’-.‘ “A. z,
‘47- ,mn. V V.

,gr’fUl‘

rm

'-:M'A
,:

 

s3. r
v»..4‘_
.3 ‘
.. VM‘LL“:
.1151 -~
~ “I
. fawn,»
.mv
~_ ...-

*" ' ~ ‘ (-4... ..
~ I ‘ .7 “figumr.
. ‘ H ‘ .l‘,
- l I , y 4‘ ‘ ‘
7 h ‘ A ' ‘ ».. 4. . .. u.
“3“ “I. I c 7 ' - ‘ . I ~
um. :u ~1‘-;,:.rmfi.:...- .4 Ky”: '11-?!
> J ' J ‘ ' g m .. ., .
~ “‘ r v: mum. ~
. " s. . l
..

w . ,~
bun“
u. ‘
u

5's...“

' 9i
‘ V‘ "k
- .w

.33..
~ If !k

5 xiii:
at - v

3 ’ .o‘ ‘ _ A

‘ l A >3 1
an 3.4—. '9'"!

«Jr. .w V '

~ m 11a "

' k

 

 

 

 

 

4 1 .
m. .
‘ ‘-.x..',
1“ u v
‘ .' x c"

- .5;-

4"“.-

:1
11%.-
.. 1 .

-'.' 1
.71!

‘JF’J. '

.
Mu
h.” ‘
44' a... . ,
Al

~l
“yuan,“ “w
'o wg.

f '

.."'
V" . {u

. r‘ N,
. r1. "3”,: 233m”.
1* v . . -.
m l P... .3)”
' .. m V
' N7
3‘ m

.. ’2‘,” ‘
w 4. N;
‘5: f" if},

..

{x '1‘.

s.
“y.

"‘ .3543 «3:3
.9

5

 

:
PM W I
' . .. v y ‘
‘ I h” n: .1:
'.-. w rv-w
”'3' I 11m.,,’, ‘0),
' ‘1’ w ,-

A, ”we?" ‘

.

J:
1-,». ‘ 1W
V ,. ‘ .

u . w . .0 .

.1 . 157'”. J...‘
3! 4V!» y. , “3;?
.t’yfi‘fi-‘flfii‘y: In.

 

TYWUBRA

l 2“Ml

 

 

 

 

 

 

 

IHIWIWHHHHWUH«WWW mo

3 1293 0105

This is to certify that the

dissertation entitled

ELECTRON PARAMAGNETIC RESONANCE STUDIES OF UNPAIRED
ELECTRON DISTRIBUTIONS IN ALKALIDES AND ELECTRIDES

presented by

Dae Ho Shin

has been accepted towards fulfillment
of the requirements for

 

 

Ph. D. degreein ChemiStry

07.04%“,

Maj?» profesW

Date _ApIiJ_,_23_l_9_9.L_

MSU is an Affirmative Action/Equal Opportunity Institution 042771

 

 

__‘

LIBRARY
Michigan State
University 1

 

 

I

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.

 

DATE DUE DATE DUE DATE DUE

. i l
|[__l_i__J

V
II 1 II ___|
ll il l
JI II I
II I II

MSU Is An Affirmative Action/Equal Opportunity Institution
cMMMI

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ELECTRON PARAMAGNETIC RESONANCE STUDIES OF UNPAIRED
ELECTRON DISTRIBUTIONS IN ALKALIDES AND ELECTRIDES

Dae Ho Shin

A DISSERTATION

Submitted to Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Chemistry
1 992

{V51 5672

ABSTRACT

ELECTRON PARAMAGNE'I‘IC RESONANCE STUDIES OF UNPAIRED
ELECTRON DISTRIBUTIONS IN ALKALIDES AND ELECTRIDES

by
Dae Ho Shin

The nature of the trapped electron in alkalides and electrides
was explored by X-band EPR. G-band EPR, and pulsed EPR techniques.
The EPR spectra of six compounds of known-structure reveal that
excess electrons in these salts are trapped at vacant anionic sites and
can be considered similar to F-centers. Hyperfine splitting is observed
when the complexed cation is exposed to the anionic site. but not
when the cation is well-shielded by inclusion in a sandwich structure
formed by two crown ether molecules. ‘

The g-values of the contact systems, K+HMHCYNa‘,
Rb‘l'HMHCYNa‘. and Cs+HMHCYNa' are 2.0029, 1.9983, and 1.9833.
respectively. The g-values of the isolated systems, Cs+(1806)2Na' and
Cs+(1505)2Na' are 2.0022 and 2.0020, respectively and are close to
the free electron value. The % atomic character at the cations in
K+HMHCYNa‘, Rbfl-IMHCYNa‘, and Cs‘l'HMI-ICYNa’ are 6.48, 10.5. and
11.9 %, respectively.

A new crystalline sodide. Na'l'HMHCYNa’ was synthesized and
characterized by EPR spectroscopy. The g-values of three sodides of

ii

unknown-structure, Na+HMHCYNa', K+18C6Na', and Rb+18C6Na' are
2.0010, 2.0023, and 1.9974, respectively. The % atomic characters of
the cations in Na+HMHCYNa'. K+18C6Na', and Rb+18C6Na‘ are 1.16.
18.9. and 16.3 %, respectively. The latter two compounds exhibit
spin-pairing with spin-pairing energies of 1.94 x 10'2. 2.11 x 10'2 eV.
respectively.

Crystallized pure Cs+(18C6)2e‘ has a nearly axially symmetric

EPR signal, both at X-band (10 GHz) and at G-band (250 GHz).
Crystallized pure Cs+(18C6)ZCS' shows no evident separation of g-value
at X-band but shows a separation at G-band. The increased resolution

at 250 GHz completely separates the parallel and perpendicular
components, and agrees with the results at X-band for Cs+(18C6)2e'.

The EPR pattern at 250 GHz for electrons trapped in Cs+(1806)2Na’
is similar that of Cs+(18C6)2e'. These results show that the unpaired

electron in pure electrides is localized on the EPR time scale at the
same type of anionic site as is the F-center in alkalides.

Pulsed EPR studies of CstHMHCYNa' show two magnetically
distinct groups of weakly coupled 133Cs nuclei; one with an isotropic
electron-nuclear hyperfine (Fermi contact) coupling of 0.34 MHz and
the other with a contact coupling of less than 0.1 MHz. Analysis of
these data by computer simulation shows that the number of Cs nuclei
that give rise to these interactions and their distance from the
paramagnetic center is consistent with the hypothesis that the
trapped electrons occupy vacant anionic sites. The results indicate
that the spread of the unpaired electron spin density along the axis
formed by the "contact ion pair" may be greater than that in the plane
perpendicular to this axis.

iii

To my parents

iv

ACKNOWLEDGEMENTS

I wish to express my sincere gratitude to Dr. James L. Dye for
his guidanCe, encouragement, and support through this study. I would
like to thank to Dr. John L. McCracken, Ahmed S. Ellaboudy, Dr. Marc
DeBacker, and Dr. Gerald T. Babcock for their helpful discussions and
advices. Thanks are also extended to all of the member of Dr. Dye's
research group with whom I worked, in particular to Drs. Rui H.
Huang and Jineun Kim. I would like thank Drs. David E. Budil, Keith A.
Earle, and Jack H. Freed at Cornell University their helpful discussions
and advice for the high-field electron paramagnetic resonance studies.
I would like to thank the glassblowers at Michigan State University:
Keki Mistry, Manfred Langer, Scott Bankroff.

I would like to thank Professor Youngsang Choi at Korea
University for his encourgement and support and thanks to all my
friends of Songwoo club for thier encouragement.

I am grateful for financial support from the National Science
Foundation Solid State Chemistry Grant (Grant DMR 87-14751) for a
research assistantship, and for support from the Center for
Fundamental Research at Michigan State University, _ the CNRS
URA253, and NATO Grant No 0106/88. I thank the Illinois EPR
Research Center for EPR analysis software.

Special thanks go to my parents and mother-in-law for their
endless encouragement, understanding and support. A special thank-
you goes to my wife, Sanghee for her unending understanding and
patience which was essential for the completion of this degree.

I would like to dedicate this thesis to my parents.

TABLE OF CONTENTS

CHAPTER PAGE
LIST OF TABLES ..................................................................................................... 1
HST OF FIGURES ................................................................................................... 2
CHAPTER I INIRODUCTION ................................................................. 1
LA Solvated Electrons in Solutions ................................................ 2
LA. 1 Metal-Ammonia Solutions (MAS) .................................. 2
I.A.2 Metal-Amine, Amide and Ether Solutions ................. 4
LB. Trapped Electrons in Solid Systems ...................................... 7
LB. 1 Glassy Systems ..................................................................... 7
1.3.2 Color Centers ........................................................................ 9
LC. Alkalides and Electrides ............................................................ 1 1
LC. 1 Alkalidas ............................................................................... l 1
I.C.2 Elect-ides ............................................................................. 14
ID Objectivw of This Work .............................................................. 17
CHAPTER II EXPERIMENTAL METHODS ........................................ 19
II.A Syntheses and Sample Handling ............................................ 19
ILA. 1 Purification of Metals, Complexants and Solvents
II.A.2 Syntheses ofAlkalidesandElectIides '.' III'II.’ 122222712 '''''''' i 3
KB. Description of Instrumental Experiments ......................... 23
11.3.1 X—band EPR ......................................................................... 23
11.3.2 G-band EPR ........................................................................ .23
11.8.3 The Pulsed EPR spectrometer ................................... 26
CHAPTER III THEORY .............................................................................. .29
III.A Solid State EH2 ............................................................................. 29
III .A. 1 g-valu ................................................................................... 29

vi

III.A.2 Nuclear Hyperfine Interaction .................................... 31

III.A.3 line Shape ........................................................................... 34

III .A. 3.1 Gaussian and Lorentzian shapes ..................... 34

III.A.3.2 Relaxation ................................................................ 36

III .B High-frequency EPR .................................................................... 39
III.C Electron Spin Echo Envelope Modulation ......................... 43
III.C. 1 Nature of Electron Spin Echo Modulation ............. 43
III.C.2 Analysis of Echo Modulation ........................................ 48
III.C.2.1 TWO-pulse spin echo modulation pattern ..48

III.C.2.2 Three-pulse Echo Modulation Pattern ........ 53

111 .D. Simulation in Disordered Systems ....................................... 54

CHAPTER IV EPR STUDIES OF ELECTRONS TRAPPED IN

SODIDES ............................................................................. 55
[VA Introduction .................................................................................. 55
NB Experimental Section ............................................................... 59
NC Results and Discussion for Sodides of Known-structure
IV C "1' """""" Results 'IIIIIIIIIIIIII I I I I I I I I .' I I I I 23333333113313
IV C 2 Discussion .......................................................................... 69
IV D Results and Discussion for Sodides of Three Unknown-
Structure ........................................................................................ 71
IV E References ...................................................................................... 83

CHAPTER V X-BAND AND G-BAND EPR STUDIES OF

ELECTRIDES AND TWO ALKALIDES ...................... 87

VA Introduction .................................................................................. 88
V.B Experimental methods ............................................................. 91
VB. 1 Sample Preparation .................................................................... 91
V.B.2 Instrumentation ........................................................................... 92
V.C Results and Discussion .............................................................. 93
V.C. 1 (swim .................................................................................. 93
V.C.2 Cs*11806)21\h' ............................................................................... 99

vii

V.C.3 Csfllm .............................................................................. 100

V1) Conclusions ................................................................................... 107
V.E Refm .................................................................................... 107
CHAPTER v1 PULSED EPR STUDIES FOR Cs+HMHCYNa' ...... 1 10
VI.A Introduction ................................................................................. 1 11
VI.B Materials and Methods ............................................................ l 15
v1.0 Results and Discussion ............................................................ 1 17
VLD Acknowledgments ..................................................................... 127
VLE References .................................................................................... 128

CHAPTER VII CONCLUSIONS and SUGGESTIONS FOR FUTURE

WORK .................................................................................. 130

VILA General Conclusions ................................................................. 130
VII.B ' Suggestions for Future Work ................................................. 132
BIBILOGRAPHY ................................................................................................... 134

viii

LIST OF TABLES
PAGE

Table 4-1 Magnetic parameters calculated from the EPR spectra
of sodides ........................................................................................ 63

ix

LIST OF FIGURES

PAGE
Figure 2-1 K-cell for the synthesis of alkalides and electrides ...... 21
Figure 2-2 Block diagram of G-band EPR spectrometer ................... 25
Figure 2-3 Sample holder for G-band EPR. ............................................ 26

Figure 2-4 Schematic Block Diagram of Pulsed EPR
spectrometer ............................................................................... .28

Figure 3- 1 The saturation curve for a homogeneously broadened
line (solid line) and an inhomogeneous line (dotted
line) ................................................................................................. .38

Figure 3-2 Approximate shape of a high frequency EPR
spectrum with a anisotropic g factor (a) and 150 GHz
spectrum (first derivative) of perdeuterated
nitroxide radical (b) compared to a 10 GHz spectrum

(c). both in the solid state ....................................................... 41
Figure 3-3 Diagram showing the origin of electron spin-echo
modulation. .................................................................................... 45
Figure 3-4 Illustration of modulation of a Two-pulse (a) and a
Three-pulse (b) Spin Echo Decay Envelope ..................... 47
Figure 4-1 Representations of the ionic packing in (A)
Cs+(HMHCY)-Na' and (B) Cs+(18C6)2-Na'. Each Na‘
ions is surrounded by eight complexed cations, four
of which are shown here ........................................................ 58
Figure 4-2 EPR spectra of (A) K+(HMHCY)~Na',(B)
Rb+(HMHCY)-Na'(C), Cs+(HMHCY)-Na' and (D)
simulated EPR spectrum of Rb+(HMI-ICY)-Na' ................ 61
Figure 4-3 EPR spectrum of Cs+(1806)2-Na' ........................................ 65

Figure 4-4 Power saturation curve of Cs+(HMHCY)-Na'. The
solid line is the least-squares best fit of the data for a
Lorentzian line shape ................................................................. 66

Figure 4-5

Figure 4-6
Figure 4-7

Figure 4-8

Figure 4-9

Temperature dependence of intensities of EPR
spectral lines of (A) Rb+(HMHCY)-Na' and (B)

Cs+(1806)2-Na' ............................................................................. 68
X-band EPR spectrum of Na”HMHCYNa‘ ............................ 72
X—band EPR spectrum of K"(18C6)Na' ................................ 74
X-band EPR spectrum of Rb+(18C6)Na‘ .............................. 75
Power saturation curve of Na+HMHCYNa' .......................... 77

Figure 4-10Temperature dependence of power saturation curve

ofK‘IfiH‘Ia' ................................................................................. 78
Figure 4-1 lPower saturation curve of Rb+(18C6)Na‘ ............................. 80
Figure 4-12Temperature dependence of areas of EPR spectra of

Rb+(1&36)Na' .................................................................................. 81
Figure 4-13Temperature dependence of areas of EPR spectra of

K"(18(3)Na‘ .................................................................................... 82
Figure 5-1 (A) X-band spectrum and (B) the simulation

spectrurnof Cs+(1806)2e' .......................................................... 94
Figure 5-2 G-band EPR spectra of (A) Cs+(1806)2e' and (B)

CbfilBOBhNa' ................................................................................ 95
Figure 5-3. Temperature dependence of the intensity of the X-

band EPR spectrum of Cs+(18C6)-2e' .................................... 97
Figure 5-4 Power saturation curve of (A) Cs+(18C6)-2e' and (B)

MIBOG-ghh' ............................................................................. 101
Figure 5-5 X-band EPR spectrum of Cs+(l8C6)2CS' ............................ 103
Figure 5-6 G-band EPR spectrum of Cs+(18C6)2CS' ............................ 104
Figure 5-7 Temperature dependence for Cs+(18C6)2CS' at X-

band .................................................................................................. 106
Figure 6-1 Computer simulation of the cation-anion packing in

Cs+(HMHCY)Na' from x-ray crystallographic data .......... l 13

xi

Figure 6-2 Stimulated echo ESEEM data and associated
frequency spectrum obtained for Cs+(HMHCY)Na' ........ 1 18

Figure 6-3 ESEEM spectra obtained for Cs+(HMHCY)Na' at two
different magnetic field positions within the EPR
absorption envelope ................................................................... 120

Figure 6-4 A comparison of "experimental" and simulated l33Cs
ESEEM data obtained from Cs+(HMHCY)Na' ....... 124

xii

CHAPTER I

INTRODUCTION

Alkalides and electrides are compounds in which the anions are
alkali metal anions and trapped electrons respectively. This thesis
will emphasize the characterization of the anionic site in alkalides and
the electron locales in electrides. The primary techniques used to
characterize the trapping site are X-band electron paramagnetic
resonance (EPR), G-band EPR and pulsed EPR spectroscopy. This
chapter will review background material about the trapped electron in
liquids and solids. First, the solvated electron in liquids will be
introduced and then the trapped electron (F-center) in ionic solids
and localized electrons in aqueous frozen systems and in organic glassy
solids will be discussed. The description of these systems will focus
on their structures and on the magnetic properties of the electron.

Studies of solvated electrons originated with the investigation of
active metals (alkali and alkaline earth metals plus Eu and Yb)
dissolved in ammonia. amines and certain polyethers. These electrons
show similar types of aggregate formation as do trapped electrons and
ions in the solid state. These considerations may be expanded to the
interpretation of the results obtained for polycrystalline alkalides and
electrides. Finally, certain issues about the charge distribution for
electrons trapped at anionic sites will be addressed in order to put the

present work in perspective.

I.A. Solvated Electrons in Solution

LA. 1 Metal-Ammonia Solutions

Since Weyl discovered that sodium and potassium metals form
blue metal-ammonia solutions (MAS) when dilute and bronze colored
solution when concentrated [1]. this field has resulted in seven
conferences named "Colloque Weyl" [2, 3, 4, 5. 6. 7, 8]. The most
striking feature of metal-ammonia solutions are electrons in insulating
liquids. The physical properties of these solutions change drastically
with the concentration of electrons. The electrons in dilute solution
are localized as solvated electrons, while in concentrated solutions
they are delocalized to form a “Fermi gas”. Many physical properties
of alkali metal-ammonia solutions have been studied as a function of
metal concentration, temperature and pressure. In this section the
magnetic properties will be emphasized.

Hutchison and Pastor first reported the magnetic susceptibility
of MAS by EPR in the nonmetallic region of sodium- and potassium-
ammonia solutions [9]. Essig and Schindewolf measured the magnetic
susceptibility over a wide concentration range by EPR. The results
from EPR [10, 11, 12] and static Gouy measurements [13, 14, 15, 16]
are in good agreement. A comparison was made by Harris and
Logowski. in describing their EPR data in the nonmetallic region of
alkali metal-ammonia solutions [17]. The magnetic susceptibility is
independent of the alkali metal used. The most important feature of
the electronic susceptibility in MAS is strong reduction of the molar

3

paramagnetism between 0.01 and 1 mole percent metal (MPM). which
indicates formation of diamagnetic species usually designated as e2= or
(e'-M+-e'). EPR spectra of dilute MAS show an extremely narrow
symmetrical line with only a few miligauss linewidth [18. 19]. Above
1.0 MPM the susceptibility reflects the progressive electron
delocalization that leads to metallic behavior. Increasing the metal
concentration to the region of the nonmetal to metal transition yields
the highly asymmetrical EPR line shape that is known as Dysonian line
shape [20]. This lineshape is characteristic of metallic samples whose
thickness is comparable to or greater than the skin depth for
electronic conductivity.

O'Reilly [21, 22] observed the Knight shifts [23) for all the nuclei
in alkali MAS at 298 K in the region of 0.1 to 1.0 mole/1. All the nuclei
except 1H show positive values for the Knight shift. This indicates
hyperfine interaction with the paramagnetic excess electrons because
of M+- e' interactions. Negative shifts for 1H result from spin-
polarization by the excess electrons on the electrons of N and H via N-
H bonding [24].

In summary the electrons in very dilute MAS behave as non-
interacting localized electrons, while the electrons at high
concentrations exist as free electrons in normal liquid metal. The
spin-pairing interaction between the dissolved electrons proceeds
prior to the nonmetal to metal transition. The fundamental nature of
the pair-wise interaction between solvated electrons to form the spin-

paired species is not clear.

4

I.A.2 Metals in Other Solvents: Amines, Ethers Amides, etc

The decrease in the dielectric constant and donicity of other
solvents for the alkali metals (compared with ammonia) affects the
solvation energ' of the cation and the electron as well as the strength
of the electron-cation interaction. As a result, the solubility decreases
dramatically and the association of the solvated electron with the
solvated cation is stronger than in MAS so that one no longer has a
weakly interacting ion-pair species.

The optical absorption spectra of alkali metal-amine and -ether
solutions depend on the alkali metal [25]. Generally there are two
peaks, the solvated electron band and a higher energy peak which
depends on the metal. Solutions of the alkali metals (except Li and
Na) in ethylenediamine (EDA) showed absorption peaks due to both
alkali anions and solvated electrons. Only the solvated electron band
was observed in Li-EDA solutions and only the Na' band was observed
in solutions of Na in EDA. The variations in intensities of the two

peaks of optical spectra can be explained via the equilibrium

 

M _ M“ + 26501., (H)

which lies far to the right for lithium and far to the left for sodium.
The EPR spectra of alkali metal solutions in amines depend on
the metal and the solvent. Solutions of lithium in methylamine can be

described as ammonia-like; a narrow singlet EPR signal was observed

5

similar to the EPR signals of dilute MAS [26, 27]. Upon changing to
ethylamine as the solvent, an eight-line EPR pattern was observed
that arose from hyperfine coupling to four nitrogens [28]. Sodium and
potassium in methylamine solutions showed no resolved hyperfine
splitting and had nearly the free-electron g value (2.0023). By
contrast, rubidium and cesium solutions in methylamine showed
resolved hyperfine splitting due to coupling of the electron spin to a
single alkali metal nucleus plus a central narrow peak of the solvated
electron.

The assignment of the species M‘, as a “genuine” alkali metal
anion with two electrons in the outer s orbital in metal-amine and
metal-ether solutions was verified by alkali metal NMR spectra [29,30].
These studies made it clear that it was not merely a cluster of solvated
cations and solvated electrons. Recent NMR studies of solutions of
alkali-metals in certain amides (Hexamethyl phosphoramide, DEA.
DMP. DPA) showed a sharp signal (8 ~ 15 MHz at 8 ~ 62 ppm) for only
sodium solutions [31]. The sodium signal is caused by Na’ in terms of
the chemical shift, but no Na+ NMR signal was observed. Solutions of
alkali metals in hexamethylphosphoramide (HMPA), which has a high
dielectric constant (29.6 at 298 K), showed a single EPR line [32]
similar to the EPR signals of MAS. A single 23Na NMR peak
corresponding to Na' was observed in the Na-HMPA solution but the
Na+ peak was not observed [33]. When alkali metal-HMPA solutions
were frozen, glassy blue solids were formed. EPR results of the frozen
solutions were different from the unfrozen solutions [34]. These EPR
results indicate the existence of several discrete localized excess

electrons similar to those in amines or ethers.

6

A simple quantitative ion-pairing model for alkali metal solutions
was first proposed by Dye [35], and also applied by Catterrall [32].
According to this model, the species formed in the ion-pairing
equilibrium

 

Ms'+ es' ‘_ Ms+e31 (1-2)

can vary from a solvent-separated or solvent-shared species at low
temperatures or in high dielectric constant solvents to a contact ion-
pair in less polar solvents and / or at high temperature. This behavior
is continuous as the center of electron charge density approaches that
of the solvated cation. Collapse to a solvated atom would be an
extreme case that leads to loss of ion-dipole salvation energy for both
the cation and the electron. As a result, a compromise is reached that
balances the Coulomb attraction between M+ and e' and the ion-dipole

interactions of both ions with the solvent. The lifetime of the _
monomeric species (MS) is governed by the electron-nuclear

correlation time, t and the hyperfine coupling constant (HFC)

M

corresponds to the electron density at the nucleus. In solvents of high
dielectric constant (HMPA. NH3), the average lifetime of MS is shorter

than the inverse of the HFC. Thus. an averaged signal from c" and Ms
is observed as a single EPR line. In low dielectric media the lifetime is
long enough to observe separate signals from e-solv and M+-e'. The g-
values of the solvated electron in metal solutions are close to the free

electron value.

7

LB. Trapped Electrons in Solid Systems
1.3.1 Glassy Systems

The mechanism for the solvation of the electron in fluids has
been reviewed. In glassy or solid systems the trapped electron can be
assumed to have a similar equilibrium structure after complete
solvaticn. The theoretical ideas concerning electron localization
should be applicable to liquids, glasses and solid. The most universally
accepted model will be presented. even though Golden and Tuttle [36.
37] advocate a “solvated solvent anion model”, with major reference to
the interpretation of optical spectra.

An electron is trapped in a glass or solvent by two mechanisms.
The first step is the localization of the itinerant electron at a pre-
existing site and the second step is the trapping into the lowest
energy configuration. The first step is very fast (on the order of 10 to
40 picoseconds) in glasses. The amorphorous glassy structure has a
number of sites created by random molecular orientation of the
dipoles which can serve as initial traps for electrons. The time-scales
of localization into pre-existing traps were obtained by picosecond
pulse radiolysis experiments [38]. Recently. femtosecond studies on
the birth of electrons in water showed that there are three well-
defined states [39, 40, 41]: highly reactive dry electrons, initially
localized but unsolvated wet electrons and fully solvated electrons.

The structure of the equilibrium solvaticn shell of a trapped
electron in a glassy matrix has been studied by EPR techniques.

'h'aditional EPR measurement showed only a broad line because of the

8

weak couplings. Kevan [42] investigated the weak hyperfine
interaction by using electron spin echo modulation (ESEEM)
techniques which can provide such structural information as the
distance between the electron and the interacting nucleus as well as
the number of nuclei interacting with a trapped electron. The average
geometric structure of the solvated electron in frozen 10 M NaOH
solution and frozen ethanol solutions [43. 44] has been investigated by
ESEEM. The structure of the frozen aqueous solution was
independent of the nature of the cation; thus, the hyperfine coupling
results from the protons on water. The structure proposed on the
basis of ESEEM measurements is an octahedral arrangement of six
water molecules oriented with an O-H bond directed toward the
center of the electron cavity. The geometric structure of a trapped
electron in ethanol showed that four molecules were arranged
tetrahedrally to form the electron cavity. The results of ESEEM were
interpreted on the basis of the semi-continuum model proposed by
two groups [45, 46].

The semi-continuum model, an extension of the simple model of
Jortner [47]. assumes that the excess electron is trapped in a
spherical cavity of radius rc created by the finite number, 2 of first
shell molecules. The first shell molecules are considered as ideal
dipoles in their electrostatic interactions with the electron and are
assigned a spatial radius. rs. Outside the sum of these two radii the
solvent is described as a dielectric continuum. The energy of the
trapped electron is determined by long range interactions with the

continuum via screened Coulombic polarization and short range
interaction with the first solvaticn shell. Typical values of z and rc are

9

4 - 8 and 1.7 - 2.2 A. respectively. Recent EPR and ENDOR spectra of
electrons in KCN showed 17 hyperfine features due to the coupling to
the first shell of K+ ions [48]. The 14N ENDOR results showed a
strong hyperfine coupling to nitrogen, with A = 38.6 MHz and Q = 0.9
MHz at 210 K. but below this temperature the 14N coupling was lost.
This result means that there is considerable delocalization into the
first shell of CN' ions. This was expected because of the presence of
low-lying empty orbitals.

The major improvements of this model are that the energy
required to orient the first solvaticn shell can be explained and the
strongest dipole attractions of the electron with the first solvaticn
shell are explicitly included. The trapped electron at medium
concentrations. in which the electron is localized at the cavity has
been described. The trapped electron at low concentrations in solids,
which reduces the Coulombic repulsions of cations bordering the

cavity will be reviewed in the next section.

1.3.2 Color Centers

The trapped electron in solids was first reported 70 years ago.
Alkali halides become colored when they are exposed to high energy
radiation [49]. The radiation results in the formation of excitons.
mobile excited state species which consist of an electron bound to a
hole. The exciton can dissociate in the vicinity of an anion vacancy to

give a localized electron (F-center) and a localized hole (V-center)

10

species. The definition of an F-center is an electron trapped at an
anion vacancy.

Several parameters have an effect on the stable formation of the
localized electron state. including the radiation energy, the pressure
and the temperature. These can affect the mechanism of the
excitation and the nature of the excitonic species [50]. Color centers
in alkali halides can be produced by exposure to UV radiation which
strips the valence electron from the halide anion. The electron is
initially weakly bound to the remaining halide atom at an energy just
below the conduction band. The electron may subsequently be
trapped at a pre-existing vacancy to form an F-center. Harder
radiation can actually create the anionic vacancy by ejecting an anion
from its lattice site. The electron can then be trapped at the vacant
site to form an F-center. Typical color centers can have concentrations
of 1018 electrons/cm3.

The optical spectrum of F-centers [51] in an alkali halide crystal
consists of a broad bell-shaped absorption band. The position of the
band depends on temperature. pressure and the nature of the alkali
halide. The breadth of the band increases with increasing
temperature, while the oscillator strength remains constant. An
empirical equation known as the Mollwo-Ivey relationship [47] roughly

accounts for these phenomena

E = 17.7a‘1-84

in which E is the energ' in eV of the absorption maximum and a is the
interionic distance. According to this relationship, the interionic

11

distance will have a larger range of values for increased thermal
vibration in the lattice [47].

The simplest wave function for the trapped electron can be
approximated as that of a particle in a cubic box of length 2a. A more
complex potential well similar to the Madelung energy, has also been
used. The idea that the electron might interact with more than one
shell of nearest neighbors is substantiated by EPR and ENDOR studies.
Hyperfine interactions due to ions as far away as the eighth neighbor
shell have been observed for F-centers in KBr [52]. These results
indicate that the electron has long range interactions with the ionic
lattice. The bulk of the electron density (63%) is, however, located
inside the vacancy, and 90% of the electron density is found within
the first two shells of ionic neighbors.

The F-center is similar to the trapped electron, which is weakly
bound to its surroundings. The F-center concepts can be applied to
explain the local structure of electrons trapped at anionic sites and
the resulting electronic charge distribution in electrides and in
electrons trapped at anion vacancies in alkalides.

I.C. Alkalides and Electrides
LC. 1 Alkalides
Since the discovery of the first salt of an alkali metal anion in

1974 [53, 54] the physical properties of alkalides and electrides have
been extensively studied. The structures of 19 alkalides and 4

12

electrides were recently reported at Colloque Weyl VII [8]. The
stabilization of alkali metal anions and trapped electrons in solids is
due to complexation of the cation by cyclic or bicyclic polyethers or
polyamines, which makes the synthesis of alkalides and electrides
thermodynamically feasible.

The n52 ground state of the alkali metal anion is intrinsically
stable because of the positive electron affinities of gaseous alkali metal
atoms that range from 0.62 eV (Li) to 0.47 eV (Cs) [55]. The transition
as2 -> nslnpl of the alkali metal anion dominates the spectrum since
the ionization energy is higher than the excitation that is optically
allowed. The wavenumber maidmum depends on the metal anion and
ranges from 15400 cm"1 ( 1.9 eV) for Na" to 9600 cm'1 (1.2 eV) for
Cs" [56]. The excited state wave function is sensitive to the
surroundings such as the host solvent or crystal and the spectra are
similar to those of the charge-transfer-to-solvent spectra of halide ions
[57]. A second absorbance at ~ 20000 cm"1 (2.5 eV). which appears as
a shoulder for a sodide might be due to a transition from the ground
state to the conduction band. Recently several photophysical effects
have been studied for Na+cryptand[2.2.2]Na' ( Na+C222Na' ) [58. 59.
60]. First, the excitons produced by 2.0 eV photons are extremely
mobile and have the characteristics of exiton-polaritons [60].
Secondly, nearly reversible photobleaching of Na“ can be induced by an
intense laser pulse at 605 nm or at 302 nm [61].

The optical spectra alone did not prove the existence of genuine
alkali metal anions with a spherical or nearly spherical charge
distribution because of alternative possibilities formed by aggregation

of the solvated or complexed cation and two solvated electrons or with

13

an electron pair [62]. The nuclear magnetic resonance (NMR)
technique was used to prove the existence of M' in solution and in
crystalline alkalides as “genuine” anions [63, 64, 65. 66]. Separate
NMR signals were detected that corresponded to M+ and M'. The
former is observed at the chemical shift of Na+ in model compounds
and the latter agrees with the chemical shift of Na'(g) to within a few
ppm and is insensitive to the host solvent or lattice [13, 16, 67].
These results indicate that the ground state of Na". both in solution
and in the solid state is not significantly perturbed by the
surroundings. Larger shifts of the NMR peak from the gas phase for
other alkali metal anions may result from the mixing of other states
into the n52 ground state [14, 68,69, 70, 71, 72].

Even though most alkalides appear bright and metallic, none
shows metallic conductivity. For Na+C222Na’ [73], the temperature
dependence of the conductivity is characteristic of an intrinsic
semiconductor with a band gap of 2.4 to 2.5 eV. Other alkalides also
show a logarithmic dependence of the resistance on l/T but. in most
cases, this temperature dependence of the conductivity is caused by
defect electrons.

X-ray structure studies of alkalides prove that M' is present as a
distinct anion and that there is essentially complete charge transfer to
form the complexed cations and the alkali metal anion. The space
occupied by the alkali metal anion is much larger than that of the
alkali metal cation. Their large size and low surface charge density
tend to make them polarizable so that they can deform upon contact
with other atoms. The crystal structures of alkalides fall into three

14

categories: (1) structures with isolated anionic sites. (2) structures
with anion dimers or chains and (3) structures with cation-anion pairs.

2 electron

Because all alkali metal anions have the ns
configuration. pure alkalides are diamagnetic. However. the magnetic
susceptibilities of alkalides have been investigated [74] because
alkalides are prepared from solutions that always contain some
solvated electrons. which results in trapped electrons in the
polycrystalline alkalides. These trapped electrons give rise to a small
“Curie tail” at low temperature. The concentrations of trapped
electrons in alkalides are high enough to detect. so the EPR technique
has been recently used to study the nature of the trapping site or the

electron charge distribution [22, 75, 76].
I.C.2 Electrides

Since the first electride. Cs+(1806)2e', was isolated and
identified in 1982 [77] the optical. electrical and magnetic properties
of electrides have been investigated. Crystalline electrides are still
more difficult to synthesize and work with than alkalides because
trapped electrons are more reactive than alkali metal anions. The
electrides have been classified as containing localized or delocalized
electrons on the basis of the optical, electrical and magnetic
properties.

The optical spectra of localized electrides show a distinct
absorption in the near IR (6000 cm'1 - 9000 cm'l) [78] indicating a
minimum band gap of 0.5 to 1.1 eV. Most electrides fall into this
category and have trapped electrons in potential wells of depth at least

15

0.5 eV. By contrast. the optical spectrum [25] of a delocalized
electride, K+C222e'. is similar to the plasma absorption of metallic
metal-ammonia solutions [79] with a rising absorbance across the
visible and well into the IR.

Powder conductivities of localized electrides [80] show both
ionic conductivity and semiconductor behavior. The observed
resistance and nonohmic behavior result from concentration
polarization and/or a resistive barrier at the sample-electrode

interface as well as a Schottky barrier [81]. The activation energies for
ionic conductivity are about 1.1 eV for Cs+(18C6)2e' and 0.6 eV for

Cs+(15C5)2e' (both are localized electrides). Ionic conductivity could
result from the transfer of Cs+ between anionic sites in the lattice.
The delocalized electride K+C222e' shows high conductivity with an
activation energy of 66 ~ 67 kJ/mole. This shows that the electron in
this delocalized electride is more weakly bound than in localized
electrides.

The magnetic susceptibilities of most localized electrides such
as Cs+(18C6)2e' [22] show only Curie-Weiss paramagnetism which
indicates that the trapped electrons do not interact strongly with each
other. The small negative Weiss constant of this compound indicates
weak antiferromagnetic coupling, but it exhibits no magnetic
transition. The localized electride, Cs+(15C5)2e'. shows an
antiferromagnetic transition with a Neel temperature of 4.6 K and a
first-order phase transition at 295 K [82]. The magnetic behavior of
Li+C2lle' [83] and K+C222e' [84] indicates the existence of spin-
paired singlet ground states. The temperature-dependence of the
magnetic susceptibility yields a singlet-triplet splitting for the latter

l6

electride of 0.05 - 0.1 eV. This behavior shows that either there is a
thermally accessible triplet state or temperature dependent electron-
pair dissociation [84].

The crystal structures of the localized electrides Cs+(18C6)2e'
[85. 86,87] and Cs+(15C5)2e' [88]. and the delocalized electride,
K+C222e' [84. 89] provide information about their behavior by
comparison with alkalides of similar structure. The former. the
localized electrides. have anionic sites that are isolated from each
other with constricted channels that join one site to its neighboring
sites. The latter. K+C222e', has anionic sites that are connected
through short, open channels in two dimensions. The anionic sites in
K+C222e' exist in pairs so that two trapped electrons are close
enough to interact with one another. The structure and properties of
this electride indicate that electron-pairs exist in a singlet ground
state which has a thermally accessible triplet state and the electron
mobility is high. 5

The electron locales cannot be determined by X-ray diffraction '
because of the extremely low scattering of a single electron. EPR
spectroscopy has been used to investigate electron locales and the
interactions between trapped electrons and their surroundings in
electrides. Since exchange effects often dominate in pure electrides.
EPR or ENDOR technique cannot give us information about local
interactions. However, we can eliminate exchange effects by studying
isostructural alkalides that contain low concentrations of trapped
electrons. This subject will be introduced in detail in the following

section.

17

ID Objectives of This Work

Since we cannot locate the electron in electrides by X-ray
diffraction due to low scattering of an electron, much effort has been
devoted in attempts to determine the locale of the trapped electron.
Since we expect the complexant to be polarized with negative oxygens
and positive -CH2- groups . it is assumed that the trapped electron
wavefunction will extend into -CH2- framework of the complexant
molecules. X-band and G-band EPR. ENDOR and ESEEM techniques
are powerful tools for the investigation of paramagnetic species and
electron charge distributions and hence have been brought to bear on
this problem.

The objectives of the present work can be summarized as
attempts to answer the following questions:

(1) What is the general location of the unpaired electron in
electrides and alkalides ?

To probe the likely location location of trapped electrons in

electrides we can take advantage of isostructural alkalides that

correspond to electrides. The paramagnetic sites of
isostructural alkalides and electrides will be compared with

known-structure electrides and alkalides in Chapters IV and V .

The anionic sites of the unknown-structure alkalides can be

deduced from the comparison to the results of known-structure

alkalides.

(2) What is the local charge distribution of the trapped electron
in electrides and alkalides ?

18

To probe the local unpaired electron density of electrons

trapped at anionic sites in alkalides. the ESEEM technique will

be used. since we can obtain information about the distance

between the trapped electron and the interacting nucleus and

the number of interacting nuclei by using ESEEM. The results

will be discussed in Chapter VI.

(3) What is the approximate wavefunction of the trapped
electron ?

To obtain the approximate wavefunction of the trapped electron.

alkalides that have contact ion-pairs and those that have isolated

anions will be investigated to determine the hyperfine

interactions and g values as well as their anisotropies. The

results will be discussed in Chapters IV - VI.

(4) What is the interaction among these trapped electrons ?

To probe the interaction among trapped electrons. the spin

exchange and the temperature dependence of the intensity as

well as the relaxation properties of alkalides and electrides will

be investigated and discussed in Chapters IV and V.

The conclusions of this present work and suggestions for future

work will be presented in Chapter VII.

CHAPTER II
EXPERIMENTAL METHODS
II.A Syntheses and Sample Handling
HA. 1 Purification of Metals. Complexants and Solvents

High purity metals and complexants are required for the reliable
syntheses of alkalides and electrides. The solvents must be dry and
free of oxygen and reducible impurities.

Sodium. potassium (99.95%) and rubidium (99.93 %) were
obtained from Johnson Matthey Inc. in 5 gram argon-filled glass
ampoules. Cesium metal donated by the Dow Chemical company was
used. The bulk metals were redistributed into small diameter tubes (2
- 5 mm ID.) under high vacuum (< 10°5torr) as described elsewhere
[76, 90]. The number of moles of metal can be calculated from the
length of the metal in a glass tube of known diameter.

15-crown-5 (98%), 18-crown-6 (98%). cryptand [2.2.2] (98%)
were obtained from Aldrich Chemical Company. 12-crown-4 was
bought from Sigma. The solid 18-crown-6 (18C6) and cryptand [2.2.2]
(C222) were purified by sublimation under high vacuum (< 10'5 torr)
The liquids 12-crown-4 and 15-crown-5 were distilled at 10'5 torr to
remove impurities. Hexamethyl hexacyclen (HMHCY) was obtained by
methylation of the precursor. hexacyclen [91], which was obtained

19

2 0
from Aldrich Chemical Company. HMHCY was purified as described

elsewhere [92].

Dimethylether(Me20, anhydrous) and trimethylamine (Me3N,
anhydrous) were obtained from Matheson. Diethylether (DEE),
99.95%) was obtained from E. M. Science. The solvents were purified
by first distilling them under vacuum over calcium hydride to remove
most of the water. The solvents were then transferred into bottles
containing Na films or NaK alloy, with benzophenone. The solvent was
stirred until the solution was deep blue. which indicated that radical
anions and/ or dianions of benzophenone were stable in the solvent.
The solvents were then transferred to cylindrical glass bottles in the
cases of DEE and Me3N and to clean stainless steel tanks for Mezo.
The solvents were repeatedly frozen in liquid nitrogen and pumped to

remove soluble gases. DEE was stored over NaK alloy.

II.A.2 Syntheses of Alkalides and Electrides

A “K-cell" has been developed for the syntheses of alkalides and
electrides as shown in Figure 2-1. All glassware was soaked in aqua
regia overnight. The rinsed K-cell was dried in the oven for more
than one day prior to use. The synthesis of alkalides and electrides is
described in detail elsewhere [93. 94]. The reactions to form

alkalides and electrides are given by the equations

M +N + nC —> WCnN' (2-l)

21

Sample
Fingers

 

Figure 2-1. K—cell for the synthesis of alkalides and electrides

22

and
M + nC —- ane' (2-2)

in which M and N are the alkali metals Na, K. Rb and Cs (M can also
be Li) C is a complexant. l2C4, 15C5. 1806, C222. HMHCY etc. and n
is 1 for a one-to-one cationic complex cation and 2 for a sandwich
complex.

All handling of the solutions and products during synthesis is
carried out at temperature below - 40°C after evacuation of the vessel
to ~ 10'5 torr. The synthetic methods have been described in detail
elsewhere [95]. The proper molar ratio of the metal(s) and
complexants (usually about two millimoles of the compound) are
introduced into a previously evacuated and degassed K-cell in a
helium-filled dry box. Both arms are then sealed off under high
vacuum. The metal is distilled under vacuum to make a film on the
wall of bulb A in Figure 2-1 and then the arm is sealed off. The
solvent. Me20 is added to dissolve the complexant and then the
solution is transferred from bulb B to A to dissolve the metal. The
resulting blue solution is then transferred from bulb B to A after all
metal has been dissolved. A less polar solvent (Me3N or DEE) is then
distilled in as a co-solvent to yield polycrystalline salts. The solvent is
removed and the powder is vacuum-dried. These poly-crystalline
samples are then transferred into the storage fingers and sealed off.
Fingers of alkalides are stored at - 75°C in a freezer and electrides are
stored in a Dewar that contains liquid nitrogen.

The polycrystalline samples are transferred from the finger into
an EPR tube while cold under a dry nitrogen atmosphere in a glove

23

bag. The 4 mm commercial fused silica EPR tubes are then sealed off

under high vacuum.
II.B Description of Instrumental Methods
NB. 1 X-band EPR

EPR spectra were recorded on a Bruker 200 D spectrometer at
9.5 GHz. A rectangular TE102 cavity was used. An ER350 gaussmeter
was used to measure the magnetic field strength with 1 mG resolution.
Microwave frequencies were measured with a Hewlett-Packard 5425L
frequency counter with 10 kHz resolution. The temperature was
controlled either with flowing cold nitrogen or with a Varian 4540
temperature controller. The temperature of samples was calibrated
with a copper-Constantan thermocouple inserted into the EPR sample
Dewar and a Doric DS-350 digital readout system. Due to the thermal
instability of the samples, the temperature was generally kept below -
40°C. Data were collected with an IBM-compatible Dell computer.

II.B.2 G-band EPR

The high frequency EPR spectra were obtained at Cornell
University with a G-band EPR spectrometer developed by the research
group of J. H. Freed [96]. The block diagram of the far—IR EPR
spectrometer used in this study is shown in Figure 2-2. The FIR
source is a Millitech Corp. PLS-F phase locked solid state source
which delivers 3-5 mW at 250 GHz (WR-4 waveguide). A semiconfocal

24

Fabry-Perot resonator was used for the sample cavity: the cavity was
tuned by controlling the distance between two mirrors. The
modulation frequency was 65 kHz. The field was swept by using a
superconducting solenoid (Ho = 8.9 '1‘) driven by an HP6032A power
supply that provided a point-to-point resolution of 0.188 G up to a
sweep width of 560 G. The temperature was controlled in the range
of - 120°C to - 40°C by using a heater and regulating the flow rate of
cold nitrogen gas. The temperature stability was about :i: 3°C.

The sample holder for the G-band EPR spectrometer is shown
in Figure 2-3. Both Teflon and polymethylpentene (TPX) had been
previously used as material for the construction of the sample holder.
Teflon, TPX and Z-cut quartz had been used as windows for the sample
holder because they have low absorbance in the FIR. Because Teflon
would react with our sample, it was not used for the present study.
and Z-cut quartz was chosen for the window. When the sample holder
was put into the liquid nitrogen, however, the Z-cut quartz window
popped out due to differential contraction of the sample holder with
respect to the window. To overcome this problem Rexolite (cross-
linked polystyrene) was chosen as a material of construction for both
the sample holder and the window. The transmittance of far IR (FIR)
radiation was such that Rexolite proved to be a satisfactory material: it
was also stable with respect to both solvents and samples. Even
though there were several tool marks apparent on the window, the

optical performance was not compromised because the surface was flat
to better that M 8.

 

 

 

 

 

 

 

 

 

:1"

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

r————
u‘ CI—IiI-II
L":
L
ur-
A
: L
‘r
O
c L—w e

 

 

 

 

 

Figure 2-2. Block diagram of the G-bandl EPR spectrometer. A:
Superconducting Solenoid and sweep coil, B: 250 GHz Source, C: 100
Hz reference oscillator, D: Detecto,r E: Cavity and field modulation
coil, F: Quasi-optical beam guide, G: Main coil power supply H: current
programmer, I: Sweep coil power supply, J: Computer, K: Lock-in
amplifier, L: Field modualtion and lock-in reference oscillator. M:
Tuning screw, N and O: Vapor-cooled leads, P: LHe indicator. 9: LHe
transfer tube, R: Bath temperature and heater resistor. S: LHe blow-off
Valves. [96]

26

For the 250 GHz EPR studies. the polycrystalline samples were
ground in an agate mortar below - 50°C under a dry nitrogen
atmosphere in a glove bag. The samples were loaded into the sample
holder and then sealed with a Mylar tape. Since the radius of the FIR
beam in the cavity is 2 mm, a larger sample volume could used than at
X—band. The amount of sodide sample filled the sample cell up to half

of its height but less sample was used for electrides and for
Cs+(18celgcs'.

0.01M mun

 

O-NINO
0.30 nun
p——.i
L 7.0 nun on
25.4 m INA

Figure 2-3. Sample holder for G-band EPR [96]
11.3.3 The Pulsed EPR Spectrometer

The sample preparation methods used were the same as for X-
band EPR and samples were kept in the liquid nitrogen Dewar that
contains liquid nitrogen. The pulsed EPR spectrometer used in this
study was recently constructed at Michigan State University by Prof. J.
L. McCracken. A block diagram of the pulsed EPR spectrometer is
shown in Figure 2-4. A microwave synthesizer (Gigatronics Model
610), operating from 6 to 18 GHz, was used as a microwave source.

The microwave bridge (capable of operating over 6 to 18 GHz) consists

27

of three major components: the microwave transmitter, the cavity,
and the microwave receiver. Microwave pulses are generated by pulse
modulating a phase-locked, cw klystron with a fast PIN diode switch.
The low power output pulses are passed through a 0° / 180° phase
modulator (General Microwave Model F1938) and a coaxial attenuator
and then amplified to the level of approximate 1 kW by a pulsed
traveling wave tube. The high power pulses are then passed through
an attenuator and delivered to the sample.

The cavity used in this work is of the reflection type and
employs a folded half-wave resonator [97] and the X-band Gordon
coupling arrangement developed by Britt and Klein [98]. A
conventional 4 mm o.d. EPR tube can be used for this cavity and the
sample can be introduced from the top of the Dewar without removing
the header assembly.

The microwave receiver uses a double balanced mixer as a
detection element (RHG Model DMl-18AB) in a homodyne
arrangement. A low-noise GaAs FET amplifier (Avantek model AWT-
18635) is used in the receiver, with a medium-power, high-speed PIN
diode limiter (Innowave, model VPL-6018) and a fast PIN diode switch
(General Microwave, model F91 14) serving to protect it from damage
by higher-power microwave pulses. A second PIN diode switch is used
to attenuate the mixer input during microwave pulsing. An Apple
Macintosh-Cx computer controls the pulse sequences and collects the
ESE envelopes by using a modified version of the dead-time
reconstruction protocol described by Mims [99]. Data collection and
analysis software were written by using the C language.

28

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

an? (Pug /._ __,
sirens /: 2; 3
I 2 I 2
35m“ \‘ s
Plhwu §‘ § 6“ ‘
—eB.
13* ,/\~
mm
DOUG“!

 

 

 

..s...

 

 

 

Figure 2-4. Schematic Block Diagram of Pulsed EPR spectrometer

CHAPTER III

THEORY

III.A Solid State EPR
III.A. 1 g-value

The isotropic g-value in EPR relates the transition frequency v to
the magnetic field H via v = gBeH in which Be is the electronic Bohr
magneton. The g-value depends on the wavefunction of the unpaired
electrons in atoms or molecules and the difference in the magnetic
properties and interactions of all electrons with spins a and B. The
deviation of the g-value from 2.0023 is determined by the contribution
of orbital angular momentum (i.e., p-, d-character) to the
wavefunction. If the spin-orbit interaction is small so that it may be
considered as a perturbation of the Zeeman term [100] the spin
Hamiltonian is

18pm = BeHog-S (3- l)

where g is now an effective g tensor (no longer a g value because of
molecular anisotropy) and S is an operator corresponding to an
effective spin. If we neglect any hyperfine interaction and the nuclear

Zeeman term, the total Hamiltonian will be

29

_ 3 o
J: germ. + geS) + as (3-2)

where B e is electron Bohr magneton and {is the spin-orbit interaction

constant. In order to calculate the g tensor in Eq. 3-1 for an S = 1/ 2
system, it is instructive to proceed through the first order
wavefunction obtained when the L-S term is considered as a small
perturbation [101, 102]. If the zeroth order wavefunctions are the

pure l0,a> and l0,[3> functions, where 0 indicates the ground state,

the first order wavefunctions are

l+> = l0,a> - S [<nl§L-S|0.ci>/(En - Eo)]ln>

and

|-> = l0,B> - S [<nl§L-Sl0,B>/(En - Eo)]|n> (3-3)

where n gives the number of the excited state. These wavefunctions
are used to calculate the matrix elements of Berra. + geS) in the true

Hamiltonian in Eq. 3-2 and they are compared with the corresponding
matrix elements of the spin Hamiltonian Eq. 3-1. The effective spin
operator 8 is defined as

Sz|+>= 1/2|+>, Sz|->= l/2|->
Sx|+> = 1/2|->, Syl+> = 1/2|-> etc.

in analog’ to S acting on Ia> and |B>.

31

For a linear molecule (or for any molecule with an axis of trigonal
or higher symmetry) the principal components of the effective g

tensor can be described as

g" = ge - 22'; S <0|Lzln><0l Lzln>/(En - E0) 3-4
gi=ge~25S<0|Lx|n><0le|n>/(En-Eo) 3-5

The expression for gll is simplified if |0> is orbitally nondegenerate,
since <0leln> = 0 in Eq. 3-4, resulting in g" = ge. Note however,

that second order perturbation theory results in a nonvanishing term

in Eq. 3—4, so gll could be slightly less than ge. In any event, g i

obtained from Eq. 3-5 can vary considerably from g. because of the
ability of Lx(= Ly) to couple excited states with the ground state. The

deviation of g i from g, will depend on whether the excited state has

the properties of an electron in a p or n-orbital.
III.A.2 Nuclear Hyperfine Interaction

Hyperfine splittings of the energy level result from the

interaction of a nucleus or nuclei with the electronic magnetic

moment. The strength of the interaction depends on 111/1 and on the

distribution of unpaired electron spin density at the nucleus. The
Hamiltonian of the hyperfine interaction, th is the sum of Fermi

contact and electron-nuclear magnetic-dipole interaction terms. For a
hyperfine interaction with one magnetic nucleus, the Hamiltonian is
given by

32

4M = gefiegnfinm. - S)~r/r3 + 3(s-rxr-n/r5 + 8n8(r)S-I/3] 3-6

where fin is nuclear Bohr magneton and gn is nuclear g-factor. The

third term is the Fermi contact interaction and contains the Dirac

function, 8, [103] to provide a nonzero value at the nucleus itself.

Frosch and Foley [104] reduced this Hamiltonian to

4m. = aLzSz + bI-S + chSZ 3-7

where a = gefiegnfin<llr3>

b = g,,is,,g,,15n[sirme)I2 /3 - <(3c0529 - l)/2r'3>]
c = gefiegnfindScosze - l)/2r’3>

I‘I’(0)i2 is the probability of finding the electron at the nucleus

(depends on the s-orbital character), r is the distance between the

electron and the nucleus, and 9 is the angle between r and the
molecular axis.

The L-I interaction is negligible so the contact term and the
dipolar term can be expressed by

A180 = gofiegnfinl‘P(0)|281t/3 3-8

_ 2 _ -3 -
Adip — (3cos 9 l)/2r 3 9

33

With the DI term neglected, the Hamiltonian can be written for one

nucleus as

IN = I-A-S 3 - 1 0
For aidal systems

elm. = AilSzIz + A J_(lex + Syly) 3- 1 1
so that from Eq. 3-8 and 3-9

These can be represented as A tensor referred to its principle axes.

A=Alsol+Adip 3-12

where 1 is the unit matrix and A dip is a traceless tensor. The

Hamiltonian of the hyperfine interaction between two or more nuclei
and the electron is given by

Hm: Bums 3-13
7 t

The experimentally determined values of I‘I‘(0) l 2 and <r’3> are

characteristic of the electronic wavefunctions of atoms. Therefore

34

these can provide a test of any atomic wavefunction derived

theoretically.
III.A.3 Lineshapes

The shapes of most lines in magnetic resonance are Gaussian or
Lorentzian, or a combination of both The manner in which these
shapes combine depends on whether the spin system is a gas, liquid
or solid, and whether the line is homogeneous or inhomogeneous.

Here only solid systems will be discussed.
III.A.3.1 Gaussian and Lorentzian shapes

The analytical first derivative expression for a Gaussian

absorption lineshape as a function of the magnetic field H is

Y'G = 1.649 yin 915—591 exp {-0.5[LH—9112] 3-14

and the corresponding expression for a Lorentzian is

re = (:‘°A:0‘)’92 3-15
[3 + ———l

 

3 5
where y'm denotes the maximum amplitude and AH is the peak-to-

peak width. These lineshapes are normalized in terms of amplitude.

The number of spins in the sample is proportional to the area.

A =1 Y(H-H°) = r (H - H0)Y&H-H°) dH 3'16
0

0

The various linebroadening mechanisms are characterized by the
moments of the line <(H - Ho)n>, n = 2, 3 . . . .

_ n _1_ ” _ n+1 ' _
<(H Ho) > (n+1) I. (H Ho )Ymm dB 317

The relation of the area and moments to other parameters has been
reviewed elsewhere [105, 106].

A combination of Lorentzian and Gaussian lines can result from
an exchange-narrowed line and from an inhomogeneously broadened
line. The former is Lorentzian in the center, and Gaussian in the wing
and the latter is a superposition of many narrow Lorenztians
compromising a Gaussian envelope. The Voigt convolution lineshape

is obtained for the inhomogeneous case.

 

 

Y _H =Mfili'a) 8“sz 3-13
m J 7‘ AHG AHL 2 (H-H) 2
1’2 (——(1}11)1n2+[211n2{——39—}-x]

_°° AH1/2 AH”:

where the subscript G denotes Gaussian, and L signifies Lorentzian.

36

III.A3.2 Relaxation

There are two principal types of resonance lines in solids. They
arise from homogeneous and inhomogeneous linebroadening
respectively [107,108,106]. Homogeneous broadening may be caused
by dipolar interactions, the spin-lattice interaction, diffusion of the
spin excitation, and motional narrowing. Inhomogeneous broadening
arises from anisotropic effects, unresolved hyperfine structures, and
inhomogeneities in the magnetic field. The linewidth of a
homogeneously broadened line is proportional to the inverse of the
spin-spin relaxation time, T2. In many solids the principal mechanism
of homogeneous broadening is the dipolar interaction between all

neighboring spins. and this produces a Gaussian lineshape. When
exchange effects become pronounced, the spin-lattice (T1) and spin-

spin relaxation (T2) times become equal. The spin-lattice relaxation of

solids may be caused by a direct process that involves one lattice
vibration phonon, or an indirect Raman process that involves two
phonons.

Two methods have been used to measure relaxation times: the
saturation method [108 109] and the pulse method [105, 106, 110].
In the saturation method, one observes spectra at a number of power
levels up to and beyond the oneset of saturation. The pulse method
entails the excitation of the sample with appropriate pulses of
radiofrequency energy, after which one monitors the recovery to
equilibrium. Here, only the saturation method will be discussed. It
uses the following simplified equation

37

 

y'm=s3/2y'81 =y'r9. IF 3 3-19
Pg2T1T2 ‘2—
4

1+

where P is the microwave power, Yin is peak-to-peak amplitude, Y8]
denotes the maximum amplitude below saturation, and s is the
saturation factor. Equation 3-19 is used for saturation curve fitting.

The peak-to-peak width is given by

Pg2T1T2 ” 2

3-20

T2 can be determined from the homogeneous linewidth below

saturation.
T2 = ___2_O_ 3-21
1[5891191)

and T1 can be obtained from the value of microwave power at

maximum as shown in Figure 3-1.

-7 0
T1= 1.97 x10 [8pr 3-21
4ngax

 

The peak-to-peak first derivative amplitude y'm can be plotted as
a function of the square root of the microwave power P, and Pmax is
the microwave power at the maximum of the saturation curve. The

dashed line is an extrapolation of the linear dependence at low powers

[106].

38

~—-——————

/ Inhomogeneously broadened line

ESR Signal amplitude

  
 

Homogeneously broadened line

 

 

Figure 3-1. The saturation curve for a homogeneously broadened line

(solid line) and an inhomogeneous line (lashed line).

39

[11.8 High frequency EPR

Since systematic investigations with high frequency EPR were
first reported in 1976 [111), several general reviews on EPR studies
from the radio frequency region to the far infrared have appeared
[112, 113,114]. The magnetic field at resonance is determined by H =
hv/gB. If paramagnetic centers with different g values are present, the

difference in the field positions of the resonances is proportional to v:

=1! LHL -
AH [3(1 g2) 322

This illustrates the fundamental reason for high frequency EPR: to get
an enhanced spectral resolution. For most organic radicals. the

relative differences Ag/ g do not exceed 10'4 to 10'3 corresponding to
line separations AH of 0.3 to 3 G at 10 GHz, which can be difficult to
detect. If the linewidth does not increase with frequency, we need a
frequency of v > 100 GHz to get satisfactory resolution.

A homogeneous EPR line is dependent on spin-lattice and phase

relaxation and on spin-spin dipolar and spin exchange interactions.

The spin-lattice relaxation rate depends on the Zeeman frequency to in

different ways [1 l3] given by

1/1‘l ~ (on 3-23

with a power factor, n, that ranges from 0 (modulation of anisotropy

hyperfine interaction, HFI) to 4 (direct relaxation process). The

40

homogeneous line width arising by phase relaxation frequently is
related to the average anisotropic magnetic interaction and can be

described by

2
l/T2 ~ re(Agan(o/g + AAan) to 3-24

where Agan is the anisotropy of the g value, AAam is the anisotropy of

the HFI and re is the correlation time for motional averaging. As for

inhomogeneous broadening, it does not depend on a) when it is caused
by unresolved HFI or spin-spin interaction, but it depends on a) when
it comes from a dispersion of g values. We can expect that the
theoretical prediction of the frequency dependence of the line width
will be difficult and only experiment can give an answer at present. At
moderate temperatures the line width can determined by Eq. 3-24,
but the increased anisotropy at high frequency can be compensated for
by a slight temperature increase since 1c is exponentially dependent
on 1 /T. This also allows one to measure shorter 1c than can be done at
X-band.

For powdered samples, the EPR spectrum results from signals

from all possible orientations as in Figure 3-2a. The line shape may be
obtained as the convolution of the individual line shapes fo(H) and the

distribution function, fngl. that describes the angular dependence of
the g value according to [l 15]

gm ~ l/iVHI 3-25

41

lei

(bl

 

(I, I:

 

<1————

 

2A, 24, A, A,
__... . ~— 4‘ I H— K—ud—u-o

506

(c)

 

Figure 3-2. Approximate shape of a high frequency EPR spectrum with
an anisotropic g factor (a) and 150 GHz spectrum (first derivative) of
perdeuterated nitrmdde radical (b) compared to a 10 GHz spectrum
(c). both in the solid state [113].

42
where VH = [(5H/89)2 + (8H/8¢)2]1/2, 9 and c are the polar and
azimuthal angles determining the orientation of the molecule in the
laboratory frame. At the turning points, at which 9 = 0, c = 0 (g = gx)
and 9 =90° (g = g). the line shape is close to a stepwise 6 function.
while for 6 = 0, ¢ = 90° (g = gy) it is close to a 8 function. When the
first derivative of f(H) is detected in the regions of g = gx, g =gz we
observe an almost pure absorption function fo(H) and at g = gy an
almost pure first derivative fo(H) as shown Figure 3-2b. This is true
only if the intrinsic line width AHO is small compared to the field
shifts Hx - Hy and Hy - HZ. When anisotropic hyperfine structure is
present (Figure 3-2b). single-crystal-like spectra are observed if the

following relations are valid:
Ay + AZ < (lgZ - gyl /[3g2)hv 3-26
Ax + AZ < (ng - gyl /Bg2)hv 3-27

Adding the line width, these equations may be given by

2
[3g (AI-loy+AI-Ioz+ lAyl + iAzl) < lgy-gzlhv 3-28

where AHoy and AHW are the intrinsic linewidths of the y and 2

components. This is considered as the high resolution condition for

solid state EPR spectra, and is fulfilled only at high enough frequency.
Since high frequency EPR studies are performed with strong

magnetic fields, the relation between the values of the external

magnetic field and the local field of the electron is dramatically

43

changed, resulting in a change in the axis direction of nuclear spin

quantization. A nucleus feels the electronic magnetic field He ~ 10 kG

for an electron-nuclear distance of l A, so the nuclear spin is
quantized along He at X-band EPR: however, it is nearly along the

external field at 250 GHz ( Ho = 89 kG). For a paramagnetic center
with i = 1/2 and S = 1/2 the EPR spectrum in the z direction of Ho

will consist of four lines [115,116].

For the transitions with AIZ = 0 the splitting is given by

AH(AIZ = 0) = 2(R+ - R_)

 

Y 2
Rt=4l,\/A§x +A§y+ (Aurfiho)

and intensities equal to

2
A7): + A7,)! ‘l" (A27. ' 4 ZrlHO)
70 3-29

 

_ =i-J_
“All-O) 2 32 R..-R.

For the All: i: 1 transitions.

AH(AIZ = 1) 21R+ - R-) and .1141). = a 1) = 1 - .1173). = 0)

”LC Electron Spin Echo Modulation

III.C.l Nature of Electron Spin Echo Modulation

44

After spin echoes were discovered in nuclear magnetic
resonance by Hahn, modulation phenomena in electron spin echoes
were also found and were first reported in 1961. The basic theory of
the modulation effect was described by Rowan. Hahn. and Mims [117].
The physical origin of electron spin echo modulation can be described
in either classical or quantum mechanical terms. Figure 3-3 shows
the classical picture of spin echo envelope modulation. The amplitude
of the echo modulation depends on the orientation of He”, on the
electron-nuclear distance r and on the number of an equivalent nuclei
at r. An analysis of an echo modulation pattern gives information about
the number and distance of weak dipolarly interacting nuclei as well as
their indentity from the modulation frequency.

The quantum-mechanical picture of echo modulation can be
explained in terms of a spin level energy diagram. For I = 1/2. S =
1/2. there are two allowed EPR transitions and two forbidden EPR
transitions. If the microwave pulse has sufficient magnitude to excite
both transitions. it produces a branching of nuclear frequencies that
modulate a single electron spin level. The two sets of electrons
precess at two different frequencies that are separated by the nuclear
frequency. Interference between these two precession frequencies
generates a modulation of the electron magnetization at the nuclear
frequency. Electron spins from upper levels that are excited into
lower levels generate modulation of the nuclear frequency. If a second
microwave pulse is applied before these induced nuclear modulations
have decayed. the electron magnetization will show the additional sum

and difference modulation frequencies. Thus the two-pulse spin echo

is modulated by these four nuclear frequencies (”01‘ (0B. ma- (DB. (0a + (DB.

45

Ho

Hem»

 

 

(b)

   

-22122223222 2"?

He

 

Figure 3-3. Diagram showing the origin of electron spin-echo
modulation. (a) A nucleus of spin I at distance r from the electron
precesses around an effective magnetic field Hem” due to the vector
sum of Ho and the electron dipolar field at the nucleus He. The
precession of I produces a time-dependent magnetic field of
amplitude AHn(1)(t) at the electron. (b) Some I nuclei at the right
precession position in (a) can follow the sudden field change by a
microwave pulse and begin to precess about Hemz) to produce a
different amplitude magnetic field AHnmm at the electron. The
interference between the modulation of the electron at both “fund“ 1)
and ynHemg) produces modulation beats in the electron precession at
the nuclear frequencies. After a second microwave pulse this

modulation appears in the electron spin-echo signal.

46

This is simplified when weak nuclear coupling to the electrons exists
(r > 0.3 nm) so that the nuclear frequencies can in the upper and lower

electron spin manifolds are about same (ma ~ COB = (on). Therefore the

observed frequencies are at con and 2mn, with the the latter also weak

for even longer distance interactions.

Figure 3-4 shows the pulse sequences for a two-pulse echo (90°-
1-180") and a three-pulse echo (90°-t-90°-T-90°). The three-pulse
sequence is sometimes called a stimulated echo. because the second
90° pulse puts the spins into a holding pattern in the z-direction until
the third 90° pulse generates the rephasing in the xy plane to
stimulate the echo modulation. Generally the interpulse time 1: is fixed
and T is varied to generate the echo decay curve for a three-pulse
experiment. The three-pulse echo as a function of T decays as the
spin-lattice time T1 since during time T the electron spins are
oriented along the z-direction. Thus the three-pulse echo decays
more slowly than the two-pulse echo. The three-pulse echo may be
modulated only by the nuclear frequencies and not by the sum and ‘
difference frequencies. The first pulse generates modulation at the
nuclear frequencies; the second pulse incorporates the sum and
difference frequencies: the third pulse causes interference of the sum
and difference frequencies to leave only the nuclear frequencies. In
the three-pulse echo experiment the first two pulses generate a weak
two-pulse echo at time t after the second pulse. Therefore, at T = 1
this two-pulse echo interferes with the three-pulse echo detection.
This can be minimized by selecting 1: to correspond to a minimum in
the two-pulse echo modulation and can be nearly eliminated by

appropriate phase cycling [1 18].

47

rrm1"
'I...II.I
I..'.IIH
”main“ J] W
0—'
five-pulse

fl
’I’.»

fl
,r.:: :-'-‘.d .;-.- -

 

 

 

l
l
]

 

 

 

 

 

 

 

 

 

F22:

 

 

 

 

 

Three-pulse

Figure 3-4. Illustration of modulation of a Two-pulse (a) and a Three-
pulse (b) Spin Echo Decay Envelope.

48

III.C.2 Analysis of Echo Modulation

To obtain explicit hyperfine information from spin-echo
modulation it is necessary to calculate the expected modulation
pattern for a certain assumed hyperfine interaction or electron-
nuclear geometry. Rowan, Hahn, and Mims [117] first presented a
density matrix formalism for simulating echo modulation patterns and
obtained explicit expressions for the I =1/2, S = 1/2 case. Later Mims
rewrote the formalism and discussed the approximations and
limitations involved for both two-pulse and three-pulse echo

modulation [119, 120]

III.C.2.1 No-pulse spin echo modulation pattern

The total time dependence of the spin echo intensity Vccho can

be described as

3-30

echo = Vdecay Vmod

To calculate Vmod it is easier to use variant density matrix formalism

[121]. Any wavefunction for a system can be expanded in terms of a

complete set of orthonormal functions

WM) = 2 Cniq.t)Un(q) 3-31

4 9
with the time dependence all in the coefi‘lcients cm The energy of a

real system that consists of many spins can be found by the ensemble

average of the energ' operator H , as in the following equation:

E = va = .2... 6262mm.) 3-32

where we used Eq. 3-31 to replace the wavefunction ‘I‘ and the bar

represents an ensemble average. the density matrix p“ is define as the

 

matrix of the coefficient products C:nCn. The emery is given by
E = Trace (pH) 3-33

The matrix elements of p are calculated from the equation of motion

for the density matrix

ap/at = 21ti/h [p.Hl 3-34

in which the brackets represent the commutator of p and H.

To apply Eq. 3-33 the appropriate Hamiltonian and an
expression for g must be obtained. Here we do not include any
relaxation terms in the spin Hamiltonian because these will affect
Vdecay but not Vmod- Therefore the appropriate Hamiltonian for echo
modulation alone is

H=H +H 3-35
0 t

5 0
where Ho is the ordinary static Hamiltonian in the absence of a

microwave pulse and Ht is the time-dependent part associated with a

pulse. By assuming that the high field and point dipole

approximations are valid for the anisotropic hyperfine interaction, the
static Hamiltonian Ho becomes

Ho = [3.lgeHoSz - [SugnHoIz + 11521; + [(3cos29 - 1)Iz + 2sin6cosOI,‘]Sz
KW 3-36

13

where H0 is the external field, a is the hyperfine coupling, r is the

distance between the electron and nucleus and 6 is the angle between
H0 and the position vector :- joining the electron and nucleus. The
time-dependent Hamiltonian Ht is given by

H: = 2gBHISy cos(coet) 3-37

H1 is the rotating component of the microwave field at frequency me.

Let us return to the application of Eq. 3-33 to calculate the echo
modulation. The density matrix p(21) is time-dependent so that

Trace(pH) will depend only the time dependent part of H given by Eq.
3-37. The normalized echo modulation Vmod(21:) is given by

Tr[p(21)Syl

3-38
Tr[p(0)Syl

 

Vmod (213) =

51

where the denominator is the normalization factor and p(O) is the

time dependent equilibrium density matrix in the high-temperature
approximation that exists prior to the first pulse. Since the electron
Zeeman interaction dominates H0 in the high-temperature
approximation the thermal equilibrium density matrix is given by

[117]

p(o) = 1 (1 _ gBHOSZ

25 + 1 kT ) 3'39

 

 

Now from Eq. 13-34 a formal solution is obtained when H is

independent of time
p(t) = exp(-th/h)p(0)exp(th/h) 3-40

To apply Eq. 3-40 the time dependence in H is eliminated by
transforming the Hamiltonian to the electron rotating frame. This is
equivalent to subtracting the electron Zeeman term H

Hr = H ' gBHoSz 3-41
11,1011) = H - gBHoSz 3-42
Hr(on) = III-(Off) + 2gBH18y ~ ZgBH 15y 3-43

The density matrix p(t) is obtained from Eq. 3-40 by successively

applying the appropriate time-independent Hamiltonians. Let R] =
expl-iHIt/h) then

52

R1 = exp (-igBH1Sy n/h) 3-44
R2 = exp (-iHr(offlt/h) 3—45
R3 = exp (~i2gBHISy 1t/h) 3-46
therefore

3 t t #
p(2‘t) = 112R3R2R1p(O)R.2 R3 R2 R1 3-47

Using Eq. 3-47 and 3-39, Vmo d(21) is evaluated [117, 119].

Here the simplest case (I = 1/2 and S = 1/2) which has an
isotropic g value and no quadrupole interaction will be discussed. For
a S = 1/2. I = 1/2 system the result is

Vmod(2'c) = 1- 2ksin2(ma/2)sin2(cop/2) 3-48

where k = [maB/macofl ]2 , m1 = ganHo/ h
ma = [(A/2 + £01)2 + (B/21211/2

m5 = [(A/2 - (:01)2 + (B/2)211/2

A = %“— (3cos02 - 1) + 21m

 

53

B = ll_elln_ (3cosesin9)
r3
Eq. 3-48 can be rewritten in the equivalent form [122]

Vmod = l — k[2-2cos(mat) -2cos(copt) + cos(a)a- mph + cos(ma + nigh]

3-49

which clearly shows that the nuclear frequencies and their sum and

difference occur in the modulation pattern.

III.C.2.2 Three-pulse Echo Modulation Pattern

Three-pulse echo modulation usually occurs over a longer time
scale than two-pulse modulation because of the longer interval time T.
This may be sensitive to weaker hyperfine interactions than two-pulse
echo modulation. The simulation of three-pulse echo modulation is a
straightforward extension of the formalism used for the two—pulse case
[1 19, 120]. Mims showed that the three-pulse modulation expression
can obtained simply from the two-pulse modulation expression
without using density matrix methods by following the procedures
given below:
1. Write the two-pulse expression with cos(coat) or sin(coar) replaced
by coslcoah + Tl] or sinlmah + T)].

2. Write the two-pulse expression with cos(mpr) or sin(mpt) replaced by
cos[coB('c + T)] or sinlcoph: + T)].

54

3. Add the expressions (1) and (2) and divided by two to normalize.
III.D. Simulation in Disordered Systems

If the nuclear spin-spin interaction is neglected, the amplitude
of the spin-echo modulation V“mod for n nuclei is

n
V31“! = 2 Vfilod 3-50
181

This equation holds for both identical and nonidentical nuclei, so the
modulation depth increases as the number of interacting nuclei
increases for identical nuclei.

In disordered systems the echo modulation pattern is obtained
by averaging over all orientations. Kevan et al. [1221 suggested a
spherical model in which an effective interaction distance is used for

the closest shell of nuclei. The amplitude of the echo modulation is

Vmod = [Nmoduoflmn 3-51

which is a function of r (distance between electron and the interacting
nucleus), 1 (hyperfine coupling constant). and n (the number of

interacting nuclei with an electron).

CHAPTER IV

EPR STUDIES OF ELECTRONS TRAPPED IN SODIDES

This chapter is in the form of a paper that has been published in
the Journal of Physical Chemistry, and which is entitled “EPR Studies
of Electrons Trapped in Sodides”. Supplementary materials and the
results for sodides of unknown—structure are added. This chapter
includes some work by Dr. Ahmed Ellaboudy and Dr. Marc DeBacker.

The EPR spectra of six sodides of known structure reveal that
excess electrons in these salts are trapped at vacant anionic sites and
can be considered similar to F-centers. Hyperfine splitting is observed
when the complexed cation is exposed to the anionic site. but not
when the cation is well-shielded by inclusion in a sandwich structure
formed by two crown ether molecules. The g-values. Tle relaxation
times, hyperfine splittings. and dependence of intensities on

temperature are reported and discussed.

IV.A Introduction

It is now well established that alkali metal ions can have the
oxidation number - l as well as the usual + 1 value. 1’6 A number of
ionic salts that contain alkali metal anions have been crystallized and
have had their structures determined by single crystal X-ray difi'raction

methods. 7'13 In these compounds. called alkalides, the

55

56

thermodynamics is driven by the trapping of an alkali cation by a
complexant such as a crown ether or a cryptand. These compounds
may be represented by Ma+(C)an’. in which Ma and Mb are the same
or different alkali metals, C is the complexant. and n is l or 2.

It is also possible to synthesize electrides; salts in which the
anion has been replaced by an electron. “'20 The X-ray structures of
these materials show large vacancies or "empty" regions where anions
were located in alkalides. ll. 13' 15- 17- 21 The electron density in these
cavities is. however too small to be detected by X-ray crystallography.
Electron trapping at all of the anionic sites is inferred from the
physical properties and the similarity of the structures to those of
alkalides having the same complexed cation.

Isolated trapped electrons are paramagnetic so that EPR
spectroscopy can sometimes be used to probe the charge distribution
around the trapping sites. In many cases. however, rapid electron
exchange occurs to yield only a single exchange-narrowed line. in
which case little information can be gained from the EPR spectrum of
the pure electride (The same thing occurs for the solvated electron in
liquid ammonia). Pure alkalides are intrinsically diamagnetic with an
ns2 structure that gives rise to a lS0 state. but they usually contain
defect electrons that can be studied by EPR methods. Electron
trapping occurs in crystalline alkalides because they are synthesized
from solutions that contain dissolved alkali metals and complexants.
In such solutions the majority anions, M', are in equilibrium with
solvated electrons that may become trapped in the alkalide crystals.4
In the case of sodides the equilibrium strongly favors Na" vs e' 22'23;
thus among the alkalides. sodides contain the smallest concentrations

57

of defect electrons. The crystal structures show that, in all sodides
studied to date, the anions are separated from one another. Trapped
electrons, present in small concentration, are therefore isolated from
one another, which avoids the problem of exchange-narrowmg of the
EPR spectrum.

The EPR spectra of a number of alkalides and electrides
prepared by solvent evaporation 24. 25 or crystallization 14. 2530 show
that many complications can arise. Electrons can be trapped at
several sites, temperature-dependent spin-pairing can occur,
exchange rates can vary depending on the preparation method, and
observable hyperfine coupling to cations can occur. In general, when
the cations are well-shielded from the anions by inclusion in a crown
ether sandwich or in a cryptand cage. no hyperfine splitting occurs.
indicating that the electrons are not trapped by individual alkali
cations to form, for example. an “expanded atom” within the cage.
When. however, the crystal structure shows or the composition
suggests. that the alkali cation is exposed to the anionic site, hyperfine
splitting by interaction with a single alkali cation is frequently
observed.”

The present study was undertaken to verify these general
observations and to study in detail the EPR behavior of two classes of
sodides of known crystal structure. In one type. each Cs+ ion is
sandwiched between two crown ether molecules and each Na“ ion is
surrounded by eight such complexed cations at roughly equal
distances. In the other class of sodides. each complexed K+, Rb+ or
Cs+ ion is in contact (or nearly so) with one Na' and at a much larger

distance from other anionic sites as determined from the X-ray crystal

58

 

Figure 4- l . Representations of the ionic packing in (A)
Cs+(HMHCY)-Na' and (B) Cs+(18C6)2-Na'. Each Na' ions is surrounded

by eight complexed cations, four of which are shown here.

59

structure. 10 In this class. the cation is complexed by the fully
methylated aza-crown analog. hexamethyl hexacyclen (HMHCY). 31. 32
The packing of the complexed cations and Na ' anions is shown in
Figure 4-1 for Cs+(I-IMHCY)-Na' and Cs+(18C6)2-Na'.

IV.B Experimental Section

All sodides were synthesized according to previously described
procedures. 1037 The compounds were precipitated or recrystallized
from trimethylamine or dimethyl ether solutions. The purification of
solvents and complexants and the handling of alkali metals have been
described in detail elsewhere. 3-10-2733 All steps in the preparation
processes were carried out at temperatures below - 40 °C. The
samples were kept in sealed tubes at low temperatures. The sodide
samples were loaded into EPR tubes (4 mm o.d. clear fused T08
commercial quartz tubes) under dry nitrogen. After loading the
sample. the EPR tube was sealed ofi' under vacuum (1x10"5 torr). The
EPR spectra were obtained by using a mum rectangular cavity in a
Bruker 200D EPR Spectrometer operating at 9.4 GHz (X-band). The
temperature was controlled by a Varian 4540 temperature controller
or by adjusting the flow rate of cold nitrogen. An ER350 NMR
Gaussmeter was used to measure the magnetic field with 1 m6
resolution. The microwave frequency was measured to 0.01 MHz by an
HP5245 Frequency Counter. The g-values were obtained directly by
measuring the magnetic field strength and the microwave frequency.
The data were collected with an IBM-AT microcomputer. The
nonlinear least-squares curve fitting program, KINFIT 34 was used to

60

fit the saturation curves with equations given by Poole 35 and the
powder EPR spectra were simulated with a program developed by M.J.
Nilges. 36'39

IV.C Results and Discussion for Known-structure Sodides
IV.C. 1 Results

The sodides can be divided into two kinds of systems in terms of
their single crystal structures. One type (contact systems) has the
sodide anion in contact or nearly in contact with the metal cation
(Fig. 4- 1a). Electrons trapped in such sodides show distinct hyperfine
patterns. The other type (isolated systems) has trapped electrons
isolated from the metal cation (Fig. 4- lb). Such systems show no
resolved hyperfine interactions.

The EPR spectra of contact systems

The EPR spectra of electrons trapped in M+(HMHCY)-Na' with
M+ = K+, Rb". Cs+. are shown in Figure 4-2. A hyperfine structure
consisting of 214-1 lines is observed. From these spectra. it is possible
to measure the isotropic part of the hyperfine coupling constant Aiso

and to calculate the electron density according to
A180 = (83/3)ngNBNI‘Ys(O)I2 (1)

where B is the electronic Bohr magneton and I‘I‘s(0) I 2 is the

probability distribution function for the electron evaluated at the

61

.-azéoEEEm
do 638% Eu BEE...“ .8 on... 32.90%?» .6.

-azéoazEEm .8.-az.$o:25+n .5 3 3.8% Eu .3. as

 

 

 

 

 

6 2
nucleus. The subscript N refers to the nuclear values of g and B. The
electron densities at the cations K+, Rb+and Cs+ are 0.49, 1.60 and
3.13 x1030 rn’3 respectively. horn these values, the percent atomic
character of each of these cations was calculated (Table 4- 1).

Each hyperfine component of Rb+(HMHCY) -Na' and
Cs+(HMHCY)-Na' shows a first derivative powder pattern that can be
described by axially symmetric g and A tensors. The EPR spectrum of
K+ (HMHCY)-Na- shows a more nearly isotropic hyperfine pattern and a
“broad-wing” EPR peak. Satisfactory representations of these spectra
could be simulated by using the spin Hamiltonian. 40
H. = Bs-g-H + mm + “is - BNI-gN-H (2)
where H is the applied Zeeman field vector, 8 and I are the electron

and nuclear spin operators, A is the hyperfine tensor and D is the

dipolar operator. The g tensors of Rb+(HMHCY)-Na' and
Cs+(HMHCY)-Na', obtained by simulation. show that g" values are

2.0083 and 1.996, and g i values are 1.9933 and 1.977, respectively.

The g-tensor of K+(HMHCY')-Na' yields an isotropic g-value of 2.0029.
The perpendicular components, A l of the hyperfine coupling tensors

due to the isotopes 85Rb and 8“’Rb are 100 and 349 MHz respectively
and the corresponding parallel components, A“, are 109 and 362 MHz.

The A 1 value for Cs+(HMI-ICY)-Na' is 266 MHz and A" is 302 MHz. The
isotropic hyperfine coupling constants, A130 of M+(HMHCY)-Na', are

given in Table 4- 1 .

Table 4- 1

sodides

Sodides
Cs(18C6)2Na
K(18€6)Na

Rbl8C6Na

Cs(lSC5)2Na

Cs(12C4)2Na

NaI-IMHCYNa

KHMHCYNa

RbHMI-ICYNa

63

Magnetic parameters calculated from the EPR spectra of

g—value

2.0023a
2.(X)22

2.0023

2.0023c
1.9974f

2.0020

2.11125

2.0010f
2.00m=

2.0029

1.9983

CsHMI-IC‘I'NIIe 1.9833

AHW(G)

0.97
2.43

3.35c
5.02h

5c
13/115°-f

2.21

4.40

1.6
1.2

2.85

5.25/133

8.8

%atomic

18.9

16.3

1.16

6.48

10.5

11.9

aMfidenfirstistbenmwereentrallim.
b.8tandarddeviafionesfimaiesofmelsadigitsregiveninparentheses
c.Valuesaregivenforthecenualpeak.

dNearlyindependentoftempemmre-seetext
c.111edataforCsIMiCYNaarefamemethyl deuteratedeompomd.

f. Values are given for h peaks.
3. Values are given for

b and 87m».

< 6 1110'2
1.24

2.3

5.16(7)x10'2
21(3)

2.73x10'3

12(2)
4.5(3)

33(3)

ccmT

Curie

0.0194 eV

0.0211 eV

Curie

(d)
Curie

Curie

64

EPR spectra of isolated systems

The EPR spectrum of Cs+(18C6)2-Na' (Figure 4-3) shows two
signals, a broad line and a narrow central line. The intensity ratio of
the two peaks depends on the synthesis. No resolved hyperfine
splitting is observed; however, the line broadening probably results
from super-hyperfine coupling to a number of surrounding nuclei

rather than to a distribution of g-values. The results of high frequency
EPR studies of Cs+(18C6)2-Na' agree with this conclusion. 41 The

spectra of Cs+(15C5)2-Na' and Cs+(12C4)2-Na' show only a single line.
The g-values of Cs+(15C5)2-Na' and Cs+(12C4)2-Na' are close to the

free electron value. The peak-to-peak widths and g-values are given in
Table 4-1.
Power saturation studies

The saturation curves of most sodides (first derivative amplitude
plotted as a function of the square root of the microwave power)
demonstrate homogeneous line broadening characteristic of a single
type of environment. For example, the saturation curves of
K+(HMHCY)-Na', Rb+(HMHCY)-Na' and methyl deuterated
Cs+(HMHCY)-Na' are characteristic of such Lorenztian line broadening.
A fit of the saturation curve for methyl deuterated Cs+ (HMHCYTNa' is
shown in Figure 4-4. The nonlinear least squares program KINFIT 34
was used to fit the saturation curve by the equation: 35

H1 (3)

y'm = viii
(1 + H?§?1T2F

65

3G

 

Figure 4-3. EPR spectrum of Cs+(1806)2-Na'.

66

 

g 0.5‘
g 0.4‘
0.3“

0.2‘

 

0.1 " p _ _

 

 

o 0.05 0.1 0.35 0.2 0.25 0.3
mmdmm ~

Figure 4-4. Power saturation curve of Cs+(I-Iltfl-ICY)-Na'. The solid line
is the least-squares best fit of the data for a Lorentzian line shape.

 

6 7
The best fit values of T1e and the estimated standard deviations are

given in Table 4-1. The EPR spectrum of trapped electrons in
Cs+(18C6)2-Na' could not be saturated in the range 0 to 0.1 W,

permitting only an upper bound estimate of Tre-
Temperature behavior

The EPR intensities in these systems generally follow the 1 IT
dependence characteristic of Curie law behavior. Although pure
sodides are diamagnetic, the magnetic susceptibility data show a
“Curie law tail” that is characteristic of a small concentration of
trapped electrons. There is no significant variation in the g-value with

temperature. The EPR intensities of Rb+(I-IMHCY)-Na' and
Cs+(18C6)2-Na' are shown as a function of UT in Figure 4-5. The spin

susceptibilities of trapped electrons in Cs+(18C6)2-Na',

Cs+(HMI-ICY)-Na' and Rb+(HMHCY)-Na' follow the Curie law: that is,
the concentration of unpaired spins is constant in this temperature
range and the trapped electrons do not strongly interact with each
other. The peak-to-peak width of the EPR signal is independent of
temperature in the range 130 K to 250 K. The magnetic parameters
of the sodides are summarized in Table 1. It should be noted that one
of sodides studied, K+(HMHCY)-Na', did not show any temperature
dependence of the signal intensity in the range of 190 K to 240 K.
However, the intensity increased between 240 K and 260 K. This
phenomenon is similar to that observed for Li+C2l 1~e' 24.
Rb+(18C6)-Na’ and K+(18C6)-Na‘ systems. 30 This might result from
spin pairing or antiferromagnetic coupling between electrons with

different temperature dependences in the two sites.

68

 

 

a".
45 "'
a".
I..-
‘ 41 . d H
a"...
35+ ..---. (A)
.1"
g .-"
.-I I
2.51 "I...

T" ......

0.000400005000011 0.004 0.0000005400045000“ 0.005 0.0052 0.0054
1

 

 

 

...... (a)

o
o
.0
.0

 

 

Figure 4-5. Temperature, dependence of intensities of EPR spectral

0.005 0.0055m0005 0.0055 0.007 0.0075
1

lines of (A) Rb"'(HMHCY)-Na' and (B) Cs+(18C6)2-Na'.

69

The temperature dependence of the intensity was not measured for
Cs+(15C5)2-Na' and Cs+(12C4)2-Na'.

IV.C.2 Discussion

The differences in the structures of the two families of
compounds studied readily explains the fact that a hyperfine EPR
pattern is observed in the case of the HMHCY complexes, while none
is seen for the sandwich complexes. The number of peaks in the
pattern in the former case corresponds to the interaction of each
electron with a single nucleus with spin number 7/2, 5/2 or 3/2 as
appropriate. In the case of Rb+(HMHCY)-Na’, patterns for both
rubidium isotopes are observed. Hyperfine patterns have already been
reported for other complexes that contain only one crown ether
molecule per cation, such as Rb+(1 8C 6)-Na' where unpaired electrons
apparently have easy access to the rubidium nuclei. 18' 23 Such cases
are not considered here because of the lack of structural information.

In most of these systems, anisotropy is observed as expected
from the structure. The isotropic part of the hyperfine coupling
constant can be used to determine the percent atomic character of
the cation in contact with the electron. The values reported in Table
4- 1 show that the charge transfer becomes more favorable when the
cation becomes less shielded by the complexant. As the size of the
cation increases, it moves further out of the “pocket” of the
complexant, thus permitting greater overlap with the wavefunction of
the trapped electron. The 1 1.9 % atomic character in the cesium
case is similar to that of cesium in ethylamine at room temperature. 42

70

The crown-ether sandwich complexes of cesium do not show
any resolved hyperfine splitting, indicating that the electron density at

the nucleus is small. This agrees with the independent determination
of 0.033 % atomic character that was obtained for Cs+(18C6)2.e'

(which is isostructural with Cs+(18C6)2-Na') by susceptibility and

cesium Knight shift measurements. 43

As Table 4- 1 shows, except for the last two salts, the g-values are
close to that of the free electron, in agreement with the view that the
electron is trapped in a large anionic site with little spin-orbit
coupling. The last two compounds have much bulkier cations that are
not as well shielded by the complexant. The significantly lower g-
values obtained in these cases indicate that the Rb+.e' and Cs+.e'
systems are not spherical, but rather have significant spin-orbit
contributions. Similar g-values were observed for the corresponding
“monomers” in ethylamine solutions 42 which have been described as
contact ion-pairs between solvated electrons and solvated metal ions.
44 The significance of the negative g-shift was previously discussed by
M.C.R. Symons 45 who observed that when silver cations solvated in a
rigid matrix gained one electron to form trapped atoms, there was a
positive g—shift, whereas a negative g-shift implies that the electron
density is not spherically distributed about the cation.

The results described in this chapter are in complete accord
with the “F-center model” of trapped electrons in alkalides and
electrides. According to this picture, electrons are trapped at normal
anionic sites, but the electron density can penetrate somewhat into

the surroundings. resulting in Fermi contact density at nearby nuclei.

When the alkali cations are well shielded by the complexant and

 

71

rather uniformly distributed around the anionic site, the contact
density at M+ is small and no hyperfine splitting is observed. When,
however, the anionic site is in contact (or close) to a single alkali
cation, considerable overlap occurs, resulting in a distinct hyperfine
pattern. The decrease in the g-value and the anisotropy of the
hyperfine coupling show that the unpaired electron density is not
spherically symmetric about the alkali cation in these cases.

The temperature dependences of the EPR intensities for various
sodide systems show two different kinds of behavior: Curie law and
spin-pairing. The former result indicates that the trapped electrons
are rather isolated from each other while the latter implies the
presence of spin pairing or antiferromagnetic coupling between
trapped electrons, which must therefore be relatively close to one
another.

ENDOR studies of the interactions of the unpaired spins of
electrons trapped in Cs+(HMHCY)'Na’ with protons and with
neighboring Cs"' and Na' ions were reported. 31

ND Results and Discussion for Sodides of Three Unknown-Structure

EPR spectra

The EPR parameters of sodides of unknown-structure are
summarized in Table 4- 1 . The EPR spectrum of Na+HMHCYNa' shows
four hyperfine peaks due to Na+ (I = 3/2) in Figure 4-6. The hyperfine
coupling constant is isotropic, 10.3 MHz, corresponding to 1.16 %
atomic character. The g-value is 2.0010, close to the free electron
value. The hyperfine interaction results from Fermi contact interaction

72

 

210m
2%
1900'

1700'

 

1600‘

 

1500'

 

 

 

1 t v t t t . f . t .
”gasoassoaamaasoaammogu‘gwmmmmm

Figure 4-6. X-band EPR spectrum of Na1'l-1MHCYNa'.

73

between the trapped electron and the sodium cation as with the other
M+HMHCYNa' systems. This indicates that the structure of
Na+HMHCYNa' is probably similar to those of the other M+HMHCYNa'
salts.10 .The g-value indicates that the spin-orbit interaction is small.

The EPR spectrum of K+18C6Na‘ shown in Figure 4-7 has a
single central peak with a 3.9 G linewidth and four hyperfine peaks as
for dilute metal-amine solutions. 42 The hyperfine splitting due to
potassium in metal-amine solution increase with temperature in the
range of -80 0C to 80 oC and the g-values of alkali metal-amine
solutions decrease with higher atomic weight (from K to Cs) at given
temperature. The hyperfine coupling constant for polycrystalline
K+18C6Na' is 43.7 MHz which corresponds to 18.9 % atomic
character. This % atomic character is close to that given by the
hyperfine coupling at about 60 0C in ethylamine. The g-value is 2.0023
for both peaks and is isotropic. The isotropic hyperfine interaction of
K+18C6Na' is due to Fermi contact interaction between the trapped
electron and the potassium cation (1 = 3/ 2). The isotropies of both
parameters suggest that the charge distribution of an electron in the
vacant anionic site of K+18C6Na' might be symmetric. The g-value
indicates negligible spin-orbit interaction. The central single peak
might arise from the electron trapped at an interstitial site that
interacts weakly with its surroundings.

The EPR spectrum of Rb+18C6Na' shown in Figure 4-8 has a
strong central single line and 10 hyperfine peaks due to the two
isotopes 87Rb (I = 3/2) and 85Rb (I=5/2) as is the case for metal-amine
solutions. Both the hyperfine interaction and the g- value are isotrpic.
The isotropic hyperfine coupling constants are 58.8 G (35Rb) and

74

100

 

 

Figure 4-7. X—band EPR spectrum of K*(18C6)Na'

 

75

 

1MG

 

Figure 4-8.

 

 

 

 

 

 

 

X-band EPR spectrum of Rb*(18C6)Na'

76

199.6 (87Rb) G, which corresponds to 16.3 % atomic character. The
anisotropic hyperfine coupling constant can arise from both the Fermi
contact interaction and the dipolar interaction between the trapped
electron and the rubidium cation. The g-value of the hyperfine peak is
1.9974 which indicates the presence of spin-orbit interactions. The
spin-orbit interaction might arise from the mixing of unoccupied p-
states into the valence state. The intensity of a central peak with a g-
value of 2.0023 varied with the synthesis. Therefore, there are two
types of trapped electrons: One type is in contact with the rubidium
cation and the other might be trapped at an interstitial site. The
interaction between trapped electrons in both types of sites to yield
spin-pairing is indicated by the temperature dependence, as shown in
Figures 4-12 and 4-13. The axial symmetries of the g-value and the
hyperfine coupling constant of the hyperfine signal indicate that the
electron charge distribution might be non-spherical.
Power saturation studies

The saturation curve of Na+HMHCYNa' is shown in Figure 4-9. ’
The saturation curve corresponds to homogeneous line broadening.
The spin-lattice relaxation time, T1, of Na+HMHCYNa' obtained by the
saturation method, is 1 x 10‘3 s. The saturation curve of K+18C6Na'
also indicates a Lorenztian line shape as shown in Figure 4-10. The
spin-lattice relaxation time is 1.24 x 10"4 s at 183 K. The saturation
curve of K+18C6Na' was observed as a function of the temperature as
shown in Figure 4-10. As the temperature is increased, the maximum
position of the saturation curve moves to higher microwave power.
which means the spin-lattice relaxation time decreases. This result

indicates that the spin-lattice relaxation might arise from diploar

77

 

I
I
2+:'

 

 

0 005 0:1 035 0'2 055 021 005 014 0.115 05
Star-Imam

Figure 4-9. Power saturation curve of Na+HMHCYNa'.

78

 

'1 . .
5.1““ .
Cl 4 I o -
:1 .° ,
>5 ‘ a: .
8 ($72” a a
‘4 d‘ ‘° 0 I
3:: .1! x a .
.o . :. ° ,
3 5045 ; a
v ' 1°:
75 1 ° : . 0
.9 ° 5
Q)
33

 

r r* V I" I' h r T r If r r U r r " ‘— U T r
O 50 100 150 230

S uare root. of ower
q mm” P .

Figure 4- 10. Temperature dependence of power saturation curve of

K+18C6Na'. Symbol .; -40 °C. a: -80 0c. o: -100 00, x: -120 cc.

79

interactions or direct spin-phonon interactions. The saturation curve
of the central peak for Rb+18C6Na' corresponds a Gaussian line shape
as shown in Figure 4-1 1. This indicates the presence of unresolved
hyperfine coupling to hydrogen or sodium nuclei. The saturation
curve of the hyperfine peak for Rb+18C6Na' corresponds to mixing of
Lorenztian and Gaussian line shapes. An approximate spin-lattice
relaxation time of 2.3 x 10'4 s was obtained from the maximum of the
saturation curve.
Temperature behavior

As mentioned earlier, most alkalides follow the Curie law. The
temperature dependence of the intensity for Na+HMHCYNa' also
shows Curie law behavior. The intensity decreases as the temperature
is increased. This implies that the trapped electron is isolated and
that there is no significant interaction between spins. The total
number of unpaired spins is constant in this temperature range. The
area of the EPR signals for K+18C6Na' and Rb+18C6Na' was studied as
a function of temperature for both the hyperfine and the central peak.
The log of the area is a decreasing linear function of the inverse of the
temperature as shown in Figures 4-12 and 4-13. This implies an
equilibrium between unpaired spins and paired spins that shifts to the
unpaired side as the temperature is increased. This phenomenon is
similar to that of Li+(C21 1)e' 24 and indicates antiferromagnetic
coupling between electrons in two different sites. A possible
explanation is given by the equation.

80

 

(D

7‘ 9'
«o
«0-
6" e-
4-
s-

54

O
to
0

WW

0
0
fi
.
Q
0

24

e-
o
‘1
G'
0

 

0.05 0.1 0'15 02
Squaw root of power

Figure 4-1 1. Power saturation curve of Rb*(18C6)Na'.

 

0.25

81

 

 

 

 

Figure 4-12. Temperature dependence of areas of EPR spectra of
Rb*(18C6)Na’.

82

 

m him)
9
I

 

 

 

7.. I
I
6- '__
5. - I - -
I I
4‘ . I ' I I
010004 ' ' 0.004 m 0.0040 00052

Figure 4-13. Temperature dependence of areas of EPR spectra of
K‘*(18CB)Na'.

83

 

ea- + ei-

 

Where ea' represents the electron at the anionic site and e; is the

electron at the interstitial site. The spin pairing energies obtained
from the initial slope are 1.94 x10"2 and 2.11 x10"2 eV for K+18C6Na'
and Rb+18C6Na', respectively.

IV.E References

(1) Dye, J. L.; Ceraso, J. M.; Lok, M. T.; Barnett, B. L.; Tehan, F. J. J.
Am. Chem. Soc. 1974, 96, 608.

(2) Dye, J. L. Angew. Chem. 1979. 1.8,. 587.

(3) Van Eek, B.: Le., L. D.: Dye, J. L. Inorg. Chem. 1982, 2;, 1966.

(4) Dye, J. L. Prog. Inorg. Chem 1984, 32, 329.

(5) Dye, J. L.; Ellaboudy, A. Chemistry Britain 1984, 2_Q, 210.

(6) Dye, J .L.: DeBacker, M. G. Ann. Rev. Phys. Chem. 1987, 38, 271.

(7) Tehan. F. J.: Barnett. B. L.; Dye J. L. J. Am. Chem. Soc. 1974, 26.
7203.

(8) Huang, R. H.; Ward, D. L.; Kuchenmeister, M. E.: Dye, J. L. J. Am.
Chem. Soc 1987, .193, 5561. ’

(9) Dye, J. L.; Huang, R. H.; Ward, D. L. J. Coord. Chem. B. 1988, .18,
121.

(10) Kuchenmeister, M. E.; Dye, J. L. J. Am. Chem. Soc. 1989, L11,
935.

(11) Dawes, S. 8.; Ward, D. L.; Fussa-Rydel, 0.: Huang, R. H.: Dye J. L.
Inorg. Chem 1959, 25, 2132. ‘

84

(12) Huang, R. H.: Ward, D. L.; Dye J. L. J. Am. Chem. Soc. 1989, 1.1.1..
5707.

(13) (a) Ward, D. L.; Kuchenmeister, M. E.: Dye, J. L. Acta. Cryst. 1990,
£45, 1831. (b) Huang, R. H.: Ward, D. L.; Dye, J. L. Acta. Cryst. 1990.
935, 1833. (c) Huang, R. H.; Ward, D. L.; Dye, J. L. Acta. Cryst. 1990.
935, 1835. (d) Ward, D. L.; Huang R. H.: Dye, J. L. Acta. Cryst. 1990.
Q45, 1838.

(14) Ellaboudy, A. S.: Dye, J. L.; Smith, P. B. J. Am. Chem Soc. 1983.
.105, 6490.

(15) Dawes, S. B.; Ward, D. L.; Huang, R. H.: Dye, J. L. J. Am. Chem. Soc.
1986, 108, 3534.

(16) Dye, J. L. Scientific American 1987, 251, 66.

(17) Huang, R. H.: Faber, M. K.: Moeggenborg, K. J.: Dye, J. L. Nature ,
1988, 3_3_1, 599.

(18) Dye, J. L. Valency , The Robert A. Welch Foundation Conference
on Chemical Research XXXII 1988, 65.

(19) Dye, J. L. Science 1990, 2g, 663.

(20) Dye. J. L.; Huang, R. H. Chem. in Britain 1990, 26, 239.

(21) Ward, D. L.; Huang, R. H.: Dye. J. L. Acta Crysta. C. 1988. 9.44.
1374.

(22) Dye, J. L.; Yemen, M. R.; Dague, M. G.: Lehn, J. M. J. Chem. Phys.
1978, m, 1665.

(23) DeBacker, M. G.: Dye, J. L. J. Phys. Chem. 1971, 15, 3092.

(24) Landers, J. S.: Dye, J. L.; Stacy, A.: Sienko, M. J. J. Phys. Chem.
1981, 85,, 1096.

(25) DaGue, M. G. Ph.D. Dissertation, Michigan State University, 1979.

85

(26) Issa. D: Ellaboudy, A.: Janakiraman. R.: Dye, J. L. J. Phys. Chem.
1984, 88, 3847.

(27) Dye, J. L. J. Phys.Chem. 1984, 85, 3842.

(28) Ellaboudy, A. S., Ph.D. Dissertation, Michigan State University,
1984.

(29) Dawes, S. B. Ph.D. Dissertation, Michigan State University, 1986.
(30) Shin, D. H.: Dye, J. L., unpublished results.

(31) Ellaboudy, A. S.: Bender, C.J.: Kim, J : Shin, D. H.; Kuchenmeister,
M. E; Babcock, G. T.; Dye, J. L. J. Am. Chem. Soc., in press.

(32) l, 4, 7. 10. 13. 16-hexaaza - 1, 4. 7. 10, 13, 16 -
hexamethylcyclooctadecane

(33) Dye, J. L. J. Phys. Chem. 1980, 84, 1084.

(34) Nicely, V. A.: Dye, J. L. J. Chem. Educ. 1971, 43, 443.

(35) Poole, C. P. Electron Spin Resonance,2nd ed.: John Wiley & Sons,
1983. p 590.

(36) Weil, J. J. Magn. Res. 1975, 18., 113.

(37) Nilges, M.J. Ph.D. Dissertation, University of Illinois, Urbana,
1979.

(38) Belford, R. L.; Nilges, M. J. Computer Simulation of Powder
spectra, EPR symposium, let Rocky Mt. Conf., Denver, Co, 1979.

(39) Maurice, A. M. Ph.D. Dissertation, University of Illinois, Urbana.
1980.

(40) Abragam, A.: Bleaney, B. EPR of Transition Ions: Clarendon Press:
Oxford, 1970.

(41) Shin, D. H.: Dye, J. L.; Budil, D. E.: Earle, K. A.: Freed, J. H..
unpublished results.

(42) Dye, J. L.; Dalton, L. R. J. Phys. Chem. 1967, 11, 184.

86

(43) Dawes, S. B.: Ellaboudy, A. S.: Dye J. L. J. Am. Chem. Soc. 1987,

1.92. 3508.
(44) Dye, J. L. Pure Appl. Chem. 1977. 42. 3.
(45) Symons, M. C. R., discussion in reference 42.

CHAPTER V

HIGH FIELD AND LOW FIELD EPR STUDIES OF AN ELECTRIDE AND
TWO ALKALIDES

This chapter is the form of the draft that will be submitted to
the Journal of Physical Chemistry. Dr. David E. Budil and Dr. Keith A.
Earle at Cornell University helped me to obtain and discuss the G—band
spectra.

The EPR spectra of polycrystalline samples of Cs+(18-crown-
6)2X', in which X' = 6, Na' or CS', were studied at both X-band (9 GHz
and G-band (250 GHz). The spectra of the electride at both
frequencies, and the temperature and saturation behavior at X-band.
correspond to electron localization on the EPR time scale at a single
type of asymmetric site with weak coupling to surrounding nuclei.
The results are in agreement with the “F-center" model, in which
electrons serve to balance the charge of the complexed cations with
the center of charge of each electron at an anionic site. Defect
electrons in the alkalides Cs+(1806)2Na' and Cs+(18C6)2CS' show EPR
signals from several sites in each case, with the strongest signal
originating from electrons trapped at anionic vacancies. This signal in
Cs+(18C6)2Na', and that of isostructural electride, Cs+(18C6)2e', have
nearly the same g-anisotropy, indicating similar electron-trapping
sites. The intensities of two EPR signals from CS+(18C6)2CS‘ decrease
in the same manner as the temperature is reduced, suggesting the
presence of a common spin-paired precursor that dissociates to

populate both types of sites.
8 7

88

VA Introduction

Since the isolation of the first salt of an alkali metal anion in
1974 1-2, we have characterized many of the physical properties of
alkalides and electrides. Polycrystalline alkalides and electrides are
synthesized from solutions that contain the alkali cation, complexed by
a crown ether, cryptand or aza-analog, and an equal concentration of
either alkali metal anions or solvated electrons. However, no solution
contains exclusively M' or e“. Rather, a dissociation equilibrium is

present as given by

 

 

M' + complexant M+ complexant + 26-301v (1)

As a result, electrons are always trapped in crystalline alkalides. The
concentration of trapped electrons depends on the synthesis method
used. For example, slow crystallization and an excess of alkali metal
tend to produce lower concentrations of trapped electrons.

A major goal of EPR studies of alkalides and electrides is to
determine the nature of the electron trapping site(s) and the degree
of overlap of the trapped electron wavefunction with nearby nuclei. In
most electrides studied to date, the concentrations and exchange
rates are so high that only a single exchange-narrowed EPR line is
seen at X-band. (The electride described in this chapter is an
exception:) Electron-trapping in alkalides provides an opportunity to
study the nature of trapped electrons in the absence of exchange.

89

The electronic wavefunction of the trapped electron in an
alkalide can have a significant spatial extent, which leads to hyperfine
interactions with nearby nuclei. The electron density at the alkali
cation due to the trapped electron changes with the structure of the
anionic site for both alkalides and electrides. The most obvious
indication of this electronic charge distribution is the EPR line
broadening and hyperfine splitting due to Fermi contact and/or
electron nuclear dipolar interaction. Generally, when the cation is
well-shielded within a cryptand cage or in a sandwich crown-ether
complex, the contact electron density at the cation due to the trapped
electron is small. 3 By contrast, if the alkali cation is exposed to the
anionic site, as in a one-to-one crown ether complex. or when a
methylated aza-crown is used 3-4 the contact electron density of the
trapped electron at the cation can be large. For the former case, no
hyperfine splitting is observed due to the low contact electron density
at the cation and the interaction of the electron with a number of
nuclei. The latter case shows hyperfine splitting due to a relatively
strong interaction between each trapped electron and a single cation.

The X-band EPR spectrum of Cs+(18C6)2Na' showed at least two
signals, a strong broad line and a narrow central line with much
smaller integrated intensity. 3 The intensity ratio of the two peaks
depended on the synthesis. No resolved hyperfine splitting or g-
anisotropy were observed: the line broadening could have resulted
from either super-hyperfine coupling to a number of surrounding
nuclei or to a distribution of g-values. 3 The use of high field EPR in
the present study was initiated to resolve this uncertainty.

9 0

Previous EPR studies of Cs+(1806)2CS' showed the presence of
at least two electron trapping sites with complex temperature
behavior. 5 Rotation of a single crystal demonstrated the presence of
g-anisotropy. No identification of the sites responsible for the EPR
peaks was made at the time.

Electrides are crystalline compounds in which trapped or
intinerant electrons are present in amounts equal to those of the
complexed cations. 5'13 Thus, electrons serve in place of the anions of
alkalides to balance the cationic charge. The physical properties of
electrides and their structural similarity to corresponding alkalides
strongly suggest that electrons are trapped stoichiometrically at all of
the anionic sites. The crystal structures of electrides show large
vacancies at the locations of the anionic sites, but the trapped
electrons cannot be directly detected because of the low electron
density.

Previous studies of the X-band EPR spectra of Cs+(1806)2e' at
temperatures as low as 2.9 K showed only a single narrow (0.5 G) line
whose width was independent of temperature. The lineshape became
Dysonian at higher temperatures, indicative of high microwave
conductivity. The activation energy for this conductivity was only 0.05
eV, much lower than the apparent d.c. activation energy of 0.45 eV.
These results indicated rapid electron exchange, even at the lowest
temperatures measured. 5

Recent d.c. and ac. powder conductivity studies of electrides 14
have revealed that contamination of the electride Cs+(18C6)2e‘ with
C5' drastically affects the conductivity, increasing the electronic
contribution by several orders of magnitude. Apparently, the presence

91

of small amounts of excess cesium provides a mechanism for electron
migration and exchange that is not present in the pure electride. The
effect on the EPR spectrum is also dramatic as described in this
chapter.

The present study of the X-band and G-band EPR spectra of
three compounds that contain the complexed cesium cation,
Cs+(18C6)2. was initiated in attempt to separate the effects of multiple

trapping sites. hyperfine broadening and g—anisotropy on the EPR
spectra of Cs+(18C6)2e°, Cs+(l8C6)2Na' and Cs+(1806)2Cs'.

V.B Experimental Methods

V.B.l Sample Preparation

The sample preparation methods used for X-band EPR studies
have been described elsewhere. 15 For 250 GHz EPR (G-band) studies.
polycrystalline samples of Cs+(1806)2Na' and Cs+(18C6)2e', and
single crystals of Cs+(18C6)2Cs' were ground with a mortar and pestle ‘
below -50 °C under a dry nitrogen atmosphere in a glove bag. The
samples for the high field studies were loaded into the sample holder
described below under cold nitrogen, and then sealed with a Mylar
film. A larger sample volume could be used than at X-band. An amount
of sample was used that filled about half of the sample holder.
V.B.2 Sample holder

The sample holder has been previously described. 16 It is
cylindrical in shape with a diameter of 3.8 mm and depth of 10.2 mm.
Polymethylpentene (TPX), Teflon and Z-cut quartz had been previously
used as window materials for the sample holder, because they have

92

low absorbance in the FIR. Because Teflon might react with our
samples, Z-cut quartz was first chosen as the window material. When
the sample holder was put into liquid nitrogen, however, the quartz
window tended to pop out because of differential contraction of the
sample holder and the window. Finally, Rexolite (cross-linked
polystyrene) was chosen for the window. Transmittance of FIR
radiation showed that the Rexolite is sufficiently transparent in the
FIR to use as a sample holder. It is also stable with respect to the
solvent and samples. Even though the windows had some tool marks.
the optical performance was not compromised because the surface
was flat to better than M 8. The samples were stored under liquid
nitrogen in a Dewar.

V.B.3 Instrumentation

X-band EPR spectra were obtained with a Bruker 200D EPR
spectrometer with a TE102 rectangular cavity. An ER350 NMR
gaussmeter was used to measure the field to :i:1 mG resolution. The
microwave frequency was measured to 0.01 MHz with an HP5245
frequency counter. The g-values of X-band spectra were obtained
directly from the magnetic field strength and the microwave
frequency. The temperature was controlled by adjusting the flow rate
of cold nitrogen.

The FIR EPR spectrometer developed by J .H. Freed et al. 13 was
used to obtain the high frequency EPR spectra. The FIR source was a
Millitech Corp. PLS-3F phase-locked solid state source that delivered
3-5 mW at 250 GHz (via a WR-4 waveguide). A semiconfocal Fabry-

Perot resonator was used for the sample cavity; the cavity was tuned by

93

controlling the distance between two mirrors. The modulation
frequency was 65 kHz. The field was swept by using a
superconducting solenoid driven by an HP6032A power supply that
provided point-to-point resolution of 0.188G. The temperature was
controlled in the range -120 0C to - 40 °C by using a heater and
regulating the flow rate of cold nitrogen gas. The temperature drift
was about :i: 3 °C. The sweep width was about 50 o.

V.C Results and Discussion

V.C.l Cs+(18C6)2e'
The compounds Cs+(18C6)2e' and Cs+(18C6)2Na‘ are

isostructural with the metal cation and the metal anion or trapped
electron rather isolated from one another. 7 Presumably, electrons are
trapped at anionic vacancies, although the presence of interstitial
electrons and ions cannot be ruled out. Ceside-free Cs+(l8C6)2e'
appears to be primarily an ionic conductor with an activation energy of

about 1. 1 eV: the conduction mechanism is probably closely related to
that of Cs+(15C5)2e'. 14

As shown in Figure 5-1, the EPR spectrum of Cs+(18C6)2e' that

is free of contamination by CS" is not exchange-narrowed, but rather
shows axially symmetric g-anisotropy that is only partially resolved at
9.5 GHz. There is no observable hyperfine splitting. The
perpendicular component (g l) is 2.0021 and the parallel component
(g") is 2.0024. At 250 GHz, as shown in Figure 5-2, the extremes of
the spectrum are spread out by about 26 times relative to those of the
X-band spectrum. At high resolution, however, the rhombic symmetry

94

 

 

 

................

 

 

 

 

 

3424 3425

 

Figure 5-1 . (A) X-band spectrum (solid line) and (B) the simulation
spectrum (dotted line) of Cs+(18C6)2e'.

95

 

 

L

— es 1 8500.003

A‘AAAAIJALIIIAAAIJLA

Signal Intensity (orb. units)
5 L 1 A A

LA

 

 

 

lleALlLkAAILLALIALAAIALLLIAHI
370 350 390 400 410 420 430 440
Sweep field (Gauss)
'IYVYTrYTYTTVTTV‘I'VYVT‘I'U'1—rT
b—eschGZeDOJ

Signal Intensity (arb. units)
U ' r ‘1' '— r f f I 1 I U I F‘ U

AJAA‘AJAJIAJAAILALLW

 

 

;WflJ—H—H—M
.550 370 380 390 400 410 420 430
Sweep field (Gauss)

Figure 5-2. G-band EPR spectra of (A) Cs+(18C6)2e' and (B)
Cs*(18C6)2Na'.

96

of the g-anisotropy is evident, although it is nearly axial. This rhombic
symmetry is consistent with the shape of the cavity as shown by the
single crystal structure: that is, the electron distribution is not
expected to be spherical in the anion vacancy. The isotropic g-value of
the trapped electron in Cs+(18C6)2e' is close to the free electron g-
value and indicates that contributions due to spin-orbit interactions
are small.

The X-band EPR spectra were simulated by using the
Hamiltonian. "'19

ll
HS=B¢SgH+21iAiS-Buligifi (2)
i

are also shown in Figure 5-1. The simulations confirm that there is
negligible hyperfine interaction (0.06 MHz) between cesium cations
and an electron trapped in the anionic vacancy.

The temperature dependences of the linewidth, lineshape, and .
intensity were studied at X-band and the temperature dependences of
the linewidth and lineshape were studied at G-band. The intensity of
the X—band EPR spectrum is plotted as a function of inverse
temperature in Figure 5-3 and shows that the spin susceptibility of the
trapped electron follows the Curie law, indicating that the trapped
electrons are not spin-paired at these temperature.

The high-field EPR spectrum at low modulation amplitude and
at the higher temperatures showed some fine-structure between the
major broad peaks. This was attributed to the presence of a few

crystals that had not been ground finely enough to yield a powder

97

Temperatre of 180629
- Gin-1350 Cs( )

 

19.5. .........
19 ................
18.5+
184

1 7.5‘

WW
I

17*

 

 

 

5 fl . . . r
160'.“ 0.005 0055 030,?“ 0.0055 0.007 0.0075

Figure 5-3. Temperature dependence of the intensity of the X-band
EPR spectrum of Cs+(1806)-2e'.

98

pattern. The line separation of the high field EPR spectrum increased

from 15.3 G to 19 G as the temperature was decreased in the range of
-43 0C to -129 °C. The separation between g1 and g" was 0.65 G at 9.5

GHz, while the corresponding separation was 17G at 250 GHz. This
agrees with the expected resolution enhancement of a factor of 26 at

250 GHz.
The saturation curve at X-band for Cs+(18C6)2e' shows that the

line shape is nearly Lorenztian. A fit of the saturation curve is shown
in Figure 5-4a. The nonlinear least squares program KINFIT 20 was

used to fit the saturation curve by the equation. 2 1

H1
(1 31L :WF

 

ya. = 34% (3)

The presence of a single Lorenztian line is indicative of a single type of
trapping site in the electride.

Attempts to obtain the electron spin echo envelope modulation
(ESEEM) spectrum of Cs+(18C6)2e' resulted in a pronounced free
induction decay signal (FID) with no well-defined echo modulation
signal, indicating a rather long value of T2. When the field was varied
across the resonance field, the off-resonance FID signal collapsed.
This also indicates that the EPR spectrum of Cs+(18C6)2e' is
homogeneous.

The results are all in accord with the assumption that most of
the unpaired electrons in Cs+(18C6)2e' are localized in the anionic

cavities. The nearly axially symmetric g-anisotropy of the trapped

99

electron is in agreement with the structure of the cavity (diameter ~4
A and length ~6A). Of course, the electron density can spread onto
atoms in the vicinity of the cavity, but the overlap with Cs+ and with
neighboring trapped electrons is small.

V.C.2 Cs+(18C6)2Na'
As indicated above, Cs+(18C6)2Na' is isostructural with

Cs+(18C6)2e': each anion is surrounded by eight nearest-neighbor
complexed cations. The X-band EPR spectrum of Cs+(18C6)2Na'

shows three signals, a main broad peak, a minor broad peak, and a
narrow central peak. 3 The intensities of these three peaks at X-band
change from sample to sample . In this work, the intensity ratio of the
narrow peak to the main broad peak was very small, both at X-band
and at G-band, and the minor broad peak was nearly absent. No
resolved hyperfine splitting was observed. The g-values of the broad
peak and the narrow peak at X—band are 2.0022 and 2.0023
respectively. The narrow peak probably arises from exchange-
narrowing due to itinerant electrons. The broader peak results from
trapped electrons that interact with surrounding hydrogens and
complexed cesium cations. The broadening results from
superhyperfine coupling to a number of surrounding nuclei and also
yields a small negative g shift. The presence of three signals shows
that several different trapping sites are present in Cs+(18C6)2Na' and
that the trapped electrons are isolated from each other. The g-values
are all close to the free electron value, which suggests that the spin-
orbit interaction is very small.

. 100
The X-band EPR intensity of the major signal in Cs+(18C6)2.Na'
increases linearly with the inverse temperature, showing that the spin
susceptibility of the trapped electron in Cs+(18C6)2Na' follows the
Curie law. 3 This indicates that the concentration of unpaired
electrons is constant in this temperature range. The linewidth is

independent of temperature in the range 130 K to 250 K.
The g-anisotropy of the Cs+(18C6)2Na' EPR spectrum at G-band

is basically similar to that of the Cs+(18C6)2e' spectrum as shown in

Figure 5-2. This suggests that the major signal arises from F-center
electrons trapped at anionic vacancies.

As indicated above, several sites were observed at X—band.
However, only a single major signal was evident at the high field. The
spin concentration responsible for the central narrow peak was
probably too small to yield a detectable peak at G-band in the sample
used. It should be noted that the integrated central peak at X-band
varied from sample to sample and was always much smaller than that
of the broad peak. The broad peak observed at X-band would have
masked any anisotropy of the g-value.

The saturation curve at X-band for Cs+(18C6)2Na' shown in

Figure 5-4b, does not reach a maximum in the range 0 to 0.1 W. This
permits only an upper bound estimate of T1‘, (< 6 x 10‘6 sec) and

supports the assumption that the linewidth originates from unresolved
hyperfine spin packets.

V.C.3 Cs+(18C6)2C5'
The crystal structure of Cs+(18C6)2CS' shows that there are

seven complexed cesium cations around each CS' ion at distances of

101

 

 

 

 

r’ I I

0 0.05 0.1 0'15 0.2 0.25 03 0.05 04 0.315 0.5
Wmde)

ThspowarsaiixationarveotCstecsNa

 

1,5, . '
g .

 

 

 

100 '
I
I
50 _ '
.1!"-
0 0.05 01 0.15 03 0'25 03

Ila-Imam

Figure 5-4. Power saturation curve of (A) Cs+(18C6)-2e‘ and (B)
C8+( l 806) ~2Na'.

102

8.09 to 9.65 A. 22 Both cations and anions form zigzag chains parallel
to the b-axis with uniform interionic distances of 8.78 and 8.86 A,
respectively. Each cesium anion is 8.12 A from another cesium anion
in an adjacent chain. Thus, the cesium anions are relatively isolated
from one another and from the cesium cations.

Previous X-band EPR spectra of polycrystalline Cs+(18C6)2C5'
showed two overlapping signals. 5 One was a narrow peak (0.62 G) at
the free electron g-value. The other was a smaller and broader peak
that had g-anisotropy, as demonstrated by the spectrum of a single
crystal at different orientations. In the present work, the X-band EPR
spectrum of polycrystalline Cs+(18C6)2C5‘ shown in Figure 5-5 also
shows a broad peak and a central narrow peak, similar to the X-band
EPR spectrum of Cs+(1806)2Na'.

The line widths of the broad peak and the narrow peak at X-
band are 15.1 G and 0.64 G, and the g-values are 1.9987 and 2.0020.
respectively. Cs+(18C6)2CS' samples obtained from difi‘erent syntheses
were used for the X-band and G-band studies. Rather large crystals
were grown and crushed to prepare the sample for G-band EPR, while
a polycrystalline sample was used for the X-band studies. The G-band
EPR spectrum of Cs+(18C6)2C5' shown in Figure 5-6 has a strong peak
and a weak peak, each with an axially symmetric g-value. The signals
correspond to the broad peak and the narrow peak observed at X-
band. The separations of g" and g i for the strong peak and the weak
peak are 17.6 G and 16.8 G at G-band, which would correspond to
0.68 G and 0.64 G at X-band, respectively. The g-anisotropy of the
broad peak would be unobservable, while that of the narrow peak could
be masked by broad peak or by exchange narrowing. If the latter

103

 

SG

 

Figure 5-5. X-band EPR spectrum of Cs+(18C6)2Cs'.

104

 

 

 

 

 

 

 

 

 

 

1000 .. I I I I I I FI rrfl I I fIII l I I I I If! IITI rI I.fi
" ‘1

500 - m ..

' -1

" d

0 - A] _

t -]

500 ' '

P I

" .1
-1000 - u -
s - 4

5 c1
_1500 L1 1111 l a r l a r n LL41 r l I r r r r l r l r r l r r n L

360 .370 380 390 400 410 420 430
SWeep field (C)

Figure 5-6. G-band EPR spectrum of Cs+(1806)205'.

105

explanation is correct. the exchange rate would be faster than 1.9
x106 see1 but slower than 5 x107 sec-1.

The temperature dependence of the X-band intensities of the
two EPR peaks of Cs+(18C6)2CS' is shown in Figure 5-7. The intensity

increases with increasing temperature from - 70 °C to - 24 0C, while
below - 70 0C the temperature dependence follows Curie-law behavior.
The temperature dependence could result from the presence of spin-
paired electrons that can dissociate to populate both sites above -70 °C

according to

62 : ea' + e“ (4)

where ear and er represent trapped electrons at F-center and
interstitial sites, respectively. At lower temperatures, the rate of this
process might be too slow to affect the unpaired electron
concentration. Another explanation is that there might be a
composition change from Cs+(18C6)2C5' to Cs+(18C6)e' as the

temperature is increased above - 70 °C. according to.

Cs*(18C6)2Cs' ":2 Cs+(18C6)2e’ + Cs (5)

This phenomenon would result in an increase in the EPR intensity at

higher temperature.

106

Temperature study (or Cs(1806)205

2-
1.]
1.8]
1.7- .

21.0

515 *

31.41 ..,
1.3‘ 4. e-
1.2* o
1.11

 

 

 

1 v . . . f t .
0034 0.0045 0.005 0.0(55 0.131116 0.0055 0.007 0.0075 0.005

Figure 5-7. Temperature dependence of the intensity of the X-band
EPR spectrum of Cs+(18C6)2Cs'.

107

V.D Conclusion

The only EPR signal from Cs+(18C6)2e' and the major signal
from Cs+(18C6)2Na' and Cs+(18C6)2CS' result from electrons trapped
at anion vacancies. In the electride, the resulting g-anisotropy is
observed at both G-band and X-band. while in the alkalides the g-
anisotropy can only be resolved at G-band. In all case, there is
evidence for superhyperfine interaction of the trapped electron with a
number of surrounding nuclei. but, as anticipated for trapped electron
in the rather isolated anion vacancies, there is no strong coupling to
one, or a few nuclei. The anisotropy of the g-value results from the
non-spherical shape of the cavity and suggests that the ground state of
the trapped electron is not strictly describable as an 5 state.

In the alkalides. there are other trapping sites than the F-
center, but their nature cannot be deduced from the EPR spectra.
The temperature dependence of the EPR intensities for Cs+(18C6)2C5'
shows that a common spin-paired species can dissociate as the

temperature is raised to increase the EPR intensities of both signals.
V.E References

1. Dye, J. L.; Ceraso.J. M.; Lok, M. T.: Barnett. B. L.; Tehan, F. J. J. Am.
Chem. Soc. 1974, 96, 608.

2. Tehan, F. J.: Barnett, B. L.; Dye, J. L. J. Am Chem. Soc. 1974, 25,,
7203.

3. Shin, D. H.; DeBacker, M. G.: Ellaboudy, A. S.: Dye. J. L. J. Phys.
Chem. 1991. 95. 7085.

108

4. Ellaboudy, A. S.; Bender. C. J.: Kim, J.: Shin, D. H.; Kuchenmeister,
M. E.:Babcock. G. T.: Dye, J. L. J. Am. Chem Soc. 1991. 1_l_3. 1605.

5. Issa. D.: Ellaboudy, A. S.; Janakiraman. R.: Dye. J. L. J. Phys. Chem.
1984. 88, 3847.

6. Ellaboudy. A. S.: Dye, J. L.; Smith, P. B. J. Am. Chem Soc. 1983, 105,
6490.

7. Dawes. S. 3.: Ward. D. L.; Huang, R. H.; Dye, J. L. J. Am. Chem. Soc.
1986, 108, 3534.

8. Dye, J. L.; DeBacker, M. G. Ann. Rev. Phys. Chem 1987, 38, 271.

9- Dye. J. L. in W
W 1988. 65.

10 Dawes. S. B.: Ward, D. L.; Fussa-Rydel, 0.: Huang. R. H.; Dye. J. L.
Inorg. Chem 1989. 28,, 2132.

11. Dye, J. L. Science 1990, _2_4_7_, 663.

12. Dye, J. L.; Huang, R. H. Chem Br. 1990. 16, 239.

13. Dawes, S. B.: Eglin, J. L.; Moeggenborg, K. J.:Kim, J.: Dye, J. L. J.
Am Chem Soc. 1991. 113. 1605.

14. Moeggenborg, K. J.: Papaioannou, J .: Dye, J. L. Chem Mater. 1991.
3,, 514.

15. Dye, J. L. J. Phys. Chem 1984, 88, 3842.

16. Lynch, w. 3.; Earle x A.: Freed, J. 11., Rev. Sci. Instrum ress.
5.9.(8). 1345.

17. Weil, J. J. Magn. Res. 1975. 18., 1 13.

18. Nilges, M. J. Ph.D. Dissertation, University of Illinois at Urbana.
1979.

19. Belford. R. L.; Nilges. M. J, W
W. Denver. CO. 1979.

109

20. Nicely. V. A.: Dye. J. L. J. Chem Educ. 1971, 48. 443.

21. Poole, C. P. W, John Wiley 8: Sons.
1983 p 590.

22. Huang, R. H.; Ward, D. L.; Kuchenmeister, M. E.: Dye, J. L. J. Am
Chem Soc. 1987, 109. 5561.

CHAPTER VI

PULSED EPR STUDIES OF POLYCRYSTALLINE CESIUM
HEXAMETHYL HEXACYC LEN SODIDE

This chapter is in the form of a paper that has been submitted to
the Journal of Applied Magnetic Resonance. The final version was
written with the assistance of Professor John L. McCracken.

Abstract

The electron spin echo envelope modulation (ESEEM)
technique of pulsed EPR spectroscopy has been used to measure weak
1330s hyperfine couplings to trapped electrons in polycrystalline
cesium hexamethyl hexacyclen sodide. Two magnetically distinct
groups of weakly coupled 133Cs nuclei were found: one with an
isotropic electron-nuclear hyperfine (Fermi contact) coupling of 0.34
MHz and the other with a contact coupling less than 0.1 MHz.
Analysis of these data by computer simulation shows that the number
of Cs nuclei that give rise to these interactions and their distance from
the paramagnetic center is consistent with the hypothesis that the
trapped electrons occupy vacant anion sites. The results indicate that
the spread of unpaired electron spin density, along the axis formed by
the "contact ion pair," may be greater than that in the plane

perpendicular to this axis.

110

111

VI.A Introduction

Electrides are a class of solids that consist of complexed metal
cations and trapped electrons in a well-defined structural
arrangement. As a class. electrides represent extremes, in which
trapped electrons are localized at one limit and are able to move from
site to site at the other. The degree of localization of trapped
electrons depends markedly on the metal cation and complexant used
for the synthesis. For cesium 18-crown-6 electride, Cs+(18C6)2e'.
cesium cations are complexed by two 1806 crown ethers. and the
trapped electrons are localized with separation distances of 8-10 A. 1-2
A much difi'erent situation is found for K+(C222)e', where strong inter-
electron interactions have been observed. 3 Possible uses of these
compounds for the doping of organic semiconductors. 4 and as
chemical reagents for the preparation of small metal particles. 5 have
been reported. Because their chemical and physical properties
depend on the nature of their trapped electrons, it is important that
the details of these trapping sites be understood.

EPR spectroscopy provides an ideal vehicle for the study of
electron-trapping sites in these materials. The ability of EPR methods
to focus on the immediate environment of the unpaired electron spin
and measure the amount of unpaired spin density that is distributed
over the molecular framework of a material gives it advantages over
other spectroscopic techniques for the study of these sites.
Unfortunately, attempts to use cw-EPR and ENDOR methods for such
studies on electrides have met with little success, most likely because

of the high concentration of paramagnetic centers in these materials.

112

Alkalides are a closely related group of compounds, in which alkali
metal anions serve as the "counterions" to the complexed metal
cations. 3 Trapped electrons are also found in these materials as a
result of dissociation of electrons from alkali metal anions during their
formation. The concentration of trapped electrons can be controlled
for alkalides by varying the concentration of metal relative to
complexant during synthesis. Because the concentration of
paramagnetic centers can be kept low and X-ray crystallographic
studies have shown that alkalides and their corresponding electrides
are isostructural, 7 these materials provide an ideal system for the
study of electron-trapping sites using EPR methods.

In the present study. we have used the electron spin echo
envelope modulation (ESEEM) technique of pulsed EPR spectroscopy
to study electron-trapping sites in the thermally stable alkalide.
cesium hexamethyl hexacyclen sodide (Cs+(HMHCY)Na'). 3 A
computer simulation of the cation-anion packing in this compound.
generated using X-ray crystallographic data, 9 is shown in Fig. 6-1.
The cesium cations in this material are complexed by HMHCY, a
methylated nitrogen analog of l8-crown-6. X-ray data show that
nitrogens 4. 7. 13, and 16 of the complexant are coplanar. and that
the Cs+ ion is located 0.9 A above the center of this plane (Fig. 6-1A).
Nitrogens l and 10 are located 1.1 A below this plane with their
methyl groups closing ofi‘ the bottom of the cation "cup.” The cesium
cations are coordinated to all six HMHCY nitrogens with Cs-N
distances that range from 3.2 - 3.35 A. The closest Na' ion is located
4.26 A above the Cs+ ion, forming a contact-ion pair. In the unit cell.
these ions are held in a staggered arrangement, yielding a distorted

113

 

Figure 6-1. Computer simulation of the cation-anion packing in
Cs+(HMHCY)Na‘ from x-ray crystallographic data: (A) the molecular
unit. (B) cutaway view dawn the b axis. and (C) cutaway view down the
alaxis.

114

octahedral coordination geometry between Na' and its six nearest
complexed Cst neighbors. The Na'-Cs+ distances in this distorted
octahedral arrangement range from 7.2 - 8.6 A for the five more
distant cations and 4.26 A for the contact pair. 9 It has been proposed
that the trapped electrons in this material occupy vacant Na‘ sites.

The chief goal of EPR studies on alkalides has been to precisely
determine electron locales. Previous cw-EPR and cw-ENDOR studies
of Cs+(HMHCY)Na' have provided valuable information toward reaching
this goal. 1° The X—band cw-EPR spectrum of this material shows a
large hyperfine splitting to a single Cs+ ion with the isotropic, or
Fermi contact portion of the coupling being 98G. Parallel ENDOR
studies showed additional magnetic couplings between the unpaired
electron spin and protons of the complexant, 23Na and 133Cs nuclei.
These observations are supportive of the current picture of the
electron-trapping site, as described above, in that a single, large l33Cs
hyperfine coupling is observed due to the trapped electron spin being
"in contact" with one complexed Cs+ cation and that additional
couplings to 23Na and 133Cs. as seen by using ENDOR. were small.
These small couplings are consistent with the 8-10 A distance
between adjacent Na° sites, and the distances between the trapped
electron spin and five of its Cs+ nearest neighbors. For the purpose of
defining electron locales, one also needs information concerning the
number of nuclei involved in a particular coupling. Unfortunately, this
information is lost in a standard ENDOR measurement. In an attempt
to measure hyperfine coupling constants and obtain quantitative
information regarding the number of interactions. we have studied

Cs+(HMHCY)Na' by using the ESEEM method of pulsed EPR

115

spectroscopy. Because ESEEM techniques are best suited for the
study of weakly coupled nuclei with small magnetic moments and
large nuclear spins, they may be ideal for the characterization of
paramagnetic centers in alkalides. In this chapter, the results of X-
band ESEEM studies on Cs+(HMHCY)Na‘ are presented. Evidence for
hyperfine coupling between trapped electrons and two magnetically
distinct sets of Cs+ ions was obtained. These data are analyzed and
yield results in agreement with the current picture regarding the

location of trapped electrons in this material.

VLB Materials and Methods

Polycrystalline samples of Cs+(HMHCY)Na' were prepared
according to literature procedures. 3'1 1 The complexant, hexacyclen.
was purchased as the sulfate salt (Aldrich Chemical) and methylated,
using published methods. 12

Pulsed EPR studies were performed with a home-built
spectrometer recently constructed at Michigan State University. The
microwave bridge is capable of operation over a bandwidth of 6 to 18
GHz and has a transmitter that employs two microwave pulse channels
for the implementation of different phase-cycling or pulse-swapping
schemes. 13” A microwave synthesizer (Gigatronics, model 610)
serves as the source for this instrument, and each pulse channel
consists of a low-power, high-speed PIN diode switch (General
Microwave model FM864—BH). a high-speed 0°/180° wideband phase
modulator (General Microwave model F 1938) and an isolator. The

low-power pulses from these arms are combined and fed into a

116

medium-power GaAs FET amplifier (Avantek model SWL-89-0437) and
a IKW pulsed travelling wave tube amplifier (Applied Systems
Engineering, model 1 17). The cavity used in these measurements was
of the reflection type and employed a folded half-wave resonator 15
and the X-band Gordon coupling arrangement developed by Britt and
Klein”. Experiments were carried out at 4.2K. using a home-built
liquid helium immersion dewar. The microwave receiver utilizes
wideband components and a double balanced mixer (RHG model DM2-
18 AB) in a conventional homodyne arrangement. A low-noise GaAs
FET amplifier (Avantek model AWF-18635) is used in the receiver,
with a medium-power. high-speed PIN diode limiter (Innowave,
model VPL-6018) and a fast PIN diode switch (General Microwave,
model F9114) serving to protect it from damage by higher-power
microwave pulses.

The spectrometer is controlled by a McIntosh llx
microcomputer (Apple Computer) via an IEEE—488 interface (National
Instruments) to a four-channel digital delay and gate generator
(Stanford Research, Model DG535) and a Stanford Research SR245
"computer interface” module. The digital delay and gate generator is
used to supply the accurate pulse delays required for ESEEM
measurements. as a programmable clock for controlling the overall
repetition rate of our measurements, and supplies trigger pulses to a
gated integrator (Stanford Research model 250) responsible for
measuring spin echo intensities. The SR245 computer interface
module serves to digitize the gated integrator output signal, count the
number of pulse sequences repeated at a given set of microwave pulse

spacings, and to clear the gated integrator after its analog output has

117

been read. Data collection and analysis software was written using the
C language (Symantec). ESEEM spectra were obtained from time
domain data, using a modified version of the dead-time reconstruction
protocol described by Mims. 17 Simulations of l33Cs ESEEM functions
were performed on a Microvax 11 computer (Digital Equipment) using

a published theoretical treatment. 13-19

VI.C Results and Discussion

The cw-EPR spectrum of Cs+(HMHCY)Na‘ has been reported. 10
The spectrum has eight major peaks split about g = 1.98 that have
been attributed to hyperfine coupling between the trapped electron
and its complexed Cs+ counterion 4.26 A away. Analysis of this
spectrum by computer simulation showed a nearly isotropic g matrix
(gu = 1.996, g = 1.977] and an axial Cs hyperfine tensor with Al =
93.7 and A" = 106.3 gauss. ESEEM data were collected at three
different field positions across the low field Cs hyperfine component
at g = 2.25 and at a higher field where the EPR signal is maximized (g
= 1.78). Because the anisotropy in the resolved Cs hyperfine splitting
is small and the spectral width sampled with our 15 nsec hard
microwave pulses is greater than ten gauss. no orientation selection
effects were observed in the data. 23“ Three-pulse, stimulated echo
ESEEM data collected at g = 2.21 are shown in Fig. 6-2. The time
domain data were taken using a tau value (spacing between the first
two microwave pulses) of 225 nsec. 1024 data points were taken with
the first 1000 spaced at 15 nsec increments, starting at 1:+T = 270

nsec. The last 24 points were used to record the baseline and were

 

A 1""
’ 1

 

 

 

 

b
11llLAllliLLjLLlJllLlllllllLLLllllLlllj11111111111111]!llLllAlllllllIllllllll

 

 

 

 

 

Frequency (MHz)-

Figure 6-2. Stimulated . echo ESEEM data and associated frequency
spectrum obtained for Cs+(HMHCY)Na'. Conditions for this
measurement were: microwave frequency, 9.412 GHz: magnetic field
strength. 3043G: microwave pulse power, 80W (15 nsec FWHM): tau
value, 225 nsec: starting T, 30 nsec.: sample temperature, 4.2: pulse
sequence repetition rate, 5 Hz:- 12 events were averaged for each time
point with 1024 pts being collected at 15 nsec increments.

119

collected with the gated integrator trigger pulse set to a value 100
nsec after the echo. Figure 6-2A shows that the ESEEM observed for
Cs+(I-Il\iHCY)Na‘ is fairly shallow, with modulation depths being < 20%
of the overall spin echo amplitude. The frequency spectrum for these
data (Fig. 6-2B) shows a large, broad component centered at 0.5 MHz
and two pairs of narrow lines centered at the l33Cs Larrnor frequency
of 1.7 MHz. This pattern of four lines was observed at all of the field
positions examined in this study. Three-pulse ESEEM spectra
collected at g = 2.25 and g = 1.78 are shown in Fig. 6-3. The set of
lines centered at 1.68 MHz at 2980 G (Fig. 6-3A) shift to a center
frequency of 2.1 MHz at 3770 G (Fig. 6-3B), consistent with their
assignment to weakly coupled l33Cs nuclei.

The broad, lower-frequency peaks observed in the spectra
shown in Figs. 6-2 and 6-3 most likely arise from magnetically coupled
14N nuclei. Because a large amount of unpaired electron spin density
is present at the Cs cation closest to the proposed Na' vacancy. it is
reasonable to assume that couplings to the nitrogen nuclei of the
HMHCY complexant should be observed. This idea is supported by
previous ENDOR studies 10 where proton hyperfine couplings as large
as 4.0 MHz were assigned to the methyl protons of the HMHCY
complexant based on isotopic substitution work. Additional, weak
ESEEM frequency components were observed at 3.4, 4.2. and 4.6 MHz
and may arise from hyperfine coupling to 14N or 23Na nuclei. These
components were best observed at short tau values (< 150 nsec) in

stimulated echo experiments. Multifrequency ESEEM studies aimed

120

 

e)’

 

 

 

 

 

 

 

Figure 6-3. ESEEM spectra obtained for Cs+(HMHCY)Na‘ at two
difi'erent magnetic field positions within the EPR absorption envelope.
Measurement conditions were as in Fig. 6-2 except for (a) magnetic
field strength, 2980G: tau value, 220 nsec, and for (b) magnetic field
strength. 3770G: tau value. 190 nsec. Time domain data points were
collected at 10 nsec intervals for both spectra.

121

at enhancing the modulations arising from these couplings and
determining their origin are planned.

Computer simulations of the 133Cs ESEEM data shown in Figures
2 and 3 were undertaken to test our current hypothesis regarding the
location of trapped electrons in these materials. Our calculations
made use of the theoretical treatment of Shubin and Dikanov, 18 where
analytical expressions for two- and three-pulse ESEEM functions were
derived for I > 1/2 nuclei. This formalism was developed using
perturbation methods and applies to conditions where anisotropic
hyperfine and nuclear quadrupole interactions are small compared to
the nuclear Zeeman splitting. According to the above assumption, the

primary ESEEM is described by the expression:

v? (1:) = 1 - :- I(I+1) Ev; [1 - 2 cos 21m cos 21091) G(Yt)

+ g. cos 211:(2vrt) (3171) + £- COS ZulA‘tll

 

(6-l)
where
7 = 3.29312.
4 h1(21-1) '
3 1-1
G(x) = 2111+1)(21+1)m§1[m+1) - m(m+1)]cos 21t(2m+1)x ,

eQ is the nuclear quadrupole moment and sz is a component of the
electric field gradient tensor. 1: is the pulse width and v1 is the
modulation harmonic of nucleus 1. Because multiple 133Cs nuclei are

involved in the observed coupling, individual three-pulse ESEEM

122

simulations were combined using the spherical model approximation
to the product rule. 22 Our analysis was guided by the x-ray crystal
structure of Cs+(HMHCY)Na' 9 and the hypothesis that the trapped
electrons in these materials occupy vacant anion sites. The
complexed Cs+ ions would then be positioned about this vacant anion
site in a distorted octahedral arrangement. Figure 613 shows that
there are four complexed Cs+ ions that are nearly coplanar with the
proposed trapping sites, with the cations positioned at distances of
7.5. 8.1. 8.2, and 8.6 A. The remaining two complexed Cs‘l' ions are
perpendicular to this plane. One is centered at a distance of 4.25 A
from the proposed vacant Na' site (Fig. 6-1A) and is the ion that
strongly interacts with the trapped electron giving rise to the
observed splitting in the cw-EPR spectrum. The second is located
directly opposite to this, at a distance of 7.2 A, and is shielded from
the trapping site by complexant (Fig. 6—1C).

Because the cesium ESEEM data provide evidence for two
magnetically distinct sets of coupled nuclei, our modeling was done
using two sets of coupling parameters. One set considered the Fermi
contact portion of the hyperfine coupling to be 0.34 MHz, as measured
from the ESEEM spectra. while the second set considered the contact
interaction to be < 0. 1 MHz. For both parameter sets. the dipole-
dipole distances and number of contributing nuclei were varied within
limits defined by the x-ray structure of the material. To simplify our
calculations further, the Cs+ nuclear quadrupole coupling constants
were set to zero. The effects of a weak nuclear quadrupole
interaction, within the framework of the pereturbation treatment used

here, are to enhance the damping of the observed modulations. 23

123

Because the damping is also affected by a background decay function of
unknown form 24 and nuclear quadrupole interactions are expected to
be the same for all of the complexed Cs+ ions, this assumption will not
affect our analysis. The implications of ignoring nuclear quadrupole
interactions will be discussed in greater detail below.

To facilitate comparison between calculated ESEEM functions
and those obtained experimentally, the ESEEM spectrum of Fig. 6-3A
was treated with a windowing function to isolate the four peaks
centered at 1.7 MHz and the component at 0 MHz. The resulting
frequency spectrum was then backtransformed to give the result
shown in Fig. 6-4A. Our best simulation results are shown in Figs. 6-
4B and 6-4C. This simulation was obtained by using a model that
considered one cesium nucleus at 5.8 A with a contact coupling of
0.34 MHz, and a second set of four cesium nuclei at a dipole-dipole
distance of 8.1 A with a contact coupling of 0.07 MHz. Because the
amplitudes of both sets of modulation components are comparable, the
set of four cations must be at the longer distance and were assigned
the smaller isotropic hyperfine coupling constant. The idea that the
four "in-plane" cesium ions couple to the trapped electron in a similar
manner and are distinct from the "axial" Cs cations is in good
agreement with the current view that the trapped electrons occupy
vacant Na' sites. The weak-contact coupling and long dipole-dipole
distance of 8. 1 A found for these four ions are also in agreement with
this model. The electron-nuclear coupling for the odd Cs+ ion, which

124
A) 1.0

 

echo amplitude

 

 

 

° 5 A A 3 ' 10
tau+T(usec)

8)

 

echo amplitude

 

 

 

 

tau + T (nsec)

C) . a

 

 

1 A l 1 A l l j l l

 

 

 

oIIIIIIIIIII

 

«F

Frequency (rt-tr)

Figure 6-4. The time domain data shown in (A) were obtained by
backtransformation of the Cs ESEEM frequency components from the
spectrum of Fig. 6-3A along with the component at 0 MHz (a 0.4 MHz

width was used in the windowing ofthis peak). (B) shows the result of
an ESEEM simulation where 4 Cs nuclei with A,” a 0.07 MHz and r =

8.1 . and 1 Cs nucleus with A,” a 0.34 MHz and r a 5.8 were

considered

125

is most likely the "axial" cation opposite the "contact pair," is
described by a higher contact coupling. 0.34 MHz, and a dipole-dipole
distance of 5.8 A. This distance is much shorter than the 7.2 A
distance obtained using x-ray crystallographic techniques and most
likely indicates that appreciable unpaired electron spin density is
delocalized onto the complexant molecule of this cation.

Alternative models for simulating the Cs ESEEM were
considered, but the calculated distances obtained using these models
were less plausible than those described above. For example, models
where only the four complexed Cs+ ions coplanar with the vacant Na“
site contributed to the observed couplings were considered. If one
adopts a model for which two cesium cations are strongly coupled and
two are more weakly coupled, all Cs+ ion dipole-dipole distances must
be < 6.5 A to predict modulation depths in agreement with those
found experimentally. If one considers one of the four in-plane Cs+
ions to be more tightly coupled than the other three, a dipole-dipole
distance of < 6 A must be used for it. Although the x—ray crystal
structure of this material shows that all of the distances between the
central Na’ site and the four in-plane Cs+ ions are slightly different.
their structural relationship to the central Na' site is so similar that
both of these models seem less plausible than the one presented
above.

The results of our ESEEM analysis for the "stronger" coupled
cesium ion differ from those reported for recent ENDOR studies of
Cs+(HMHCY)Na'1°. In this ENDOR work, a pair of lines split by 0.31
MHz about the 13305 larmor frequency was observed. The analysis of
these data considered the source of line broadening for the Cs ENDOR

126

peaks to be due to nuclear quadrupole interactions and reported a
value of 5.3 MHz for e2qQ. This value is high, if one compares it to
literature values reported for cesium halide molecules studied in the
gas phase”. However. there is little or no precedence for the
measurement of 133Cs+ quadrupole coupling parameters in the solid
state. The choice to ignore the effects of dipole-dipole coupling in the
analysis of the l33Cs+ ENDOR was based on the long, 7.2 A. distance
reported for the nearest cation. As stated above, if nuclear quadrupole
coupling is ignored in the ESEEM analysis, a dipole-dipole distance of
5.8 A is required to account for the modulation depths. or amplitudes.
observed experimentally. If weak nuclear quadrupole interactions are
included in our ESEEM simulations, only the damping of the
predicted functions is affected. and the 5.8 A dipole-dipole distance is
still required to predict signal amplitudes in agreement with
experiment. The inclusion of larger nuclear quadrupole interactions
in the simulations would affect both observed modulation frequencies
and amplitudes and may allow for longer dipole-dipole distances. To
study these effects, the calculations must be done numerically, as
outlined by Mims. 25-27 Although it is clear that electron-nuclear
dipole-dipole coupling is important in this system, the effects of larger
nuclear quadrupole couplings remain to be seen. Data from ongoing
solid-state NMR studies and further development of our ESEEM
analysis methods will allow the relative contributions of these
interactions to be sorted out. ‘

In conclusion, the results of ESEEM studies on Cs+(HMHCY)Na'
presented in this work are consistent with the proposal that trapped

electrons in this material occupy vacant Na‘ sites. 5 The most likely

127

model for the two distinct sets of weak l33Cs magnetic couplings
reported here is that the four Cs cations in the ac plane(Fig. 6-1B) are
nearly equivalent and weakly coupled, while the "axial" Cs"' found in
the bc plane, and shielded from the trapped electron by the
complexant molecule, is more strongly coupled. The small isotropic
hyperfine couplings measured for these distinct cesium ions show that
a significant amount of unpaired electron spin density is found at
atoms > 8 A away from the "contact pair." The proposed difference in
couplings between trapped electrons and complexed Cs+ ions in the
ac plane and the more distant Cs+ ion perpendicular to the ac plane
may lead to the onset of interesting electrical properties, as doping
levels are varied and further characterization of these materials is
done. Because the EPR spectrum of the polycrystalline sodide is
mostly isotropic, confirmation of our assignment of the larger cesium
hyperfine coupling will require single crystal ESEEM studies. The
detailed information regarding electron locales obtained in these
‘ studies will be important for reaching a full understanding of their
chemical and physical properties.

VI.D Acknowledgements

This project was supported by grants from the Michigan State
University Center for Fundamental Materials Research, by National
Science Foundation Solid-State Chemistry Grant No. DMR 9017292,
and by NIH Grant No. GM 45795. We are thankful for the technical
assistance of M. Rabb, R. Geyer, and M. Langer in the construction of
the pulsed EPR Spectrometer.

128

VI.E References

l.

10.

ll.
12.

13.

D. Issa. A. S. Ellaboudy, R. Janakiraman. and J. L. Dye, J. Phys.
Chem. 88. 3847 (1984).

J. L. Dye and A. S. Ellaboudy, Chem Br. 20. 210 (1984).

R. H. Huang, M. K. Faber. K. J. Moeggenborg, D. L. Ward, and J. L.
Dye. Nature 331, 599 (1988).

R. Liepins and M. Aldissi, Mol. Cryst. Liq. Cryst. 105. 151 (1984).
K. L. Tsai and J. L. Dye, J. Am. Chem Soc. 113, 1650 (1991).

J. L. Dye and M. G. DeBacker, Ann. Rev. Phys. Chem 38, 271
(1987).

D. L. Ward, R. H. Huang. M. E. Kuchenmeister, and J. L. Dye, Acta
Crystallogr. C46. 1831 (1990).

M. E. Kuchenmeister and J. L. Dye, J. Am Chem Soc. 111, 935
(1989).

D. L. Ward, M. E. Kuchenmeister, and J. L. Dye, manuscript in
preparation.

A. S. Ellaboudy. C. J. Bender. J. Kim, D.-H. Shin. M. E.
Kuchenmeister. G. T. Babcock, and J. L. Dye, J. Am Chem Soc.
113, 2347 (1991).

J. L. Dye, J. Phys. Chem 88. 3842 (1984).

A. G. M. Barrett, C. R. A. Godfrey, D. M. Hollinshead, P. A.
Prokopiou, D. H. R. Barton, R. B. Boar, L. Joukhador. J. F.
McGhie, S. C. Misra, J. Chem Soc. Perkin, Trans. 1, 1501
(1981).

J .-M. Fauth, A. Schweiger, L. Braunschweiler, J. Forrer, and R. R.
Ernst, J. Magn. Reson. 66, 74 (1986).

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.
26.
27.

129

A. Angerhofer, R. J. Massoth. and M. K. Bowman, IsraelJ. Chem
28, 227 (1988).

C. P. Lin, M. K. Bowman, and J. R. Norris, J. Magn. Reson. 65.
369 (1985).

R. D. Britt and M. P. Klein, J. Magn. Reson. 74, 535 (1987).

W. B. Mims, J. Magn. Reson. 59. 291 (1984).

A. A. Shubin and S. A. Dikanov, J. Magn. Reson. 52, 1 (1983).

S. A. Dikanov and A. V. Ashtashkin in "Advanced EPR." A. J. Hoff,
ed., 59, Elsevier, Amsterdam (1989).

B. M. Hoffman, J. Martinsen, and R. A. Venters, J. Magn. Reson.
59, 110 (1984).

G. C. Hurst. T. A. Henderson, and R. W. Kreilick, J. Am Chem
Soc. 107, 7294 (1985).

S. A. Dikanov, A. A. Shubin. and V. N. Parmon, J. Magn. Reson.
42, 474 (1981).

A. A. Shubin and S. A. Dikanov, J. Magn. Reson. 64, 185 (1985).
L. Kevan in "Time Domain Electron Spin Resonance." L. Kevan
and R. N. Schwartz. eds., 279, Wiley-Interscience, New York,
1979.

G. Graff and O. Runolfsson, Z. Physik 187, 140 (1965).

W. B. Mims, Phys. Rev. B 5, 2409 (1972).

W. B. Mims, Phys. Rev. B. 6, 3543 (1972).

CHAPTER VII
CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK
VII.A General Conclusions

Crystalline alkalide and electride salts can be prepared as stable
compounds in vacuo at low temperature and always contain the
trapped electrons to different extents due to the presence in solution
of solvated electrons as a result of the dissociation equilibrium. The
value of X-band and G-band EPR and pulsed EPR spectroscopy to study
the trapped electrons in alkalides and electrides has been
demonstrated. A new crystalline sodide. NatHMHCYNa' was
synthesized and characterized by EPR spectroscopy.

The hyperfine splittings of X-band EPR spectra for K+HMHCYNa'
, RthMHCYNa', and Cs+HMHCYNa' confirm the formation of a
contact-ion pair between a trapped electron and a cation and these
EPR spectra are in agreement with the single crystal structures. The
hyperfine splittings of three sodides of unknown-structure, K+18C6Na'
. Rb+ 18C6Na' and Na+HMHCYNa' indicate the presence of substantial
contact between the trapped electron and the cation. The central
single peak of K+18C6Na' and Rb+18C6Na' probably arises from the
trapped electron at an interstitial site. The g-values of hyperfine
peaks for the above sodides are smaller than the free electron value.
2.0023 and show a small spin-orbit interaction.

The trapped electron in the sandwich complexed sodide.

Cs+(18C6)2Na‘ is isolated from the cations and shows no resolved

130

131

hyperfine splitting because of shielding of the cations by the pair of
complexant molecules. Two additional trapping sites exist for the
sandwich complexed alkalides, Cs+(18C6)2Na' and Cs+(18C6)2C5'. An
additional narrow central peak of Cs+(18C6)2Na' and Cs+(18C6)2CS'
probably corresponds to electron trapping at an interstitial site.
whereas the broad peak corresponds to the trapped electron at the
vacant anionic site. Electrons in alkalides and electrides are trapped
at anionic vacant sites as F-centers. The g—values of sandwich
complexed sodides are close to the free electron value, which shows a
negligible spin-orbit interaction.

The X-band and G-band EPR studies of pure crystalline
Cs+(18C6)2e' have confirmed that the electron is trapped at the
anionic site. The electronic charge distribution of the trapped
electron for Cs+(18C6)2e' is non-spherical and is in agreement with
the shape of the cavity. The contamination of Cs+(18C6)2e' by small
amounts of Ce is apparently responsible for the previously observed
line narrowing presumably due to rapid spin-spin exchange.

In present work, most sodides except Rb+18C6Na' and
Cs+(18C6)2Na' show nearly Lorenztian lineshapes. The lineshapes of
Rb+18C6Na- and Cs+(18C6)2Na' correspond to a combination of
Lorenztian and Gaussian shapes.

The temperature dependences of the EPR intensities of most
sodides follow the Curie-law and these results confirm that the
trapped electrons do not strongly interact with one another. The
temperature dependences of K+1806Na', Rb+18C6Na', and
Cs+(18C6)2C5', on the other hand, show spin-paring between trapped

electrons of two different site. The spin-pairing energies of

l 3 2
K+18C6Na' and Rb+18C6Na', and Cs+(18C6)2CS' are 1.19 x10'2, 2.11
x10‘2, and 1.24 x10"2 eV, respectively.

The strong hyperfine coupling due to contact-ion pair between a
trapped electron and a Cst cation was observed with EPR
spectroscopy for Cs‘tHMHCYNa'. The weak hyperfine coupling
between a trapped electron and five surrounding Cs+ cations in
CstHMHCYNa' was observed by ESEEM studies and is in agreement
with the ENDOR results. Two distinct sets of weak 133Cs hyperfine
couplings are observed. The four Cs cations in the ac plane are nearly
equivalent and weakly coupled. The "ardal" Cs+ cation in the be plane
is shielded hour the trapped electron by the complexant molecule, but
is more strongly coupled than are the other four “distant” Cs+ ions.
The results of ESEEM suggest that the electronic charge distribution
of the trapped electron in Csfl-IMHCYNa' is elliptical.

VII.B. Suggestions for Future Work

Much progress has been made in the last several years in the
study of alkalides and electrides. Crystal structure determinations, the
synthesis of more stable compounds, and the application of these
compounds by using their strong reducing power are important steps
which have been taken. Several suggestions for further study can be
made based on the results of the present work.

1. ESEEM, and pulsed EPR spectroscopy in general, have
proven useful to study the local structure of the trapped electron in
Cs+HMHCYNa' , whose crystal structure is known. Further
investigations of ESEEM for the sodides of Rb+18C6Rb'. K+1806Na'.

133

and Rb+18CNa', which show strong hyperfine coupling between a
trapped electron and a cation, should be made. It may possible to
determine the local structure and electron charge distribution of the
trapped. electron for sodides of unknown-structure.

2. One of the advantages of the pulsed-ENDOR method
compared with cw-ENDOR is that the entire sequence can usually be
made short enough to exclude unwanted relaxation. At X-band
magnetic fields. the proton ENDOR spectra often overlap with and
obscure the spectra of the important heteronuclei such as 14N, 13C .
This technique leads to enhancement of the intensities of
heteronulcear signals and the suppression of proton signals.
Cs+HMHCYNa', whose methyl groups have been substituted by 13C
should be investigated by the pulsed-ENDOR. The results of ESEEM
and cw-ENDOR for Cstl-IMHCYNa' could then be compared with the
results of the pulsed-ENDOR studies.

3. A primitive experiment of photoinduced EPR for Rb+18C6Na'
has given promising results. The combination of a cw-EPR or pulsed
EPR and a portable YAG laser makes it attractive to study the electron
distribution in excited states by using photoinduced EPR
spectroscopy.

4. Single crystal EPR is powerful way to investigate the local
structure around an unpaired electron. The single crystal EPR should
be studied to investigate the local structure near trapped electrons in
electrides. A two dimensional goniometer should be developed which
can operate below -40 °C in order to study the single crystal EPR
spectra of alkalides and electrides as a function of orientation.

BIBILOGRAPHY

1. J. C Thompson, Electrons in Liquids Ammonia. Oxford University
Press, Oxford 1976.

2. G. LePoutr and M. J. Sienko, Metal-Anunonia Solution. Clloque Weyl
I, W. A. Benzamin. New York 1964.

3. J. J. Lagowski and M. J. Sienko, Metal-Ammonia Solution,
Butterwirth, London 1970.

4. J. J ortner and N. R. Kestner, Electrons in Fluids, Sping-Verlag, New
York 1973.

5. J. Phys. Chem. 19 (1975).

6. J. Phys. Chem. M (1980).

7. J. Phys. Chem. 88. (1984).

8. J. de Physique £911.. Colloque No. C5 (1991).

9. C. A. Huchison and R. C. Pastor, J. Chem Phys., 21, 1959. (1953).
10. A. Demortier, M. G. DeBacker and G. LePoutre, J. Chirn. Phys., 380
(1972).

11. R. L. Harris andJ. J. Lagowsli, J. Phys. Chem. 85, 896 (1981).

12. C. A. Huchison and R. C. Pastor, Rev. Mod. Phys., 25, 285 (1953).
13. A. Depreister, J. Fackeure and J. P. LeLieur, J. Phys. Chem. 8.5..
272 (1981).

14. S. Freed and N. Sugerman, J. Chem Phys., 11. 354 (1943).

15. J. P. LeLieur and R. Rigny, J. Chem Phys., 59, 1142 (1973).

16. J. P. LeLieur and R. Rigny, J. Chem Phys., 53, 1148 (1973).

17. I. M. Dmitrenko and I. O. kulik, Phys. Stat. SOL, (1)164, K13 (1974).
18. D. E. O'Reilly, J. Chem Phys., 35,. 1856 (1961).

134

135

19. V. L. Pollak. J. Chem Phys., 34. 864 (1961).

20. R. J. Peck and W. S. Glaunsinger, J. Phys. Chem, 84, 1176 (1980).
21. D. E. O'Reilly, J. Chem Phys., 41, 3736 (1964).

22. D. E. O'Reilly, J. Chem. Phys., 4;, 3729' (1964).

23. F. Seitz and D. Tumball, Solid State Physics Vol.2, Academic Press.
New York (1957).

24. M. Niibe and Y. Nakamura. J. Phys. Chem, 88, 5068, (1984).

25. R. R. Dewald and J. L. Dye, J. Phys. Chem, 68, 121 (1964).

26. D. M. Holton. P. P. Edward, W. McFarlane and B. Wood, J. Am
Chem Soc., 105, 2104 (1983).

27. Y. Nakamura. T. Toma and M. Shimoji, Phys. Lett.. A50, 373
(1977).

28. J. L. Dye and L. R. Dalton, J. Phys. Chem, 11,, 184 (1967).

29. J. M. Ceraso and J. L. Dye, J. Chem Phys. 5;, 1585, )1975).

30. J. L. Dye, C. W. Andrew and J. M. Ceraso, J. Phys. Chem 19, 3076
(1975).

31. D. C. Johnson, C. Page, D. M. Holton. B. Wood, W. McFarlane and P.
P. Edward.

32. R. Catterrall, L. P. Stoduloski and M. C. Symons, J. Chem Soc. (a).
437 (1968).

33. P. P. Edward, S.C. Grey and D. M. Holton. J. Chem Soc. Comm.
1185 (1981).

34. R. R. Catterrall and P. P. Edward. J. Phys. Chem, 22, 3010 (1975).
35. J. L. Dye, Pure Appl. Chem. 49, 3 (1977).

36. S. Golden. C. Guttman and T. R. Tattle, J. Am Chem Soc., 81, 135
(1965).

136

37. S. Golden, C. Guttman and T. R. Tuttle, J. Phys. Chem. 44, 3791
(1966).

38. W. J. Chase and J. W. Hunt. J. Phys. Chem. 19, 2835 (1975).

39. H. Lu, F. H. Long, R. M. Bowman K. B. Eisenthal.J. Phys. Chem. 9.3.
27 (1989).

40. Y. Gaudiel, S. Pommeret, A. Migus and A. Antonetti, J. Phys. Chem.
93,. 3880 (1989).

41. A. Migus, Y. Gaudiel,J. L. Martin and A. Antonetti, J. Phys. Chem.
58, 1559 (1987).

42. L. Kevan. J. Phys. Chem. BA. 1232 (1980).

43. L. Kevan, Acc. Chem Res., 14, 138 (1981).

44. D. F. Feng and L. Kevan, Chem Rev.. m, l (1980).

45. D. A. Copeland, N. R. kestner and J. Jortner, J. Chem Phys., 5.3..
1189 (1970).

46. K. Fueki, D. F. Feng and L. Kevan, J. Am Chem Soc., 95, 1389
(1973).

47. J. Jortner. Mal. Phys., 5. 257 (1962).

48. T. Miyazaki. N. Iwata. K. Fueki and H. Hase, J. Phys. Chem. 941..
1702 (1990).

49. B. Henderson, Defects in Crystalline Solids, Crane Russack & Co..
New York 1972.

50. H. Ivey, Phys. Rev.. 12, 341 (1947).

51. J. J. Markham, F-centers in Alkali Halides, Academic Press, New
York 1966.

52. W. B. Fowler, The Physics of Color Centers, Academic Press. New
York 1968.

137

53. J. L. Dye. J. M. Ceraso, M. K. Lok. B. L. Barnett, and F. T. Tehan, J.
Am Chem Soc., 96, 608 (1974).

54. F. J. Tehan, B. L. Barnett and J. L. Dye, J. Am Chem Soc., 95, 7203
(197 4).

55. T. A. Patterson, H. Hotop, A. Kasdan, D. W. Norcross and W. C.
Lineberger, Phys. Rev. Lett.. 32,, 189, (1974).

56. J. L. Dye, M. R. Yemen, M. G. Dague and J. M. Lehn, J. Chem Phys.,
58, 1665 (1978).

57. M. F. Fox and E. Hayon, J. Chem Soc. Faraday Trans. I. 12, 1990
(1976).

58. R. S. Bannwart, S. A. Solin, M. G. DeBacker and J. L. Dye, J. Am
Chem Soc., 1.1.1.. 552 (1989).

59. G. Xu, T. -R. Park, R. S. Banwart. A. Sieradzan. M. G. DeBacker. S. A.
Solin and J. L. Dye, J. de Physique-Colloque de Physque, in press.

60. T. -R. Park. S. A. Solin and J. L. Dye, Solid State Commum. 8;, 59
(1992).

61. M. G. DeBacker. F. X. Sauvage and and J. L. Dye, Chem Phys. Lett..
113,, 291 (1990).

62. J. L. Dye, Pure Appl. Chem. 49. 3 (1977).

63. A. S. Ellaboudy, M. L. Tinkham, B. Van Eck, J. L. Dye and P. B.
Smith. J. Phys. Chem, 88, 3852 (1984).

64. J. M. Ceraso and J. L Dye, J. Phys. Chem, 61,, 1585 (1974).

65. J. L. Dye. C. W. Andrew and J. M. Ceraso, J. Phys. Chem, 29,, 3076
(1975).

66. P. P. Edward, S. C. Guy, D. M. Holton and W. McFarlane. J. Chem
800. Chem Commun.,]_9_8_1, 1185.

67. P. P. Edward, J. Phys. Chem, 88,, 3772 (1984).

138

68. N. C. Pyper and P. P. Edwar, J. Am Chem Soc., .198, 78 (1986).
69. M. L. Tinkham and J. L. Dye. J. Am Chem Soc., .191, 6129 (1985).
70. P. P. Edward, A. S. Ellaboudy and D. M. Holton. Nature. 311, 242
(1985L.

71. A. S. Ellaboudy, M. L. Tinkham, B. Van Eek, J. L. Dye and P. B.
Smith, J. Phys. Chem. 99, 14, (1986).

72. S. B. Dawes, A. S. Ellaboudy and J. L. Dye, J. Am Chem Soc., m,
3508 (1987). _

73. J. Papaioannou, S. Janeicke. J. Solid State Chem 61, 122 (1987).
74. D. Issa. A. S. Ellaboudy. R. Janakiraman and J. L. Dye, J. Phys.
Chem, 88,, 3847 (1984).

75. A. S. Ellaboudy. C. J. Bender. J. Kim, D. H. Shin, M. E.
Kuchenmeister, G. T. Babcock and J. L. Dye. J. Am Chem Soc., 113..
2347 (1991).

76. A. S. Ellaboudy, Ph.D. Dessertation, Michigan State University
1984.

77. D. lssa and J. L. Dye, J. Am Chem. Soc., 19:1, 3871 (1982).

78. M. K. Farber, Ph.D. Dessertation, Michigan State University 1985.
79. J. C. Thompson, Electrons in Liquid Ammonia. Oxford University
Press 1976.

80. K. J. Moeggenborg, J. Papaioannou and J. L. Dye, Chem Mater., 3,
514 1991.

8 1 . K. J. Moeggenborg, Ph.D. Dessertation, Michigan State University
1990.

82. S. B. Dawes, J. L. Eglin, K. J. Moeggenborg, J. Kim and J. L. Dye.
193, 1605, J. Am Chem Soc. (1991).

139

83. J. S. Landers, J. L. Dye, A. Stacy and M. J. Sienko, J. Phys. Chem.
85,, 1096 (1981).

84. R. H. Huang, M. K. Faber, K. J. Moeggenborg, D. L. Ward and J. L.
Dye, Nature, 331, 599 (1988).

85. S. B. Dawes, D. L. Ward, R. H. Huang and J. L. Dye, J. Am Chem
Soc., .108, 3534 (1986).

86. J. L. Dye, Scientific American. 251, 66 (1987).

87. J. L. Dye, Prog, Inorg. Chem, 32, 327 (1984).

88. R. H. Huang, M. E. Keuchenmeister and J. L. Dye, Acta Crystallogr.
C, in press.

89. D. L. Ward, R. H. Huang and J. L. Dye, J. Crystallogr., Q44, 1374
(1988).

90. D. Issa. Ph.D. Dissertation. Michigan State University, 1982.

91. A. G. M. Barrett. C. R. A. Godfrey, D. M. Hollinshead, P. A.
Prokopiou, D. H. R. Barton, R. B. Boar, L. Joukhadar. J. M. McGhie, S. C.
Misra, J. Chem Soc. Perkin I 1501 (1981).

92. M. E. Kuchenmeister, Ph.D. Dissertation. Michigan State
University, 1989.

93. M. G. DeBacker and J. L. Dye, Ann. Rev. Phys. Chem. 38, 271
(1987).

94. M. E. Kuchenmeister and J. L. Dye, J. Am Chem Soc., LL]... 935
(1989).

95. J. L. Dye, J. Phys. Chem. 88,, 3842 (1984).

96. W. B. Lynch, K. A. Earle, and J. H. Freed, Rev. Sci. Instr. 52, 1345
(1988).

97. C. P. Lin, M. K. Bowman, and J. R. Norris, J. Magn. Reson., 55, 369
(1985).

98. R. D. Britt and M. P. Klein, J. Magn. Reson., 14, 535 (1987).

140

99. W. B. Mims, J. Magn. Reson.. 59.. 291 (1984).

100. A. Abragham, and M. H. L Pryce, Proc. Roy. Soc., A205, 135
(1951).

101. A. Crarrington. and A. D. McLachlan, Introduction to Magnetic
Resonance. Harper & Row, New York 1967.

102. J. E. Wertz and J. R. Bolton, Electron Spin Resonance:
Elementary Theory and Practical Applications. McGraw-Hill, New York
1972.

103. E. Fermi, Z. Physik, 60. 320 (1930).

104. R. A. Frosch, H. M. Foley, Phys. Rev.. 88, 1337 (1952).

105. C. P. Poole, Jr. and H. A. Farach. Bull. Magn. Reson., 1. 162
(1980).

106. C. P. Poole. Jr., Electron Spin Resonance, Welly. New York 2nd.
Chap. 12 1983.

107. A. Abragham, Principles of Nuclear Magnetism. Oxford University
Press, London, Chap. 10 1961.

108. C. P. Poole, Jr., and H. A. Farach. Relaxation in Magnetic
Resonance. Academic Press, New York 1971.

109. H. S. Gutosky, D. W. McCall, and C. P. Slitcher, J. Chem Phys., 21.
279 (1953).

110. E. Phkurshima and S. B. W. Roeder. Experimental Pulse N110? and:
A Nuts and Bolts Approch. Addison-Welly. reading, MA 1981.

1 1 1. 0. Ya. Grinberg, A. A. Dubinskii. V. F. Shuvalov, L. G. Oranskii, V. I.
Kurochkin. and Ya. Lebedev, Dolk. Phys. Chem, 230, 923 (1976).

1 12. 0. Ya. Grinberg, A. A. Dubinskii, and Ya. Lebedev, Russ. Chem
Rev.. 52, 850 (1983).

141

113. J. A. Weil, M. K. Bowman, J. R. Morton, M. D. Timken, Electron
Magnetic Resonance of the Solid state, Can. Soc. Chem., Ottawa p.21
1987.

114. L. Kevan and M. K. Bowman, Modern Pulsed and CW EPR. 1990.
115. G. M. Zhidomirodov, Ya. S. Lebedev, S. N. Dobryakov, N. Ya.
Shteinshneider. A. K. Chirkov, and V. A. Gubanov, Interpretation of
Complex EPR spectra, India Oxonian 'Press Pvt Ltd. New Delhi, p.79
1985.

116. J. A. Well, M. K. Bowman, J. R. Morton, M.D. Timken, Electron
Magnetic Resonance of the Solid state. Can. Soc. Chem., Ottawa p.45
1987.

117. L. G Rowan, E. L. Hahn, and W. B. Mims, Phys. Rev.. 1.31, A61
(1965).

1 18. J. ,M. Fauth, A. Schweiger, L. Braunschweiger. J. Forrer, and R. R.
Ernst, J. Magn Reson. 56 74 (1986).

119. W. B. Mims, Phys. Rev.. _B_§, 2409 (1972).

120. W. B. Mims, Phys. Rev.. Bi, 2409 (1972).

121. C. P. Slitcher, Principle of Magnetic Resonance. Harper & Row.
New York, p.127, 1963.

122. G. M. Zhidomirov and K. M. Salikhov, Theor. Exp Chem, 4. 332
(1968).

123. L. Kevan, M. K. Bowman, P. A. Narayana. R. K. Boeckman, V. F.
Yudanov, and Yu. D. Tsvetkov, J. Chem Phys., 63, 409 (1975).

"‘11111111111111111 ~