 ( 1 6 ) 7 3 . 6 6 ( 1 1 ) 1 3 6 . 4 3 ( 6 ) 4 5 1 T a b l e 6 . 1 6 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r N a o , 3 1 ( 2 ) A g 2 E u L 1 9 ( 2 ) T e 4 a t 3 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A g [ l ] - T e [ 2 ] - A g [ 1 ] x 2 A g [ l ] - T e [ 2 ] - A g [ 2 ] x 4 A g [ 2 ] - T e [ 2 ] - A g [ 2 ] x 2 E u [ 1 ] - T e [ 3 ] - E u [ l ] x 2 E u [ l ] - T e [ 3 ] - E u [ 2 ] x 4 E u [ l ] - T e [ 3 ] - T e [ 4 ] x 4 E u [ l ] - T e [ 3 ] - T e [ 4 ] x 4 E u [ 2 ] - T e [ 3 ] - E u [ 2 ] x 2 E u [ 2 ] - T e [ 3 ] - T e [ 4 ] x 4 E u [ 2 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 E u [ 1 ] - T e [ 4 ] - E u [ 1 ] x 2 E u [ l ] - T e [ 4 ] - E u [ 2 ] x 4 E u [ l ] - T e [ 4 ] - T e [ 3 ] x 4 E u [ l ] - T e [ 4 ] - T e [ 3 ] x 4 E u [ 2 ] - T e [ 4 ] - E u [ 2 ] x 2 E u [ 2 ] - T e [ 4 ] - T e [ 3 ] x 4 E u [ 2 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 1 ] - A g [ 1 ] - T e [ 1 ] x 2 T e [ 1 ] - A g [ 1 ] - T e [ 2 ] x 4 T e [ l ] - A g [ 1 ] - A g [ 2 ] x 4 T e [ 1 ] - A g [ 1 ] - A g [ 2 ] x 4 T e [ 2 ] - A g [ l ] - T e [ 2 ] x 2 T e [ 2 ] - A g [ l ] - A g [ 2 ] x 4 T e [ 2 ] - A g [ l ] - A g [ 2 ] x 4 A g [ 2 ] - A g [ l l - A g [ 2 1 x 8 A g [ 2 ] - A g [ l l - A g [ 2 ] x 4 T e [ l ] - A g [ 2 ] - T e [ l ] x 2 T e [ l ] - A g [ 2 ] - T e [ 2 ] x 2 9 9 6 3 ( 1 2 ) 6 5 . 0 5 0 2 ) 9 8 . 8 3 ( 1 8 ) 8 0 3 7 ( 9 ) 1 2 5 . 4 5 ( 8 ) 6 3 1 7 ( 8 ) 1 1 7 . 0 8 ( 1 0 ) 8 1 5 3 ( 8 ) 6 2 2 9 ( 7 ) 1 l 7 . 4 8 ( 1 1 ) 9 0 4 2 ( 1 0 ) 8 9 5 2 ( 7 ) l 7 6 . 3 3 ( 1 1 ) 8 0 4 0 ( 8 ) 1 2 5 . 4 9 ( 9 ) 6 2 6 3 ( 8 ) 1 1 7 . 1 8 0 2 ) 8 1 . 4 8 ( 8 ) 6 2 8 7 ( 8 ) 1 1 7 . 4 2 ( 9 ) 9 0 5 0 ( 1 0 ) 8 9 5 2 ( 7 ) 1 7 6 . 1 7 0 1 ) 1 0 1 . 3 1 0 5 ) 1 1 4 . 5 1 0 3 ) 5 6 8 1 ( 1 3 ) 1 2 2 . 6 7 ( 1 4 ) 9 9 6 0 ( 1 4 ) 5 7 . 7 2 0 2 ) 1 2 3 . 2 6 0 8 ) 9 0 . 2 6 0 7 ) 1 7 8 . 1 7 0 8 ) 1 0 2 . 1 0 0 5 ) 1 1 4 . 5 6 0 4 ) 9 9 3 7 ( 1 2 ) 6 3 . 6 3 ( 1 4 ) 9 8 . 4 3 ( 1 9 ) 7 9 . 8 0 0 0 ) 1 2 2 . 7 0 ( 9 ) 6 1 0 9 ( 8 ) 1 1 5 . 8 6 0 0 ) 8 0 9 7 ( 8 ) 6 1 4 4 ( 7 ) 1 1 4 . 2 7 0 2 ) 8 5 . 2 9 ( 1 1 ) 8 8 9 1 ( 7 ) 1 7 4 . 2 4 0 2 ) 7 9 7 7 ( 8 ) 1 2 2 . 2 1 0 0 ) 6 1 5 8 ( 8 ) 1 1 3 . 6 5 ( 1 2 ) 8 1 0 5 ( 9 ) 6 0 5 5 ( 8 ) 0 6 2 9 ( 9 ) 8 5 0 6 ( 1 0 ) 8 8 9 1 ( 6 ) 1 7 3 . 9 7 0 2 ) 1 0 0 . 8 9 0 7 ) 1 1 2 . 8 5 ( l 7 ) 5 5 5 1 ( 1 3 ) 1 2 2 . 1 9 0 4 ) 9 9 2 1 ( 1 5 ) 5 6 . 9 6 ( 1 2 ) 1 2 1 . 1 ( 2 ) 8 7 9 ( 2 ) 1 7 7 . 3 ( 2 ) 1 0 1 . 7 2 0 7 ) 1 1 3 . 4 0 0 9 ) 9 9 . 8 5 0 2 ) 6 6 4 4 ( 1 4 ) 9 9 . 2 3 0 9 ) 8 0 . 9 3 ( 1 0 ) 1 2 8 . 2 3 ( 9 ) 6 5 3 8 ( 9 ) 1 1 8 . 1 4 0 0 ) 8 1 9 7 ( 8 ) 6 3 2 2 ( 7 ) 1 2 0 . 6 8 ( 1 3 ) 9 5 . 8 3 ( 1 3 ) 9 0 5 1 ( 7 ) 1 7 9 . 6 5 ( 1 4 ) 8 0 9 2 ( 8 ) 1 2 8 . 7 0 ( 9 ) 6 3 6 6 ( 8 ) 1 2 0 . 5 9 0 3 ) 8 1 8 5 ( 9 ) 6 5 2 4 ( 9 ) 1 1 8 3 4 ( 1 0 ) 9 6 . 1 2 0 3 ) 9 0 5 1 ( 7 ) 1 7 9 . 6 4 0 4 ) 1 0 1 . 7 1 0 7 ) 1 1 6 . 1 9 0 7 ) 5 8 . 1 5 0 4 ) 1 2 3 . 1 5 0 4 ) 9 9 . 9 4 0 6 ) 5 8 . 4 9 0 2 ) 1 2 5 . 5 ( 2 ) 9 2 7 ( 2 ) 1 7 9 4 0 ( 1 8 ) 1 0 2 . 4 6 0 7 ) 1 1 5 . 6 9 0 9 ) 4 5 2 T a b l e 6 . 1 7 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r K C q u u T e 4 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f f i c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 4 3 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 6 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 6 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 8 ' o r d e r s a t e l l i t e s [ I > 2 6 ( I ) ] R 1 s t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m i n a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e K C q u u T e 4 8 2 8 . 5 1 0 0 K 0 . 7 0 9 2 6 A M o n o c l i n i c P m ( 0 [ 3 1 / 2 ) 0 a = 4 . 3 8 6 2 ( 5 ) A , o = 9 0 0 b = 4 . 4 0 7 4 ( 7 ) A , [ 3 : 9 0 ° c = 1 1 . 2 2 2 8 0 6 ) A , y = 9 0 ° 0 . 2 8 2 2 ( 6 ) b ‘ + 1 / 2 c ‘ 2 1 6 . 9 6 ( 5 ) A 3 1 6 . 3 3 9 5 g / c m 3 2 5 . 5 2 7 m m ' 1 3 4 8 0 . 2 7 x 0 . 0 4 x 0 . 0 1 m m 3 3 . 0 1 t o 2 9 4 3 ° - 6 < = h < = 5 , - 6 < = k < = 6 , - 1 5 < = l < = 1 5 , - 1 < = m < = 1 4 9 2 5 ( 1 5 3 3 m a i n + 3 3 9 2 s a t e l l i t e s ) 2 9 2 3 ( 9 8 3 m a i n + 1 9 4 0 s a t e l l i t e s ) [ R i m = 0 . 0 4 7 2 ] 9 3 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 2 9 2 3 / 0 / 1 2 1 1 . 9 2 R o b s = 0 . 0 5 2 7 , w R o i , s = 0 . 1 3 0 8 R a n = 0 . 0 8 1 4 , w R a u = 0 . 1 4 0 1 R o b s = 0 . 0 4 1 8 , w R o b , = 0 . 1 1 9 9 R a n = 0 . 0 4 3 1 , w R a n = 0 . 1 2 0 1 R o b , = 0 . 1 1 6 2 , w R o t , s = 0 . 1 8 6 7 R , " = 0 . 2 5 1 3 , w R a u = 0 . 2 2 9 8 0 . 0 0 0 4 2 0 ) 0 . 0 3 5 9 a n d 0 . 7 7 7 6 4 . 0 3 a n d - 2 . 8 9 e . A ' 3 R = X I I F o l - I F e H / 2 1 6 . 1 . w R = { 2 1 0 1 1 8 . 1 2 - 1 1 3 . 1 9 2 1 / 2 1 0 1 1 3 1 4 1 1 1 ” a n d w = 1 / < o Z ( I ) + 0 . 0 0 1 6 I ’ ) 4 5 3 T a b l e 6 . 1 8 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) , o c c u p a n c i e s a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K C q u u T e a a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x y 2 O c c u p a n c y U . . . l E u 0 0 0 2 7 4 9 1 1 1 ( 1 ) s i n , 1 - 7 3 ( 4 ) - 3 ( 3 ) - 3 ( 2 ) c o s , 1 - 6 5 ( 4 ) 3 ( 3 ) - 2 ( 1 ) T e [ l ] 0 5 0 0 4 ( 4 ) 5 0 0 0 3 6 3 9 ( 1 ) 1 1 1 ( 1 ) s i n , 1 - 2 5 ( 3 ) 0 ( 2 ) 1 ( 2 ) c o s , 1 - 1 1 ( 2 ) 0 ( 3 ) 0 ( 1 ) T e [ 2 ] 0 9 9 9 4 ( 4 ) 0 6 3 7 3 ( 2 ) 1 1 2 ( 1 ) s i n , 1 - 4 8 ( 3 ) 2 ( 1 ) 2 ( 2 ) c o s , 1 2 2 ( 2 ) 4 ( 3 ) - 1 ( 1 ) T e [ 3 ] 0 5 0 0 2 ( 6 ) 0 3 6 2 ( 2 ) 1 1 2 ( 1 ) s i n , 1 - 3 3 ( 1 ) - 2 2 ( 8 ) 0 ( 1 ) c o s , 1 - 2 9 3 ( 6 ) 3 ( 1 ) - 2 ( 3 ) T e [ 4 ] 0 1 7 ( 6 ) 5 0 0 0 3 5 9 ( 2 ) 1 1 3 ( 1 ) s i n , 1 3 7 ( 1 ) 8 ( 9 ) 0 ( 1 ) c o s , 1 3 2 2 ( 7 ) - 1 ( 1 ) 0 ( 3 ) C u [ 1 ] 0 9 9 7 6 ( 8 ) 5 0 0 0 5 1 1 2 ( 3 ) 1 1 7 ( 1 ) s i n , 1 - 7 0 ( 1 5 ) 1 ( 1 ) 1 3 ( 6 ) c o s , 1 3 ( 1 ) 2 5 ( 1 1 ) 0 ( 1 ) C u [ 2 ] 0 4 9 8 5 ( 8 ) 0 5 1 0 8 ( 3 ) 1 2 1 ( 1 ) s i n , 1 - 6 8 ( 1 5 ) 1 ( 1 ) 1 1 ( 6 ) c o s , 1 2 ( 1 ) 2 7 ( 1 3 ) 0 ( 1 ) K 0 5 0 0 4 ( 1 3 ) 5 0 0 0 7 7 5 1 ( 6 ) 1 1 3 ( 1 ) s i n , 1 - 4 ( 1 9 ) 8 ( 1 5 ) 1 5 ( 6 ) c o s , 1 5 ( 2 0 ) 7 ( 1 3 ) - 1 8 ( 7 ) 4 5 4 T a b l e 6 . 1 9 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K C q u u T e a a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 E u 0 9 ( 1 ) 7 ( 1 ) 1 7 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 - 1 0 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 0 ) 0 ( 1 ) c o s , 1 - 1 0 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) T e [ l ] 0 9 ( 1 ) 6 ( 1 ) 1 8 ( 1 ) 0 1 ( 1 ) 0 s i n , 1 - 1 0 ) - 1 0 ) 0 ( 1 ) 0 ( 1 ) - 2 0 ) - 1 0 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 0 ) 2 ( 1 ) T e [ 2 ] 0 1 1 ( 1 ) 8 ( 1 ) 1 7 ( 1 ) 0 1 ( 1 ) 0 s i n , 1 0 ( 1 ) - 1 0 ) 2 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 1 ( 1 ) - 1 0 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) T e [ 3 ] 0 1 2 ( 1 ) 6 ( 1 ) 1 7 ( 1 ) 0 1 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 2 ( 1 ) 0 ( 1 ) 2 ( 1 ) c o s , 1 - 3 ( 2 ) 0 ( 1 ) 9 ( 2 ) 0 ( 1 ) 0 ( 2 ) 0 ( 1 ) T e [ 4 ] 0 1 3 ( 1 ) 1 0 ( 1 ) 1 5 ( 1 ) 0 2 ( 1 ) 0 s i n , 1 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 0 ) 0 ( 1 ) 1 ( 1 ) c o s , 1 5 ( 2 ) 2 ( 1 ) — 1 ( 2 ) 0 ( 1 ) - 1 ( 2 ) 0 ( 1 ) C u [ 1 ] 0 2 6 ( 2 ) 9 ( 1 ) 1 7 ( 2 ) 0 0 ( 1 ) 0 s i n , 1 - 3 ( 4 ) 2 ( 2 ) 1 0 ( 4 ) 0 ( 1 ) - 5 ( 3 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 2 ) 0 ( 1 ) 7 ( 2 ) C u [ 2 ] 0 1 4 ( 2 ) 3 2 ( 1 ) 1 6 ( 2 ) 0 0 ( 1 ) 0 s i n , 1 0 ( 3 ) 3 ( 3 ) 7 ( 4 ) 0 ( 1 ) — 2 ( 3 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 2 ) 0 ( 1 ) 1 1 ( 2 ) K 0 1 4 ( 2 ) 1 1 ( 1 ) 1 4 ( 2 ) 0 1 ( 1 ) 0 s i n , 1 3 ( 3 ) 4 ( 2 ) - 3 ( 3 ) 1 ( 2 ) 1 ( 2 ) 3 0 ) c o s , 1 4 ( 3 ) - 5 ( 3 ) 3 ( 4 ) 1 ( 2 ) - 1 ( 2 ) - 2 ( 2 ) 4 5 5 T a b l e 6 . 2 0 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K C q u u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e E u - T e [ l ] x 4 3 . 2 8 1 ( 2 ) 3 . 2 5 9 ( 2 ) 3 . 3 0 4 ( 2 ) E u - T e [ 3 ] x 2 3 . 4 2 0 ( 3 ) 3 . 3 6 6 ( 4 ) 3 . 4 7 4 ( 4 ) E u - T e [ 4 ] x 2 3 . 4 3 1 ( 3 ) 3 . 4 2 8 ( 3 ) 3 . 4 3 6 ( 3 ) E u - C u [ 1 ] x 2 3 . 4 9 1 ( 4 ) 3 . 4 7 8 ( 5 ) 3 . 5 0 4 ( 5 ) E u - C u [ 2 ] x 2 3 . 4 8 4 ( 5 ) 3 . 4 7 9 ( 7 ) 3 . 4 8 9 ( 7 ) T e [ l ] - C u [ 1 ] 2 . 7 5 7 ( 6 ) 2 . 7 3 3 ( 8 ) 2 . 7 8 0 ( 8 ) T e [ l ] - C u [ 1 ] 2 . 7 3 7 ( 6 ) 2 . 7 3 0 ( 8 ) 2 . 7 4 4 ( 8 ) T e [ l ] - C u [ 2 ] x 2 2 . 7 5 2 ( 4 ) 2 . 7 4 0 ( 4 ) 2 . 7 6 4 ( 4 ) T e [ 2 ] - C u [ 1 ] x 2 2 . 6 1 9 ( 4 ) 2 . 6 0 8 ( 4 ) 2 . 6 3 0 ( 4 ) T e [ 2 ] - C u [ 2 ] x 2 2 . 6 1 6 ( 6 ) 2 . 6 1 6 ( 5 ) 2 . 6 1 6 ( 8 ) T e [ 2 ] - K x 4 3 . 4 7 0 ( 9 ) 3 . 4 5 5 ( 9 ) 3 . 4 8 4 ( 9 ) T e [ 3 ] - T e [ 4 ] x 2 3 . 1 0 5 ( 4 ) 2 . 9 3 4 ( 4 ) 3 . 2 8 4 ( 4 ) T e [ 3 ] - T e [ 4 ] x 2 3 . 1 1 8 ( 4 ) 2 . 9 4 8 ( 4 ) 3 . 2 9 0 ( 4 ) C u [ 1 ] - C u [ 2 ] x 4 3 . 1 0 6 ( 6 ) 3 . 0 8 6 ( 6 ) 3 . 1 2 7 ( 6 ) T a b l e 6 . 2 1 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K C q u u T e a a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ l ] - E u - T e [ l ] x 4 8 4 3 8 ( 6 ) 8 3 6 8 ( 6 ) 8 5 0 7 ( 6 ) T e [ l ] - E u - T e [ l ] x 4 8 3 8 3 ( 5 ) 8 3 7 7 ( 5 ) 8 3 8 9 ( 5 ) T e [ l ] - E u - T e [ l ] x 4 1 4 2 . 5 5 ( 8 ) 1 4 2 . 3 7 ( 8 ) 1 4 2 . 7 2 ( 8 ) T e [ l ] - E u - T e [ 3 ] x 4 7 9 5 3 ( 7 ) 7 9 0 8 ( 7 ) 8 0 0 0 ( 7 ) T e [ l ] - E u - T e [ 3 ] x 4 1 3 2 . 4 2 ( 8 ) 1 3 1 . 8 7 ( 8 ) 1 3 2 . 9 8 ( 8 ) T e [ l ] - E u - T e [ 4 ] x 4 7 9 4 1 ( 7 ) 7 7 . 4 3 ( 7 ) 8 1 3 6 ( 7 ) T e [ l ] - E u - T e [ 4 ] x 4 1 3 2 . 7 9 ( 8 ) 1 2 9 . 7 2 ( 8 ) 1 3 5 . 7 9 ( 8 ) T e [ l ] - E u - C u [ 1 ] x 4 4 7 . 5 5 ( 1 2 ) 4 7 3 1 ( 1 3 ) 4 7 . 7 8 ( 1 3 ) T e [ l ] - E u - C u [ 1 ] x 4 9 9 9 6 ( 1 1 ) 9 9 6 9 ( 1 2 ) 1 0 0 . 2 3 ( 1 2 ) T e [ l ] - E u - C u [ 2 ] x 4 4 7 8 9 ( 7 ) 4 7 5 7 ( 6 ) 4 8 2 1 ( 6 ) T e [ l ] - E u - C u [ 2 ] x 4 9 9 8 1 ( 1 1 ) 9 9 4 1 ( 1 0 ) 1 0 0 . 2 1 ( 1 0 ) T e [ 3 ] - E u - T e [ 3 ] x 2 7 9 7 7 ( 7 ) 7 9 7 1 ( 8 ) 7 9 8 0 ( 7 ) T e [ 3 ] - E u - T e [ 4 ] x 4 5 4 . 1 4 ( 7 ) 5 1 3 2 ( 7 ) 5 6 9 6 ( 7 ) T e [ 3 ] - E u - C u [ 1 ] x 4 1 2 6 . 3 8 ( 1 2 ) 1 2 5 . 9 2 ( 1 3 ) 1 2 6 . 8 4 ( 1 3 ) 4 5 6 T a b l e 6 . 2 1 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K C q u u T e a , a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 3 ] - E u - C u [ 2 ] x 2 T e [ 3 ] - E u - C u [ 2 ] x 2 T e [ 4 ] - E u - T e [ 4 ] x 2 T e [ 4 ] - E u - C u [ 1 ] x 2 T e [ 4 ] - E u - C u [ 1 ] x 2 T e [ 4 ] - E u - C u [ 2 ] x 4 C u [ 1 ] - E u - C u [ 1 ] x 2 C u [ 1 ] - E u - C u [ 2 ] x 4 C u [ 2 ] - E u - C u [ 2 ] x 2 E u - T e [ 1 ] - E u x 4 E u - T e [ l ] - E u x 4 E u - T e [ 1 ] - E u x 4 E u - T e [ 1 ] - C u [ 1 ] x 4 E u - T e [ 1 ] - C u [ 1 ] x 4 E u - T e [ 1 ] - C u [ 2 ] x 4 E u - T e [ 1 ] - C u [ 2 ] x 4 C u [ 1 ] - T e [ l ] - C u [ 1 ] x 2 C u [ 1 ] - T e [ l ] - C u [ 2 ] x 4 C u [ 2 ] - T e [ l ] - C u [ 2 ] x 2 C u [ 1 ] - T e [ 2 ] - C u [ 1 ] x 2 C u [ 1 ] - T e [ 2 ] - C u [ 2 ] x 4 C u [ 1 ] - T e [ 2 ] - K x 4 C u [ 1 ] - T e [ 2 ] - K x 4 C u [ 2 ] - T e [ 2 ] - C u [ 2 ] x 2 C u [ 2 ] - T e [ 2 ] - K x 4 C u [ 2 ] - T e [ 2 ] - K x 4 K - T e [ 2 ] - K x 8 K - T e [ 2 ] - K x 4 E u - T e [ 3 ] - E u x 2 E u - T e [ 3 ] - T e [ 4 ] x 4 E u - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 1 0 0 . 9 7 0 4 ) 1 7 8 . 9 8 0 3 ) 7 9 9 8 ( 8 ) 1 0 0 . 8 6 ( 9 ) 1 7 7 . 5 9 0 4 ) 1 2 6 . 5 6 ( 1 0 ) 7 8 . 2 8 0 0 ) 5 2 8 9 ( 1 1 ) 7 8 . 1 3 0 5 ) 8 4 3 0 ( 6 ) 8 3 8 3 ( 5 ) 1 4 2 . 5 5 ( 9 ) 6 9 9 8 ( 1 2 ) 1 3 6 . 5 9 ( 6 ) 6 9 6 8 ( 1 4 ) 1 3 6 . 6 8 ( 1 7 ) 1 0 6 . 0 ( 2 ) 6 8 . 7 9 0 7 ) 1 0 6 . 4 l ( 1 7 ) 1 1 4 . 5 9 0 8 ) 7 2 . 7 9 0 4 ) 7 2 8 1 ( 1 7 ) 1 4 0 . 7 ( 2 ) 1 1 4 . 1 ( 2 ) 7 3 . 2 8 ( 1 9 ) 1 4 0 . 5 9 0 6 ) 7 8 8 6 ( 1 9 ) 1 2 7 . 1 ( 2 ) 7 9 7 7 ( 7 ) 6 3 2 7 ( 8 ) 1 1 6 . 9 3 ( 9 ) 9 0 6 9 ( 1 2 ) 8 9 5 4 ( 1 0 ) 1 7 6 . 3 1 0 3 ) 1 0 0 . 2 0 0 4 ) 1 7 7 . 9 7 0 5 ) 7 9 7 6 ( 8 ) 1 0 0 . 6 4 ( 9 ) 1 7 6 . 4 6 0 5 ) 1 2 4 . 2 0 0 1 ) 7 7 8 0 ( 1 0 ) 5 2 4 2 ( 1 1 ) 7 7 . 7 8 0 7 ) 8 3 9 0 ( 6 ) 8 3 7 7 ( 5 ) 1 4 2 . 2 6 ( 8 ) 6 9 5 1 ( 1 2 ) 1 3 6 . 4 9 ( 6 ) 6 9 4 6 ( 1 4 ) 1 3 6 . 3 0 0 7 ) 1 0 5 . 5 ( 2 ) 6 8 . 1 1 0 8 ) 1 0 5 . 9 4 0 7 ) 1 1 4 . 5 4 0 8 ) 7 2 2 3 ( 1 2 ) 7 2 . 4 6 ( 1 6 ) 1 3 9 . 9 2 0 8 ) 1 1 3 . 8 ( 2 ) 7 3 0 7 ( 1 9 ) 1 4 0 . 2 6 ( 1 4 ) 7 8 . 7 6 0 9 ) 1 2 6 . 6 ( 2 ) 7 9 7 1 ( 9 ) 6 1 0 4 ( 7 ) 0 5 6 8 ( 9 ) 8 4 . 9 2 ( 1 2 ) 8 9 2 5 ( 1 1 ) 1 7 4 . 0 8 0 3 ) 1 0 1 . 7 7 0 4 ) l 7 9 . 8 2 ( 7 ) 8 0 0 9 ( 9 ) 1 0 1 . 0 5 ( 9 ) 1 7 9 4 4 0 0 ) 1 2 8 . 8 4 ( 1 0 ) 7 8 . 7 8 0 0 ) 5 3 3 6 ( 1 2 ) 7 8 4 8 ( 1 8 ) 8 4 6 9 ( 6 ) 8 3 8 9 ( 5 ) 1 4 2 . 8 5 ( 8 ) 7 0 4 7 ( 1 2 ) 1 3 6 . 6 8 ( 6 ) 6 9 9 1 ( 1 5 ) 1 3 7 . 0 5 0 7 ) 1 0 6 . 4 ( 2 ) 6 9 4 8 ( 1 8 ) 1 0 6 . 8 8 0 7 ) 1 1 4 . 6 4 0 8 ) 7 3 3 5 ( 1 2 ) 7 3 . 1 6 ( 1 6 ) 1 4 1 . 3 8 ( 1 8 ) 1 1 4 . 5 ( 2 ) 7 3 . 4 8 0 9 ) 1 4 0 . 9 2 0 4 ) 7 8 9 5 ( 1 9 ) 1 2 7 . 6 ( 2 ) 7 9 8 0 ( 7 ) 6 5 5 5 ( 8 ) 1 1 8 0 7 ( 9 ) 9 6 . 5 7 ( 1 4 ) 9 0 0 4 ( 1 1 ) 1 7 9 8 1 0 2 ) 4 5 7 T a b l e 6 . 2 1 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K C q u u T e a a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . E u - T e [ 4 ] - E u x 2 E u - T e [ 4 ] - T e [ 3 ] x 4 E u - T e [ 4 ] - T e [ 3 ] x 4 E u - T e [ 4 ] - K x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - K x 4 T e [ 3 ] - T e [ 4 ] - K x 4 E u - C u [ 1 ] - E u x 2 E u - C u [ 1 ] - T e [ 1 ] x 4 E u - C u [ 1 ] - T e [ 2 ] x 2 E u - C u [ 1 ] - T e [ 2 ] x 2 E u - C u [ 1 ] - C u [ 2 ] x 4 E u - C u [ 1 ] - C u [ 2 ] x 4 T e [ 1 ] - C u [ 1 ] - T e [ 1 ] x 2 T e [ 1 ] - C u [ 1 ] - T e [ 2 ] x 4 T e [ l ] - C u [ 1 ] - C u [ 2 ] x 4 T e [ l ] - C u [ 1 ] - C u [ 2 ] x 4 T e [ 2 ] - C u [ 1 ] - T e [ 2 ] x 2 T e [ 2 ] - C u [ 1 ] - C u [ 2 ] x 4 T e [ 2 ] - C u [ 1 ] - C u [ 2 ] x 4 C u [ 2 ] - C u [ 1 ] - C u [ 2 ] x 8 C u [ 2 ] - C u [ 1 ] - C u [ 2 ] x 4 E u - C u [ 2 ] - E u x 2 E u - C u [ 2 ] - T e [ 1 ] x 4 E u - C u [ 2 ] - T e [ 2 ] x 2 E u - C u [ 2 ] - T e [ 2 ] x 2 E u - C u [ 2 ] - C u [ 1 ] x 4 E u — C u [ 2 ] - C u [ 1 ] x 4 T e [ 1 ] - C u [ 2 ] - T e [ 1 ] x 2 T e [ l ] - C u [ 2 ] - T e [ 2 ] x 4 T e [ 1 ] - C u [ 2 ] - C u [ 1 ] x 4 T e [ 1 ] - C u [ 2 ] - C u [ 1 ] x 4 7 9 9 2 ( 7 ) 6 2 7 1 ( 7 ) 1 1 6 8 5 ( 1 0 ) 1 2 7 . 6 3 0 5 ) 9 0 2 4 ( 1 1 ) 8 9 5 4 ( 1 0 ) 1 7 6 . 2 6 ( 1 3 ) 6 4 . 9 8 ( 1 5 ) 1 1 4 . 9 8 0 6 ) 7 8 . 2 9 0 0 ) 6 2 . 2 1 ( 1 0 ) 8 3 . 5 6 ( 1 0 ) 1 6 1 . 8 4 0 7 ) 6 3 . 4 4 ( 1 4 ) 1 1 6 . 6 5 ( 1 9 ) 1 0 5 . 9 6 ( 1 7 ) 1 0 9 2 0 ( l 6 ) 5 5 . 7 6 ( 1 5 ) 1 2 4 . 1 6 0 8 ) 1 1 4 . 5 9 0 8 ) 5 3 5 7 ( 1 4 ) 1 2 6 . 9 ( 2 ) 9 0 3 8 ( 1 9 ) 1 7 9 . 7 ( 2 ) 7 8 . 1 3 0 1 ) 6 2 . 3 8 0 1 ) 8 4 . 0 0 ( 1 5 ) 1 6 1 . 9 ( 2 ) 6 3 . 7 2 ( 1 5 ) 1 1 6 . 4 0 0 8 ) 1 0 6 . 4 0 0 7 ) 1 0 9 . 1 8 0 7 ) 5 5 . 6 7 ( 1 4 ) 1 2 4 . 8 ( 2 ) 7 9 8 5 ( 8 ) 6 1 9 8 ( 7 ) 1 1 3 0 9 ( 1 2 ) 1 2 4 . 5 6 ( 1 5 ) 8 4 . 3 5 0 2 ) 8 9 2 5 ( 8 ) 1 7 3 . 9 4 0 3 ) 6 2 . 5 9 ( 1 5 ) 1 1 4 . 4 2 0 6 ) 7 7 . 9 0 0 5 ) 6 1 6 8 ( 9 ) 8 3 . 2 5 0 3 ) 1 6 1 . 3 3 0 6 ) 6 3 3 9 ( 1 5 ) 1 1 6 . 1 2 ( 1 6 ) 1 0 5 . 5 ( 2 ) 1 0 8 . 8 0 0 9 ) 5 5 . 5 6 ( 1 6 ) 1 2 3 . 9 6 0 7 ) 1 1 4 . 2 ( 3 ) 5 3 . 2 7 0 4 ) 1 2 6 . 4 ( 3 ) 9 0 3 ( 2 ) 1 7 9 . 4 ( 3 ) 7 7 . 7 8 0 5 ) 6 2 . 1 8 ( 1 3 ) 8 3 9 ( 2 ) 1 6 1 . 6 ( 3 ) 6 3 . 5 9 0 4 ) 1 1 6 . 2 1 0 7 ) 1 0 6 . 0 ( 2 ) 1 0 8 . 7 3 0 9 ) 5 5 1 4 ( 1 4 ) 1 2 4 . 5 ( 3 ) 7 9 9 8 ( 6 ) 6 3 4 0 ( 7 ) 1 2 0 . 5 8 0 3 ) 1 3 0 6 8 ( 1 5 ) 9 6 . 4 3 ( 1 4 ) 9 0 0 4 ( 1 1 ) 1 7 9 . 8 2 0 2 ) 6 7 . 4 8 0 5 ) 1 1 5 . 6 0 ( 1 6 ) 7 8 . 6 8 ( 1 5 ) 6 2 7 5 ( 9 ) 8 3 8 6 ( 1 3 ) 1 6 2 . 3 6 ( 1 6 ) 6 3 . 4 9 ( 1 5 ) 1 1 7 . 1 9 0 6 ) 1 0 6 . 4 ( 2 ) 1 0 9 . 5 9 0 9 ) 5 5 . 9 6 0 6 ) 1 2 4 . 3 6 ( l 7 ) 1 1 5 . 0 ( 3 ) 5 3 8 6 ( 1 4 ) 1 2 7 . 4 ( 3 ) 9 0 4 ( 2 ) 1 8 0 7 8 . 4 8 0 5 ) 6 2 . 5 7 ( 1 3 ) 8 4 1 ( 2 ) 1 6 2 . 1 ( 3 ) 6 3 . 8 5 0 4 ) 1 1 6 . 6 0 0 7 ) 1 0 6 . 8 ( 2 ) 1 0 9 . 6 3 0 9 ) 5 6 . 2 1 0 4 ) 1 2 5 . 1 ( 3 ) 4 5 8 T a b l e 6 . 2 2 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r K o , 9 7 ( 2 ) A g 2 E u 1 , 0 3 ( 2 ) T e 4 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 0 4 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 6 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R l S t o r d e r s a t e l l i t e s [ I > 2 o ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e K 0 . 9 7 ( 2 ) A 8 2 E u 1 0 3 ( 2 ) T e 4 9 2 1 . 7 1 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A M o n o c l i n i c P m ( 0 [ 3 1 / 2 ) 0 a = 4 . 4 6 4 1 ( 5 ) A , 0 1 = 9 0 ° b = 4 . 4 9 6 4 ( 8 ) A , B = 9 0 ° c = 1 1 . 3 5 0 1 ( 1 7 ) A , y = 9 0 ° 0 . 2 8 5 3 ( 5 ) b ‘ + 1 / 2 c ‘ 2 2 7 8 2 ( 6 ) A 3 1 6 . 7 1 5 9 g / c n n 3 2 4 . 1 2 9 m m " 3 8 5 0 . 2 5 x 0 . 1 5 x 0 0 1 m m 3 2 . 9 8 t o 2 9 0 4 ° - 5 < = h < = 6 , - 6 < = k < = 6 , - 1 5 < = l < = 1 5 , - 1 < = m < = 1 4 6 6 3 ( 1 4 1 9 m a i n + 3 2 4 4 s a t e l l i t e s ) 2 9 5 2 ( 9 8 1 m a i n + 1 9 7 1 s a t e l l i t e s ) [ R i m = 0 . 0 6 0 2 ] 9 5 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 2 9 5 2 / 2 8 / 1 2 3 2 . 8 5 R o b , = 0 . 0 7 5 4 , w R o b , = 0 . 1 9 9 9 R , “ = 0 . 1 1 1 3 , w R a u = 0 . 2 1 1 3 R o b s = 0 . 0 5 7 7 , w R o b , = 0 . 1 5 4 1 R . " = 0 . 0 6 1 3 , w R a u = 0 . 1 5 5 4 R o b , = 0 . 1 4 9 7 , w R o b S = 0 . 3 0 6 7 R , " = 0 . 2 7 9 9 , w R a u = 0 . 3 3 5 3 0 . 0 0 0 5 4 ( 1 0 ) 0 . 0 4 3 9 a n d 0 . 8 5 0 1 6 . 8 6 a n d - 6 . 1 8 6 A 3 R = 2 1 0 1 4 1 7 . “ / 2 | F , | , w R = { 2 ‘ [ w ( | 1 = , | 2 - [ 1 : 1 5 2 ] / > : [ w ( | 1 ~ ‘ , | “ ) ] } ” 2 a n d w = 1 / ( o Z ( I ) + 0 . 0 0 1 6 1 2 ) 4 5 9 T a b l e 6 . 2 3 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) , o c c u p a n c i e s a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r K o _ 9 7 ( 2 ) A g 2 E u 1 . o 3 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x y 2 O c c u p a n c y U . . , q E u [ l ] 0 0 0 2 7 4 9 0 . 6 7 8 ( 1 1 ) 1 3 ( 1 ) s i n , 1 - 7 0 ( 8 ) 1 4 ( 5 ) 0 ( 3 ) c o s , 1 - 6 2 ( 7 ) - 1 6 ( 5 ) 0 ( 2 ) E u [ 2 ] 0 4 9 9 1 ( 7 ) 5 0 0 0 7 9 7 0 ( 3 ) 0 . 3 4 7 ( 1 1 ) 1 3 ( 1 ) s i n , 1 - 9 8 ( 1 0 ) - 2 5 ( 1 0 ) - 3 ( 3 ) c o s , 1 1 3 2 ( 1 4 ) - 1 9 ( 7 ) 4 ( 4 ) T e [ l ] 0 5 0 1 1 ( 8 ) 5 0 0 0 3 6 6 8 ( 3 ) 1 1 5 ( 1 ) s i n , 1 - 4 8 ( 9 ) 8 ( 3 ) 0 ( 3 ) c o s , 1 - 2 1 ( 4 ) - 1 8 ( 6 ) 0 ( 1 ) T e [ 2 ] 0 1 9 ( 8 ) 0 6 8 7 0 ( 3 ) 1 2 0 ( 1 ) s i n , 1 - 4 4 ( 8 ) - 9 ( 4 ) 0 ( 3 ) c o s , 1 3 0 ( 5 ) - 1 4 ( 6 ) 0 ( 2 ) T e [ 3 ] 0 4 9 8 6 ( 1 0 ) 0 3 9 3 ( 3 ) 1 2 1 ( 1 ) s i n , 1 - 4 7 ( 1 ) - 3 0 ( 1 0 ) 3 ( 1 ) c o s , 1 - 3 8 3 ( 1 0 ) 4 ( 1 ) 2 3 ( 4 ) T e [ 4 ] 0 1 0 0 0 9 ( 9 ) 5 0 0 0 3 7 9 ( 3 ) 1 1 7 ( 1 ) s i n , 1 4 9 ( 1 ) 5 ( 1 0 ) 2 ( 1 ) c o s , 1 4 1 0 ( 1 0 ) - 1 ( 1 ) 1 9 ( 4 ) A g [ l ] 0 9 9 6 4 ( 7 ) 5 0 0 0 5 3 3 3 ( 3 ) 1 2 0 ( 1 ) s i n , 1 - 8 5 ( 3 0 ) 0 ( 1 ) 2 8 ( 5 ) c o s , 1 1 0 ( 3 ) - 3 ( 9 ) - 3 ( 1 ) A g [ 2 ] 0 4 9 6 9 ( 6 ) 0 5 3 1 9 ( 3 ) 1 1 6 ( 1 ) s i n , 1 - 2 5 ( 2 0 ) 0 ( 1 ) 1 8 ( 5 ) c o s , 1 3 ( 2 ) - 4 ( 8 ) - 2 ( 1 ) K [ l ] 0 0 0 2 7 4 9 0 . 3 2 2 ( 1 1 ) 1 3 ( 1 ) s i n , 1 - 7 0 ( 8 ) 1 4 ( 5 ) 0 ( 3 ) c o s , 1 - 6 2 ( 7 ) - 1 6 ( 5 ) 0 ( 2 ) K [ 2 ] 0 4 9 9 1 5 0 0 0 7 9 7 0 0 . 6 5 3 ( 1 1 ) 1 3 ( 1 ) s i n , 1 - 9 8 ( 1 0 ) - 2 5 ( 1 0 ) - 3 ( 3 ) c o s , 1 1 3 2 ( 1 4 ) - 1 9 ( 7 ) 4 ( 4 ) 4 6 0 T a b l e 6 . 2 4 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r K o _ 9 7 ( 2 ) A g 2 E u 1 _ 0 3 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 E u [ l ] 0 8 ( 1 ) 6 ( 1 ) 2 4 ( 1 ) 0 - 1 ( 1 ) 0 s i n , 1 - 1 ( 2 ) 0 ( 1 ) 2 ( 1 ) 0 ( 1 ) 1 ( 1 ) - l ( 1 ) c o s , 1 - 1 ( 1 ) 0 ( 1 ) 2 ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) E u [ 2 ] 0 1 2 ( 2 ) 1 6 ( 1 ) 1 0 ( 2 ) 0 2 ( 1 ) 0 s i n , 1 - 1 ( 2 ) 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) - 3 ( 2 ) c o s , 1 1 ( 3 ) 0 ( 2 ) 0 ( 2 ) - 1 ( 1 ) 1 ( 2 ) - 2 ( 1 ) T e [ l ] 0 1 2 ( 1 ) 1 0 ( 1 ) 2 4 ( 1 ) 0 1 ( 1 ) 0 s i n , 1 - 5 ( 2 ) 1 ( 1 ) 4 ( 2 ) 0 ( 1 ) - 2 ( 1 ) 0 ( 1 ) c o s , 1 - 2 ( 1 ) 0 ( 1 ) 2 ( 1 ) - 1 ( 1 ) - l ( 1 ) 0 ( 1 ) T e [ 2 ] 0 1 3 ( 1 ) 1 3 ( 1 ) 3 6 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 - 4 ( 1 ) 1 ( 1 ) 0 ( 2 ) 0 ( 1 ) 0 ( 1 ) - 2 ( 1 ) c o s , 1 2 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 2 ( 1 ) T e [ 3 ] 0 2 4 ( 2 ) 1 6 ( 1 ) 2 5 ( 1 ) 0 1 ( 1 ) 0 s i n , 1 - 3 ( 1 ) 0 ( 1 ) 2 ( 1 ) 7 ( 1 ) 0 ( 1 ) - 2 ( 1 ) c o s , 1 - 2 3 ( 3 ) 1 ( 2 ) 1 6 ( 2 ) - 1 ( 1 ) - 4 ( 2 ) 0 ( 1 ) T e [ 4 ] 0 1 6 ( 2 ) 8 ( 1 ) 2 7 ( 1 ) 0 - 3 ( 1 ) 0 s i n , 1 2 ( 1 ) 0 ( 1 ) - 1 ( 1 ) - 3 ( 1 ) 0 ( 1 ) - 2 ( 1 ) c o s , 1 2 0 ( 2 ) 0 ( 2 ) - 8 ( 2 ) 0 ( 1 ) 1 ( 2 ) 0 ( 1 ) A g [ l ] 0 1 9 ( 2 ) 1 9 ( 1 ) 2 2 ( 1 ) 0 - 2 ( 1 ) 0 s i n , 1 - 8 ( 3 ) 2 ( 2 ) 1 2 ( 2 ) 0 ( 1 ) - 6 ( 2 ) 0 ( 1 ) c o s , 1 1 ( 1 ) 0 ( 1 ) - l ( 1 ) - 1 ( 2 ) 1 ( 1 ) - 4 ( 2 ) A g [ 2 ] 0 1 4 ( 1 ) 1 0 ( 1 ) 2 5 ( 1 ) 0 - 1 ( 1 ) 0 s i n , 1 - 4 ( 2 ) 2 ( 2 ) 1 0 ( 2 ) 0 ( 1 ) - 4 ( 2 ) 0 ( 1 ) c o s , 1 1 ( 1 ) 0 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 ( 2 ) K [ l ] 0 8 ( 1 ) 6 ( 1 ) 2 4 ( 1 ) 0 - 1 ( 1 ) 0 s i n , 1 - 1 ( 2 ) 0 ( 1 ) 2 ( 1 ) 0 ( 1 ) 1 ( 1 ) - 1 ( 1 ) c o s , 1 - 1 ( 1 ) 0 ( 1 ) 2 ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) K [ 2 ] 0 1 2 ( 2 ) 1 6 ( 1 ) 1 0 ( 2 ) 0 2 ( 1 ) 0 s i n , 1 - 1 ( 2 ) 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) - 3 ( 2 ) c o s , 1 1 ( 3 ) 0 ( 2 ) 0 ( 2 ) - 1 ( 1 ) 1 ( 2 ) - 2 ( 1 ) 4 6 1 T a b l e 6 . 2 5 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r K 0 , 9 7 ( 2 ) A g 2 E u 1 , 0 3 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e E u [ l ] - T e [ l ] x 4 3 . 3 5 0 ( 5 ) 3 . 3 3 0 ( 4 ) 3 . 3 7 0 ( 5 ) E u [ l ] - T e [ 3 ] x 2 3 . 4 4 6 ( 6 ) 3 . 3 8 3 ( 7 ) 3 . 5 1 1 ( 7 ) E u [ l ] - T e [ 4 ] x 2 3 . 4 6 6 ( 5 ) 3 . 4 5 7 ( 5 ) 3 . 4 8 1 ( 5 ) E u [ 2 ] - T e [ 2 ] x 2 3 . 3 9 7 ( 6 ) 3 . 3 5 7 ( 6 ) 3 . 4 3 8 ( 6 ) E u [ 2 ] - T e [ 2 ] x 2 3 . 4 1 4 ( 6 ) 3 . 3 7 3 ( 6 ) 3 . 4 5 5 ( 7 ) E u [ 2 ] - T e [ 4 ] x 2 3 . 5 2 6 ( 7 ) 3 . 4 6 8 ( 8 ) 3 . 5 8 4 ( 8 ) T e [ l ] - A g [ l ] 2 . 9 4 0 ( 8 ) 2 . 9 0 5 ( 1 2 ) 2 . 9 7 5 ( 1 2 ) T e [ l ] - A g [ l ] 2 . 9 0 8 ( 8 ) 2 . 9 0 2 ( 1 2 ) 2 . 9 1 5 ( 1 1 ) T e [ l ] - A g [ 2 ] x 2 2 . 9 2 7 ( 5 ) 2 . 9 0 8 ( 5 ) 2 . 9 4 5 ( 5 ) T e [ l ] - K [ l ] x 4 3 . 3 5 7 ( 5 ) 3 . 3 3 2 ( 5 ) 3 . 3 8 1 ( 5 ) T e [ 2 ] - A g [ l ] x 2 2 . 8 4 6 ( 5 ) 2 . 8 3 1 ( 5 ) 2 . 8 6 1 ( 5 ) T e [ 2 ] - A g [ 2 ] 2 . 8 6 0 ( 8 ) 2 . 8 3 9 ( 1 1 ) 2 . 8 8 1 ( 1 1 ) T e [ 2 ] - A g [ 2 ] 2 . 8 2 5 ( 8 ) 2 . 8 2 0 ( 1 1 ) 2 . 8 3 0 ( 1 1 ) T e [ 2 ] - K [ 2 ] x 2 3 . 4 1 4 ( 6 ) 3 . 3 7 3 ( 6 ) 3 . 4 5 5 ( 6 ) T e [ 2 ] - K [ 2 ] x 2 3 . 3 9 7 ( 6 ) 3 . 3 5 7 ( 6 ) 3 . 4 3 8 ( 6 ) T e [ 3 ] - T e [ 4 ] x 2 3 . 1 6 3 ( 6 ) 2 . 9 4 0 ( 5 ) 3 . 3 9 8 ( 6 ) T e [ 3 ] - T e [ 4 ] x 2 3 . 1 8 1 ( 6 ) 2 . 9 6 1 ( 5 ) 3 . 4 0 7 ( 6 ) T e [ 3 ] - K [ l ] x 2 3 . 4 3 6 ( 6 ) 3 . 3 3 3 ( 7 ) 3 . 5 4 3 ( 7 ) T e [ 4 ] - K [ l ] x 2 3 . 4 6 6 ( 5 ) 3 . 4 5 7 ( 5 ) 3 . 4 8 1 ( 5 ) T e [ 4 ] - K [ 2 ] x 2 3 . 5 3 6 ( 7 ) 3 . 4 5 3 ( 8 ) 3 . 6 1 9 ( 8 ) A g [ l ] - A g [ 2 ] x 4 3 . 1 6 6 ( 8 ) 3 . 1 4 3 ( 9 ) 3 . 1 9 0 ( 9 ) T a b l e 6 . 2 6 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K o . 9 7 ( 2 ) A g 2 E u 1 , 0 3 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - E u [ l ] - T e [ 1 ] x 4 8 4 3 1 ( 1 1 ) 8 3 . 5 8 ( 1 1 ) 8 5 . 0 3 ( 1 1 ) T e [ 1 ] - E u [ 1 ] - T e [ 1 ] x 4 8 3 . 4 6 ( 1 1 ) 8 3 . 2 9 ( 1 1 ) 8 3 . 6 3 ( l l ) T e [ 1 ] - E u [ 1 ] - T e [ 1 ] x 4 1 4 1 . 7 3 ( 1 4 ) 1 4 1 . 5 9 ( 1 5 ) l 4 1 . 8 8 ( 1 5 ) T e [ l ] - E u [ l ] - T e [ 3 ] x 4 7 9 4 9 ( 1 2 ) 7 8 3 0 ( 1 2 ) 8 0 . 7 3 ( 1 2 ) T e [ l ] - E u [ l ] - T e [ 3 ] x 4 1 3 2 . 8 7 ( 1 2 ) 1 3 2 . 0 7 ( 1 2 ) l 3 3 . 6 6 ( 1 2 ) T e [ 1 ] - E u [ 1 ] - T e [ 4 ] x 4 7 9 3 4 ( 1 1 ) 7 7 . 2 6 ( 1 1 ) 8 1 . 4 0 ( 1 1 ) T e [ 1 ] - E u [ 1 ] - T e [ 4 ] x 4 1 3 3 . 3 4 ( 1 4 ) 1 2 9 6 1 ( 1 3 ) 1 3 7 . 0 1 ( 1 4 ) 4 6 2 T a b l e 6 . 2 6 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K o , 9 7 ( 2 ) A g 2 E u 1 , 0 3 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 3 ] - E u [ l ] - T e [ 3 ] x 2 T e [ 3 ] - E u [ l ] - T e [ 4 ] x 4 T e [ 4 ] - E u [ l ] - T e [ 4 ] x 2 T e [ 2 ] - E u [ 2 ] - T e [ 2 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 2 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 2 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 3 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 3 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 4 ] x 4 T e [ 2 ] - E u [ 2 ] - T e [ 4 ] x 4 T e [ 4 ] - E u [ 2 ] - T e [ 4 ] x 2 E u [ 1 ] - T e [ l ] - E u [ 1 ] x 8 E u [ 1 ] - T e [ 1 ] — E u [ 1 ] x 4 E u [ 1 ] - T e [ 1 ] - A g [ 1 ] x 4 E u [ 1 ] - T e [ l ] - A g [ 1 ] x 4 E u [ 1 ] - T e [ 1 ] - A g [ 2 ] x 4 E u [ 1 ] - T e [ 1 ] - A g [ 2 ] x 4 A g [ 1 ] - T e [ 1 ] - A g [ 1 ] x 2 A g [ 1 ] - T e [ 1 ] - A g [ 2 ] x 4 A g [ 2 ] - T e [ l ] - A g [ 2 ] x 2 E u [ 2 ] - T e [ 2 ] - E u [ 2 ] x 8 E u [ 2 ] - T e [ 2 ] - E u [ 2 ] x 4 E u [ 2 ] - T e [ 2 ] - A g [ l ] x 4 E u [ 2 ] - T e [ 2 ] - A g [ l ] x 4 E u [ 2 ] - T e [ 2 ] - A g [ 2 ] x 4 E u [ 2 ] - T e [ 2 ] - A g [ 2 ] x 4 A g [ 1 ] - T e [ 2 ] - A g [ 1 ] x 2 A g [ l ] - T e [ 2 ] - A g [ 2 ] x 4 A g [ 2 ] - T e [ 2 ] - A g [ 2 ] x 2 E u [ 1 ] - T e [ 3 ] - E u [ l ] x 2 E u [ l ] - T e [ 3 ] — E u [ 2 ] x 4 E u [ l ] - T e [ 3 ] - T e [ 4 ] x 4 E u [ l ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 8 0 8 5 ( 1 2 ) 5 4 8 0 ( 1 0 ) 8 0 . 9 7 0 1 ) 8 2 . 8 9 0 6 ) 8 1 9 0 ( 1 3 ) 1 3 7 . 0 ( 2 ) 8 2 . 2 7 ( l 4 ) 1 3 4 . 7 ( 2 ) 8 2 . 7 1 ( 1 6 ) 1 3 4 . 2 9 0 6 ) 7 8 . 4 2 ( 1 5 ) 8 4 . 1 1 ( 1 2 ) 1 4 1 . 7 3 0 5 ) 7 2 . 5 2 0 7 ) 1 3 6 . 0 0 ( 1 1 ) 7 1 9 9 ( 1 9 ) 1 3 6 . 1 ( 3 ) 9 9 5 ( 3 ) 6 5 4 ( 2 ) 1 0 0 . 3 8 ( 1 8 ) 8 2 . 4 0 0 5 ) 1 3 6 . 9 8 0 8 ) 7 2 4 ( 2 ) 1 3 7 . 6 ( 3 ) 7 2 . 9 5 ( 1 8 ) 1 3 7 9 2 0 3 ) 1 0 4 . 4 ( 2 ) 6 7 . 4 2 ( 1 9 ) 1 0 3 . 5 ( 3 ) 8 0 . 8 5 0 3 ) 1 2 6 . 1 9 0 6 ) 6 3 . 2 8 ( 1 2 ) 1 1 7 . 3 1 0 5 ) 9 1 0 4 ( 1 7 ) 8 0 2 3 ( 1 4 ) 5 1 . 0 5 0 0 ) 8 0 5 2 ( 1 1 ) 8 1 . 5 5 0 6 ) 8 1 . 7 2 0 3 ) 1 3 6 . 7 ( 2 ) 8 0 3 4 ( 1 4 ) l 3 0 6 1 ( l 9 ) 8 1 9 7 ( 1 7 ) 1 3 3 . 4 1 ( 1 6 ) 7 8 0 5 ( 1 6 ) 8 3 . 9 8 ( 1 3 ) 1 4 1 . 4 7 0 4 ) 7 2 . 0 7 0 6 ) 1 3 5 . 7 5 0 1 ) 7 1 . 7 1 0 8 ) 1 3 5 . 8 ( 3 ) 9 8 6 ( 3 ) 6 5 0 ( 2 ) 1 0 0 . 0 4 0 8 ) 8 2 . 2 8 ( 1 5 ) 1 3 6 . 4 4 ( 1 8 ) 7 1 . 7 ( 2 ) 1 3 7 . 4 ( 3 ) 7 2 . 1 3 ( 1 8 ) 1 3 7 . 6 2 0 3 ) 1 0 3 . 7 0 0 0 ) 6 6 . 9 4 ( 1 5 ) 1 0 2 . 8 ( 3 ) 8 0 . 2 3 0 5 ) 1 2 2 . 1 1 ( 1 6 ) 6 0 2 2 ( 1 2 ) 1 1 5 4 9 ( 1 4 ) 8 3 6 7 ( 1 7 ) 8 1 . 3 9 0 4 ) 5 8 . 5 9 0 0 ) 8 1 . 2 1 ( 1 1 ) 8 4 . 2 3 0 7 ) 8 2 . 1 0 0 3 ) 1 3 7 . 2 ( 2 ) 8 4 . 1 6 ( l 4 ) 1 3 8 . 7 ( 2 ) 8 3 4 9 ( 1 8 ) 1 3 5 . 1 7 0 5 ) 7 8 . 7 2 0 6 ) 8 4 . 2 3 0 3 ) 1 4 1 . 9 9 0 4 ) 7 2 . 9 8 ( 1 6 ) 1 3 6 . 2 6 0 1 ) 7 2 . 2 7 0 8 ) 1 3 6 . 3 ( 3 ) 1 0 0 . 5 ( 3 ) 6 5 8 ( 2 ) 1 0 0 . 7 3 0 8 ) 8 2 . 5 0 0 6 ) 1 3 7 . 5 0 0 8 ) 7 3 . 2 ( 2 ) 1 3 7 . 9 ( 3 ) 7 3 . 7 8 0 8 ) 1 3 8 . 2 1 0 3 ) 1 0 5 . 0 ( 2 ) 6 7 . 8 9 0 5 ) 1 0 4 . 2 ( 3 ) 8 1 3 9 ( 1 5 ) 1 3 0 . 1 4 0 5 ) 6 6 . 4 5 ( l 4 ) 1 1 8 . 8 7 0 4 ) 9 8 6 ( 2 ) 4 6 3 T a b l e 6 . 2 6 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r K o , 9 7 ( 2 ) A g 2 E u 1 , 0 3 ( 2 ) T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 8 9 2 9 ( 1 3 ) 8 8 . 8 5 0 3 ) 8 9 . 9 6 0 4 ) T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 1 7 5 1 9 0 9 ) 1 7 2 . 2 7 0 9 ) 1 7 9 . 4 7 0 7 ) E u [ l ] - T e [ 4 ] - E u [ l ] x 2 8 0 . 8 8 0 2 ) 8 0 1 5 ( 1 4 ) 8 1 . 4 2 ( 1 4 ) E u [ l ] - T e [ 4 ] — E u [ 2 ] x 4 1 2 5 . 9 3 0 5 ) 1 2 2 . 2 2 0 5 ) 1 2 9 . 6 3 ( 1 5 ) E u [ l ] - T e [ 4 ] - T e [ 3 ] x 4 6 2 2 3 ( 1 1 ) 6 1 . 2 7 ( 1 1 ) 6 3 . 0 7 ( 1 1 ) E u [ l ] - T e [ 4 ] - T e [ 3 ] x 4 1 1 7 . 0 1 0 7 ) 1 1 2 . 4 7 0 8 ) 1 2 1 . 5 ( 2 ) E u [ 2 ] - T e [ 4 ] - E u [ 2 ] x 2 7 8 . 4 1 ( 1 6 ) 7 8 . 0 5 0 8 ) 7 8 . 7 2 0 8 ) E u [ 2 ] - T e [ 4 ] - T e [ 3 ] x 4 6 3 . 7 2 ( l 3 ) 6 0 9 5 ( 1 3 ) 6 6 6 7 ( 1 5 ) E u [ 2 ] - T e [ 4 ] - T e [ 3 ] x 4 1 1 6 5 4 ( 1 6 ) 1 1 5 . 0 0 0 5 ) 1 1 7 8 6 ( 1 5 ) T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 9 0 . 4 0 0 7 ) 8 2 8 9 ( 1 7 ) 9 8 . 4 ( 2 ) T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 8 9 2 9 ( 1 3 ) 8 8 . 8 5 0 1 ) 8 9 . 9 6 0 4 ) T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 1 7 5 . 1 6 0 8 ) 1 7 2 . 1 8 0 9 ) 1 7 9 . 4 4 0 7 ) T e [ l ] — A g [ l ] - T e [ l ] x 2 9 9 5 ( 2 ) 9 8 . 6 ( 2 ) 1 0 0 . 5 ( 2 ) T e [ l ] - A g [ l ] - T e [ 2 ] x 4 1 1 3 . 9 ( 2 ) 1 1 3 . 4 ( 3 ) 1 1 4 . 4 ( 3 ) T e [ l ] - A g [ l ] - A g [ 2 ] x 4 5 7 4 2 ( 1 9 ) 5 6 9 2 ( 1 9 ) 5 7 . 9 0 0 9 ) T e [ 1 ] - A g [ 1 ] - A g [ 2 ] x 4 1 2 2 . 1 9 0 9 ) 1 2 1 . 7 1 0 9 ) 1 2 2 . 6 7 0 9 ) T e [ 2 ] - A g [ l ] - T e [ 2 ] x 2 1 0 4 . 3 8 0 9 ) 1 0 3 . 2 ( 2 ) 1 0 5 . 5 ( 2 ) T e [ 2 ] - A g [ l ] - A g [ 2 ] x 4 5 6 . 5 0 ( 1 8 ) 5 6 0 6 ( 1 7 ) 5 6 9 4 ( 1 7 ) T e [ 2 ] - A g [ l ] - A g [ 2 ] x 4 1 2 4 . 8 ( 3 ) 1 2 3 . 4 ( 4 ) 1 2 6 . 1 ( 4 ) A g [ 2 ] - A g [ l ] - A g [ 2 ] x 8 9 0 5 ( 3 ) 8 9 6 ( 4 ) 9 1 4 ( 4 ) A g [ 2 ] - A g [ l ] — A g [ 2 ] x 4 1 7 9 . 1 ( 3 ) 1 7 8 . 4 ( 3 ) 1 7 9 . 6 ( 2 ) T e [ l ] - A g [ 2 ] - T e [ l ] x 2 1 0 0 3 8 0 8 ) 9 9 9 ( 2 ) 1 0 0 . 8 ( 2 ) T e [ l ] - A g [ 2 ] - T e [ 2 ] x 4 1 1 3 . 8 ( 2 ) 1 1 3 . 5 7 0 8 ) 1 1 4 . 0 5 0 7 ) T e [ l ] - A g [ 2 ] - A g [ l ] x 4 5 7 . 5 0 0 8 ) 5 7 . 1 1 0 8 ) 5 7 8 8 ( 1 8 ) T e [ l ] - A g [ 2 ] - A g [ l ] x 4 1 2 3 . 5 ( 3 ) 1 2 3 . 1 ( 2 ) 1 2 4 . 0 ( 2 ) T e [ 2 ] - A g [ 2 ] - T e [ 2 ] x 2 1 0 3 . 5 ( 2 ) 1 0 2 . 8 ( 2 ) 1 0 4 . 2 ( 2 ) T e [ 2 ] - A g [ 2 ] - A g [ l ] x 4 5 6 3 3 ( 1 9 ) 5 5 . 7 2 0 7 ) 5 6 . 9 4 ( 1 7 ) T e [ 2 ] - A g [ 2 ] - A g [ l ] x 4 1 2 3 . 2 ( 2 ) 1 2 2 . 6 6 0 9 ) 1 2 3 . 7 6 0 9 ) A g [ l ] - A g [ 2 ] - A g [ l ] x 8 9 0 4 ( 3 ) 9 0 0 ( 3 ) 9 0 7 ( 3 ) A g [ l ] - A g [ 2 ] - A g [ l ] x 4 1 7 9 . 4 ( 2 ) 1 7 9 . 3 ( 3 ) 1 7 9 . 4 4 0 9 ) 4 6 4 T a b l e 6 . 2 7 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r R b C u 2 E u T e 4 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 8 . 9 8 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ‘ ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 s t o r d e r s a t e l l i t e s [ I > 2 0 ’ ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m i n a n d T m c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e R b C u 2 E u T e 4 8 7 4 . 9 1 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A M o n o c l i n i c P m ( 0 ] 3 1 / 2 ) 0 a = 4 . 3 9 8 4 ( 7 ) A , a = 9 0 0 b = 4 . 4 2 8 1 ( 7 ) A , 1 3 = 9 0 ° c = 1 1 . 5 5 1 0 ( 1 7 ) A , y = 9 0 ° 0 . 2 6 5 6 ( 8 ) b ‘ + 1 / 2 c ' 2 2 4 . 9 7 ( 6 ) A 3 1 6 . 4 5 5 7 g / c m 3 2 9 . 3 8 9 m m ' 1 3 6 6 0 . 5 0 x 0 . 1 0 x 0 . 0 1 m m 3 2 . 9 1 t o 2 8 . 9 8 ° - 6 < = h < = 5 , - 6 < = k < = 6 , - 1 6 < = l < = 1 5 , - 1 < = m < = 1 4 3 4 5 ( 1 3 2 0 m a i n + 3 0 2 5 s a t e l l i t e s ) 2 9 0 0 ( 9 4 7 m a i n + 1 9 5 3 s a t e l l i t e s ) [ 8 , m = 0 . 0 8 1 7 ] 9 6 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 2 9 0 0 / 0 / 1 0 9 1 . 8 7 R o b , = 0 . 0 6 5 6 , w a o b , = 0 . 1 4 3 0 R . " = 0 . 1 0 7 7 , w k , “ = 0 . 1 5 1 2 R o b , = 0 . 0 5 0 9 , w R o b s = 0 . 1 3 5 2 R , “ = 0 . 0 5 2 8 , w R a u = 0 . 1 3 5 6 R o b , = 0 . 1 5 0 1 , w R o b s = 0 . 2 1 3 1 R a l l = 0 . 3 1 6 2 , w k , J l = 0 . 2 6 9 7 0 . 0 0 0 2 5 0 ) 0 . 0 4 9 6 a n d 0 . 9 0 5 7 5 . 5 3 a n d - 4 . 3 8 6 A 3 R = 2 | | F , | - | 1 = , | | / 2 1 m , w R = { 2 [ w ( | 1 ~ ‘ . , | 2 - | 1 = . | Z ) ’ - ] / 2 [ w ( | F o | 4 ) ] } ” 2 a n d w = 1 / ( 6 2 0 ) + 0 0 0 1 6 1 2 ) 4 6 5 T a b l e 6 . 2 8 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) , o c c u p a n c i e s a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r R b C u 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x y 2 O c c u p a n c y U e q E u 0 0 0 2 7 4 9 1 9 ( 1 ) s i n , 1 - 7 2 ( 5 ) 1 6 ( 4 ) - 1 ( 2 ) c o s , 1 - 6 3 ( 4 ) - 1 8 ( 5 ) - l ( 2 ) T e [ l ] 0 5 0 0 2 ( 5 ) 5 0 0 0 3 5 9 4 ( 2 ) 1 1 0 ( 1 ) s i n , 1 - 5 3 ( 5 ) 3 ( 3 ) - 2 ( 3 ) c o s , 1 - 2 5 ( 3 ) - 7 ( 7 ) - 1 ( 2 ) T e [ 2 ] 0 1 0 0 0 1 ( 4 ) 0 6 2 3 8 ( 2 ) 1 1 1 ( 1 ) s i n , 1 - 6 4 ( 5 ) - 1 ( 3 ) 5 ( 3 ) c o s , 1 2 6 ( 2 ) - 2 ( 6 ) - 2 ( 1 ) T e [ 3 ] 0 5 0 3 3 ( 7 ) 0 4 3 0 ( 2 ) 1 1 1 ( 1 ) s i n , 1 - 4 8 ( 1 ) 4 2 ( 1 3 ) 0 ( 1 ) c o s , 1 - 3 5 4 ( 1 0 ) - 6 ( 2 ) 1 ( 4 ) T e [ 4 ] 0 3 4 ( 7 ) 5 0 0 0 4 2 9 ( 2 ) 1 1 3 ( 1 ) s i n , 1 4 3 ( 1 ) - 4 3 ( 1 4 ) 0 ( 1 ) c o s , 1 3 1 8 ( 1 0 ) 6 ( 2 ) - 2 ( 4 ) C u [ 1 ] 0 3 6 ( 9 ) 5 0 0 0 5 0 2 5 ( 3 ) 1 1 7 ( 1 ) s i n , 1 0 0 0 c o s , 1 0 0 0 C u [ 2 ] 0 5 0 1 8 ( 9 ) 0 5 0 2 1 ( 3 ) 1 2 0 ( 1 ) s i n , 1 - 2 9 ( 1 1 ) 0 5 ( 6 ) c o s , 1 0 ( 1 ) 0 0 ( 1 ) R b 0 5 0 0 9 ( 7 ) 5 0 0 0 7 7 7 6 ( 3 ) l 1 1 ( 1 ) s i n , 1 - 8 6 ( 1 0 ) - 2 7 ( 1 1 ) - 6 ( 4 ) c o s , 1 1 0 3 ( 1 2 ) - 2 3 ( 9 ) 7 ( 4 ) 4 6 6 T a b l e 6 . 2 9 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r R b C u 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 E u 0 7 ( 1 ) 8 ( 1 ) 1 2 ( 1 ) 0 - 3 ( 1 ) 0 s i n , 1 - 1 0 ) 1 ( 1 ) - 2 0 ) 0 ( 1 ) 0 ( 1 ) 2 ( 1 ) c o s , 1 0 ( 1 ) 1 ( 1 ) - 2 0 ) 0 ( 1 ) 0 ( 1 ) - 2 0 ) T e [ l ] 0 8 ( 1 ) 8 ( 1 ) 1 4 ( 1 ) 0 - 2 ( 1 ) 0 s i n , 1 4 ( 1 ) 0 ( 1 ) 1 0 ( 2 ) 0 ( 1 ) 1 ( 1 ) - 1 0 ) c o s , 1 - 2 0 ) 0 ( 1 ) 5 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) T e [ 2 ] 0 8 ( 1 ) 1 1 ( 1 ) 1 4 ( 1 ) 0 . 4 0 ) 0 s i n , 1 - 3 0 ) 0 ( 1 ) 1 ( 2 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) c o s , 1 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 0 ) 0 ( 1 ) 1 ( 1 ) T e [ 3 ] 0 8 ( 1 ) 1 1 ( 1 ) 1 5 ( 1 ) 0 - 3 0 ) 0 s i n , 1 - 1 0 ) - 1 0 ) - 1 0 ) 0 ( 2 ) 0 ( 1 ) 5 2 ) c o s , 1 5 ( 2 ) - 5 ( 2 ) - 4 ( 2 ) 0 ( 1 ) - 2 ( 2 ) 1 ( 1 ) T e [ 4 ] 0 1 3 ( 1 ) 1 2 ( 1 ) 1 4 ( 1 ) 0 - 2 0 ) 0 s i n , 1 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) - 6 ( 2 ) 0 ( 1 ) 5 0 ) c o s , 1 5 ( 2 ) - 1 ( 2 ) 8 ( 3 ) 1 ( 1 ) 0 ( 2 ) 1 ( 1 ) C u [ 1 ] 0 2 4 ( 2 ) 1 7 ( 1 ) 9 ( 1 ) 0 1 ( 1 ) 0 S i n , 1 O 0 0 0 O 0 c o s , 1 0 0 O 0 0 0 C u [ 2 ] 0 1 2 ( 2 ) 3 9 ( 2 ) 9 ( 2 ) 0 1 ( 1 ) 0 s i n , 1 2 ( 2 ) - 8 ( 5 ) - 5 ( 4 ) 0 3 ( 3 ) 0 c o s , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 0 ( 1 ) 0 R b 0 1 1 ( 1 ) 1 4 ( 1 ) 9 ( 1 ) 0 4 0 ) 0 s i n , 1 0 ( 2 ) 0 ( 2 ) 4 ( 2 ) 1 ( 1 ) 2 ( 1 ) . 2 0 ) c o s , 1 0 ( 2 ) 0 ( 2 ) — 4 ( 2 ) 0 ( 1 ) - 3 ( 2 ) - 2 ( 2 ) 4 6 7 T a b l e 6 . 3 0 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r R b C u 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e E u - T e [ 1 ] x 4 3 . 2 8 6 ( 3 ) 3 . 2 6 3 ( 3 ) 3 . 3 1 0 ( 3 ) E u - T e [ 3 ] 3 . 4 1 4 ( 4 ) 3 . 3 4 2 ( 6 ) 3 . 4 8 6 ( 6 ) E u - T e [ 3 ] 3 . 4 3 1 ( 4 ) 3 . 3 5 6 ( 6 ) 3 . 5 0 9 ( 6 ) E u - T e [ 4 ] x 2 3 . 4 3 5 ( 4 ) 3 . 4 1 4 ( 5 ) 3 . 4 5 3 ( 5 ) E u - C u [ 1 ] x 2 3 . 4 8 1 ( 4 ) 3 . 4 7 4 ( 4 ) 3 . 4 8 8 ( 4 ) E u - C u [ 2 ] x 2 3 . 4 6 3 ( 6 ) 3 . 4 5 0 ( 8 ) 3 . 4 7 5 ( 7 ) T e [ l ] - C u [ 1 ] 2 . 7 4 0 ( 5 ) 2 . 7 2 0 ( 5 ) 2 . 7 5 9 ( 5 ) T e [ l ] - C u [ 1 ] 2 . 7 6 3 ( 5 ) 2 . 7 4 1 ( 5 ) 2 . 7 8 5 ( 5 ) T e [ l ] - C u [ 2 ] x 2 2 . 7 6 0 ( 4 ) 2 . 7 5 4 ( 5 ) 2 . 7 6 7 ( 5 ) T e [ 2 ] - C u [ 1 ] x 2 2 . 6 2 0 ( 3 ) 2 . 6 1 7 ( 3 ) 2 . 6 2 4 ( 3 ) T e [ 2 ] - C u [ 2 ] 2 . 6 0 4 ( 6 ) 2 . 5 8 9 ( 7 ) 2 . 6 1 9 ( 7 ) T e [ 2 ] - C u [ 2 ] 2 . 6 1 6 ( 6 ) 2 . 6 0 1 ( 7 ) 2 . 6 3 2 ( 7 ) T e [ 2 ] - R b x 4 3 . 5 8 9 ( 6 ) 3 . 5 7 1 ( 6 ) 3 . 6 0 7 ( 6 ) T e [ 3 ] - T e [ 4 ] x 4 3 . 1 2 2 ( 6 ) 2 . 9 3 2 ( 5 ) 3 . 3 2 0 ( 5 ) T e [ 3 ] - R b x 2 3 . 7 8 4 ( 7 ) 3 . 7 6 7 ( 6 ) 3 . 8 0 1 ( 7 ) T e [ 4 ] - R b x 2 3 . 7 7 9 ( 7 ) 3 . 7 4 2 ( 8 ) 3 . 8 1 6 ( 8 ) C u [ 1 ] - C u [ 2 ] x 2 3 . 1 2 6 ( 4 ) 3 . 1 1 7 ( 5 ) 3 . 1 3 5 ( 5 ) C u [ 1 ] - C u [ 2 ] x 2 3 . 1 1 5 ( 4 ) 3 . 1 0 6 ( 5 ) 3 . 1 2 4 ( 5 ) T a b l e 6 . 3 1 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r R b C u 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ l ] - E u - T e [ l ] x 4 8 4 . 7 1 ( 8 ) 8 4 1 2 ( 8 ) 8 5 2 9 ( 8 ) T e [ l ] - E u - T e [ l ] x 4 8 3 9 8 ( 8 ) 8 3 8 1 ( 8 ) 8 4 1 6 ( 8 ) T e [ 1 ] - E u - T e [ 1 ] x 4 1 4 3 . 3 7 ( 1 2 ) 1 4 3 . 2 3 ( 1 3 ) 1 4 3 . 5 2 ( 1 3 ) T e [ l ] - E u - T e [ 3 ] x 4 7 9 2 4 ( 1 0 ) 7 8 . 4 0 ( 1 0 ) 8 0 1 3 ( 1 0 ) T e [ 1 ] - E u - T e [ 3 ] x 4 1 3 2 . 1 8 ( 1 3 ) 1 3 1 . 4 3 ( 1 2 ) l 3 2 . 9 1 ( 1 2 ) T e [ l ] - E u - T e [ 4 ] x 4 7 8 . 9 8 ( 1 0 ) 7 7 . 1 1 ( 1 0 ) 8 0 8 2 ( 1 0 ) T e [ l ] - E u - T e [ 4 ] x 4 1 3 2 . 6 7 ( 1 0 ) 1 2 9 6 9 ( 1 0 ) 1 3 5 . 5 9 ( 1 0 ) T e [ l ] - E u - C u [ 1 ] x 4 4 8 0 9 ( 9 ) 4 7 . 7 1 ( 9 ) 4 8 4 7 ( 9 ) T e [ l ] - E u - C u [ 1 ] x 4 1 0 0 . 9 0 ( 1 0 ) 1 0 0 . 3 7 ( 9 ) 1 0 1 . 4 2 ( 9 ) T e [ l ] - E u - C u [ 2 ] x 4 4 8 2 0 ( 8 ) 4 7 8 4 ( 8 ) 4 8 5 4 ( 8 ) 4 6 8 T a b l e 6 . 3 1 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r R b C u 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 1 ] - E u - C u [ 2 ] x 4 T e [ 3 ] - E u - T e [ 3 ] x 2 T e [ 3 ] - E u - T e [ 4 ] x 4 T e [ 3 ] - E u - C u [ 1 ] x 2 T e [ 3 ] - E u - C u [ 2 ] x 2 T e [ 3 ] - E u - C u [ 2 ] x 2 T e [ 3 ] - E u - C u [ 1 ] x 2 T e [ 4 ] - E u - T e [ 4 ] x 2 T e [ 4 ] - E u - C u [ 1 ] x 2 T e [ 4 ] - E u - C u [ 1 ] x 2 T e [ 4 ] - E u - C u [ 2 ] x 4 C u [ 1 ] - E u - C u [ 1 ] x 2 C u [ 1 ] - E u - C u [ 2 ] x 4 C u [ 2 ] - E u - C u [ 2 ] x 2 E u - T e [ 1 ] - E u x 4 E u - T e [ 1 ] - E u x 4 E u - T e [ 1 ] - E u x 4 E u - T e [ l ] - C u [ 1 ] x 4 E u - T e [ l ] - C u [ 1 ] x 4 E u - T e [ l ] - C u [ 2 ] x 4 E u - T e [ 1 ] - C u [ 2 ] x 4 C u [ 1 ] - T e [ l ] - C u [ 1 ] x 2 C u [ 1 ] - T e [ 1 ] - C u [ 2 ] x 4 C u [ 2 ] - T e [ l ] - C u [ 2 ] x 2 C u [ 1 ] - T e [ 2 ] - C u [ 1 ] x 2 C u [ 1 ] - T e [ 2 ] - C u [ 2 ] x 4 C u [ 1 ] — T e [ 2 ] - b e 4 C u [ 1 ] - T e [ 2 ] — b e 4 C u [ 2 ] - T e [ 2 ] - C u [ 2 ] x 2 C u [ 2 ] - T e [ 2 ] - R b x 4 C u [ 2 ] - T e [ 2 ] - R b x 4 R b - T e [ 2 ] - R b x 8 R b - T e [ 2 ] - R b x 4 E u - T e [ 3 ] - E u x 2 1 0 0 . 5 1 0 2 ) 7 9 . 9 5 0 0 ) 5 4 . 2 9 0 0 ) 1 2 6 . 5 7 ( 1 0 ) 1 0 0 . 9 4 0 4 ) 1 7 9 . 1 8 0 4 ) 1 2 5 . 9 4 0 0 ) 8 0 . 3 1 0 1 ) 1 0 0 . 3 2 ( 9 ) 1 7 7 . 6 1 0 1 ) 1 2 6 . 4 8 0 1 ) 7 8 9 9 ( 7 ) 5 3 5 2 ( 1 0 ) 7 8 . 7 2 0 5 ) 8 4 . 6 7 ( 9 ) 8 3 9 8 ( 8 ) 1 4 3 . 3 8 0 3 ) 6 9 8 8 ( 9 ) 1 3 6 . 4 0 0 0 ) 6 9 4 6 ( 1 5 ) 1 3 6 . 8 4 0 7 ) 1 0 6 . 1 3 ( 1 6 ) 6 9 0 0 ( 1 5 ) 1 0 6 . 7 ( 2 ) 1 1 5 3 4 ( 1 5 ) 7 3 5 2 ( 1 3 ) 7 5 3 4 ( 1 2 ) 1 4 2 1 5 0 5 ) 1 1 4 . 8 ( 2 ) 7 5 . 6 5 ( l 4 ) 1 4 1 . 5 2 0 1 ) 7 6 . l 9 ( 1 2 ) 1 2 0 . 7 1 0 5 ) 7 9 9 5 ( 9 ) 1 0 0 . 4 5 0 2 ) 7 9 8 4 ( 1 1 ) 5 1 2 0 ( 9 ) 1 2 6 . 2 2 0 0 ) 9 9 . 9 1 0 5 ) 1 7 8 . 4 6 0 6 ) 1 2 5 . 5 9 0 0 ) 7 9 . 8 6 0 1 ) 9 9 8 8 ( 1 0 ) 1 7 5 . 9 8 0 3 ) 1 2 4 . 0 3 0 2 ) 7 8 9 4 ( 7 ) 5 3 2 5 ( 9 ) 7 8 5 5 ( 1 7 ) 8 4 4 9 ( 9 ) 8 3 8 1 ( 8 ) 1 4 3 . 1 2 0 3 ) 6 9 4 2 ( 9 ) 1 3 6 . 1 6 ( 1 1 ) 6 9 2 0 ( 1 4 ) 1 3 6 . 4 2 0 7 ) 1 0 6 . 0 4 ( 1 7 ) 6 8 . 7 4 0 5 ) 1 0 6 . 5 ( 2 ) 1 1 5 1 0 ( 1 6 ) 7 3 . 0 8 ( 1 3 ) 7 5 . 0 6 ( 1 2 ) 1 4 1 2 3 0 4 ) 1 1 4 . 8 ( 3 ) 7 5 . 0 3 0 2 ) 1 4 1 . 1 0 0 3 ) 7 5 8 6 ( 1 3 ) 1 2 0 . 0 0 0 4 ) 7 9 . 8 4 0 2 ) 1 0 0 . 5 7 0 2 ) 8 0 0 0 ( 9 ) 5 7 3 8 ( 9 ) 1 2 6 . 9 4 ( 1 0 ) 1 0 2 . 0 3 0 5 ) 1 8 0 1 2 6 . 3 0 ( 1 0 ) 8 0 6 2 ( 1 1 ) 1 0 0 . 8 1 0 0 ) 1 7 9 . 7 9 0 1 ) 1 2 8 . 8 5 ( 1 1 ) 7 9 0 4 ( 7 ) 5 3 7 7 ( 1 0 ) 7 8 . 8 8 0 7 ) 8 4 8 3 ( 9 ) 8 4 1 6 ( 8 ) 1 4 3 . 6 3 0 3 ) 7 0 3 3 ( 9 ) l 3 6 . 6 3 ( 1 1 ) 6 9 . 7 1 0 4 ) 1 3 7 . 2 5 0 7 ) 1 0 6 . 2 1 ( 1 7 ) 6 9 2 5 ( 1 5 ) 1 0 6 . 9 ( 2 ) 1 1 5 5 8 ( 1 6 ) 7 3 . 9 4 0 4 ) 7 5 . 6 2 0 2 ) 1 4 3 . 0 5 0 4 ) 1 1 4 . 8 ( 3 ) 7 6 . 2 8 ( 1 2 ) 1 4 1 . 9 5 0 2 ) 7 6 . 5 1 ( l 3 ) 1 2 1 . 4 1 0 4 ) 8 0 0 0 ( 8 ) 4 6 9 T a b l e 6 . 3 1 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r R b C u 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . E u - T e [ 3 ] - T e [ 4 ] x 4 E u - T e [ 3 ] - T e [ 4 ] x 4 E u - T e [ 3 ] - R b x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - R b x 4 T e [ 4 ] - T e [ 3 ] - R b x 4 R b - T e [ 3 ] - R b x 2 E u - T e [ 4 ] — E u x 2 E u - T e [ 4 ] - T e [ 3 ] x 4 E u - T e [ 4 ] - T e [ 3 ] x 4 E u - T e [ 4 ] - R b x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - R b x 4 T e [ 3 ] - T e [ 4 ] - R b x 4 R b - T e [ 4 ] - R b x 2 E u - C u [ 1 ] - E u x 2 E u - C u [ 1 ] - T e [ 1 ] x 4 E u - C u [ 1 ] - T e [ 2 ] x 2 E u - C u [ 1 ] - T e [ 2 ] x 2 E u - C u [ 1 ] - C u [ 2 ] x 4 E u - C u [ 1 ] - C u [ 2 ] x 4 E u - C u [ l ] - b e 2 T e [ 1 ] - C u [ 1 ] - T e [ 1 ] x 2 T e [ 1 ] - C u [ 1 ] - T e [ 2 ] x 4 T e [ 1 ] - C u [ 1 ] - C u [ 2 ] x 4 T e [ l ] - C u [ 1 ] - C u [ 2 ] x 4 T e [ 1 ] - C u [ 1 ] - R b T e [ l ] - C u [ 1 ] - R b T e [ 2 ] - C u [ 1 ] - T e [ 2 ] x 2 T e [ 2 ] - C u [ 1 ] - C u [ 2 ] x 4 6 3 . 0 8 0 0 ) 1 1 6 . 9 6 ( l 3 ) 1 2 8 . 1 6 0 4 ) 9 0 . 6 8 0 6 ) 8 9 4 0 ( 1 5 ) 1 7 5 . 7 6 0 8 ) 6 5 . 2 3 ( 1 2 ) 1 1 4 . 4 0 0 5 ) 7 1 . 6 1 0 2 ) 8 0 2 6 ( 9 ) 6 2 . 4 7 ( 1 0 ) 1 1 6 9 6 ( 1 3 ) 1 2 8 . 0 7 0 4 ) 9 0 5 5 ( 1 5 ) 8 9 4 0 ( 1 5 ) 1 7 5 8 6 0 8 ) 6 5 . 7 1 ( 1 2 ) 1 1 4 . 1 3 0 5 ) 7 1 3 2 ( 1 4 ) 7 9 0 0 ( 9 ) 6 2 2 6 ( 9 ) 8 2 8 2 ( 9 ) 1 6 1 . 8 0 0 3 ) 6 2 . 9 4 ( 1 4 ) 1 1 6 4 8 ( 1 7 ) 1 2 9 . 6 6 0 1 ) 1 0 6 . 1 3 ( 1 6 ) 1 0 8 . 3 7 0 3 ) 5 5 . 4 8 ( 1 4 ) 1 2 4 . 2 4 0 5 ) 1 6 1 . 2 9 0 7 ) 9 2 5 8 ( 1 5 ) 1 1 5 3 5 ( 1 7 ) 5 3 0 0 ( 1 3 ) 6 0 4 6 ( 1 0 ) 1 1 5 . 7 9 0 2 ) 1 2 4 . 6 5 ( 1 4 ) 8 4 . 5 6 ( 1 6 ) 8 8 . 7 2 0 4 ) 1 7 3 . 3 1 0 7 ) 6 4 . 1 6 0 1 ) 1 1 0 . 7 2 0 7 ) 7 1 . 4 0 0 4 ) 8 0 0 5 ( 1 2 ) 6 1 4 3 ( 9 ) 1 1 3 . 1 7 ( 1 6 ) 1 2 5 2 5 0 3 ) 8 4 . 6 5 0 6 ) 8 8 . 7 2 0 8 ) 1 7 3 . 4 8 ( 1 7 ) 6 3 5 7 ( 1 3 ) 1 1 2 7 8 ( 1 6 ) 7 1 . 0 7 0 5 ) 7 8 8 2 ( 9 ) 6 1 . 7 8 ( 9 ) 8 2 6 2 ( 9 ) 1 6 1 . 5 7 ( 1 3 ) 6 2 . 5 7 ( 1 4 ) 1 1 5 . 9 2 0 7 ) 1 2 8 . 7 5 0 1 ) 1 0 6 . 0 4 ( 1 7 ) 1 0 7 . 8 2 0 2 ) 5 5 3 1 ( 1 4 ) 1 2 4 . 1 1 ( 1 5 ) 1 6 0 . 3 8 0 7 ) 9 1 5 9 ( 1 5 ) 1 1 5 2 0 ( 1 7 ) 5 2 5 3 ( 1 3 ) 6 5 . 7 5 ( 1 1 ) 1 1 7 . 8 9 ( 1 2 ) 1 3 1 . 5 7 0 4 ) 9 6 . 9 8 0 9 ) 9 0 5 2 ( 1 7 ) 1 8 0 6 6 . 3 6 0 1 ) 1 1 7 . 9 4 0 8 ) 7 1 . 7 3 0 2 ) 8 0 3 7 ( 8 ) 6 3 6 4 ( 9 ) 1 2 0 . 7 6 ( 1 7 ) 1 3 0 . 8 7 0 3 ) 9 6 . 8 1 0 9 ) 9 0 5 2 ( 1 7 ) 1 8 0 6 7 9 8 ( 1 4 ) 1 1 5 . 3 3 0 5 ) 7 1 . 5 5 0 5 ) 7 9 1 6 ( 9 ) 6 2 . 7 6 ( 1 0 ) 8 3 0 2 ( 9 ) 1 6 2 . 0 4 ( 1 3 ) 6 3 . 3 1 0 4 ) 1 1 7 . 0 6 0 7 ) 1 3 0 5 5 0 1 ) 1 0 6 . 2 1 0 7 ) 1 0 8 . 9 4 0 2 ) 5 5 . 6 6 0 4 ) 1 2 4 . 3 6 0 5 ) 1 6 2 . 2 1 ( 1 7 ) 9 3 . 5 8 ( 1 5 ) 1 1 5 . 4 9 0 7 ) 5 3 4 9 ( 1 3 ) 4 7 0 T a b l e 6 . 3 1 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r R b C u 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 2 ] - C u [ 1 ] - C u [ 2 ] x 4 T e [ 2 ] - C u [ 1 ] - R b x 2 C u [ 2 ] - C u [ 1 ] - C u [ 2 ] x 8 C u [ 2 ] - C u [ 1 ] - C u [ 2 ] x 4 C u [ 2 ] - C u [ 1 ] - R b x 2 C u [ 2 ] - C u [ 1 ] - R b x 2 E u - C u [ 2 ] - E u x 2 E u - C u [ 2 ] - T e [ 1 ] x 4 E u - C u [ 2 ] - T e [ 2 ] x 2 E u - C u [ 2 ] - T e [ 2 ] x 2 E u - C u [ 2 ] - C u [ 1 ] x 4 E u - C u [ 2 ] — C u [ 1 ] x 4 T e [ 1 ] - C u [ 2 ] - T e [ 1 ] x 2 T e [ l ] - C u [ 2 ] - T e [ 2 ] x 4 T e [ 1 ] - C u [ 2 ] - C u [ 1 ] x 4 T e [ 1 ] - C u [ 2 ] - C u [ 1 ] x 4 T e [ 2 ] - C u [ 2 ] - T e [ 2 ] x 2 T e [ 2 ] - C u [ 2 ] - C u [ 1 ] x 4 T e [ 2 ] - C u [ 2 ] - C u [ 1 ] x 4 C u [ 1 ] - C u [ 2 ] - C u [ 1 ] x 4 C u [ 1 ] - C u [ 2 ] - C u [ 1 ] x 4 C u [ 1 ] - C u [ 2 ] - C u [ 1 ] x 4 T e [ 2 ] - R b - T e [ 2 ] x 8 T e [ 2 ] - R b - T e [ 2 ] x 4 T e [ 2 ] - R b - T e [ 3 ] x 4 T e [ 2 ] - R b - T e [ 3 ] x 4 T e [ 2 ] - R b - T e [ 4 ] x 4 T e [ 2 ] - R b - T e [ 4 ] x 4 T e [ 2 ] - R b - C u [ 1 ] x 2 T e [ 2 ] - R b - C u [ 1 ] x 2 T e [ 3 ] - R b - T e [ 3 ] x 2 T e [ 3 ] - R b - T e [ 4 ] x 4 T e [ 3 ] - R b - C u [ 1 ] x 2 T e [ 4 ] - R b - T e [ 4 ] x 2 1 2 6 . 5 3 ( 1 9 ) 6 4 . 0 8 0 2 ) 9 0 . 1 8 0 4 ) 1 7 9 . 6 7 0 8 ) l l 3 . 6 8 ( l 4 ) 6 6 5 8 ( 1 4 ) 7 8 . 7 2 0 2 ) 6 2 . 4 4 ( 1 3 ) 8 3 0 4 ( 1 5 ) 1 6 2 . 1 ( 2 ) 6 3 . 5 2 ( 1 1 ) 1 1 6 . 7 4 0 4 ) 1 0 6 . 7 ( 2 ) 1 0 8 . 5 9 ( 1 4 ) 5 5 1 9 ( 1 0 ) 1 2 4 . 7 ( 2 ) 1 1 4 . 8 ( 2 ) 5 3 5 5 ( 1 1 ) 1 2 6 . 4 8 ( 1 4 ) 9 0 . 6 0 0 5 ) 8 9 6 1 ( 7 ) 1 7 9 . 6 2 0 8 ) 7 6 0 9 ( 1 2 ) 1 2 0 . 7 0 0 8 ) 9 2 4 0 ( 1 3 ) 1 3 9 . 7 4 0 8 ) 9 2 . 6 4 ( 1 5 ) 1 3 9 . 4 2 0 7 ) 4 0 9 9 ( 8 ) 8 6 . 5 1 ( 1 3 ) 7 1 . 6 6 ( l 4 ) 4 8 . 8 9 0 2 ) 1 3 2 . 0 1 0 5 ) 7 1 . 3 2 0 3 ) 1 2 5 . 8 8 0 9 ) 6 3 . 6 2 ( 1 2 ) 8 9 . 9 6 0 4 ) 1 7 9 . 5 7 0 4 ) 1 1 3 . 2 3 0 3 ) 6 6 1 6 ( 1 5 ) 7 8 5 5 ( 1 7 ) 6 2 . 2 8 ( 1 1 ) 8 2 . 5 5 ( 1 8 ) 1 6 1 . 6 ( 3 ) 6 3 . 2 9 ( 1 1 ) 1 1 6 . 5 1 0 4 ) 1 0 6 . 5 ( 3 ) 1 0 8 . 2 4 ( 1 3 ) 5 4 . 8 0 0 0 ) 1 2 4 . 3 2 0 6 ) 1 1 4 . 8 ( 3 ) 5 3 . 4 5 0 2 ) 1 2 6 . 1 9 0 8 ) 9 0 2 6 ( 1 8 ) 8 9 6 1 ( 7 ) 1 7 9 4 6 0 8 ) 7 5 . 2 9 ( 1 2 ) 1 2 0 1 9 0 9 ) 9 0 7 1 ( 1 3 ) 1 3 6 . 4 7 0 7 ) 9 2 0 7 ( 1 5 ) 1 3 8 . 7 6 0 7 ) 4 0 5 0 ( 7 ) 8 6 2 1 ( 1 3 ) 7 1 0 5 ( 1 4 ) 4 6 . 0 5 ( 1 2 ) 1 2 9 . 3 4 ( 1 6 ) 7 1 . 0 7 0 3 ) 1 2 7 . 1 8 0 9 ) 6 4 5 4 ( 1 2 ) 9 0 . 4 0 0 4 ) 1 7 9 . 7 4 0 9 ) 1 1 4 . 1 2 0 3 ) 6 6 . 9 9 ( 1 5 ) 7 8 . 8 8 0 7 ) 6 2 . 6 1 0 1 ) 8 3 . 5 4 ( 1 9 ) 1 6 2 . 6 ( 3 ) 6 3 7 6 ( 1 2 ) 1 1 6 . 9 6 ( 1 4 ) 1 0 6 . 8 ( 3 ) 1 0 8 . 9 4 0 3 ) 5 5 . 5 8 ( 1 0 ) 1 2 5 . 0 9 ( 1 6 ) 1 1 4 . 8 ( 3 ) 5 3 . 6 5 0 2 ) 1 2 6 . 7 7 0 8 ) 9 0 . 9 2 0 8 ) 8 9 6 1 ( 7 ) 1 7 9 . 7 4 0 6 ) 7 6 . 8 9 0 3 ) 1 2 1 . 2 0 0 9 ) 9 4 0 3 ( 1 3 ) 1 4 3 . 0 0 0 7 ) 9 3 2 3 ( 1 5 ) 1 4 0 . 0 7 ( 1 6 ) 4 1 4 8 ( 8 ) 8 6 8 2 ( 1 3 ) 7 2 . 1 3 0 4 ) 5 1 . 7 2 0 3 ) 1 3 4 . 5 8 0 5 ) 7 1 . 5 5 0 4 ) 4 7 1 T a b l e 6 . 3 2 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r R b A g 2 E u T e 4 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 1 3 0 R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 6 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R l S t o r d e r s a t e l l i t e s [ I > 2 0 ’ ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m i n a n d T m c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e R b A g 2 E u T e 4 9 6 3 . 6 1 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A M o n o c l i n i c P m ( O B l / 2 ) 0 a = 4 . 4 8 1 4 ( 7 ) A , a = 9 0 0 b = 4 . 4 9 2 8 ( 8 ) A , 1 3 = 9 0 ° c = 1 1 . 9 1 9 9 ( 1 9 ) A , y = 9 0 ° 0 . 2 6 2 5 ( 7 ) b ‘ + 1 / 2 c ‘ 2 4 0 0 0 0 ) A 3 1 6 . 6 6 4 8 g / c m 3 2 7 . 1 4 m i n " 4 0 2 0 . 2 0 x 0 . 1 6 x 0 . 0 2 m m 3 2 . 8 2 t o 2 9 . 1 3 ° - 6 < = h < = 6 , - 6 < = k < = 5 , - 1 6 < = 1 < = 1 6 , - l < = m < = 1 5 5 7 8 ( 1 7 3 8 m a i n + 3 8 4 0 s a t e l l i t e s ) 3 3 5 4 ( 1 1 5 5 m a i n + 2 1 9 9 s a t e l l i t e s ) [ R i m = 0 . 0 3 6 8 ] 9 9 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 3 3 5 4 / 0 / 1 2 1 2 . 2 6 R o b , = 0 . 0 5 3 3 , w R o b s = 0 . 1 4 2 7 R a l l = 0 . 0 7 5 5 , a n l = 0 . 1 5 2 2 R o b , = 0 . 0 3 6 9 , w R o b , = 0 . 1 1 4 1 R , 1 1 = 0 . 0 3 7 4 , w k , “ = 0 . 1 1 4 3 R o b , = 0 . 1 3 8 9 , w R o b s = 0 . 2 3 3 8 R , l l = 0 . 2 3 5 5 , w R . . . = 0 . 2 6 4 3 0 . 0 0 0 6 0 ( 7 ) 0 . 0 3 0 4 a n d 0 . 5 4 1 1 5 . 1 6 a n d - 8 . 5 3 6 A 3 R = Z | | F o | - | F c | | / 2 1 1 : 1 , w R = { 2 [ w ( | 1 i ? — 1 1 0 1 6 2 ] / 2 [ w ( | 1 = , | 4 ) ] } " 2 a n d w = l / ( O ' 2 ( I ) + 0 . 0 0 1 6 I Z ) 4 7 2 T a b l e 6 . 3 3 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) , o c c u p a n c i e s a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r R b A g 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x y z O c c u p a n c y U 1 , q E u 0 0 0 2 7 4 9 1 9 ( 1 ) s i n , 1 9 2 ( 3 ) - 1 3 ( 2 ) — 4 ( 1 ) c o s , 1 8 1 ( 2 ) 1 5 ( 2 ) - 3 ( 1 ) T e [ l ] 0 5 0 0 0 ( 4 ) 5 0 0 0 3 5 3 0 ( 1 ) 1 1 0 ( 1 ) s i n , 1 2 4 ( 3 ) - 2 ( 2 ) 2 ( 2 ) c o s , 1 1 2 ( 2 ) 5 ( 3 ) 1 ( 1 ) T e [ 2 ] 0 - 2 ( 3 ) 0 6 5 5 0 ( 1 ) 1 1 1 ( 1 ) s i n , 1 4 7 ( 3 ) 5 ( 2 ) 1 ( 2 ) c o s , 1 - 2 5 ( 2 ) 9 ( 3 ) 0 ( 1 ) T e [ 3 ] 0 4 9 9 8 ( 4 ) 0 5 0 7 ( 1 ) 1 1 7 ( 1 ) s i n , 1 0 ( 1 ) - 9 ( 5 ) 0 ( 1 ) c o s , 1 1 ( 5 ) 1 ( 1 ) - 2 ( 2 ) T e [ 4 ] 0 - 7 ( 4 ) 5 0 0 0 5 0 3 ( 1 ) 1 1 8 ( 1 ) s i n , 1 - 4 ( 1 ) - 7 ( 5 ) 0 ( 1 ) c o s , 1 - 2 8 ( 6 ) 1 ( 1 ) - 2 ( 2 ) A g [ 1 ] 0 3 ( 5 ) 5 0 0 0 5 1 4 6 ( 2 ) 1 1 2 ( 1 ) s i n , 1 - 3 1 1 ( 5 ) - 2 ( 1 ) - 4 ( 2 ) c o s , 1 1 4 ( 1 ) - 3 9 ( 6 ) 0 ( 1 ) A g [ 2 ] 0 5 0 0 1 ( 6 ) O 5 1 4 6 ( 2 ) 1 1 0 ( 1 ) s i n , 1 4 0 6 ( 5 ) 5 ( 1 ) - 1 ( 2 ) c o s , 1 - 1 9 ( 1 ) 1 0 5 ( 6 ) 0 ( 1 ) R b 0 5 0 0 2 ( 5 ) 5 0 0 0 7 9 3 2 ( 2 ) 1 1 1 ( 1 ) s i n , 1 3 2 ( 5 ) 1 2 ( 4 ) - 2 ( 2 ) c o s , 1 - 4 2 ( 6 ) 9 ( 3 ) 3 ( 2 ) 4 7 3 T a b l e 6 . 3 4 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r R b A g 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 E u 0 7 ( 1 ) 6 ( 1 ) 1 4 ( 1 ) 0 - 1 ( 1 ) 0 s i n , 1 0 ( 1 ) 1 ( 1 ) 2 ( 1 ) 0 ( 1 ) 3 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 1 ( 1 ) 2 ( 1 ) 0 ( 1 ) 3 ( 1 ) 0 ( 1 ) T e [ l ] 0 8 ( 1 ) 6 ( 1 ) 1 4 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 1 ( 1 ) 1 ( 1 ) - 2 ( 1 ) 0 ( 1 ) 6 ( 1 ) — 1 ( 1 ) c o s , 1 1 ( 1 ) 0 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) 3 ( 1 ) 1 ( 1 ) T e [ 2 ] 0 9 ( 1 ) 7 ( 1 ) 1 6 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 3 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 0 ( 1 ) T e [ 3 ] 0 2 3 ( 1 ) 1 4 ( 1 ) 1 3 ( 1 ) 0 - 1 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) T e [ 4 ] 0 2 6 ( 1 ) 1 4 ( 1 ) 1 3 ( 1 ) 0 - 1 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 3 ( 1 ) 0 ( 1 ) A g [ l ] 0 1 2 ( 1 ) 8 ( 1 ) 1 5 ( 1 ) 0 - 1 ( 1 ) 0 s i n , 1 - 1 ( 2 ) - 1 ( 1 ) 9 ( 2 ) 0 ( 1 ) 0 ( 2 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 5 ( 1 ) 0 ( 1 ) 2 ( 1 ) A g [ 2 ] 0 2 ( 1 ) 1 2 ( 1 ) 1 5 ( 1 ) 0 - 1 ( 1 ) 0 s i n , 1 - 1 ( 2 ) - 1 ( 1 ) 0 ( 2 ) 0 ( 1 ) 2 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 4 ( 1 ) 0 ( 1 ) 3 ( 1 ) R b 0 1 2 ( 1 ) 1 0 ( 1 ) 1 3 ( 1 ) 0 - 1 ( 1 ) 0 s i n , 1 - 1 ( 1 ) 0 ( 1 ) 4 ( 1 ) 1 ( 1 ) 0 ( 1 ) - 1 ( 1 ) c o s , 1 1 ( 1 ) 0 ( 1 ) - 6 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 4 7 4 T a b l e 6 . 3 5 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r R b A g 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e E u - T e [ l ] x 4 3 . 3 2 4 ( 2 ) 3 . 2 8 6 ( 2 ) 3 . 3 6 1 ( 2 ) E u - T e [ 3 ] x 2 3 . 4 4 5 ( 3 ) 3 . 4 1 5 ( 3 ) 3 . 4 7 4 ( 3 ) E u - T e [ 4 ] x 2 3 . 4 5 1 ( 2 ) 3 . 4 4 5 ( 2 ) 3 . 4 5 6 ( 2 ) E u - A g [ l ] x 2 3 . 6 8 3 ( 3 ) 3 . 6 6 4 ( 3 ) 3 . 6 9 8 ( 3 ) E u - A g [ 2 ] x 2 3 . 6 7 7 ( 3 ) 3 . 6 0 0 ( 4 ) 3 . 7 5 6 ( 4 ) T e [ l ] - A g [ l ] x 2 2 . 9 5 7 ( 3 ) 2 . 8 5 1 ( 4 ) 3 . 0 6 3 ( 4 ) T e [ l ] - A g [ 2 ] x 2 2 . 9 6 0 ( 3 ) 2 . 9 3 4 ( 3 ) 2 . 9 8 2 ( 3 ) T e [ 2 ] - A g [ l ] x 2 2 . 8 0 3 ( 3 ) 2 . 7 7 9 ( 3 ) 2 . 8 2 3 ( 3 ) T e [ 2 ] - A g [ 2 ] x 2 2 . 7 9 9 ( 4 ) 2 . 6 7 9 ( 4 ) 2 . 9 2 2 ( 4 ) T e [ 2 ] - R b x 4 3 . 5 7 4 ( 3 ) 3 . 5 5 8 ( 3 ) 3 . 5 9 0 ( 3 ) T e [ 3 ] - T e [ 4 ] x 4 3 . 1 7 4 ( 3 ) 3 . 1 6 4 ( 3 ) 3 . 1 8 5 ( 3 ) T e [ 3 ] - R b x 2 3 . 8 0 3 ( 4 ) 3 . 7 9 7 ( 4 ) 3 . 8 0 8 ( 4 ) T e [ 4 ] - R b x 2 3 . 7 9 4 ( 4 ) 3 . 7 8 8 ( 5 ) 3 . 7 9 9 ( 5 ) A g [ l ] - A g [ 2 ] x 4 3 . 1 7 6 ( 4 ) 2 . 9 7 0 ( 3 ) 3 . 3 9 1 ( 4 ) T a b l e 6 . 3 6 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r R b A g 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ l ] - E u - T e [ l ] x 8 8 5 . 0 4 ( 5 ) 8 4 . 1 2 ( 5 ) 8 5 . 9 9 ( 5 ) T e [ l ] - E u - T e [ l ] x 4 1 4 5 . 3 4 ( 7 ) 1 4 5 . 1 3 ( 7 ) 1 4 5 . 5 5 ( 7 ) T e [ l ] - E u - T e [ 3 ] x 4 7 7 . 7 1 ( 5 ) 7 6 9 0 ( 5 ) 7 8 5 5 ( 5 ) T e [ l ] - E u - T e [ 3 ] x 4 1 3 1 . 6 5 ( 6 ) 1 3 1 . 4 8 ( 6 ) 1 3 l . 8 3 ( 6 ) T e [ l ] - E u - T e [ 4 ] x 4 7 7 6 0 ( 5 ) 7 6 9 7 ( 5 ) 7 8 2 3 ( 5 ) T e [ l ] - E u - T e [ 4 ] x 4 1 3 1 . 7 0 ( 6 ) l 3 0 . 4 3 ( 6 ) 1 3 3 . 0 0 ( 6 ) T e [ l ] - E u - A g [ l ] x 4 4 9 5 6 ( 6 ) 4 7 2 0 ( 6 ) 5 1 9 6 ( 6 ) T e [ l ] - E u - A g [ l ] x 4 1 0 0 1 4 ( 6 ) 9 8 0 7 ( 6 ) 1 0 2 . 2 2 ( 6 ) T e [ l ] - E u - A g [ 2 ] x 4 4 9 7 0 ( 4 ) 4 9 0 4 ( 5 ) 5 0 3 5 ( 5 ) T e [ l ] - E u - A g [ 2 ] x 4 1 0 0 . 0 7 ( 6 ) 9 8 6 0 ( 6 ) 1 0 1 . 4 8 ( 6 ) T e [ 3 ] - E u - T e [ 3 ] x 2 8 1 . 1 8 ( 5 ) 8 1 0 4 ( 6 ) 8 1 3 0 ( 6 ) T e [ 3 ] - E u - T e [ 4 ] x 4 5 4 7 6 ( 5 ) 5 4 4 1 ( 5 ) 5 5 . 1 2 ( 5 ) T e [ 3 ] - E u - A g [ l ] x 4 1 2 6 . 9 3 ( 6 ) 1 2 4 . 1 7 ( 6 ) 1 2 9 . 7 1 ( 6 ) T e [ 3 ] - E u - A g [ 2 ] x 2 1 0 1 . 8 4 ( 7 ) 1 0 1 . 0 2 ( 8 ) 1 0 2 . 6 8 ( 8 ) 4 7 5 T a b l e 6 . 3 6 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r R b A g 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 3 ] - E u - A g [ 2 ] x 2 T e [ 4 ] - E u - T e [ 4 ] x 2 T e [ 4 ] - E u - A g [ 1 ] x 2 T e [ 4 ] - E u - A g [ 1 ] x 2 T e [ 4 ] - E u - A g [ 2 ] x 4 A g [ 1 ] - E u - A g [ 1 ] x 2 A g [ 1 ] - E u - A g [ 2 ] x 4 A g [ 2 ] - E u - A g [ 2 ] x 2 E u - T e [ 1 ] - E u x 8 E u - T e [ 1 ] - E u x 4 E u - T e [ 1 ] - A g [ 1 ] x 4 E u - T e [ 1 ] - A g [ 1 ] x 4 E u - T e [ 1 ] - A g [ 2 ] x 4 E u - T e [ l ] - A g [ 2 ] x 4 A g [ 1 ] - T e [ 1 ] - A g [ 1 ] x 2 A g [ 1 ] - T e [ 1 ] - A g [ 2 ] x 4 A g [ 2 ] - T e [ l ] - A g [ 2 ] x 2 A g [ 1 ] - T e [ 2 ] - A g [ 1 ] x 2 A g [ l ] - T e [ 2 ] - A g [ 2 ] x 4 A g [ 1 ] - T e [ 2 ] - R b x 4 A g [ l ] - T e [ 2 ] - R b x 4 A g [ 2 ] - T e [ 2 ] - A g [ 2 ] x 2 A g [ 2 ] - T e [ 2 ] - R b x 4 A g [ 2 ] - T e [ 2 ] - R b x 4 R b - T e [ 2 ] - R b x 8 R b - T e [ 2 ] - R b x 4 E u - T e [ 3 ] - E u x 2 E u - T e [ 3 ] - T e [ 4 ] x 4 E u - T e [ 3 ] - T e [ 4 ] x 4 E u - T e [ 3 ] - R b x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 8 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - R b x 4 T e [ 4 ] - T e [ 3 ] - R b x 4 1 7 6 . 9 3 ( 8 ) 8 1 2 3 ( 5 ) 1 0 1 . 7 4 ( 5 ) 1 7 6 . 0 6 ( 6 ) 1 2 6 . 9 5 ( 6 ) 7 5 2 1 ( 5 ) 5 1 1 2 ( 5 ) 7 5 1 0 ( 8 ) 8 5 0 6 ( 6 ) 1 4 5 . 3 5 ( 8 ) 7 1 5 3 ( 6 ) l 3 4 . 8 3 ( 5 ) 7 1 3 4 ( 7 ) 1 3 4 . 9 6 0 0 ) 9 8 5 6 ( 1 0 ) 6 4 9 3 ( 9 ) 9 8 8 6 ( 9 ) 1 0 6 . 6 0 0 0 ) 6 9 0 4 ( 8 ) 7 6 7 8 ( 7 ) 1 4 1 . 2 0 ( 9 ) 1 0 6 . 3 4 ( 1 2 ) 7 7 0 1 ( 8 ) 1 4 1 . 0 7 ( 7 ) 7 7 8 9 ( 7 ) 1 2 5 0 ( 9 ) 8 1 1 8 ( 6 ) 6 2 7 1 ( 5 ) 1 1 7 . 3 9 ( 7 ) 1 2 7 . 8 2 ( 7 ) 9 0 0 9 ( 8 ) 1 7 9 7 7 ( 9 ) 6 5 2 5 ( 7 ) 1 1 4 . 6 7 ( 9 ) 1 7 6 . 0 6 ( 8 ) 8 1 0 5 ( 5 ) 1 0 1 . 2 3 ( 5 ) 1 7 5 . 1 4 ( 6 ) 1 2 6 . 7 4 ( 6 ) 7 4 . 7 3 ( 5 ) 4 8 1 8 ( 5 ) 7 5 0 4 ( 8 ) 8 4 3 8 ( 6 ) 1 4 5 . 0 1 ( 8 ) 7 0 4 7 ( 6 ) 1 3 3 7 4 ( 5 ) 6 9 1 6 ( 7 ) 1 3 1 . 7 1 0 0 ) 9 8 1 1 ( 1 1 ) 6 1 3 6 ( 8 ) 9 7 8 0 ( 1 0 ) 1 0 5 8 0 0 0 ) 6 5 6 0 ( 8 ) 7 4 7 8 ( 8 ) 1 3 7 . 8 6 ( 9 ) 1 0 6 . 0 2 ( 1 3 ) 7 5 4 6 ( 8 ) 1 4 0 . 1 6 ( 8 ) 7 7 8 2 ( 7 ) 1 2 4 . 8 4 0 0 ) 8 1 0 4 ( 7 ) 6 2 3 9 ( 6 ) 1 1 6 . 9 6 ( 8 ) 1 2 7 . 5 5 ( 7 ) 8 9 8 9 ( 9 ) 1 7 9 . 6 6 0 0 ) 6 5 0 0 ( 7 ) 1 1 4 3 5 ( 1 0 ) 1 7 7 . 7 6 ( 8 ) 8 1 4 0 ( 5 ) 1 0 2 . 3 0 ( 5 ) 1 7 7 . 5 9 ( 6 ) 1 2 7 . 1 4 ( 6 ) 7 5 5 7 ( 5 ) 5 4 1 5 ( 6 ) 7 5 1 3 ( 7 ) 8 5 7 2 ( 6 ) 1 4 5 7 0 ( 8 ) 7 2 . 6 7 ( 7 ) 1 3 5 9 4 ( 5 ) 7 3 4 8 ( 7 ) 1 3 8 . 1 8 0 0 ) 9 8 . 8 8 0 1 ) 6 8 4 7 ( 9 ) 9 9 7 0 ( 1 0 ) 1 0 7 . 2 1 0 0 ) 7 2 5 7 ( 8 ) 7 8 8 4 ( 8 ) 1 4 4 . 6 1 ( 1 0 ) 1 0 6 5 1 ( 1 2 ) 7 8 5 8 ( 8 ) 1 4 2 0 0 ( 8 ) 7 7 9 5 ( 7 ) 1 2 5 . 3 6 ( 9 ) 8 1 3 0 ( 7 ) 6 3 0 2 ( 6 ) 1 1 7 . 8 3 ( 8 ) 1 2 8 . 0 9 ( 7 ) 9 0 2 9 ( 9 ) 1 7 9 . 8 5 ( 8 ) 6 5 5 0 ( 7 ) 1 1 4 . 9 9 0 0 ) 4 7 6 T a b l e 6 . 3 6 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r R b A g 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . R b - T e [ 3 ] - R b x 2 E u - T e [ 4 ] - E u x 2 E u - T e [ 4 ] - T e [ 3 ] x 4 E u - T e [ 4 ] - T e [ 3 ] x 4 E u - T e [ 4 ] - R b x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 8 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - R b x 4 T e [ 3 ] - T e [ 4 ] - R b x 4 R b - T e [ 4 ] - R b x 2 E u - A g [ l ] - E u x 2 E u - A g [ l ] - T e [ 1 ] x 4 E u - A g [ 1 ] - T e [ 2 ] x 2 E u - A g [ l ] - T e [ 2 ] x 2 E u - A g [ 1 ] - A g [ 2 ] x 4 E u - A g [ 1 ] - A g [ 2 ] x 4 T e [ 1 ] - A g [ 1 ] - T e [ 1 ] x 2 T e [ 1 ] - A g [ 1 ] - T e [ 2 ] x 4 T e [ 1 ] - A g [ 1 ] - A g [ 2 ] x 4 T e [ 1 ] - A g [ 1 ] - A g [ 2 ] x 4 T e [ 2 ] - A g [ l ] - T e [ 2 ] x 2 T e [ 2 ] - A g [ l ] - A g [ 2 ] x 4 T e [ 2 ] - A g [ l ] - A g [ 2 ] x 4 A g [ 2 ] - A 8 1 1 ] - A g [ 2 ] X 4 A g [ 2 ] - A 8 1 1 ] - A g [ 2 ] X 4 A g [ 2 ] - A 8 1 1 ] - A g [ 2 ] X 4 E u - A g [ 2 ] - E u x 2 E u - A g [ 2 ] - T e [ 1 ] x 4 E u - A g [ 2 ] - T e [ 2 ] x 2 E u - A g [ 2 ] - T e [ 2 ] x 2 E u - A g [ 2 ] - A g [ 1 ] x 4 E u - A g [ 2 ] - A g [ 1 ] x 4 T e [ 1 ] - A g [ 2 ] - T e [ 1 ] x 2 T e [ l ] - A g [ 2 ] - T e [ 2 ] x 4 7 2 4 1 ( 6 ) 8 1 2 4 ( 6 ) 6 2 5 2 ( 5 ) 1 1 7 . 4 5 ( 8 ) 1 2 7 . 8 6 ( 7 ) 9 0 2 0 ( 8 ) 1 7 9 7 4 ( 9 ) 6 5 4 7 ( 7 ) 1 1 4 7 2 ( 8 ) 7 2 3 5 ( 8 ) 7 5 1 8 ( 5 ) 5 8 9 0 ( 6 ) 8 8 9 9 ( 6 ) 1 6 3 . 7 4 ( 9 ) 6 4 3 0 ( 7 ) 1 1 5 5 7 ( 1 0 ) 9 8 5 6 ( 1 0 ) 1 1 2 9 2 ( 9 ) 5 7 6 9 ( 8 ) 1 2 2 . 1 9 0 0 ) 1 0 6 . 5 3 0 0 ) 5 5 3 4 ( 8 ) 1 2 4 . 6 3 ( 1 1 ) 9 0 3 9 ( 1 0 ) 8 9 6 2 ( 8 ) 1 7 5 . 6 4 ( 1 1 ) 7 5 1 0 ( 6 ) 5 8 9 4 ( 7 ) 8 9 2 8 ( 9 ) 1 6 4 . 3 5 0 2 ) 6 4 5 9 ( 8 ) 1 1 5 3 9 ( 9 ) 9 8 7 3 ( 9 ) 1 1 2 9 2 ( 1 0 ) 7 2 2 9 ( 7 ) 8 0 9 3 ( 7 ) 6 1 8 3 ( 5 ) 1 1 6 4 6 ( 8 ) 1 2 7 . 3 1 ( 7 ) 8 9 . 8 4 0 0 ) 1 7 9 6 2 ( 1 0 ) 6 5 3 7 ( 7 ) 1 1 4 . 5 0 ( 8 ) 7 2 3 1 ( 9 ) 7 4 8 3 ( 7 ) 5 7 3 4 ( 6 ) 8 8 2 9 ( 8 ) 1 6 2 8 4 0 0 ) 6 3 8 1 ( 7 ) 1 1 1 4 1 ( 1 0 ) 9 8 . 1 1 0 2 ) 1 0 9 1 9 ( 9 ) 5 4 1 9 ( 7 ) 1 1 9 . 8 8 ( 1 0 ) 1 0 6 . 1 2 ( 1 2 ) 5 5 0 8 ( 7 ) 1 1 9 4 0 0 2 ) 8 3 0 4 ( 9 ) 8 8 3 8 ( 9 ) 1 7 3 0 0 0 1 ) 7 5 0 4 ( 7 ) 5 7 4 1 ( 7 ) 8 5 . 9 8 0 0 ) 1 6 0 7 4 ( 1 3 ) 6 1 . 7 9 ( 8 ) 1 1 3 . 8 3 ( 9 ) 9 8 2 4 ( 1 1 ) 1 0 8 . 8 7 0 0 ) 7 2 5 4 ( 7 ) 8 1 5 3 ( 7 ) 6 3 2 0 ( 5 ) 1 1 8 . 4 1 ( 8 ) 1 2 8 . 3 9 ( 7 ) 9 0 5 6 ( 1 0 ) 1 7 9 . 8 5 ( 8 ) 6 5 5 8 ( 7 ) 0 4 9 5 ( 8 ) 7 2 3 9 ( 9 ) 7 5 4 3 ( 7 ) 6 0 4 0 ( 6 ) 8 9 8 3 ( 9 ) 1 6 5 . 0 9 ( 1 0 ) 6 4 6 3 ( 8 ) 1 1 9 6 1 ( 1 2 ) 9 8 8 8 ( 1 2 ) 0 6 5 8 ( 8 ) 6 1 3 2 ( 9 ) 1 2 4 . 3 8 0 0 ) 1 0 6 . 7 3 ( 9 ) 5 5 6 8 ( 7 ) 1 2 9 7 4 0 4 ) 9 7 9 4 ( 1 2 ) 9 1 3 7 ( 9 ) 1 8 0 7 5 1 3 ( 5 ) 6 0 4 6 ( 7 ) 9 2 . 7 7 0 1 ) 1 6 7 . 9 9 0 4 ) 6 7 5 7 ( 9 ) 1 1 6 9 7 ( 9 ) 9 9 0 1 ( 1 0 ) 1 1 7 . 0 6 0 0 ) 4 7 7 T a b l e 6 3 6 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r R b A g 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 1 ] - A g [ 2 ] - A g [ l ] x 4 T e [ 1 ] - A g [ 2 ] - A g [ 1 ] x 4 T e [ 2 ] - A g [ 2 ] - T e [ 2 ] x 2 T e [ 2 ] - A g [ 2 ] - A g [ l ] x 4 T e [ 2 ] - A g [ 2 ] - A g [ l ] x 4 A 8 1 1 ] - A g [ 2 ] - A 8 1 1 ] X 4 A 8 1 1 ] - A g [ 2 1 - A 8 1 1 ] X 4 A 8 0 ] - A g [ 2 ] - A 8 1 1 ] X 4 T e [ 2 ] - R b - T e [ 2 ] x 8 T e [ 2 ] - R b - T e [ 2 ] x 4 T e [ 2 ] - R b - T e [ 3 ] x 4 T e [ 2 ] - R b - T e [ 3 ] x 4 T e [ 2 ] - R b - T e [ 4 ] x 4 T e [ 2 ] - R b - T e [ 4 ] x 4 T e [ 3 ] - R b - T e [ 3 ] x 2 T e [ 3 ] - R b - T e [ 4 ] x 4 T e [ 4 ] - R b - T e [ 4 ] x 2 5 7 4 2 ( 8 ) 1 2 2 5 4 0 2 ) 1 0 6 3 4 0 1 ) 5 5 6 0 ( 8 ) 1 2 4 . 2 3 0 0 ) 9 0 3 5 ( 1 0 ) 8 9 6 2 ( 8 ) 1 7 5 . 3 8 ( 1 1 ) 7 7 8 2 ( 7 ) 1 2 5 . 1 0 0 0 ) 9 0 0 2 ( 6 ) 1 3 7 . 9 4 0 0 ) 9 0 0 6 ( 8 ) 1 3 7 . 8 9 ( 7 ) 7 2 4 1 ( 7 ) 4 9 3 6 ( 6 ) 7 2 3 5 ( 7 ) 5 6 8 1 ( 7 ) 1 1 7 4 1 ( 1 3 ) 1 0 6 . 0 2 ( 1 3 ) 5 2 0 9 ( 7 ) 1 2 1 . 8 3 ( 9 ) 8 3 . 0 7 ( 1 0 ) 8 8 3 8 ( 9 ) 1 7 2 . 7 5 0 1 ) 7 7 8 0 ( 7 ) 1 2 4 . 8 5 ( 1 0 ) 8 9 6 8 ( 6 ) 1 3 7 . 4 2 0 0 ) 8 9 8 3 ( 8 ) 1 3 7 . 5 6 ( 7 ) 7 2 3 1 ( 7 ) 4 9 1 2 ( 6 ) 7 2 3 1 ( 8 ) 5 7 9 6 ( 7 ) 1 2 7 . 7 4 0 4 ) 1 0 6 . 5 1 0 1 ) 5 9 3 8 ( 9 ) 1 2 6 . 5 7 0 0 ) 9 8 1 7 ( 1 2 ) 9 1 3 7 ( 9 ) 1 7 9 . 9 0 0 1 ) 7 7 8 3 ( 7 ) 1 2 5 . 3 5 0 0 ) 9 0 3 7 ( 6 ) 1 3 8 . 4 6 0 0 ) 9 0 2 9 ( 8 ) 1 3 8 . 2 2 ( 7 ) 7 2 5 2 ( 7 ) 4 9 6 2 ( 6 ) 7 2 3 9 ( 8 ) 4 7 8 T a b l e 6 . 3 7 . C r y s t a l d a t a a n d s t r u c t u r e r e f r n e m e n t f o r C s A g 2 E u T e 4 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 0 7 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 o ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 s t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m i n a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e C s A g 2 E u T e 4 1 0 1 1 1 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A M o n o c l i n i c P m ( 0 1 3 1 / 2 ) 0 a = 4 . 4 9 1 1 ( 6 ) A , o = 9 0 ° b = 4 . 5 0 6 8 ( 7 ) A , 1 3 = 9 0 ° c = 1 2 3 4 8 4 0 8 ) A , ' y = 9 0 ° 0 . 2 6 3 1 ( 6 ) b ’ + 1 / 2 c ‘ 2 4 9 9 4 ( 6 ) A 3 1 6 . 7 1 4 7 g / c m 3 2 4 . 8 9 5 m m " 4 2 0 0 . 1 9 x 0 . 1 1 x 0 . 0 2 m m 3 2 . 7 4 t o 2 9 . 0 7 0 - 6 < = h < = 5 , - 6 < = k < = 6 , - 1 7 < = 1 < = 1 7 , - 1 < = m < = 1 4 8 9 2 ( 1 3 9 8 m a i n + 3 4 9 4 s a t e l l i t e s ) 3 3 1 7 ( 1 0 6 5 m a i n + 2 2 5 2 s a t e l l i t C S ) [ R i n t = 0 . 0 3 1 3 ] 9 6 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 3 3 1 7 / 0 / 1 0 3 1 . 7 4 R o b , = 0 . 0 4 1 5 , w R o b , = 0 . 1 0 9 4 R , “ = 0 . 0 6 2 4 , w k . " = 0 . 1 1 7 0 R o b , = 0 . 0 2 4 8 , w R o b , = 0 . 0 7 4 3 8 , ” : 0 . 0 2 5 8 , w R a l l = 0 . 0 7 4 8 R o b , = 0 . 1 0 0 5 , w R o b , = 0 . 1 7 2 0 8 , ” : 0 . 1 7 3 3 , w R . . . , = 0 . 1 8 8 8 0 . 0 0 0 5 6 ( 7 ) 0 . 0 7 2 1 a n d 0 . 5 2 4 0 4 . 4 2 a n d 4 5 9 6 A 3 R = 2 1 1 1 3 1 - 1 8 1 1 / 2 1 1 1 . 1 . w R = { 2 1 0 1 1 3 . 1 2 - 1 1 3 1 0 7 1 / 2 1 0 1 1 1 . 1 5 1 } “ 2 a n d W = 1 / ( 9 1 0 ) + 0 - 0 0 1 6 I Z ) 4 7 9 T a b l e 6 . 3 8 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) , o c c u p a n c i e s a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C s A g 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x y 2 O c c u p a n c y U e q E u 0 0 0 2 7 4 9 1 6 ( 1 ) s i n , 1 8 9 ( 1 ) - 9 ( 2 ) - 1 ( 1 ) c o s , 1 7 9 ( 1 ) 1 0 ( 2 ) - l ( 1 ) T e [ l ] 0 5 0 0 2 ( 3 ) 5 0 0 0 3 4 9 4 ( 1 ) 1 6 ( 1 ) s i n , 1 3 5 ( 2 ) - 1 ( 1 ) - 4 ( 1 ) c o s , 1 1 8 ( 1 ) 2 ( 3 ) - 2 ( 1 ) T e [ 2 ] 0 2 ( 2 ) 0 6 3 8 8 ( 1 ) 1 6 ( 1 ) s i n , 1 6 0 ( 2 ) 2 ( 1 ) - 1 ( 1 ) c o s , 1 - 2 8 ( 1 ) 5 ( 2 ) 0 ( 1 ) T e [ 3 ] 0 4 9 9 9 ( 5 ) 0 5 7 8 ( 1 ) 1 6 ( 1 ) s i n , 1 8 9 ( 1 ) - 5 2 ( 5 ) 0 ( 1 ) c o s , 1 4 8 5 ( 3 ) 1 0 ( 1 ) 2 ( 2 ) T e [ 4 ] 0 4 ( 4 ) 5 0 0 0 5 8 0 ( 1 ) 1 1 0 ( 1 ) s i n , 1 - 6 8 ( 1 ) 3 3 ( 5 ) 1 ( 1 ) c o s , 1 - 3 7 1 ( 3 ) - 6 ( 1 ) 5 ( 1 ) A g [ l ] 0 - 4 ( 4 ) 5 0 0 0 5 0 5 3 ( 1 ) 1 1 2 ( 1 ) s i n , 1 0 0 0 c o s , 1 0 0 0 A g [ 2 ] 0 4 9 9 6 ( 3 ) 0 5 0 4 8 ( 1 ) 1 1 2 ( 1 ) s i n , 1 0 0 0 c o s , 1 0 0 0 C s 0 4 9 9 8 ( 3 ) 5 0 0 0 7 9 4 5 ( 1 ) 1 8 ( 1 ) s i n , 1 6 2 ( 2 ) 1 1 ( 3 ) - 3 ( 1 ) c o s , 1 - 8 2 ( 2 ) 9 ( 2 ) 4 ( 1 ) 4 8 0 T a b l e 6 . 3 9 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r C s A g 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 E u 0 3 ( 1 ) 4 ( 1 ) 1 0 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 3 ( 1 ) - 1 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 2 ( 1 ) 1 ( 1 ) T e [ l ] 0 4 ( 1 ) 5 ( 1 ) 7 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) T e [ 2 ] 0 4 ( 1 ) 4 ( 1 ) 8 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) T e [ 3 ] 0 1 ( 1 ) 7 ( 1 ) 9 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) - 6 ( 1 ) 0 ( 1 ) 2 ( 1 ) c o s , 1 1 ( 1 ) - 2 ( 1 ) 2 ( 1 ) 1 ( 1 ) - 2 ( 1 ) 0 ( 1 ) T e [ 4 ] 0 1 5 ( 1 ) 8 ( 1 ) 7 ( 1 ) 0 1 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 5 ( 1 ) - 3 ( 1 ) 3 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) - 5 ( 1 ) - 1 ( 1 ) - 1 5 ( 1 ) - 1 ( 1 ) A g [ l ] 0 1 9 ( 1 ) 9 ( 1 ) 7 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 0 0 0 0 0 0 c o s , 1 0 0 0 0 0 0 A g [ 2 ] 0 9 ( 1 ) 1 6 ( 1 ) 1 0 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 0 0 0 0 0 0 c o s , 1 0 0 0 0 0 0 C s 0 9 ( 1 ) 9 ( 1 ) 5 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 0 ( 1 ) 1 ( 1 ) 2 ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) c o s , 1 1 ( 1 ) - 1 ( 1 ) - 2 ( 1 ) 0 ( 1 ) - 2 ( 1 ) 1 ( 1 ) 4 8 1 T a b l e 6 . 4 0 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C s A g 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e E u - T e [ l ] x 4 3 . 3 2 8 8 ( 1 6 ) 3 . 2 9 8 4 ( 1 6 ) 3 . 3 5 8 8 ( 1 6 ) E u - T e [ 3 ] x 2 3 . 4 5 1 ( 2 ) 3 . 3 4 1 ( 3 ) 3 . 5 6 6 ( 3 ) E u - T e [ 4 ] x 2 3 . 4 5 7 6 ( 1 9 ) 3 . 4 4 1 ( 2 ) 3 . 4 7 0 8 ( 1 8 ) E u - A g [ l ] x 2 3 . 6 7 6 7 ( 1 5 ) 3 . 6 7 2 6 ( 1 5 ) 3 . 6 8 0 5 ( 1 5 ) E u - A g [ 2 ] x 2 3 . 6 6 8 9 ( 1 8 ) 3 . 6 3 4 4 ( 1 8 ) 3 . 7 0 2 8 ( 1 8 ) T e [ l ] - A g [ l ] 2 . 9 6 0 ( 2 ) 2 . 9 4 2 ( 3 ) 2 . 9 7 7 ( 3 ) T e [ l ] - A g [ l ] 2 . 9 5 5 ( 2 ) 2 . 9 4 6 ( 3 ) 2 . 9 6 5 ( 3 ) T e [ l ] - A g [ 2 ] x 2 2 . 9 5 9 9 ( 1 7 ) 2 . 9 5 5 8 ( 1 7 ) 2 . 9 6 3 9 ( 1 7 ) T e [ 2 ] - A g [ l ] x 2 2 . 7 9 2 3 ( 1 4 ) 2 . 7 9 0 1 ( 1 5 ) 2 . 7 9 4 3 ( 1 5 ) T e [ 2 ] - A g [ 2 ] 2 . 7 9 1 ( 2 ) 2 . 7 6 8 ( 2 ) 2 . 8 1 5 ( 2 ) T e [ 2 ] - A g [ 2 ] 2 . 7 8 7 ( 2 ) 2 . 7 6 3 ( 2 ) 2 . 8 1 2 ( 2 ) T e [ 2 ] - C s x 4 3 . 7 1 8 2 ( 1 8 ) 3 . 6 9 6 0 ( 1 8 ) 3 . 7 4 0 7 ( 1 8 ) T e [ 3 ] - T e [ 4 ] x 4 3 . 1 8 7 ( 3 ) 2 . 9 3 7 ( 2 ) 3 . 4 4 2 ( 3 ) T e [ 3 ] - C s x 2 3 . 9 6 0 ( 2 ) 3 . 9 3 6 ( 2 ) 3 . 9 7 6 ( 2 ) T e [ 4 ] - C s x 2 3 . 9 5 5 ( 3 ) 3 . 8 8 5 ( 3 ) 4 . 0 2 7 ( 3 ) A g [ 1 ] - A g [ 2 ] x 4 3 . 1 8 1 1 ( 1 6 ) 3 . 1 8 1 1 ( 1 6 ) 3 . 1 8 1 1 ( 1 6 ) T a b l e 6 . 4 1 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C s A g 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ l ] - E u - T e [ l ] x 4 8 5 2 2 ( 4 ) 8 4 3 5 ( 4 ) 8 6 1 0 ( 4 ) T e [ l ] — E u - T e [ l ] x 4 8 4 8 4 ( 4 ) 8 4 6 8 ( 4 ) 8 5 0 0 ( 4 ) T e [ l ] - E u - T e [ l ] x 4 1 4 5 . 7 3 ( 5 ) 1 4 5 . 6 2 ( 5 ) 1 4 5 . 8 6 ( 5 ) T e [ l ] - E u - T e [ 3 ] x 4 7 7 6 1 ( 5 ) 7 6 5 3 ( 5 ) 7 8 7 4 ( 5 ) T e [ l ] - E u - T e [ 3 ] x 4 1 3 1 . 4 8 ( 5 ) 1 3 0 . 3 1 ( 5 ) 1 3 2 . 6 0 ( 5 ) T e [ l ] - E u - T e [ 4 ] x 4 7 7 3 8 ( 4 ) 7 4 9 9 ( 4 ) 7 9 8 1 ( 4 ) T e [ l ] - E u - T e [ 4 ] x 4 1 3 1 . 6 6 ( 5 ) 1 2 8 . 1 7 ( 4 ) 1 3 5 . 1 7 ( 5 ) T e [ l ] - E u - A g [ l ] x 4 4 9 6 0 ( 4 ) 4 9 3 1 ( 4 ) 4 9 8 9 ( 4 ) T e [ l ] - E u - A g [ l ] x 4 1 0 0 . 4 7 ( 4 ) 9 9 8 2 ( 4 ) 1 0 1 . 1 2 ( 4 ) T e [ l ] - E u - A g [ 2 ] x 4 4 9 7 6 ( 3 ) 4 9 3 0 ( 3 ) 5 0 2 2 ( 3 ) T e [ l ] - E u - A g [ 2 ] x 4 1 0 0 . 3 5 ( 4 ) 1 0 0 . 2 4 ( 4 ) 1 0 0 . 4 5 ( 4 ) T e [ 3 ] - E u - T e [ 3 ] x 2 8 1 . 1 2 ( 5 ) 8 0 9 7 ( 6 ) 8 1 2 0 ( 5 ) 4 8 2 T a b l e 6 . 4 1 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C s A g 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 3 ] - E u - T e [ 4 ] x 4 T e [ 3 ] - E u - A g [ 1 ] x 4 T e [ 3 ] - E u - A g [ 2 ] x 2 T e [ 3 ] - E u - A g [ 2 ] x 2 T e [ 4 ] - E u - T e [ 4 ] x 2 T e [ 4 ] - E u - A g [ 1 ] x 2 T e [ 4 ] - E u - A g [ 1 ] x 2 T e [ 4 ] - E u - A g [ 2 ] x 4 A g [ l ] - E u - A g [ 1 ] x 2 A g [ l ] - E u - A g [ 2 ] x 4 A g [ 2 ] - E u - A g [ 2 ] x 2 E u - T e [ 1 ] - E u x 4 E u - T e [ 1 ] - E u x 4 E u - T e [ 1 ] - E u x 4 E u - T e [ 1 ] - A g [ 1 ] x 4 E u - T e [ 1 ] - A g [ 1 ] x 4 E u - T e [ 1 ] - A g [ 2 ] x 4 E u - T e [ 1 ] - A g [ 2 ] x 4 A g [ 1 ] - T e [ 1 ] - A g [ 1 ] x 2 A g [ 1 ] - T e [ 1 ] - A g [ 2 ] x 4 A g [ 2 ] - T e [ l ] - A g [ 2 ] x 2 A g [ 1 ] - T e [ 2 ] - A g [ 1 ] x 2 A g [ l ] - T e [ 2 ] - A g [ 2 ] x 4 A g [ l ] - T e [ 2 ] - C s x 4 A g [ 1 ] - T e [ 2 ] - C s x 4 A g [ 2 ] - T e [ 2 ] - A g [ 2 ] x 2 A g [ 2 ] - T e [ 2 ] - C s x 4 A g [ 2 ] - T e [ 2 ] - C s x 4 C s - T e [ 2 ] - C s x 4 C s - T e [ 2 ] - C s x 4 C s - T e [ 2 ] - C s x 4 E u - T e [ 3 ] - E u x 2 E u - T e [ 3 ] - T e [ 4 ] x 4 E u - T e [ 3 ] - T e [ 4 ] x 4 5 4 8 9 ( 4 ) 1 2 6 . 8 7 ( 4 ) 1 0 1 . 6 8 ( 5 ) 1 7 7 . 1 8 ( 5 ) 8 1 4 2 ( 5 ) 1 0 1 4 5 0 ) 1 7 5 . 9 2 ( 4 ) 1 2 6 . 7 7 ( 4 ) 7 5 6 0 ( 3 ) 5 1 3 2 ( 3 ) 7 5 5 1 ( 4 ) 8 5 2 0 ( 4 ) 8 4 8 4 ( 3 ) 1 4 5 . 7 4 ( 6 ) 7 1 2 8 ( 4 ) 1 3 4 . 7 3 ( 4 ) 7 1 0 4 ( 4 ) 1 3 4 . 8 9 ( 7 ) 9 8 8 0 ( 7 ) 6 5 0 2 ( 5 ) 9 9 1 6 ( 6 ) 1 0 7 . 6 1 ( 6 ) 6 9 4 6 ( 5 ) 7 9 3 8 ( 4 ) 1 4 2 . 5 5 ( 6 ) 1 0 7 . 2 4 ( 7 ) 7 9 6 2 ( 4 ) 1 4 2 . 4 7 ( 3 ) 7 4 6 1 ( 4 ) 7 4 3 2 ( 4 ) 1 1 7 6 9 ( 5 ) 8 1 . 1 2 ( 5 ) 6 2 7 0 ( 5 ) 1 1 7 0 9 ( 6 ) 5 1 0 8 ( 4 ) 1 2 6 . 1 9 ( 4 ) 1 0 0 . 2 6 ( 5 ) 1 7 5 . 8 0 ( 5 ) 8 0 9 2 ( 4 ) 1 0 1 . 1 8 ( 4 ) 1 7 4 . 8 7 ( 5 ) 1 2 3 . 7 9 ( 4 ) 7 5 5 6 ( 3 ) 5 1 0 6 ( 3 ) 7 5 4 7 ( 4 ) 8 4 8 7 ( 5 ) 8 4 6 8 ( 3 ) 1 4 5 . 4 3 ( 5 ) 7 0 8 5 ( 4 ) 1 3 4 . 3 7 ( 4 ) 7 0 7 2 ( 4 ) 1 3 4 3 4 ( 6 ) 9 8 6 2 ( 7 ) 6 4 7 6 ( 5 ) 9 8 9 8 ( 6 ) 1 0 7 . 5 7 ( 6 ) 6 9 1 4 ( 5 ) 7 8 9 9 ( 4 ) 1 4 1 . 7 9 ( 6 ) 1 0 7 . 2 0 ( 7 ) 7 9 1 4 ( 4 ) 1 4 2 . 1 8 ( 4 ) 7 4 5 5 ( 4 ) 7 4 2 2 ( 4 ) l 1 7 3 1 ( 5 ) 8 0 9 7 ( 5 ) 5 9 2 2 ( 5 ) 1 1 5 7 6 ( 6 ) 5 8 8 3 ( 4 ) 1 2 7 . 5 8 ( 4 ) 1 0 3 . 1 3 ( 5 ) 1 7 8 . 6 0 ( 5 ) 8 1 7 2 ( 4 ) 1 0 1 . 7 8 ( 4 ) 1 7 7 . 3 9 ( 4 ) 1 2 9 . 7 5 ( 4 ) 7 5 6 3 ( 3 ) 5 1 5 9 ( 3 ) 7 5 5 4 ( 4 ) 8 5 5 2 ( 5 ) 8 5 0 0 ( 3 ) 1 4 6 0 5 ( 5 ) 7 1 7 1 ( 4 ) 1 3 5 . 0 9 0 ) 7 1 3 7 ( 4 ) 1 3 5 . 4 3 ( 6 ) 9 8 9 8 ( 7 ) 6 5 2 9 ( 5 ) 9 9 3 4 ( 7 ) 1 0 7 . 6 4 ( 6 ) 6 9 7 8 ( 5 ) 7 9 7 7 ( 4 ) 1 4 3 . 3 1 ( 6 ) 1 0 7 . 2 7 ( 7 ) 8 0 1 0 ( 5 ) 1 4 2 . 7 5 0 ) 7 4 6 7 ( 4 ) 7 4 4 3 ( 4 ) 1 1 8 0 8 ( 5 ) 8 1 2 0 ( 4 ) 6 6 4 1 ( 6 ) 1 1 8 0 5 ( 6 ) 4 8 3 T a b l e 6 . 4 1 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C s A g 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . E u - T e [ 3 ] - C s x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - C s x 4 T e [ 4 ] - T e [ 3 ] - C s x 4 C s - T e [ 3 ] - C s x 2 E u - T e [ 4 ] - E u x 2 E u - T e [ 4 ] - T e [ 3 ] x 4 E u - T e [ 4 ] - T e [ 3 ] x 4 E u - T e [ 4 ] - C s x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - C s x 4 T e [ 3 ] - T e [ 4 ] - C s x 4 C s - T e [ 4 ] - C s x 2 E u - A g [ 1 ] - E u x 2 E u - A g [ l ] - T e [ 1 ] x 4 E u - A g [ 1 ] - T e [ 2 ] x 2 E u - A g [ l ] - T e [ 2 ] x 2 E u - A g [ 1 ] - A g [ 2 ] x 4 E u - A g [ 1 ] - A g [ 2 ] x 4 T e [ 1 ] - A g [ 1 ] - T e [ 1 ] x 2 T e [ 1 ] - A g [ 1 ] - T e [ 2 ] x 4 T e [ 1 ] - A g [ 1 ] - A g [ 2 ] x 4 T e [ 1 ] - A g [ 1 ] - A g [ 2 ] x 4 T e [ 2 ] - A g [ l ] - T e [ 2 ] x 2 T e [ 2 ] - A g [ l ] - A g [ 2 ] x 4 T e [ 2 ] - A g [ l ] - A g [ 2 ] x 4 A g [ 2 ] - A 8 1 1 ] - A g [ 2 ] X 4 A g [ 2 ] - A g [ 1 ] - A g [ 2 ] X 4 A g [ 2 ] - A 8 1 1 ] - A g [ 2 ] X 4 E u - A g [ 2 ] - E u x 2 1 2 8 . 5 3 ( 6 ) 9 0 5 4 ( 8 ) 8 9 4 3 ( 6 ) 1 7 4 . 4 6 ( 9 ) 6 6 0 8 ( 5 ) 1 1 3 7 4 ( 7 ) 6 9 3 7 ( 4 ) 8 1 3 5 ( 4 ) 6 2 3 8 ( 5 ) 1 1 7 5 4 ( 7 ) 1 2 8 . 5 3 ( 5 ) 9 0 5 6 ( 8 ) 8 9 4 3 ( 7 ) 1 7 4 . 7 6 ( 9 ) 6 6 4 0 ( 5 ) 1 1 3 4 2 ( 6 ) 6 9 2 0 ( 4 ) 7 5 6 0 ( 3 ) 5 9 0 7 ( 4 ) 8 8 3 9 ( 3 ) 1 6 3 9 8 ( 5 ) 6 4 2 1 ( 4 ) 1 1 5 6 8 ( 6 ) 9 8 8 0 ( 7 ) 1 1 2 6 7 ( 5 ) 5 7 5 4 ( 4 ) 1 2 2 . 3 2 ( 5 ) 1 0 7 . 6 1 ( 6 ) 5 5 2 6 ( 4 ) 1 2 4 . 9 9 ( 7 ) 9 0 2 1 ( 5 ) 8 9 8 0 ( 3 ) 1 7 9 8 0 ( 7 ) 7 5 5 1 ( 4 ) 1 2 3 . 9 9 ( 6 ) 8 2 5 6 ( 7 ) 8 8 7 6 ( 7 ) 1 7 1 . 2 4 ( 8 ) 6 4 8 6 ( 5 ) 1 0 9 1 9 ( 7 ) 6 9 1 4 ( 5 ) 8 1 2 2 ( 5 ) 6 1 2 8 ( 4 ) 1 1 2 6 8 ( 7 ) 1 2 5 1 9 ( 5 ) 8 2 9 9 ( 7 ) 8 8 7 6 ( 6 ) 1 7 1 . 7 7 ( 8 ) 6 3 6 9 ( 5 ) 1 1 1 9 0 ( 7 ) 6 9 1 6 ( 5 ) 7 5 4 6 ( 3 ) 5 8 4 6 ( 4 ) 8 8 2 9 ( 3 ) l 6 3 . 8 9 ( 5 ) 6 3 5 4 ( 4 ) 1 1 5 0 3 ( 5 ) 9 8 6 2 ( 7 ) 1 1 2 0 6 ( 5 ) 5 7 3 6 ( 4 ) 1 2 2 . 1 4 ( 5 ) 1 0 7 . 5 9 ( 7 ) 5 4 7 4 ( 4 ) 1 2 4 . 4 5 0 ) 9 0 2 1 ( 5 ) 8 9 8 0 ( 3 ) 1 7 9 8 0 ( 7 ) 7 5 4 7 ( 4 ) 1 3 3 . 0 9 ( 6 ) 9 9 2 4 ( 9 ) 9 0 7 1 ( 7 ) 1 7 9 . 7 7 ( 9 ) 6 7 4 4 ( 5 ) 1 1 8 2 7 ( 8 ) 6 9 4 9 ( 4 ) 8 1 4 5 ( 4 ) 6 3 7 2 ( 5 ) 1 2 2 2 8 ( 8 ) l 3 1 . 7 2 ( 5 ) 9 8 4 5 ( 9 ) 9 0 7 1 ( 7 ) 1 7 9 8 8 ( 8 ) 6 9 1 9 ( 6 ) 1 1 4 8 1 ( 6 ) 6 9 2 3 ( 4 ) 7 5 7 3 ( 3 ) 5 9 6 6 ( 4 ) 8 8 5 0 ( 3 ) 1 6 4 . 0 8 ( 5 ) 6 4 8 7 ( 4 ) 1 1 6 3 1 ( 6 ) 9 8 9 8 ( 7 ) 1 1 3 2 6 ( 5 ) 5 7 7 1 ( 4 ) 1 2 2 . 4 9 ( 5 ) 1 0 7 . 6 3 ( 6 ) 5 5 7 7 ( 4 ) 1 2 5 5 2 ( 7 ) 9 0 2 1 ( 5 ) 8 9 8 0 ( 3 ) 1 7 9 8 0 ( 7 ) 7 5 5 4 ( 4 ) 4 8 4 :E T a b l e 6 . 4 1 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C s A g 2 E u T e 4 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . t - A g [ 2 ] - T e [ 1 ] x 4 E - A g [ 2 ] - T e [ 2 ] x 2 E u - A g [ 2 ] - T e [ 2 ] x 2 E - A g [ 2 ] - A g [ 1 ] x 4 E u - A g [ 2 ] - A g [ l ] x 4 T e [ 1 ] - A g [ 2 ] - T e [ 1 ] x 2 T e [ l ] - A g [ 2 ] - T e [ 2 ] x 4 T e [ 1 ] - A g [ 2 ] - A g [ 1 ] x 4 T e [ 1 ] - A g [ 2 ] - A g [ 1 ] x 4 T e [ 2 ] - A g [ 2 ] - T e [ 2 ] x 2 T e [ 2 ] - A g [ 2 ] - A g [ l ] x 4 T e [ 2 ] - A g [ 2 ] - A g [ l ] x 4 A 8 1 1 ] - A g [ 2 1 - A 8 1 1 ] X 4 A 8 1 1 1 - A g [ 2 1 - A g [ l l X 4 A 8 1 1 ] - A g [ 2 ] - A 8 1 1 ] X 4 T e [ 2 ] - C s - T e [ 2 ] x 4 T e [ 2 ] - C s - T e [ 2 ] x 4 T e [ 2 ] - C s - T e [ 2 ] x 4 T e [ 2 ] - C s - T e [ 3 ] x 4 T e [ 2 ] - C s - T e [ 3 ] x 4 T e [ 2 ] - C s - T e [ 4 ] x 4 T e [ 2 ] - C s - T e [ 4 ] x 4 T e [ 3 ] - C s - T e [ 3 ] x 2 T e [ 3 ] - C s - T e [ 4 ] x 4 T e [ 4 ] - C s - T e [ 4 ] x 2 t : C : 5 9 1 8 ( 4 ) 8 8 6 9 ( 5 ) 1 6 4 . 0 7 ( 7 ) 6 4 5 0 ( 4 ) 1 1 5 6 7 ( 5 ) 9 9 1 6 ( 6 ) 1 1 2 6 8 ( 5 ) 5 7 4 8 ( 4 ) 1 2 2 . 7 5 0 ) 1 0 7 . 2 4 0 ) 5 5 3 1 ( 4 ) 1 2 4 . 5 4 ( 5 ) 9 0 1 9 ( 5 ) 8 9 8 0 ( 3 ) 1 7 9 . 8 0 ( 7 ) 7 4 6 5 ( 4 ) 7 4 3 2 ( 4 ) 1 1 7 . 6 9 ( 5 ) 9 4 5 6 ( 4 ) 1 4 0 . 4 1 ( 6 ) 9 4 8 0 ( 5 ) 1 4 0 . 2 5 ( 5 ) 6 9 4 7 ( 5 ) 4 7 4 3 ( 5 ) 6 9 2 0 ( 5 ) 5 8 9 8 ( 4 ) 8 7 6 6 ( 5 ) 1 6 3 . 0 2 ( 7 ) 6 4 0 7 ( 4 ) 1 1 5 2 5 ( 5 ) 9 9 0 2 ( 6 ) 1 1 2 1 9 ( 5 ) 5 7 1 4 ( 5 ) 1 2 2 . 5 1 ( 7 ) 1 0 7 . 2 0 ( 7 ) 5 5 1 3 ( 4 ) 1 2 4 . 3 6 ( 5 ) 9 0 1 9 ( 5 ) 8 9 8 0 ( 3 ) 1 7 9 8 0 ( 7 ) 7 4 3 1 ( 4 ) 7 4 2 2 ( 4 ) 1 1 7 4 2 ( 5 ) 9 2 3 4 ( 4 ) 1 3 6 . 4 8 ( 5 ) 9 3 9 3 ( 5 ) 1 3 9 . 7 4 ( 5 ) 6 9 0 2 ( 5 ) 4 3 8 6 ( 5 ) 6 9 1 6 ( 5 ) 5 9 3 9 ( 5 ) 8 9 7 1 ( 5 ) 1 6 5 1 4 ( 7 ) 6 4 9 2 ( 4 ) 1 1 6 1 0 ( 5 ) 9 9 3 0 ( 6 ) 1 1 3 1 5 ( 5 ) 5 7 8 2 ( 5 ) 1 2 2 . 9 9 ( 7 ) 1 0 7 . 2 7 ( 7 ) 5 5 4 9 ( 4 ) 1 2 4 . 7 2 ( 5 ) 9 0 1 9 ( 5 ) 8 9 8 0 ( 3 ) 1 7 9 8 0 ( 7 ) 7 4 9 9 ( 4 ) 7 4 4 3 ( 4 ) 1 1 7 . 9 7 ( 5 ) 9 6 8 1 ( 4 ) 1 4 4 . 3 3 ( 6 ) 9 5 6 8 ( 5 ) 1 4 0 . 7 5 ( 5 ) 6 9 7 1 ( 5 ) 5 1 1 6 ( 5 ) 6 9 2 3 ( 4 ) 4 8 5 T a b l e 6 . 4 2 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C s A g 2 E u T e 4 a t 3 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f f i c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 1 1 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 6 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f f i c i e n t T m a n d T m “ c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e C s A g 2 E u T e 4 1 0 1 1 3 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A M o n o c l i n i c P m ( 0 [ 3 1 / 2 ) 0 a = 4 . 5 0 9 4 ( 4 ) A , a = 9 0 ° b = 4 . 5 2 2 6 ( 4 ) A , 1 3 = 9 0 ° c = 1 2 . 3 9 6 2 ( 1 3 ) A , y = 9 0 ° 0 . 2 6 5 0 ( 4 ) b ‘ + 1 / 2 c ‘ 2 5 2 . 8 1 ( 4 ) A 3 2 1 3 . 2 7 7 g / c m 3 4 9 . 2 2 5 m m " 4 2 0 0 . 1 9 x 0 . 1 1 x 0 . 0 2 m m 3 3 . 4 0 t o 2 9 0 ° - 5 < = h < = 6 , - 6 < = k < = 6 , - 1 7 < = l < = 1 7 , - 1 < = m < = 1 7 0 8 7 ( 2 3 0 8 m a i n + 4 7 7 9 s a t e l l i t e s ) 3 8 4 6 ( 1 3 5 0 m a i n + 2 4 9 6 s a t e l l i t e s ) [ R a t = 0 . 0 2 4 0 ] 9 9 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 3 8 4 6 / 0 / 1 0 3 2 . 0 6 R o b , = 0 . 0 4 0 3 , w R o b , = 0 . 1 2 2 0 1 1 . 1 , : 0 . 0 5 2 4 , w i t , l l = 0 . 1 2 7 5 R o b , = 0 . 0 2 8 0 , w R . . . , = 0 . 0 8 4 1 8 , " : 0 . 0 2 8 8 , w k , “ = 0 . 0 8 7 6 R 0 , , = 0 . 0 9 4 1 , w R o b s = 0 . 1 8 5 9 R , “ = 0 . 1 4 3 1 , w R , 1 1 = 0 . 1 9 4 5 0 0 0 0 8 9 ( 7 ) 0 . 0 7 2 1 a n d 0 . 5 2 4 0 3 . 3 2 a n d - 3 8 7 6 A 3 R = l e F o l - c h l l / Z l F o l , w R = { 2 [ W ( I F 0 | 2 - I F c I Z I Z ] / E D A / ( 0 1 1 0 0 " 2 a n d W = 1 / ( < 5 2 ( 1 1 4 9 0 0 1 6 1 2 ) 4 8 6 T a b l e 6 . 4 3 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C s A g 2 E u T e 4 a t 3 0 0 K w i t h e . s . d . ’ s . A t o m W a v e x y 2 O c c u p a n c y U 1 , q E u 0 0 0 2 7 4 9 1 1 8 ( 1 ) s i n , 1 8 3 ( 1 ) - 7 ( 1 ) 2 ( 1 ) c o s , 1 7 3 ( 1 ) 8 ( 1 ) 1 ( 1 ) T e [ l ] 0 4 9 9 9 ( 3 ) 5 0 0 0 3 4 8 9 ( 1 ) 1 1 7 ( 1 ) s i n , 1 2 6 ( 2 ) 0 ( 1 ) 3 ( 1 ) c o s , 1 1 3 ( 1 ) 1 ( 2 ) 2 ( 1 ) T e [ 2 ] 0 0 ( 2 ) 0 6 3 7 6 ( 1 ) 1 2 0 ( 1 ) s i n , 1 5 6 ( 2 ) 2 ( 1 ) 1 ( 1 ) c o s , 1 - 2 6 ( 1 ) 5 ( 2 ) - 1 ( 1 ) T e [ 3 ] 0 5 0 1 0 ( 5 ) 0 5 7 5 ( 1 ) 1 2 1 ( 1 ) s i n , 1 8 6 ( 1 ) - 3 4 ( 4 ) - 1 ( 1 ) c o s , 1 4 6 9 ( 3 ) 6 ( 1 ) - 3 ( 1 ) T e [ 4 ] 0 7 ( 4 ) 5 0 0 0 5 7 8 ( 1 ) 1 2 4 ( 1 ) s i n , 1 - 6 9 ( 1 ) 2 6 ( 4 ) - 1 ( 1 ) c o s , 1 - 3 7 7 ( 3 ) - 5 ( 1 ) - 3 ( 1 ) A g [ l ] 0 - 1 0 ( 4 ) 5 0 0 0 5 0 4 9 ( 2 ) 1 3 5 ( 1 ) s i n , 1 0 0 0 c o s , 1 0 0 0 A g [ 2 ] 0 4 9 9 5 ( 3 ) 0 5 0 4 5 ( 2 ) 1 3 5 ( 1 ) s i n , 1 0 0 0 c o s , 1 0 0 0 C s 0 4 9 9 7 ( 3 ) 5 0 0 0 7 9 4 3 ( 1 ) 1 2 5 ( 1 ) s i n , 1 5 3 ( 2 ) 1 0 ( 2 ) 2 ( 1 ) c o s , 1 - 7 1 ( 2 ) 8 ( 2 ) - 3 ( 1 ) 4 8 7 T a b l e 6 . 4 4 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r C s A g 2 E u T e 4 a t 3 0 0 K w i t h e . s . d . ’ s . A t o m W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 E u 0 1 5 ( 1 ) 1 5 ( 1 ) 2 5 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) T e [ l ] 0 1 4 ( 1 ) 1 4 ( 1 ) 2 2 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) - l ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) T e [ 2 ] 0 1 9 ( 1 ) 1 7 ( 1 ) 2 5 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) T e [ 3 ] 0 2 1 ( 1 ) 2 0 ( 1 ) 2 4 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) - 8 ( 1 ) - 1 ( 1 ) 2 ( 1 ) c o s , 1 1 ( 1 ) - 1 ( 1 ) 3 ( 1 ) 1 ( 1 ) - 4 ( 1 ) 0 ( 1 ) T e [ 4 ] 0 3 0 ( 1 ) 2 2 ( 1 ) 2 0 ( 1 ) 0 - 1 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 8 ( 1 ) - l ( 1 ) 2 ( 1 ) c o s , 1 - 1 ( 1 ) 1 ( 1 ) 2 ( 1 ) - 1 ( 1 ) - 8 ( 1 ) 0 ( 1 ) A g [ l ] 0 5 3 ( 1 ) 2 5 ( 1 ) 2 7 ( 1 ) 0 - 1 ( 1 ) 0 s i n , 1 0 0 0 0 0 0 c o s , 1 0 0 0 0 0 0 A g [ 2 ] 0 2 6 ( 1 ) 5 0 ( 1 ) 3 0 ( 1 ) 0 - 1 ( 1 ) 0 s i n , 1 0 0 0 0 0 0 c o s , 1 0 0 0 0 0 0 C s 0 2 7 ( 1 ) 2 7 ( 1 ) 2 0 ( 1 ) 0 - 1 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) - l ( 1 ) 0 ( 1 ) 1 ( 1 ) 1 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) - 2 ( 1 ) 0 ( 1 ) 4 8 8 T a b l e 6 . 4 5 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C s A g 2 E u T e 4 a t 3 0 0 K w i t h e . s . d . ’ s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e E u - T e [ l ] x 4 3 . 3 4 0 2 ( 1 2 ) 3 . 3 1 1 3 ( 1 2 ) 3 . 3 6 8 7 ( 1 3 ) E u - T e [ 3 ] 3 . 4 6 4 ( 2 ) 3 . 3 6 4 ( 2 ) 3 . 5 6 9 ( 2 ) E u - T e [ 3 ] 3 . 4 7 2 ( 2 ) 3 . 3 5 9 ( 2 ) 3 . 5 8 5 ( 2 ) E u - T e [ 4 ] x 2 3 . 4 7 2 5 ( 1 6 ) 3 . 4 5 8 1 ( 1 7 ) 3 . 4 8 2 9 ( 1 6 ) E u - A g [ l ] x 2 3 . 6 8 7 3 ( 1 6 ) 3 . 6 8 3 8 ( 1 6 ) 3 . 6 9 0 7 ( 1 6 ) E u - A g [ 2 ] x 2 3 . 6 8 1 0 ( 1 9 ) 3 . 6 5 2 3 ( 1 9 ) 3 . 7 0 9 3 ( 1 9 ) T e [ l ] - A g [ l ] 2 . 9 7 4 ( 2 ) 2 . 9 6 7 ( 2 ) 2 . 9 8 1 ( 2 ) T e [ l ] - A g [ l ] 2 . 9 6 8 ( 2 ) 2 . 9 5 5 ( 2 ) 2 . 9 8 0 ( 2 ) T e [ l ] - A g [ 2 ] x 2 2 . 9 7 2 8 ( 1 7 ) 2 . 9 7 0 2 ( 1 7 ) 2 . 9 7 5 4 ( 1 7 ) T e [ 2 ] - A g [ l ] x 2 2 . 7 9 5 8 ( 1 4 ) 2 . 7 9 3 4 ( 1 4 ) 2 . 7 9 8 1 ( 1 4 ) T e [ 2 ] - A g [ 2 ] 2 . 7 9 5 ( 2 ) 2 . 7 7 2 ( 2 ) 2 . 8 1 8 ( 2 ) T e [ 2 ] - A g [ 2 ] 2 . 7 9 1 ( 2 ) 2 . 7 7 0 ( 2 ) 2 . 8 1 3 ( 2 ) T e [ 2 ] - C s x 4 3 . 7 3 8 7 ( 1 7 ) 3 . 7 2 3 3 ( 1 7 ) 3 . 7 5 4 2 ( 1 7 ) T e [ 3 ] - T e [ 4 ] x 2 3 . 2 0 2 ( 2 ) 2 . 9 5 4 ( 2 ) 3 . 4 5 5 ( 2 ) T e [ 3 ] - T e [ 4 ] x 2 3 . 1 9 5 ( 2 ) 2 . 9 5 1 ( 2 ) 3 . 4 5 3 ( 2 ) T e [ 3 ] - C s x 2 3 . 9 7 4 ( 2 ) 3 . 9 6 2 ( 2 ) 3 . 9 8 1 ( 2 ) T e [ 4 ] - C s 3 . 9 7 1 ( 2 ) 3 . 8 9 7 ( 3 ) 4 . 0 4 8 ( 3 ) T e [ 4 ] - C s 3 . 9 6 7 ( 2 ) 3 . 8 9 2 ( 3 ) 4 . 0 4 3 ( 3 ) A g [ 1 ] - A g [ 2 ] x 4 3 . 1 9 1 7 ( 1 7 ) 3 . 1 9 1 7 ( 1 7 ) 3 . 1 9 1 7 ( 1 7 ) T a b l e 6 . 4 6 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C s A g 2 E u T e 4 a t 3 0 0 K w i t h e . s . d . ’ s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ l ] - E u - T e [ l ] x 4 8 5 2 2 ( 3 ) 8 4 3 6 ( 3 ) 8 6 1 1 ( 3 ) T e [ l ] - E u — T e [ l ] x 4 8 4 9 2 ( 3 ) 8 4 8 6 ( 3 ) 8 5 0 0 ( 3 ) T e [ l ] - E u - T e [ l ] x 4 1 4 5 . 9 4 ( 5 ) 1 4 5 . 8 8 ( 5 ) 1 4 6 . 0 2 ( 5 ) T e [ l ] - E u - T e [ 3 ] x 4 7 7 . 5 7 ( 4 ) 7 6 4 0 ( 4 ) 7 8 7 8 ( 4 ) T e [ l ] - E u - T e [ 3 ] x 4 1 3 1 . 4 3 ( 4 ) 1 3 0 . 3 4 ( 4 ) 1 3 2 . 4 6 ( 4 ) T e [ l ] - E u - T e [ 4 ] x 4 7 7 3 5 ( 4 ) 7 5 1 5 ( 4 ) 7 9 5 8 ( 4 ) T e [ l ] - E u - T e [ 4 ] x 4 1 3 1 . 5 6 ( 4 ) 1 2 8 . 0 3 ( 4 ) 1 3 5 . 1 3 ( 4 ) T e [ l ] - E u - A g [ l ] x 4 4 9 6 6 ( 4 ) 4 9 3 5 ( 4 ) 4 9 9 7 ( 4 ) T e [ l ] - E u - A g [ l ] x 4 1 0 0 . 5 5 ( 4 ) 9 9 9 4 ( 4 ) 1 0 1 . 1 6 ( 4 ) T e [ l ] - E u - A g [ 2 ] x 4 4 9 8 1 ( 3 ) 5 0 2 8 ( 3 ) 4 9 3 5 ( 3 ) 4 8 9 T a b l e 6 . 4 6 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C s A g 2 E u T e 4 a t 3 0 0 K w i t h e . s . d . ’ s . T e [ 1 ] - E u - A g [ 2 ] x 4 T e [ 3 ] - E u - T e [ 3 ] x 2 T e [ 3 ] - E u - T e [ 4 ] x 4 T e [ 3 ] - E u - A g [ 1 ] x 4 T e [ 3 ] - E u - A g [ 2 ] x 2 T e [ 3 ] - E u - A g [ 2 ] x 2 T e [ 4 ] - E u - T e [ 4 ] x 2 T e [ 4 ] - E u - A g [ 1 ] x 2 T e [ 4 ] - E u - A g [ l ] x 2 T e [ 4 ] - E u - A g [ 2 ] x 4 A g [ 1 ] - E u - A g [ 1 ] x 2 A g [ l ] - E u - A g [ 2 ] x 4 A g [ 2 ] - E u - A g [ 2 ] x 2 E u - T e [ 1 ] - E u x 4 E u - T e [ 1 ] - E u x 4 E u - T e [ 1 ] - E u x 4 E u - T e [ 1 ] - A g [ 1 ] x 4 E u - T e [ 1 ] — A g [ l ] x 4 E u - T e [ l ] - A g [ 2 ] x 4 E u — T e [ 1 ] - A g [ 2 ] x 4 A g [ 1 ] - T e [ 1 ] - A g [ 1 ] x 2 A g [ 1 ] - T e [ 1 ] - A g [ 2 ] x 4 A g [ 2 ] - T e [ l ] - A g [ 2 ] x 2 A g [ 1 ] - T e [ 2 ] - A g [ l ] x 2 A g [ l ] - T e [ 2 ] - A g [ 2 ] x 4 A g [ 1 ] - T e [ 2 ] - C s x 4 A g [ 1 ] - T e [ 2 ] - C s x 4 A g [ 2 ] - T e [ 2 ] - A g [ 2 ] x 2 A g [ 2 ] - T e [ 2 ] - C s x 4 A g [ 2 ] - T e [ 2 ] - C s x 4 C s - T e [ 2 ] - C s x 4 C s - T e [ 2 ] - C s x 4 C s - T e [ 2 ] - C s x 4 E u - T e [ 3 ] - E u x 2 1 0 0 . 4 9 0 ) 8 1 0 7 ( 5 ) 5 4 8 3 ( 4 ) 1 2 6 . 8 8 ( 4 ) 1 0 1 . 7 2 ( 4 ) 1 7 7 . 3 0 ( 5 ) 8 1 3 5 ( 4 ) 1 0 1 . 4 6 ( 3 ) 1 7 6 . 0 0 ( 4 ) 1 2 6 . 7 9 ( 4 ) 7 5 6 5 ( 3 ) 5 1 3 4 ( 3 ) 7 5 5 8 ( 4 ) 8 5 2 5 ( 3 ) 8 4 9 2 ( 3 ) 1 4 5 . 9 5 ( 6 ) 7 1 2 0 ( 4 ) 1 3 4 . 6 5 ( 4 ) 7 1 0 0 ( 4 ) 1 3 4 . 8 1 ( 6 ) 9 8 7 4 ( 7 ) 6 4 9 9 ( 5 ) 9 9 0 5 ( 6 ) 1 0 7 . 9 6 ( 6 ) 6 9 6 2 ( 5 ) 7 9 3 6 ( 4 ) 1 4 2 . 5 4 ( 6 ) 1 0 7 . 6 4 ( 7 ) 7 9 5 9 ( 4 ) 1 4 2 . 5 2 ( 3 ) 7 4 4 4 ( 3 ) 7 4 2 0 ( 3 ) 1 1 7 3 6 ( 5 ) 8 1 0 7 ( 4 ) 1 0 0 . 3 8 ( 4 ) 8 0 8 5 ( 5 ) 5 0 9 6 ( 4 ) 1 2 6 . 1 4 ( 4 ) 1 0 0 . 2 2 ( 5 ) 1 7 5 . 7 5 ( 5 ) 8 1 1 3 ( 4 ) 1 0 1 . 2 3 ( 3 ) 1 7 4 . 9 6 ( 4 ) 1 2 3 . 9 2 ( 4 ) 7 5 6 0 ( 3 ) 5 1 1 4 ( 3 ) 7 5 5 3 ( 4 ) 8 4 9 2 ( 4 ) 8 4 8 6 ( 3 ) 1 4 5 . 6 7 ( 6 ) 7 0 8 5 ( 4 ) 1 3 4 . 3 4 ( 4 ) 7 0 7 0 ( 4 ) 1 3 4 . 3 9 ( 5 ) 9 8 6 2 ( 7 ) 6 4 9 3 ( 5 ) 9 8 9 3 ( 6 ) 1 0 7 . 9 0 ( 6 ) 6 9 2 7 ( 5 ) 7 9 1 0 ( 4 ) 1 4 1 . 8 4 ( 5 ) 1 0 7 . 5 8 ( 7 ) 7 9 1 3 ( 4 ) 1 4 2 2 2 0 ) 7 4 3 0 ( 3 ) 7 4 1 2 ( 3 ) 0 7 0 2 ( 5 ) 8 0 8 5 ( 5 ) 1 0 0 . 5 9 ( 4 ) 8 1 . 1 8 ( 5 ) 5 8 8 5 ( 4 ) 1 2 7 . 6 4 ( 4 ) 1 0 3 . 2 6 ( 5 ) 1 7 8 . 8 8 ( 5 ) 8 1 4 6 ( 4 ) 1 0 1 . 7 6 ( 4 ) 1 7 7 . 3 8 ( 4 ) 1 2 9 . 6 7 ( 4 ) 7 5 6 9 ( 3 ) 5 1 5 4 ( 3 ) 7 5 6 2 ( 4 ) 8 5 5 7 ( 4 ) 8 5 0 0 ( 3 ) 1 4 6 2 3 ( 6 ) 7 1 5 6 ( 4 ) 1 3 4 . 9 6 ( 4 ) 7 1 3 1 ( 4 ) 1 3 5 . 2 3 ( 5 ) 9 8 8 5 ( 7 ) 6 5 0 5 ( 5 ) 9 9 1 6 ( 6 ) 1 0 8 0 2 ( 6 ) 6 9 9 7 ( 5 ) 7 9 6 3 ( 4 ) 1 4 3 . 2 6 ( 5 ) 1 0 7 . 7 0 ( 7 ) 8 0 0 5 ( 4 ) 1 4 2 . 8 1 ( 3 ) 7 4 5 7 ( 3 ) 7 4 2 7 ( 3 ) 1 1 7 7 0 ( 5 ) 8 1 1 8 ( 4 ) 4 9 0 T a b l e 6 . 4 6 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C s A g 2 E u T e 4 a t 3 0 0 K w i t h e . s . d . ’ s . E u - T e [ 3 ] - T e [ 4 ] x 4 E u - T e [ 3 ] - T e [ 4 ] x 4 E u - T e [ 3 ] - C s x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - T e [ 4 ] x 4 T e [ 4 ] - T e [ 3 ] - C s x 4 T e [ 4 ] - T e [ 3 ] - C s x 4 C s - T e [ 3 ] - C s x 2 E u - T e [ 4 ] - E u x 2 E u - T e [ 4 ] - T e [ 3 ] x 4 E u - T e [ 4 ] - T e [ 3 ] x 4 E u - T e [ 4 ] - C s x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - T e [ 3 ] x 4 T e [ 3 ] - T e [ 4 ] - C s x 4 T e [ 3 ] - T e [ 4 ] - C s x 4 C s - T e [ 4 ] - C s x 2 E u - A g [ 1 ] - E u x 2 E u - A g [ 1 ] - T e [ 1 ] x 4 E u - A g [ 1 ] - T e [ 2 ] x 2 E u - A g [ 1 ] - T e [ 2 ] x 2 E u - A g [ 1 ] - A g [ 2 ] x 4 E u - A g [ 1 ] - A g [ 2 ] x 4 T e [ 1 ] - A g [ 1 ] - T e [ l ] x 2 T e [ 1 ] - A g [ l ] - T e [ 2 ] x 4 T e [ l ] - A g [ 1 ] - A g [ 2 ] x 4 T e [ 1 ] - A g [ 1 ] - A g [ 2 ] x 4 T e [ 2 ] - A g [ l ] - T e [ 2 ] x 2 T e [ 2 ] - A g [ l ] - A g [ 2 ] x 4 T e [ 2 ] - A g [ l ] - A g [ 2 ] x 4 A g [ 2 ] - A 8 1 1 ] - A g [ 2 ] X 4 A g [ 2 ] - A 8 1 1 ] - A g [ 2 ] X 4 6 2 6 4 ( 5 ) 1 1 7 . 1 0 ( 6 ) 1 2 8 . 4 6 ( 6 ) 9 0 4 0 ( 7 ) 8 9 4 8 ( 5 ) 1 7 4 . 5 8 ( 8 ) 6 6 0 7 ( 5 ) 1 1 3 6 7 ( 6 ) 6 9 3 7 ( 4 ) 8 1 2 7 ( 4 ) 6 2 3 8 ( 4 ) 1 1 7 . 5 0 ( 6 ) 1 2 8 . 5 2 ( 5 ) 9 0 6 1 ( 7 ) 8 9 4 8 ( 6 ) 1 7 4 . 8 2 ( 7 ) 6 6 3 9 ( 5 ) 1 1 3 3 9 ( 6 ) 6 9 2 1 ( 4 ) 7 5 6 6 ( 4 ) 5 9 0 8 ( 4 ) 8 8 1 8 ( 3 ) 1 6 3 8 3 ( 6 ) 6 4 2 3 ( 4 ) 1 1 5 7 4 ( 6 ) 9 8 7 4 ( 7 ) 1 1 2 6 2 ( 5 ) 5 7 5 8 ( 5 ) 1 2 2 . 3 2 ( 5 ) 1 0 7 . 9 7 ( 7 ) 5 5 1 8 ( 4 ) 1 2 5 . 1 1 ( 7 ) 9 0 2 2 ( 5 ) 8 9 8 3 ( 3 ) 5 9 3 0 ( 4 ) 1 1 5 7 1 ( 5 ) 1 2 4 . 1 7 ( 5 ) 8 2 5 3 ( 6 ) 8 8 9 8 ( 4 ) 1 7 1 . 5 1 ( 7 ) 6 4 9 9 ( 4 ) 1 0 9 . 2 4 0 ) 6 9 1 7 ( 4 ) 8 0 9 8 ( 4 ) 6 1 4 0 ( 4 ) 1 1 2 7 7 ( 6 ) 1 2 5 0 3 ( 5 ) 8 2 9 7 ( 6 ) 8 8 9 8 ( 6 ) 1 7 1 . 7 9 ( 7 ) 6 3 5 5 ( 5 ) 1 1 1 9 8 ( 6 ) 6 9 1 7 ( 4 ) 7 5 6 0 ( 4 ) 5 8 4 3 ( 4 ) 8 8 1 0 ( 3 ) 1 6 3 . 7 8 ( 6 ) 6 3 6 3 ( 4 ) 1 1 5 . 1 1 ( 6 ) 9 8 6 2 ( 7 ) 1 1 2 1 0 ( 5 ) 5 7 5 2 ( 5 ) 1 2 2 . 2 6 ( 5 ) 1 0 7 . 8 8 ( 7 ) 5 4 6 7 ( 4 ) 1 2 4 . 6 3 ( 7 ) 9 0 2 2 ( 5 ) 8 9 8 3 ( 3 ) 6 6 2 1 ( 5 ) 1 1 8 1 4 ( 5 ) 1 3 2 . 7 7 ( 5 ) 9 8 9 6 ( 8 ) 9 0 4 8 ( 6 ) 1 7 9 9 0 ( 7 ) 6 7 2 5 ( 4 ) 1 1 8 0 8 ( 7 ) 6 9 4 7 ( 4 ) 8 1 . 4 2 ( 4 ) 6 3 5 6 ( 4 ) 1 2 2 . 1 0 ( 7 ) 1 3 1 . 8 7 ( 4 ) 9 8 5 8 ( 8 ) 9 0 4 8 ( 6 ) 1 7 9 8 9 ( 7 ) 6 9 3 0 ( 6 ) 1 1 4 7 2 ( 6 ) 6 9 2 4 ( 4 ) 7 5 7 1 ( 4 ) 5 9 7 1 ( 4 ) 8 8 2 8 ( 3 ) 1 6 3 . 9 0 ( 6 ) 6 4 8 2 ( 4 ) 1 1 6 3 5 ( 6 ) 9 8 8 5 ( 7 ) 1 1 3 1 3 ( 5 ) 5 7 6 4 ( 5 ) 1 2 2 . 3 8 ( 5 ) 1 0 8 . 0 5 ( 7 ) 5 5 6 8 ( 4 ) 1 2 5 . 5 8 ( 7 ) 9 0 2 2 ( 5 ) 8 9 8 3 ( 3 ) 4 9 1 T a b l e 6 . 4 6 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C s A g 2 E u T e 4 a t 3 0 0 K w i t h e . s . d . ’ s . A g [ 2 ] - A 8 1 1 ] - A g [ 2 ] X 4 E u - A g [ 2 ] - E u x 2 E u - A g [ 2 ] - T e [ 1 ] x 4 E u - A g [ 2 ] - T e [ 2 ] x 2 E u - A g [ 2 ] - T e [ 2 ] x 2 E u - A g [ 2 ] - A g [ 1 ] x 4 E u - A g [ 2 ] - A g [ l ] x 4 T e [ 1 ] - A g [ 2 ] - T e [ 1 ] x 2 T e [ l ] - A g [ 2 ] - T e [ 2 ] x 4 T e [ 1 ] - A g [ 2 ] - A g [ 1 ] x 4 T e [ 1 ] - A g [ 2 ] - A g [ 1 ] x 4 T e [ 2 ] - A g [ 2 ] - T e [ 2 ] x 2 T e [ 2 ] - A g [ 2 ] - A g [ l ] x 4 T e [ 2 ] - A g [ 2 ] - A g [ l ] x 4 A 8 0 ] - A g [ 2 1 - A 8 1 1 ] X 4 A g [ 1 ] - A g [ 2 ] - A 8 1 1 ] X 4 A g [ l l - A g [ 2 ] - A 8 1 1 ] X 4 T e [ 2 ] - C s - T e [ 2 ] x 4 T e [ 2 ] - C s - T e [ 2 ] x 4 T e [ 2 ] - C s - T e [ 2 ] x 4 T e [ 2 ] - C s - T e [ 3 ] x 4 T e [ 2 ] - C s - T e [ 3 ] x 4 T e [ 2 ] - C s - T e [ 4 ] x 4 T e [ 2 ] - C s - T e [ 4 ] x 4 T e [ 3 ] - C s - T e [ 3 ] x 2 T e [ 3 ] - C s - T e [ 4 ] x 4 T e [ 4 ] - C s - T e [ 4 ] x 2 1 7 9 . 8 2 ( 8 ) 7 5 5 8 ( 4 ) 5 9 1 5 ( 4 ) 8 8 4 5 ( 5 ) 1 6 3 . 9 1 ( 7 ) 6 4 4 5 ( 4 ) 1 1 5 6 8 ( 5 ) 9 9 0 5 ( 7 ) 1 1 2 5 8 ( 5 ) 5 7 5 2 ( 4 ) 1 2 2 . 6 7 ( 7 ) 1 0 7 . 6 4 ( 7 ) 5 5 1 9 ( 4 ) 1 2 4 . 6 5 ( 5 ) 9 0 1 1 ( 5 ) 8 9 8 3 ( 3 ) 1 7 9 . 8 2 ( 8 ) 7 4 4 7 ( 3 ) 7 4 2 0 ( 3 ) 1 1 7 3 6 ( 5 ) 9 4 1 7 ( 4 ) 1 4 0 . 6 0 ( 5 ) 9 4 9 5 ( 4 ) 1 4 0 . 4 0 ( 4 ) 6 9 4 6 ( 4 ) 4 7 4 8 ( 4 ) 6 9 2 1 ( 4 ) 1 7 9 . 8 2 ( 8 ) 7 5 5 3 ( 4 ) 5 8 9 9 ( 4 ) 8 7 4 9 ( 5 ) 1 6 3 . 0 2 ( 7 ) 6 4 0 8 ( 4 ) 1 1 5 3 1 ( 5 ) 9 8 9 8 ( 7 ) 1 1 2 2 2 ( 5 ) 5 7 3 4 ( 4 ) 1 2 2 . 4 3 ( 7 ) 1 0 7 . 5 8 ( 7 ) 5 5 0 0 ( 4 ) 1 2 4 . 4 6 ( 5 ) 9 0 1 1 ( 5 ) 8 9 8 3 ( 3 ) 1 7 9 . 8 2 ( 8 ) 7 4 0 9 ( 3 ) 7 4 1 2 ( 3 ) 0 7 1 1 ( 5 ) 9 2 7 3 ( 4 ) 1 3 6 . 9 6 ( 5 ) 9 3 8 6 ( 4 ) 1 3 9 . 7 7 ( 4 ) 6 9 0 5 ( 4 ) 4 4 0 0 ( 4 ) 6 9 1 7 ( 5 ) 1 7 9 . 8 2 ( 8 ) 7 5 6 2 ( 4 ) 5 9 3 1 ( 4 ) 8 9 4 0 ( 5 ) 1 6 4 . 8 1 ( 7 ) 6 4 8 1 ( 4 ) 1 1 6 0 5 ( 5 ) 9 9 1 2 ( 7 ) 1 1 2 9 3 ( 5 ) 5 7 7 0 ( 4 ) 1 2 2 . 9 2 ( 7 ) 1 0 7 . 7 0 ( 7 ) 5 5 3 8 ( 4 ) 1 2 4 . 8 4 ( 5 ) 9 0 1 1 ( 5 ) 8 9 8 3 ( 3 ) 1 7 9 . 8 2 ( 8 ) 7 4 8 5 ( 3 ) 7 4 2 7 ( 3 ) 1 1 7 6 2 ( 5 ) 9 6 8 4 ( 4 ) 1 4 4 . 2 3 ( 5 ) 9 6 0 6 ( 4 ) 1 4 0 9 9 ( 4 ) 6 9 6 8 ( 5 ) 5 1 . 1 1 ( 4 ) 6 9 2 4 ( 4 ) 4 9 2 T a b l e 6 . 4 7 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C u o _ 6 3 ( 2 ) E u T e 2 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e C r y s t a l s y s t e m S p a c e g r o u p C e n t e r i n g v e c t o r U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) q - v e c t o r ( 2 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 2 1 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 3 o ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 3 o ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 3 o ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) F i n a l R 2 ' “ d o r d e r s a t e l l i t e s [ I > 3 o ( I ) ] R 2 “ d o r d e r s a t e l l i t e s ( a l l d a t a ) T m a n d T 1 , fl a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e C 1 1 0 . 6 3 ( 2 ) E 1 1 T € 2 4 4 9 . 1 1 0 0 . 0 ( 3 ) K M o n o c l i n i c X m ( 0 1 3 1 0 ) ( O B 2 0 ) 0 ( 0 0 1 / 2 1 / 2 0 ) a = 4 . 4 5 3 6 ( 2 ) A , 0 1 = 9 0 ° b = 4 . 4 7 2 3 ( 2 ) A , 0 = 9 0 ° c = 2 0 . 2 9 8 2 ( 6 ) A , y = 9 0 ° 0 . 2 9 1 0 ( 2 ) b ' 0 . 3 5 5 7 ( 3 ) b ‘ 4 0 4 . 3 0 ( 3 ) A 3 4 7 . 3 7 5 8 g / c t n 3 3 2 . 7 3 5 m m " 0 . 1 4 x 0 . 1 1 x 0 . 0 2 m m 3 1 . 6 2 t o 2 9 2 1 ° - 6 < = h < = 6 , - 6 < = k < = 6 , - 2 7 < = 1 < = 2 7 , - 1 < = = m < = 1 1 7 3 2 6 ( 1 6 2 1 m a i n + 1 5 7 0 5 s a t e l l i t e s ) 9 0 1 5 ( 9 4 7 m a i n + 4 0 2 8 s a t e l l i t e s ) [ 8 , m = 0 . 0 4 9 1 ] 9 7 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 9 0 1 5 / 0 / 3 4 7 2 . 4 6 R o b , = 0 . 0 6 2 2 , w R o b , = 0 . 2 0 8 5 R . “ = 0 . 1 0 8 1 , w i t , “ = 0 . 2 2 6 7 R o b , = 0 . 0 3 8 0 , w u o b , = 0 . 1 3 3 2 R , “ = 0 . 0 3 8 4 , W K , “ = 0 . 1 3 4 2 R o b , = 0 . 0 9 6 3 , w R o b , = 0 . 2 2 3 7 R , “ = 0 . 1 5 6 9 , w k . “ = 0 . 2 4 1 6 R o b , = 0 . 1 4 5 3 , w R o b , = 0 . 3 1 0 5 R , “ = 0 . 2 9 3 1 , w k , “ = 0 . 3 4 7 8 0 . 0 5 3 1 a n d 0 . 4 6 6 4 3 . 5 4 a n d - 3 . 6 5 e . A ' 3 R = E I I F e l - c h l l / 2 1 8 . 1 . w R = { 2 1 0 1 8 1 2 - 1 8 1 0 2 1 / 2 1 0 1 8 1 0 1 1 ” a n d W = 1 / ( 6 2 ( I ) + 0 - 0 0 1 6 1 2 ) 4 9 3 T a b l e 6 . 4 8 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C u o , 6 3 ( 2 ) E u T e 2 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x y 2 O c c u p a n c y U c q E u [ l a ] 0 2 5 4 9 7 5 4 9 1 2 9 7 1 1 6 ( 1 ) s i n , 1 0 - 1 7 ( 2 ) 0 c o s , 1 - 2 ( 2 ) 0 2 0 ( 1 ) s i n , 2 0 - 1 0 ( 2 ) 0 c o s , 2 - 2 2 ( 2 ) 0 0 ( 1 ) s i n , 3 0 - 1 ( 2 ) 0 c o s , 3 - 4 4 ( 2 ) 0 - 2 ( 1 ) s i n , 4 0 2 ( 4 ) 0 c o s , 4 - 1 ( 4 ) 0 0 ( 1 ) E u [ l b ] 0 - 2 5 0 0 ( 2 ) - 7 4 5 1 - 1 3 0 0 ( 1 ) 1 1 7 ( 1 ) s i n , 1 0 2 ( 2 ) 0 c o s , 1 3 ( 2 ) 0 2 5 ( 1 ) s i n , 2 0 5 ( 2 ) 0 c o s , 2 3 6 ( 2 ) ' 0 0 ( 1 ) s i n , 3 0 1 1 ( 2 ) 0 c o s , 3 - 3 9 ( 2 ) 0 2 ( 1 ) s i n , 4 0 1 ( 4 ) 0 c o s , 4 - 2 ( 3 ) 0 1 ( 1 ) T e [ l a ] 0 2 5 2 2 ( 3 ) 7 5 4 9 3 2 1 1 ( 1 ) 1 1 3 ( 1 ) s i n , 1 0 4 2 ( 2 ) 0 c o s , 1 2 ( 2 ) 0 - 8 ( 1 ) s i n , 2 0 - 1 ( 5 ) 0 c o s , 2 - 1 ( 8 ) 0 0 ( 2 ) s i n , 3 0 - 1 ( 2 ) 0 c o s , 3 - 7 ( 2 ) 0 0 ( 1 ) s i n , 4 0 1 ( 4 ) 0 c o s , 4 2 ( 4 ) 0 1 ( 1 ) 4 9 4 T a b l e 6 . 4 8 . ( C o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C u o , 6 3 ( 2 ) E u T e 2 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 1 b ] 0 - 2 4 7 9 ( 3 ) - 7 4 5 1 - 3 2 1 3 ( 1 ) 1 2 ( 1 ) s i n , 1 0 - 4 0 ( 2 ) 0 c o s , 1 — 2 ( 2 ) 0 - 9 ( 1 ) s i n , 2 0 1 ( 4 ) 0 c o s , 2 0 ( 4 ) 0 0 ( 1 ) s i n , 3 0 1 ( 2 ) 0 c o s , 3 - 5 ( 2 ) 0 0 ( 1 ) s i n , 4 0 5 ( 4 ) 0 c o s , 4 - 3 ( 3 ) 0 - 2 ( 1 ) T e [ 2 a ] 0 2 4 7 6 ( 5 ) 2 5 4 9 2 ( 1 ) 1 6 ( 1 ) s i n , 1 0 - 7 5 ( 2 ) 0 c o s , 1 6 ( 4 ) 0 1 6 ( 1 ) s i n , 2 0 - 2 ( 3 ) 0 c o s , 2 1 2 5 ( 3 ) 0 - 2 ( 1 ) s i n , 3 0 - 3 1 ( 2 ) 0 c o s , 3 - 1 5 2 ( 3 ) 0 6 ( 1 ) s i n , 4 0 4 ( 5 ) 0 c o s , 4 - 1 2 ( 4 ) 0 0 ( 1 ) T e [ 2 b ] 0 - 2 5 1 6 ( 6 ) - 2 4 5 1 5 ( 1 ) 1 7 ( 1 ) s i n , 1 0 1 0 2 ( 3 ) 0 c o s , 1 - 8 ( 4 ) 0 1 1 ( 1 ) s i n , 2 0 1 4 ( 3 ) 0 c o s , 2 - 1 5 8 ( 3 ) 0 - 1 ( 1 ) s i n , 3 0 - 4 0 ( 2 ) 0 c o s , 3 - 1 7 3 ( 4 ) 0 - 7 ( 1 ) s i n , 4 0 - 9 ( 5 ) 0 c o s , 4 - 1 3 ( 4 ) 0 - 5 ( 1 ) 4 9 5 T a b l e 6 . 4 8 . ( C o n t ’ d ) A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C u o _ 6 3 ( 2 ) E u T e 2 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . C u [ 1 a ] O 2 5 3 6 ( 1 9 ) 2 5 4 9 2 5 0 2 ( 4 ) 0 . 5 6 2 ( 9 ) 3 0 ( 1 ) s i n , 1 0 9 4 ( 1 3 ) 0 c o s , 1 - 8 ( 1 2 ) 0 - 4 ( 3 ) s i n , 2 0 1 0 ( 1 3 ) 0 c o s , 2 3 0 ( 1 1 ) 0 - 1 2 ( 3 ) s i n , 3 0 5 2 ( 1 1 ) 0 c o s , 3 1 9 5 ( 3 0 ) 0 - 2 2 ( 3 ) s i n , 4 0 1 4 ( 1 9 ) 0 c o s , 4 - 5 4 ( 1 6 ) 0 8 ( 5 ) C u [ 1 b ] 0 - 2 4 6 4 ( 1 1 ) - 2 4 5 1 - 2 5 0 1 ( 2 ) 0 . 7 0 0 ( 8 ) 1 0 ( 1 ) s i n , 1 0 - 4 0 ( 8 ) 0 c o s , 1 — 6 ( 7 ) 0 3 ( 2 ) s i n , 2 0 4 1 ( 8 ) 0 c o s , 2 1 1 ( 6 ) 0 - 6 ( 1 ) s i n , 3 0 - 2 1 ( 7 ) 0 c o s , 3 - 9 5 ( 1 6 ) 0 4 ( 2 ) s i n , 4 0 - 1 8 ( 1 1 ) 0 c o s , 4 4 1 ( 1 0 ) 0 - 2 ( 2 ) T a b l e 6 . 4 9 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r C u o , 6 3 ( 2 ) E u T e 2 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 E u [ l a ] 0 1 2 ( 1 ) 1 1 ( 1 ) 2 6 ( 1 ) 0 - 2 0 ) 0 s i n , 1 0 o 0 0 ( 1 ) 0 0 ( 1 ) c o s , 1 0 ( 1 ) - 1 0 ) 5 ( 1 ) 0 - 3 0 ) 0 s i n , 2 0 0 0 1 ( 1 ) 0 0 ( 1 ) c o s , 2 1 ( 1 ) 1 ( 1 ) - 2 0 ) 0 0 ( 1 ) 0 s i n , 3 0 0 0 1 ( 1 ) 0 - 2 0 ) c o s , 3 0 ( 1 ) - 1 0 ) 0 ( 1 ) 0 - 2 0 ) 0 s i n , 4 0 0 0 1 ( 1 ) 0 0 ( 1 ) c o s , 4 0 ( 1 ) 2 ( 1 ) 2 ( 1 ) 0 - l ( 1 ) 0 4 9 6 T a b l e 6 . 4 9 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r C u o , 6 3 ( 2 ) E u T e 2 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . E u [ l b ] 0 1 5 ( 1 ) 1 0 ( 1 ) 2 6 ( 1 ) 0 2 ( 1 ) 0 s i n , 1 0 0 0 0 ( 1 ) 0 - 2 ( 1 ) c o s , 1 - 2 ( 1 ) - 2 ( 1 ) 4 ( 1 ) 0 - 3 ( 1 ) 0 s i n , 2 0 0 0 1 ( 1 ) 0 1 ( 1 ) c o s , 2 0 ( 1 ) - 1 ( 1 ) 1 ( 1 ) 0 - l ( 1 ) 0 s i n , 3 0 0 0 - 1 ( 1 ) 0 2 ( 1 ) c o s , 3 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 0 ( 1 ) 0 s i n , 4 0 0 0 1 ( 1 ) 0 0 ( 1 ) c o s , 4 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 0 ( 1 ) 0 T e [ l a ] 0 1 0 ( 1 ) 9 ( 1 ) 2 0 ( 1 ) 0 1 ( 1 ) 0 s i n , 1 0 0 0 - 1 ( 1 ) 0 1 ( 1 ) c o s , 1 0 ( 1 ) 1 ( 1 ) - 1 ( 1 ) 0 1 ( 1 ) 0 s i n , 2 0 0 0 0 ( 1 ) 0 0 ( 1 ) c o s , 2 - 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 0 ( 1 ) 0 s i n , 3 0 0 0 1 ( 1 ) 0 1 ( 1 ) c o s , 3 1 ( 1 ) - 1 ( 1 ) - l ( 1 ) 0 1 ( 1 ) 0 s i n , 4 0 0 0 0 ( 1 ) 0 0 ( 1 ) c o s , 4 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 0 ( 1 ) 0 T e [ l b ] 0 1 2 ( 1 ) 9 ( 1 ) 1 5 ( 1 ) 0 - 1 ( 1 ) 0 s i n , 1 0 0 0 1 ( 1 ) 0 0 ( 1 ) c o s , 1 0 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) 0 1 ( 1 ) 0 s i n , 2 0 0 0 0 ( 1 ) 0 0 ( 1 ) c o s , 2 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 0 ( 1 ) 0 s i n , 3 0 0 0 1 ( 1 ) 0 0 ( 1 ) c o s , 3 1 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) 0 0 ( 1 ) 0 s i n , 4 0 0 0 0 ( 1 ) 0 - 1 ( 1 ) c o s , 4 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 - 1 ( 1 ) 0 T a b l e 6 . 4 9 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r C u o , 6 3 ( 2 ) E u T e 2 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 2 a ] 0 1 5 ( 1 ) 1 9 ( 1 ) 1 3 ( 1 ) 0 1 ( 1 ) 0 s i n , 1 0 0 0 - 1 ( 1 ) 0 1 ( 1 ) c o s , 1 - 1 1 ( 1 ) - 2 ( 1 ) - 1 ( 1 ) 0 1 ( 1 ) 0 s i n , 2 0 0 0 1 ( 1 ) 0 1 ( 1 ) c o s , 2 2 ( 1 ) 1 ( 1 ) - 2 ( 1 ) 0 - 2 ( 1 ) 0 s i n , 3 0 0 0 0 ( 1 ) 0 0 ( 1 ) c o s , 3 0 ( 1 ) - 2 ( 1 ) - 1 ( 1 ) 0 1 ( 1 ) 0 s i n , 4 0 0 0 2 ( 1 ) 0 0 ( 1 ) c o s , 4 - 1 ( 1 ) 0 ( 1 ) 4 ( 1 ) 0 2 ( 1 ) 0 T e [ 2 b ] 0 2 1 ( 1 ) 1 7 ( 1 ) 1 5 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 0 0 0 0 ( 1 ) 0 - 2 ( 1 ) c o s , 1 1 2 ( 1 ) - 1 ( 1 ) - 1 ( 1 ) 0 1 ( 1 ) 0 s i n , 2 O 0 0 1 ( 1 ) 0 1 ( 1 ) c o s , 2 - 2 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 0 - 2 ( 1 ) 0 s i n , 3 0 0 0 1 ( 1 ) 0 0 ( 1 ) c o s , 3 0 ( 1 ) - 2 ( 1 ) - 1 ( 1 ) 0 - 3 ( 1 ) 0 s i n , 4 0 0 0 3 ( 1 ) 0 1 ( 1 ) c o s , 4 1 ( 1 ) 3 ( 1 ) 1 ( 1 ) 0 - 2 ( 1 ) 0 C u [ 1 a ] 0 3 0 ( 3 ) 2 2 ( 2 ) 3 2 ( 2 ) 0 0 ( 1 ) 0 s i n , 1 0 0 0 0 ( 2 ) 0 2 ( 2 ) c o s , 1 5 ( 3 ) - 8 ( 3 ) 3 ( 3 ) 0 0 ( 2 ) 0 s i n , 2 0 0 0 4 ( 2 ) 0 - 3 ( 2 ) c o s , 2 - 2 1 ( 4 ) - 1 3 ( 3 ) 2 0 ( 3 ) 0 0 ( 3 ) 0 s i n , 3 0 0 0 6 ( 2 ) 0 5 ( 2 ) c o s , 3 - 1 5 ( 3 ) - 6 ( 2 ) 1 ( 2 ) 0 2 ( 2 ) 0 s i n , 4 0 0 0 0 ( 3 ) 0 - 2 ( 3 ) c o s , 4 1 3 ( 4 ) 1 ( 4 ) 2 ( 5 ) 0 5 ( 3 ) 0 4 9 8 T a b l e 6 . 4 9 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r C u o , 6 3 ( 2 ) E u T e 2 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . C u [ 1 b ] 0 s i n , 1 c o s , 1 s i n , 2 c o s , 2 s i n , 3 c o s , 3 s i n , 4 c o s , 4 1 6 ( 1 ) 0 4 ( 2 ) 0 7 ( 2 ) 0 - 1 ( 2 ) 0 5 ( 2 ) 1 1 ( 1 ) 0 - 5 ( 2 ) 0 5 ( 2 ) 0 - 4 ( 1 ) 0 7 ( 2 ) 4 ( 1 ) 0 1 ( 1 ) 0 - 3 ( 2 ) 0 - 2 ( 1 ) 0 4 ( 2 ) 0 1 ( 1 ) 0 - 1 ( 1 ) 0 - 1 0 ) 0 1 ( 1 ) 0 1 ( 1 ) 0 - 1 0 ) 0 - 2 0 ) o - 5 0 ) 0 4 ( 1 ) 0 - 1 0 ) 0 1 ( 2 ) 0 - 2 0 ) 0 0 ( 2 ) 0 T a b l e 6 . 5 0 . F o u r i e r c o m p o n e n t s o f t h e o c c u p a t i o n a l m o d u l a t i o n f o r C u o , 6 3 ( 2 ) E u T e 2 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e O c c u p a t i o n a l c o m p o n e n t C u [ 1 a ] s i n , 1 0 c o s , 1 - 0 . 0 6 5 ( 1 4 ) C u [ 1 a ] s i n , 2 0 c o s , 2 - 0 . 0 0 3 ( 1 8 ) C u [ 1 a ] s i n , 3 0 c o s , 3 - 0 . 0 6 0 ( 9 ) C u [ 1 a ] s i n , 4 0 c o s , 4 0 0 2 ( 3 ) C u [ 1 b ] s i n , 1 0 c o s , 1 0 . 0 2 6 ( 1 2 ) C u [ 1 b ] s i n , 2 0 c o s , 2 - 0 . 0 1 9 ( 1 6 ) C u [ 1 b ] s i n , 3 0 c o s , 3 - 0 . 0 4 6 ( 8 ) C u [ 1 b ] s i n , 4 0 c o s , 4 0 0 2 ( 2 ) 4 9 9 T a b l e 6 . 5 1 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C u o , 6 3 ( 2 ) E u T e 2 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e E u [ l a ] - T e [ l a ] x 2 3 . 3 0 3 ( 4 ) 3 . 2 8 3 ( 4 ) 3 . 3 2 9 ( 4 ) E u [ l a ] - T e [ l b ] x 2 3 . 3 1 5 ( 4 ) 3 . 2 8 9 ( 4 ) 3 . 3 4 0 ( 4 ) E u [ l a ] - T e [ 2 a ] x 2 3 . 4 5 1 ( 4 ) 3 . 4 2 5 ( 4 ) 3 . 4 7 9 ( 4 ) E u [ l a ] - T e [ 2 b ] x 2 3 . 4 4 4 ( 5 ) 3 . 3 6 4 ( 8 ) 3 . 5 5 6 ( 8 ) E u [ l a ] - C u [ 1 a ] x 2 3 . 3 1 1 ( 1 6 ) 3 . 2 3 3 ( 1 5 ) 3 . 3 7 2 ( 1 5 ) E u [ l a ] - C u [ 1 b ] 3 . 2 9 4 ( 9 ) 3 . 2 0 9 ( 1 3 ) 3 . 3 6 4 ( 1 0 ) E u [ l a ] - C u [ 1 b ] 3 . 3 1 3 ( 9 ) 3 . 2 5 2 ( 1 1 ) 3 . 3 7 5 ( 1 1 ) E u [ l b ] - T e [ l a ] x 2 3 . 3 0 2 ( 4 ) 3 . 2 8 0 ( 4 ) 3 . 3 2 4 ( 4 ) E u [ l b ] - T e [ l a ] x 2 3 . 3 1 5 ( 4 ) 3 . 2 8 6 ( 4 ) 3 . 3 4 0 ( 5 ) E u [ l b ] - T e [ l b ] 3 . 8 8 2 ( 4 ) 3 . 8 0 1 ( 7 ) 3 . 9 5 9 ( 7 ) E u [ l b ] - T e [ 2 a ] 3 . 4 6 3 ( 5 ) 3 . 4 1 2 ( 8 ) 3 . 5 4 3 ( 8 ) E u [ l b ] - T e [ Z a ] 3 . 4 5 0 ( 5 ) 3 . 4 0 8 ( 8 ) 3 . 5 1 7 ( 8 ) E u [ l b ] - T e [ 2 b ] x 2 3 . 4 6 9 ( 5 ) 3 . 4 4 3 ( 5 ) 3 . 5 0 0 ( 5 ) E u [ l b ] - O r [ l a ] x 2 3 . 2 8 9 ( 1 7 ) 3 . 2 5 0 ( 1 7 ) 3 3 5 ( 3 ) E u [ l b ] - C u [ 1 b ] x 2 3 . 3 0 8 ( 9 ) 3 . 2 6 8 ( 8 ) 3 . 3 5 5 ( 8 ) T e [ l a ] - C u [ 1 a ] x 2 2 . 6 6 2 ( 1 5 ) 2 . 6 0 7 ( 1 5 ) 2 . 7 2 8 ( 1 6 ) T e [ l a ] - C u [ 1 b ] x 2 2 . 6 5 1 ( 1 0 ) 2 . 6 0 3 ( 1 2 ) 2 . 6 9 9 ( 1 2 ) T e [ l b ] - C u [ 1 a ] x 2 2 . 6 5 1 ( 1 7 ) 2 . 5 2 6 ( 1 8 ) 2 . 7 7 3 ( 1 9 ) T e [ l b ] - C u [ 1 b ] x 2 2 . 6 6 3 ( 8 ) 2 . 6 3 6 ( 8 ) 2 . 6 9 0 ( 9 ) T e [ 2 a ] - T e [ 2 b ] x 4 3 . 1 5 9 ( 5 ) 2 . 9 3 5 ( 5 ) 3 . 2 8 0 ( 5 ) C u [ 1 a ] - C u [ 1 b ] x 4 3 . 1 5 9 ( 1 8 ) 3 . 0 5 0 ( 1 9 ) 3 . 2 7 1 ( 1 8 ) T a b l e 6 . 5 2 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C u o , 6 3 ( 2 ) E u T e 2 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ l a ] - E u [ l a ] - T e [ l b ] x 4 7 2 . 5 5 ( 7 ) 7 1 9 2 ( 1 0 ) 7 3 . 1 5 ( 1 1 ) T e [ l a ] - E u [ l a ] - T e [ 2 a ] x 2 1 3 9 6 0 ( 1 1 ) l 3 8 7 8 ( 1 3 ) 1 4 0 . 4 0 ( 1 1 ) T e [ l a ] - E u [ l a ] - T e [ 2 b ] x 2 1 3 9 7 1 ( 1 0 ) 1 3 8 . 9 5 ( 8 ) 1 4 0 . 8 5 ( 1 7 ) T e [ l a ] - E u [ l a ] - Q l [ 1 a ] x 2 4 2 . 5 ( 3 ) 4 0 9 ( 3 ) 4 4 3 ( 3 ) T e [ l a ] - E u [ l a ] - C u [ 1 b ] x 2 4 2 3 4 ( 1 0 ) 4 1 3 7 ( 9 ) 4 3 2 0 ( 9 ) T e [ l b ] - E u [ l a ] - T e [ l b ] x 4 8 5 2 2 ( 1 0 ) 8 4 . 4 1 ( 1 3 ) 8 6 4 7 ( 1 3 ) 5 0 0 T a b l e 6 . 5 2 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C u o _ 6 3 ( 2 ) E u T e 2 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ l b ] - E u [ l a ] - T e [ l b ] x 4 T e [ l b ] - E u [ l a ] - T e [ l b ] x 4 T e [ l b ] - E u [ 1 a ] - T e [ 2 a ] x 4 T e [ l b ] - E u [ 1 a ] - T e [ 2 a ] x 4 T e [ l b ] - E u [ l a ] - T e [ 2 b ] x 4 T e [ l b ] - E u [ l a ] - T e [ 2 b ] x 4 T e [ l b ] - E u [ l a ] - C u [ 1 a ] x 4 T e [ l b ] - E u [ l a ] - C u [ 1 a ] x 4 T e [ l b ] - E u [ l a ] - C u [ 1 b ] x 4 T e [ l b ] - E u [ l a ] - C u [ 1 b ] x 4 T e [ 2 a ] - E u [ l a ] - T e [ 2 a ] x 2 T e [ 2 a ] - E u [ l a ] - T e [ 2 b ] x 4 T e [ 2 a ] - E u [ l a ] - C u [ 1 a ] x 2 T e [ 2 a ] - E u [ l a ] - C u [ 1 a ] x 2 T e [ 2 a ] - E u [ l a ] - C u [ 1 b ] x 4 T e [ 2 b ] - E u [ l a ] - T e [ 2 b ] x 2 T e [ 2 b ] - E u [ l a ] - C u [ 1 a ] x 4 T e [ 2 b ] - E u [ l a ] - C u [ 1 b ] x 2 T e [ 2 b ] - E u [ l a ] - C u [ 1 b ] x 2 C u [ 1 a ] - E u [ l a ] - C u [ 1 a ] x 2 C u [ 1 a ] - E u [ l a ] - C u [ 1 b ] x 4 C u [ 1 b ] - E u [ l a ] - C u [ 1 b ] x 2 T e [ l a ] - E u [ l b ] - T e [ l a ] x 6 T e [ l a ] - E u [ l b ] - T e [ l a ] x 4 T e [ l a ] - E u [ l b ] - T e [ l b ] x 4 T e [ 1 a ] - E u [ l b ] - T e [ 2 a ] x 4 T e [ l a ] - E u [ l b ] - T e [ 2 a ] x 4 T e [ l a ] - E u [ l b ] - T e [ 2 b ] x 4 T e [ l a ] - E u [ l b ] - T e [ 2 b ] x 4 T e [ l a ] - E u [ l b ] - C u [ 1 a ] x 4 T e [ l a ] - E u [ l b ] - C u [ 1 a ] x 4 T e [ l a ] - E u [ l b ] - C u [ 1 b ] x 4 T e [ l a ] - E u [ l b ] - C u [ 1 b ] x 4 T e [ l a ] - E u [ l b ] - T e [ l a ] x 2 8 4 5 9 ( 9 ) 1 4 4 . 9 7 0 0 ) 7 7 8 4 ( 9 ) 1 3 1 . 7 3 0 0 ) 7 8 1 7 ( 1 0 ) 1 3 1 . 6 7 0 3 ) 4 7 5 ( 2 ) 1 0 3 . 7 ( 3 ) 4 7 6 ( 2 ) 1 0 3 . 4 ( 2 ) 8 0 . 7 9 0 1 ) 5 4 5 1 ( 1 1 ) 9 7 1 ( 4 ) 1 7 7 . 2 ( 3 ) 1 2 4 . 2 ( 2 ) 8 0 6 7 ( 1 0 ) 1 2 4 . 4 ( 3 ) 9 7 3 7 ( 1 2 ) 1 7 7 5 9 0 7 ) 8 4 9 ( 4 ) 5 7 1 ( 4 ) 8 4 . 7 6 0 9 ) 8 5 2 5 ( 1 1 ) 1 4 5 . 0 6 ( 1 1 ) 7 2 5 9 ( 1 0 ) 7 8 2 4 ( 1 1 ) 1 3 1 . 4 8 ( 1 3 ) 7 8 0 1 ( 1 1 ) 1 3 1 . 6 4 0 2 ) 4 7 6 ( 4 ) 1 0 3 . 5 ( 3 ) 4 7 . 4 3 0 4 ) 1 0 3 . 8 2 0 8 ) 8 4 6 0 ( 1 0 ) 8 4 2 1 ( 9 ) l 4 3 . 6 7 ( 1 7 ) 7 5 9 6 ( 9 ) 1 2 9 . 3 4 ( 8 ) 7 6 . 9 5 0 0 ) 1 2 9 . 8 5 0 3 ) 4 5 9 ( 2 ) 1 0 0 . 9 ( 3 ) 4 6 7 ( 2 ) 1 0 2 . 1 ( 2 ) 7 9 2 1 ( 1 4 ) 5 0 7 5 ( 1 1 ) 9 6 0 ( 4 ) 1 7 5 . 2 ( 3 ) 1 2 1 . 4 ( 2 ) 7 9 7 5 ( 1 6 ) 1 2 2 . 2 ( 2 ) 9 6 . 3 5 0 8 ) 1 7 6 . 7 ( 2 ) 8 2 3 ( 4 ) 5 4 4 ( 4 ) 8 3 4 ( 3 ) 8 4 3 6 ( 1 0 ) 1 4 3 . 4 4 0 6 ) 7 1 . 7 2 0 2 ) 7 7 . 2 3 ( 1 1 ) 1 2 9 8 0 ( 1 3 ) 7 5 8 4 ( 1 2 ) 1 2 8 . 7 1 0 0 ) 4 6 3 ( 4 ) 1 0 1 . 9 ( 3 ) 4 6 2 9 ( 1 2 ) 1 0 1 . 9 2 0 8 ) 8 4 3 0 ( 1 1 ) 8 4 9 3 ( 9 ) 1 4 6 . 2 1 ( 1 7 ) 7 9 5 5 ( 1 1 ) 1 3 4 . 1 8 ( 9 ) 7 9 7 8 ( 9 ) 1 3 3 . 7 5 0 3 ) 4 9 0 ( 2 ) 1 0 6 . 7 ( 3 ) 4 8 4 ( 2 ) 1 0 4 . 6 ( 2 ) 8 2 2 1 ( 1 4 ) 5 6 5 4 ( 1 1 ) 9 8 4 ( 4 ) 1 7 9 . 4 ( 3 ) 1 2 6 . 8 ( 2 ) 8 1 . 4 8 ( 1 6 ) 1 2 6 . 0 ( 3 ) 9 8 . 3 7 0 8 ) 1 7 9 . 0 ( 2 ) 8 6 9 ( 4 ) 6 0 1 ( 4 ) 8 6 1 ( 3 ) 8 6 6 8 ( 1 4 ) 1 4 6 . 7 9 0 7 ) 7 3 4 1 ( 9 ) 7 9 2 6 ( 1 1 ) 1 3 3 . 2 3 0 2 ) 8 0 . 2 3 0 4 ) 1 3 4 . 6 3 ( 9 ) 4 8 9 ( 4 ) 1 0 5 . 0 ( 3 ) 4 8 8 1 ( 1 3 ) 1 0 5 . 7 ( 2 ) 8 4 . 9 3 0 0 ) 5 0 1 T a b l e 6 . 5 2 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C u o _ 6 3 ( 2 ) E u T e 2 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ l b ] - E u [ l b ] - T e [ 2 a ] x 2 T e [ l b ] - E u [ l b ] - T e [ 2 b ] x 2 T e [ l b ] - E u [ l b ] - C u [ l a ] x 2 T e [ l b ] - E u [ l b ] - C u [ 1 b ] x 2 T e [ 2 a ] - E u [ l b ] - T e [ 2 a ] x 2 T e [ 2 a ] - E u [ l b ] - T e [ 2 b ] x 4 T e [ 2 a ] - E u [ l b ] - C u [ 1 a ] x 2 T e [ 2 a ] - E u [ l b ] - C u [ 1 a ] x 2 T e [ 2 a ] - E u [ l b ] - C u [ 1 b ] x 4 T e [ 2 b ] - E u [ l b ] - T e [ 2 b ] x 2 T e [ 2 b ] - E u [ l b ] — C u [ 1 a ] x 4 T e [ 2 b ] - E u [ l b ] - C u [ 1 b ] x 2 T e [ 2 b ] - E u [ l b ] - C u [ 1 b ] x 2 C u [ 1 a ] - E u [ l b ] - C u [ 1 a ] x 2 C u [ 1 a ] - E u [ l b ] - C u [ 1 b ] x 4 C u [ 1 b ] - E u [ l b ] - C u [ 1 b ] x 2 E u [ l a ] - T e [ l a ] - E u [ l b ] x 4 E u [ l a ] - T e [ l a ] - C u [ 1 a ] x 2 E u [ l a ] - T e [ l a ] - C u [ 1 b ] x 2 E u [ l b ] - T e [ l a ] - E u [ l b ] x 8 E u [ l b ] - T e [ l a ] - E u [ l b ] x 4 E u [ l b ] - T e [ l a ] - C u [ 1 a ] x 4 E u [ l b ] - T e [ l a ] - C u [ 1 a ] x 4 E u [ l b ] - T e [ l a ] - C u [ 1 b ] x 4 E u [ l b ] - T e [ l a ] - C u [ 1 b ] x 4 C u [ 1 a ] - T e [ l a ] - C u [ l a ] x 2 C u [ 1 a ] - T e [ l a ] - C u [ 1 b ] x 4 C u [ 1 b ] - T e [ l a ] - C u [ 1 b ] x 2 E u [ l a ] - T e [ l b ] - E u [ l a ] x 8 E u [ l a ] - T e [ l b ] - E u [ l a ] x 4 E u [ l a ] - T e [ l b ] - E u [ l b ] x 4 E u [ l a ] - T e [ l b ] - C u [ 1 a ] x 4 E u [ l a ] - T e [ l b ] - C u [ l a ] x 4 E u [ l a ] - T e [ l b ] - C u [ 1 b ] x 4 l 3 9 . 8 9 ( 9 ) 1 3 9 8 0 ( 1 1 ) 4 2 3 8 ( 1 6 ) 4 2 5 ( 2 ) 8 0 2 1 ( 9 ) 5 4 3 2 ( 9 ) 9 7 . 5 1 ( 1 8 ) 1 7 7 . 3 ( 2 ) 1 2 4 . 4 5 0 7 ) 8 0 3 4 ( 1 1 ) 1 2 4 . 4 ( 4 ) 9 7 3 ( 2 ) 1 7 7 . 2 ( 2 ) 8 4 9 ( 3 ) 5 7 2 ( 3 ) 8 5 1 ( 2 ) 1 0 7 . 2 8 0 0 ) 5 7 . 2 ( 3 ) 5 6 8 2 ( 1 3 ) 8 4 8 5 ( 1 1 ) 1 4 5 0 8 0 4 ) 6 6 2 ( 3 ) 1 3 6 . 9 ( 2 ) 6 6 3 ( 3 ) 1 3 6 . 8 ( 3 ) 1 1 4 . 4 ( 5 ) 7 3 0 ( 5 ) 1 1 4 . 0 ( 3 ) 8 4 8 3 ( 1 0 ) 1 4 4 . 9 5 0 0 ) 1 0 7 . 3 5 0 0 ) 6 6 4 ( 4 ) 1 3 6 . 8 ( 6 ) 6 6 2 6 ( 1 7 ) l 3 9 4 6 ( 1 5 ) 1 3 8 . 7 5 ( 1 3 ) 4 0 2 3 ( 1 6 ) 4 1 4 ( 2 ) 7 9 6 6 ( 1 4 ) 5 0 8 0 ( 9 ) 9 4 8 9 ( 1 7 ) 1 7 5 . 8 ( 2 ) 1 2 2 . 5 5 0 6 ) 7 8 3 0 ( 1 4 ) 1 2 1 . 8 ( 4 ) 9 6 3 ( 2 ) 1 7 5 . 0 ( 2 ) 8 3 2 ( 3 ) 5 4 . 7 ( 3 ) 8 3 . 4 ( 3 ) 1 0 6 . 1 3 ( 1 1 ) 5 5 1 ( 4 ) 5 5 5 3 ( 1 2 ) 8 4 . 3 8 0 7 ) 1 4 4 . 5 6 ( 9 ) 6 3 4 ( 3 ) 1 3 4 . 8 ( 3 ) 6 5 1 ( 3 ) 1 3 6 . 1 ( 3 ) 1 1 1 . 2 ( 6 ) 7 1 0 ( 5 ) 1 1 3 . 3 ( 3 ) 8 4 5 2 ( 1 0 ) 1 4 4 . 6 8 ( 8 ) 1 0 6 . 3 2 ( 8 ) 6 5 5 ( 4 ) 1 3 5 . 7 ( 6 ) 6 4 8 8 ( 1 7 ) 1 4 0 7 7 ( l 6 ) 1 4 0 . 8 5 ( 1 0 ) 4 4 . 7 1 0 6 ) 4 3 7 ( 2 ) 8 0 6 5 ( 8 ) 5 6 8 0 ( 9 ) 9 9 9 2 ( 1 7 ) 1 7 9 . 0 ( 2 ) 1 2 6 . 1 8 ( 1 7 ) 8 2 2 2 ( 1 1 ) 1 2 6 . 3 ( 4 ) 9 8 3 ( 2 ) 1 7 9 . 3 ( 2 ) 8 7 0 ( 4 ) 5 9 6 ( 3 ) 8 7 4 ( 3 ) 1 0 8 . 4 3 0 0 ) 5 9 2 ( 3 ) 5 8 1 8 ( 1 1 ) 8 5 2 1 ( 1 0 ) 1 4 5 . 8 0 0 0 ) 6 8 7 ( 3 ) 1 3 9 . 3 ( 3 ) 6 7 8 ( 3 ) 1 3 8 . 0 ( 3 ) 1 1 6 . 8 ( 5 ) 7 5 3 ( 5 ) 1 1 5 . 1 ( 4 ) 8 5 2 2 ( 1 3 ) 1 4 5 3 6 0 0 ) 1 0 8 . 4 0 ( 9 ) 6 7 3 ( 4 ) 1 3 8 . 0 ( 6 ) 6 7 . 9 0 0 7 ) 5 0 2 T a b l e 6 . 5 2 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C u o , 6 3 ( 2 ) E u T e 2 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . E u [ l a ] - T e [ l b ] - C u [ 1 b ] x 4 E u [ l b ] - T e [ l b ] - C u [ 1 a ] x 2 E u [ l b ] - T e [ l b ] - C u [ 1 b ] x 2 C u [ 1 a ] - T e [ l b ] - C u [ 1 a ] x 2 C u [ 1 a ] - T e [ l b ] - C u [ 1 b ] x 4 C u [ 1 b ] - T e [ l b ] - C u [ 1 b ] x 2 E u [ l a ] - T e [ 2 a ] - E u [ l a ] x 2 E u [ l a ] - T e [ 2 a ] - E u [ l b ] x 4 E u [ l a ] - T e [ 2 a ] - T e [ 2 b ] x 4 E u [ l a ] - T e [ 2 a ] - T e [ 2 b ] x 4 E u [ l b ] - T e [ 2 a ] - E u [ l b ] x 2 E u [ l b ] - T e [ 2 a ] - T e [ 2 b ] x 4 E u [ l b ] - T e [ 2 a ] - T e [ 2 b ] x 4 T e [ 2 b ] - T e [ 2 a ] - T e [ 2 b ] x 8 T e [ 2 b ] - T e [ 2 a ] - T e [ 2 b ] x 4 E u [ l a ] - T e [ 2 b ] - E u [ l a ] x 2 E u [ l a ] - T e [ 2 b ] - E u [ l b ] x 4 E u [ l a ] - T e [ 2 b ] - T e [ 2 a ] x 4 E u [ l a ] - T e [ 2 b ] - T e [ 2 a ] x 4 E u [ l b ] - T e [ 2 b ] - E u [ l b ] x 2 E u [ l b ] - T e [ 2 b ] - T e [ 2 a ] x 4 E u [ l b ] - T e [ 2 b ] - T e [ 2 a ] x 4 T e [ 2 a ] - T e [ 2 b ] - T e [ 2 a ] x 8 T e [ 2 a ] - T e [ 2 b ] - T e [ 2 a ] x 4 E u [ l a ] - C u [ 1 a ] - E u [ l a ] x 2 E u [ l a ] - C u [ 1 a ] - E u [ l b ] x 4 E u [ l a ] - C u [ 1 a ] - T e [ l a ] x 2 E u [ l a ] - C u [ 1 a ] - T e [ l a ] x 2 E u [ l a ] - C u [ 1 a ] - T e [ l b ] x 4 E u [ l a ] - C u [ 1 a ] - C u [ 1 b ] x 4 E u [ l a ] - C u [ 1 a ] - C u [ 1 b ] x 4 E u [ l b ] — C u [ l a ] - E u [ l b ] x 2 E u [ l b ] - C u [ 1 a ] - T e [ l a ] x 4 E u [ l b ] - C u [ 1 a ] - T e [ l b ] x 2 1 3 6 . 9 6 ( 1 6 ) 5 6 7 ( 2 ) 5 7 1 ( 2 ) 1 1 3 . 9 ( 4 ) 7 2 9 ( 3 ) 1 1 4 . 3 ( 3 ) 8 0 7 7 ( 1 1 ) 1 2 5 . 8 0 ( 1 3 ) 6 2 6 6 ( 9 ) 1 1 7 . 3 6 0 4 ) 8 0 2 3 ( 9 ) 6 3 . 1 5 ( 1 0 ) 1 1 7 0 4 ( 1 3 ) 9 0 3 5 ( 1 5 ) 1 7 7 . 7 3 0 7 ) 8 0 . 6 6 0 0 ) 1 2 5 . 8 4 0 3 ) 6 3 0 2 ( 1 0 ) 1 1 7 2 0 ( 1 3 ) 8 0 . 3 0 0 1 ) 6 2 8 2 ( 1 0 ) 1 1 7 2 1 ( 1 4 ) 9 0 2 9 ( 1 6 ) 1 7 7 . 5 6 0 8 ) 8 5 0 ( 4 ) 1 2 2 . 6 ( 5 ) 8 0 3 ( 3 ) 1 6 5 . 1 ( 6 ) 6 6 1 ( 4 ) 6 1 1 ( 3 ) 1 1 8 . 3 ( 5 ) 8 4 . 9 ( 4 ) 6 6 . 4 ( 4 ) 8 0 3 ( 4 ) 1 3 5 . 2 6 ( l 7 ) 5 5 8 ( 2 ) 5 6 2 ( 2 ) 1 1 1 . 6 ( 4 ) 7 0 8 ( 3 ) 1 1 2 . 5 ( 3 ) 8 0 . 3 6 0 5 ) 1 2 3 . 0 9 0 2 ) 6 1 1 0 ( 9 ) 1 1 3 5 4 0 9 ) 7 9 . 6 7 0 5 ) 6 1 5 6 ( 9 ) 1 1 5 7 4 0 2 ) 8 5 4 0 ( 1 8 ) 1 7 4 . 3 9 0 7 ) 7 9 7 5 ( 1 6 ) 1 2 2 . 0 1 0 2 ) 6 0 8 6 ( 1 1 ) 1 1 5 . 3 9 0 2 ) 7 9 6 0 ( 1 5 ) 6 0 9 5 ( 9 ) 1 1 3 . 2 ( 2 ) 8 4 9 6 ( 2 0 ) 1 7 3 5 8 0 7 ) 8 3 4 ( 4 ) 1 1 9 . 2 ( 5 ) 7 8 1 ( 3 ) 1 6 1 . 4 ( 6 ) 6 5 1 ( 4 ) 5 9 1 ( 3 ) 1 1 6 . 8 ( 6 ) 8 3 2 ( 4 ) 6 3 8 ( 4 ) 7 7 . 3 ( 4 ) 1 3 8 . 5 0 0 7 ) 5 8 0 ( 2 ) 5 8 1 7 ( 1 9 ) 1 1 7 . 0 ( 7 ) 7 5 2 ( 4 ) 1 1 6 . 0 ( 3 ) 8 1 0 6 ( 1 0 ) 1 2 8 . 8 5 0 3 ) 6 3 9 9 ( 1 0 ) 1 2 0 . 3 ( 2 ) 8 0 6 5 ( 7 ) 6 5 5 8 ( 1 0 ) 1 1 8 . 9 7 0 2 ) 9 4 1 ( 2 ) 1 8 0 8 1 . 4 8 ( 1 6 ) 1 2 9 . 4 0 0 3 ) 6 5 8 5 ( 1 0 ) 1 1 9 . 2 6 ( 1 3 ) 8 1 0 6 ( 1 5 ) 6 3 . 8 9 0 0 ) 1 2 1 . 0 ( 2 ) 9 4 . 7 ( 2 ) 1 8 0 8 6 7 ( 5 ) 1 2 6 . 2 ( 5 ) 8 2 9 ( 5 ) 1 6 8 . 4 ( 6 ) 6 7 . 3 ( 4 ) 6 3 2 ( 3 ) 1 1 9 . 5 ( 6 ) 8 7 0 ( 5 ) 6 9 1 ( 4 ) 8 3 2 ( 5 ) 5 0 3 T a b l e 6 . 5 2 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C u o , 6 3 ( 2 ) E u T e 2 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . E u [ l b ] - C u [ 1 a ] - T e [ l b ] x 2 E u [ l b ] - C u [ 1 a ] - C u [ 1 b ] x 4 E u [ l b ] - C u [ l a ] - C u [ 1 b ] x 4 T e [ l a ] - C u [ 1 a ] - T e [ l a ] x 2 T e [ l a ] - C u [ 1 a ] - T e [ l b ] x 4 T e [ l a ] - C u [ 1 a ] - C u [ 1 b ] x 4 T e [ l a ] - C u [ 1 a ] - C u [ 1 b ] x 4 T e [ l b ] - C u [ 1 a ] - T e [ l b ] x 2 T e [ l b ] - C u [ 1 a ] - C u [ 1 b ] x 4 T e [ l b ] - C u [ l a ] - C u [ 1 b ] x 4 C u [ 1 b ] - C u [ 1 a ] - C u [ 1 b ] x 8 C u [ 1 b ] - C u [ 1 a ] - C u [ 1 b ] x 4 E u [ l a ] - C u [ 1 b ] - E u [ l a ] x 2 E u [ l a ] - C u [ 1 b ] - E u [ l b ] x 4 E u [ l a ] - C u [ 1 b ] - T e [ l a ] x 2 E u [ l a ] - C u [ 1 b ] - T e [ l a ] x 2 E u [ l a ] - C u [ 1 b ] - T e [ l b ] x 4 E u [ l a ] - C u [ 1 b ] - C u [ 1 a ] x 4 E u [ l a ] - C u [ 1 b ] - C u [ 1 a ] x 4 E u [ l b ] - C u [ 1 b ] - E u [ l b ] x 2 E u [ l b ] - C u [ 1 b ] - T e [ l a ] x 4 E u [ l b ] - C u [ 1 b ] - T e [ l b ] x 2 E u [ l b ] - C u [ 1 b ] - T e [ l b ] x 2 E u [ l b ] - C u [ 1 b ] - C u [ 1 a ] x 4 E u [ l b ] - C u [ 1 b ] - C u [ 1 a ] x 4 T e [ l a ] - C u [ 1 b ] - T e [ l a ] x 2 T e [ l a ] - C u [ 1 b ] - T e [ l b ] x 4 T e [ l a ] - C u [ 1 b ] - C u [ 1 a ] x 4 T e [ l a ] - C u [ 1 b ] - C u [ 1 a ] x 4 T e [ l b ] - C u [ 1 b ] - T e [ l b ] x 2 T e [ l b ] - C u [ 1 b ] - C u [ 1 a ] x 4 T e [ l b ] - C u [ 1 b ] - C u [ 1 a ] x 4 C u [ l a ] - C u [ 1 b ] - C u [ 1 a ] x 8 C u [ 1 a ] - C u [ 1 b ] - C u [ 1 a ] x 4 1 6 5 . 7 ( 6 ) 6 1 5 ( 3 ) 1 1 8 . 6 ( 5 ) 1 1 4 . 3 ( 6 ) 1 0 7 . 0 ( 6 ) 5 3 3 ( 3 ) 1 2 6 . 5 ( 6 ) 1 1 4 . 0 ( 6 ) 5 3 6 ( 3 ) 1 2 6 . 2 ( 5 ) 9 0 3 ( 5 ) 1 7 7 . 8 ( 6 ) 8 4 . 7 ( 2 ) 1 2 2 . 7 ( 3 ) 8 0 4 ( 3 ) 1 6 5 . 6 ( 4 ) 6 6 3 ( 2 ) 6 1 6 ( 3 ) 1 1 8 . 6 ( 3 ) 8 5 0 ( 2 ) 6 6 1 ( 2 ) 8 0 3 ( 2 ) 1 6 5 . 3 ( 3 ) 6 1 . 1 ( 3 ) 1 1 8 . 4 ( 4 ) 1 1 4 . 0 ( 3 ) 1 0 7 . 1 ( 3 ) 5 3 7 ( 3 ) 1 2 6 . 3 ( 4 ) 1 1 4 . 3 ( 3 ) 5 3 4 ( 3 ) 1 2 6 . 5 ( 4 ) 9 0 . 3 ( 5 ) 1 7 8 . 4 ( 5 ) 1 6 4 . 6 ( 5 ) 5 9 . 2 ( 3 ) 1 1 6 0 ( 5 ) 1 1 2 0 ( 6 ) 1 0 3 . 5 ( 5 ) 5 1 1 ( 3 ) 1 2 2 . 2 ( 7 ) 1 1 1 . 6 ( 6 ) 5 2 2 ( 3 ) 1 2 4 . 5 ( 5 ) 8 7 3 ( 7 ) 1 7 5 . 6 ( 6 ) 8 3 . 4 ( 3 ) 1 2 0 . 4 ( 3 ) 7 8 4 ( 3 ) 1 6 3 . 4 ( 4 ) 6 5 5 ( 2 ) 6 0 6 ( 3 ) 1 1 7 2 ( 3 ) 8 4 2 7 ( 1 8 ) 6 5 . 0 ( 2 ) 7 8 3 ( 2 ) 1 6 3 . 5 ( 3 ) 5 9 . 8 ( 3 ) 1 1 5 . 9 ( 3 ) 1 1 3 . 3 ( 3 ) 1 0 5 . 2 ( 3 ) 5 1 8 ( 4 ) 1 2 4 . 3 ( 4 ) 1 1 3 . 1 ( 5 ) 5 0 8 ( 3 ) 1 2 4 . 7 ( 5 ) 8 7 8 ( 6 ) 1 7 7 . 2 ( 6 ) 1 6 6 . 8 ( 7 ) 6 3 6 ( 4 ) 1 2 0 . 8 ( 5 ) 1 1 6 . 8 ( 6 ) 1 1 0 . 5 ( 6 ) 5 5 2 ( 3 ) 1 3 1 . 1 ( 7 ) 1 1 7 . 0 ( 1 0 ) 5 5 4 ( 4 ) 1 2 7 . 9 ( 6 ) 9 2 9 ( 5 ) 1 7 9 . 8 ( 6 ) 8 6 . 1 ( 3 ) 1 2 5 . 3 ( 3 ) 8 2 2 ( 3 ) 1 6 7 . 9 ( 3 ) 6 7 . 4 3 ( 1 8 ) 6 3 . 3 ( 3 ) 1 1 9 . 9 ( 3 ) 8 6 . 1 ( 3 ) 6 7 4 ( 2 ) 8 2 1 ( 2 ) 1 6 7 . 1 ( 3 ) 6 2 1 ( 3 ) 1 2 0 . 8 ( 3 ) 1 1 5 . 1 ( 5 ) 1 0 9 . 3 ( 4 ) 5 5 6 ( 3 ) 1 2 8 . 1 ( 4 ) 1 1 5 . 9 ( 5 ) 5 5 5 ( 3 ) 1 2 8 . 4 ( 5 ) 9 2 6 ( 6 ) 1 7 9 . 9 ( 4 ) 5 0 4 R e f e r e n c e s 1 ( a ) Y a k e l , ; H . L . J r . A c t a C r y s t . B 1 9 8 2 , 2 4 , 1 9 6 8 . ( b ) S a i k i , A . ; I s h i z a w a , N . ; M i z u t a n i , N . ; K a t o , M . A c t a C r y s t . B 1 9 8 4 , 4 0 , 7 6 . 2 C a r i o , L . ; L a f o n d , A . ; P a l v a d e a u , P . ; D e u d o n , C . ; M e e r s c h a u t , A . J . S o l i d S t a t e C h e m . 1 9 9 9 , 1 4 7 , 5 8 . 3 O h a r a , H . ; S a s a k i , S . ; K o n o i k e , Y . ; T o y o d a , T . ; Y a m a w a k i , K . ; T a n a k a , M . P h y s i c a B : C o n d e n s e d M a t t e r 2 0 0 4 , 3 5 0 , 3 5 3 . 4 ( a ) M a l l i a k a s , C . ; B i l l i n g e , S . J . L . ; K i m , H . J . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 5 , 1 2 7 , 6 5 1 0 . ( b ) M a l l i a k a s , C . D . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 6 , 1 2 8 , 1 2 6 1 2 . 5 T h e a t o m i c r a d i u s o f L a 3 + i n a n i n e - c o o r d i n a t e d s i t e i s ~ 1 . 2 1 A . F o r t h e s a m e c o o r d i n a t i o n g e o m e t r y E u 2 + h a s a r a d i u s o f ~ 1 3 0 A . T h i s l e n g t h b e c o m e s ~ 1 . 2 5 A w h e n E u 2 + s i t s o n e i g h t - c o o r d i n a t e d s i t e . A t o m i c r a d i i w e r e t a k e n f r o m S h a n n o n , R . D . A c t a C r y s t A 1 9 7 6 , 3 2 , 7 5 1 . 6 P a t s c h k e , R . ; B r a z i s , P . ; K a n n e w u r f , C . R . ; K a n a t z i d i s , M . G . M a t e r . C h e m . 1 9 9 9 , 9 , 2 2 9 3 . 7 P a t s c h k e , R . a n d K a n a t z i d i s M . P h y s . C h e m . C h e m . P h y s . 2 0 0 2 , 4 , 3 2 6 6 . 8 M a l l i a k a s , C . D . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 7 , 1 2 8 , 1 2 6 1 2 . 9 X - A R E A , I P D S S o f t w a r e , S T O E & C i e G m b H , D a r m s t a d t , 2 0 0 6 . 1 0 P e t r i c e k , V . ; D u s e k , M . I n s t i t u t e o f P h y s i c s , P r a h a , C z e c h R e p u b l i c , 2 0 0 0 . 1 1 S h e l d r i c k , G . M . S H E L J Q - 9 7 : P r o g r a m f o r C r y s t a l S t r u c t u r e R e fi n e m e n t ; U n i v e r s i t y o f G o t t i n g e n , G e t t i n g e n , G e r m a n y , 1 9 9 7 . 1 2 C o l d i e r , G ; S c h a f e r , H ; W o l l , P . Z . N a t w f o r s c h . 1 9 8 5 , 4 0 b , 1 0 9 7 . 1 3 M a l l i a k a s , C . D . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 6 , 1 2 8 , 1 2 6 1 2 1 4 S i n g h , D . P l a n e w a v e s , P s e u d o p o t e n t i a l s , a n d t h e L A P W m e t h o d ; K l u w e r A c a d e m i c : B o s t o n , M A , 1 9 9 4 . 1 5 P e r d e w , J . P . , B u r k e , K . , E m z e r h o f , M . , P h y s . R e v . L e t t . 1 9 9 6 , 7 7 , 3 8 6 5 - 3 8 6 8 . 5 0 5 1 6 B i l b a o C r y s t a l l o g r a p h i c S e r v e r , ( h t t p : / / w w w . c r y s t . e h u . e s ) . 1 7 h t t p : / / w w w . b e l l - l a b s . c o m / p r o j e c t / P O R T / d o c / p o r t h o c t a r g z , G a y 1 9 8 3 . 1 8 K o e l l i n g , D . D . , H a r m o n , B . , J . P h y s . C 1 9 7 7 , 1 0 , 3 1 0 7 1 9 B l a h a , P . , S c h w a r z , K . , M a d s e n , G . , K v a s n i c k a , D . , L u i t z , J . , W I E N 2 K , A n A u g m e n t e d P l a n e W a v e + L o c a l O r b i t a l s P r o g r a m f o r C a l c u l a t i n g C r y s t a l P r o p e r t i e s ; K a r l h e i n z S c h w a r z , T e c h . U n i v . , W i e n , V i e n n a , 2 0 0 1 . 5 0 6 C h a p t e r 7 C u , U T e 3 ( 0 S x < 0 . 5 ) : E v o l u t i o n o f t h e I n c o m m e n s u r a t e C h a r g e D e n s i t y W a v e M o d u l a t i o n s i n t h e L i n e a r C h a i n s o f T e l l u r i u m a n d S t r i p e s o f C o p p e r v i a S u c c e s s i v e I n t e r c a l a t i o n o f C o p p e r i n a - U T e 3 5 0 7 7 . 1 . I n t r o d u c t i o n A c t i n i d e p o l y c h a l c o g e n i d e s h a v e b e e n f a s c i n a t e d b e c a u s e o f t h e n u m e r o u s s t r u c t u r a l m o t i f s t h e y c a n a d o p t s . l U r a n i u m i n p a r t i c u l a r l y , b e c a u s e o f i t s a b i l i t y t o b e s t a b l e i n s e v e r a l o x i d a t i o n s t a t e s ( 3 , 4 , 5 a n d 6 + ) h a s s h o w n a p l e t h o r a o f d i f f e r e n t s t r u c t u r e s w i t h i n t h e p o l y c h a l c o g e n i d e f a m i l y . A f e w r e p r e s e n t a t i v e e x a m p l e s o f U r a n i u m o r T h o r i u m c o n t a i n i n g p o l y c h a l c o g e n i d e p h a s e s i n c l u d e t h e s u l fi d e s K é c m z u z s l s , 2 R b U 2 S n g 3 a n d A M U Q 3 ( A = a l k a l i o r a l k a l i n e e a r t h m e t a l , M = 3 d m e t a l , Q = 8 , S e , T c ) , 4 t h e s e l e n i d e s , K 2 U P 3 S e g , 5 K 2 T h P 3 S e 9 , 6 C s 4 T h 2 P 5 S e 1 7 , 6 a n d R b 4 U 1 P a S e 2 6 , 7 K U 2 S b S C g , 3 a n d t e l l u r i d e s C s U T e 6 , 4 ’ 8 C s n g f s U T e 3 ( ) , 6 , 4 ’ 8 C s T i U T e s , 4 T 1 1 1 5 6 U T e 3 . 9 T e l l u r i u m f r o m t h e o t h e r h a n d h a s t h e t e n d e n c y t o f o r m h y p e r v a l e n t T e “ ' T e i n t e r a c t i o n 1 0 a n d d i s t o r t , e s p e c i a l l y w h e n f o u n d i n p l a n a r a r r a n g e m e n t s , i n a v a r i e t y o f ( T e x ) 2 ‘ o l i g o m e r i c p a t t e r n s . l l M o d u l a t i o n s a r e c r e a t e d b e c a u s e o f i n s t a b i l i t i e s o n t h e F e r m i s u r f a c e a n d t h i s s o - c a l l e d P e i e r l s d i s t o r t i o n i s t h e r m o d y n a m i c a l l y f a v o r a b l e d u e t o p h o n o n - e l e c t r o n i n t e r a c t i o n s . T h e r e s u l t o f t h e s e i n t e r a c t i o n s i s a s p a t i a l m o d u l a t i o n o f t h e d i f f u s e e l e c t r o n d e n s i t y i n t o c h a r g e d e n s i t y w a v e s ( C D W s ) . T h e s h o r t l i s t o f a c t i n i d e - c o n t a i n i n g p h a s e s w i t h p l a n a r n e t s o f c h a l c o g e n t h a t p o s s e s C D W - t y p e d i s t o r t i o n s i n c l u d e A T h 2 S e 5 ( A = K , R b ) ‘ 2 a n d C u x U T e 3 ( x = 0 . 2 5 , 0 . 3 3 ) . 1 3 N e v e r t h e l e s s t h e d e t a i l e d C D W s t r u c t u r e s o f t h e s e c o m p o u n d s r e m a i n u n k n o w n . T h e t e l l u r i d e m e m b e r C u x U T e g c a n b e s e e n a s a C u - i n t e r c a l a t e d p r o d u c t o f t h e l a y e r e d 0 1 - U T e 3 p a r e n t c o m p o u n d . T h e U T e 3 p h a s e c r y s t a l l i z e s i n t o t w o p o s s i b l e f o r m s . T h e s o - c a l l e d 0 - U T e 3 a d o p t s t h e Z r S e 3 s t r u c t u r e t y p e 1 4 a n d t h e B - U T e 3 p h a s e c r y s t a l l i z e s i n t h e N d T e 3 s t r u c t u r e t y p e , 1 5 F i g u r e 7 . 2 . T h e C u a t o m s i n t e r c a l a t e b e t w e e n t h e l a y e r s o f a - U T e 3 . S i n c e t h e C D W d i s t o r t i o n s a r e s e n s i t i v e t o t h e F e r m i s u r f a c e t o p o l o g y , a 5 0 8 s u c c e s s i v e i n c o r p o r a t i o n o f C u + i o n s i n t o t h e s t r u c t u r e w i l l c o n t i n u o u s l y c h a n g e t h e F e r m i l e v e l t h u s t h e C D W m o d u l a t i o n s . I n t h i s w o r k w e s u c c e e d e d i n s o l v i n g t h e i n c o m m e n s u r a t e C D W m o d u l a t e d s t r u c t u r e s o f t h r e e d i f f e r e n t d i s t o r t e d C u x U T e 3 p h a s e s w i t h x = 0 1 4 ( 1 ) , 0 1 8 ( 1 ) a n d 0 4 0 ( 1 ) . S u r p r i s i n g l y , b e s i d e s t h e d i s t o r t e d l i n e a r c h a i n s o f T e f o u n d i n t h e s e c o m p o u n d s w e o b s e r v e d a n u n u s u a l o r d e r i n g o f t h e C u i o n s i n t o c l u s t e r s w i t h a r e a s o n a b l e a v e r a g e C u - C u d i s t a n c e o f ~ 2 . 6 A . T h i s u n i q u e a r r a n g e m e n t o f C u a t o m s s e e m s t o b e c o r r e l a t e d t o t h e o b s e r v e d d i s t o r t i o n s i n t h e p l a n a r T e n e t s . I n t h e C u - r i c h i n t e r c a l a t e d c o m p o u n d t h e c l u s t e r s o f C u a t o m s a n d d i s t o r t e d p a i r s o f T e w e r e f o u n d t o f o r m s t r i p e s a s a r e s u l t o f a m o d u l a t i o n w a v e t h a t i s o r i e n t a t e d a l o n g t h e t h r e e - d i m e n s i o n s . 7 . 2 . E x p e r i m e n t a l S e c t i o n 7 . 2 . 1 . R e a g e n t s T h e f o l l o w i n g r e a g e n t s w e r e u s e d a s o b t a i n e d . U r a n i u m m e t a l , ~ 1 m m t u r n i n g s , C e r a c , M i l w a u k e e , W I ; T e l l u r i u m c h u n k s , T e l l u r e x C o r p , T r a v e r s e C i t y , M I ; T e l l u r i u m ( I V ) b r o m i d e , A l f a A e s a r , W a r d H i l l , M A . A c t i v a t e d C o p p e r — C o p p e r m e t a l ( 4 0 m e s h , C e r a c , M i l w a u k e e , W I ) w a s fi r s t a c t i v a t e d b y w a s h i n g i t w i t h c o p i o u s a m o u n t s o f d i l u t e h y d r o c h l o r i c a c i d . T h i s s t e p w a s n e c e s s a r y t o r e m o v e t h e o x i d e l a y e r f r o m t h e fi n e p a r t i c l e s ( p o w d e r ) a n d t o e n s u r e s t o i c h i o m e t r i c r e a c t i o n o f C u . 5 0 9 7 . 2 . 2 . S y n t h e s i s a - U T e 3 — a - U T e 3 w a s s y n t h e s i z e d f r o m a s t o i c h i o m e t r i c m i x t u r e o f u r a n i u m ( 1 . 0 m m o l ) a n d t e l l u r i u m ( 3 . 0 m m o l ) m e t a l t h a t w a s s e a l e d u n d e r v a c u u m i n a q u a r t z t u b e a n d h e a t e d t o 8 0 0 ° C f o r 5 d a y s . T h e t u b e w a s t h e n c o o l e d t o 3 0 0 ° C a t a r a t e o f 4 ° C / h , f o l l o w e d b y q u e n c h i n g t o r o o m t e m p e r a t u r e a t a r a t e o f 1 0 ° C / h . T h e m a j o r i t y o f t h e r e a c t i o n p r o d u c t w a s p o l y c r y s t a l l i n e p o w d e r a n d a f e w r e l a t i v e b i g ( ~ 2 5 0 u m ) s i n g l e c r y s t a l s o f t h e t a r g e t p h a s e . fl - U T e 3 - A l t h o u g h fi - U T e 3 i s t h e r m o d y n a m i c a l l y m o r e s t a b l e f r o m t h e a - p h a s e a n d a n e x t e n d e d h e a t i n g / a n n e a l i n g t e m p e r a t u r e p r o fi l e f r o m t h e o n e u s e d f o r t h e s y n t h e s i s o f a - U T e 3 c o u l d b e u s e d , a v a p o r t r a n s p o r t s y n t h e t i c p r o c e d u r e w a s p r e f e r r e d t o o b t a i n s i n g l e c r y s t a l s o f g o o d q u a l i t y . S t o i c h i o m e t r i c m i x t u r e o f u r a n i u m ( 1 . 0 m m o l ) a n d t e l l u r i u m ( 3 . 0 m m o l ) m e t a l t o g e t h e r w i t h a s m a l l a m o u n t o f T e B r 4 ( ~ 4 0 t i m e s l e s s t h e t o t a l m a s s o f t h e r e a c t a n t s ) w a s s e a l e d u n d e r v a c u u m i n a 9 m m q u a r t z t u b e ( ~ 2 5 c m l e n g t h ) . T h e t u b e w a s p l a c e d i n a d u a l - z o n e f u r n a c e w i t h t h e s i d e o f t h e r e a c t a n t s t o b e a t 9 5 0 ° C . T h e t e m p e r a t u r e d i f f e r e n c e b e t w e e n t h e t w o z o n e s w a s 1 5 0 ° C ( T c o t d = 8 0 0 ° C ) a n d t h e r e a c t i o n w a s k e p t a t t h i s t e m p e r a t u r e f o r 2 d a y s . T h e t u b e w a s t h e n c o o l e d t o r o o m t e m p e r a t u r e i n ~ 1 0 h . H i g h q u a l i t y p l a t e - l i k e s i n g l e c r y s t a l s u p t o ~ 3 m m i n s i z e w e r e g r o w n o n t h e s i d e o f t h e t u b e t h a t w a s a t 8 0 0 ° C , F i g u r e 7 . 1 . T h e c r y s t a l s w e r e s o a k e d i n a c e t o n e t o w a s h o f f t r a c e s o f T e B r 4 f r o m t h e s u r f a c e . C u x U T e 3 — T h e p r o c e d u r e f o r t h e s y n t h e s i s o f C u x U T e 3 w a s t h e s a m e a s d e s c r i b e d a b o v e f o r B - U T C 3 . I n a d d i t i o n , a n a m o u n t o f a c t i v a t e d c o p p e r ( d e p e n d e d o n t h e t a r g e t x - v a l u e ) w a s m i x e d w i t h t h e r e a c t a n t s . F o r l o w c o n c e n t r a t i o n o f C u ( x ~ 0 . 1 - 0 . 2 ) t h e 5 1 0 p r o d u c t w a s f o u n d t o c o n t a i n s i n g l e c r y s t a l s w i t h d i f f e r e n t s u p e r s t r u c t u r e s d u e t o s m a l l v a r i a t i o n s i n t h e a t o m i c f r a c t i o n o f t h e i n t e r c a l a t e d a t o m s o f C u . F i g u r e 7 . 1 . S E M i m a g e o f a s i n g l e c r y s t a l o f C u m i m U T e g u s e d f o r r e s i s t i v i t y m e a s u r e m e n t . T y p i c a l c r y s t a l s i z e i s ~ 3 m m i n l e n g t h . 7 . 2 . 3 . P h y s i c a l M e a s u r e m e n t s S e m i q u a n t i t a t i v e E n e r g y D i s p e r s i v e S p e c t r o s c o p y ( E D S ) — T h e a n a l y s e s w e r e p e r f o r m e d w i t h a J E O L J S M - 3 5 C s c a n n i n g e l e c t r o n m i c r o s c o p e e q u i p p e d w i t h a N o r a n V a n t a g e E D S ( S i z L i ) d e t e c t o r . C r y s t a l s w e r e m o u n t e d o n a n a l u m i n u m s t a g e w i t h c a r b o n t a p e . D a t a w e r e a c q u i r e d o n s e v e r a l c r y s t a l s a n d d i f f e r e n t r e g i o n s o f e a c h c r y s t a l u s i n g a n a c c e l e r a t i n g v o l t a g e o f 2 5 k V a n d a c c u m u l a t i o n t i m e o f 4 0 s . S i n g l e C r y s t a l X - r a y D i fi ‘ r a c t i o n — A l l t h e t e m p e r a t u r e d e p e n d e n t m e a s u r e m e n t s w e r e p e r f o r m e d o n t h e s a m e s i n g l e c r y s t a l f o r s o m e o f t h e C U X U T C 3 c o m p o u n d s . S i n g l e c r y s t a l s w e r e q u e n c h e d f r o m r o o m t e m p e r a t u r e t o 1 0 0 K . T h e h e a t i n g r a t e f o r w a r m i n g r a m p s w a s ~ 2 0 0 K / h . T y p i c a l a c q u i s i t i o n t i m e w a s ~ 2 4 h . S u m m a r y t a b l e o f c r y s t a l d a t a a n d d e t a i l e d c r y s t a l l o g r a p h i c t a b l e r e p o r t s f o r e a c h i n d i v i d u a l C U X U T C 3 a n a l o g u e a n d t e m p e r a t u r e c a n b e f o u n d i n T a b l e s 8 . 1 - 8 . 1 8 . I n t e n s i t y d a t a w e r e c o l l e c t e d o n a S T O E I P D S H d i f f r a c t o m e t e r e q u i p p e d w i t h a g r a p h i t e m o n o c h r o m a t i z e d M o r a d i a t i o n ( A = 5 1 1 0 . 7 1 0 7 3 A ) a n d a n I m a g e P l a t e ( I P ) d e t e c t o r . T h e d a t a w e r e c o l l e c t e d w i t h a n ( o - s c a n t e c h n i q u e f r o m 0 - 1 8 0 ° a n d a n a r b i t r a r y ( p - a n g l e . D a t a r e d u c t i o n w a s p e r f o r m e d w i t h t h e X - A r e a p a c k a g e . 1 6 T h e l e n g t h d e t e r m i n a t i o n a n d r e fi n e m e n t o f t h e q - v e c t o r s w a s p e r f o r m e d w i t h t h e P e a k l i s t 1 . 0 6 s o f t w a r e p a r t o f t h e X - A r e a s u i t e u s i n g a l e a s t s q u a r e r e fi n e m e n t a l g o r i t h m . A n a n a l y t i c a l a b s o r p t i o n c o r r e c t i o n w a s p e r f o r m e d ( X - S h a p e w i t h i n X - A r e a ) a n d a l l s t r u c t u r e s w e r e r e fi n e d w i t h J A N A 2 0 0 0 s o f t w a r e . l 7 D i r e c t m e t h o d s o f S H E L X T L s o f t w a r e 1 8 w e r e u s e d t o fi n d t h e a t o m i c p o s i t i o n s i n t h e s u b c e l l . S a t e l l i t e r e fl e c t i o n s o f fi r s t o r d e r w e r e o b s e r v e d a n d u s e d f o r t h e r e fi n e m e n t . A s i n g l e m o d u l a t i o n w a v e f o r p o s i t i o n a l a n d t h e r m a l p a r a m e t e r s w a s u s e d . O n l y t h e s y m m e t r y a l l o w e d F o u r i e r t e r m s w e r e r e fi n e d . T e m p e r a t u r e w a s c o n t r o l l e d b y a n O x f o r d C r y o s t r e a m 7 0 0 P l u s c r y o s t a t . M a g n e t i c S u s c e p t i b i l i t y M e a s u r e m e n t s — A N I P M S Q u a n t u m D e s i g n S Q U I D m a g n e t o m e t e r w a s u s e d t o m e a s u r e t h e m a g n e t i c r e s p o n s e o f s o m e o f t h e C u x U T e 3 c o m p o u n d s o v e r t h e r a n g e o f 2 - 3 0 0 K . S i n g l e c r y s t a l s o f e a c h s a m p l e w e r e m e a s u r e d p a r a l l e l a n d p e r p e n d i c u l a r t o t h e a p p l i e d m a g n e t i c fi e l d i n r e s p e c t t o t h e p l a t e g e o m e t r y o f t h e c r y s t a l s . A p e r p e n d i c u l a r fi e l d c o r r e s p o n d s t o a m a g n e t i z a t i o n d i r e c t i o n a l o n g t h e c - a x i s . A p a r a l l e l m a g n e t i c fi e l d c o r r e s p o n d s t o a r a n d o m d i r e c t i o n a l o n g t h e a b - p l a n e . A fi e l d d e p e n d e n t m a g n e t i c s u s c e p t i b i l i t y a t 3 0 0 K w a s fi r s t i n v e s t i g a t e d i n t h e r a n g e o f 0 — 1 T t o e n s u r e a l i n e a r r e s p o n s e o f t h e m a g n e t i z a t i o n . S u b s e q u e n t t e m p e r a t u r e d e p e n d e n t s t u d i e s w e r e t h e n p e r f o r m e d a t a c o n s t a n t fi e l d o f 3 , 0 0 0 G . T h e e f f e c t i v e m a g n e t i c m o m e n t , 1 1 . 1 5 , w a s c a l c u l a t e d f r o m t h e f o l l o w i n g f o r m u l a : u e g = 2 8 1 8 x 1 / Z M ' T 5 1 2 w h e r e [ M i s t h e i n v e r s e o f t h e s l o p e t a k e n f r o m t h e l i n e a r r e g i o n o f t h e 1 / 1 , , v s T p l o t ( 2 ’ 1 7 i s t h e m o l a r m a g n e t i c s u s c e p t i b i l i t y ) . C h a r g e t r a n s p o r t m e a s u r e m e n t s - E l e c t r i c a l c o n t a c t f o r t h e r e s i s t i v i t y m e a s u r e m e n t a t l o w t e m p e r a t u r e ( 2 - 3 0 0 K ) w a s m a d e u s i n g s i l v e r p a i n t a n d C u w i r e d i r e c t l y o n t o t h e s i n g l e c r y s t a l s u r f a c e o f C l l e T e 3 ( x = 0 , 0 . 1 0 , 0 . 4 0 ) . M e a s u r e m e n t s w e r e m a d e f o r a r b i t r a r y c u r r e n t d i r e c t i o n s i n t h e a b - p l a n e u s i n g a s t a n d a r d f o u r p o i n t c o n t a c t g e o m e t r y ( A C ) i n a Q u a n t u m D e s i g n P h y s i c a l P r o p e r t y M e a s u r e m e n t S y s t e m ( P P M S ) . E l e c t r i c a l r e s i s t i v i t y d a t a a t h i g h t e m p e r a t u r e ( 3 0 0 - 7 0 0 K ) w e r e m e a s u r e d a s a f u n c t i o n o f t e m p e r a t u r e o n s i n g l e c r y s t a l s o f C u x U T e g ( x = 0 , 0 1 4 ( 1 ) , 0 1 8 ( 1 ) a n d 0 4 0 ( 1 ) ) . E l e c t r i c a l c o n t a c t s f o r t h e r e s i s t i v i t y m e a s u r e m e n t s w e r e m a d e u s i n g g o l d p a i n t a n d C u w i r e d i r e c t l y o n t h e c r y s t a l s u r f a c e . M e a s u r e m e n t s w e r e m a d e f o r a r b i t r a r y c u r r e n t d i r e c t i o n s i n t h e a b — p l a n e u s i n g a s t a n d a r d f o u r p o i n t c o n t a c t g e o m e t r y ( A C ) . W e u s e d a h o m e m a d e r e s i s t i v i t y a p p a r a t u s e q u i p p e d w i t h a K e i t l r l e y 2 1 8 2 A N a n o v o l t r n e t e r , 6 2 2 0 P r e c i s i o n C u r r e n t S o u r c e , a n d a h i g h t e m p e r a t u r e v a c u u m c h a m b e r ( ~ 5 ' 1 0 " 3 t o r r ) c o n t r o l l e d b y a K - 2 0 M M R S y s t e m . 7 . 3 . R e s u l t s a n d D i s c u s s i o n S u b c e l l D e s c r i p t i o n o f a - U T e 3 — T h e s t r u c t u r e o f a - U T e 3 c r y s t a l l i z e d i n t h e Z r S e 3 s t r u c t u r e t y p e ( P 2 1 / m ) . I t i s c o m p o s e d b y t w o p u c k e r e d l a y e r s o f ( U T e ) t h a t a r e s a n d w i c h e d b y p l a n a r n e t s o f T e m a k i n g a n U T e 3 s l a b . T h e s l a b s t h e n s t a c k a l o n g t h e c - a x i s c r e a t i n g v a n d e r W a a l s g a p s . T h e s t r u c t u r e c a n b e e n s e e n a s a d i s t o r t e d v e r s i o n o f t h e N d T e 3 s t r u c t u r e t y p e i n w h i c h t h e N d T e 3 s l a b s h a v e b e e n s h i f t e d i n r e s p e c t t o e a c h 5 1 3 o t h e r i n t h e a b p l a n e a s s h o w n i n F i g u r e 7 2 A . F u r t h e r m o r e , t h e p l a n a r n e t s o f T e c o n s i s t o f d i m e r s o r i e n t e d a l o n g t h e a - a x i s w i t h T e - T e d i s t a n c e s o f 2 . 7 5 0 ( 2 ) A , F i g u r e 7 2 B . T h e d i m e r s a r e s e p a r a t e d fi ' o m e a c h o t h e r i n a d i s t a n c e o f 3 . 0 6 1 A ( a l o n g a - a x i s ) . T h e v e r t i c a l s e p a r a t i o n ( a l o n g b - a x i s ) o f t h e l i n e a r c h a i n s i s 4 . 2 0 5 ( 1 ) A . E a c h U a t o m i s c o o r d i n a t e d t o e i g h t T e a t o m s i n a b i c a p p e d t r i g o n a l p r i s m a t i c e n v i r o n m e n t T h e s e t r i g o n a l p r i s m s s t a c k a l o n g t h e b - a x i s t o f o r m w e d g e - s h a p e d c o l u m n s b y s h a r i n g t r i a n g u l a r f a c e s . L a y e r s a r e t h e n f o r m e d w h e n n e i g h b o r i n g c o l u m n s s h a r e b o t h t h e i r c a p p i n g a n d a p e x m o n o t e l l u r i d e s , F i g u r e 7 2 A . S u b c e l l D e s c r i p t i o n o f , B - U T e 3 — T h e a v e r a g e s t r u c t u r e o f B - U T e 3 c r y s t a l l i z e s i n t h e N d T e 3 s t r u c t u r e t y p e ( C m c m ) . I t c o n s i s t s o f p u c k e r e d d o u b l e l a y e r s o f ( U T e ) t h a t a r e s a n d w i c h e d b y s q u a r e n e t s o f T e m a k i n g a n U T e 3 s l a b . T h e s l a b s t h e n s t a c k a l o n g t h e b - a x i s c r e a t i n g v a n d e r W a a l s g a p s . T h e f o r m u l a c a n b e m o r e e x p r e s s l y w r i t t e n a s ( U T e ) 2 + ( T e 2 ) 2 ’ , F i g u r e 7 2 C . T h i s g i v e s a n a v e r a g e o x i d a t i o n s t a t e o f t h e T e a t o m s i n t h e n e t o f 1 - t h a t i s d i f f e r e n t f r o m t h e a v e r a g e e l e c t r o n c o u n t o f - 0 5 f o u n d i n t h e L n T e 3 ( L n = L a n t h a n i d e ) f a m i l y s i n c e U i s i n t h e 4 + o x i d a t i o n s t a t e ( v e r i fi e d b y m a g n e t i c s u s c e p t i b i l i t y m e a s u r e m e n t s ) . T h e U a t o m i s i n a m o n o c a p p e d t e t r a g o n a l a n t i p r i s m o f T e a t o m s . T h e T e a t o m s a r e s u r r o u n d e d b y fi v e U a t o m s i n a t e t r a g o n a l p y r a m i d a l g e o m e t r y . T h e a p p a r e n t T e — T e d i s t a n c e s i n t h e s q u a r e n e t a r e 3 . 1 0 3 ( 1 ) A , F i g u r e 7 . 2 D . S u b c e l l D e s c r i p t i o n o f C u x U T e 3 — T h e a v e r a g e s t r u c t u r e o f C u x U T e g c a n b e s e e n a s a n i n t e r c a l a t i o n p r o d u c t o f C u i n t o t h e v a n d e r W a a l s g a p s o f a - U T e g . T h e C u a t o m s i n t e r c o n n e c t t h e W e ; s l a b s c r e a t i n g a t h r e e - d i m e n s i o n a l l y c o n n e c t e d s t r u c t u r e , F i g u r e 7 3 A . T h e C u a t o m i s l o c a t e d i n a d i s t o r t e d t e t r a h e d r a l e n v i r o n m e n t o f T e a t o m s . T h e p l a n a r n e t o f T e a t o m s d o e s n o t c o n t a i n d i s c r e t e d i m e r s a n y m o r e l i k e i n a - U T e 3 b u t t h e 5 1 4 T e a t o m s f o r m i n fi n i t e l i n e a r c h a i n s a l o n g t h e a - a x i s . T h e s h o r t e s t T e - T e d i s t a n c e i n t h e c h a i n s i s n o w 3 . 0 3 3 ( 2 ) A ( 2 . 7 5 0 ( 2 ) A i n d i m e r s o f a - U T e 3 ) a n d t h e l o n g e s t 3 . 0 6 1 ( 2 ) A ( 3 . 3 5 2 ( 2 ) A d i s t a n c e b e t w e e n d i m e r s ) , F i g u r e 7 3 8 . I n t e r e s t i n g l y , a n u n u s u a l f e a t u r e i n t h e a v e r a g e C u x U T e 3 i s t h e p r e s e n c e o f z i g z a g c h a i n s o f C u a t o m s w i t h C u - C u d i s t a n c e s o f 2 . 5 7 ( l ) A , F i g u r e 7 . 3 C . A l t h o u g h t h i s s h o r t d i s t a n c e i s r e a s o n a b l e f o r a C u - C u i n t e r a c t i o n ( d l o - d m ) i s n o t c l e a r f r o m t h i s a v e r a g e d i s o r d e r e d m o d e l i f t h e t w o p a r t i a l l y v a c a n t s i t e s o f C u g e n e r a t e d b y s y m m e t r y a r e o c c u p i e d b y C u a t o m s a t t h e s a m e t i m e . S u p e r c e l l D e s c r i p t i o n o f C u x U T e 3 B a s e d o n a M o d u l a t i o n q - v e c t o r — T h e C D W d i s t o r t i o n s i n t h e C u x U T e 3 s e r i e s f o u n d t o b e v e r y s e n s i t i v e t o t h e a v e r a g e o x i d a t i o n s t a t e o n t h e T e a t o m s i n t h e p l a n a r n e t . T h e e l e c t r o n c o u n t i n c r e a s e s w i t h t h e c o n c e n t r a t i o n o f i n t e r c a l a t e d C u a t o m s . F o r x = 0 1 4 ( 1 ) t h e a v e r a g e o x i d a t i o n s t a t e o n t h e T e a t o m s i n t h e n e t b e c o m e s - 1 0 7 ( 1 ) w i t h a m o d u l a t i o n q - v e c t o r 0 . 1 0 4 0 ( 4 ) a ' - 0 . 0 2 8 4 ( 7 ) c ' . W i t h a s m a l l i n c r e a s e i n x - v a l u e t o 0 1 8 ( 1 ) t h e q - v e c t o r c h a n g e s s i g n i fi c a n t l y t o 0 . 1 7 9 ( 1 ) a ‘ - 0 . 0 8 6 ( 3 ) c ' w h i l e t h e o x i d a t i o n s t a t e i s n o w - 1 . 0 9 ( 1 ) . F i n a l l y , w h e n t h e c o n c e n t r a t i o n o f i n t e r c a l a t e d C u a t o m s r e a c h e s 0 4 0 ( 1 ) t h e C D W m o d u l a t i o n v e c t o r b e c o m e s 0 . 2 2 2 5 ( 8 ) a m + 0 . 2 7 1 1 ( 5 ) b ’ + 0 . 5 1 3 0 ) c ' . T h e d i s t o r t e d p a t t e r n s i n C u x U T e 3 s e r i e s c a n b e s e e n a s a s e q u e n c e o f d i m e r s a n d m o n o m e r s a t a b o n d i n g t h r e s h o l d o f 2 . 9 A , F i g u r e 7 . 7 - 7 . 8 . T h e w i d e d i s t r i b u t i o n o f T e - T e d i s t a n c e s f o r a l l t h r e e m e m b e r s i s s h o w n i n F i g u r e 7 . 4 . I n m o r e d e t a i l s , t h e m i n i m u m T e - T e d i s t a n c e i n C u m a m U T e g a t 1 0 0 K i s 2 . 7 8 2 ( 3 ) A a n d t h e m a x i m u m 3 . 2 8 9 ( 3 ) A . F o r C u 0 1 3 ( 1 ) U T e 3 t h e m i n i m u m d i s t a n c e i s 2 . 7 6 6 ( 2 ) A a n d t h e m a x i m u m 3 . 2 7 9 ( 2 ) A . I n C u o 4 m ) U T e 3 t h e m i n i m u m a n d m a x i m u m d i s t a n c e s a r e 2 . 8 4 3 ( 2 ) A a n d 3 . 2 1 3 ( 2 ) A r e s p e c t i v e l y . F r o m F i g u r e 7 . 4 i s a p p a r e n t t h a t w i t h i n c r e a s i n g t h e e l e c t r o n c o u n t o n t h e 5 1 5 0 1 - U T e 3 ( Z r S e g - t y p e ) , e 3 B — U T . ( N o r m - t y p e ) T e n e t t h e d i s t r i b u t i o n o f T e - T e d i s t a n c e s i n t h e d i m e r s c o m p a r e d t o t h e d i s t a n c e s f o u n d i n t h e o t h e r o l i g o m e r s g r a d u a l l y c o n v e r g e s . ( A ) ( C ) ( B ) ( D ) 2 ° 3 5 2 § 2 ) H A [ 4 2 1 9 0 ) ‘ 2 . 7 5 0 ( 2 ) r — c H F i g u r e 7 . 2 . ( A ) S t r u c t u r e o f a — U T e 3 ( Z r S e 3 - t y p e ) . ( B ) L i n e a r c h a i n s o f T e i n a - U T e 3 ( b o n d l e n g t h s a r e i n d i c a t e d ) . ( C ) S t r u c t u r e o f B - U T e ; ( N d T e 3 - t y p e ) . ( B ) S q u a r e n e t o f T e i n B - U T e 3 ( b o n d l e n g t h s a r e i n d i c a t e d ) . 5 1 6 ( A ) o , 0 c , 0 ( B ) \ 1 / \ / , I . i 1 . [ 4 2 0 5 0 ) / ’ 9 \ / * 3 . 0 3 3 ( 2 ) 3 . 0 6 1 ( 2 ) O O d — O C O O O O , V . C u ( C ) . 5 . " 1 . , 1 C T e . . \ 9 / / U . ‘ - . / 1 i \ O 1 . 2 . 5 7 0 ) , t 3 ' ' ' ' / . \ . . c , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H M . - — — . a 4 — f . . F i g u r e 7 . 3 . ( A ) A v e r a g e u n d i s t o r t e d s t r u c t u r e o f C u x U T e 3 . ( B ) U n d i s t o r t e d l i n e a r c h a i n s o f T e i n C u x U T e 3 . B o n d l e n g t h s a r e i n d i c a t e d ( C ) L i n e a r c h a i n s o f C u i n t h e a v e r a g e C u x U T e g s t r u c t u r e . 3 . 3 5 3 . 3 0 3 . 2 5 - 3 . 2 0 @ 3 1 5 8 3 . 1 0 C . . 3 3 - 0 5 . . . . , . . . 2 . 3 . 0 0 - / ’ \ ‘ \ I m . - . . $ 2 . 9 5 3 - 0 - r € 2 . 9 0 - [ 2 2 . 8 5 — 2 . 8 0 — C U 0 1 4 ( 1 ) U T 6 3 " " " " C “ 0 . 1 8 ( 1 ) U T C 3 2 ' 7 5 I " " " C u 0 4 0 ( 1 ) U T ¢ 3 T 2 . 7 0 A I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 t - d i r e c t i o n F i g u r e 7 . 4 . T e [ 2 ] - T e [ 3 ] d i s t a n c e s f o u n d i n t h e d i s t o r t e d n e t o f C u x U T e 3 ( x = 0 1 4 ( 1 ) , 0 1 8 ( 1 ) a n d 0 4 0 ( 1 ) ) fi ' o m t h e s u p e r s p a c e a n a l y s i s b a s e d o n a q - v e c t o r a s a f u n c t i o n o f t - d i r e c t i o n . 5 1 7 S u r p r i s i n g l y , w e f o u n d t h a t t h e d i s t o r t e d C u a t o m s a r e l o n g r a n g e o r d e r e d a n d t h e y f o r m z i g z a g - s h a p e d c l u s t e r s o f v a r i o u s l e n g t h s . T h e fi r s t a t t e m p t t o m o d e l t h e C u - s i t e a s a d i s o r d e r e d o n e w i t h a r e fi n e d a v e r a g e o c c u p a n c y e q u a l t o x w a s n o t a c c e p t a b l e . H i g h r e s i d u a l s i n t h e d i f f e r e n c e F o u r i e r m a p w i t h l o c a l m a x i m a ( p e a k s ) a n d m i n i m a ( h o l e s ) d e n s i t i e s ( > 1 5 e ' A ' 3 ) a l o n g t h e m o d u l a t i o n t - d i r e c t o r w e r e o b s e r v e d . T h i s s u g g e s t e d t h a t a n o c c u p a t i o n a l m o d u l a t i o n m a y b e p r e s e n t . T h e a p p l i c a t i o n o f a s i n g l e o c c u p a t i o n a l w a v e s u c c e s s f u l l y d e s c r i b e d t h e e l e c t r o n r e s i d u a l i n t e n s i t y a l o n g t h e m o d u l a t i o n . T h e o c c u p a n c y o f t h e C u - s i t e v a r i e s c o n t i n u o u s l y b e t w e e n 0 a n d ~ 0 . 2 5 f o r C u o , 1 4 ( 1 ) U T e 3 , a n d f r o m 0 t o ~ 0 . 4 5 f o r C u o , 1 4 ( 1 ) U T e 3 . F o r t h e m o r e C u - r i c h C u o , 1 4 ( 1 ) U T e 3 p h a s e t h e o c c u p a n c y f r a c t i o n c h a n g e s f r o m ~ 0 . 1 0 t o ~ 0 . 7 5 , F i g u r e 7 . 5 . T h e C u - C u b o n d d i s t r i b u t i o n w i t h i n t h e c l u s t e r s d o e s n o t c h a n g e s i g n i fi c a n t l y . T h e m i n i m u m C u - C u d i s t a n c e i n C u o _ 1 4 ( 1 ) U T e 3 i s 2 . 5 7 ( 5 ) A a n d t h e m a x i m u m 2 6 7 ( 6 ) A . T h e m i n i m u m a n d m a x i m u m d i s t a n c e s i n C u o , 1 3 ( 1 ) U T e 3 a n d C 1 1 0 _ 4 o ( 1 ) U T e 3 a r e 2 5 2 ( 4 ) A t o 2 . 5 7 ( 5 ) A , a n d 2 . 4 7 3 ( 2 ) A t o 2 . 5 4 8 ( 2 ) A r e s p e c t i v e l y . 5 1 8 1 1 1 4 1 1 1 1 1 1 0 - 8 0 _ 1 1 ' 1 1 1 ' 1 ' 1 ' 1 ' 1 ' 1 ' 1 " 0 ' 7 5 T C u 0 . 4 0 ( 1 ) U T € = 3 ‘ : 0 . 7 0 - _ 0 . 6 5 - _ 0 . 6 0 - _ 0 . 5 5 - - C “ 0 . 1 8 ( 1 ) U T C 3 > 1 0 . 5 0 - ° 0 . 4 5 . 3 0 . 4 0 P 5 0 . 3 0 7 0 0 . 2 5 - 0 . 2 0 - _ 0 . 1 5 - C U T . C 0 . 1 0 _ u 0 1 4 ( 1 ) 3 0 . 0 5 0 . “ ) I 1 I 1 I 1 I 1 L 1 I 1 I 1 I 1 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1 . 0 t - d i r e c t i o n F i g u r e 7 . 5 . O c c u p a t i o n a l c u r v e s o f C u a t o m s f o u n d i n C u x U T e 3 ( x = 0 1 4 ( 1 ) , 0 1 8 ( 1 ) a n d 0 4 0 ( 1 ) ) f r o m t h e s u p e r s p a c e a n a l y s i s b a s e d o n a q - v e c t o r a s a f u n c t i o n o f t - d i r e c t i o n . T h e s e q u e n c e o f o l i g o m e r s i n t h e C D W d i s t o r t e d T e p a t t e r n s a n d f r e q u e n c y o f d i m e r s i s c o r r e l a t e d t o t h e o c c u p a t i o n a l m o d u l a t i o n s f o u n d i n t h e C u p l a n e . T h e a v e r a g e T e - T e d i s t a n c e s o f t h e a t o m s l o c a t e d a b o v e a n d b e l l o w t h e r e g i o n s w i t h C u v a c a n c i e s a r e s h o r t e r t h a n 2 . 9 A , a n d w h e n C u a t o m s a r e p r e s e n t t h e c o r r e s p o n d i n g d i s t a n c e a r e l o n g e r , F i g u r e 7 . 6 A . T h e s h o r t a n d l o n g T e - T e b o n d i n g ( l i n e a r d i s t o r t e d c h a i n s ) o c c u r s a l o n g t h e a - a x i s f o r t h e l o w C u - l o a d e d c o m p o u n d s , C u o , 1 4 ( 1 ) U T e 3 a n d C u o , 1 g ( 1 ) U T e 3 . T h e z i g z a g c h a i n s o f C u r u n a l o n g t h e b - a x i s p e r p e n d i c u l a r t o t h e d i s t o r t e d T e c h a i n s , F i g u r e 7 . 6 B . T h e d e n s i t y o f d i m e r s i n c r e a s e s w i t h d e c r e a s i n g C u c o n c e n t r a t i o n , F i g u r e 7 . 7 . I n t h e h i g h C u - l o a d e d p h a s e C u o , 4 0 ( 1 ) U T e 3 t h e d i m e n s i o n a l i t y o f t h e C D W d i s t o r t i o n s i n c r e a s e s a n d t h e m o d u l a t i o n s n o w p r o p a g a t e a l o n g t h e b - a x i s t o o . T h e o r i e n t a t i o n o f t h e q - v e c t o r i s a l o n g a l l t h r e e d i r e c t i o n s ( 0 . 2 2 2 5 ( 8 ) a ' + 0 . 2 7 1 1 ( 5 ) b ‘ + 0 . 5 1 3 ( 1 ) c ‘ ) . T h i s s i t u a t i o n r e s u l t 5 1 9 i n a m o r e c o m p l e x a r r a n g e m e n t o f T e m o n o m e r s a n d C u c l u s t e r s , F i g u r e 7 . 8 . S u r p r i s i n g l y , t h e C u o l i g o m e r s t h a t a r e m a i n l y c o m p o s e d b y t e t r a m e r s a n d o c c a s i o n a l l y t r i m e r s a n d d i m e r s s e e m t o l i n e i n s t r i p e s a l o n g t h e d i a g o n a l o f t h e a b - p l a n e . A t t h e s a m e t i m e , d i m e r s o f T e a t o m s l i e b e t w e e n t h e C u o l i g o m e r s t o f o r m s t r i p e s t o o . T h e c o r r e l a t i o n o f C u o l i g o m e r s a n d p r e s e n c e o f T e d i m e r s c a n b e r a t i o n a l i z e d u s i n g e l e c t r o n c o u n t . T h e m o r e r e d u c e d T e i s t h e l o n g e r t h e b o n d s b e c o m e . T h e T e a t o m s c o o r d i n a t e d o n C u a t o m s w i l l b e m o r e r e d u c e d i n r e s p e c t w i t h t h e T e a t o m s l o c a t e d a b o v e v a c a n c i e s . T h e r e f o r e t h e a v e r a g e T e - T e b o n d s o f t h e l a t e r w i l l b e l o n g e r t h a n t h e o n e s i n t h e f o r m e r s p e c i e s . I t i s a m a z i n g t h o u g h h o w l o c a l i z e d t h e e l e c t r o n s a r e j u g g i n g f r o m t h e d i s t o r t e d p a t t e r n s f o u n d i n t h e C u x U T e 3 f a m i l y . I t s e e m s t h a t t h e u n d i s t o r t e d o n e - d i m e n s i o n a l f r a m e w o r k o f a - U T e 3 f a v o r s t h e s e p a r a t i o n o f T e o l i g o m e r s a n d p r e v e n t s t h e d i f f u s i o n o f e l e c t r o n s b e t w e e n l i n e a r c h a i n s o f T e . 5 2 0 . 0 . . 0 . o o o o . 9 9 o 3 ‘ b ‘ 0 3 o o 0 d 0 . 6 o o o o . o d . 0 o . . 0 . o d o o d o o d o o o o o o o o 9 P : \ I 0 ? d d d d d o o o o o o d o b o d b ) o B b ( . l o h s e r h t g n i d n o . b . A 0 . 9 . 2 d n a ‘ c ) 7 ( 4 8 2 0 . 0 . 0 . o q o o d o 6 9 9 P o d o o d o o d o o d ? P F o d o o d o a 5 2 1 o o o 0 P I o d o \ . i n o d o ) a . 9 o o o d o ¥ b o d o ‘ 8 o d o 9 o 9 ' P o d o p 1 1 1 1 1 1 1 1 1 1 . Q . P o d o f t : o Q ? P 1 1 1 1 1 1 1 1 1 1 l - I I D o o d o 4 ’ o d o , 0 o - o o o o o o o o o o o P o d o o P o c o o P o d o o 9 o d o o . 0 . 0 . 0 . 0 . F i g u r e 7 . 6 . ( A ) D i s t o r t e d T e p a t t e r n o f C l l o _ 1 3 ( 1 ) U T e 3 a t 1 0 0 K w i t h q = 0 . 1 0 4 0 ( 4 ) a * - 0 . 0 2 8 4 ( 7 ) c * a n d 2 . 9 A b o n d i n g t h r e s h o l d v i e w e d d o w n t h e b - a x i s . T h e f o r m a t i o n o f T e - T e d i m e s i n t h e r e g i o n s w h e r e t h e r e i s n o C u a t o m s i s a p p a r e n t . ( B ) D i s t o r t e d T e p a t t e r n o f C u o , 1 3 ( 1 ) U T e 3 a t 1 0 0 K v i e w e d d o w n t h e c - a x i s a t a b o n d i n g t h r e s h o l d o f 2 . 9 A . T h e o c c u p a n c y c u t o f f w a s s e t t o t h e a v e r a g e v a l u e o f 0 . 1 8 . 1 1 1 1 1 1 1 1 1 1 F i g u r e 7 . 7 . D i s t o r t e d T e p a t t e r n o f C u o , 1 4 ( 1 ) U T e 3 a t 1 0 0 K w i t h q = 0 . 1 0 4 0 ( 4 ) a ‘ - 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 o c c u p a n c y c u t o f f w a s s e t t o t h e a v e r a g e v a l u e o f 0 . 1 4 . 1 1 1 1 1 ~ ~ — — a o — o n ~ ~ a 1 1 1 1 1 ~ m a m — l l l l l é . 0 . O . 0 . . O . d o o o n — o o o o n o o ° ~ . ° o — o o o o o o o ° . ° o o - — o o o o o ° - . ° o d o — o o o o o o o o o o o o — o , 9 9 9 . 9 9 . 9 9 9 9 o d o o o o — o o o o o o o d o o o o — o o o ’ o o o i o o o o — o o d o o d o o f o o o o — o o d o o x ; o o 9 . 9 9 9 , 9 ) 1 9 9 9 o o o o d o o o — o o o o d o o d x o o o o — o o d o o d o o o o — o o o o o o d o o o o — o o d o o d o ‘ , 9 , 9 , 9 , 9 9 9 9 9 , 9 o — o d o o d o o d o o — o o — o o d o o d ‘ o o o o — o o n o o d o o « ( o o — o o — - o d o o d o o o o — o o o o . 8 9 , 9 ’ 9 9 9 « f o o — o o o o d o o d o o o o — o o d o o d o o o o — o o o o c o o d o o o o — o o d o o o o o o — o 9 9 9 , 9 9 9 9 9 9 , 9 9 o c o o d o u — o o — o o o ’ o o d o o o o — o o d o o c o o o o o — o o — o o d o o d o o o — o o d o o d o o d o I 9 , 9 I 9 , 9 9 9 9 o o o d o o d o o o o — o o d o o d o o o o — o o o o d o o d o o o o — o o n o o J : o o o — o o o o d o , 9 ‘ 9 , 9 9 9 , 9 9 r 9 9 , 9 o — o o — o o d o o d o o o o - u o o d o o d o o o o u — o o o o d o o d o o o o - o o d o o d o o d o o — o o , 9 , 9 9 f 9 9 { 9 9 9 o q o o o c — o o d o o d f o o o o — o o o o o o d o o o o — o o o ’ o o o o o o — o o o o d o o o o o l b 1 : ‘ o ‘ 4 9 : 6 9 \ D o ’ p o d o o d o o o o - o o c o o d o o d o o — o o o o d o o : { o o o o — o o o / o o < { o o d o o — o o o o d o o d o 9 9 , 9 ) 9 9 9 9 9 9 o — o o o o o d o o o o — o o d o o d o o d o o o o — o o d o o d o o o o — o o d o o d ’ o o d o o o o — o o d o 9 , 9 9 9 9 9 9 9 o o o — o o d o o d o o o t — o o o o d o o d o o o - - o o o o o « ( o o o o — o o o o c o o d o o o o — o , 9 , 9 9 9 9 P P 9 9 y o d o o o — o o o o c o o o o o — o o — o o o ’ o o d \ o o o o n — o o d o o d o o d o o — o o — o o o o o o o o ‘ 9 9 9 9 9 ‘ 0 9 o o o o d o o o o n . o o o d o o d o o o o I - o o d o o d o o o — o o o d o o 0 : . o o — o o o o d o , 9 9 , 9 9 , 9 9 9 . ) 1 o — o o O . o d o o d o o — o o — o o o o o a ; o o o — o o o o o d o o d o o — o o — o o d o o d o o o o — o o 0 . 9 9 , 9 9 9 o o o — o o o o d o o d o o o o — o o d o o ' o o o o — o o o o d o o d o o o o - - o o o o { o o o o — o , P P P 3 P , 9 ( P f ’ P o o o o d o o — o o o o o o o q ’ o o o o — o o o o O J . o o o — o o o o d o o d o o o o — o o o ’ o o d o o a \ o 9 f , 9 f 9 9 9 9 , 9 o o o d o o o j \ o o o o — o o o o c ( o o o o — o o o o o o d o o o o n - o o d o o c ( o o o o — o o o o d o , 9 9 , 9 9 9 9 9 ) 9 o — o o o o d o o d o o o — o o d o o « ( o o o o — o o o o d o o d ’ \ o o o — o d o o d o o o o I — o o o 9 9 9 , 9 P f 9 9 o d o o o o - o o d o o o o o o o — o o d o o o ’ o o q ' o o — o o — o o o o o r : o o o — n o d o o d o o o o — o 9 9 9 , 9 ) 9 f , 9 ; o d o o d o o o o — o o d o o d o o o o — o o o o d o o \ o o o — o d o o d o o o o — o o o o d / o o a o 9 9 , 9 , 9 9 9 f , 9 . 9 o n - o d o o d o o o — o d o o o o ° \ ° — o — o o d o o d o o o o — o o o o n o o o o o — o o I - o o d o 9 9 t 9 f o o a n o o o o d o o o o — o o o o d o o d o o o o - o o D . o ° ~ . ° o o o — o o o o o o o o o o o o — , 9 f 9 9 , 9 9 } ’ P 9 k 9 o d o o o — o o o o o o o d o o — o o I - o o d o o d o o o o - u o o d o o d o o d o — o - o o o o o o o 9 , 9 9 9 9 f ) f , 9 o o o o d o o o o — o o o o d o o d o o o o - n o o d o o d o o o o — o o o o o o o o o o - u o o o o d ' o 9 9 9 f 9 9 9 9 o — o o d o o ( o o d o — o o o o o o d o o o o — o o d o o \ o o o o o — o o o o d o o d o o o o n - o d o 9 9 , 9 , 9 9 , 9 , 9 o o o o o o q l o o o — o o d o o d o o o o — o o d o o o o o d o o o o — o o o o o d o o o o — o 9 9 , 9 , 9 9 o — o o o o d o o d o o o o — o o o o o o o o o o — o o o o d o 0 4 3 o o o — o o d o o ‘ o o o ¢ ( 9 9 9 9 , 9 , 9 > , 9 o o o — o o — o o d o o o o o o — o o d o o o o o d o — o — o o d o o d o o o — o o o o o o F i g u r e 7 . 8 . D i s t o r t e d T e p a t t e r n o f C u o . 4 0 ( l ) U T e 3 w i t h q = 0 . 1 0 4 0 ( 4 ) a ' - 0 . 0 2 8 4 ( 7 ) c ‘ a t 1 0 0 K a n d 2 . 9 A b o n d i n g t h r e s h o l d . T h e o c c u p a n c y c u t o f f w a s s e t t o t h e a v e r a g e v a l u e o f 0 . 4 0 . M a g n e t i c s u s c e p t i b i l i t y m e a s u r e m e n t s o f , B - U T e 3 a n d C u a a U T e 3 — V a r i a b l e t e m p e r a t u r e m a g n e t i c s u s c e p t i b i l i t y d a t a f o r B - U T C 3 a n d C u o _ 4 U T e 3 w e r e m e a s u r e d i n t h e r a n g e o f 2 - 3 0 0 K a t 5 0 0 0 G i n b o t h z e r o - fi e l d a n d fi e l d c o o l e d m o d e s . B o t h p h a s e s s h o w e d a m a x i m u m a t 6 K a n d 3 K r e s p e c t i v e l y . A b o v e t h i s t e m p e r a t u r e t h e d a t a f o l l o w t h e C u r i e / W e i s s l a w . A p e g v a l u e o f 3 . 3 4 1 1 3 a n d a W e i s s c o n s t a n t o f - 5 1 K w e r e 5 2 2 e s t i m a t e d b y l i n e a r fi t t i n g o f t h e l / x M v s T d a t a f o r B - U T e 3 , F i g u r e 7 . 9 . T h e d a t a i n d i c a t e a n i t f e r r o m a g n e t i c o r d e r i n g a t l o w t e m p e r a t u r e s c o n s i s t e n t w i t h a U 4 + c o n fi g u r a t i o n . N o d i f f e r e n c e w a s o b s e r v e d b e t w e e n z e r o - fi e l d a n d fi e l d c o o l e d d a t a . A s m a l l d i f f e r e n c e a t h i g h fi e l d s i n t h e fi e l d d e p e n d e n t c u r v e s w a s o b s e r v e d b e t w e e n t h e t w o o r i e n t a t i o n s o f t h e s i n g l e c r y s t a l s i n r e s p e c t t o t h e m a g n e t i c fi e l d ( p a r a l l e l a n d p e r p e n d i c u l a r t o t h e T e n e t ) , F i g u r e 7 . 1 0 . T h e m a g n e t i c r e s p o n s e o f t h e C u i n t e r c a l a t e d c o m p o u n d C u o . 4 U T e 3 s h o w e d s i m i l a r b e h a v i o r w i t h t h e o n e o b s e r v e d f o r B - U T e 3 . T h e r e i s a n a n t i f e r r o m a g n e t i c t r a n s i t i o n a t 3 K a n d a W e i s s c o n s t a n t o f - 1 2 1 K , F i g u r e 7 . 1 1 . T h e t r a n s i t i o n r e m a i n e d t h e s a m e a t b o t h c r y s t a l o r i e n t a t i o n s w i t h a r e l a t i v e s m a l l d i f f e r e n c e i n t h e m a g n e t i z a t i o n s i g n a l , F i g u r e 7 . 1 2 . 0 . 0 2 5 . , . . . , . , . , . , . , . 3 0 0 6 K Z F C P a r a l l e l t o T e n e t . C O 0 ' . - . ' - 2 5 0 0 . 0 2 0 4 . - I I - ' fl . 1 . " I I - a A 2 0 0 a 0 . 0 1 5 . , 3 I . . . - x 1 5 I " ‘ 1 5 0 \ < 1 8 ) p e fi = 3 . 3 4 “ a " " v x $ 0 . 0 1 0 9 = - 5 1 K i i e f f m fl c = 3 6 3 u fi f o r U 4 + . . 1 0 0 0 . 0 0 5 M M _ 5 0 0 4 O 8 0 A 1 2 0 i 1 6 0 i 2 0 0 I 2 4 0 2 8 0 3 2 0 T e m p e r a t u r e ( K ) F i g u r e 7 . 9 . T e m p e r a t u r e d e p e n d e n t m a g n e t i c s u s c e p t i b i l i t y f o r B - U T C 3 . 5 2 3 ) l e o m / u w m e ( m x § I I f I I T P e r p e d i c u l a r t o T e n e t . P a r a l l e l t o T e n e t 0 1 0 0 0 0 2 0 6 0 0 ' 3 0 6 0 0 ‘ 4 0 6 0 0 ‘ F i e l d ( 0 e ) F i g u r e 7 . 1 0 . F i e l d d e p e n d e n t m a g n e t i z a t i o n c u r v e f o r B - U T e 3 a t 5 K . 5 0 0 0 0 6 0 0 0 0 0 - 0 2 0 - 3 K Z F C P a r a l l e l t o T e n e t 0 . 0 1 8 v i i - ' - ' . . - 0 . 0 1 6 - . . . - I - . a . — 9 0 0 1 4 - \ 5 f O . I . g 0 . 0 1 2 - 1 ' 5 I . . . 3 8 2 “ e f f : ' “ a 3 0 ' 0 " ) e = - 1 2 1 K £ 0 0 0 8 ” : 1 ? c h = 3 . 6 3 a s f o r I f 0 0 0 6 “ M u m 0 . 0 0 4 r 0 4 0 8 0 1 2 0 1 6 0 2 0 0 2 4 0 2 8 0 T e m p e r a t u r e ( K ) 2 5 0 2 0 0 1 5 0 - 1 0 0 5 0 F i g u r e 7 . 1 1 . T e m p e r a t u r e d e p e n d e n t m a g n e t i c s u s c e p t i b i l i t y f o r C u o , 4 U T e 3 . 5 2 4 l / x m V I V ‘ l V I I ' T Y I ‘ 1 r f I 1 r V ' I ‘ V l U I I r I V T 0 . 0 3 0 _ Z F C P e r p e n d i c u l a r t o T e p l a n e . . O 0 o F O O O Q 0 0 0 . 0 2 5 » . _ E O B . E t o . Q ) e V 0 K g Z F C P a r a l l e l t o T e p l a n e . 0 . 0 2 0 » 0 . _ . . 0 0 . o O . . . . . . O O . 0 . 0 . . 0 . . O . . . . . . . . . 0 0 1 5 L 1 . | . i . 1 . 1 r 1 1 1 L 1 4 1 . 1 , 1 _ 1 ‘ , ‘ 1 0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 T e m p e r a t u r e ( K ) F i g u r e 7 . 1 2 . F i e l d d e p e n d e n t m a g n e t i z a t i o n c u r v e f o r C u o , 4 U T e 3 a t 5 K . R e s i s t i v i t y m e a s u r e m e n t s o f a - U T e 3 , , B - U T e 3 a n d C u x U T e 3 ( x = 0 . 1 0 , 0 . 4 0 ) — R e s i s t i v i t y d a t a f o r a - U T e 3 , B - U T e 3 a n d C u x U T e 3 ( x = 0 . 1 0 , 0 . 4 0 ) w e r e c o l l e c t e d i n t h e r a n g e o f 2 - 3 0 0 K . A q u a l i t a t i v e d i f f e r e n c e b e t w e e n t h e m e m b e r s w i t h d i f f e r e n t l o a d i n g o f C u a n d b e t w e e n a a n d B - p h a s e w a s o b s e r v e d . T h e a - U T e ; a n d C u m U T e g c o m p o u n d s s h o w e d a s e m i c o n d u c t i n g b e h a v i o r a s s e e n i n t h e r e s i s t i v i t y v s t e m p e r a t u r e p l o t i n F i g u r e 7 . 1 3 . T h e r e s i s t i v i t y f o r C u o _ 2 U T e 3 v a r i e s f r o m 1 0 m ! ) c m a t 2 4 0 K t o m o r e t h a n 1 M D c m a t 2 K . T h e c o r r e s p o n d i n g v a l u e s f o r t h e r e s i s t i v i t y o f a — U T e 3 w e r e 1 0 0 m ! ) c m t o m o r e t h a n 1 M D c m ( a b o v e t h e r e a d i n g r a n g e o f t h e i n s t r u m e n t ) r e s p e c t i v e l y . T h e A r r h e n i u s p l o t o f C u o . 2 U T e 3 d i d n o t s h o w a l i n e a r b e h a v i o r s u g g e s t i n g t h a t t h e c a r r i e r e x c i t a t i o n d o e s n o t f o l l o w a s i m p l e m e c h a n i s m , F i g u r e 7 . 1 4 . T h e t w o a p p a r e n t a c t i v a t i o n e n e r g i e s w e r e ~ 3 m e V a n d ~ 3 1 m e V . 5 2 5 ) y t i v i t s i s e R ( n l 1 o o o _ 1 0 0 : S 1 0 9 5 3 : " . 2 1 . 3 2 ’ : 8 “ 0 . 1 0 . 0 1 = ” . 1 1 1 . 1 1 1 4 1 . J . 1 . 1 1 1 . 1 4 1 . 1 : 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 2 4 0 T e m p e r a t u r e ( K ) F i g u r e 7 . 1 3 . R e s i s t i v i t y v s . l o w t e m p e r a t u r e p l o t f o r a - U T e 3 a n d C u o , 2 U T e 3 . . 4 _ _ 6 n l 4 L m l 4 l r J 4 J n l n J 4 J 1 0 2 5 0 5 0 0 7 5 0 1 0 0 0 1 2 5 0 1 5 0 0 1 7 5 0 2 0 0 0 2 2 5 0 2 5 0 0 1 / k T F i g u r e 7 . 1 4 . A r r h e n i u s p l o t o f t h e r e s i s t i v i t y f o r C u o _ 2 U T e 3 . 5 2 6 T h e h i g h t e m p e r a t u r e r e s i s t i v i t y d a t a i n t h e r a n g e o f 3 0 0 - 7 0 0 K d i d n o t s h o w a n y d i s c o n t i n u i t i e s i n d i c a t i v e o f a C D W t r a n s i t i o n , F i g u r e 7 . 1 5 . 1 0 l ' l ' I T F ' l ' 1 l I l t P O 8 - _ : 8 : s % 6 - . _ E . l Z E 4 - _ i n “ . C D < 1 ) a : 2 - - * 3 . l 1 I . I . L 1 I . I m l . I . I 3 0 0 3 5 0 4 0 0 4 5 0 5 0 0 5 5 0 6 0 0 6 5 0 7 0 0 T e m p e r a t u r e ( K ) F i g u r e 7 . 1 5 . R e s i s t i v i t y v s . h i g h t e m p e r a t u r e p l o t f o r C U o _ 2 U T 6 3 . T h e C u o _ 4 U T e 3 p h a s e s h o w e d a m e t a l l i c b e h a v i o r , F i g u r e 7 . 1 6 . T h e r e s i s t i v i t y r a n g e s f r o m ~ 1 . 5 m c m a t 2 K t o ~ 4 . 5 m ! ) c m a t 2 6 0 K . T h e r e i s a l s o a c h a n g e i n t h e s l o p e o f t h e r e s i s t i v i t y v s t e m p e r a t u r e p l o t a r o u n d 1 9 0 K . T h e s i n g l e c r y s t a l X - r a y d i f f r a c t i o n e x p e r i m e n t a t 3 0 0 K a n d 1 0 0 K t h o u g h d i d n o t s h o w a n y c h a n g e i n t h e t w o s u p e r s t r u c t u r e s . T h e t e m p e r a t u r e d e p e n d e n t r e s i s t i v i t y m e a s u r e m e n t o n B - U T e 3 r e v e a l e d a n o m a l i e s b e l l o w 5 0 K a s s h o w n i n F i g u r e 7 . 1 7 . D o w n t o 1 0 0 K ( l i m i t o f o u r l o w t e m p e r a t u r e d e v i c e ) t h e s t r u c t u r e o f B - U T e g ( N d T e g - t y p e ) p o s s e s a n i d e a l n e t o f T e a t o m s . I t w o u l d b e s u r p r i s i n g i f a n i d e a l s q u a r e n e t o f T e a t o m s w i t h a n a v e r a g e o x i d a t i o n s t a t e o f - 1 r e a l l y e x i s t s a t t h e t e m p e r a t u r e r a n g e f r o m 2 - 1 0 0 K . A l t h o u g h t h e r e i s n o 5 2 7 ) m c m h O ( N y t i v i t s i s e R i s t r u c t u r a l p r o o f o f t h e n e t d i s t o r t s , w e b e l i e v e t h a t t h e o b s e r v e d a n o m a l i e s i n t h e r e s i s t i v i t y d a t a c o r r e s p o n d t o C D W t r a n s i t i o n s . 5 . 0 1 l I I Y I T l I 1 j r T I I 4 . 5 b - C u o . 4 U T 6 3 4 . 0 - - $ 3 . 5 L - E 3 0 - - a ? - > E 2 . 5 - - 8 . - 0 4 2 . 0 - - 1 . 5 - « 1 . 0 1 I 1 I L I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 1 I 0 2 0 4 O 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 T e m p e r a t u r e ( K ) F i g u r e 7 . 1 6 . R e s i s t i v i t y v s . l o w t e m p e r a t u r e p l o t f o r C u o , 4 U T e 3 . 4 1 I ' I ' I 1 I ' I ' I I I I I ' I ' I ' fi g I ' I ' I ' I 1 5 K I — 1 I l I 1 l g 1 l O 1 0 2 0 4 O 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 3 0 0 T e m p e r a t u r e ( K ) F i g u r e 7 . 1 7 . R e s i s t i v i t y v s . l o w t e m p e r a t u r e p l o t f o r B - U T e 3 . 5 2 8 7 . 4 . C o n c l u s i o n s I n t e r c a l a t i o n o f C u a t o m s i n t h e v a n d e r W a a l s g a p o f U T e 3 s t a b i l i z e s t h e a - U T e 3 p h a s e . A s u c c e s s i v e i n c r e a s e i n c o n c e n t r a t i o n o f C u g r a d u a l l y i n c r e a s e s t h e F e r m i l e v e l . T h i s c r e a t e s a b r u p t c h a n g e s i n t h e l e n g t h a n d o r i e n t a t i o n o f t h e m o d u l a t i o n q - v e c t o r . T h e c r o s s - p l a n e i n t e r a c t i o n s ( a l o n g c - a x i s ) i n c r e a s e w i t h C u s i n c e t h e e m p t y s p a c e o f t h e v a n d e r W a a l s g a p i s o c c u p i e d b y a t o m s . T h e o r b i t a l o v e r l a p b e t w e e n C u a n d T e a t o m s i n c r e a s e s t h e t h r e e - d i m e n s i o n a l c h a r a c t e r o f t h e s t r u c t u r e w h i l e t h e c o n c e n t r a t i o n o f i n t e r c a l a t e d a t o m s i n c r e a s e s . T h i s i s a p p a r e n t b y t h e l e n g t h e n i n g o f t h e i n c o m m e n s u r a t e c o m p o n e n t o f t h e q - v e c t o r a l o n g c * . I n C u x U T e g f o r x = 0 . 1 4 ( 1 ) t h e a b s o l u t e v a l u e o f t h e c o m p o n e n t i s 0 . 0 2 8 4 ( 7 ) c ' . F o r x = 0 1 8 ( 1 ) a n d 0 . 4 0 ( 1 ) t h e q - v e c t o r c o m p o n e n t b e c o m e s 0 . 0 8 6 ( 3 ) c ' a n d 0 . 5 1 3 ( 1 ) c ‘ r e s p e c t i v e l y . A n i n t e r e s t i n g f e a t u r e i n t h e s e C u x U T e 3 c o m p o u n d s i s t h e l o n g r a n g e o r d e r i n g o f t h e C u a t o m s a n d v a c a n c i e s i n a f o r m o f c l u s t e r s w i t h a n a v e r a g e C u - C u d i s t a n c e o f ~ 2 . 6 A . T o t h e b e s t o f o u r k n o w l e d g e t h i s i s a u n i q u e a r r a n g e m e n t t h a t s e e m s t o b e c o r r e l a t e d t o t h e C D W d i s t o r t i o n s . T h e T e - T e d i s t a n c e s o f t h e a t o m s l o c a t e d a b o v e o r b e l l o w t h e c l u s t e r s o f C u a r e s i g n i fi c a n t l y e l o n g a t e d ( m o r e t h a n 2 . 9 A ) i n r e s p e c t e d t o t h e o t h e r T e a t o m s t h a t l i e o n t o p o f v a c a n c i e s . T h i s b e h a v i o r c a n b e e x p l a i n e d b y e l e c t r o n c o u n t a r g u m e n t s t h a t p r e d i c t a d e c r e a s e o f t h e T e - T e d i s t a n c e w i t h o x i d a t i o n . I n t e r e s t i n g l y , t h e e x t r a e l e c t r o n s t h a t a r e a d d e d i n t h e s y s t e m a f t e r t h e i n t e r c a l a t i o n o f C u a t o m s a r e m o r e l o c a l i z e d i n t h e d i s t o r t e d T e n e t . T h e q u a s i - o n e - d i m e n s i o n a l c h a r a c t e r o f t h e l i n e a r l y d i s t o r t e d T e n e t s s e e m s t o p r o m o t e t h i s c h a r g e s e p a r a t i o n . S i m i l a r b e h a v i o r w a s n o t o b s e r v e d f o r t h e q u a s i - t w o - d i m e n s i o n a l R E T e g ; 1 9 a n d A M R E T e 4 2 0 m e m b e r s i n w h i c h e l e c t r o n s a r e f o u n d t o b e d e l o c a l i z e d i n t h e p l a n a r d i s t o r t e d T e n e t s . 5 2 9 T a b l e 7 . 1 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C u o _ . 4 ( 1 ) U T e 3 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( O O O ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 1 2 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 0 ’ ( I ) ] R l S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m . . . a n d T m a x c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e C U 0 . 1 4 ( 1 ) U T 6 3 6 2 7 . 2 1 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A M o n o c l i n i c P 2 , / m ( 6 0 y ) 0 0 a = 6 . 0 6 0 3 ( 1 0 ) A , a = 9 0 0 b = 4 . 1 9 9 2 ( 3 ) A , B = 9 8 . 4 2 8 ( 6 ) ° c = 1 0 . 2 9 4 3 ( 7 ) A , y = 9 0 ° 0 . 1 0 4 0 ( 4 ) a ‘ - 0 . 0 2 8 4 ( 7 ) e ‘ 2 5 9 . 3 5 ( 3 ) A 3 2 8 . 0 2 8 6 g / c m 3 1 7 . 5 2 2 m m " 5 0 4 0 . 2 0 x 0 . 1 0 x 0 . 0 2 m m 3 3 . 3 5 t o 2 9 . 1 2 ° - 8 < = h < = 8 , - 5 < = k < = 5 , - 1 4 < = 1 < = 1 4 , - 1 < = m < = 1 9 5 5 0 2 2 6 5 [ R i m = 0 . 0 8 0 8 ] 9 5 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 2 2 6 5 / 0 / 8 3 1 6 . 2 1 R . . . = 0 . 0 8 3 2 , w R . . . = 0 . 1 7 0 3 R 8 1 1 : 0 . 0 9 1 9 , W R a n = 0 . 1 7 1 6 R . . . = 0 . 0 5 1 3 , w R . . . = 0 . 1 0 7 2 R . l l = 0 . 0 5 1 4 , w R . 1 1 = 0 . 1 0 7 2 R . . . = 0 . 2 1 2 1 , w R . . . = 0 . 4 2 9 7 R . l l = 0 . 2 5 4 3 , w R . l l = 0 . 4 4 0 2 2 4 . 1 ( 1 2 ) 0 . 0 1 9 0 a n d 0 . 4 7 5 9 8 . 0 4 a n d - 7 . 0 2 e . A ' 3 R = l e F o l - I F c l l / 2 1 m , w R = { 2 : [ w 0 F o F - I R W ] / £ [ w ( I F . I “ ) 1 } ‘ ” a n d w = 1 / ( a ’ ( 1 ) + 0 . 0 0 1 6 1 2 ) 5 3 0 T a b l e 7 . 2 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C u o , 1 4 ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s . A t o m W a v e x y 2 O c c u p a n c y U . q U 0 7 8 9 0 ( 1 ) 2 5 4 9 1 6 1 5 ( 1 ) 1 2 2 ( 1 ) s i n , 1 4 2 ( 1 ) 0 5 5 ( 1 ) c o s , 1 - 1 7 ( 1 ) 0 - 2 0 ( 1 ) T e [ l ] 0 2 6 6 0 ( 2 ) 2 5 4 9 6 2 2 ( 1 ) 1 2 2 ( 1 ) s i n , 1 3 5 ( 2 ) 0 5 3 ( 2 ) c o s , 1 2 ( 2 ) 0 2 2 ( 2 ) T e [ 2 ] 0 3 9 6 9 ( 2 ) 2 5 4 9 6 5 9 4 ( 1 ) 1 2 5 ( 1 ) s i n , 1 1 9 ( 3 ) 0 3 5 ( 2 ) c o s , 1 - 4 9 ( 2 ) 0 - 1 6 ( 2 ) T e [ 3 ] 0 9 2 4 0 ( 2 ) 2 5 4 9 6 6 7 6 ( 2 ) 1 2 9 ( 1 ) s i n , 1 2 4 ( 3 ) 0 7 2 ( 2 ) c o s , 1 1 2 1 ( 3 ) 0 - 9 ( 2 ) C u 0 9 1 5 ( 7 0 ) 2 5 4 9 4 5 4 5 ( 3 0 ) 0 . 1 3 8 ( 7 ) 2 9 s i n , 1 3 5 ( 5 0 ) 0 5 ( 2 0 ) c o s , 1 - 5 ( 9 0 ) 0 - 6 5 ( 4 0 ) T a b l e 7 . 3 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r C u o _ 1 4 ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s . A t o m W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 U 0 2 0 ( 1 ) 1 7 ( 1 ) 2 9 ( 1 ) 0 6 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 0 ( 1 ) 0 c o s , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 0 ( 1 ) 0 T e [ l ] 0 1 9 ( 1 ) 2 0 ( 1 ) 2 9 ( 1 ) 0 5 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 0 ( 1 ) 0 c o s , 1 0 ( 1 ) - 1 ( 1 ) 1 ( 1 ) 0 0 ( 1 ) 0 T e [ 2 ] 0 2 5 ( 1 ) 2 4 ( 1 ) 2 9 ( 1 ) 0 9 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 0 - 1 ( 1 ) 0 c o s , 1 - 1 ( 1 ) 0 ( 1 ) 3 ( 1 ) 0 1 ( 1 ) 0 T e [ 3 ] 0 2 9 ( 1 ) 2 3 ( 1 ) 3 4 ( 1 ) 0 0 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 1 ( 1 ) 0 c o s , 1 - 5 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 2 ( 1 ) 0 C u 0 4 7 3 8 2 0 O 0 5 3 1 T a b l e 7 . 4 . F o u r i e r c o m p o n e n t s o f t h e o c c u p a t i o n a l m o d u l a t i o n f o r C u o _ 1 4 ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s . A t o m W a v e O c c u p a t i o n a l c o m p o n e n t C u s i n , 1 - 0 . 0 4 3 ( 1 0 ) c o s , 1 - 0 . 1 2 0 ( 1 0 ) T a b l e 7 . 5 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C 1 m , 1 4 ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e U - T e [ l ] 3 . 1 8 7 0 ( 1 9 ) 3 . 1 7 6 9 ( 1 9 ) 3 . 1 9 7 3 ( 1 9 ) U - T e [ l ] 3 . 2 0 7 ( 2 ) 3 . 1 9 8 ( 2 ) 3 . 2 1 6 ( 2 ) U - T e [ l ] x 2 3 . 0 9 7 6 ( 1 9 ) 3 . 0 9 5 9 ( 1 9 ) 3 . 0 9 9 3 ( 1 9 ) U - T e [ 2 ] x 2 3 . 1 1 3 ( 2 ) 3 . 1 0 5 ( 2 ) 3 . 1 2 2 ( 2 ) U - T e [ 3 ] x 2 3 . 1 0 4 8 ( 1 8 ) 3 . 0 9 3 3 ( 1 8 ) 3 . 1 1 6 3 ( 1 8 ) U - C u 3 2 9 ( 5 ) 3 2 3 ( 4 ) 3 3 4 ( 4 ) T e [ 2 ] - T e [ 3 ] 2 . 8 8 1 ( 3 ) 2 . 7 8 2 ( 3 ) 2 . 9 8 1 ( 3 ) T e [ 2 ] - T e [ 3 ] 3 . 1 8 7 ( 3 ) 3 . 0 8 2 ( 3 ) 3 . 2 8 9 ( 3 ) T e [ 2 ] - C u 2 6 0 ( 5 ) 2 5 6 ( 5 ) 2 6 4 ( 5 ) T e [ 3 ] - C u 2 5 5 ( 5 ) 2 . 4 9 ( 5 ) 2 6 2 ( 5 ) T e [ 3 ] - C u x 2 2 4 4 ( 3 ) 2 3 8 ( 2 ) 2 5 0 ( 3 ) C u - C u x 2 2 6 2 ( 5 ) 2 5 7 ( 5 ) 2 6 7 ( 6 ) T a b l e 7 . 6 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C u o _ 1 4 ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ l ] - U - T e [ l ] 1 4 3 . 1 4 ( 7 ) 1 4 1 . 6 5 ( 7 ) 1 4 4 . 6 1 ( 7 ) T e [ l ] - U - T e [ l ] x 4 7 6 5 9 ( 5 ) 7 6 1 2 ( 5 ) 7 7 0 5 ( 5 ) T e [ l ] - U - T e [ 2 ] x 2 7 6 1 2 ( 5 ) 7 5 5 1 ( 5 ) 7 6 7 1 ( 5 ) T e [ l ] - U - T e [ 3 ] x 2 1 2 9 . 0 9 ( 5 ) 1 2 7 . 8 3 ( 5 ) 1 3 0 . 3 4 ( 4 ) T e [ l ] - U - C u x 3 1 3 3 . 6 ( 9 ) 1 3 3 . 2 ( 9 ) 1 3 3 . 9 ( 9 ) T e [ l ] - U - T e [ 2 ] x 2 1 2 7 . 6 4 ( 4 ) 1 2 6 . 5 0 ( 4 ) 1 2 8 . 7 7 ( 4 ) T e [ l ] - U - T e [ 3 ] x 2 7 3 9 6 ( 6 ) 7 3 2 3 ( 6 ) 7 4 6 8 ( 6 ) T e [ l ] - U - C u 8 3 . 3 ( 9 ) 8 1 . 7 ( 9 ) 8 4 . 9 ( 9 ) T e [ l ] - U - T e [ l ] 8 5 3 5 ( 5 ) 8 5 2 9 ( 5 ) 8 5 4 0 ( 5 ) T e [ l ] - U - T e [ 2 ] x 2 8 8 5 3 ( 5 ) 8 7 9 4 ( 5 ) 8 9 1 1 ( 5 ) T e [ l ] - U - T e [ 2 ] x 2 1 5 2 . 7 1 ( 6 ) 1 5 1 . 6 7 ( 6 ) 1 5 3 . 7 3 ( 6 ) 5 3 2 T a b l e 7 . 6 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C u o , 1 4 ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s . T e [ l ] — U - T e [ 2 ] - U - T e [ 2 ] - U - T e [ 2 ] - U - T e [ 3 ] - U - T e [ 3 ] - U - U - T e [ l ] - U - T e [ 2 ] - U - T e [ 2 ] - U - T e [ 2 ] - U - T e [ 2 ] - T e [ 3 ] x 2 T e [ 2 ] T e [ 3 ] x 2 C u x 2 T e [ 3 ] C u x 2 U x 4 U T e [ 3 ] x 2 T e [ 3 ] x 2 C u x 2 T e [ 3 ] - T e [ 2 ] - T e [ 3 ] T e [ 3 ] - T e [ 2 ] - C u T e [ 3 ] - T e [ 2 ] - C u U - T e [ 3 ] - U - T e [ 3 ] - U - T e [ 3 ] - U - T e [ 3 ] - U - T e [ 3 ] - U T e [ 2 ] x 2 T e [ 2 ] x 2 C u x 2 C u x 2 T e [ 2 ] - T e [ 3 ] - T e [ 2 ] T e [ 2 ] - T e [ 3 ] - C u T e [ 2 ] - T e [ 3 ] - C u x 4 - C u x 2 - C u C u - T e [ 3 ] C u - T e [ 3 ] U - C u - T e [ 2 ] U - C u - T e [ 3 ] U - C u - T e [ 3 ] x 2 U - C u - C u x 2 T e [ 2 ] - C u T e [ 2 ] - C u T e [ 3 ] - C u T e [ 3 ] - C u - T e [ 3 ] T e [ 2 ] - C u - T e [ 3 ] x 2 - C u x 2 T e [ 3 ] - C u - T e [ 3 ] x 3 - C u x 4 - C u x 2 8 7 3 3 ( 5 ) 8 4 8 2 ( 5 ) 5 5 2 0 ( 5 ) 7 0 . 1 ( 6 ) 8 5 1 0 ( 5 ) 4 4 . 8 ( 2 ) 1 0 3 . 4 7 ( 5 ) 8 4 8 2 ( 6 ) 6 2 2 4 ( 5 ) 1 1 5 . 6 8 ( 6 ) 1 0 1 . 8 ( 8 ) 1 7 6 . 8 4 ( 1 1 ) 5 5 . 2 ( 1 1 ) 1 2 7 . 9 ( 1 1 ) 8 5 1 0 ( 6 ) 1 1 9 . 4 6 ( 7 ) 6 2 5 5 ( 5 ) 1 0 3 . 2 ( 7 ) 7 1 . 6 ( 9 ) 1 7 6 . 8 4 ( 1 2 ) 1 2 0 . 1 ( 1 0 ) 9 1 . 3 ( 1 2 ) 6 3 . 2 ( 1 1 ) 1 1 8 . 8 ( 1 3 ) 1 6 9 ( 2 ) 1 2 3 ( 2 ) 6 3 . 7 ( 1 0 ) 9 7 . 0 ( 1 6 ) 6 8 . 0 ( 1 2 ) 1 1 2 . 7 ( 1 3 ) 8 9 . 7 ( 1 5 ) 1 1 6 . 8 ( 1 3 ) 5 6 . 3 ( 1 3 ) 1 5 3 ( 3 ) 8 6 7 8 ( 5 ) 8 4 5 3 ( 5 ) 5 5 1 9 ( 5 ) 6 9 . 4 ( 6 ) 8 4 . 7 1 ( 5 ) 4 4 . 2 ( 2 ) 1 0 2 . 8 8 ( 5 ) 8 4 5 3 ( 6 ) 6 1 . 4 2 ( 5 ) 1 1 4 . 4 0 ( 6 ) 9 9 . 9 ( 8 ) 1 7 5 . 4 9 ( 1 1 ) 5 3 . 5 ( 1 1 ) 1 2 7 . 3 ( 1 1 ) 8 4 . 7 1 ( 6 ) 1 1 8 . 1 2 ( 7 ) 6 1 2 8 ( 5 ) 1 0 0 . 4 ( 7 ) 7 0 . 7 ( 9 ) 1 7 5 . 3 3 ( 1 2 ) 1 1 7 . 5 ( 1 0 ) 8 9 . 4 ( 1 2 ) 6 0 . 9 ( 1 0 ) 1 1 4 . 4 ( 1 3 ) 1 6 7 ( 2 ) 1 2 2 ( 2 ) 6 2 . 2 ( 9 ) 9 4 . 8 ( 1 7 ) 6 4 . 6 ( 1 2 ) 1 1 1 . 9 ( 1 3 ) 8 6 . 7 ( 1 6 ) 1 1 4 . 6 ( 1 4 ) 5 4 . 5 ( 1 4 ) 1 5 2 ( 3 ) 8 7 8 8 ( 5 ) 8 5 1 0 ( 5 ) 5 7 2 4 ( 5 ) 7 0 8 ( 6 ) 8 5 4 9 ( 5 ) 4 5 4 ( 3 ) 1 0 4 . 0 7 ( 5 ) 8 5 1 0 ( 6 ) 6 3 0 7 ( 5 ) 1 1 6 . 9 9 ( 6 ) 1 0 3 . 7 ( 8 ) 1 7 8 . 1 7 ( 1 1 ) 5 7 . 0 ( 1 1 ) 1 2 8 . 6 ( 1 1 ) 8 5 4 9 ( 6 ) 1 2 0 . 8 3 ( 7 ) 6 3 8 2 ( 5 ) 1 0 5 . 9 ( 7 ) 7 2 . 5 ( 9 ) l 7 8 . 3 5 ( 1 2 ) 1 2 2 . 8 ( 1 0 ) 9 3 . 3 ( 1 2 ) 6 5 . 6 ( 1 1 ) 1 2 3 . 4 ( 1 4 ) 1 7 1 ( 2 ) 1 2 5 ( 2 ) 6 5 . 1 ( 9 ) 9 9 . 1 ( 1 7 ) 7 1 . 5 ( 1 4 ) 1 1 3 . 6 ( 1 2 ) 9 2 . 8 ( 1 7 ) 1 1 8 . 9 ( 1 4 ) 5 8 . 2 ( 1 5 ) 1 5 3 ( 2 ) 5 3 3 T a b l e 7 . 7 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C q u g m U T e 3 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( 1 ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 9 . 3 2 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ' ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m . . . a n d T m . . . c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e C 1 1 0 . 1 8 ( 1 ) U T € 3 6 3 3 . 5 1 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A M o n o c l i n i c P 2 1 / m ( ( 1 0 y ) 0 0 a = 6 . 0 6 0 3 ( 1 0 ) A , a = 9 0 ° b = 4 . 1 9 8 0 ( 8 ) A , 1 3 = 9 8 . 1 7 1 ( 1 4 ) ° c = 1 0 . 2 8 1 3 ( 1 9 ) A , y = 9 0 0 0 . 1 7 9 ( 1 ) a " - 0 . 0 8 6 ( 3 ) c ‘ 2 5 8 . 9 1 ( 8 ) A 3 2 8 . 1 2 4 g / c m 3 1 7 . 9 5 3 m m " 5 0 6 0 . 1 5 x 0 . 0 9 x 0 . 0 2 m m 3 3 . 1 0 t o 2 9 . 3 2 ° - 8 < = h < = 8 , - 5 < = k < = 5 , - 1 4 < = 1 < = 1 4 , - 1 < = m < = l 1 2 0 2 8 ( 3 7 4 6 m a i n + 8 2 8 2 s a t e l l i t e s ) 2 3 4 6 ( 7 7 7 m a i n + 1 5 6 9 s a t e l l i t e S ) [ R i m = 0 . 0 5 5 9 ] 9 6 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 2 3 4 6 / 0 / 9 5 2 . 7 5 R . . . = 0 . 0 5 1 8 , w R . . . = 0 . 1 6 2 8 R . l l = 0 . 0 5 7 4 , w R . l l = 0 . 1 6 4 6 R . . . = 0 . 0 3 8 5 , w R . . . = 0 . 1 0 0 0 R . l l = 0 . 0 3 8 6 , w R . l l = 0 . 1 0 0 2 R . . . = 0 . 1 0 3 8 , w R . . . = 0 . 2 4 0 8 R . " = 0 . 1 2 6 0 , w R . u = 0 . 2 4 4 1 0 . 0 0 3 5 5 0 3 ) 0 . 0 2 4 3 a n d 0 . 4 0 9 6 7 . 3 0 a n d - 3 . 2 0 e . A ' 3 R = l e F o l - I F e l l / 2 1 m , w R = { 2 [ W ( | F o | 2 - 1 1 8 0 2 ] / 2 [ w ( I F . I ‘ ) T } " 2 a n d w = 1 / ( o z < 1 ) + o . 0 0 1 6 1 2 ) 5 3 4 T a b l e 7 . 8 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C u o _ 1 3 ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x y 2 O c c u p a n c y U . q U 0 7 9 0 5 ( 1 ) 2 5 4 9 1 6 2 4 ( 1 ) 1 1 5 ( 1 ) s i n , 1 3 1 ( 1 ) 0 3 9 ( 1 ) c o s , 1 - 1 3 ( 1 ) 0 - 2 4 ( 1 ) T e [ l ] 0 2 6 5 9 ( 1 ) 2 5 4 9 6 1 0 ( 1 ) 1 1 5 ( 1 ) s i n , 1 1 7 ( 1 ) 0 3 7 ( 1 ) c o s , 1 6 ( 1 ) 0 3 0 ( 1 ) T e [ 2 ] 0 3 9 8 7 ( 1 ) 2 5 4 9 6 6 0 2 ( 1 ) 1 2 0 ( 1 ) s i n , 1 - 2 3 ( 1 ) 0 4 ( 1 ) c o s , 1 - 9 1 ( 1 ) 0 - 2 3 ( 1 ) T e [ 3 ] 0 9 1 6 9 ( 1 ) 2 5 4 9 6 6 8 0 ( 1 ) 1 2 1 ( 1 ) s i n , 1 - 1 1 ( 1 ) 0 6 9 ( 1 ) c o s , 1 1 7 9 ( 1 ) 0 - 1 9 ( 1 ) C u 0 1 0 6 5 ( 6 0 ) 2 5 4 9 4 6 8 5 ( 3 0 ) 0 . 1 8 0 ( 7 ) 2 6 ( 1 1 ) s i n , 1 1 2 5 ( 4 0 ) 0 4 5 ( 2 0 ) c o s , 1 1 1 5 ( 7 0 ) 0 1 5 ( 4 0 ) T a b l e 7 . 9 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r C q u g m U T e g a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 U 0 1 3 ( 1 ) 1 4 ( 1 ) 1 7 ( 1 ) 0 3 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 0 ( 1 ) 0 c o s , 1 1 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 0 ( 1 ) 0 T e [ l ] 0 1 3 ( 1 ) 1 7 ( 1 ) 1 7 ( 1 ) 0 3 ( 1 ) 0 s i n , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 0 ( 1 ) 0 c o s , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 1 ( 1 ) 0 T e [ 2 ] 0 1 9 ( 1 ) 2 0 ( 1 ) 2 1 ( 1 ) 0 7 ( 1 ) 0 s i n , 1 - 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) 0 0 ( 1 ) 0 c o s , 1 - 1 ( 1 ) 2 ( 1 ) 1 ( 1 ) 0 0 ( 1 ) 0 T e [ 3 ] 0 2 0 ( 1 ) 2 0 ( 1 ) 2 2 ( 1 ) 0 - 1 ( 1 ) 0 s i n , 1 - 2 ( 1 ) 1 ( 1 ) - 1 ( 1 ) 0 2 ( 1 ) 0 c o s , 1 - 4 ( 1 ) 1 ( 1 ) 1 ( 1 ) 0 2 ( 1 ) 0 5 3 5 T a b l e 7 . 9 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r C u o _ 1 g ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . C u 0 2 4 ( 1 3 ) 5 5 ( 3 0 ) 1 3 ( 1 3 ) 0 2 7 ( 1 2 ) 0 s i n , 1 - 6 ( 9 ) 2 1 ( 1 6 ) - 5 ( 9 ) 0 1 4 ( 8 ) 0 c o s , 1 - 1 3 ( 1 5 ) 3 5 ( 3 0 ) - 7 ( 1 6 ) 0 2 8 ( 1 3 ) 0 T a b l e 7 . 1 0 . F o u r i e r c o m p o n e n t s o f t h e o c c u p a t i o n a l m o d u l a t i o n f o r C u o , 1 3 ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e O c c u p a t i o n a l c o m p o n e n t C u s i n , 1 - 0 . 1 0 7 ( 7 ) c o s , 1 - 0 . 2 0 3 ( 6 ) T a b l e 7 . 1 1 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C u o , 2 o ( 2 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e U - T e [ l ] x 2 3 . 2 0 1 6 ( 1 1 ) 3 . 1 8 9 2 ( 1 1 ) 3 . 2 1 3 9 ( 1 1 ) U - T e [ l ] x 2 3 . 0 9 4 3 ( 8 ) 3 . 0 9 1 4 ( 8 ) 3 . 0 9 7 3 ( 8 ) U - T e [ 2 ] x 2 3 . 1 0 5 6 ( 9 ) 3 . 0 9 3 6 ( 9 ) 3 . 1 1 7 0 ( 9 ) U - T e [ 3 ] x 2 3 . 1 1 7 6 ( 9 ) 3 . 0 9 4 6 ( 9 ) 3 . 1 4 1 1 ( 9 ) U - C u 3 . 4 2 ( 4 ) 3 3 7 ( 5 ) 3 5 0 ( 5 ) T e [ 2 ] - T e [ 3 ] 2 . 9 3 1 3 ( 1 6 ) 2 . 7 6 6 0 ( 1 6 ) 3 . 0 9 9 5 ( 1 6 ) T e [ 2 ] - T e [ 3 ] 3 . 1 3 1 5 ( 1 6 ) 2 . 9 8 0 3 ( 1 6 ) 3 . 2 7 9 2 ( 1 6 ) T e [ 2 ] - C u 2 4 9 ( 4 ) 2 3 7 ( 4 ) 2 5 8 ( 5 ) T e [ 3 ] - C u x 3 2 5 0 ( 5 ) 2 4 1 ( 5 ) 2 5 7 ( 5 ) C u - C u x 2 2 5 7 ( 4 ) 2 5 2 ( 5 ) 2 6 4 ( 4 ) T a b l e 7 . 1 2 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C 1 1 0 , 1 g ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ l ] - U - T e [ l ] x 2 1 4 2 . 3 8 ( 3 ) 1 4 0 . 6 0 ( 3 ) 1 4 4 . 1 6 ( 3 ) T e [ l ] - U - T e [ l ] x 4 7 6 0 2 ( 2 ) 7 5 5 6 ( 2 ) 7 6 4 8 ( 2 ) T e [ l ] - U - T e [ 2 ] x 2 7 6 0 6 ( 3 ) 7 4 9 5 ( 3 ) 7 7 . 1 5 ( 3 ) T e [ l ] - U - T e [ 3 ] x 2 1 2 9 . 9 1 ( 2 ) 1 2 7 . 9 6 ( 2 ) 1 3 1 . 8 4 ( 2 ) 5 3 6 T a b l e 7 . 1 2 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C u o _ 1 3 ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 1 ] - U - C u x 3 T e [ 1 ] - U - T e [ 1 ] x 4 T e [ 1 ] - U - T e [ 2 ] x 2 T e [ 1 ] - U - T e [ 3 ] x 2 T e [ 1 ] - U - C u T e [ 1 ] - U - T e [ 1 ] x 2 T e [ 1 ] - U - T e [ 2 ] x 2 T e [ l ] - U - T e [ 2 ] x 2 T e [ 1 ] — U - T e [ 3 ] x 2 T e [ l ] - U - T e [ 3 ] x 2 T e [ 2 ] - U - T e [ 2 ] x 2 T e [ 2 ] - U - T e [ 3 ] x 2 T e [ 2 ] - U - T e [ 3 ] x 2 T e [ 2 ] - U - C u x 2 T e [ 3 ] - U - T e [ 3 ] x 2 T e [ 3 ] - U - C u x 2 U - T e [ 1 ] - U x 2 U - T e [ 1 ] - U x 4 U - T e [ 1 ] - U x 4 U - T e [ l ] - U x 2 U - T e [ 2 ] - U x 2 U - T e [ 2 ] - T e [ 3 ] x 2 U - T e [ 2 ] - T e [ 3 ] x 2 U - T e [ 2 ] - C u x 2 T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 T e [ 3 ] - T e [ 2 ] - C u T e [ 3 ] - T e [ 2 ] - C u U - T e [ 3 ] - U x 2 U - T e [ 3 ] - T e [ 2 ] x 2 U - T e [ 3 ] - T e [ 2 ] x 2 U - T e [ 3 ] - C u x 2 U - T e [ 3 ] - C u x 2 U - T e [ 3 ] - C u x 2 T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 1 3 3 . 9 ( 8 ) 7 6 5 7 ( 2 ) 1 2 8 . 0 0 ( 2 ) 7 3 4 7 ( 3 ) 8 4 . 1 ( 8 ) 8 5 4 3 ( 2 ) 8 8 0 8 ( 2 ) 1 5 2 . 0 8 ( 3 ) 8 7 2 8 ( 2 ) 1 5 0 . 0 4 ( 3 ) 8 5 0 5 ( 2 ) 5 6 2 2 ( 3 ) 1 1 0 7 8 ( 3 ) 7 0 . 6 ( 5 ) 8 4 6 4 ( 2 ) 4 5 1 ( 2 ) 1 4 2 . 3 9 ( 3 ) 1 0 3 . 4 2 ( 2 ) 1 0 3 . 9 8 ( 3 ) 8 5 4 3 ( 3 ) 8 5 0 4 ( 3 ) 6 2 0 9 ( 3 ) 1 1 5 . 9 3 ( 3 ) 1 0 0 . 1 ( 8 ) 1 7 6 . 9 7 ( 5 ) 5 3 . 7 ( 1 1 ) 1 2 9 . 0 ( 1 1 ) 8 4 6 5 ( 3 ) 1 2 0 . 2 1 ( 3 ) 6 1 . 7 0 ( 3 ) 9 9 . 4 ( 7 ) 7 3 8 ( 8 ) 1 4 7 . 3 ( 1 0 ) 1 7 6 . 9 6 ( 5 ) 1 3 3 . 3 ( 8 ) 7 5 7 7 ( 2 ) 1 2 6 . 3 5 ( 2 ) 7 1 9 7 ( 3 ) 8 1 . 6 ( 7 ) 8 5 3 3 ( 2 ) 8 7 2 3 ( 2 ) 1 5 0 . 5 5 ( 3 ) 8 6 3 9 ( 2 ) l 4 7 . 8 6 ( 3 ) 8 4 6 6 ( 2 ) 5 2 9 4 ( 3 ) 1 0 8 . 2 2 ( 3 ) 6 9 . 4 ( 5 ) 8 3 8 6 ( 2 ) 4 3 9 4 ( 1 8 ) 1 4 0 . 5 3 ( 3 ) 1 0 2 . 6 1 ( 2 ) 1 0 3 . 4 9 ( 3 ) 8 5 3 3 ( 3 ) 8 4 6 6 ( 3 ) 6 0 7 3 ( 3 ) 1 1 3 7 8 ( 3 ) 9 7 . 9 ( 7 ) 1 7 4 . 7 5 ( 5 ) 5 1 . 8 ( 1 0 ) 1 2 7 . 9 ( 1 1 ) 8 3 8 6 ( 3 ) 1 1 7 . 7 1 ( 3 ) 5 9 6 7 ( 2 ) 9 7 . 4 ( 7 ) 7 1 . 9 ( 8 ) 1 4 2 . 6 ( 1 0 ) 1 7 4 . 4 9 ( 5 ) 1 3 4 . 7 ( 7 ) 7 7 3 8 ( 2 ) 1 2 9 . 6 2 ( 2 ) 7 4 9 3 ( 3 ) 8 5 8 ( 8 ) 8 5 5 3 ( 2 ) 8 8 9 2 ( 2 ) 1 5 3 . 5 8 ( 3 ) 8 8 . 1 6 ( 2 ) 1 5 2 . 1 9 ( 3 ) 8 5 4 5 ( 2 ) 5 9 5 2 ( 3 ) 1 1 3 . 3 7 ( 3 ) 7 1 . 7 ( 5 ) 8 5 4 2 ( 2 ) 4 5 9 ( 3 ) 1 4 4 . 2 2 ( 3 ) 1 0 4 . 2 4 ( 2 ) 1 0 4 . 4 7 ( 3 ) 8 5 5 3 ( 3 ) 8 5 4 5 ( 3 ) 6 3 4 5 ( 3 ) 1 1 8 . 1 2 ( 3 ) 1 0 3 . 2 ( 8 ) 1 7 9 . 1 1 ( 5 ) 5 6 . 7 ( 1 1 ) 1 2 9 . 6 ( 1 0 ) 8 5 4 2 ( 3 ) 1 2 2 . 7 5 ( 3 ) 6 3 7 3 ( 3 ) 1 0 2 . 2 ( 7 ) 7 6 4 ( 8 ) 1 5 3 . 9 ( 1 0 ) 1 7 9 . 5 0 ( 5 ) 5 3 7 T a b l e 7 . 1 2 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C q u g m U T e ; a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . T e [ 2 ] - T e [ 3 ] - C u T e [ 2 ] - T e [ 3 ] - C u x 4 T e [ 2 ] - T e [ 3 ] - C u C u - T e [ 3 ] - C u x 4 C u - T e [ 3 ] - C u x 2 U - C u - T e [ 2 ] U - C u - T e [ 3 ] U - C u - T e [ 3 ] x 2 U - C u - C u x 2 T e [ 2 ] - C u - T e [ 3 ] T e [ 2 ] - C u - T e [ 3 ] x 2 T e [ 2 ] - C u - C u x 2 T e [ 3 ] - C u - T e [ 3 ] x 6 T e [ 3 ] - C u - C u x 4 T e [ 3 ] - C u - C u x 2 C u - C u - C u x 2 1 2 3 . 8 ( 9 ) 9 1 . 5 ( 1 0 ) 5 3 3 ( 9 ) 6 1 . 2 ( 1 0 ) 1 1 2 . 6 ( 1 2 ) 1 6 7 ( 2 ) 1 1 9 . 9 ( 1 6 ) 6 1 2 ( 9 ) 9 1 . 0 ( 1 4 ) 7 3 . 0 ( 1 3 ) 1 1 4 . 1 ( 1 1 ) 9 6 . 5 ( 1 5 ) 1 1 8 . 4 ( 1 2 ) 5 9 . 5 ( 1 3 ) 1 4 8 ( 2 ) 1 1 0 ( 2 ) 1 2 3 . 0 ( 9 ) 8 6 . 8 ( 1 0 ) 5 1 . 5 ( 9 ) 5 9 . 3 ( 9 ) 1 1 1 . 1 ( 1 2 ) 1 6 5 ( 2 ) 1 1 7 . 9 ( 1 5 ) 5 9 . 4 ( 1 0 ) 8 8 . 5 ( 1 3 ) 7 0 . 6 ( 1 5 ) 1 1 1 . 4 ( 1 3 ) 9 5 . 7 ( 1 7 ) 1 1 4 . 7 ( 1 1 ) 5 8 . 6 ( 1 2 ) 1 4 2 ( 2 ) 1 0 6 ( 2 ) 1 2 4 . 6 ( 1 0 ) 9 4 . 7 ( 1 0 ) 5 4 9 ( 9 ) 6 4 . 9 ( 1 0 ) 1 1 4 . 6 ( 1 1 ) 1 7 0 . 7 ( 1 9 ) 1 2 1 . 2 ( 1 6 ) 6 2 . 3 ( 1 0 ) 9 2 . 6 ( 1 5 ) 7 4 . 6 ( 1 5 ) 1 1 7 . 9 ( 1 2 ) 9 7 . 9 ( 1 5 ) 1 2 0 . 9 ( 1 2 ) 6 0 . 1 ( 1 4 ) 1 5 2 ( 2 ) 1 1 3 ( 3 ) 5 3 8 T a b l e 7 . 1 3 . C r y s t a l d a t a a n d s t r u c t u r e r e fi n e m e n t f o r C u o , 4 o ( 1 ) U T e 3 a t 1 0 0 K . E m p i r i c a l f o r m u l a F o r m u l a w e i g h t T e m p e r a t u r e W a v e l e n g t h C r y s t a l s y s t e m S p a c e g r o u p U n i t c e l l d i m e n s i o n s q - v e c t o r ( l ) V o l u m e Z D e n s i t y ( c a l c u l a t e d ) A b s o r p t i o n c o e f fi c i e n t F ( 0 0 0 ) C r y s t a l s i z e T h e t a r a n g e f o r d a t a c o l l e c t i o n I n d e x r a n g e s R e fl e c t i o n s c o l l e c t e d I n d e p e n d e n t r e fl e c t i o n s C o m p l e t e n e s s t o 0 = 2 1 . 5 2 ° R e fi n e m e n t m e t h o d D a t a / r e s t r a i n t s / p a r a m e t e r s G o o d n e s s - o f - fi t o n F 2 F i n a l R i n d i c e s [ I > 2 0 ( I ) ] R i n d i c e s ( a l l d a t a ) F i n a l R m a i n i n d i c e s [ I > 2 0 ' ( I ) ] R m a i n i n d i c e s ( a l l d a t a ) F i n a l R 1 S t o r d e r s a t e l l i t e s [ I > 2 0 ( I ) ] R 1 S t o r d e r s a t e l l i t e s ( a l l d a t a ) E x t i n c t i o n c o e f fi c i e n t T m . . . a n d T . . . ) . c o e f fi c i e n t s L a r g e s t d i f f . p e a k a n d h o l e C 1 1 0 . 4 0 ( 1 ) U T C 3 6 4 6 . 2 1 0 0 . 0 ( 3 ) K 0 . 7 0 9 2 6 A t r i c l i n i c P - 1 ( a B y ) 0 a = 6 . 0 8 5 6 ( 6 ) A , a = 9 0 ° b = 4 . 2 0 0 5 ( 4 ) A , 1 3 = 9 9 . 0 3 7 ° c = 1 0 . 3 3 2 6 ( 1 1 ) A , y = 9 0 ° 0 . 2 2 2 5 ( 8 ) a ‘ + 0 . 2 7 1 1 ( 5 ) b ’ + 0 . 5 1 3 ( 1 ) c ‘ 2 6 0 . 8 5 ( 5 ) A 3 2 8 . 2 2 5 2 g / c m 3 1 8 . 6 1 6 m m ’ 1 5 1 9 0 . 1 6 x 0 . 1 4 x 0 . 0 8 m m 3 1 . 8 9 t o 2 9 . 1 4 ° - 8 < = h < = 8 , - 6 < = k < = 6 , - 1 4 < = l < = 1 3 , - 1 < = m < = 1 7 4 4 4 ( 2 4 6 9 m a i n + 4 9 7 5 s a t e l l i t e s ) 3 8 5 6 ( 1 2 7 7 m a i n + 2 5 7 9 s a t e l l i t e S ) [ R i m = 0 . 0 3 9 8 ] 9 5 % F u l l - m a t r i x l e a s t - s q u a r e s o n F 2 3 8 5 6 / 0 / 1 4 0 1 . 2 2 R . . . = 0 . 0 4 7 9 , w R . . . = 0 . 0 9 5 3 R . 1 1 = 0 . 0 7 6 4 , w R . 1 1 = 0 . 1 0 2 6 R . . . = 0 . 0 3 3 1 , w R . . . = 0 . 0 7 9 6 R . “ = 0 . 0 3 4 1 , w R . 1 1 = 0 . 0 7 9 8 R . . . = 0 . 1 2 6 7 , w R . . . = 0 . 2 1 2 7 R 3 1 1 = 0 . 2 3 0 3 , W R 1 1 1 1 = 0 . 2 5 0 8 0 . 0 0 0 2 5 9 0 . 0 2 1 2 a n d 0 . 0 5 7 3 3 . 7 6 a n d 4 1 2 6 A 3 R = 2 | | F . | - | F . | | / 2 1 1 7 . 1 , w R = { 2 [ w ( | l = ? | 2 - 1 1 5 . 1 6 2 ] / z [ w ( | 1 = . | “ ) ] } “ 2 a n d w = l / ( O ' 2 ( I ) + 0 . 0 0 1 6 1 2 ) 5 3 9 T a b l e 7 . 1 4 . A t o m i c c o o r d i n a t e s ( x 1 0 4 ) , F o u r i e r c o m p o n e n t s o f t h e d i s p l a c i v e m o d u l a t i o n ( x 1 0 4 ) a n d e q u i v a l e n t i s o t r o p i c d i s p l a c e m e n t p a r a m e t e r s ( A 2 x 1 0 4 ) f o r C u o . 4 o ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e x y 2 O c c u p a n c y U . . . U 0 7 9 2 3 ( 1 ) 2 5 0 0 ( 1 ) 1 6 2 9 ( 1 ) 1 1 1 ( 1 ) s i n , 1 2 4 ( 1 ) 0 ( 1 ) 2 0 ( 1 ) c o s , 1 1 ( 1 ) - 1 3 ( 1 ) - 1 5 ( 1 ) T e [ l ] 0 2 6 6 0 ( 1 ) 2 5 0 1 ( 1 ) 5 9 3 ( 1 ) 1 1 1 ( 1 ) s i n , 1 1 7 ( 1 ) - 5 ( 2 ) 1 7 ( 1 ) c o s , 1 - 5 ( 1 ) - 4 9 ( 3 ) - 9 ( 1 ) T e [ 2 ] 0 4 0 1 3 ( 1 ) 2 4 9 4 ( 1 ) 6 6 3 2 ( 1 ) 1 1 4 ( 1 ) s i n , 1 - l 2 6 ( 2 ) - 4 5 ( 3 ) - 5 1 ( 1 ) c o s , 1 - 1 9 ( 2 ) 6 ( 3 ) 2 4 ( 1 ) T e [ 3 ] O 9 0 5 4 ( 1 ) 2 5 0 2 ( 1 ) 6 6 9 2 ( 1 ) . 1 1 4 ( 1 ) s i n , 1 7 6 ( 2 ) - 8 4 ( 3 ) 1 ( 1 ) c o s , 1 1 6 5 ( 2 ) 1 0 ( 3 ) - 4 1 ( 1 ) C u 0 9 6 3 ( 1 1 ) 2 4 7 3 ( 1 9 ) 4 6 6 3 ( 6 ) 0 . 3 9 9 ( 6 ) 6 ( 2 ) s i n , 1 - 3 2 ( 9 ) - 2 1 ( 1 7 ) 3 ( 6 ) c o s , 1 - 4 3 ( 1 7 ) - 4 5 ( 3 0 ) 0 ( 1 0 ) T a b l e 7 . 1 5 . F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r C u o , 4 o ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e U 1 1 U 2 2 U 3 3 U 1 2 U 1 3 U 2 3 U 0 1 3 ( 1 ) 7 ( 1 ) 1 4 ( 1 ) 0 ( 1 ) 3 ( 1 ) 0 ( 1 ) s i n , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) T e [ l ] 0 1 4 ( 1 ) 7 ( 1 ) 1 3 ( 1 ) 1 ( 1 ) 3 ( 1 ) 1 ( 1 ) s i n , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) T e [ 2 ] 0 1 8 ( 1 ) 8 ( 1 ) 1 6 ( 1 ) 0 ( 1 ) 6 ( 1 ) 0 ( 1 ) s i n , 1 - 1 ( 1 ) 1 ( 1 ) - 1 ( 1 ) 1 ( 1 ) - 1 ( 1 ) 0 ( 1 ) c o s , 1 - 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) T e [ 3 ] 0 1 9 ( 1 ) 9 ( 1 ) 1 5 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) s i n , 1 - 2 ( 1 ) 0 ( 1 ) - 1 ( 1 ) 1 ( 1 ) 1 ( 1 ) 0 ( 1 ) c o s , 1 0 ( 1 ) 0 ( 1 ) 1 ( 1 ) 0 ( 1 ) 0 ( 1 ) 0 ( 1 ) 5 4 0 T a b l e 7 . 1 5 . ( C o n t ’ d ) F o u r i e r c o m p o n e n t s o f t h e a t o m i c t h e r m a l p a r a m e t e r s m o d u l a t i o n ( x 1 0 3 ) f o r C u o _ 4 o ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . C u 0 9 ( 4 ) 4 ( 4 ) 5 ( 4 ) 3 ( 3 ) 1 ( 2 ) - 4 ( 3 ) s i n , 1 - 1 2 ( 3 ) — 3 ( 4 ) - 6 ( 3 ) 1 ( 2 ) - 2 ( 2 ) - 3 ( 2 ) c o s , 1 - 2 1 ( 6 ) - 6 ( 7 ) - l 4 ( 6 ) 5 ( 4 ) - 5 ( 4 ) - 9 ( 4 ) T a b l e 7 . 1 6 . F o u r i e r c o m p o n e n t s o f t h e o c c u p a t i o n a l m o d u l a t i o n f o r C u o _ 4 o ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m W a v e O c c u p a t i o n a l c o m p o n e n t C u s i n , 1 - 0 . 1 8 7 ( 1 1 ) c o s , 1 - 0 . 4 0 4 ( 1 1 ) T a b l e 7 . 1 7 . B o n d l e n g t h s d i s t r i b u t i o n s [ A ] f o r C u o _ 4 o ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e D i s t a n c e M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e U - T e [ l ] 3 . 2 1 3 9 ( 1 0 ) 3 . 1 9 4 7 ( 1 0 ) 3 . 2 3 3 0 ( 1 0 ) U - T e [ l ] 3 . 2 2 8 8 ( 1 2 ) 3 . 2 2 1 7 ( 1 2 ) 3 . 2 3 6 0 ( 1 2 ) U - T e [ l ] x 2 3 . 0 9 1 0 ( 1 2 ) 3 . 0 8 5 5 ( 1 2 ) 3 . 0 9 6 7 ( 1 2 ) U - T e [ 2 ] 3 . 1 1 2 9 ( 1 4 ) 3 . 0 9 3 5 ( 1 4 ) 3 . 1 3 0 6 ( 1 4 ) U — T e [ 2 ] 3 . 1 1 6 1 ( 1 4 ) 3 . 1 0 3 8 ( 1 4 ) 3 . 1 2 7 0 ( 1 4 ) U - T e [ 3 ] x 2 3 . 1 3 3 3 ( 1 3 ) 3 . 0 9 5 2 ( 1 3 ) 3 . 1 7 1 4 ( 1 3 ) U - C u 3 . 3 7 8 ( 1 0 ) 3 . 3 6 5 ( 1 1 ) 3 . 3 9 5 ( 1 1 ) T e [ 2 ] - T e [ 3 ] 3 . 0 2 9 5 ( 1 6 ) 2 . 8 4 3 5 ( 1 6 ) 3 . 2 1 3 5 ( 1 6 ) T e [ 2 ] - T e [ 3 ] 3 . 0 5 7 9 ( 1 6 ) 2 . 9 2 9 4 ( 1 6 ) 3 . 1 8 7 9 ( 1 6 ) T e [ 2 ] - C u 2 . 5 4 0 ( 1 0 ) 2 . 4 6 7 ( 9 ) 2 . 5 9 4 ( 1 0 ) T e [ 3 ] - C u 2 . 5 7 1 ( 1 1 ) 2 . 4 3 8 ( 1 3 ) 2 . 6 6 8 ( 1 3 ) T e [ 3 ] - C u x 2 2 . 5 2 6 ( 1 2 ) 2 . 4 6 1 ( 1 4 ) 2 . 5 7 5 ( 1 4 ) C u - C u x 2 2 . 5 4 8 ( 1 7 ) 2 . 4 7 3 ( 1 9 ) 2 . 6 0 8 ( 1 9 ) 5 4 1 T a b l e 7 . 1 8 . B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C u o . 4 o ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . A t o m A v e r a g e A n g l e M i n i m u m A n g l e M a x i m u m A n g l e T e [ 1 ] - U - T e [ 1 ] x 2 l 4 1 . 6 7 ( 3 ) l 4 1 . 3 1 ( 3 ) 1 4 2 . 0 4 ( 3 ) T e [ l ] - U - T e [ l ] x 8 7 6 1 3 ( 3 ) 7 5 3 8 ( 3 ) 7 6 9 0 ( 3 ) T e [ l ] - U - T e [ 2 ] x 2 7 5 1 7 ( 3 ) 7 3 3 3 ( 3 ) 7 7 0 4 ( 3 ) T e [ l ] - U - T e [ 3 ] x 2 l 3 0 . 7 3 ( 4 ) 1 2 9 . 0 5 ( 4 ) 1 3 2 . 3 7 ( 4 ) T e [ 1 ] - U - C u x 3 1 3 3 . 0 2 ( 1 6 ) 1 3 2 . 1 4 ( 1 6 ) 1 3 3 . 6 8 ( 1 6 ) T e [ l ] - U - T e [ 2 ] x 2 1 2 9 . 0 8 ( 4 ) 1 2 7 . 7 6 ( 4 ) 1 3 0 . 3 5 ( 4 ) T e [ l ] - U - T e [ 3 ] x 2 7 2 9 3 ( 3 ) 7 1 0 1 ( 3 ) 7 4 9 0 ( 3 ) T e [ l ] - U - C u 8 5 3 7 ( 1 6 ) 8 5 . 0 0 ( 1 6 ) 8 5 . 8 7 ( 1 6 ) T e [ l ] - U - T e [ l ] x 2 8 5 6 1 ( 3 ) 8 4 8 5 ( 3 ) 8 6 3 8 ( 3 ) T e [ l ] - U - T e [ 2 ] x 2 8 7 . 7 6 ( 3 ) 8 6 7 0 ( 3 ) 8 8 8 3 ( 3 ) T e [ l ] - U - T e [ 2 ] x 2 1 5 1 . 3 3 ( 3 ) 1 4 9 . 2 8 ( 3 ) 1 5 3 . 3 9 ( 3 ) T e [ l ] - U - T e [ 3 ] x 2 8 6 8 2 ( 3 ) 8 5 . 8 7 ( 3 ) 8 7 . 7 8 ( 3 ) T e [ l ] - U - T e [ 3 ] x 2 1 4 8 . 9 1 ( 4 ) 1 4 7 . 0 3 ( 4 ) 1 5 0 . 8 3 ( 4 ) T e [ 2 ] - U - T e [ 2 ] x 2 8 4 8 4 ( 4 ) 8 4 5 3 ( 4 ) 8 5 1 8 ( 4 ) T e [ 2 ] - U - T e [ 3 ] x 2 5 8 0 5 ( 3 ) 5 4 6 0 ( 3 ) 6 1 3 9 ( 3 ) T e [ 2 ] - U - T e [ 3 ] x 2 1 1 2 . 0 4 ( 3 ) 1 0 8 . 7 6 ( 3 ) 1 1 5 . 2 8 ( 3 ) T e [ 2 ] - U - C u x 2 7 0 . 8 4 ( 1 7 ) 6 7 9 4 ( 1 7 ) 7 3 . 0 2 ( 1 7 ) T e [ 3 ] - U - T e [ 3 ] x 2 8 4 2 7 ( 3 ) 8 3 5 5 ( 3 ) 8 4 9 7 ( 3 ) T e [ 3 ] - U - C u x 2 4 5 4 1 ( 1 8 ) 4 4 2 6 ( 1 8 ) 4 6 2 7 ( 1 8 ) U - T e [ 1 ] - U x 2 1 4 1 . 6 7 ( 4 ) 1 4 1 . 5 6 ( 4 ) 1 4 1 . 7 8 ( 4 ) U - T e [ l ] - U x 8 1 0 3 . 9 9 ( 3 ) 1 0 3 . 8 1 ( 3 ) 1 0 4 . l 9 ( 3 ) U - T e [ l ] - U x 2 8 5 6 2 ( 3 ) 8 5 3 5 ( 3 ) 8 5 8 8 ( 3 ) U - T e [ 2 ] - U x 2 8 4 8 1 ( 3 ) 8 4 4 1 ( 3 ) 8 5 2 7 ( 3 ) U - T e [ 2 ] - T e [ 3 ] x 2 6 1 3 0 ( 3 ) 5 9 8 9 ( 3 ) 6 2 8 0 ( 4 ) U - T e [ 2 ] - T e [ 3 ] x 2 1 1 7 . 2 7 ( 4 ) 1 1 4 . 5 6 ( 4 ) 1 1 9 . 9 7 ( 4 ) U - T e [ 2 ] - C u x 2 9 9 2 ( 2 ) 9 7 . 6 ( 2 ) 1 0 1 . 3 ( 2 ) T e [ 3 ] - T e [ 2 ] - T e [ 3 ] x 2 1 7 7 . 4 5 ( 5 ) l 7 4 . 6 7 ( 5 ) 1 7 9 . 8 2 ( 6 ) T e [ 3 ] - T e [ 2 ] - C u 5 3 . 7 ( 2 ) 5 3 . 2 ( 2 ) 5 4 3 ( 2 ) T e [ 3 ] - T e [ 2 ] - C u 1 2 8 . 4 ( 2 ) 1 2 6 . 2 ( 2 ) 1 3 1 . 0 ( 2 ) U - T e [ 3 ] - U x 2 8 4 2 1 ( 3 ) 8 3 3 9 ( 3 ) 8 5 0 4 ( 3 ) U - T e [ 3 ] - T e [ 2 ] x 2 1 2 0 . 6 8 ( 5 ) 1 1 7 . 6 4 ( 5 ) 1 2 3 . 6 7 ( 5 ) U - T e [ 3 ] - T e [ 2 ] x 2 6 0 6 5 ( 3 ) 5 8 6 2 ( 3 ) 6 2 7 9 ( 4 ) U - T e [ 3 ] - C u x 2 9 7 9 ( 2 ) 9 5 0 ( 2 ) 1 0 2 . 1 ( 2 ) 5 4 2 T a b l e 7 . 1 8 . ( C o n t ’ d ) B o n d a n g l e s d i s t r i b u t i o n s [ ° ] f o r C u o , 4 o ( 1 ) U T e 3 a t 1 0 0 K w i t h e . s . d . ’ s i n p a r e n t h e s e s . U - T e [ 3 ] - C u x 2 U - T e [ 3 ] - C u x 2 T e [ 2 ] - T e [ 3 ] - T e [ 2 ] x 2 T e [ 2 ] - T e [ 3 ] - C u T e [ 2 ] - T e [ 3 ] - C u x 2 T e [ 2 ] - T e [ 3 ] - C u T e [ 2 ] — T e [ 3 ] - C u x 2 C u - T e [ 3 ] - C u x 4 C u - T e [ 3 ] - C u x 2 U - C u - T e [ 2 ] U - C u - T e [ 3 ] U - C u - T e [ 3 ] x 2 U - C u - C u x 2 T e [ 2 ] - C u - T e [ 3 ] T e [ 2 ] - C u - T e [ 3 ] x 2 T e [ 2 ] - C u - C u x 2 T e [ 3 ] - C u - T e [ 3 ] x 4 T e [ 3 ] - C u - C u x 4 T e [ 3 ] - C u - T e [ 3 ] x 2 T e [ 3 ] - C u - C u x 2 C u - C u — C u x 2 7 2 3 ( 2 ) 1 4 4 . 5 ( 2 ) 1 7 7 . 4 2 ( 5 ) 1 2 4 . 7 8 ( 1 9 ) 9 4 . 2 ( 2 ) 5 2 8 3 ( 1 8 ) 8 4 . 3 ( 2 ) 6 0 . 0 ( 4 ) 1 1 2 . 1 ( 3 ) 1 6 6 . 3 ( 4 ) 1 2 0 . 1 ( 3 ) 6 2 3 ( 2 ) 9 2 6 ( 4 ) 7 3 5 ( 3 ) 1 1 2 . 7 ( 4 ) 9 5 5 ( 4 ) 1 2 0 . 0 ( 5 ) 5 9 . 1 ( 3 ) 1 1 2 . 6 ( 4 ) 1 5 0 . 9 ( 5 ) 1 1 0 . 3 ( 5 ) 7 0 8 5 ( 1 9 ) 1 4 0 . 5 ( 2 ) 1 7 5 . 0 0 ( 5 ) 1 2 2 . 8 8 ( 1 9 ) 9 3 3 ( 2 ) 5 0 9 8 ( 1 8 ) 8 2 . 7 ( 2 ) 5 9 . 4 ( 4 ) 1 1 0 6 ( 3 ) 1 6 5 . 1 ( 4 ) 1 1 7 . 9 ( 4 ) 6 1 . 4 ( 2 ) 9 1 6 ( 4 ) 7 0 . 7 ( 3 ) 1 1 1 . 6 ( 5 ) 9 4 . 7 ( 5 ) 1 1 7 . 9 ( 4 ) 5 8 . 3 ( 4 ) 1 1 2 . 1 ( 5 ) 1 4 9 . 6 ( 4 ) 1 0 9 . 3 ( 6 ) 7 4 . 3 ( 2 ) 1 4 8 . 9 ( 2 ) 1 7 9 . 7 8 ( 6 ) 1 2 6 . 3 5 ( 1 9 ) 9 4 . 7 ( 2 ) 5 5 3 8 ( 1 9 ) 8 6 4 ( 2 ) 6 0 . 7 ( 4 ) 1 1 4 . 7 ( 3 ) 1 6 7 . 4 ( 4 ) 1 2 3 . 0 ( 4 ) 6 2 9 ( 2 ) 9 3 9 ( 4 ) 7 5 4 ( 3 ) 1 1 4 2 ( 5 ) 9 6 1 ( 5 ) 1 2 2 . 0 ( 4 ) 6 0 . 3 ( 4 ) 1 1 3 2 ( 5 ) 1 5 2 . 2 ( 4 ) 1 1 1 . 9 ( 6 ) 5 4 3 R e f e r e n c e s 1 N a r d u c c i A . A . ; I b e r s , J . A . C h e m . M a t e r . 2 0 0 0 , 1 0 , 2 8 1 1 . 2 S u t o r i k , A . C . ; P a t s c h k e , R . ; S c h i n d l e r , J . ; K a n n e w u r f , C . R . ; K a n a t z i d i s , M . G . C h e m . E u r . J . 2 0 0 0 , 6 , 1 6 0 1 - 1 6 0 7 . 3 C h o i , K . - S . ; K a n a t z i d i s , M . G . C h e m . M a t e r . 1 9 9 9 , 1 1 ( 9 ) , 2 6 1 3 . 4 ( a ) C o d y , J . A . ; I b e r s , J . A . I n o r g . C h e m . l 9 9 5 , 3 4 , 3 1 6 5 . ( b ) S u t o r i k , A . C . ; A l b r i t t o n - T h o m a s , J . ; H o g a n , T . ; K a n n e w u r f , C . R . ; K a n a t z i d i s , M . G . C h e m . M a t e r . 1 9 9 6 , 8 , 7 5 1 . 5 C h o n d r o u d i s , K . ; K a n a t z i d i s , M . G . C . R . A c a d . S c i . P a r i s 1 9 9 6 , 3 2 2 , 8 8 7 . 6 P i c c o l i P . M . B . ; A b n e y K . D . ; S c h o o n o v e r J . R . ; D o r h o u t P . K . I n o r g . C h e m . 2 0 0 0 , 3 9 ( 1 4 ) , 2 9 7 0 . 7 C h o n d r o u d i s , K . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 1 9 9 7 , 1 1 9 , 2 5 7 4 . 8 C o d y , J . A . ; M a n s u e t t o , M . F . ; P e l l , M . A . ; C h i e n , S . ; I b e r s , J . A . J . A l l o y s C o m p d . 1 9 9 5 , 2 1 9 , 5 9 . 9 T o u g a i t , O . ; D a o u d i , A . ; P o t e l , M . ; N o " e l , H . M a t e r . R e s . B u l l . 1 9 9 7 , 3 2 , 1 2 3 9 . 1 0 P a p o i a n , G . ; H o f fi n a n n , R . , A n g e w . C h e m . I n t . E d . 2 0 0 0 , 3 9 , 2 4 0 8 . 1 1 P a t s c h k e , R . ; K a n a t z i d i s M . G . P h y s . C h e m . C h e m . P h y s . 2 0 0 2 , 4 , 3 2 6 6 . 1 2 C h o i , K . - S . ; P a t s c h k e , R . ; B i l l i n g e , S . J . L . ; W a n e r , M . J . ; D a n t u s , M . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 1 9 9 8 , 1 2 3 , 1 0 7 0 6 . 1 3 P a t s c h k e , R . ; B r e s h e a r s , J . D ; B r a z i s , P . ; K a n n e w u r f , C . R . B i l l i n g e , S . J . L . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 1 , 1 2 0 , 4 7 5 5 . 1 4 K r o e n e r t , W . ; P l i e t h , K . N a t u r w i s s e n s c h a fi e n 1 9 5 8 , 4 5 , 4 1 6 . 1 5 L i n , W . ; S t e i n f m k , H . ; W e i s s , E . J . I n o r g . C h e m . 1 9 6 5 , 4 , 8 7 7 . 1 6 X - A R E A , I P D S S o fi w a r e , S T O E & C i e G m b H , D a r m s t a d t , 2 0 0 6 . 1 7 P e t r i c e k , V . ; D u s e k , M . I n s t i t u t e o f P h y s i c s , P r a h a , C z e c h R e p u b l i c , 2 0 0 0 . 5 4 4 1 8 S h e l d r i c k , G . M . S H E L fl - 9 7 : P r o g r a m f o r C r y s t a l S t r u c t u r e R e fi n e m e n t ; U n i v e r s i t y o f G é t t i n g e n , G o t t i n g e n , G e r m a n y , 1 9 9 7 . 1 9 ( a ) M a l l i a k a s , C . ; B i l l i n g e , S . J . L . ; K i m , H . J . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 5 , 1 2 7 , 6 5 1 0 . ( b ) K i m , H . J . ; M a l l i a k a s , C . D . ; T o m i c , A . ; T e s s m e r , S . H . ; K a n a t z i d i s M . G . ; B i l l i n g e , S . J . L . P h y s . R e v . L e t t . 2 0 0 6 , 9 6 , 2 2 6 4 0 1 . ( c ) M a l l i a k a s , C . D . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 6 , 1 2 8 , 1 2 6 1 2 . 2 0 M a l l i a k a s , C . D . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 7 , 1 2 9 , 1 0 6 7 7 . 5 4 5 C h a p t e r 8 C o n c l u s i o n s a n d O u t l o o k 5 4 6 T h e n e w i n f o r m a t i o n r e p o r t e d i n t h i s D i s s e r t a t i o n r e g a r d i n g t h e C D W d i s t o r t i o n s i n p o l y t e l l u r i d e s o p e n s f r e s h p e r s p e c t i v e s o n h o w t o t h i n k a b o u t t h e s e s y s t e m s . A n o v e r v i e w o f t h e m o s t i m p o r t a n t r e s u l t s w i l l b e p r e s e n t e d i n t h i s C h a p t e r . S i z e e f f e c t ( s e c t i o n 8 . 1 ) a n d t e m p e r a t u r e ( s e c t i o n 8 . 2 ) , a n d d i m e n s i o n a l i t y ( s e c t i o n 8 . 3 ) o n C D W m o d u l a t i o n s w i l l b e d i s c u s s e d . F u r t h e r m o r e , a n o u t l o o k f o r C D W m a t e r i a l s d e s i g n ( s e c t i o n 8 . 5 ) a n d t h e r m o e l e c t r i c a p p l i c a t i o n ( 8 . 6 ) w i l l b e r e p o r t e d . 8 . ] . S i z e e f f e c t o n C h a r g e D e n s i t y W a v e m o d u l a t i o n s ( C h e m i c a l p r e s s u r e ) I n C h a p t e r 2 a s y s t e m a t i c s t u d y o n t h e e f f e c t o f t h e R E s i z e ( R E = R a r e e a r t h ) i n t h e C D W d i s t o r t i o n s i n R E T e 3 a t 3 0 0 K w a s p r e s e n t e d . l F r o m t h e b i g g e r i n s i z e L a t o t h e s m a l l e r D y a t o m t h e l e n g t h o f t h e i n c o m m e n s u r a t e c o m p o n e n t o f t h e q - v e c t o r i n c r e a s e s f r o m 0 . 2 7 5 1 ( 4 ) ( L a T e 3 ) t o 0 . 2 9 8 4 ( 3 ) ( D y T e 3 ) , T a b l e 8 . 1 . T h e l a n t h a n i d e c o n t r a c t i o n d e c r e a s e s t h e T e - T e d i s t a n c e s a n d t h i c k n e s s o f t h e R E T e 3 s l a b s w h i l e t h e s e p a r a t i o n o f t h e s l a b s t h a t i s d e fi n e d b y t h e v a n d e r W a a l s g a p r e m a i n s p r a c t i c a l l y c o n s t a n t a t a d i s t a n c e o f ~ 3 . 6 A . T h e a v e r a g e T e - T e d i s t a n c e i n t h e d i s t o r t e d T e n e t s d e c r e a s e s fi ' o m 3 . 0 9 5 ( 5 ) A i n L a T e 3 t o 3 . 0 2 5 ( 3 ) A i n D y T e 3 . T h i s s o - c a l l e d c h e m i c a l p r e s s u r e i n fl u e n c e s t h e C D W d i s t o r t i o n s . T h e C D W t r a n s i t i o n t e m p e r a t u r e ( T c n w ) d e c r e a s e s w i t h i n c r e a s i n g p r e s s u r e . F o r C e T e 3 t h e T C D w i s w e l l a b o v e 4 5 0 K a n d f o r T m T e 3 i s a t ~ 2 4 0 K . 2 T h e T c n w g o e s b e l l o w r o o m t e m p e r a t u r e f o r E T T C 3 , H o T e 3 a n d T m T e 3 t h a t e x h i b i t a n i d e a l s q u a r e n e t a t 3 0 0 K j u d g i n g fi o m t h e v a n i s h i n g o f t h e m o d u l a t i o n v e c t o r . T h e e f f e c t o f c h e m i c a l p r e s s u r e i s m o r e a p p a r e n t i n t h e R E T e 2 f a m i l y . T h e s y n t h e s i s o f t h e R E T e 2 - . . ( R E = L a , C e , P r , N d , S m , G d , T b , D y , Y b ) f a m i l y w a s fi r s t r e p o r t e d i n 1 9 6 0 u s i n g a d i r e c t c o m b i n a t i o n o f t h e p u r e e l e m e n t s a t h i g h 5 4 7 t e m p e r a t u r e . 3 ’ 4 ’ 5 ' 6 ’ 7 S e v e r a l a t t e m p t s 3 t o p r e p a r e H o T e 2 - , . a n d E r T e z - . . r e s u l t e d i n a m i x t u r e o f t h e m o n o - a n d t r i t e l l u r i d e s m a k i n g t h e a u t h o r s t o p r e d i c t t h a t R E T e 2 - . . p h a s e s w i t h T e - T e d i s t a n c e s o f l e s s t h a n 3 . 0 1 5 A d o n o t f o r m . A f e w y e a r s l a t t e r a h i g h p r e s s u r e ( ~ 5 0 K b a r s ) h i g h t e m p e r a t u r e ( ~ 1 3 0 0 ° C ) s y n t h e s i s f o r Y T e 2 - , . , H o T e 2 - , . , E r T e 2 - , . , T m T e 2 - , . , L u T e z - . . , a n d L u T e 3 w a s r e p o r t e d . 8 T h e a v e r a g e e l e c t r o n c o u n t o f t h e p l a n a r T e n e t s i n t h e R E T e 2 - . . f a m i l y i s - ( 1 - x ) a n d i t i s m u c h l o w e r t h a n t h e a v e r a g e o x i d a t i o n s t a t e o f - 0 . 5 f o u n d i n t h e R E T e 3 f a m i l y . S i n c e t h e T e a t o m s a r e m o r e r e d u c e d i n t h e R E T e 2 . . . m e m b e r s t h e y h a v e a t e n d e n c y t o b e f u r t h e r a p a r t a n d s e p a r a t e d w i t h l o n g e r d i s t a n c e s f r o m t h e o n e s p r e s e n t i n t h e R E T e ; f a m i l y . T h e e x t r e m e c a s e w o u l d b e a p l a n a r n e t o f i s o l a t e d T e z ' a t o m s w i t h d i s t a n c e s o f m o r e t h a n 4 A . A l t h o u g h t h e C D W d i s t o r t i o n i n m o s t o f t h e R E T e 2 . . . m e m b e r s i s u n k n o w n u p t o d a t e ( L a T e 2 9 a n d S m T e 2 . . . 1 0 a r e t h e o n l y t w o c o m p o u n d s w i t h r e s o l v e d d i s t o r t i o n s ) , a n d l i t t l e i s k n o w n a b o u t t h e r o l e o f v a c a n c i e s , s o m e g e n e r a l c o m m e n t s c a n b e m a d e . I t s e e m s t h a t v a c a n c i e s a c t a s a p r e s s u r e r e l i e f m e d i u m t o t h e c h e m i c a l p r e s s u r e e f f e c t a s t h e l a n t h a n i d e a t o m g e t s s m a l l . I n t e r e s t i n g l y , o n l y t h e l a r g e r L a 3 + a t o m l l ( m i n i m u m c h e m i c a l p r e s s u r e ) c a n f o r m a s t o i c h i o m e t r i c c o m p o u n d w i t h n o v a c a n c i e s ( L a T e z ) a l t h o u g h a n o f f - s t o i c h i o m e t r i c p h a s e ( L a T e 2 - x ) h a s b e e n r e p o r t e d . 1 2 I n c o n t r a s t t o R E T e 2 - . . a n d R E T e 3 p h a s e s , t h e R E z T e s f a m i l y i s s t r u c t u r a l l y a l m o s t u n e x p l o r e d . T h e R E z T e s i s a n i n t e r g r o w t h c o m p o u n d c o m p o s e d o f l a y e r s f o u n d i n R E T e 2 a n d R E T e 3 s u b s t r u c t u r e s . T h i s r e s u l t i n t h e c o e x i s t e n c e o f t w o i n d i v i d u a l T e n e t s w i t h d i f f e r e n t a v e r a g e o x i d a t i o n s t a t e s o f 0 . 5 - a n d 1 - a n d t w o m o d u l a t i o n v e c t o r s ( C h a p t e r 5 ) . M o s t o f t h e c h a r a c t e r i z a t i o n w o r k h a s b e e n d o n e f o r s z T e 5 . , . 1 3 a n d t h e s y n t h e s i s o f m o s t o f t h e R E z T e s c o m p o u n d s h a s b e e n r e p o r t e d . T h e a n a l o g u e s w i t h t h e l a r g e r l a n t h a n i d e 5 4 8 a t o m , L a z T e s , 1 2 8 a n d C 6 2 T 6 5 , 1 4 a r e r e p o r t e d t o b e h i g h t e m p e r a t u r e p h a s e s . I n t h e R E z T e s f a m i l y h y p o s t o i c h i o m e t r y i s a l s o p r e s e n t i n t h e T e " n e t t h a t a g a i n i t m a y b e d u e t o t h e h i g h e r a p p l i e d p r e s s u r e . A d e t a i l e d s t r u c t u r a l s t u d y o f R E T e 2 - . . a n d R E z T e 5 - , . w i t h t e m p e r a t u r e a n d R E i s n e c e s s a r y i n o r d e r t o e l u c i d a t e a n d c o m p a r e t h e i r C D W d i s t o r t i o n s a n d u n d e r s t a n d t h e e x a c t r o l e o f v a c a n c i e s . 8 . 2 . T e m p e r a t u r e e f f e c t o n C h a r g e D e n s i t y W a v e m o d u l a t i o n s I n C h a p t e r 3 t h e r o l e o f t e m p e r a t u r e o n t h e C D W m o d u l a t i o n s i n R E T e 3 w a s p r e s e n t e d . 1 5 T h e t e m p e r a t u r e d e p e n d e d ( 1 0 0 — 5 0 0 K ) s i n g l e c r y s t a l X - r a y d i f f r a c t i o n e x p e r i m e n t g a v e u n i q u e i n f o r m a t i o n f o r t h e b e h a v i o r o f t h e C D W p e r i o d i c i t y , T a b l e 8 . 2 . T h e C D W m o d u l a t i o n d e p e n d e n c e a s a f u n c t i o n o f d e c r e a s i n g R E r a d i u s a n d d e c r e a s i n g t e m p e r a t u r e f o l l o w s o p p o s i t e t r e n d s , e v e n t h o u g h b o t h f a c t o r s c a u s e a u n i t c e l l c o n t r a c t i o n . I t s e e m s t h a t t h e b a n d d i s p e r s i o n i s e f f e c t e d d i f f e r e n t l y w i t h t e m p e r a t u r e a n d R E s i z e a n d t h a t i n fl u e n c e s t h e o v e r a l l t o p o l o g y o f t h e F e r m i s u r f a c e . T h u s , t h e n e s t i n g p r o p e r t i e s c h a n g e . I n t e r e s t i n g l y , t h e b a n d s t r u c t u r e c a l c u l a t i o n s ( D F T ) c a p t u r e t h e t r e n d o f t e m p e r a t u r e a n d R E s i z e . T h e o r e t i c a l c a l c u l a t i o n s w e r e p e r f o r m e d b y Z s o l t R a k a n d P r o f . S u b h e n d r a D . M a h a n t i a t t h e P h y s i c s D e p a r t m e n t a t M i c h i g a n S t a t e U n i v e r s i t y . T h e s u b c e l l s ( i . e . u n d i s t o r t e d s t r u c t u r e s ) o f L a T e 3 , Y T e 3 a n d L u T e 3 w e r e u s e d i n t h e c a l c u l a t i o n a n d t h e t e m p e r a t u r e p a r a m e t e r w a s m o d e l e d b y s i m p l e c h a n g i n g t h e v o l u m e o f e a c h c e l l . Q u a l i t a t i v e l y , t h e r e s u l t s a r e i n a g r e e m e n t w i t h t h e e x p e r i m e n t a l o b s e r v a t i o n s t h a t s h o w e d q u a n t i t a t i v e l y a m u c h l a r g e c h a n g e o f t h e n e s t i n g v e c t o r ( q - 5 4 9 v e c t o r ) . D e t a i l e d a n a l y s i s o f t h e t h e o r e t i c a l r e s u l t s i s i n p r o g r e s s i n o r d e r t o u n d e r s t a n d t h e p h y s i c s b e h i n d t h i s a n o m a l o u s b e h a v i o r . 8 . 3 . D i m e n s i o n a l i t y e f f e c t 0 1 1 C h a r g e D e n s i t y W a v e d i s t o r t i o n s I n C h a p t e r 4 t h e s t u d y o f a n i n t e r g r o w t h A M R E T e 4 ( A = N a , K ; M = C u , A g ; R E = L a , C e ) p h a s e w a s r e p o r t e d . 1 6 T h e s t r u c t u r e c a n b e s e e n a s a c o m b i n a t i o n o f n e u t r a l R i fl e . a n d A M T e l a y e r s i n a 1 : 1 r a t i o . T h e a v e r a g e o x i d a t i o n s t a t e o n t h e p l a n a r d i s t o r t e d T e n e t ( R E T e 3 s u b s t r u c t u r e ) r e m a i n s 0 5 - s i n c e t h e r e i s n o a p p a r e n t e l e c t r o n t r a n s f e r b e t w e e n t h e l a y e r s . S u r p r i s i n g l y , d e s p i t e t h e f a c t t h a t t h e d i s t o r t e d T e n e t s i n A M R E T e 4 a n d M R 3 a r e i s o e l e c t r o n i c t h e l e n g t h o f t h e m o d u l a t i o n q - v e c t o r c h a n g e s s i g n i fi c a n t l y f r o m ~ 2 / 7 i n R E T e 3 t o ~ 1 / 3 , T a b l e 8 . 3 . T h e r e p o r t o f t h e e f f e c t o f t h e c r o s s - p l a n e i n t e r a c t i o n s o n t h e C D W m o d u l a t i o n s g a v e n e w i n f o r m a t i o n a n d a d i f f e r e n t p e r s p e c t i v e o n h o w w e s h o u l d t h i n k a b o u t C D W d i s t o r t i o n s . I n C h a p t e r 6 , t h e C D W m o d u l a t i o n s f o u n d i n C u x E u T e z a n d A M z E u T e 4 f a m i l y ( C h a p t e r 6 ) g i v e a d d i t i o n a l i n f o r m a t i o n t o t h e d i m e n s i o n a l i t y i s s u e . T h e d i f f e r e n t s i z e o f t h e a l k a l i m e t a l c a t i o n t h a t i s l o c a t e d i n b e t w e e n t h e d i s t o r t e d T e n e t s i n t h e q u a s i - t w o - d i m e n s i o n a l A M z E u T e 4 g a v e a s e r i e s o f i s o e l e c t r o n i c c o m p o u n d w i t h d i f f e r e n t l a y e r - l a y e r s e p a r a t i o n . A d e c r e a s e i n t h e l e n g t h o f t h e q - v e c t o r w a s o b s e r v e d w i t h t h e i n c r e a s e o f t h e a l k a l i m e t a l s i z e , T a b l e 8 . 4 . W h e n t h e a l k a l i m e t a l w a s s u b s t i t u t e d w i t h E u 2 + a t o m s t o g i v e t h e i s o s t r u c t u r a l C u x E u T e z c o m p o u n d w h i c h h o w e v e r n o w l a c k a v a n d e r W a a l s g a p t h e p r e s e n c e o f t w o m o d u l a t i o n s a l o n g t h e s a m e d i r e c t i o n w a s o b s e r v e d . T h i s i s a u n i q u e b e h a v i o r t h a t h a s n o t b e e n s e e n b e f o r e i n a n y o f t h e r e p o r t e d C D W d i s t o r t e d l a y e r e d p o l y t e l l u r i d e s y s t e m s . A p l a u s i b l e e x p l a n a t i o n s u g g e s t s t h a t t h e r e i s a c o m p e t i t i o n 5 5 0 b e t w e e n t h e m o d u l a t i o n s c o m i n g fi ' o m c r o s s - p l a n e i n t e r a c t i o n s a n d t h e d i s t o r t i o n s t h a t r i s e f r o m i n - p l a n e i n t e r a c t i o n s ( c h e m i c a l p r e s s u r e ) . T h e d i s t o r t i o n s t r e s s t h a t i s g e n e r a t e d f r o m t h e t w o c o m p e t i n g e f f e c t s i s r e l i e v e d o n t h e v a n d e r W a a l s g a p t h a t g i v e s o n e o v e r a l l a v e r a g e m o d u l a t i o n v e c t o r i n A M z E u T e 4 . I n t h e e x t e n d e d t h r e e - d i m e n s i o n a l C u x E u T e z s t r u c t u r e t h e r e i s n o v a n d e r W a a l s g a p a n d t h e t w o d i f f e r e n t e f f e c t s s e e m t o b e e x p r e s s e d w i t h t w o d i f f e r e n t m o d u l a t i o n v e c t o r s . T h e e x i s t e n c e o f t w o C D W m o d u l a t i o n s a l o n g t h e s a m e d i r e c t i o n c a n n o t b e e x p l a i n e d w i t h t h e i n f o r m a t i o n w e h a v e s o f a r f r o m t h e b e h a v i o r o f t h e C D W d i s t o r t i o n s f o u n d i n R E T e 2 - , . , R E T C 3 , R E z T e 5 - , . , a n d M R . . . T h e i n t e r p r e t a t i o n w e g a v e a b o v e g i v e s a r e a s o n a b l e a n s w e r b u t i t m a y n o t b e t h e o n l y o n e . A s y s t e m a t i c s t u d y o f t h e A R E 3 T e g l 7 f a m i l y a s a f u n c t i o n o f A a n d R E s i z e , a n d t e m p e r a t u r e m a y g i v e m o r e i n f O r m a t i o n . 8 . 4 . I n d e x i n g a n d p r o p e r c h a r a c t e r i z a t i o n o f m o d u l a t e d s t r u c t u r e s D u r i n g o u r s t u d y o f t h e R E T e 3 s e r i e s s e v e r a l p u b l i c a t i o n s f r o m d i f f e r e n t g r o u p s m a i n l y o n p h y s i c a l c h a r a c t e r i z a t i o n ( t r a n s p o r t p r o p e r t i e s , A R P E S , S T M ) w e r e r e p o r t e d . A q u e s t i o n / i s s u e t h a t w a s a d d r e s s e d w a s a b o u t t h e i n d e x i n g o f t h e s e i n c o m m e n s u r a t e m o d u l a t e d s t r u c t u r e s . S T M d a t a s u g g e s t e d 1 8 t h a t t h e f u n d a m e n t a l q - v e c t o r i s ~ 5 / 7 ( l - q ) a n d n o t ~ 2 / 7 ( q ) . I n t h i s s e c t i o n w e a d d r e s s t h e p r o b l e m s a n d a r t i f a c t s t h a t m a y c o m e f r o m i n d e x i n g m o d u l a t e d s t r u c t u r e s u s i n g i n t e n s i t y i n f o r m a t i o n f r o m r e fl e c t i o n s o b t a i n e d fi o m e l e c t r o n d i f f r a c t i o n a n d S T M e x p e r i m e n t s . E l e c t r o n d i f fi ' a c t i o n h a s p r o v e n t o b e a p o w e r f u l t o o l f o r d e t e c t i n g w e a k l o n g r a n g e s u p e r c e l l m o d u l a t i o n s . T h e h i g h e n e r g y o f e l e c t r o n s t y p i c a l l y u s e d i n a T E M ( Z 5 5 1 2 0 0 K e V ) p r o d u c e s e l e c t r o n d i f fi a c t i o n i m a g e s t h a t a r e v e r y s e n s i t i v e t o s m a l l d i s t o r t i o n s i n r e s p e c t w i t h a n X - r a y d i f f r a c t i o n p a t t e r n o b t a i n e d f r o m a n i n h o u s e X - r a y s i n g l e c r y s t a l d i f f r a c t o m e t e r . T h e i n t e g r a t e d i n t e n s i t y c a l c u l a t e d f r o m a n e l e c t r o n d i f f r a c t i o n p a t t e r n t h o u g h h a s t o b e c o r r e c t e d f o r p o s s i b l e d y n a m i c s c a t t e r i n g e f f e c t s t h a t m a y c o m e f r o m c o r r e l a t i o n b e t w e e n c r y s t a l l o g r a p h i c p l a n e s p e r p e n d i c u l a r t o t h e b e a m . A g o o d e x a m p l e w o u l d b e t h e s e l e c t e d a r e a e l e c t r o n d i f f r a c t i o n p a t t e r n t h a t w a s c o l l e c t e d o n C e T e ; a t r o o m t e m p e r a t u r e ( F i g u r e 2 . 3 ) , F i g u r e 8 . 1 . A s s u m i n g t h a t t h i s w a s t h e o n l y i n f o r m a t i o n w e h a d f r o m t h i s s y s t e m r e g a r d i n g t h e f u n d a m e n t a l q - v e c t o r w e c o u l d c o n c l u d e t h a t t h e q - v e c t o r i s a c t u a l l y ~ 5 / 7 s i n c e t h e p e a k s a t t h i s p o s i t i o n a r e m o r e i n t e n s e t h a n t h e o n e s f o u n d a t ~ 2 / 7 . F u r t h e r m o r e t h e r e i s a s e t o f s a t e l l i t e r e fl e c t i o n s a r o u n d e v e r y m a i n r e fl e c t i o n . S T M o n t h e o t h e r h a n d i s o n e o f t h e f u n d a m e n t a l t e c h n i q u e s u s e d f o r t h e d i r e c t o b s e r v a t i o n o f C D W d i s t o r t i o n s i n l a y e r e d c o m p o u n d s . T h r o u g h a t u n n e l i n g m e c h a n i s m , e l e c t r o n s a r e e j e c t e d o r a d d e d o n t h e s u r f a c e o f t h e m a t e r i a l t h r o u g h a c o n d u c t i n g fi n e t i p ( 1 1 m s i z e ) . I t i s i m p o r t a n t t o u n d e r s t a n d t h a t t h e S T M t i p d o e s n o t “ s e e ” t h e a t o m s d i r e c t l y b u t i n s t e a d i t i n t e r a c t s w i t h t h e d e n s i t y o f s t a t e s a r o u n d t h e a t o m s . I n t h a t s e n s e , d e p e n d i n g o n t h e b i a s o f t h e t i p ( p o s i t i v e b i a s r e m o v e s e l e c t r o n s a n d n e g a t i v e b i a s a d d s e l e c t r o n s o n t h e s u r f a c e ) a t o m s i n t h e S T M i m a g e s m a y a p p e a r b r i g h t e r o r d a r k e r . T h e r e f o r e , t h e i n t e n s i t y o f t h e p e r i o d i c i t y p e a k s i n t h e F o u r i e r t r a n s f o r m o f t h e “ r e a l s p a c e ” i m a g e o b t a i n e d f r o m S T M w i l l d e p e n d o n t h e b i a s a s w e l l . 1 9 T h e r e f o r e , t h e a s s i g n m e n t o f a f u n d a m e n t a l v e c t o r f r o m F F T S T M d a t a w i l l n e v e r b e u n e q u i v o c a l s i n c e f o r a l m o s t e v e r y t i p b i a s t h e r e i s a c o r r e s p o n d i n g F F T p a t t e r n w i t h d i f f e r e n t r e l a t i v e i n t e n s i t i e s . 5 5 2 T h e d a t a w e r e p o r t e d a n d u s e d f o r t h e r e fi n e m e n t s d e s c r i b e d i n t h i s D i s s e r t a t i o n c o m e f r o m s i n g e c r y s t a l X - r a y d i f f r a c t i o n e x p e r i m e n t s . I n t h i s c a s e , w e c a n e a s i l y r e c o n s t r u c t t h e r e c i p r o c a l s p a c e a n d s t u d y t h e p o s i t i o n a n d i n t e n s i t y o f e a c h r e fl e c t i o n . T h e d a t a w e h a v e c o l l e c t e d o n a l l R E T e 3 m e m b e r s s u g g e s t a q - v e c t o r o f ~ 2 / 7 a l o n g 0 * . P r o c e s s i o n p h o t o g r a p h s f r o m t h e d a t a c o l l e c t e d o n C e T e 3 a t 1 0 0 K a l o n g t h e l o n g b - a x i s ( k = 0 , 1 , 2 ) v e r i f y t h e p r e s e n c e o f s a t e l l i t e r e fl e c t i o n s a t q ~ 2 / 7 a r o u n d t h e m a i n r e fl e c t i o n s , F i g u r e 8 . 2 . F u r t h e r m o r e , a l l t h e o b s e r v e d r e fl e c t i o n s o b e y t h e e x t i n c t i o n c o n d i t i o n o f a C - c e n t e r e d s y s t e m ( h + k = 2 n ) . C r y s t a l l o g r a p h i c a l l y t h e r e i s n o d i f f e r e n c e i n i n d e x i n g e i t h e r w i t h a q - v e c t o r c o m p o n e n t o f 2 / 7 o r 5 / 7 ( l - q ) e s p e c i a l l y w h e n t h e l a t t i c e c e n t e r i n g i s C t y p e . I n m o r e d e t a i l , a l l t h e o b s e r v e d r e fl e c t i o n s c a n b e e n i n d e x e d i n t h r e e - d i m e n s i o n a l s p a c e a s h , k , l + m * q . w h e r e m i s t h e i n d e x a l o n g t h e f o u r t h d i m e n s i o n a n d q c t h e c o m p o n e n t o f t h e q v e c t o r ( 0 . 2 8 a l o n g 0 * ) . E a c h r e fl e c t i o n c a n b e i n d e x e d w i t h t h e n e w v e c t o r q . ’ = l - q c a s h ’ , k ’ , l ’ + m ’ * ( 1 - q . ) . S i n c e a g i v e n r e fl e c t i o n r e p r e s e n t s a u n i q u e p o i n t i n t h e r e c i p r o c a l l a t t i c e w e h a v e h ’ = h , k ’ = k , l ’ + m ’ = l a n d m ’ = - m w h i c h m e a n s t h a t t h e C - c e n t e r i n g c o n d i t i o n w i l l n o t b e e f f e c t e d f r o m t h e t r a n s f o r m a t i o n . T h i s i s n o t t r u e f o r a n y o t h e r t y p e o f c e n t e r i n g ( A o r B ) . A p r o p e r c h a r a c t e r i z a t i o n p r o t o c o l f o r t h i s t y p e o f i n c o m m e n s u r a t e m o d u l a t e d s t r u c t u r e s s h o u l d i n v o l v e s i n g l e c r y s t a l d i f f r a c t i o n s t u d i e s ( i n h o u s e X - r a y s / s y n c h r o t r o n o r n e u t r o n s ) a c c o m p a n i e d w i t h t h e r m o d y n a m i c m e a s u r e m e n t s ( m a i n l y h e a t c a p a c i t y ) f r o m a w i d e t e m p e r a t u r e r a n g e f o r t h e i n v e s t i g a t i o n o f ( a d d i t i o n a l ) w e a k s t r u c t u r a l t r a n s i t i o n s . T r a n s p o r t p r o p e r t i e s o n s i n g l e c r y s t a l s a n d n o t p e l l e t s m a d e f r o m p o l y c r y s t a l l i n e p o w d e r s w o u l d a l s o b e u s e f u l f o r t h i s r e a s o n . A d d i t i o n a l l y , t o t a l 5 5 3 ) s t i n U y r a r t i b r A ( y t i s n e t n I 1 . N 2 ' s c a t t e r i n g t e c h n i q u e s , l i k e P D F , c o u l d g i v e m o r e i n f o r m a t i o n h i d d e n u n d e r n e a t h t h e B r a g g p e a k s ( d i f f u s e s c a t t e r i n g ) r e g a r d i n g t h e s h o r t r a n g e o r d e r i n g o f t h e C D W . 2 0 ( A ) . . . . . . . . . . . , . . 7 1 1 _ 0 . 2 8 5 c " I l 1 0 . 2 8 5 0 3 " _ 5 1 I 5 1 1 R e c i p r o c a l s p a c e F i g u r e 8 . 1 . ( A ) S e l e c t e d a r e a e l e c t r o n d i f f r a c t i o n ( S A E D ) p a t t e r n f o r C e T e 3 a t t h e [ 0 1 0 ] . o r i e n t a t i o n s h o w i n g t h e 7 - f o l d s u p e r l a t t i c e . ( B ) I n t e n s i t y s c a n a l o n g t h e c * a x i s o f t h e S A E D p a t t e r n ( s h o w n i n r e c t a n g u l a r b o x ) a n d a p p r o x i m a t e i n d e x i n g b a s e d o n s u p e r c e l l . T h e q - v e c t o r i s a l s o i n d i c a t e d . 5 5 4 ( A ) “ f ( B ) . 3 * F i g u r e 8 . 2 . P r o c e s s i o n p h o t o g r a p h o f C e T e 3 a t 1 0 0 K o f ( A ) T h e h O l l a y e r . ( B ) T h e h l l l a y e r . ( C ) T h e h 2 1 l a y e r . R o w s o f r e fl e c t i o n s w i t h h = 2 n a r e a b s e n t s i n c e t h e s t r u c t u r e i s C - c e n t e r e d . 5 5 5 ( C ) 3 * F i g u r e 8 . 2 . ( C o n t ’ d ) P r e c e s s i o n p h o t o g r a p h o f C e T e 3 a t 1 0 0 K o f ( A ) T h e h 0 1 l a y e r . ( B ) T h e h l l l a y e r . ( C ) T h e h 2 1 l a y e r . R o w s o f r e fl e c t i o n s w i t h h = 2 n a r e a b s e n t s i n c e t h e s t r u c t u r e i s C - c e n t e r e d . 8 . 5 . D e s i g n o n n e w C h a r g e D e n s i t y W a v e m a t e r i a l s T h e n u m b e r o f C D W c o m p o u n d s i s l i m i t e d w i t h r e s p e c t t o t h e k n o w n s u p e r c o n d u c t i n g p h a s e s . P o l y c h a l c o g e n i d e a n d h a l i d e fl u x e s a r e u s e f u l s y n t h e t i c t o o l s f o r t h e d i s c o v e r y a n d c r y s t a l g r o w t h o f n e w C D W p h a s e s . T h e e x i s t e n c e a n d s t r u c t u r e o f i n t e r g r o w t h c o m p o u n d s l i k e R E z T e s , A M R E T e 4 , a n d K z A g 4 R E 2 T e 1 o c o u l d b e u s e d a s a m o d e l f o r t h e d e s i g n o f n e w p o l y t e l l u r i d e C D W p h a s e s . I t m a y b e p o s s i b l e t o c o m b i n e l a y e r s o f d i f f e r e n t c o m p o u n d s t h a t h a v e s i m i l a r i n p l a n e c e l l p a r a m e t e r s ( i . e . N a C u T e a n d K 2 A g 4 T e 4 ) w i t h t h e [ R E T e 3 ] o r [ R E z T e s ] l a y e r a n d c r e a t e h o m o l o g o u s s e r i e s o f c o m p o u n d s . F o r e x a m p l e , p h a s e s l i k e A M R E z T e . t h a t c o m b i n e a [ A M T e ] a n d [ R E z T e s ] l a y e r c o u l d e x i s t . 5 5 6 ) ) 1 3 1 ( ( 9 2 5 4 0 8 . 0 3 . 3 . ) ) 6 ) ) ) 5 1 2 2 4 ( ( ( ( ( 4 4 5 6 7 3 6 5 4 8 ) A ( 9 5 9 9 9 . 9 . . . 2 . 2 2 2 2 e e ) ) 2 ) ) c 5 2 3 3 1 ) n ( ( ( ( ( a 5 5 0 0 3 t 9 9 5 3 8 g a r e v s 0 0 0 0 i . . . . A D 3 3 3 3 r o t c e v - q * c ’ ‘ ' ’ ’ ‘ ' c c c c c c c ) ) ) ) ) ) ) ) 4 3 4 3 4 3 5 3 ( ( ( ( ( ( ( ( 1 1 8 7 4 6 7 4 5 0 1 2 7 1 5 8 7 9 8 8 9 9 8 8 2 2 2 2 2 2 2 2 . 0 . . . . . . . 0 0 0 0 0 0 0 2 0 . 3 A A ) ) 5 6 ( ( 4 0 5 3 1 9 3 2 4 4 = = c c , , A A ) ) 2 5 ( ( 8 3 2 5 5 3 5 . 5 2 2 = = b b , , A A ) ) 4 6 ( ( 3 4 8 9 0 3 . 9 2 . 4 4 3 6 T 3 C y T D Y 5 5 7 T a b l e 8 . 1 . S u m m a r y o f s u p e r c e l l p a r a m e t e r s o f R E T e 3 ( R E = L a , C e , P r , N d , S m , G d , T b , D y , Y ) a t 3 0 0 K . C o m p o u n d C e l l p a r a m e t e r s ( A ) M i n i m u m D i s t a n c e M a x i m u m D i s t a n c e ( A ) L a T e 3 C e T e ; P r T e 3 N d T e 3 S m T e 3 G d T e 3 T b T e 3 a = 4 . 3 9 4 4 ( 8 ) A , b = 2 6 . 2 2 7 ( 4 ) A , c = 4 . 4 0 7 6 ( 7 ) A l 1 : 8 4 . 3 7 3 2 ( 5 ) A , b = 2 5 . 9 7 3 ( 4 ) A , c = 4 . 3 8 4 9 ( 5 ) A a : 4 3 5 6 9 ( 9 ) A , b = 2 5 8 9 6 ( 5 ) A , c = 4 3 6 6 6 ( 9 ) A . 6 : 4 3 4 3 3 ( 6 ) A , b = 2 5 8 0 9 ( 4 ) A , c = 4 . 3 5 3 8 ( 5 ) A 6 : 4 . 3 2 1 8 ( 6 ) A , b = 2 5 . 6 0 9 ( 5 ) A , c = 4 . 3 3 4 2 ( 8 ) A a 4 2 9 9 5 ( 8 ) A , b = 2 5 4 2 0 ( 6 ) A , c = 4 3 0 7 8 ( 9 ) A “ ‘ " fl m ‘ - " n w m N " , = 4 2 9 4 7 ( 7 ) A , b = 2 5 4 0 4 ( 4 ) A , c = 4 2 9 6 8 ( 9 ) A 0 . 2 9 6 9 ( 5 ) c ‘ 3 . 0 6 8 ( 3 ) 3 . 0 3 9 ( 4 ) 1 3 . 0 2 5 ( 3 ) 3 . 0 5 9 8 ( 1 8 ) 2 . 9 4 3 ( 2 ) 2 . 9 4 2 0 ( 1 6 ) 2 . 9 9 1 ( 2 ) 2 . 9 7 3 3 ( 1 1 ) 3 . 2 6 1 ( 5 ) 3 . 2 3 5 0 ( 1 7 ) 3 . 1 9 7 ( 2 ) 3 . 1 7 8 6 ( 1 7 ) 3 . 1 4 4 ( 3 ) 3 . 1 1 3 ( 3 ) 3 . 0 9 0 ( 4 ) m e ) ) 8 6 9 ) 9 5 7 7 ) ) ) ) ) ) ) ) ) u c 7 3 1 1 1 3 1 1 1 2 1 m ) n ( ( ( ( ( ( ( ( ( ( ( a 6 1 5 1 7 3 4 2 1 9 1 5 i 4 t 5 3 ( 3 4 3 8 8 5 3 0 6 x s 1 9 4 1 2 2 2 2 1 1 8 i . . . 2 1 1 . 1 1 1 0 4 ( 9 6 0 a M D 3 . . . 3 3 . . . . 3 3 3 3 3 3 3 3 3 ) ) ) ) ) ) ) ) ) ) 5 6 6 5 8 ) 6 9 8 6 2 1 1 1 2 1 1 1 1 1 ) 4 ( ( ( ( ( ( ( ( ( ( ( ( 9 5 6 1 9 9 9 7 9 3 2 4 2 2 0 2 8 0 4 8 7 5 4 2 9 9 3 3 1 3 9 3 3 4 5 9 . . . 9 9 9 9 . 9 9 9 9 2 2 2 . . . . 2 . . . . 2 2 2 2 2 2 2 2 ) ) ) ) e e g c ) ) 8 7 ) ) ) 8 8 ) ) ) 7 3 1 1 2 3 2 1 1 2 3 4 a ) n ( ( ( ( ( ( ( ( ( ( ( ( r A a 0 8 4 7 3 0 0 7 0 3 9 7 t 9 7 9 1 3 2 3 1 6 2 1 0 e ( s 0 0 6 6 0 0 0 3 2 0 0 0 v i . . 0 0 . . . 0 0 . . . A D 3 3 . . 3 3 3 . . 3 3 3 3 3 3 3 r o t c e v - q c c ) ) 4 3 ( ( 7 0 5 9 7 7 2 2 ‘ ’ ‘ ‘ ‘ ‘ ‘ ‘ ‘ c c c c c c c c c ) ) ) ) ) ) ) ) ) 4 3 3 5 5 3 3 4 4 ( ( ( ( ( ( ( ( ( 4 5 4 7 2 6 5 6 2 2 6 8 0 1 2 3 2 9 8 8 8 9 9 9 9 9 0 2 2 2 2 2 2 2 2 3 . . . . . . . . . . . 0 0 0 0 0 0 0 0 0 0 0 A ) 8 ( 1 9 7 2 . 4 = c , A ) 6 ( 4 6 1 . 5 2 = b . 1 4 0 0 1 4 6 2 4 = d n u o p ; 3 ; 3 3 3 3 3 3 g 3 e e e e 3 e e e e e e e m T T T T T T T T e T o m a e d d T b y o r T r T m C L C S P N G T Y D H E T 5 5 8 T a b l e 8 . 2 . S u m m a r y o f s u p e r c e l l p a r a m e t e r s o f R E T e 3 ( R E = L a , C e , P r , N d , S m , G d , T b , D y , H o , E r , T m , Y ) a t 1 0 0 K . C e l l p a r a m e t e r s M i n i m u m D i s t a n c e ( A ) a = 4 . 3 7 7 9 ( 1 0 ) A , b = 2 6 . 1 4 9 ( 5 ) A , c = 4 . 3 9 6 8 ( 8 ) A i n : 4 . 3 5 6 6 ( 6 ) A , b = 2 5 . 9 2 0 ( 3 ) A , c = 4 . 3 7 2 2 ( 5 ) A a = 4 . 3 4 7 5 ( 9 ) A , b = 2 5 . 8 0 0 ( 5 ) A , c = 4 . 3 5 4 8 ( 9 ) A a = 4 . 3 3 1 6 ( 7 ) A , b = 2 5 . 7 0 5 ( 5 ) A , c = 4 . 3 4 1 9 ( 7 ) A a = 4 . 3 0 5 5 ( 6 ) A , b = 2 5 . 5 5 3 ( 5 ) A , c = 4 . 3 2 4 7 ( 6 ) A a = 4 . 2 9 5 4 ( 4 ) A , b = 2 5 . 4 4 3 ( 2 ) A , c = 4 . 3 0 9 7 ( 5 ) A a = 4 . 2 8 4 0 ( 7 ) A , b = 2 5 . 3 1 2 ( 4 ) A , c = 4 . 2 9 3 2 ( 9 ) A a : 4 . 2 8 0 1 ( 7 ) A , b = 2 5 . 3 0 7 ( 5 ) A , c = 4 . 3 0 5 2 ( 9 ) A n : 4 . 2 8 3 1 ( 6 ) A b = 2 5 . 2 5 0 ( 5 ) A , c = 4 . 2 8 8 7 ( 6 ) A 6 : 4 . 2 7 2 3 ( 8 ) A , b = 2 5 . 2 0 3 ( 4 ) A , c = 4 . 2 8 5 5 ( 6 ) A 0 0 . 2 8 2 5 ( 5 ) c [ 1 m e ) ) ) ) ) ) ) ) u c 9 4 2 4 3 3 2 4 m ) n ( ( ( ( ( ( ( ( a 2 7 5 2 4 3 9 0 i A t 0 3 7 9 6 7 3 6 x s ( 4 4 2 3 2 2 2 2 i . . . . . . . . D 3 3 3 3 3 3 3 3 a M i l i ‘ m e ) ) ) ) ) ) ) ) ) u 2 4 2 9 5 3 3 3 4 c m ) n ( ( ( ( ( ( ( ( ( a 6 9 2 8 0 5 6 7 9 i A t 9 2 7 5 1 8 1 7 9 n s 8 9 9 9 9 9 0 9 9 ( i i D M . . . . . . . . . 2 2 2 2 3 2 2 2 2 ' 1 ! 1 5 I ' ‘ 1 i 1 3 ; e e ) ) ) ) ) ) ) ) ) g c 9 4 2 2 4 2 4 2 4 a ) n ( ( ( ( ( ( ( ( ( a 5 3 1 3 7 2 2 5 7 r A t 4 8 2 3 4 2 4 0 2 e ( s v i A D 1 1 1 1 1 1 1 1 1 . . . . . . . . . 3 3 3 3 3 3 3 3 3 ' - . ; 7 g 1 i ~ I l l I i 3 . ) e C ‘ c 2 . ' ’ ’ ‘ ‘ c c c c c c / 2 1 / 1 2 2 2 2 2 / / / / / 1 1 1 1 1 “ ' b b , + r a o + + + + + + ) ) L t ‘ . 8 7 c b b = e ) v 0 E - 1 R q ( 8 5 ) 7 ( 6 6 4 ‘ ‘ ‘ ‘ ' ( ( b b b b b 1 1 ) ) ) ) ) 8 2 8 4 5 8 8 6 6 ( ( ( ( ( 3 3 0 8 1 0 2 . . 5 3 6 6 3 0 0 ; 5 5 8 6 6 g A , u C = M 3 3 . 0 3 3 3 3 3 3 . . . . . . 0 0 0 0 0 0 l ’ E 1 ' i A A ) ; ) 7 1 1 ( A A A A A A ) 8 A ) K , a N = ) ) ) ) ) 3 4 3 3 3 7 0 3 ( ( ( ( ( ( 6 0 5 8 6 7 7 9 0 5 4 9 8 3 9 1 ( 0 6 3 0 2 1 8 7 7 2 7 . . . . 8 . - . . 1 1 0 0 1 0 9 9 9 A 2 2 2 2 2 1 1 1 ( 4 e T E R M 2 = = = = = = = = = c c c c c c c C , c , , A , , . , , , A A A A A A A A ) 6 ) ) ) ) ) ) ) 8 6 4 3 8 7 6 ( ) 7 ( ( ( ( ( ( ( 7 ( 0 0 1 7 5 7 3 A 5 0 2 7 1 8 6 7 8 2 3 5 1 4 9 0 4 4 4 4 4 4 3 5 . . . . . . . 4 4 4 4 4 4 4 4 4 = 7 5 2 4 f o s r S . e = = = = = = = = t e m b b b b b b b b A b , a s ) A A A A A A A A , , , , . , , , r a p l l e r 5 e ) ) ) ) ) ) ( ) ) t 9 6 3 4 6 6 e ( ( ( ( ( ( 8 0 6 m 5 5 9 1 5 0 3 9 ( a 4 8 6 2 2 1 5 3 3 c r 4 4 0 2 4 4 8 1 7 r a 4 4 4 4 4 3 e p . . . . . . . 4 1 p 4 4 4 4 4 4 4 4 “ u l : s l : = = = = = = f a e n 1 C ' a n 1 . l i F a a ' a o y r K a 0 m m “ 3 T 0 3 ‘ e ‘ ‘ m L fl e u a t a a w “ 4 e T a L - c L 3 n ? f e e 3 f m d “ 9 4 4 l 4 , . 8 e l b a T u . T K T K m 8 K u K I fi ‘ 1 o 6 0 e a g C A p 0 8 C L f 6 0 0 0 A g 0 1 7 0 0 g f , m 3 u 1 u . 1 3 - ’ f o 0 a o 2 C C t t t a a t C $ K a a K K a E g E N a 5 5 9 K A g c e T e “ a = 4 . 4 6 5 7 ( 9 ) A , b = 4 . 4 9 2 7 ( 8 ) A , c = 2 1 . 5 2 5 ( 4 ) A 0 . 3 3 8 1 ( 8 ) b ‘ + 1 / 2 c ‘ 5 3 . 1 6 0 ( 8 ) 1 2 . 9 0 7 ( 8 ) 3 . 4 2 2 ( 8 ) ‘ i l K C u C e T e 4 a t 1 0 0 K I 3 . 3 1 8 ( 2 ) i 1 i . . . . - . - . . . . . . . — . . . . . . . . . . . . . A ; m e ) ) ) ) ) ) ) ) ) u c 5 4 5 4 6 3 3 2 5 m n ( ( ( ( ( ( ( ( ( a 4 9 4 8 0 1 2 3 0 i t x s a i D M m e 8 2 8 9 2 8 4 5 8 2 3 2 3 3 1 4 4 2 . . . . . . . . . 3 3 3 3 3 3 3 3 3 ) ) f 7 T 3 ) ) ) ) ) ) ) ) u c ( 5 ( 3 4 5 5 3 2 2 5 n ( ( ( ( ( ( ( ( m ) 1 4 a 3 4 0 2 7 1 7 5 i t n s i i D M A 6 ( 9 8 7 3 4 3 6 5 3 3 9 9 9 9 9 9 9 1 9 . . . . . . . . 2 2 2 2 2 2 2 2 3 2 I ' 1 : ) 3 ) ) ) ; : ; ) e ) e 5 ) 6 3 5 4 ) ) ) g 4 3 ( ( ( ( c 6 3 2 n ( ( ( ( a ) ( ( 3 7 2 9 a 5 3 4 5 r A 0 4 2 t 6 7 9 3 8 5 e ( 5 9 1 0 s 1 1 1 1 1 1 v i A D 0 1 1 . . . . 3 3 3 3 ' - 3 3 3 3 : 3 3 ’ ’ ‘ ’ c c ’ c I ; c 2 c c c c 2 2 2 2 2 / / 2 / / / / 2 / 1 1 l l 1 1 1 / 1 b b ) ) 2 3 + + + + + + + + ( ( . ) g r o t A b b ‘ ‘ ‘ b b b c e b b b ) ) ) ) ) , ) ) ) 9 5 6 7 6 4 u C = v 7 5 6 - ( ( ( ( ( 8 2 3 q 2 4 ( 8 ( ( 2 6 5 1 0 0 0 2 3 1 2 3 5 = _ 1 1 2 5 1 6 6 6 1 2 3 3 6 M . . 3 8 2 2 2 2 q q 0 . 0 0 2 0 0 7 1 5 _ 0 1 0 0 1 3 : 0 . A A A A A A A ) ) ) ) ) ) ) 6 A ) R 7 8 4 9 8 3 1 7 , ( ( ( 8 ( 0 ( ( ( K 7 8 9 4 2 1 1 1 ( 1 1 1 1 7 5 7 2 1 9 8 6 9 , a 8 2 2 6 5 1 4 9 5 1 5 7 2 9 3 3 N . . 0 . . . . . 0 1 1 l 1 1 2 2 1 l 1 1 1 1 1 1 = = = = = — — — = - — - c c c c c c c c ; s C , b = A ( 4 e T u A f o s r t e m a r a M 6 ( 2 8 2 . 0 2 c . A ) 2 ( 3 2 7 4 . ( 6 3 5 4 . . , , , , , , , A A A A A A A A ) ) ) ) ) ) ) ) 6 7 7 7 4 7 8 7 E ( ( ( ( ( ( ( ( z 0 9 1 8 6 5 8 4 M 3 2 9 9 8 6 2 7 7 5 2 0 2 4 9 0 3 4 4 4 4 4 5 5 . . . . . . . 4 4 4 4 4 4 4 4 4 = = = = = = = = = e b b b b b b b b b s r , , , A , , , A A A A A A A ) , A ) e ) ) ) t 7 5 6 5 ( 2 ) ) ) ) 2 7 7 6 4 p 6 ( e ( ( ( ( ( ( l a 1 1 9 9 7 8 5 8 m 2 6 4 4 1 4 l r 6 3 9 8 9 0 8 3 e 3 a 4 3 1 , 4 4 5 c . 4 . . . p r 4 4 4 4 4 4 4 4 4 e l p l = = = — = u e a a s a C t ' i 1 a f o y r a m 4 4 e e T 4 8 T 4 T e 0 ) ) T ( 1 “ ( ) ° 9 1 9 2 ( 1 1 - 3 1 l m ‘ 0 “ . u u u E g S 2 n 2 u E r 4 4 4 2 6 T d “ 8 A E 4 e e e U . 4 n . 8 e l b a C A ) e 2 T > 8 0 1 T u T T B u u ) u ‘ K K A K K K K K K K 1 ( ( E E o ( 0 1 1 u ) u ( ° 0 0 1 0 0 0 2 2 0 3 0 0 p 0 8 8 u q 8 0 0 0 0 0 ( g 0 g 0 6 0 . m 1 1 1 1 1 - C . q 7 1 1 0 3 ° 0 9 A A 3 0 o 3 C b s s a t t t 3 0 t t t t t t u T N N N C a a a R a K K a a C a C a C a 5 6 0 ( A ) R b A g 2 E u T e 4 a t 1 0 0 K . 3 : l 1 n = u m i l 1 i i i l a = 4 . 4 = 6 4 l ( 5 ) A , b 4 . 4 9 6 4 ( 8 ) A , c = 1 1 3 5 0 1 ( 1 7 ) A 0 2 8 5 3 ( 5 ) b + 1 / 2 c i i l i . . . . . . a n M ~ fl 1 _ . . . . . . l i I i l l 1 . . o u t “ . . . - u - m u l l - l r m u fl u “ 4 1 I : : I i 1 3 . 2 3 4 ( 4 ) * b ) 2 ( 6 6 o 1 l . e T * 0 b 3 + 2 / E 1 * 3 R a 4 = ) g : A q ( 2 * b ) 1 ( 6 * 3 b 3 1 ) z K 3 2 . 0 = 2 q o 4 ) t 6 ) 6 7 ( T ( 4 2 6 3 u 5 1 6 3 E . 2 M . 0 A A 0 H o 4 ‘ ) * t 5 c C \ ) ( T 1 1 E ( 6 “ 6 8 R 3 2 / 1 , 1 2 3 + ) M / . 3 . 0 2 6 T 6 * ( A I 0 a U 3 ) - 7 . 0 ( 5 + x 2 1 ” s e s a h _ 5 e T z 3 ) p I e . 1 0 d ( = 9 ) 1 i r u s 1 3 l ( l 0 3 q — e t ) y _ 2 l o ( p 1 d ( e t r o t s i d * * c 0 W 2 2 / D / 1 1 C + n + * * b b w o n ” ) 1 ( 6 ” 3 ) 3 7 0 ( 5 + 5 6 T 2 I ” 2 1 m 3 ) S “ 1 ( 3 : ' 9 1 1 ‘ 3 E ) 4 ) 8 k I 3 ( 9 / 4 2 2 0 0 U 5 C 3 = . 3 2 0 7 7 ( e ( 6 6 6 6 9 9 2 2 h t f o . . t q O 0 s = . q , , c ) + - o m x * f * a a o } ) ) s 7 r 7 e ( o ( 6 6 t T 6 6 c e 9 9 3 v 8 n ( 2 2 . n 2 3 . 1 I o 0 0 e T Z 7 i * 4 e O x 1 l 6 0 / T / 0 c N g A . 2 C = = 2 t a . _ ) T . 2 1 + ( ‘ 2 4 3 / I _ l q E 1 ( u 3 d g R u , 3 € + 2 o 0 E a T 1 a a m * 3 ‘ t B 3 b 3 l * e 3 \ 0 / E t 3 / 8 x 6 . I b 2 h 0 M ) 3 3 4 ( 2 - 1 R / c l f C T 1 2 K A 1 1 8 1 0 A 4 2 E 5 3 : 3 3 7 3 R / . 2 0 0 ' . ] 0 q , I ‘ 3 . r _ i . : 3 T + a * a o w e i L 2 v / r 1 e v O 3 [ . . ’ 8 0 0 5 6 . . 6 i i . 3 0 8 . 0 0 . 1 r u g i F 0 0 O 0 6 3 e 5 6 1 7 ' 8 . 6 . C h a r g e D e n s i t y W a v e s D i s t o r t i o n s a n d T h e r m o e l e c t r i c s S e m i m e t a l s o r n a r r o w b a n d g a p s e m i c o n d u c t o r s w i t h h e a v y m e t a l s s e e m s t o b e t h e m o r e p r o m i s i n g m a t e r i a l s f o r t h e r m o e l e c t r i c a p p l i c a t i o n s . 2 1 A c o m p l e x e l e c t r o n i c s t r u c t u r e c l o s e t o t h e F e r m i l e v e l w i l l e n h a n c e t h e t h e r m o p o w e r ( s e e e x p r e s s i o n 1 . 4 ) . O n t h e o t h e r h a n d , a C D W d i s t o r t i o n o p e n s u p a g a p i n t h e F e r m i s u r f a c e w h i c h m a y c r e a t e a n a r r o w s e m i c o n d u c t o r w i t h a c o m p l e x b a n d s t r u c t u r e . N e v e r t h e l e s s , i n a l l t h e c o m p o u n d s r e p o r t e d h e r e , t h e C D W d i s t o r t i o n d o e s n o t c r e a t e a f u l l y g a p p e d F e r m i s u r f a c e b u t i n s t e a d a g a p o p e n s i n a s p e c i fi c d i r e c t i o n i n t h e F e r m i s u r f a c e . T h i s r e s u l t s i n a p o o r m e t a l l i c b e h a v i o r ( s e m i m e t a l ) i n w h i c h t h e e l e c t r i c a l c o n d u c t i v i t y i s r e l a t i v e h i g h ( c o m p a r e d t o s e m i c o n d u c t o r s ) a n d s t i l l m e t a l l i c i n c h a r a c t e r b u t t h e t h e r m o p o w e r r e m a i n s l o w ( < 1 0 0 u V / K c h a r a c t e r i s t i c f o r m e t a l s ) . P r o p e r u n d e r s t a n d i n g o f C D W d i s t o r t i o n s i n m a t e r i a l s c o u l d p r o v i d e a u n i q u e m e t h o d f o r c r e a t i n g n a r r o w b a n d g a p s e m i c o n d u c t o r s . I n t h a t s e n s e , m a n i p u l a t i o n o f C D W m o d u l a t i o n s c o u l d b e a n e x c e l l e n t s y n t h e t i c t o o l f o r d e s i g n i n g m a t e r i a l s u i t a b l e f o r t h e r m o e l e c t r i c a p p l i c a t i o n s . 8 . 7 . C l o s i n g r e m a r k s T h i s i s j u s t t h e b e g i n n i n g o f m i c r o s c o p i c u n d e r s t a n d i n g o f t h e C D W b e h a v i o r i n q u a s i - t w o - d i m e n s i o n a l s y s t e m s . I n t h i s w o r k m o s t o f t h e k n o w C D W d i s t o r t e d p o l y t e l l u r i d e s y s t e m s w e r e s y s t e m a t i c a l l y s t u d i e d , F i g u r e 8 . 3 . T h e d i s t o r t e d T e n e t s f o u n d i n t h e s e m a t e r i a l s a r e n o t e f f e c t e d o n l y b y t h e a v e r a g e e l e c t r o n c o u n t a s i t w a s o r i g i n a l l y a s s u m e d ( n u m b e r s a t t h e l e f t s i d e o f F i g u r e 8 . 3 r e p r e s e n t t h e a v e r a g e o x i d a t i o n s t a t e o f t h e T e a t o m s i n t h e C D W d i s t o r t e d n e t s ) b u t t e m p e r a t u r e , s i z e o f a t o m s a n d 5 6 2 d i m e n s i o n a l i t y p l a y a v e r y i m p o r t a n t r o l e o n d e fi n i n g t h e C D W m o d u l a t i o n s . I n t e r a c t i o n s a l o n g a l l t h r e e d i r e c t i o n s m u s t b e t a k e n i n t o a c c o u n t a n d t h e “ q u a s i ” d e s c r i p t i o n h a s t o b e u s e d w i t h c a u t i o n . T h e C D W s t u d y r e p o r t e d h e r e w a s f o c u s e d o n p o l y t e l l u r i d e c o m p o u n d s w i t h d i s t o r t e d T e n e t s . R e c e n t l y , t w o m o r e c l a s s e s o f c o m p o u n d s w i t h C D W i n s t a b i l i t i e s t h a t c o n t a i n S b a n d G a p l a n a r n e t s r e s p e c t i v e l y w e r e r e p o r t e d . S i n g l e c r y s t a l s y n c h r o t r o n d a t a a l o n g a s i n g l e z o n e r e v e a l e d C D W s u p e r s t r u c t u r e r e fl e c t i o n s i n L a A n g z t h a t a r e t e m p e r a t u r e d e p e n d e n t . 2 2 F u r t h e r m o r e , a c o m p l e t e c r y s t a l l o g r a p h i c s o l u t i o n o f C D W d i s t o r t e d G a n e t s i n G d C o l - x G a 3 G e w a s f o u n d . 2 3 T h e s t u d y o f d i s t o r t e d c o m p o u n d s w i t h d i f f e r e n t a t o m s i n p l a n a r a r r a n g e m e n t s t h a n T e c a n g i v e m o r e i n f o r m a t i o n f o r t h e b e h a v i o r o f C D W s t a t e s . I t w i l l b e v e r y e x c i t i n g t o s e e a w e l l d e v e l o p e d t h e o r y t h a t c a n e x p l a i n a n d p r e d i c t t h e e x p e r i m e n t a l r e s u l t s w e p r e s e n t e d i n t h i s t h e s i s . F u r t h e r m o r e , t h e s e n e w i n f o r m a t i o n c o n t r i b u t e d h e r e c a n b e u s e d i n c o n j u n c t i o n w i t h t h e d e v e l o p i n g u n i fi e d t h e o r y f o r t h e d e s c r i p t i o n o f C D W a n d s u p e r c o n d u c t i v i t y . T h e o r e t i c a l c a l c u l a t i o n s ( D F T ) o n t h e u n d i s t o r t e d c r y s t a l s y s t e m s w e r e v e r y u s e f u l o n d e s c r i b i n g t h e F e r m i s u r f a c e a n d c o r r e l a t i n g t h e c r y s t a l l o g r a p h i c a l l y o b s e r v e d m o d u l a t i o n q - v e c t o r t o t h e n e s t i n g v e c t o r s . A d v a n c e m e n t o n t h e d e v e l o p m e n t o f c o m p u t a t i o n a l e l e c t r o n i c s t r u c t u r e c o d e s t h a t c a n t r e a t i n c o m m e n s u r a t e s u p e r s t r u c t u r e s w i l l h e l p s i g n i fi c a n t l y o u r u n d e r s t a n d i n g o f C D W f o r m a t i o n , s t a b i l i t y , a n d d y n a m i c s . 5 6 3 R e f e r e n c e s l M a l l i a k a s , C . ; B i l l i n g e , S . J . L . ; K i m , H . J . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 5 , 1 2 7 , 6 5 1 0 . 2 R u , N . ; M a r g u l i s , G . Y . ; S h i n , K . Y . ; T o n e y , M . F . ; F i s h e r , 1 . R . c o n d - m a t / 0 6 1 0 3 I 9 . 3 D o m a n g e , L . ; F l a h a u t , J . ; P a r d o , M . P . ; C h i r a z i , A . N . ; G u i t t a r d , M . C . R . A c a d . S c i . 1 9 6 0 , 2 6 0 , 8 5 7 . 4 L i n , W . ; S t e i n fi n k , H . ; W e i s s , E . J . I n o r g . C h e m . 1 9 6 5 , 4 , 1 1 5 4 . 5 W a n g , R . ; S t e i n fi n k , H . I n o r g . C h e m . 1 9 6 7 , 6 , 1 6 8 5 . 6 P a r d o , M . P . ; F l a h a u t , J . ; D o m a n g e , L . B u l l . S o c . C h i m . F r . 1 9 6 4 , 3 2 6 7 . ' 7 W a n g , R . ; S t e i n fi n k , H . ; B r a d l e y , W . F . I n o r g . C h e m . 1 9 6 6 , 5 , 1 4 2 . 8 C a n n o n , J . F . ; H a l l , H . T . I n o r g . C h e m . 1 9 7 0 , 9 , 1 6 3 9 . 9 S t o w e , K . J . S o l i d S t a t e C h e m . 2 0 0 0 , 1 4 9 , 1 5 5 . 1 0 ( a ) P a r k , S . - M . ; P a r k , s . - J . ; K i m , s . — J . J . S o l i d S t a t e C h e m . 1 9 9 8 , 1 4 0 , 3 0 0 . ( b ) I j j a a l i , 1 . ; I b e r s , J . A . J . S o l i d S t a t e C h e m . 2 0 0 6 , 1 7 9 , 3 4 5 6 . 1 1 T h e l a r g e s t l a n t h a n i d e a t o m a m o n g t h e r a r e e a r t h s e r i e s i s E u 2 + b u t t h e E u T e z p h a s e c r y s t a l l i z e s i n a d i f f e r e n t s t r u c t u r e t y p e ( C h r i s t o s D . M a l l i a k a s a n d M e r c o u r i G . K a n a t z i d i s , u n p u b l i s h e d r e s u l t s ) . 1 2 S h i n , K . Y . ; B r o u e t , V . ; R u , N . ; S h e n , Z . X . ; F i s h e r , I . R . P h y s . R e v . B 2 0 0 5 , 7 2 , 0 8 5 1 3 2 . 1 3 ( a ) P a r d o , M . P . ; F l a h a u t , J . B u l l . S o c . C h i m . 1 9 6 7 , 1 0 , 3 6 5 8 . ( b ) D i M a s i , E . ; F o r a n , B ; A r o n s o n , M . C . ; L e e 8 . , C h e m . M a t e r . 1 9 9 4 , 6 , 1 8 6 7 . ( c ) C h a p t e r 5 . 1 4 C h u k a l i n , V . 1 . ; Y a r e m b a s h , E . I . ; V i l l e n s k i i , A . I . I n o r g . M a t e r . 1 9 6 7 , 3 , 1 3 4 1 . 1 5 M a l l i a k a s , C . D . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 6 , 1 2 8 , 1 2 6 1 2 . 1 6 M a l l i a k a s , C . D . ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 7 , 1 2 9 , 1 0 6 7 7 . 5 6 4 1 7 P a t s c h k e , R . ; H e i s i n g , J . ; S c h i n d l e r , J . ; K a n n e w u r f , C . R . ; K a n a t z i d i s , M . G . J . S o l i d S t a t e C h e m . 1 9 9 8 , 1 3 5 , 1 1 1 . 1 8 F a n g , A . ; R u , N . ; F i s h e r , 1 . R . ; K a p i t u l n i k , A . P h y s . R e v . L e t t . 2 0 0 7 , 9 9 , 0 4 6 4 0 1 . 1 9 A s y s t e m a t i c s t u d y o f t h e p e a k i n t e n s i t y o b t a i n e d f r o m F F T / S T M w i t h t i p b i a s o n S m T e ; g a v e d i f f e r e n t r e l a t i v e i n t e n s i t i e s ( M a r i a I a v a r o n e ( a t A r g o n n e N a t i o n a l L a b o r a t o r y ) , C h r i s t o s D . M a l l i a k a s a n d M e r c o u r i G . K a n a t z i d i s , u n p u b l i s h e d r e s u l t s ) 2 0 K i m , H . J . ; M a l l i a k a s , C . D . ; T o m i c , A . ; T e s s m e r , S . H . ; K a n a t z i d i s M . G . ; B i l l i n g e , S . J . L . P h y s . R e v . L e t t . 2 0 0 6 , 9 6 , 2 2 6 4 0 1 . 2 1 R o w e , D . M . , C R C H a n d b o o k o f t h e r m o e l e c t r i C S , C R C P r e s s , 1 9 9 4 . 2 2 S o n g , C . ; P a r k , J . ; K o o , J ; L e e , K . - B . ; R h e e , J . Y . ; B u d ’ k o , S . L . ; C a n fi e l d , P . C . ; H a r m o n , B . N . ; G o l d m a n , A . 1 . P h y s . R e v . B 2 0 0 3 , 6 8 , 0 3 5 1 1 3 . 2 3 Z h u r a v l e v a , M . A . ; E v a i n , M ; P e t r i c e k , V ; K a n a t z i d i s , M . G . J . A m . C h e m . S o c . 2 0 0 7 , 1 2 9 , 3 0 8 2 . 5 6 5 M I C H I G A N S Y A T E U N I V E R S I T V L I B R A R I E S 3 1 2 9 3 0 2 9 5 6 6 4 4 9