SOME P H Y SIC A L P R O P E R T IE S OF S E P A R A T E D
I S O T O P E S O F L IT H IU M

by
D on ald D uW ayne Snyd er

AN ABSTR A C T

S u b m i t t e d to the S c h o o l for A d v a n c e d G r a d u a t e S t u d i e s of
M i c h i g a n S ta te U n i v e r s i t y of A g r i c u l t u r e and
A p p lie d S c i e n c e in p a r t ia l f u lf i ll m e n t of
the r e q u i r e m e n t s for the d e g r e e of

DOCTOR OF PH ILO SOPH Y

D e p a r t m e n t of P h y s i c s and A s t r o n o m y
1957
t

Approved

y .

.)

aA

ABSTRACT

A s p art of a p r o g r a m exp loitin g iso to p ic m a s s as a probe
for i n v e s t i g a t i o n of the so lid s ta t e ,

c e r t a i n b u lk p r o p e r t i e s of

se p a ra ted lith iu m is o to p e s w e r e m e a s u r e d .

The bulk d e n s ity of

n a tu r a l lith iu m w a s f ir s t r e d e t e r m i n e d , b y f lo t a t i o n - e q u i li b r iu m and
h yd rostatic-b alan ce m ethods.
Jfc 0 . 0 0 1 g m / c m
to 2 0 ° C .

T h e v a l u e o b t a i n e d w a s 0. 5 3 1

, c o r r e c t e d for c h e m i c a l i m p u r i t i e s and r e d u c e d

T h is v a lu e is s li g h t ly l e s s than that for the c r y s t a l d e n s i t y

com p u ted fr o m X - r a y d iffra ctio n data,

0. 5 3 3 g m / c m

.

The bulk

d e n s ity of the s e p a r a te d i s o t o p e s w a s m e a s u r e d b y the h y d r o s t a t i c balance m ethod.
for lit h i u m - 6 ,

T h e v a l u e s o b t a i n e d w e r e 0. 4 6 0 ± 0. 0 0 3 g m / c m

0. 5 3 7 ± 0. 0 0 2 g m / c m ^ f o r l i t h i u m - 7 ,

corrected

f o r c h e m i c a l i m p u r i t i e s a n d r e d u c e d t o 100% i s o t o p e - c o n t e n t a t
20°C.

T h e c r y s t a l d e n s i t i e s a r e c o m p u t e d to b e 0. 4 6 2 g m / c m

a n d 0. 5 3 9 g m / c m

, resp ectively.

l e s s than the c r y s t a l d e n s i t y ,

A g a in the b u lk d e n s ity is s lig h t ly

in a c c o r d a n c e w ith u s u a l e x p e r i e n c e .

T he r e la t iv e e le c t r i c a l r e s i s t i v i t y of natu ral lith iu m w a s d e t e r m in e d
j

f r o m r o o m t e m p e r a t u r e (2 9 5 ° K ) to l i q u i d - n i t r o g e n t e m p e r a t u r e
(77°K) with a K e lv in do u b le b r id g e ,
in the l i t e r a t u r e .

the r e s u l t s a g r e e i n g w ith th o s e

The r e la t iv e r e s i s t i v i t y o f the s e p a r a te d i s o t o p e s

w a s m e a s u r e d o v e r the s a m e r a n g e ,

the r e s u l t s d i s a g r e e i n g

q u a lita t iv e ly and q u a n tita tiv e ly w ith the p r e d i c t i o n s of the B l o c h G ru n eisen theory.

A p o s s i b l e e x p l a n a t i o n l i e s in the p r e s e n c e of

r e s i d u a l r e s i s t a n c e d u e to i m p u r i t i e s .

If t h i s r e s i s t a n c e i s l a r g e

e n o u g h and d if f e r e n t en o u g h in the m a t e r i a l s ,
the d i s c r e p a n c i e s .

A n e s t i m a t e of the e f f e c t s h o w s ,

that t h is e x p l a n a t i o n i s n ot l i k e l y to h o ld .
liquid h y d r o g e n t e m p e r a t u r e
question d irectly.

it c o u ld a c c o u n t for
how ever,

A m e a s u r e m e n t at

(20°K ) o r b e l o w w o u ld s e t t l e the

If t h e f i n d i n g s a r e s u b s t a n t i a t e d ,

a seriou s

m o d i f i c a t i o n in the t r e a t m e n t of t r a n s p o r t p h e n o m e n a in m e t a l s
is c a lle d for.

SOME PH YSIC A L P R O P E R T IE S OF S E P A R A T E D
I S O T O P E S O F L IT H I U M

by
D onald D uW ayne Snyd er

A THESIS

S u b m i t t e d to th e S c h o o l fo r A d v a n c e d G r a d u a t e S t u d i e s 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 o f A g r i c u l t u r e an d
A p p lie d S c i e n c e in p a r t i a l f u l f i l l m e n t of
the r e q u i r e m e n t s for the d e g r e e of

DOCTOR O F PH ILO SOPH Y
D e p a r t m e n t of P h y s i c s and A s t r o n o m y

1957

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AC KNOW L E D G M E N T S
I w i s h 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 e s s o r D.

J.

M o n t g o m e r y for h is s u g g e s t i o n of th is p r o b l e m and for h i s g u id a n c e
and e n c o u r a g e m e n t in i t s p r o s e c u t i o n .

T he s e r v i c e s of the A t o m ic

E n e r g y C o m m i s s i o n in s u p p ly in g the s e p a r a t e d i s o t o p e s a m p l e s
for this w o r k on lo a n a r e g r e a t ly a p p r e c ia te d .

T h e c o o p e r a t i o n and

a d v i c e g i v e n b y the p e r s o n n e l of the O ak R id g e N a t io n a l L a b o r a t o r y ,
in p a r t i c u l a r Dr.

P.

S.

Baker,

w e r e v e r y helpful.

The isotope

lo a n f e e s w e r e m e t in p a r t by an A l l - C o l l e g e R e s e a r c h G ra n t
a w a r d e d to D r .

J.

C.

L ee for 1 9 5 4 -5 5 .

D e a n T h o m a s H.

w a s i n s t r u m e n t a l in m a k i n g th is a r r a n g e m e n t ,
e n c o u r a g e d and f a c i l i t a t e d the p r o g r a m .
and M r.

T h e o d o r e L.

O sgood

and h a s o t h e r w i s e

P r o f e s s o r M.

T.

Rogers

B r o w n of the C h e m i s t r y D e p a r t m e n t p r o ­

vided us w ith s o m e s p e c ia lly p r e p a r e d c h e m ic a ls .

M r.

R ichard

L e f fle r of the P h y s i c s D e p a r t m e n t v e r y k in d ly a s s i s t e d m e in p a r t
of the e x p e r i m e n t a l w o r k .

P a r t ia l su p p ort of this w o rk w a s p r o v id e d

b y a R e s e a r c h C o n t r a c t g r a n t e d to M i c h i g a n S t a t e U n i v e r s i t y b y t h e
M e t a llu r g y and M a t e r ia l s B r a n c h of the D i v i s i o n of R e s e a r c h of
the A t o m ic E n e r g y C o m m i s s i o n .

TABLE OF CONTENTS
CHAPTER
I.
II.

PAGE
INTRO DU CTIO N

1

SAMPLES

4

A.
B.
C.
III.

VI.

VIII.

N atural L ithiu m
Separated Isotopes
C rystal D ensity

12
12
14
17
18

21
21
21
24

E L E C T R I C A L RESISTIVITY:
T H E O R E T IC A L C O N SID ER A TIO N S
E L E C T R IC A L R E SIST IV ITY :A P PA R A T U S
A.
B.
C.
D.

V II .

C h oice of m ethod
F lo ta tio n -E q u ilib riu m m ethod
H y d ro sta tic-B a la n ce m ethod
P y c n o m e te r C alibration

B U L K DENSITY: R E S U L T S AND
DISCUSSION
A.
B.
C.

V.

4
5
10

B U L K DENSITY: E X P E R IM E N T A L
.. P R O C E D U R E
A.
B.
C.
D.

IV..

C h oice
^
P r o c u r e m e n t and A n a l y s i s
P rep aration

K elvin B rid ge
S am p le H old er
C ryostat
M easuring D ev ices

27
34
34
36
40
44

E L E C T R I C A L RESISTIVITY:
EX PER IM EN TA L PROCEDURE

47

E L E C T R I C A L RESISTIVITY:
A N D DISCUSSION

50

R E F E R E N C E S CITED

RESULTS

bl

CHAPTER I
INTRO DUCTIO N
The p rod u ction of e le c tr o m a g n e tic a lly -e n r ic h e d iso to p e s
by a t o m ic e n e r g y p r o j e c t s h a s m a d e a v a ila b le a new c l a s s of i m p o r ­
tant s u b s t a n c e s .

F o r the p r e s e n t stu d y i n t e r e s t l i e s in the fa c t

that i s o t o p i c m a s s b e c o m e s a p r o b e for i n v e s t i g a t i o n o f the s o li d
state.

T h e m o t i v a t i o n is that the i s o t o p e s of a g i v e n e l e m e n t c o n ­

stitute a se t of c lo s e ly r e la ted sim p le su b sta n c e s w h ich differ
s i g n i f i c a n t l y - f r o m the p o in t of v ie w of the p r o p o s e d stu d y - o n ly
in the a t o m i c m a s s .

T h is p a r a m e t e r then s e r v e s as a p r o b e for

testin g th e o r e tic a l p r e d ictio n s about certa in p h y sic a l p r o p e r tie s .
F or exam p le,

the t r e a t m e n t of e l e c t r i c a l c o n d u c t iv it y in the u s u a l

t h e o r y l e a d s to an e x p r e s s i o n for the c o n d u c t iv it y w h ic h is a fu n c tio n
o f the t e m p e r a t u r e and the a t o m i c m a s s ,
c o m p l i c a t e d fu n c tio n a l of the a t o m i c field .

and at the s a m e t i m e a
B e c a u s e of the d iff ic u lt y

i n e v a l u a t i n g t h i s f u n c t i o n a l it h a s n o t b e e n p o s s i b l e to m a k e q u a n t i ­
tative c o m p a r is o n b e tw e e n d ifferen t e le m e n ts .

P reviou s in v estig a ­

tio n s a c c o r d i n g l y h a v e b e e n c o n c e r n e d w ith the d e p e n d e n c e of c o n ­
d u c tiv ity u p on t e m p e r a t u r e for fix e d a t o m ic m a s s and a t o m i c fie ld .
T h e p r e s e n t w o r k is c o n c e r n e d w ith the d e p e n d e n c e of c o n d u c tiv ity
upon a t o m i c m a s s fo r fix e d t e m p e r a t u r e and a t o m i c fie ld .

S p ecific­

a lly , the e l e c t r i c a l c o n d u c t iv it y of s e p a r a t e d i s o t o p e s l i t h i u m - 6

z

a n d l i t h i u m - 7 i s m e a s u r e d f r o m r o o m t e m p e r a t u r e to l iq u i d n itrogen tem p era tu re.

The r e s u lt in g data a r e th en c o m p a r e d w ith

the p r e d i c t i o n s f r o m s o lid s ta te t h e o r y .
In c a r r y i n g o u t t h i s p r o g r a m ,
required.

v a r io u s a n c illa r y data a r e

T h e m e c h a n i c a l p r o p e r t i e s of the s u b s t a n c e s sh ou ld be

k n o w n , in p a r t i c u l a r the l a t t i c e c o n s t a n t and b u lk d e n s i t y ,
function of te m p e r a tu r e .
course,

as a

T h e s e data h a v e in t r in s ic in t e r e s t ,

of

and th ey h a v e s till o th er i n t e r e s t for p o s s i b l e a p p l i c a ­

t io n s in i s o t o p e e n r i c h m e n t p r o c e s s e s ; but for the p r e s e n t w o r k
th e y a r e n e e d e d for c a lc u l a t io n of r e s i s t i v i t y f r o m r e s i s t a n c e m e a s u r e ­
m ents.

C o n s e q u e n t ly the p r o g r a m w a s b e g u n w ith m e a s u r e m e n t s

of bulk d e n s ity ,

the r e s u l t s b e in g c o m p a r e d w ith th o se o b ta in ed

e a r lie r on la ttice c o n sta n ts.

The in v e stig a tio n then p r o c e e d e d

w ith m e a s u r e m e n t s of the e l e c t r i c a l r e s i s t i v i t y .

It i s t h i s w o r k

w h ic h c o n s t i t u t e s the s u b s t a n c e of th is t h e s i s .
T h e c h o i c e of l it h i u m w a s b a s e d on it s a v a i la b i li t y in
r e a s o n a b l e q u a n titie s and on the l a r g e r e l a t i v e i s o t o p i c m a s s d i f f e r ­
ence.

It h a s t h e a d d i t i o n a l a d v a n t a g e ,

of v iew ,

f r o m the s c ie n t if i c p oint

that it i s the m e t a l of l o w e s t a t o m i c n u m b e r ,

i s r e l a t i v e l y a m e n a b l e to c a l c u l a t i o n .

and h e n c e

It c r y s t a l i z e s i n a s i m p l e

s tr u c t u r e { b o d y - c e n t e r e d cu b ic) and p r o v i d e s a s tr u c t u r e of h ig h
s y m m e t r y and r e la t iv e e a s e of c a lc u la tio n .

On the o th e r hand ,

the c h e m i c a l r e a c t i v i t y of l i t h i u m m a k e s it an a w k a r d s u b s t a n c e

3

to h a n d le .

On b a la n c e ,

t h e s c i e n t i f i c a d v a n t a g e s w e r e j u d g e d to

o u t w e ig h the t e c h n i c a l d i s a d v a n t a g e s ,
study.

and it w a s c h o s e n fo r the

S o m e d a y it m a y b e p o s s i b l e t o e x t e n d t h e w o r k t o m a g ­

n e s i u m - 2 4 a n d m a g n e s i u m - 2 & a n d to c a l c i u m - 4 0 a n d c a l c i u m - 4 4 .
So fa r a s i n v e s t i g a t i o n s o f o t h e r p h e n o m e n a a r e c o n c e r n e d ,
the v a lu e o f i s o t o p i c m a s s a s a p r o b e w i l l a p p e a r m o s t c h a r a c t e r ­
i s t i c a l l y w h e r e the l a t t i c e - v i b r a t i o n s p e c t r u m is an i m p o r t a n t
f a c t o r in d e t e r m i n i n g the b e h a v i o r of the s u b s t a n c e .

Thus therm al

c o n d u c t iv it y and s p e c if ic h e a t at low t e m p e r a t u r e s should be r e s p o n ­
s i v e to v a r i a t i o n i n i s o t o p i c m a s s .

P e r h a p s a m o r e sign ifican t

r e g i o n o f p h e n o m e n a i s that w h e r e the n u c l e u s m o v e s f r o m on e
p o s i t i o n o f qua s i - e q u i l i b r i u m to a n o t h e r ,

su c h a s in s o lid or m o l t e n

lith iu m arou n d the m e lt in g p oint d u rin g v ib r a tio n or flow .
p resen t work,

it i s h o p e d ,

The

d e m o n s t r a t e s the p r a c t i c a li t y of u s in g

iso to p ic m a s s for study of bulk p r o p e r t ie s of m a tte r .

C H A P T E R II
SAMPLES
A.

C h oice
P r i o r to t h e d e v e l o p m e n t o f p r o d u c t i o n - t y p e m a s s

spectro­

g r a p h s at th e O ak R id g e N a t io n a l L a b o r a t o r y (O R N L ) and o th e r
i n s t a lla t io n s o f th is kind,

it w a s not p o s s i b l e to o b t a in b u l k q u a n t i ­

t ie s of h ig h ly e n r ic h e d sta b le is o t o p e s other than th o se of h y d r o g e n .
In e a r l y 1 9 4 6 O R N L s t a r t e d a p r o g r a m f o r t h e e n r i c h m e n t o f a l l
n a tu ra lly -o ccu rrin g stab le is o to p e s ,
b eg u n s h ip m e n ts of s a m p le s .

and b y the end o f that y e a r had

At p r e s e n t s ta b le i s o t o p e s of the

m a j o r i t y of the e l e m e n t s a r e a v a ila b le for s a le o r ,
for loan.

in s o m e c a s e s ,

A m o n g the e l e m e n t s not su p p lied a r e th o s e with on ly

on e n a t u r a lly - o c c u r r in g sta b le iso t o p e ; the m a j o r i t y of the r a d i o ­
a c t i v e e l e m e n t s ; the i n e r t g a s e s ; c e r t a i n r a r e e a r t h s ; and a few
others,

such as highly toxic ones.
T h e i n v e s t i g a t i o n s o f the d e n s i t y and the e l e c t r i c a l c o n ­

d u c tiv ity of s e p a r a t e d i s o t o p e s w e r e two p a r t s of a b r o a d e r p r o g r a m
o n the u s e o f the i s o t o p i c m a s s a s a p r o b e fo r the stu d y of the
solid state.

F o r the g e n e r a l study a m e ta l w a s d e s ir e d .

L ithiu m ,

w ith n a t u r a l i s o t o p e s L i - 6 and L i - 7 in r e a s o n a b l e a b u n d a n c e r a t i o
(L i-6,
(L i-7

7. 5 2 % ; L i - 7 ,

92.48% ),

and the l a r g e r e l a t i v e m a s s d i f f e r e n c e

- L i - 6 ) / 1 / 2 ( L i - 7 - f - L i - 6 ) = 14%, w a s a n o b v i o u s c h o i c e .

E x a m in a t io n of the O R N L In v e n to ry of E l e c t r o m a g n e t i c a l l y E n r ic h e d
I s o t o p e s sh o w e d that b oth of t h e s e i s o t o p e s w e r e a v a i la b l e in v e r y
h ig h e n r i c h m e n t s and in a d eq u a te a m o u n ts.
F r o m the stan d p oin t of th e o r y ,
th at it h a s a r a t h e r s i m p l e s t r u c t u r e ,
It i s a n a l k a l i o f l o w a t o m i c n u m b e r ,

l i t h i u m i s a t t r a c t i v e in

b o th a t o m i c and c r y s t a l l i n e .
and it c r y s t a l l i z e s in the

b o d y - c e n t e r e d c u b ic f o r m at a ll but the l o w e s t t e m p e r a t u r e s .
the sta n d p o in t of e x p e r i m e n t ,

o n the o th e r hand,

From

lithium o ffe r s

d i f f i c u l t i e s in its h a n d lin g b e c a u s e of its h ig h c h e m i c a l r e a c t i v i t y .
N on etheless,

it w a s d e c id e d that the a d v a n t a g e s of h igh r e l a t i v e

m a ss difference,

read y availab ility,

and s i m p l i c i t y of s t r u c t u r e

o u tw e ig h the d is a d v a n t a g e s of e x p e r im e n t a l d iffic u lt ie s .
B.

P r o c u r e m e n t and A n a l y s e s
W h en th e p r e s e n t w o r k w a s b e g u n in 19 5 5 ,

electr o m a g n e t­

ic a l l y - s e p a r a t e d i s o t o p e s w e r e a v a ila b le for d is tr ib u t io n on ly on
l o a n a s a p p r o v e d b y t h e U.

S.

A tom ic E n ergy C o m m is s io n .

f o r l o a n w e r e m a d e to t h e A E C b y u s i n g F o r m A E C - 1 0 0 .
r e q u e s te d a m o u n t of L i- 6 ,
that of L i - 7 ,

the r a r e r i s o t o p e ,

the m o r e c o m m o n i s o t o p e ,

per sam p le w as m ade.

w a s 500 m i l l i g r a m s ;

per sam p le.

p a r a t i o n of the lit h i u m in the e l e m e n t a l f o r m ,
ch arge of $60.

The

1000 m i l l i g r a m s .

s a m p l e s of th is s i z e the lo a n f e e w a s $50.

R equest

For

For p r e ­

a sp ecial se rv ic e

The total c h a r g e w a s thus

6

$220.,

■which w a s m e t b y a n A l l - C o l l e g e R e s e a r c h G r a n t ,

and A s t r o n o m y No.
acad em ic year

4 5 3,

1954-55.

o n 19 M a y 1 9 5 5 .

i n i t i a l l y g i v e n to D r.

J.

C.

P h ysics

L e e for the

The s a m p le s w e r e shipped fr o m O R N L

W hen th e se

sa m p les a rrived ,

it w a s found that

u n f o r tu n a te ly the c o n c e n t r a t i o n s of i m p u r i t i e s w e r e too h ig h to a llo w
m e a n i n g f u l r e s u l t s to b e o b t a i n e d .

T h e i m p u r i t i e s a p p e a r to b e

in tr o d u c e d d u r in g the t h e r m o - c h e m i c a l r e d u c t i o n of lit h iu m c h l o r i d e
to e l e m e n t a l l i t h i u m b y m e a n s o f m e t a l l i c b a r i u m i n s t a i n l e s s
steel con tain ers.

Dr.

P.

S.

p r e p a r a t i o n of the l it h iu m ,

B ak er of O RNL,

w h o s u p e r v i s e d the

s u g g e s te d that v a c u u m d is tilla t io n w ould

b e the b e s t m e t h o d of p u r if y in g the m e t a l l i c lit h i u m ,
to h a v e h i s o r g a n i z a t i o n p e r f o r m the d i s t i l l a t i o n ,
c h a r g e of $50., p e r s a m p l e .

w ithout any m e a s u r e m e n t s h a v in g

The r e d is tille d m a te r ia l w a s shipped fro m

O R N L on 3 N o v e m b e r ,
initially r e q u e ste d ,

at a n o m in a l

The m a teria l w as accord in gly returned

for p u r i f i c a t i o n ab ou t 22 Ju ly 1955,
b een m a d e on them .

and a g r e e d

1955,

in a p p r o x i m a t e l y d o u b le the a m o u n t

fo llo w in g the s u g g e s t io n of Dr.

B a k e r that it

w o u l d b e a d v a n t a g e o u s to h a v e a d d i t i o n a l m a t e r i a l t o m a k e up f o r
the a t t r i t i o n d u r i n g p r o c e s s i n g if w e w e r e to a t t e m p t f u r t h e r d i s ­
tillation .

T h e n ew s a m p l e s had the fo llo w in g a n a l y s e s .

7

L i- 6

Lot No.

Isotopic A n a ly sis

T
<0 .
-CO.
0.
<0 .
0.

0 1T
02
05
01T
01

L i-7

( e l e m e n t and w e i g h t p e r c e n t ,
Fe
K
Mg
Mn
Mo
Na

Lot No.

Isotopic A n a ly sis

1045 m g

( m a s s n u m b e r and a t o m i c p e r c e n t ) : 6,

S p ectrograp h ic A n a ly sis
Ag
A1
Ba
Ca
Cr
Cu

SS5(a) - r e d i s t i l l e d

0.
CO.
0.
<0.
<0.
0.

5
02T
02
01
01
03

Ni
Pb
Si
3n
Sr
V

668(j) - r e d i s t i l l e d

( m a s s and a t o m ic p e r c en t):

6,

T
0.
0.
0.
CO.
0.

02
01
2
0 IT
01

Fe
K
Mg
Mn
Mo
Na

0.
0.
0.
<0.
CO.
0.

3
02
02
01
01
02

p recisio n

0. 2 ± 0 . 1; 7 ,

Ni
Pb
Si
Sn
Sr
V

L 50%):

CO. 0 IT
< 0. 02T
< 0 . 05
CO. 01
< 0 . 01
CO. 02

1028 m g

S p e c t r o g r a p h i c A n a l y s i s ( e l e m e n t an d w e i g h t p e r c e n t ,
Ag
A1
Ba
Ca
Cr
Cu

96. 1 ± 0 . 1; 7 * 3 . 9 * 0 . I

1000 m g
99- 8 ± 0 . 1

p recisio n
0.
0.
<0.
CO.
CO.
<0.

02
01
05T
01
01
01

* 50%);

W ith b o th i s o t o p e s a m p l e s ,
(L i-6,

F e - 0. 5%; L i - 7 ,

ir o n a p p e a r s in v e r y g r e a t a m o u n t

F e = 0. 3%).

It i s b e l i e v e d t h a t t h e s e h i g h

a m o u n t s c a n b e l a r g e l y d i s c o u n t e d in v i e w o f the s a m p l i n g p r o ­
c e d u r e w h ic h in v o lv e d cu ttin g the m a t e r i a l w ith a s t e e l k n ife.
o n ly o t h e r i m p u r i t y in h ig h c o n c e n t r a t i o n is c a l c i u m
The so u r c e is unknown.

In t h e v a c u u m d i s t i l l a t i o n ,

e l e m e n t to r e m o v e i s s t r o n t i u m ,

The

(0. 2%) i n L i - 7 .
the h a r d e s t

b e c a u s e o f the s i m i l a r i t y of its

v a p o r p r e s s u r e c u r v e to t h a t o f l i t h i u m .

It i s g r a t i f y i n g to n o t e

that it a p p e a r s o n ly in v e r y s lig h t a m o u n t.

It i s t h i s L i - 7

sam p le

( 6 6 8 ( j )) w h i c h w a s u s e d f o r b u l k d e n s i t y a n d r e s i s t i v i t y d e t e r m i n ­
ation s,

and t h is s a m p l e of L i - 6

SS5(a)

w h ich w a s u sed for r e s i s ­

tivity d e te r m in a tio n s.
D u r in g the p r o g r e s s of the e x p e r i m e n t s ,
d istrib u tio n of stab le iso to p e s w as ch anged,
to p u r c h a s e c e r t a i n s a m p l e s .
cent L i-6,

t a i n i n g 9 9 . 3 '/o L i - 6 ,

A l l o c a t i o n s f o r 10 g r a m s o f 96 p e r ­

The latter sam p le,

f r o m Lot SS5(b) c o n ­

w a s o r d e r e d a b o u t 1 M a r c h a n d s h i p p e d 15

The c o s t w as $30.

for a to ta l of $ 1 0 5 .
follow s :

and it b e c a m e p o s s i b l e

and for 3 g r a m s o f 99 p e r c e n t L i - 6 w e r e a u t h o r iz e d

a b o u t 31 J a n u a r y 1 9 5 6 .

M arch.

the A E C p o l i c y o n

per gram ,

The an alysis,

plus $15.

handling fe e ,

as supplied by O R N L ,

is as

9

L i -6

Lot No.

SS5(b) - r e d i s t i l l e d

3000 m g

Isotop ic A n alysis:

L i-6,

99. 3 ±

0. 2%;

Li -7 ,

S p ec tro g r aphic A n a ly sis

0. 7 ±. 0. 1%

( e l e m e n t a nd w e i g h t p e r c e n t » P r e :

pr e c i s i o n ±100% ):
A1
Ba
Be
Ca
Cr
Cu

< . 0 IT
01
< . 001
25
01FT
02

Fe
K
Mg
Mn
Na
Ni

It i s t h i s L i - 6 s a m p l e
tivity d e te r m in a tio n s .

.
< .
.
< .
.
.
<

SS5(b)

Pb
Sn
Sr
V
Zn

<
<

01
01
01
01
< .
< . 25
.

.

-whi ch w a s u s e d f o r t h e r e s i s ­

The n a tu r a l lith iu m w a s p r o d u c e d b y the

L ith iu m C o r p o r a tio n of A m e r ic a ,
sod iu m grade,

05
01
01
01
02
01

M in neapolis.

It i s t h e i r l o w -

in the f o r m of 3 / 8 - i n c h d i a m e t e r r o d s w ith the

follow in g sp e cifica tio n s:

Na
K
Ca
N
Fe
M r.

T h e o d o r e L.

0 . 0 0 5%
0.0 1
0.0 2
0. 0 6
0. 00 1

B r o w n and P r o f e s s o r M a x T.

R ogers,

the C h e m i s t r y D e p a r t m e n t of M ic h ig a n State U n i v e r s i t y ,

of

kindly

f u r n is h e d the n a t u r a l l it h i u m and the i n f o r m a t i o n on its s p e c i f i c a t i o n s

10

fo r the in itia l e x p e r i m e n t s .

L a r g e r a m o u n t s ■were s u b s e q u e n t l y

o r d e r e d f r o m the L it h iu m C o r p o r a t io n of A m e r i c a .
C.

P rep aration
A l l l i t h i u m s a m p l e s w e r e s h ip p e d and s t o r e d in o il.

th eless,

they b e c a m e c o a te d w ith a dark l a y e r ,

n itr id e for the m o s t p art.

N ever­

probably lith iu m

T h e c o a tin g ca n be s c r a p e d or cut off

and the c l e a n m e t a l o b ta in e d , p r o v i d e d the f r e s h s u r f a c e is p r o ­
t e c t e d e i t h e r b y a n o n r e a c t i n g a t m o s p h e r e (e. g. , c a r b o n d i o x i d e )
o r b y c o v e r i n g it w ith a n o n r e a c t i v e s u b s t a n c e

(e. g. , p e t r o l a t u m ) .

I n i t i a l l y th e l i t h i u m w a s e x t r u d e d f r o m a s t e e l d ie in s u c h a
w a y that p e t r o l a t u m c o a t e d the e m e r g e n t w i r e .

The p etrolatu m

c o a tin g cou ld not b e s a t i s f a c t o r il y r e m o v e d in m a k in g d e n s ity
m easurem en ts,

and c o n s e q u e n t l y a n o th e r m e t h o d of p r o t e c t i n g

the s u r f a c e h ad to b e u s e d .

It w a s f o u n d t h a t c a r b o n d i o x i d e ,

dried

by p a s s i n g th r o u g h a c o lu m n of D r i e r i t e * and th r o u g h one c o n t a in in g
A n h y d r o n e ** did n o t r e a c t n o t i c e a b l y w ith l i t h i u m at r o o m t e m p e r a ­
ture.

*

T h e e x p e r i m e n t s on d e n s it y w e r e th en c a r r i e d out in a C O 2 -

D r i e r i t e : T r a d e n a m e o f t h e W. A. H a m m o n d D r i e r i t e C o m p a n y ,
X e n ia , O h io, for a n h y d ro u s C a lc iu m Sulfate

** Anhydrone:

T r a d e n a m e o f t h e J. T . B a k e r C h e m i c a l C o m p a n y ,
P h illip s b u r g , N ew J e r s e y , for a n h yd rou s M a g n e s iu m P e r c h lo r a t e

11

filled dry box,

e x c e p t w h e n it w a s n e c e s s a r y to r e m o v e the l i t h i u m

to p l a c e i t i n t h e t e m p e r a t u r e b a t h w h e r e i t w a s s u b m e r g e d i n a
n o n r e a c tin g liqu id.
P r e p a r a t i o n of the s a m p l e s for the r e s i s t i v i t y m e a s u r e m e n t s
w a s s i m p l e in th at the p e t r o l a t u m c o a t i n g g a v e the n e e d e d p r o t e c ­
tio n and did n o t i n t e r f e r e w ith the m e a s u r e m e n t s .

The lith iu m w h ich

w a s to b e p l a c e d i n t h e p r e s s f o r e x t r u s i o n w a s c a r e f u l l y c l e a n e d
of c o a tin g s

(oxides,

nitrides,

etc. ) by s c r a p in g or cutting aw ay

the s u r f a c e w h ic h had b e e n e x p o s e d .

C H A P T E R III
B U L K DENSITY:
A.

EX PER IM EN TA L PROCEDURE

C h o ice of M ethod
P r o b a b l y the m o s t a c c u r a t e m e t h o d s for d e t e r m i n a t i o n of

the d e n s ity of a so lid a r e
equilibriu m ;

(a) s p e c i f i c - g r a v i t y b o t t l e ;

(b) f l o a t i n g

(c) h y d r o s t a t i c b a l a n c e .

In m e t h o d (a) a w e i g h e d s a m p l e o f t h e s o l i d i s p l a c e d i n t h e
s p e c ific -g r a v ity bottle,

w h i c h i s t h e n f i l l e d to a m a r k e d l e v e l w it h

a liq u id that d o e s n ot r e a c t w ith the so lid .
and the s o lid is r e m o v e d .
to the m a r k e d l e v e l ,

The a s s e m b ly is w eigh ed ,

The b o ttle i s th en r e f i l l e d w ith the liqu id

and r e w e ig h e d .

T h e d e n s i t y of the s o lid c a n

b e c a l c u l a t e d f r o m the r e s u l t s of the t h r e e w e i g h i n g s .

T h is m eth od

i s s u p p o s e d to b e a c c u r a t e w i t h i n 1 p a r t i n 1 0 0 0 w h e n p r o p e r c a r e
i s t a k e n to a v o i d e n t r a p p e d g a s b u b b l e s .
is su itab le for our w ork ,

T his d e g r e e of a c c u r a c y

but the n a r r o w m o u th of the u s u a l s p e c i f i c -

g r a v it y b o t t l e m a k e s for d if f ic u lt y in i n s e r t i n g s o m e of the s a m p l e s .
H en ce this m eth o d w a s d is c a r d e d .
In m e t h o d (b), w h i c h i s b a s e d o n A r c h i m e d e s ' p r i n c i p l e ,
t h e s o l i d s a m p l e i s p l a c e d i n a v e s s e l an d c o v e r e d w i t h a n o n r e a c t i v e
liquid of s m a l l e r d e n s ity .

A n other n o n r e a c tiv e liquid of d e n s ity

h i g h e r th an th at o f th e s o li d and m i s c i b l e w it h the f i r s t liq u id i s
ad d ed until the s o lid j u s t f lo a t s in the bu lk o f the liq u id .

The density

13

of the liq u id m ix t u r e ,

'w h i c h i s t h u s t h e d e n s i t y o f t h e s o l i d ,

is

t h e n d e t e r m i n e d b y u s e o f s. p y c n o m e t e r .

T h is m ethod is sup p osed

to b e a c c u r a t e t o ' w i th i n 0 . 2 p a r t i n 1 0 0 0 .

T he a c c u r a c y is h ig h er

t h a n t h a t n e e d e d i n o u r w o r k , b u t it s e e m e d w o r t h w h i l e to u s e
t h i s m e t h o d to d e t e c t p o s s i b l e d i f f e r e n c e s in d e n s i t y f r o m s a m p l e
to s a m p l e of th e s a m e m a t e r i a l .
In m e t h o d ( c ) ,

w h ich is again b a se d on A r c h im e d e s ' p r in c ip le ,

the s o l i d s a m p l e i s f i r s t w e i g h e d w h i l e s u s p e n d e d in the a t m o s p h e r e ,
and th e n w h ile i m m e r s e d in a n o n r e a c t i v e liq u id .
the liq u id is d e t e r m in e d by p y c n o m e t e r .

The den sity of

T h e d e n s i t y of the so lid

c a n b e d e t e r m i n e d f r o m the r e s u l t s of the tw o w e i g h i n g s and o f the
pycnom eter m easu rem en t.

T h i s m e t h o d i s s u p p o s e d to b e a c c u r a t e

to w i t h i n 1 p a r t i n 1 0 0 0 w h e n p r o p e r c a r e i s t a k e n ,

in clu d in g p o s s ib le

c o r r e c t i o n s for b u o y a n t f o r c e s and the e f f e c t of s u r f a c e t e n s i o n
on the s u s p e n s i o n w i r e .

The a c c u r a c y is s u ita b le for our w o r k ,

and the a p p a r a t u s i s s im p l e .

H en ce this m eth o d w a s a ls o s e le c t e d

lor actu al u se.
W ith a ll t h e s e m e t h o d s ,

it is n e c e s s a r y to h a v e l iq u id s w h o s e

d e n s i t y is l e s s than that of the s o lid s a m p le .
a r e no

F or lith iu m there

such liqu ids under ordinary conditions.

is n e c e s s a r y to u s e a s i n k e r ,

C o n s e q u e n t l y it

w h ich for our w o r k w a s a p ie c e of

p l a t i n u m w i r e w ou n d a r o u n d the l i t h i u m s a m p l e .

E sp ecial care

14

m u s t t h e n b e t a k e n to r e m o v e g a s b u b b l e s f r o m the a s s e m b l y .
T h e m e t h o d s d e s c r i b e d a b o v e g i v e the e f f e c t i v e d e n s i t y of the
com b in ation ,
be m a d e.

and s e p a r a t e w e i g h i n g s of the s a m p l e and s i n k e r m u s t

C o r r e c t i o n for b u o y a n c y of the a t m o s p h e r e

{which m a y

b e e i t h e r c a r b o n d i o x id e o r a ir ) m u s t o f c o u r s e b e m a d e in a l l
w eighings.
B.

F lotation -E q u ilib riu m P roced u re
T h e f l o t a t i o n - e q u i l i b r i u m m e t h o d w a s t h e o n e w e c h o s e to

use first.

T h e s a m p l e w a s e x t r u d e d f r o m a p r e s s and w r a p p e d

w ith a len gth of p la tin u m w ire.

The r e la tiv e am ounts of lithium

a n d p l a t i n u m w e r e s o c h o s e n a s to g i v e a r e s u l t a n t d e n s i t y o f a b o u t
0. 7 5 g m / c m

•2

, a b o u t m i d w a y b e t w e e n the d e n s i t i e s o f the tw o liq u id s

used (benzene,

0. 87 g m / c m

3

^
h e x a n e , 0. 6 8 g m / c m P ) .

The extruded

l i t h i u m s a m p l e w a s a c y l i n d e r o f 1 / 8 in c h d i a m e t e r and 1 1 / 2 in c h
length.

T he p la tin u m sin k er w a s a 6 - in c h len g th of No.

T h e m a s s o f t h e l i t h i u m w a s a b o u t 150 m g
50 m g .

The lithium w as extruded,

36 w i r e .

, and that of the p la t in u m

w eighed,

wrapped,

in a b o t t l e o f h e x a n e w h i l e i n a C O ^ - f i l l e d d r y b o x .
w a s u s e d i n p r e f e r e n c e to c o m m e r i c a l h e l i u m ,

and p l a c e d

C arbon dioxid e

w h ich ap p aren tly

c o n t a i n s n i t r o g e n w h ic h q u i c k l y t a r n i s h e s the l it h iu m .
The lith iu m ,
bottle of h ex a n e,

w rap p ed w ith p latin u m ,

w a s s u b m e r g e d in a

w h i c h w a s t r a n s f e r r e d to a t e m p e r a t u r e b a t h

c o n t r o lle d at 2 5 °C .

S m a ll b o t t l e s of h e x a n e and b e n z e n e w e r e

15

a l r e a d y in the bath.

After eq u ilib riu m w as e sta b lish e d ,

sm all

a m o u n t s o f b e n z e n e -were a d d e d to the t e s t b o t t l e o f h e x a n e u n t il
t h e l i t h i u m s a m p l e s w e r e o b s e r v e d to b e j u s t f l o a t i n g i n t h e b u l k
of the liq u id .

It w a s o b s e r v e d tha.t t w o d r o p s o f b e n z e n e i n a b o u t

25 c c of h e x a n e p r o d u c e d a n o t i c e a b l e e f f e c t on the f l o a t i n g s a m p l e .
T h e e x t r a b o t tle of h e x a n e w a s a v a ila b le in c a s e too m u c h b e n z e n e
s h o u ld b e a d d e d to the t e s t b o t t l e .
by m ed icin e droppers,

The liq u id s w e r e tra n sp o rted

and c a r e w a s ta k e n to a s s u r e g o o d m i x i n g .

R e p r o d u c i b i l i t y b y t h i s m e t h o d w a s o f t h e o r d e r o f 3 p a r t s i n 10, 0 0 0 ,
as sh o w n b y two d e t e r m in a t io n s on one s a m p le
and No.

12 i n F i g u r e 1).

S o m e of the s a m p l e s t e s t e d ,

of h a v in g h e a v y i n c lu s i o n s or v o id s ,
ra z o r blade.
observed.

(se e t r i a l s No.

11

suspected

w e r e c a r e f u lly cut w ith a

In s e v e r a l c a s e s t h e s u s p e c t e d i m p e r f e c t i o n s w e r e

F a m i l i a r i t y w ith the t e c h n iq u e s o o n e n a b l e d u s to a s c e r ­

ta in w h e t h e r or n ot the s a m p le w a s r e a s o n a b l y good.
A fte r d e t e r m i n i n g the d e n s i t y o f the liq u id ,

the d e n s i t y o f the

lit h i u m c o u ld be c a lc u l a t e d f r o m the f o r m u la

p —

M*d A _ _ _ _ _ _ _
Ma

where

-

n„ e./fK

= m a s s of the lit h iu m ,

= d e n s i t y of the liq u id = d e n s i t y

of the c o m b in a t i o n of the lit h iu m w r a p p e d w ith p la tin u m ,
of the c o m b in a t i o n ,

Mc = m ass

M p t = m a s s o f the p l a t i n u m and ^ p t ~ d e n s i t y

16

o

©

/d

NUMBER

o J

TRIAL

n&'- u r a

In

©

*n

X

o

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o _

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£

£

—d
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v.
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( t^ V « « 6 ) A 1 I S N 3 G

o f th e p l a t i n u m ,

2 1 .4 g m /cm ^ .

C h o i c e o f t h e s a m p l e s i z e 'was

m a d e s o t h a t t h e f o r m u l a w o u l d b e n e a r l y i n s e n s i t i v e to t h e v a l u e
for d e n s ity of the p la tin u m .

A s it t u r n e d o u t ,

the s e c o n d t e r m

i n t h e d e n o m i n a t o r w a s a b o u t 0. 05% o f t h e f i r s t t e r m ,

and h e n c e

an y u n c e r t a i n t y in the d e n s i t y of platinum e x e r t s a n e g l ig i b le e f f e c t
on the fin a l r e s u l t .
w ith the lith iu m

S e v e r a l d e te r m in a tio n s of d e n s ity w e r e m a d e

a n d a r e p l o t t e d i n F i g u r e 1..

In u s i n g t h i s m e t h o d

it w a s o b s e r v e d th at the s h in y s u r f a c e of the l i t h i u m b e c a m e v i s i b l y
d a r k e n e d w h e n l e f t in the liqu id for m o r e than a few m in u t e s .
T h i s r e a c t i o n w a s t r a c e d to t h e l i q u i d o t h e r t h a n b e n z e n e ,
to t h e h e x a n e a n d t h e h e p t a n e .
sod iu m ,

Benzene,

itself,

i.e. ,

when dried over

did not d a r k e n lit h iu m e v e n w h en the lit h iu m

w as placed

in it for a p e r i o d of s e v e r a l m o n t h s .
C.

H y d rostatic-B alan ce P roced u re
T h e r e a c t i v i t y of the liq u id s o th e r than b e n z e n e ,

together

w ith the r a t h e r lo n g t i m e r e q u i r e d in the f lo t a tio n m e t h o d ,

led us

to c o n s i d e r the p o s s i b i l i t y of u s i n g the h y d r o s t a t i c - b a l a n c e m e t h o d
w h ich,

although p o s s ib ly l e s s a c c u r a te ,

w ou ld be q u ic k e r and w ou ld

e l i m i n a t e the c o n t a c t o f the lit h iu m w ith the r e a c t i v e liq u id s .

The

l it h i u m w a s p r e p a r e d and w e ig h e d in an a t m o s p h e r e of c a r b o n
dioxide.

T h e n it w a s w r a p p e d w i t h t h e p l a t i n u m s i n k e r a n d h u n g f r o m

18

a f i n e ■wire.

T h e c o m b i n a t i o n ■was s u b m e r g e d i n b e n z e n e a n d t h e n

w eig h ed again.

T h e d e n s i t y of th e b e n z e n e %as d e t e r m i n e d b y

use of a p ycn om eter,

and the d e n s i t y of the l i t h i u m w a s c a l c u l a t e d

a c c o r d i n g to th e f o l l o w i n g e q u a tio n :

P zr
jL i

iV P
/ ( W i
3' ' C a H t / I
1

w h e r e w . i s the w e i g h t of the l i t h i u m in c a r b o n d i o x i d e and w
i s t h e - w e ig h t l o s t w h e n s u b m e r g e d i n t h e b e n z e n e .
D.

P y c n o m e te r C alibration
T h e p y c n o m e t e r u s e d in the d e t e r m i n a t i o n o f the d e n s i t i e s

of the liq u id s w a s a 5- m l p y c n o m e t e r type M - 3 0 8 0 m a n u f a c t u r e d
b y t h e H.

S.

M artin C om pany,

Evanston,

Illin ois.

It w a s c a l i b r a t e d

by m a k in g four c a li b r a t io n ru n s w ith v e r y p u r e b e n z e n e and w a te r
at a s ta n d a r d t e m p e r a t u r e of Z5°C .

T he b e n z e n e had b e e n r e c r y s ­

tallized m any tim e s by P r o fe s s o r R o g ers,

who had c h e c k e d the d e n ­

sity of the r e s u lt in g m a t e r i a l v e r y a c c u r a te ly .

The w a te r had b e e n

f r e e d f r o m io n ic m a t e r i a l b y p a s s a g e th r o u g h a b e d of i o n - e x c h a n g e
resin ,

a n d i t s p u r i t y i s b e l i e v e d to e x c e e d t h a t o f o r d i n a r y c o n d u c ­

tivity w a ter.

T h e c a l i b r a t i o n c u r v e s a r e g i v e n i n F i g u r e 2.

S e v e r a l p o i n t s m u s t b e c o n s i d e r e d in c o n n e c t i o n w ith the
w e ig h in g of the s u b m e r g e d s a m p le .

T h e e f f e c t of the s u r f a c e

t e n s i o n o f the b e n z e n e w a s c a l c u l a t e d to b e a b o u t 1 d y n e , b u t s i n c e
the w i r e h o ld in g the l it h i u m w a s w e ig h e d in the s a m e p o s i t i o n b o th

S. 1100

VOLUME

(>nJ)

19

s;o b 7 * L

Z

3

S

6

pyCA/OMFTER READING
Figuye

Z

P y c n o m e t e r c a l i b r a t i o n : v o l u m e in m i l l i l i t e r s a s a f u n c t io n o f s c a l e r e a d i n g .
S ta n d a r d liqu ids: b e n z e n e and w a t e r .

zo

w ith and w ith o u t the lit h iu m ,
ten sio n w as n egligib le.

the c h a n g e in w e i g h t due to the s u r f a c e

T h e h e ig h t of the liq u id w a s k ep t n e a r l y

c o n s t a n t b e t w e e n the w e i g h i n g s so the s m a l l e f f e c t of the liq u id
d i s p la c e d b y the w ir e w a s r e n d e r e d n e g lig ib le .
a t 2 5 . 0 tfc 0. 5 ° C f o r a l l t h e w e i g h i n g s .

The box w as kept

A tem p eratu re differen ce

of 1°C w o u ld c a u s e a v a r i a t i o n in the d e n s i t y of b e n z e n e a m o u n t in g
to a b o u t 1 p a r t in 1 000,

and h e n c e in d u c e a p o s s i b l e e r r o r of th is

a m o u n t in the d e n s i t y of the l i t h i u m s a m p l e .

C H A P T E R IV
B U L K DENSITY:
A.

R E S U L T S A N D DISCUSSION

N atu ral L ithiu m
Both m eth o d s

(b) a n d (c) w e r e u s e d f o r t h e d e t e r m i n a t i o n o f

the d e n s it y of n a tu r a l lith iu m .

T h e r e s u l t s a r e p l o t t e d in F i g u r e

1.

T h e f lo t a t i o n m e t h o d g a v e an a v e r a g e v a lu e for the d e n s i t y of
0. 5 3 1 6 g m / c m

.

T he h y d r o s t a tic b a la n c e m eth o d g a v e an a v e r a g e

v a l u e o f 0. 5 3 0 5 g m / c m

•3

.

T h is a g r e e m e n t ,

s a m p le - t o - s a m p le variab ility.

we feel,

is w ith in the

It w i l l b e n o t e d t h a t t h e f l o t a t i o n

m eth o d gave a sligh tly higher value.

A p o s s ib le exp lan ation is

that d e n s e r e a c t io n p r o d u c ts w e r e fo r m e d b y the liq u id s u se d
in the f lo t a tio n m e t h o d .

T h e r e s u l t s c a n be c o n s o li d a t e d in sta tin g

t h e d e n s i t y o f n a t u r a l l i t h i u m i s 0. 5 31 g m / c m
B.

.

Separated Isotopes
T h e h y d r o s t a t i c b a la n c e m e th o d w a s u s e d e x c l u s i v e l y for the

d e n s i t y d e t e r m i n a t i o n s of the i s o t o p e s .
i n F i g u r e 3.

The r e s u lt s a r e plotted

T h e r e w e r e two b a t c h e s of lit h iu m - 6 a s d e s c r i b e d

in the s e c t i o n o f p r o c u r e m e n t of s a m p l e s .
for the d e n s i t i e s a r e a s follow s:

The average values

22

•""I
• 2SC
—
-J ^

-Q

©

(f

1 M

°

CC

°0

LxJ
CQ

<

^

00
V

>

_

to
cn

of s u c c e s s i v e

K-

O
Q_

Q_

£
<?
on

£

“0
o
o

<!
<n

sO

*~0
<-o

V
o
o
Q_

- *o

of i s o t o p e s :

0

o

O.SSOOY

©

o
o
o
to
(^ y m e ) A iisN a a

trial by h y d r o s t a t i c

—

O

3

^r>

results

\

<5>
o

Density

sa

balance,

Ui

23

Isotope

Sam ple

L i6

S S 5 (a)

L i6

S S 5 (b)

L i7

6 6 8 (j)

D ensity
0.4 7 4 7 g m / c m 3
ORNL
0 .4600
De sign ations

T -nat
Li

0. 5 3 6 8

L ith iu m C o r p o r a tio n of A m e r ic a

0. 5 3 1

S a m p le SS5(a) o f l it h i u m - 6 s e e m s a n o m a lo u s ly d e n s e .
v a lu e s found a r e r e p r o d u c ib le ,

The

and w e f e e l that t h e y a r e r e l i a b l e .

We h a d c o n j e c t u r e d t h a t e n r i c h m e n t o f t h e h e a v y i s o t o p e m i g h t
take p la c e during d istilla tio n ,

but Dr.

B a k e r in f o r m e d us that

n e g lig ib le e n r ic h m e n t o c c u r s upon d istillation .
s a m p l e that i s m u c h too d e n s e ,
estab lish ed ,

N e g le c tin g this

f o r r e a s o n s -we h a v e n o t y e t

the f o llo w in g v a l u e s for the d e n s i t i e s of n a t u r a l l it h i u m

a n d i t s i s o t o p e s c o r r e c t e d t o 100% at 2 0 ° C c a n b e g i v e n a s
Li

6

0 .4 6 0 ± 0 .0 0 2

g m /cm

3

Li

0. 5 3 7 A 0 . 0 0 3 g m / c m 3

L inat

0. 5 3 1 L 0 . 0 0 1 g m / c m 3

T h e l i m i t s a r e ou r i n f o r m a l e s t i m a t e s on the o v e r a l l a c c u r a c y of
the d e t e r m i n a t i o n s .
C o r r e c t i o n s to the r a w d e n s i t y d e t e r m i n a t i o n s m u s t b e m a d e
for four e ffe c ts:

1)

the b u o y a n t e f f e c t of the a t m o s p h e r e

o n b o t h t h e s p e c i m e n a n d t h e - w e i g h t s ; 2)

(CO 2 )

t h e c a l i b r a t i o n s to t h e

24

w eights;

3)

t h e i m p u r i t i e s i n t h e s a m p l e ; 4)

te m p e r a tu r e (20°C).
a t 2 5 ° C t o b e 2 x 10

r e d u c t i o n to s t a n d a r d

T a k i n g t h e d e n s i t y o f CO ^
^ g m /cm ^ ,

one a tm o sp h e r e

and the c e r t i f i c a t i o n of the w e i g h t s *

t h e f i r s t t w o c o r r e c t i o n s a m o u n t e d to a n i n c r e a s e o f 2. 7 p a r t s p e r
thousand.

C o r r e c t i o n s for the i m p u r i t i e s w e r e m a d e a c c o r d in g

to the f o r m u l a

where

^

= true density,

im p u rities,

M= m e a s u r e d d e n s i t y ,

A and B = %

a and b = r e s p e c t i v e im p u r it y d e n s i t i e s .

The c o r r e c ­

t i o n to 2 0 ° C w a s m a d e b y u s i n g t h e c o e f f i c i e n t o f e x p a n s i o n ^ .
T h i s c o r r e c t i o n a m o u n t s to a d d i n g 4 x 1 0 “^.
C.

C ry sta l D en sity
T h e d e n s ity for an id e a l c u b ic c r y s t a l can b e c o m p u te d f r o m
3

the e x p r e s s i o n

f*

- n M /(N a Q ) w h ere M = a to m ic w eight,

N = A vogad ro's num ber,

a

= lattice constant,

o f a t o m s i n t h e u n i t c e l l . (At r o o m t e m p e r a t u r e ,

and n = n u m b e r
lith iu m c r y s t a l ­

l i z e d i n t h e b o d y - c e n t e r e d c u b i c s t r u c t u r e f o r w h i c h n - 2. )
With the v a l u e of a G fo r n a t u r a l l i t h i u m
g m /cm

3

7

w e f i n d a v a l u e o f 0. 53 34

for the c r y s t a l d e n s i t y of n a tu r a l lith iu m .

th is value is l e s s

We n o t e t h a t

than the e x p e r i m e n t a l v a lu e of 0 .5 3 4

found by R i c h a r d s and B r i n k

3

for the bulk d e n s ity .

g m /cm ^

With m o s t

25

m a t e r i a l s t h e v a l u e o f t h e b u l k d e n s i t y i s f o u n d to b e 0. 1% to l'/o
s m a l l e r th a n the crysta.1 d e n s i t y ,
in m a c r o s c o p i c c r y s t a l s .

V a l u e s of the l a t t ic e c o n s t a n t for the

is o t o p e s g iv en by C ovington^ are:
3. 5 0 9 2 A .

in the

Li^,

a

o

= 3 . 5 1 0 7 A ; Li"^ , a ~ =

U s i n g t h e s e v a l u e s w e find the c r y s t a l d e n s i t i e s for the

i s o t o p e s to b e
g m /cm

o w i n g to t h e i m p e r f e c t f o r m a t i o n

.

Li^, £

-

0 . 4 6 2 3 g m / c m ^ and for L i ^ ,

f*

- 0. 5 3 8 9

It w i l l b e n o t e d t h a t t h e v a l u e s o f t h e b u l k d e n s i t i e s f o u n d

p r e s e n t s t u d y a r e a b o u t 0. 5% l e s s t h a n t h e c r y s t a l d e n s i t y

value s .
D.

P r o je c te d W ork
T h e w o r k d o n e on the l a t t i c e c o n s t a n t and b u lk d e n s i t y o f

l i t h i u m i s o t o p e s c o u l d v e r y p r o f i t a b l y b e e x t e n d e d to o t h e r i s o t o p e s
now a v a ila b le.

S o m e of th e s e a r e lis t e d b e lo w w ith th eir n a tu ra l

abundance ratios:

Abundance R atios

R elative M a ss
D ifference

E lem en t

Isotope s

S ilicon

2 8 , 30

92 . 17%,

3. 2%

7%

C alciu m

40, 44

96. 9%,

2. 1%

10%

M agn esiu m

24, 26

78.8% ,

11.1%

T h e s e e x a m p l e s h a v e m a s s d i f f e r e n c e s l a r g e e n o u g h to b e r e a d i l y

26

m e a s u r e d b y the t e c h n i q u e s d e s c r i b e d in t h is t h e s i s .
m ents

M easure­

o n e l e c t r i c a l r e s i s t i v i t y w ould be of i n t e r e s t .
M e a s u r e m e n t s of the d e n s i t y a s a fu n c tio n of t e m p e r a t u r e

o v e r a r e a s o n a b ly w ide ra n g e w ould be v a lu a b le.

P lans are u n d er­

w a y to m a k e t h e s e m e a s u r e m e n t s in the n e a r f u tu r e .

The m ethod

e n v i s i o n e d i s to find the c o e f f i c i e n t of l i n e a r e x p a n s i o n f r o m n e a r
the m e l t i n g p o in t (about 1 8 0 °C ) to liq u id h e l i u m t e m p e r a t u r e s ,
to c o m p u t e the b u lk d e n s i t y f r o m th is c e o f f i c i e n t .

and

CHAPTER V
E L E C T R I C A L RESISTIVITY:
In a p e r f e c t l a t t i c e ,

T H E O R E T IC A L CO N SID ER A TIO N S

the e le c t r o n s have sta tio n a r y s ta te s

in w h ic h the m e a n v e l o c i t y and h e n c e the m e a n t r a n s p o r t of c h a r g e
and e n e r g y do n o t v a n is h .
tiv itie s w ould b e z e r o .

H e n c e the e l e c t r i c a l and t h e r m a l r e s i s ­

T h e r e s i s t i v i t i e s o c c u r r i n g in p r a c t i c e

a r i s e f r o m d i s t u r b a n c e s f r o m p e r f e c t p e r i o d i c i t y of the p o t e n tia l
f ie ld in w h ic h the e l e c t r o n s m o v e .
three sources:
im p erfectio n s;

T h e se d isturban ces ca m e from

a) l a t t i c e v i b r a t i o n s ; b) i m p u r i t i e s a n d l a t t i c e
a n d c) i n t e r a c t i o n s b e t w e e n e l e c t r o n s .

p u re c r y s t a l at o r d in a r y t e m p e r a t u r e s ,
is the m o s t im p o rta n t.

F o r a good

the f i r s t of t h e s e d i s t u r b a n c e s

T h is fa ct e x p l a in s the q u a lita tiv e o b s e r v a t i o n

that the r e s i s t a n c e of an id e a l m e t a l d e c r e a s e s w ith d e c r e a s i n g
tem peratu re.

A d d i t i o n a l a n a l y s i s i s r e q u i r e d to e x p l a i n t h e q u a n t i ­

t a t i v e o b s e r v a t i o n t h a t t h e r e s i s t a n c e g o e s to z e r o a s t h e a b s o l u t e
t e m p e r a t u r e g o e s to z e r o ,

s in c e the z e r o - p o i n t m o t i o n o f the a t o m i c

c o r e s m i g h t b e e x p e c t e d to p r o d u c e a l a r g e r e s i d u a l r e s i s t a n c e f o r
all m e t a ls .

T h e e x p l a n a t i o n l i e s in the c o n d i t i o n s on s c a t t e r i n g

i m p o s e d b y the c o n s e r v a t i o n l a w s and the d i s t r i b u t io n of e l e c t r o n
ene rgie s .
D e s p i t e the s e v e r e a p p r o x i m a t i o n s w h ic h m u s t b e m a d e in

28

d e v e lo p in g the th e o r y of r e s i s t i v i t y ,

th ere is g e n e r a l a g r e e m e n t

that for t e m p e r a t u r e s far ab ove s o m e c h a r a c t e r is t ic te m p e r a tu r e
the a n a l y s i s is a d e q u a te .

Sim ilarly,

for v e r y low t e m p e r a tu r e s

the a n a l y s i s a p p e a r s r e a s o n a b l y s a t i s f a c t o r y .

B u t for i n t e r m e d i a t e

t e m p e r a t u r e s no r e a l l y s a t i s f a c t o r y t r e a t m e n t h a s a p p e a r e d .
h a s s u m m a r i z e d t h e w o r k up u n t i l 1 9 5 3 .

W ilson

T h e a n a l y s i s is too c o m ­

p l i c a t e d to s e t f o r t h b r i e f l y .
A lth o u g h it i s o n ly an a p p r o x i m a t i o n ,
the to ta l r e s i s t a n c e ^

i t i s u s e f u l to c o n s i d e r

a s m a d e up o f t h r e e p a r t s c o r r e s p o n d i n g

to t h e l a t t i c e d i s t u r b a n c e s l i s t e d a b o v e :
f

=

/ lattice vibration s

where

P
* la ttice vibrations

and t e m p e r a t u r e ,

P
'

and

f* im p u rities

/" electron -electron

is depen d en t on a to m ic m a s s

is in d ep en d en t of t e m p e r a tu r e ,
im p u rities

P

is n e g lig ib le e x c e p t at the v e r y l o w e s t

* electro n -electro n

tem peratures.

F o r t h e p r e s e n t e x p e r i m e n t s i t i s n e c e s s a r y to

f i n d a r a n g e o f t e m p e r a t u r e l o w e n o u g h f o r t h e f i r s t t e r m to s h o w
a p p r e c i a b l e d e p e n d e n c e on a t o m i c m a s s and at the s a m e t i m e
h i g h e n o u g h f o r t h e s e c o n d n o t to s w a m p it.

F o r t u n a t e l y the

t h ir d t e r m i s s m a l l e n o u g h to b e i g n o r e d .
T h e a n a l y s i s of

is b a s e d on the s c a t t e r i n g

P

' lattice vibrations
of e le c t r o n w a v e s on sound w a v e s

(p h on on s) in the c r y s t a l .

The

s c a t t e r i n g is n o t c o n t r o lle d b y the a m p litu d e of the sound w a v e a lo n e ,
but a ls o b y the r e s t r i c t i o n s of c o n s e r v a t io n of m o m e n t u m ,
servation of en ergy,

the c o n ­

and the s t a t i s t i c a l d i s t r i b u t i o n of the e l e c t r o n s .

A t l o w t e m p e r a t u r e s t h e s e l a s t f a c t o r s c o m b i n e to p r o d u c e a f i f t h p o w e r d e p e n d e n c e o f r e s i s t i v i t y o n a b s o l u t e t e m p e r a t u r e T.

At

h ig h t e m p e r a t u r e s o f c o u r s e the s q u a r e of the a m p li t u d e of the a t o m i c
c o r e d i s p l a c e m e n t is the c o n t r o l l in g f a c t o r ,
o n ly a s the f i r s t p o w e r of t e m p e r a t u r e .

and the r e s i s t i v i t y r i s e s

The detailed c o n sid e r a tio n

o f t h e s e f a c t o r s l e a d s to t h e B l o c h - G r l i n e i s e n f o r m u l a ,

w h ich a ttem p t

to h a n d le the t e m p e r a t u r e d e p e n d e n c e o f r e s i s t i v i t y w ith a s i n g l e
p aram eter,

the c h a r a c t e r i s t i c t e m p e r a t u r e

0

In p r i n c i p l e t h i s

c h a r a c t e r i s t i c t e m p e r a t u r e sh o u ld b e the s a m e a s the D e b y e c h a r a ­
cteristic tem perature

& Y )' k ut it i s m o r e

s a t i s f a c t o r y to t a k e

0

a s an a d j u s t a b l e p a r a m e t e r to b e d e t e r m i n e d b y e x p e r i m e n t .
T he e x p r e s s i o n for the r e s i s t i v i t y
atom ic m a ss M

of an e le m e n t of

a c c o r d i n g to t h e B l o c h - G r i i n e i s e n f o r m u l a i s

w h e r e B is v e r y n e a r ly a c o n s ta n t for the s a m e e le m e n t.
i s a f u n c t i o n e q u a l to

^

, where

H ere

G f*

is defined

30

and t a b u l a t e d in s u c h r e f e r e n c e s a s

2:

again st

Wilson*

i n the r e g i o n of i n t e r e s t .

The c o m p a r i s o n of the

f o r m u l a w i t h e x p e r i m e n t i s u s u a l l y m a d e b y c o m p u t i n g the
r e q u i r e d to o b t a i n a g r e e m e n t ,

G\(^)

F igure 8 shows

0

and t h e n e x a m i n i n g i t s c o n s t a n c y .

9

S u c h a c o m p a r i s o n f or l i t h i u m h a s b e e n m a d e by K e l l y & M a c D o n a l d .
F o r our p u r p o s e s it i s b e t t e r to c o m p a r e e x p e r i m e n t a l and
t h e o r e t i c a l r a t i o s of n o r m a l i z e d r e s i s t i v i t i e s

P

J FI

for two i s o t o p e s a s a f u n c t i o n of t e m p e r a t u r e .

(or r e s i s t a n c e

Rr^l )

L e t t h i s r a t i o be

c a l l e d r; we h a v e
r

Ru-JT) / R

n -

R ^ y ( T ) / Ru

*

and

u -6.

( T 0)

— ----------------------- —-------------------------------

exptl -

r ,
theor -

K

-

(

T

)

/

A

-

------------------ -------------------

7

(To)

( T---ro )--------

A (T) / A ( T.)

G ( % / t ) / g ( & / t. }
G '(e,/T)/G ($,/T .)

.

A 7 G\

h b

But s in c e

k ^

=

k

&*

w h e r e h i s P l a n c k ' s c o n s t a n t and k i s B o l t z m a n n ' s c o n s t a n t ,

* A.

H.

W ilson,

T he T h e o r y of M e ta ls ,

in

2nd ed. , ( C a m b r i d g e , 1953)

31

1.0

0 -8

0.6

2

Z = ® / T
F igu re

8

G r a p h o f d e r i v e d G r u n e i s e n f u n c t i o n G (z ) v e r s u s z.

32

the r e la t io n c o n n e c tin g c h a r a c t e r i s t i c f r e q u e n c y
ch a ra cteristic tem perature

^

is s o m e

given ele m en t,

; and s in c e

= b /n J

(ztt
where

w i th

so r t of sp r in g co n sta n t w h ich is c o n sta n t for a

it is s e e n that

= M(K/2Trk)Vb/n) = b ( * / k f
is a c o n s t a n t for isotopes of the s a m e e l e m e n t .

H e n c e the fin a l f a c t o r

in the e x p r e s s i o n for r,,
m a y be dropped.
^
theor
1
The th ree p a r a m e te r s

? Q j

and

to tw o b y d e f in i n g

=

and

Then r

theor

& (, /

@7

y =

& i/%

x

'T./T

=

,
,

becom es

y
£A" r

= G

9 *) G» ( i )

G ( y x ) G ^ y )

/’/^

m ay be reduced

We m a y c o n s i d e r

oC

c o n s t a n t fo r a g i v e n p a i r o f i s o t o p e s ,

and

e q u a l to

* = 9 j e 1= j h j / h i
S u it a b le v a l u e s of the p a r a m e t e r
r e s u lt s for n a tu ra l lith iu m .
range
and

3 3 0 ° K t o 360K.
T o

If

=

{ l o m / c .o n o

can be e stim a te d

The p a ra m eter
0 ?

is c h o sen as 295°K ,

if

=

0 7 / %

1.0200

f r o m the

li-e s i n

i s t a k e n to b e a b o u t t h e s a m e a s
the p a r a m e t e r

~

3 *r /£ is"

In t h e n e x t s e c t i o n i s s h o w n a p l o t o f r

Vx = T /r,

=

for v a lu e s of

tj

theor

l i e s in the r a n g e

1.1 S
-

against

i n t h e n e i g h b o r h o o d o f 1. 15.

T h e c u r v e i s n o t v e r y s e n s i t i v e to the e x a c t c h o i c e o f th e v a l u e of
It i s t h i s c u r v e w h i c h i s t o b e c o m p a r e d w i t h e x p e r i m e n t .

C H A P T E R VI

E L E C T R I C A L RESISTIV ITY:

APPARATUS

T h e a p p a r a t u s for th is e x p e r i m e n t c a n b e g r o u p e d into t h r e e
parts:

the s a m p l e s and h o l d e r ,

the c r y o s t a t ,

A b l o c k d i a g r a m i s s h o w n in F i g u r e 4 ,

the m e a s u r i n g d e v i c e s .

and p h o t o g r a p h s o f the a p p a r a t u s

a r e s h o w n in F i g u r e s 7b and 7c.
A.

K elvin B rid ge
T h e f o r m o f the s a m p l e w a s c h o s e n w it h the id e a o f e v e n t u a l l y

m a k in g a m e a s u r e m e n t of the a b s o lu t e r e s i s t i v i t y .
m ent,

F or such a m e a s u r e ­

the d i m e n s i o n s m u s t be k n ow n w ith h igh a c c u r a c y .

H owever

the s m a l l a m o u n t of m a t e r i a l a v a ila b le lim it e d the v o lu m e of the
sam p le.

N o w it d o e s n o t s e e m r e a s o n a b l e to s u p p o s e th a t the e f f e c t i v e

d i a m e t e r o f a l o n g l i t h i u m w i r e c a n b e m e a s u r e d to a n a c c u r a c y g r e a t e r
t h a n 10 m i c r o n s .

W ith this v a lu e ,

an a c c u r a c y o f 2 p e r c e n t in the

c r o s s s e c t i o n a r e a d e t e r m in a tio n w ould r e q u ir e
w i r e to b e n o l e s s th a n 1 m m .

T his s iz e w as

the d i a m e t e r o f

accord in gly selected .

35

<A
£:

^
cj

<u
O r
—

~

^

s:
<3

5T

V
<u
-Vj
<u

£
o
+-»
&
<u
\~ j
o
Q_

.

♦--

S.
aj
-v>
qJ

jr
.2
+->

5

■m
O
C L.

-

QJ

5-

ul

<D

a

<D
Vi
3
w
cti
0

S
Vi

o

M-l

cn
3
rd
Vi
03
a
CL
OS

-i->

5

a

fd
Vi
M
cd

• rH

xs

u
o

r—H

S 6 m p/e

<u

36

T he a m o u n ts of se p a r a te d is o t o p e s on hand w e r e only a g r a m
or two.

S everal rep lication s are d esira b le.

It w a s d e c i d e d t h a t

a b o u t 100 to 150 m g c o u l d b e u s e d fo r a s a m p l e .

The co rresp on d in g

l e n g t h o f 1 m m w i r e i s a b o u t 30 c m . , w i t h r e s i s t a n c e a b o u t 4 0
m ilo h m s at r o o m te m p e r a tu r e ,

d e c r e a s i n g to ab ou t a te n th of

that a m o u n t at 7 7 °K .
The ch o ice of a m e a s u r in g m eth od lay b e tw e e n a p o te n tio m ete r
m ethod,

w ith the c u r r e n t d e t e r m i n e d w ith the aid of a s ta n d a r d

resistor,

and the K e lv in d ou b le b r id g e .

constant,

the p o t e n t i o m e t e r m e th o d o f f e r s s o m e c o n v e n i e n c e

On the o t h e r h a n d ,

If t h e c u r r e n t c a n b e k e p t
.

the K e lv in b r id g e d o e s not r e q u i r e a p a r t i c u l a r l y

s te a d y c u r r e n t supply.

T h e c h i e f o b j e c t i o n to i t s u s e i s the e x i s t e n c e

of sp u r io u s t h e r m a l v o lta g e s .

T h ese e ffects can be elim in a ted by

r e v e r s i n g the m e a s u r i n g c u r r e n t ,

and a v e r a g i n g the r e s u l t s .

T h is

p r o c e d u r e i s s a t i s f a c t o r y p r o v i d e d the t h e r m a l v o l t a g e s do n ot
change betw een r e v e r s a ls .

W ith the p r e s e n t e x p e r i m e n t a l p r o ­

c e d u r e the c h a n g e s w e r e s lo w and no d iff ic u lt y w a s fou n d in r e ­
p e a tin g the m e a s u r e m e n t s .
B ..

S a m p le H old er
T h e s a m p l e h o l d e r w a s d e s i g n e d to f u r n i s h p h y s i c a l s u p p o r t

f o r t h e r e l a t i v e l y s o f t l i t h i u m w i r e a s w e l l a s to p r o v i d e c u r r e n t

37

and p o t e n tia l c o n t a c t s on the lit h iu m s a m p le .
s u p p o r t •was c o n s t r u c t e d s o a s t o h o l d s i x t e s t
two e a c h o f l it h i u m - b ,

The m ain sam p le
s a m p l e s at a t i m e ,

lit h iu m -7 , and n a t u r a l l it h iu m .

The d im e n ­

s i o n s w e r e k e p t s m a l l b e c a u s e of the l i m i t e d s i z e of the D e w a r f l a s k
and b e c a u s e o f th e n e e d to m i n i m i z e t e m p e r a t u r e g r a d i e n t s .
top v ie w of the s a m p l e h o ld e r is s h o w n in F i g u r e

5.

The sa m p les

a r e lo c a t e d s y m m e t r i c a l l y about the c e n t r a l b r a s s r o d ,
a s a c o m m o n le a d and su p p o rt shaft.
i n g s a r e s h o w n i n d e t a i l i n F i g u r e 6.
c o m m o n to e v e r y s a m p l e ,

w h ich s e r v e s

The in d ivid u al s a m p le m o u n t ­
One c u r r e n t le a d ,

w a s the 5 / 8 - i n c h b r a s s r o d ,

s o l d e r e d to t h e b o t t o m b r a s s p l a t e .

A

w h ich w a s

silv er-

The individu al c u r r e n t le a d s

for the s a m p l e s w e r e r u n to a n e x t e r n a l h e a v y - d u t y c u r r e n t s w i t c h .
T h e s w i t c h w a s a s i x - p o s i t i o n s w i t c h to a l l o w s e l e c t i o n o f t h e s a m p l e
for the c u r r e n t path.

The low er potential c o n ta cts,

m ade through

t h e s p r i n g - l o a d e d c o n t a c t s o l d e r e d to a b r a s s s c r e w m o u n t e d i n
lu cite,

w e r e c o n n e c t e d to a c o m m o n l e a d t h a t w e n t d i r e c t l y to t h e

K elvin b r id g e.

S i x 3 / 8 - i n c h h o l e s w e r e d r i l l e d in the u p p e r l u c i t e

p la te th r o u g h w h ic h s m a l l c o n n e c to r c lip s c o u ld b e a tta c h e d to the
upper poten tial le a d s,
and m o u n tin g .
sw itch.

s i m i l a r to t h e l o w e r o n e s i n c o n s t r u c t i o n

T h e s e l e a d s w e r e t h e n r u n to a n e x t e r n a l l i g h t - d u t y

T h i s s w i t c h w a s a s i x - p o s i t i o n s w i t c h to a l l o w s e l e c t i o n

of s a m p le .

38

W a 11 o -f
DeWdv Fld.sk

Cooling

\

figuYe

S am ple holder

(top v i e w ) .

5

39

Lucite

L ucite

L u c ite

Fi<^ u. r e

Sam ple holder

(detail).

6

40

C.

C ryostat
T h e c r y o s t a t a r r a n g e m e n t i s s h o w n s c h e m a t i c a l l y in F i g u r e 7 a ;

and p h o t o g r a p h s o f it and its c o n t e n t s a r e g i v e n in F i g u r e s

7b a n d 7 c .

The c r y o sta t its e lf c o n s is te d of a s t a in le s s - s t e e l D ew ar fla sk *
w i t h i n s i d e d i m e n s i o n s o f 6 i n c h e s d i a m e t e r a n d 18 i n c h e s d e p t h .
A c o o lin g c o il of 1/ 4 - i n c h c o p p e r tubing w a s wound around a h o llo w
b r a s s c y l i n d e r 5 i n c h e s in d i a m e t e r and 6 i n c h e s d e e p in s u c h a
w a y that the in ta k e and e x h a u s t t u b e s w e r e s id e b y s id e at the top
of the c y l i n d e r ,

a n d w e r e j o i n e d at t h e b o t t o m .

T h u s the i n c o m ­

ing c o ld and o u tg o in g w a r m e r g a s e s w e r e p l a c e d a d j a c e n t in o r d e r
to f a c i l i t a t e t h e r m a l e q u i l i b r i u m .
to t h e b r a s s c y l i n d e r .

T he Coils w e r e s o f t - s o l d e r e d

P r o v i s i o n w a s m a d e for the e x h a u s t g a s e s

to p a s s t h r o u g h a n o t h e r c o i l b e f o r e g o i n g t o t h e o u t s i d e a t m o s p h e r e .
T h is seco n d ,

and m u c h s m a l l e r c o il,

c o n s i s t e d of t h r e e tu rn s of

1 / 4 - i n c h c o p p e r tubing wound around a so lid 2 - in c h b r a s s c y lin d e r .
T h i s c y l i n d e r w a s d r i l l e d to t a k e the 5 / 8 - i n c h b r a s s r o d th a t c o n ­
s tit u te s the l o w - r e s i s t a n c e c u r r e n t lea d and m e c h a n i c a l su p p o rt
for the s a m p l e h o l d e r s .

T h is s e c o n d c o i l w a s p r o v i d e d to d e c r e a s e

* A ll - stain le s s standard open D ew ar flask , C atalog No. E2,
6 " x 18", m a n u f a c t u r e d b y H o fm a n L a b o r a t o r i e s , N e w a r k ,
New Jer s e y .

41

To liquid A/

C ryostat A rrangem ent.

To p u m p

+3

rz.

44

the h e a t flow into the t e s t c h a m b e r th r o u g h the b r a s s rod.

F o r the

s a m e r e a s o n the e l e c t r i c a l l e a d s e n t e r in g the c h a m b e r w e r e w r a p p e d
around th is co il.

We w e r e f o r tu n a te that the d e s i g n and the c o n ­

s t r u c t i o n of the c r y o s t a t w e r e su ch that e v e n on the f i r s t tr ia l
an a c c e p ta b le r a te of w a r m in g w a s obtain ed .
D-

M easu ring D ev ices
T h e b r i d g e * u s e d h a s a s t a t e d a c c u r a c y o f 0. 2 p e r c e n t .
g

F r o m the sta n d a r d a n a l y s is

o f the c i r c u i t ,

p o r t i o n a l to t h e m e a s u r i n g c u r r e n t .

It i s n e c e s s a r y to f i n d a c u r r e n t

l a r g e e n o u g h to g e t a d e q u a t e p r e c i s i o n ,
p r e v e n t undue h e a tin g of the s a m p le .

the s e n s i t i v i t y is p r o ­

a n d y e t s m a l l e n o u g h to

M o s t of the r e s i s t a n c e m e a s u r e ­

m e n t w e r e m a d e w ith a c u r r e n t of o n e - h a l f a m p e r e t h r o u g h the
sam p le.

A c h e c k f o r h e a t i n g e f f e c t s d u e to t h i s c u r r e n t s h o w e d

th a t no n o t i c e a b l e h e a t i n g o c c u r r e d at t e m p e r a t u r e s b e l o w
T h e h e a tin g e ff e c t a b o v e that t e m p e r a t u r e w a s not l a r g e ,
the r e a d i n g s w e r e ta k en w ith o u t undue d e la y ,
r e s i s t a n c e w a s l e s s than 1 p a r t in 1000.

150°K.
and w h e n

the e f f e c t on the

At r o o m t e m p e r a t u r e a

r u r r e n t o f o n e —t e n t h a m p e r e d i d n o t p r o d u c e a n y h e a t i n g e f f e c t ,
but w h e n the c u r r e n t w a s i n c r e a s e d ,

heating b e c a m e a s e r io u s factor.

* R u b ic o n Standard K elv in B r id g e , C atalog No. 1605, S e r ia l
No
8729Z m a n u f a c t u r e d b y the R u b ic o n M a n u fa c tu r in g C o m p a n y ,
P h ilad elp h ia.

It w a s f o u n d t h a t a l t h o u g h a c u r r e n t o f o n e - h a l f a m p e r e f l o w i n g f o r
a s h o r t t i m e g a v e r e s u l t s t h a t a g r e e d t o 1 p a r t i n 1 00 0 w i t h t h o s e
ob tain ed w ith o n e - te n t h a m p e r e ,
seriou s d isagreem en t.

a lengthy m e a s u r in g tim e ca u sed

At the lo w e r t e m p e r a t u r e s ,

it r e q u i r e d a

c u r r e n t of a l m o s t tw o a m p e r e s to p r o d u c e a n o t i c e a b l e h e a t i n g
effect.
The t h e r m o c o u p le s w e r e m a d e of th e r m o c o u p le c o n s ta n ta n
w ir e and c o m m o n c o p p e r w i r e ,

silv er sold ered together.

One

t h e r m o c o u p l e w a s c o n n e c t e d t o 10 c h a n n e l s o f a 1 2 - c h a n n e l r e c o r d i n g
self-b alan cin g poten tiom eter*,
to s e r v e a s r e f e r e n c e s .

the o t h e r tw o c h a n n e l s b e i n g s h o r t e d

T h is in stru m en t se r v e d as a m onitor

d u rin g the e n t ir e c o u r s e of a run.

The differen tial th erm o co u p les

w e r e c o n n e c t e d to a g a l v a n o m e t e r * * w h i c h e n a b l e d t e m p e r a t u r e
d i f f e r e n c e s o f l e s s t h a n o n e - h a l f a c e n t i g r a d e d e g r e e to b e m e a s u r e d .
A m a n u a l l y - b a l a n c e d p o t e n t i o m e t e r ^ w a s c o n n e c t e d in p a r a l l e l
w i t h t h e 1 2 - c h a n n e l r e c o r d e r to p e r m i t a m o r e p r e c i s e r e a d i n g

* M i c r o m a x M o d e l S, 4 0 0 0 0 S e r i e s ,
N orthrup C om p an y, P hiladelph ia.

m a n u f a c t u r e d b y L e e d s and

** T a b le M o d e l G a lv a n o m e t e r No. 440, 3 0 - 0 - 3 0 s c a l e ,
sen sitivity
a p p r o x i m a t e l y 0. 5 m i c r o a m p e r e
p e r d i v i s i o n , r e s i s t a n c e 50 o h m s ,
m a n u f a c t u r e d b y the W esto n I n s tr u m e n t C o m p a n y , N e w a r k , N .J .

t

P o r t a b l e M o d e l, s e l f - c o n t a i n e d g a l v a n o m e t e r and sta n d a r d c e l l ,
C atalog No. P M -4 0 m od ified , m anufactured by T h w in g -A lb ert
In str u m e n t C om pany, P h iladelph ia.

46

th an w a s a f fo r d e d b y the r e c o r d e r .
m 0. 0 5 m i l l i v o l t , ,

Its s c a l e w a s c a l i b r a t e d d i r e c t l y

c o r r e s p o n d i n g to a t e m p e r a t u r e d i f f e r e n c e o f

ab ou t Z C e n t i g r a d e d e g r e e s d e p e n d in g on the t e m p e r a t u r e .

The

g a l v a n o m e t e r * u s e d w i t h t h e K e l v i n b r i d g e h a d a s e n s i t i v i t y o f 0. 0 0 Z 9
m icro a m p ere

per m illim eter,

a n d a r e s i s t a n c e o f Z5 o h m s to g i v e

a voltage s e n s itiv ity of 0 .0 7 m ic r o v o lt

per m illim eter.

O ur e s t i m a t e for the o v e r a l l a c c u r a c y of the t e m p e r a t u r e
m e a s u r e m e n t i s ±. Z ° K ,
m en ts is

and the a c c u r a c y of the r e s i s t a n c e m e a s u r e ­

1 percent.

T a b l e M o d e l , m o v i n g lig h t b e a m , C a t a lo g No. 2 4 3 0 - C , m a n u
f a c t o r e d b y L e e d s and N o r t h r u p C o m p a n y , P h i l a d e lp h ia .

C H A P T E R VII
E L E C T R I C A L RESISTIV ITY:

EX PER IM EN TA L PROCEDURE

In p r e l i m i n a r y e x p e r i m e n t s a l e n g t h o f n a t u r a l l i t h i u m w i r e
1 m m i n d i a m e t e r a n d a b o u t 30 c m i n l e n g t h w a s w r a p p e d a r o u n d
th e g l a s s m a n d r e l w h ic h w a s p l a c e d in an i n d i v id u a l s a m p l e h o l d e r .
T h e e n d s o f the w i r e w e r e c l a m p e d in c u r r e n t c o n t a c t s ,

and

in s u la te d b r a s s s c r e w s w e r e tu rn ed into the lit h iu m for p o te n tia l
contacts.

T h e r e s i s t a n c e of the s a m p l e w a s m e a s u r e d at r o o m

tem peratu re,

and t h e n the h o l d e r c a r r y i n g the s a m p l e w a s l o w e r e d

into a 1 - li t e r D e w a r f l a s k c o n t a in in g liq u id n itr o g e n .
eq u ilib ration ,

the r e s i s t a n c e w a s a g a in m e a s u r e d .

w a s a l l o w e d to b o i l a w a y and th e s a m p l e w a r m e d ,
m en ts w e r e taken p erio d ica lly .

After
A s the n i t r o g e n

resistan ce m e a s u r e ­

A copper -con stantan therm ocouple

w a s a t t a c h e d to t h e s a m p l e h o l d e r a n d c o n n e c t e d to a r e c o r d e r .
A lso,

a d i f f e r e n t i a l t h e r m o c o u p l e w a s a t t a c h e d to th e e x t r e m i t i e s

of the s a m p le h o ld e r so that the t e m p e r a t u r e g r a d ie n t cou ld be
d eterm in ed .
appeared.

In t h e s e p r e l i m i n a r y e x p e r i m e n t s ,

T h e s m a l l s i z e o f the D e w a r f l a s k r e s u l t e d in r a p id

w a r m i n g and the c o n s e q u e n t a p p e a r a n c e
grad ien ts.

s e v e r a l d ifficu lties

of e x c e s s i v e th e r m a l

T h e p e t r o l a t u m c o v e r i n g the lith iu m b e c a m e b r ittle

a t l o w t e m p e r a t u r e s a n d w o u l d n o t s t i c k to t h e g l a s s m a n d r e l
w ithout support.

T h e e x p e r i e n c e g a i n e d in t h e s e e x p e r i m e n t s w a s

u t il i z e d in c o n s t r u c t i n g an im p r o v e d a p p a r a tu s.

48

T h is fin a l a p p a r a t u s w a s d e s c r i b e d in the p r e c e d i n g s e c t i o n .
T h e l a r g e r D e w a r f la s k and the m u lt i p le s a m p l e h o ld e r a llo w e d
better tem p era tu re control,

and p e r m i t t e d n e a r l y s im u l t a n e o u s

m e a s u r e m e n t on differen t sa m p les.

In t h e f i r s t e x p e r i m e n t s

w ith the n ew a p p a r a tu s s e v e r a l r u n s w e r e m a d e on two s a m p l e s
of n a tu ra l lith iu m .
repeated.

T h e r e s u l t s w e r e in v e r y good a g r e e m e n t w ith p u b lis h e d

r e s u l t s for n a tu ra l
lith iu m ,

T h e s a m p l e s w e r e c h a n g e d and the r u n s

lith iu m ^ .

In m a k i n g r u n s w i t h t h e n a t u r a l

g r e a t c a r e w a s t a k e n to a t t a i n t e m p e r a t u r e e q u i l i b r i u m

a n d to g e t a c c u r a t e m e a s u r e m e n t s o f t e m p e r a t u r e .
took c o n s id e r a b le tim e for e a c h te m p e r a tu r e ,
w as sought.

T h is p r o c e s s

and a q u ic k e r m e a n s

It w a s d e c i d e d to u s e t h e n a t u r a l l i t h i u m s a m p l e a s

the e l e m e n t o f a r e s i s t a n c e t h e r m o m e t e r ,

the n o r m a l i z e d r e s i s ­

ta n ce of the n a tu r a l lit h iu m s a m p le b e in g c h e c k e d a g a in s t the
c u r v e for n atu ral lith iu m ^ .

T h erm al electrica l effects w ere

e li m in a t e d b y r e v e r s i n g the c u r r e n t e a c h t im e a r e a d in g w a s
m a d e and th e n a v e r a g i n g the two r e a d in g s .

R ep rod u cib ility

w a s g o o d e n o u g h to j u s t i f y t h is p r o c e d u r e .
T h e m e t h o d of c o o li n g the t e s t c h a m b e r w a s m o d if ie d f r o m
that d e s c r i b e d e a r li e r .

A

1/ 4 - i n c h s t a i n l e s s s t e e l tube w a s run

f r o m j u s t o u t s i d e the b r a s s c y l i n d e r th r o u g h the top of the c h a m b e r ,
a n d t h e n c o n n e c t e d b y a s h o r t r u b b e r h o s e to a g l a s s f u n n e l .

49

T h rou gh this a r r a n g e m e n t,

liq u id n i t r o g e n c o u ld b e p o u r e d into

the t e s t c h a m b e r w ith o u t c o m i n g into d i r e c t c o n t a c t w ith the s a m p l e s .
M oreover,

the s a m p l e s c o u ld b e s u b m e r g e d in liq u id n it r o g e n a fter

b e i n g c o o l e d to n e a r the t e m p e r a t u r e o f the liq u id .
b r a t i o n p o in t at 7 7 ° K w a s t h e r e b y o b ta in e d .
a m o u n ts of liq u id ,

B y p o u r i n g in v a r i o u s

in c o n ju n c tio n w ith the p u m p in g a c tio n d e s c r i b e d

in the s e c t i o n on a p p a r a t u s ,
attained.

A good c a l i ­

d iffe r en t t e m p e r a t u r e s could be q u ick ly

O n ce a low t e m p e r a t u r e w a s r e a c h e d ,

subsequent read in gs

w e r e t a k e n a s t h e c h a m b e r w a r m e d up a t a r a t e o f 10 to 20 d e g r e e s
per hour.

C H A P T E R VIII
E L E C T R I C A L R E SISTIV ITY:

R E S U L T S A N D DISCUSSION

T he f ir s t m e a s u r e m e n t s w e r e m a d e on s a m p le s of n a tu ra l
lithium .

The r e sis ta n c e w as m ea su r e d from ro o m tem p eratu re

(295°K ) to liq u id n i t r o g e n t e m p e r a t u r e

(77°K).

Studies w ere m ad e

of the s e v e r a l f a c t o r s that could be c o n t r o lle d ,

su c h a s the r a te of

c o o lin g and w a r m in g ,
the t e s t c h a m b e r ,

the a t t a i n m e n t of t e m p e r a t u r e e q u i l i b r i u m in

the c u r r e n t flo w in g t h r o u g h the s a m p l e ,

d a y - t o - d a y and r u n - t o - r u n r e p r o d u c ib ility .
resistan ce,
i n F i g u r e 9.

and

T h e r e s u l t s for the

n o r m a l i z e d to t h e r o o m t e m p e r a t u r e v a l u e ,

are shown

w h e r e i n the e x p e r i m e n t a l p o in t s r e p r e s e n t the a v e r a g e

v a lu e of two r e a d in g s ,

o n e w ith the c u r r e n t in one d i r e c t i o n and the

o th er w ith the c u r r e n t r e v e r s e d .
f r o m the g ra p h for c la r ity .

S o m e of the p o in ts a r e o m itte d

T h e a . c t u a l d a t a a r e g i v e n i n T a b l e I.

T h e s o lid c u r v e r e p r e s e n t s the data of K e lly and M a c D o n a ld

.

Th e p r e s e n t e x p e r i m e n t a l r e s u l t s a g r e e w ith t h e i r s w ith in the
a c c u r a c y of the t e m p e r a tu r e m e a s u r e m e n t .
the te c h n iq u e w a s s a t i s f a c t o r y ,

It w a s c o n c l u d e d t h a t

and that the n a tu r a l lit h iu m s a m p l e s

c o u l d b e u s e d a s r e s i s t a n c e t h e r m o m e t e r s to g i v e t h e t e m p e r a t u r e
v a l u e s o f the s a m p l e s b e t t e r th an co u ld b e d one by the t h e r m o c o u p l e s ,
e s p e c i a l l y w h e n the r a te of c h a n g e of t e m p e r a t u r e w a s high.

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54

M e a s u r e m e n t s w e r e th e n m a d e on the s e p a r a t e d i s o t o p e s .
S i x s a m p l e s ' w e r e p l a c e d i n the s a m p l e h o l d e r ,
lith iu m ,

l i t h i u m - 6 , and l i t h i u m - 7 .

a s outlined e a r lie r ,

1 1.

The p r o c e d u r e follow ed w as

the n a tu r a l lith iu m s a m p le s s e r v in g a s e le m e n t s

of a r e sis ta n c e th erm o m eter.
and F i g u r e

two e a c h of n a t u r a l

T h e r e s u l t s a r e s h o w n i n F i g u r e 10

A s c a n b e s e e n in F i g u r e

of the data at lo w e r t e m p e r a t u r e s ,

10, w h i c h i s a. l i n e a r p l o t

the r e s i s t a n c e at 7 7 ° K r e l a t i v e

t o i t s v a l u e a t Z 9 5 ° K a m o u n t s to 0. 0 9 7 f o r n a t u r a l l i t h i u m ,
f o r l i t h i u m - 7 a n d 0. 116 f o r l i t h i u m - 6 .
to r o o m t e m p e r a t u r e ,
be s e e n in F ig u r e
v ariation ,

0. 108

A s the t e m p e r a t u r e r i s e s

t h e c u r v e s b e g i n to c o m e t o g e t h e r .

As can

1 1, w h i c h i s a l o g a r i t h m i c p l o t o f t h e e n t i r e

t h e c u r v e s b e g i n to c o m e t o g e t h e r a t h i g h e r t e m p e r a t u r e s ,

c o in c i d i n g o f c o u r s e at Z95°K .
a r e g i v e n i n T a b l e II.
b etw een 150°K

The n u m e r i c a l data for t h e s e r e s u l t s

E x t e n s i v e data w e r e n ot ta k e n w ith the i s o t o p e s

and r o o m te m p e r a tu r e ,

sin c e this ran ge d o e s not

y ie ld anything of p a r tic u la r in te r e st.
It i s r e g r e t t a b l e t h a t i n n o i n d i v i d u a l r u n w a s it p o s s i b l e to
get r e a d in g s on all six s a m p le s .

The p o ten tia l c o n ta c ts can be
>

m a in t a i n e d o n ly w ith d iffic u lty o v e r the w id e t e m p e r a t u r e r a n g e ,
in e v e r y r u n s o m e c o n t a c t o r o t h e r o p e n e d .

N everth eless,

the

r e p r o d u c i b i l i t y f r o m o n e r u n t o t h e n e x t i s h i g h a n d it i s b e l i e v e d
that the data sh o w n a r e r e lia b le .

a nd

o
O
o

VD

( % ) y

/ u

j d

N o r m a l i z e d r e s i s t a n c e as a function of t e m p e r a t u r e
l it h i u m - 7 (linear plot of low t e m p e r a t u r e r e g i o n )

o<
for

natural

lithium,

l i t h i u m - 6 , and

5b

-lo

10,6

L i' 6

o

L.-7

x

L i - nat a

r - 2 9 s"°k

L oy

[RITJ/RITJ]

9. S

9.0

-

©

&

*

*

A

A

A

^o°
m

/oo'

2,00

ao°

300

iOO°

2.10

2 .2 0

J
2,30

2,*0

L o $ (TewpeY'dtu.YC - °K)
f> 9 •<rt. 1 1

N o r m a l i z e d r e s i s t a n c e a s a fu n ctio n of t e m p e r a t u r e for n a tu ra l lith iu m ,
l i t h i u m - 6 , and l i t h i u m - 7 ( lo g a r it h m ic p lo t o f e n t ir e r e g io n ).

Z ^o

57

If t h e r e s i d u a l r e s i s t i v i t y i s c o n s i d e r e d to b e n e g l i g i b l e ,
c u r v e s shown m F igu re
r exptl

10 m a y b e u s e d to c o m p u t e t h e v a l u e o f

^ ^ e r e s u l t i s s h o w n in F i g u r e

^°r r th e o r '

the

12, to g eth e r with c u r v e s

e x p e r i m e n t a l r e s u l t s a r e in c o n t r a d ic t io n both

q u a l i t a t iv e l y and q u a n tita tiv e ly .
not n e g lig ib le ,

W hen the r e s i d u a l r e s i s t i v i t y is

the c u r v e for r th eo r is ch a n g ed s e r io u s ly .

If t h e

r e s i d u a l r e s i s t i v i t y i s c o n s t a n t for the d iff e r e n t m a t e r i a l s ,
w ill be r a is e d ,

and the d i s a g r e e m e n t w ill be w o r s e .

H owever,

the r e s i d u a l r e s i s t i v i t y w e r e d i f f e r e n t for e a c h m a t e r i a l ,
n e g l i g i b l e at 7 7 ° K ,

the c u r v e
if

and n o t

the c u r v e c o u ld e v e n l ie b e l o w the on e for

r theor •
E xam ination of F igure

10 s h o w s n o s t r i k i n g d i f f e r e n c e i n t h e

c u r v a t u r e s for the n o r m a l i z e d r e s i s t i v i t i e s of the t h r e e m a t e r i a l s ,
a n d w e b e l i e v e t h a t t h e r e i s n o e x p e r i m e n t a l e v i d e n c e to i n d i c a t e
su b sta n tia l r e sid u a l r e s is t iv it ie s differing stro n g ly b etw een
m a teria ls.

On the o t h e r h an d ,

the c h e m i c a l a n a l y s e s for the s a m p l e s

d o s h o w t h e p r e s e n c e o f f o r e i g n a t o m s to t h e a m o u n t o f s o m e h u n d r e d t h s
of an a to m ic p ercen t.*
sam p le are calciu m ,
percent,

T h e m o s t s e r i o u s i m p u r i t i e s in the l i t h i u m -6
0. 0 5 w e i g h t p e r c e n t ,

a n d s o d i u m 0. 0 3 w e i g h t

c o r r e s p o n d i n g t o l e s s t h a n 0 . 01 a t o m i c p e r c e n t e a c h .

T h e c h i e f i m p u r i t y in the l it h i u m - 7 s a m p le is c a lc i u m ,
percent,

c o r r e s p o n d i n g to 0 . 0 3 a t o m i c p e r c e n t .

* Fe disregarded.

0. 2 w e i g h t

The natural

'j8

^ c
L)-\.ZO

( 0 7= ^ ° K )

^ /< 9 y

= /•£>£

0.6

0.0

o

0.6

0.1

1.0

T /T o
F igure

12

R a t i o o f n o r m a l i z e d r e s i s t a n c e o f l i t h i u m - 6 to n o r m a l i z e d r e s i s t a n c e
o f l i t h i u m -7 a s a f u n c t i o n o f n o r m a l i z e d t e m p e r a t u r e .

5V

lith iu m is c o n sid e r a b ly p u r e r ,

with c a lc i u m ,

0 .0 0 3 atom ic p ercen t,

t h e c h i e f i m p u r i t y l i k e l y t o b e w i t h i n t h e b o d y o f t h e m e t a l 5-.

Few

d a ta a r e a v a i l a b l e to s u g g e s t w h at n u m e r i c a l v a l u e s sh ou ld be u s e d
fo r the a p p l i c a t i o n o f M a tth ie s s e n ’s r u le that the i n c r e a s e in r e s i s ­
t i v i t y in d i l u t e s o l i d s o l u t i o n s i s p r o p o r t i o n a l to the a t o m i c p e r c e n t
of im p u r it y ,

and in d e p e n d e n t of t e m p e r a tu r e .

for lith iu m ,

how ever,

A s an o u tsid e lim it

w e s u g g e s t that the r e l a t i v e i n c r e a s e in r e s i s ­

t i v i t y m i g h t b e 50 p e r c e n t i n c r e a s e i n r o o m t e m p e r a t u r e r e s i s t i v i t y
per

1 a to m ic p e r c e n t im p u rity.

In t h i s c a s e t h e r e s i d u a l r e s i s t a n c e s

f o r t h e i s o t o p e s w o u l d b e l e s s t h a n 0. 0 1 0 f o r t h e l i t h i u m - 6 , 0. 0 1 5
for the l i t h i u m - 7 ,
estim ates,

a n d 0. 0 0 5 f o r t h e n a t u r a l l i t h i u m .

t h e n o r m a l i z e d r e s i s t a n c e s d u e to l a t t i c e v i b r a t i o n s

b e c o m e f o r l i t h i u m - 6 , 0. 106; f o r l i t h i u m - 7 ,
lith iu m ,

W it h t h e s e

0. 0 9 3 ; f o r n a t u r a l

0. 092.
T h u s it a p p e a r s that the r e s i d u a l r e s i s t a n c e w ill not r e v e r s e

the r e l a t i v e p o s i t i o n s o f the c u r v e s fo r the i s o t o p e s a m p l e s ,

and

th at it m a y b r i n g the l i t h i u m - 7 c u r v e n e a r l y into c o i n c i d e n c e w ith
the n a tu r a l lith iu m c u r v e .

If it i s a c c e p t e d t h a t t h e c u r v e f o r

l i t h i u m -6 l i e s a b o v e the one for l it h i u m - 7 ,

then s e r io u s doubt is

t h r o w n on the a d e q u a c y of the c o n v e n t io n a l a n a l y s i s for e l e c t r i c a l
resistivity.

* N

In v i e w o f

disregard ed

the g r a v it y of th is c h a r g e ,

it w i l l b e

60

i m p o r t a n t t o e x t e n d t h e m e a s u r e m e n t s to l o w e r t e m p e r a t u r e s .
T h e p r o c e d u r e c a n b e m a in t a i n e d the s a m e , but the a p p a r a t u s m u s t
b e m o d i f i e d to p e r m i t c o o l i n g w i t h l i q u i d h e l i u m .

Such m o d ific a tio n

i s s i m p l e and i n e x p e n s i v e .
It i s n o t s u r p r i s i n g t h a t t h e c o n v e n t i o n a l t h e o r y i s n o t c o m ­
p le te ly adequate,

in v ie w of the s e v e r e a p p r o x im a t io n s m a d e in

c a r r y i n g out the c o m p u ta tio n s .
the p r e s e n t th e o ry is not e a s y ,

A c lo s e c r it ic a l e x a m in a tio n of
b u t it w o u l d s e e m t o b e c a l l e d f o r

if the p r e s e n t e x p e r i m e n t a l r e s u l t s a r e s u b s ta n tia te d .

R E F E R E N C E S CITED

1.

A. B e r n i n i a n d C.

N u o v o C i m e n t o 8 , Z41 ( 1 9 1 4 )

C antoni,

Z.

W. B .

Pearson,

C a n a d i a n J.

3.

T . W.

R i c h a r d s and F .

4.

E . J. C o v i n g t o n ,

M .S .

N,

Phys.

B rink,

T h esis,

3Z, 7 0 8 ( 1 9 5 4 )
J.

Am.

Chem .

M ic h ig a n State U n i v e r s it y , 1956

5.

N. F . M o t t an d H. J o n e s , T h e o r y o f M e t a l s ,
O x fo r d U n iv. P r e s s (1936)

6.

E.

7.

D. K. C.

8.

F.

A.

Eaw s,

9.

F.

M.

K e l l y a n d D . K. C .

H.

S on d h eim er,

Proc.

Roy.

M a c D o n a l d a n d K.

Z 9 , 1Z0 ( 1 9 0 7 )

Soc.

Soc.

Chap.

VII,

AZO3, 7 5 ( 1 9 5 0 )

M en d elssoh n ,

Proc.

Roy.

Soc.

AZOZ, 1 0 3 ( 1 9 5 0 )

E l e c t r i c a l M e a s u r e m e n t s , M c G r a w - H ill B o o k Co.
M acD onald,

C a n a d ia n J.

Phys.

3_1,

(1938)

147 ( 1 9 5 3 )