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STRUCTURAL AND ELECTRICAL PROPERTIES
OF GRAPHITE INTERCALATION COMPOUNDS
AND GRAPHITE FIBER COMPOUNDS

by

Xiao-Wen Qian

A DISSERTATION

Submitted to
Michigan State University
in Partial Fulfillment of the Requirements
for the Degree of

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1986

ABSTRACT

STRUCTURAL AND ELECTRIC PROPERTIES
OF GRAPHITE INTERCALATION COMPOUNDS
AND GRAPHITE FIBER COMPOUNDS

by

Xiao-Wen Qian

The structure of metal-ammonia K-NH liquid layers in the ternary

3

graphite intercalation compound K(NH )

3 u 33C2u at room temperature is

studied by measuring the in-plane X-ray diffuse scattering from the
as
intercalant layers. A c (q -0.88, qc") scan performed on the system

shows that the liquid layers in different graphite galleries are
uncorrelated, and the liquid layer is 2 dimensional (20). We modeled

the 2D liquid layer structure using a computer generated planar

distribution of hard K and NH3 discs. The modeled structure is the

close packing of two building blocks: N-fold clusters that are formed by

attaching four NH discs with variable radii symmetrically to a fixed

3

radius K+ disc and a unbound "spacer" NH disc. The expressions for the

3

1!
in-plane and 0 contributions to the scattering from such 2D liquids in
the galleries of graphite were deduced and applied to the generated
model. By comparing the calculated scattering pattern with the

experimental results, we concluded that the 2D K-NH liquid layers have

3

a N-fold coordinated structure that is the planar analogue of the 6-fold

coordinated structure found in bulk (30) K-NH3 solutions.

The microscopic bromine distribution in pitch-based brominated
graphite fibers has been measured with a field emission scanning

transmission electron micrOSCOpe (STEM) by monitoring the Br Ka X-ray

1
intensity. An inhomogeneous distribution of Br along the fiber is found
with two distinct cross-sectional distributions, namely: a uniform
distribution in Br-rich regions and a Gaussian-like distribution in Br-
poor regions. A model based on these Br distribution measurements is
proposed to understand the relation between the Br microstructure and
the macroscOpic residual resistance of the fiber. This model yields

semiquantitative agreement with experimental results.

ACKNOWLEDGMENT

It gives me great pleasure to acknowledge my advisor and
collaborator Professor Stuart A. Solin, who introduced me to this
research field, and whose intuitive insight and rich experiences have
guided me through every stage of this work. I thank him for his helpful
criticisms and other generous help in the time of need.

I also benefited a great deal from the collaborations with 0.11.
Hwang, D.R. Stump, B.R. York, R.M. Franco and many more. Interactions
with them gave me a unique experience that this author will remember for
a long time to come. I also thank Y.B. Fan, Y.Y. Huang, and S. Lee for
their assistance and for many interesting discussions. I am
particularly grateful to Vivion E. Shull for his invaluable assistance
in using the electron microscope and for much other help. Finally, the

financial support from NSF, NASA and Exxon are also acknowledged.

iv

FORWARD

Considerable efforts in both theory and experiment have been made
to study low dimensional, particularly 2 dimensional (2D), phenomena in
recent years. Examples of systems which exhibit 2D properties are: (1)
multi-layered structural materials including those synthesized by the
breakthrough technology of molecular beam epitaxy (MBE) and less costly
natural lamellar materials like graphite intercalation compounds
(GIC's), and clay intercalated compounds (CIC'S). (2) single layer
systems such as adsorbed layers on the surface of a substrate material
and the inversion layer in a MOSFET. In these families of low
dimensional system, GICs, in which the intercalant is monolayer or a
trilayer constituent alternating with n graphite layers in a staged
periodic superlattice structure, stand out for many special prOperties.
Among those are the atomic level epitaxy and great tunability both
structurally and electroniclly that enable us to study the whole
spectrum of dimensional effects ranging from 1D through quasi-2D, 2D-3D
crossover, and 3D phenomena. Our interests have been in low dimensional
structural and electrical properties of the GICs, and for this purpose
the first part of this thesis is devoted to detection and
characterization of a 2D metal-ammonia liquid solution structure in a
unique GIC, i.e. potassium-ammonia solution intercalated graphite
compound. The study of the structural and electric properties of other
GICs system are collected in the appendices. The second part of this

thesis deals with a different form of graphite compound, i.e. graphite

fiber compounds. The relations between the electrical properties and
structural properties of these fiber compounds are probed.

Part I and Part II of this thesis have been published or are in
press in the Physical Review and are referenced as follows, x.w. Qian,
D.R. Stump and S.A. Solin, Phys. Rev. B, 33, 5756(1985), and X.W. Qian,

S.A. Solin and J.R. Gaier, Phys. Rev. B, in press.

vi

TABLE OF CONTENTS

OVERVIEW 1

PART I: Structural Properties of Potassium-Ammonia Liquids in Graphite

I. Introduction 15
II. Experimental techniques and results 19
III. X-ray scattering from stacked 2D liquid layers 24
IV. Structural model 29
V. Radial distribution function 52
VI. Concluding Remarks 57
VII. Acknowledgment and references list 60

PART II. The Microstructural-Derived Macroscopic Residual Resistance

Brominated Graphite Fibers.

I. Introduction 64
II. Experimental techniques and justifications 66
III. The fiber resistance calculation 75
IV. Experimental results and discussions 77
V. Concluding remarks and summary 85
VI. Acknowledgment and references list 87
APPENDICES 90

Reprints and Preprints of Additional Published/Submitted Papers.

vfi

of

OVERVIEW

The subject of graphite intercalation compounds (GIC's) has become
ailarge research field mainly due to the tremendous efforts of
physicists, chemists and material scientists during the last few
decades. Major efforts of the researchers have been on the structural,
electrical and magnetic properties of these compounds, although many
other properties such as thermal transport, vibrational excitations etc.
have also been investigated. However, in this overview only the
structural properties of GICs will be briefly reviewed with stress on
the low dimensional characteristics of the material.

The understanding the structure of GIC's begins with the knowledge
of the parent material graphite. Graphite is a prototypical layered
structural material whose structure is shown in Fig. 1 [Ref. 1]. Notice

that carbon atoms are covalently bonded into a hexagonal lattice plane,

and that these planes are then stacked in the Z direction.auui bound by
'Van de Waals type interactions. The weak interplane bonding of carbon
atoms coupled with very strong intraplane bonding gives rise to a large
anisotropy in both the structural and the electronic properties of
graphite. Structurally, the anisotropy is manifested in the large
difference between the c-axis and a-axis lattice constants and force
constants. For instance the nearest carbon-carbon (C-C) distance within
the basal plane is only 1.u2 A, while the interplane distance is 3.35 A.
This anisotrOpic structure makes it possible to insert foreign species
in between the basal planes without significantly altering the integrity

of carbon layer structure. In fact many types of atoms or multi-atom

 

 

 

 

 

 

 

 

 

 

 

Fig. 1. The structure of hexagonal graphite.

 

 

6.7 A

molecules can be intercalated into graphite under apprOpriate conditions
to form a mono-atomicoxn a tri-atomic or monomolecular thick layer in
the galleries between the carbon basal planes. This intercalation
process is always accompanied by a charge transfer between the
intercahan;and host graphite. Depending on the sign of the charge
transfer, a GIC is called a donor compound if electrons are given to the
host by the intercalant, and an acceptor compound if electrons are
transferred from the carbon layer to the intercaleum” Alkali metal
intercalated GIC's are examples of donor compounds, and strongly acidic

Br intercalated into graphite are

molecules such as HNO , SbClS, 2

3
examples of the acceptor compounds.

An important and essentially unique characteristic of GIC's is the
staging phenomena, which is the periodic sequencing of carbon layers and
intercalant layers as shown in Fig. 2. The stage number n is defined by
n carbon layers in between two adjacent intercalant layers. Both
theoreticmtl and experimental studies have been conducted to understand

2’3’u It has been revealed that the

this interesting property of GIC's.
formation of the stage is driven by two fields: (1) a strain field that
INTMUCGSENIattPaCtive interaction between intercalants in the same
layer and a repulsive interaction between the intercalants in different
layers, and (2) a static electric field produced by the ionized
intercalant and mediated by host carbon layers that yield an additional

long range repulsive interaction between intercalants in different

layers. These tn“) fields are responsible for the formation and

STAGE 1 STAGE 2 STAGE n

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0000
O. I
0000 ' : "
.00 . :
"’ coo.

 

 

 

Graphite layer

0 o o o lntercalant layer

Fig. 2. The E-axis stacking sequence of graphite layers and
intercalant layers in stages 1,2, and n graphite intercalation
compounds.

stabilization of the stage structure, although other mechanisms such as

the formation of microscopic intercalant islands also play a role.5

.)
While the structural ordering in the c-axis direction, i.e.

staging phenomena, has been recently understood quite well1, many

efforts fauna also been devoted to the understanding of intercalant in-

plane structure."6 CHC's, in this aspect, provide a rich system with
which to study quasi-2D phenomena, since under many favorable conditions
the intercalant layers can be considered as a good approximation of a 2D
system

I In principle, the intercalant atoms are always in the potential
field imposed by carbon layers (particularly the two bounding layers)
and by other intercalant layers. Therefore the structnnwe of the
intercalant layer will always be affected by the carbon layer substrate

and vice versa. In fact these mutual effects have been studied by many

workers. For example, Casswell, Solin1 and Zabel6 etafl.studied the
intercalant layer structure in alkali metal intercalated GIC's, where
they found that the alkali metal-carbon interaction plays a dominant

role in the ordered phase of the alkali metal at low temperature.

Recently work by Moss7and Moret8 showed that even in the liquid phase of
the alkali metal layer at room temperature, the modulation on the liquid
structure due to the graphite layer potential is quite pronounced,
although the largest graphite substrate potential modulation is only
0.091 eV [Ref. 9]. On the other hand the presence of intercalant in the
graphite also affects the carbon layer structure. However this effect

is found to be small.chne to the strong covalent bonding between the

carbon atoms in the host layer. For example intercalation induced
change in the intraplanar carbon-carbon distance has been found to

always be less then 1%.1’10 These findings by various researchers

indicate that the carbon layer in the graphite is a rather smooth
substrate<m11flfixfl1intercalants ions or atoms can be quite mobile at
modest temperature. This unique property of GIC's give us a possibility
of create a quasi-2d system.

The key effort for obtaining a 2D intercalant layer is to eliminate
the correlations between the intercalants ixiciifferent layers, and to
lreduce the role of the substrate potential field modulation. To
eliminate the correlations between the intercalants in different layers,
one can increase the distance between them, i.e. increase the stage
number. To reduce the role of the graphite layer potential, one can
heat the system so that the potential energy imposed on the intercalant
can be compensated for by its high thermal energy. However in the

ternary alkali metal K-NH intercalated GIC K(NH )

3 3 u 33C2u, a 2D layer is

achieved by the co-intercalation of NH into the stage 2 binary

3

potassium intercalated compound KCZN' The intercalation of NH3 into a

K-intercalated GIC serves two purposes: (1) it increases the
intercalant-intercalant or guest-guest (G-G) interaction within a layer
to reduce the role of the guest-host (G-H) interaction. This is

possible because ammonia is well known as a strong solvent for alkali

metals in the 3D case11 where K atoms will immediately be ionized in the

highly polarizable ammonia liquid. Upon the insertion of NH3 into a K

occupied intercalant layer, the strong affinity of K to NH introduces a

3

competition with the carbon layer to bind K+. Consequently the
interaction between K and carbon is reduced as evidenced by the charge

12,13

back transfer observed in K(NHS) (3 compounds. Notice that

“.33 2“

because of the addition of one more interaction, i.e. the K-NH3

interaction, the role of the K-C interaction is reduced even without
reduction of K-C interaction strength. (2) Since the strong interaction
of K-NH3, the structure of each intercalant layer is dominated by (3-0
.interactionsimmuniresult in a liquid structure at room temperature.
This leaves the interaction between intercalants hicnfferent layers
limited to an average effect, thus the correlations between the

intercalant layers are absent even in a stage 1 K(NH ) where

3 H.3302u
intercalant layers are only one graphite layer apart. This is the
requirement for a 2D system.

In the first part of this thesis, the experimental verification of
such 2D metal-ammonia liquid solution structure is presented. From that

we conclude that potassium—ammonia layers in the K(NH ) form a 2D

3 4.33C2u

11-fold coordinated liquid which is the 2D structural analogue of the

 

well known 3D potassium-ammonia solutions. At the time of writirug'this

overview, other experiments such as quasi-elastic neutron scattering‘u
have remmufirmed the structure which was deduced in this work.

5

Additionally our recent work on the electrical resistivity1 and Optical

reflection and transmission prOperties16 of K(NH reveals that it.

3)xC2N

is also the electronic analogue of the corresponding 3D metal-ammonia

 

solution. i.e. it also shows a 2D Mott type metal-insulator transition.
The second part of this thesis deals with the study of graphite
fiber compounds.
Currently graphite fibers are made by two techniques: (1) the
graphitization of precursor material such as pitxni, polyacrylonitrile

(PAN), rayon fibers at high temperature17, and (2) chemical vapor

deposithm1cfi‘carbon onto microscopic carbon filaments18. These two
techniques yield two structurally different fiber products. The fiber
.made by fhxfi;technique consists of many graphite ribbons micrometer
length and several tens to several hundreds of angstrom thick. These
graphite ribbons are intertwined in such a way that statistically the
graphite basal planes are aligned along the radial directions of the
fiber as schematically shown in Fig. 3(a). The second technique
produces fibers in wmdch the graphite layer is wrapped around the axis
of the fiber to form an onion like cylindrical structure shown in Fig.
3(b). Since many foreign species can be readily intercalated into the
graphite as mentioned in the paragraphs above, insertion of many
reactants into graphite fibers can be also achieved, although the
threshold for the reaction to form a fiber compound is often
significantly higher than that for bulk graphite compounds.

Systematic study on these fiber compounds has only begun in last

19’20 While most of the efforts have been.devoted to the

few years.
practical aSpects of these compounds such as their high mechanical

strength etc., the fundamental physical basis for many properties of

' T fiber axis

 

(a)

1 fiber axis

 

Fig. 3. (a) A schematic illustration of the structure of pitch based
graphite fiber. The basal planes of the graphite layers are

statistically aligned in the radial directions, and the Zaaxes of
the graphite planes are tangential. (b) A schematic illustration

of the structure of vapor grown graphite fiber.

The Z-axes of
the graphite planes point radially outward.

10

these compounds has not been established. For example,:n;is found
experimentally that the electrical prOperties:such as electrical
resistivity of graphite fiber can be improved by adding species such as

Br or CuCl but the understanding of mechanism for such improvement is

3.
still, to our knowledge, minimal and too empirical. Therefore our
efforts to study these fiber compounds have been centered on trying to
elucidate the physical basis for their many interesting properties.

From studies of bulk GIC's, we know that propertitns such as
electrical resistivity depend critically on the the local chemical

20,21 20,21

~environment anuilocal structure of both the intercalant and
the host graphite. Therefore, a knowledge of the microscopic scale
chemical compositional distribution and structure are essentdttl‘to any
real understanding of the macrOSCOpic prOperties. Since graphite fiber
intrinsically lacks the uniformity of the structure found in its
corresponding bulk counterpart, the detection and characterization of
nflcrosmufix:level chemical compositional distribution and structure
would be especially important to understand any macroscopic level
prOperty. Guided by this thought, we present in the second part of this
thesis a study on the relation between the microscopic chemical
distribution and the macrosCOpic resistance of unique fiber'cnmnpounds,
i.e. residue brominated pitch based graphite compounds. The microscopic
prOperties are probed by using a field emission scanning transmission
electron microscope (FE-STEM), since the scale involved are in the range
of several tens of angstroms to several micrometers. We also attempted

to develop a phenomenological theory to couple the microscopic and

macroscopic properties in such fiber compounds, and used it.1x3 explain

11

the resistance changes in two different phases of brominated pitch based
graphite fibers.

Finally let me briefly mention that the special morphology of
graphite fibers sometimes can provide a convenient experimental system.
An example of this fiber application is our recent a~axis resistance

measurementonKXNH3)xC2n to study the 2D metal-insulator

transition15’16

using a vapor grown graphite fiber whose structure is
shown in Fig. 3(b). The fiber was chosen because of its large aspect

ratio.

12

References list of overview:

10.
11.

12.

13.

1H.

S.A. Solin, Adv. Chem. Phys. A9, A55(1982).

S.A. Safran, Phys. Rev. Lett. AN, 937(1980).

R. Clarke, N, Casswell, and S.A. Solin, Phys. Rev. Lett. M2,
61(1979).

D.P. DiVincenzo, C.D. Fuerst, and J.E. Fisher, Phys. Rev. B. 29,
1115(198“).

G. Kirczenow, Phys. Rev. Lett. A9, 1855(1982).

H. Zabel, in Ordering in Two Dimensions, edited by S.K. Sinha,

 

(North Holland, New York, 1980), p61.

0. Reiter, and S.C. Moss, Phys. Rev. B 33. 7209(1986).

F. Rousseaux, R. Moret, D. Guerard, P, Lagrange, and M. Lelaurain,
in Proceedings of International Symposium on Graphite Intercalation
Compounds, Tsukuba, Japan, 1985. [Synth. Met. 12, A5(1985)].

S.C. Moss, G. Reiter, C. Thompson, J.L. Robertson, J.D. Fan, and K.
Ohshinua, in Extended Abstracts of Graphite intercalation Compounds
Section of Fall MRS Meeting, 1986, (MRS, Pittsburgh, 1986).

D.E. Nixon and 0.8. Parry, J. Phys. C, 2, 1732(1969).

J.C. Thompson, Electrons in Liquid Ammonia (Clarendon, 0xford,1976).

 

B.R. York, and S.A. Solin, Phys. Rev. B, 31, 8206(1985).

R.M. Fronko, H.H. Resing, T. Tsang, X.W. Qian, and S.A. Solin, to be
published in J. Chem. Phys., [See Appendices].

Y.B. Fan, S.A. Solin, D. Newman, H. Zabel, and J.J. Rush , Phys.Rev.

B. to be published.

15.

16.

17.

18.

19.

20.

21.

13

Y.Y. Huang, x.w. Qian, S.A. Solin, J, Heremans, and 0.0. Tibbets in
Proceedings of NATO Summer School for Advanced Science and
Technology, 1986, edited by M.S. Dresselhaus, (Plenum, New York,
1986), [See Appendices].

Y.Y. Huang, Y.B. Fan, S.A. Solin, J.M. Zhang, P.C. Eklund, J.
Hermans and 0.0) Tibbets, submitted to Phys. Rev. Lett.

L.S. Singer, in Extended Abstracts of Graphite Intercalation
Compounds Section in Fall MRS meetings, 1986, (MRS,IHttsburgh,
1986).

0.0. Tibbets, C.P. Beets JR. and C.H. Olk in Extended Abstracts of
Graphite Intercalation Compounds Section of Fall MRS meetings, 1986
(MRS, Pittsburgh, 1986).

See, for example, Extented Abstracts of Graphite Intercalation
Compounds Section of Fall MRS Meeting, 1986, (MRS, Pittsburgh,
1986).

See, for example, the review article by M.S. Dresselhaus,and G.
Dresselhaus, Adv. in Phys. 30, 130(1980).

D.M. Hwang, x.w. Qian, and S.A. Solin, Phys.1hun Lett. 53.

1N73(198N).

14

PART I

STRUCTURAL PROPERTIES OF POTASSIUM-AMMONIA LIQUIDS IN GRAPHITE

15

I. Introduction

 

Metal-ammonia solutions were first intercalated into graphite
several decades ago by Rudorff and Schultze,1 the focus of whose inter-
est was primarily chemical. Ikmerest in metal-ammonia graphite
intercalation compounds (GIC's) remained dormant until the recent burst
of attention given to such compounds by Solin and coworkers.2-6 That
attention was motivated in part by the expectation that the metal am—
monia liquid in metal-ammonia GIC's might be the two-dimensional (2D)
structural analogue of bulk three-dimensional (3D) metal-ammonia solu-
tions which are cnue<of the classic systems that have been employed to
date to smnhrthe metal-insulator transition.7 Current interest in
metal-ammonia GIC's was also stimulated by the suSpicion that they might
be novel systems with which to study the effects of dimensionality on
localization8 and the metal-insulator transition in the crossover regime
between 2D and 3D behavior.

Our initial studies of the structural prOperties of the potassium
ammonia 01C,9 K(NH ) have confirmed that the K-NH liquid in that

C
3 11.33 211 3
compound is indeed the 2D structural analogue of a bulk 3D K-NH

3
solution. Preliminary reports of these initial studies have been
published9’1().and the inncpose of this paper is to provide an in-depth

presentation of the experimental and theoretical methods used to deduce

the complex structure of the K-NH 2D liquid in graphite. Before

3
proceeding, however, it will be useful to briefly summarize the ex-
perimental auui theoretical information which has been acquired to date

on the K(NH3)x02u, 0‘3 x i “.38, system and which will provide essential

input for the structural analysis which we present below.

16

The methods used by Ruddrff and coworkers1 and by Solin and

2.3

coworkers to prepare metal-ammonia GIC's are quite different, and the

resultant compounds produced by each method are distinct. Nevertheless,

the synthesis of all K-NH -0 compounds produced to date can be under—

3

stood in terms of the generalized Gibbs phase diagram11 for the ternary

system as represented by an equilateral triangle with K, NH and C at

3!

the vertices.6 Details of sample preparation for the specimens studied
here will be given later (section II),tnn.the description of current

results, including those reported here pertain to samples prepared by

3

the method of York and Solin, i.e. vapor phase ammoniation of the

stage-2 binary GIC w: [A.stage n GIC is one in which every pair of

2N'

nearest neighbor guest layers, e.g. the K-NH3 liquid layer, are

separated by n host carbon layers in a stacking sequence that exhibits
long-range C-axis order perpendicular to the graphite basal planes.123

The ammoniation of KC by NH

2” vapor to form K(NH ) C

3 x 2u'
-13

torr < PNH3 S 9.

It is sufficient

0 < x <
3 _ _

pressures in the range 10

UI

H.38 corresponding to NH3

atm. has been extensively discussed elsewhere.3’6’9

for our purpose here to note that the room temperature absorption
isotherm exhibits two plateau regions, each of which is initiated by a
sharp rise in absorption over a very small change in pressure. These

absorption steps occur at an ammonia pressure, PNH , of z 10-3 atm. and

3
-1 atm., respectively, and the latter corresponds to a stage-2 to stage-

3

1 phase transition. In that transition the system evolves from one

where every second gallery contains potassium (layer stoichiometry K012,

bulk stoichiometry K02“) with a small amount of ammonia (composition ==

K(NH3) O3C2“) to one where every gallery is occupied by potassium (layer

17

stoichiometry KC bulk stoichiometry KC ) and an excess of ammonia

2u'
(composition z K(NHB)

2N

). For PNH Z 1 atm. the system is essen-

3

= 9.5 atm. it acquires a composition of

H.3C2A

tially pure stage 1, and at P

NH
3
K(NH3)u 3302“. It is this "saturated" compound which we focus on here.
Proton nuclear magnetic resonance (NMR) measurements have been

- u 2,399
carried out on K(NH3)u.3302u

reveal several key features of the motions of the ammonia molecules in

and together with x-ray studies

the graphite galleries and of their local orientations relative to the
carbon layers, an example of which is depicted in Fig. 1.1.. First, it

.is clear that the NH3 molecules fknun only monolayers in the graphite

galleries and that at room temperature they are rotating rapidly on the
NMR time scalen. 'They are also translating rapidly as are the K+ ions.

Thus,tflmeK-NH system exhibits liquid-like behavior although rapid

3
hopping diffusion on lattice sites cannot be ruled out by the NMR

measurements. More specifically, the NH molecules are spinning rapidly

3
about their 3-fold axis [03 in Fig. 1.1] which is tilted with respect to

and precessing about the graphite c-axis [C in Fig. 1.1]. Moreover, the

average tilt angle <a> between the graphite c-axis and ammonia C3 axis
is, on the basis of both NMR“ and x-ray9 measurements, approximately 77°
and the tilt angle a fluctuates dynamically during the precesshmufl.

motion of the NH3 03 axis. In addition to proton NMR studies, carbon 13

. 13 .
NMR studies have also been carried out on K(NH3)N.33C2M

reveal that the samples are indeed stage one, i.e. there is only one

and these

type of average local environment for the NH molecule in the graphite

3
gallery.

18

 

—'a.‘5.‘.ima?““
(a)

 

(b)

Fig. 1.1. (a) Schematic scaled diagram of the ammonia molecule
sandwiched between carbon planes. The tilt angle between the
molecular 0 axis and the graphite c axis is denoted by a.

3

Planar projection of the ammonia molecule showing the resulting

"hard" disc of radius r.

19

Very recently elastic, inelastic, and quasielastic neutron scatter—

ing studies of K(NH3)N.3C24 u 302“
114

have been carriedcmn; and the preliminary quasielastic measurements

and the deuterated analogue K(ND3)

indicate two distinct diffusional motions, one presumably due to trans-

lation and one due to rotation in agreement with NMR results. Other

5

:recent measurements cfi‘the optical and electronic15 properties of the

K-NHB-C system confirm, respectively, the staging phase transitdxna and

the stage-1 character of the "saturated" compound,tnn.shed no addi-

tional light on the structural prOperties of the K-NH liquid.

3

The information established in this introductory section will be
followed by a description in section II of our experimental results and
of the novel experimental methods which we used to measure the in-plane
diffuse scattering from K(NH3)A.33C2N'

methods used to calculate the in-plane diffraction pattern are

In section III, the theoretical

described. The computer generated structural models to which the
theoretical methods are applied are described and discussed vis-a-vis
experimental results in section IV. Section V contains a discussion of
the radial distribution function deduced from the structural models we
have considered while our concluding remarks and acknowledgments are

presented in sections VI and VII, respectively.

II. Experimental Techniques and Results

 

Specimens of KC were prepared from highly-orientedlnmolytic

17

2A

graphite (HOPG)16 using the standard two-bulb method and pyrex
ampoules. Stage-2 purity was verified by (001) x-ray diffraction
studies which, together with the in-plane measurements reported here,

were carried out using MoKa radiation from a Rigaku 12kw rotating anode

20

source coupled through a vertically bent graphite monochromator to a
Huber N-circle diffractometer that housed a NaI detector.
The diffuse in-plane scattering from K(NH3)N.33C2N

and was masked by the diffuse scattering from the pyrex ampoules in

was very weak

which reactive GIC specimens are normally contained.12 Moreover, be-
cause the pressure of the ammonia vapor surrounding the specimen was =10
atm. it was not feasible to reduce the diffuse scattering from the pyrex
envelope by expanding its diameter and/or thinning its wall.18
Therefore, a sample cell was constructed from a very thin wall (< .005")
x-ray transparent aluminum can epoxied to a pyrex tube. The aluminum

can not only sustained the high NH pressure, but when it was machined

3
ffiwmn a single crystal and subsequently annealed at =500°C it yielded a
quasi-single crystal diffraction pattern that minimally interfered with
the diffuse scattering from the specimen.

The in-plane as-recorded diffraction patterns which we obtained

19,20

were corrected for several instrumental artifacts in the following

way: Let Iexp (q) be the observed in-plane diffraCCIINT patterrn 'This

contains Bragg reflections associated with both the aluminum sample can
and the ordered carbon layers. A reference pattern acquired from a
sample free region of the aluminum can was recorded, appropriately

scaled to, and subsequently subtracted from Iexp Uq). 'The Bragg peaks

1

associated with the carbon layers were removed (for clarity) from the

resulting pattern to yield Iexp (q) which is the observed diffuse
scattering. The pattern Iexp (q) was further corrected for absorption

and the Lorentz polarization factor to yield Ili(q) as follows:

21

Il(q) = Iéxp(q)[T/cose)exp(--11T/cose)]_1 x

[(1 + c0522e'c05229)/(1 + cosz2ca')]”1 . (1)

Here, T is the sample thickness, 11 is the effective absorption coeffi-
cient, 6 is the diffraction angle, and 6' is the graphite monochrometer
diffraction angle for the (00“) MoKa reflection. The corrected diffuse
scattering function I'l(q) was scaled to oscillate about the incoherent
scattering contribution

2 .
IInC(q) = 2 fm + i(m) (2)
uc

at high q and from trus scaling the ordinate scale, in electron units,
was established. In Eq. (2), fIn is the q-dependent atomic scattering
factor of the mth atom, LK3'* unit of composition which in our case is
K NH

( 3)u.33

and C atoms.

and i(m) is the Compton-modified scattering from the K, N, H,

The results of the application of the above-described procedure to
the experimentally measured Iexp (q) with q l c are shown in Fig. 1.2
together with the corresponding incoherent scattering contribution. We
have also measured a 0* scan1‘2 to establish the degree of correlation
between individual K-NH3 layers in successive galleries. The results of
this scan are shown in Fig. 1.3 which represents the as-recorded uncor—

rected data. For the scan given in Fig. 1.3, data corrections are not

required to extract the information we seek.

22

12.0 “

 

   

I

5*
o

mensrrv (ELECTRON unrrs x104)
go
0
?

 

 

 

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Fig. 1.2. The diffuse in-plane scattering (a E) [I (q)]exp from

K(NH3)u 3302” (solid line) and incoherent contribution from the

aluminum sample can and from the crystalline carbon planes have

been removed for clarity. The dash line represents the incoherent
scattering contribution.

23

 

0 ‘ .
-1.2 -0.8 -0.4 01340.4 0.8 1.2
qc>x<(A )

1 1

x _ -
Fig. 1.3. The diffuse C scattering (dis-0.88 A , -1.2 A < qc*< 1.2

-1 --1
*3
A ) from K(NH3)A.33C2U' The small peak at qc 0.80 A is due to

a surface contaminant of residual K08. The acquisition time per
channel was 32 sec.

2”

III. X-Ray Scattering from Stacked ZD Liquid Layers

 

Traditionally, there have been two basic approaches taken to
analyze data of the type shown in Fig. 1.2. Some authors prefer to use
a Bessel function back transform of I'l(q) to obtain the in-plane radial

distribution function (RDF).21 While this approach has been reasonably

successful when applied to monatomic 2D21 or 3D20 disordered systems it
is, in our opinion, seriously deficient for multiatomic systems such as

the K-NH liquid in graphite. This deficiency results from the well-

3
known difficulty of deconvolving the pair contributions (e.g. K+-K+, K+—
and NH -NH ) to the total RDF.20

“3' 3 3

Another approach, and the one that we believe is superior for
multiatomic systems, is to generate a real space model of the structure
of the disordered system and from the resultant atomic coordinates
calculate the diffraction pattern which is then compared directly to the
observed pattern in order to assess the validity of the model. Although
this method has obvious advantages, the reader should be cautioned to
consider a "good fit" to the experimental data as necessary, but not in
and of itself sufficient to verify the correctness of the structural
model of choice.22 Only when the diffraction data is taken, together
with other experimental evidence (e.g. NMR), can the correctness of a
particular structural model be confidently established.

Having chosen the methodology which we will apply to the data of

Fig. 2.2, we now address the calculational techniques which will be used
to compute the diffraction patterns of the structural models that we
have constructed (see below).

'The cross-section for x-ray scattering from a collection of atoms

or molecules, with x-ray momentum transfer ha, is

25

-> 9 ->
o(q) = oT(q)I(q) (3)
where oT(E) is the Thomson cross-section and 1(a) is the structure
function

i++
9'?
-> + k2
I<q> = Ii fk(q) e | (u)
k
+ . . . th + . .
Here rk IS the p051tion of the k atom and fk(q) IS the Fourier trans-

form of the electron density of the kth atom.
In our model.<xrlculations for x-ray scattering from potassium and
ammonia intercalated in graphite we used spherically symmetric form

factors fK(q) and f (q). At q = 0 the function fK(q) is equal to the

NH3

number of electrons in the atom. For the potassium form factor fK(q) we
renormalized the function so that fK(0) is 18 rather than 19 because the
potassium is almost completely (singly) ionized. Similarly, the form

factor for NH was assumed isotropic and was normalized so that f

3 NH (0)

3
13.

For atoms intercalated in graphite, the positions F are specified

k
by the gallery level n and position of the atom in that layer a. That
is, the index k = (no) and the position is
+ +

= 3!
rnu 8 n L + pna (5)
where 0* is a unit vector in the 0* direction, L is the spacing between

.9

layers,andpnu is a two-dimensional position vector. The in-plane

structure function 11(6), which is 1(9) with a i_a*, can be written

1+ (+ ->
Q' p “ D
e no

)

4 na‘
Il(q) = E Z fna(q>r* (q)

no'
n oa'

26

" (i )
1q pnu pn'a'

+ Z I fna(q)f;.a.(q) e (6)

n,n' n,n'
(nén')

In Eq. (6) the first term is the intralayer interference, and the
second term is the interlayer interference. If there is no correlation
between the atomic positions in different layers, timni the interlayer
interference term is identically zero. In that case, 1i(§) is the
structure function of a purely two—dimensional system.

Of course, if there is any strong correlation between the atomic
,positions.h1cflfferent layers, then the interlayer interference term
does contribute to 11(5). As an extreme example, suppose the distribu-
tions of the atoms in N of the layers is the same except for an overall
displacement of the layer in a direction perpendicular to 0*. That is,

assume that the atomic positions in these N layers are of the form

-+ + a
= +
pno. pa

n . (7)
+ . . th + . .
where Rn is the displacement of the n layer, and pa is independent of

n. Then the contribution of these N layers to the structure function

.y
Il(q) would be

'i (+ )
19 pa pa.

11(3) = FN<E) z e ra(q>r;,(q) (8)

ao'

where

N I
FN(E> = 2 e n n (9)

For example, if the Rn's are distributed randomly with IRnl i G. then

9
the expected value of FN(q) is

27

+ J1(qd) 2
FN(q) = N + N(N — 1) (—T————]
‘2'qd

(10)

The second term in Eq. (10), which is the effect of the interlayer
interference, is significant for N > 1 and a maxinnuntiisplacement d g
1/q.

In order to establish the degree of interlayer correlation it is
customary to measure a c* scan in which a diffraction pattern is
measured with q = (ql, 50*) with ql fixed, but qi i 0, and qc* variable
over some range -0 < qc* < +0. The structure function for such measure-

ments can be written as

'3) = na 9 *
I(q) Z 2 ' fna(q)fna,(q)
n d,a
-> + -)
iq *(n-n')L iq °(p - p , )
+ e C e i no n a fna(a)f:,a,(q)
n,n' a d'
(nin')

Again the second term, which is the qC*-dependent term, represents the
effect of interlayer interference. If there were a correlation of the

type represented by Eq. (7), then the interlayer interference term of

1(6) would be

' < 01.1" (A A) 1’? ’)
1Q n“” q ’ T q p "p

e 0* e l n n' e i, a a'
n,n' n,n'
(nin')

na(q n'a'(Q)°

28

+ + ->
Iql'(Rn "’ Rn.)

For strong correlations, the factor e is approximately 1;

then the major n-dependence in the summand is from the factor

iqc*(n-n')L
e , so the interlayer interference term would produce diffrac-

tion peaks at q0* = 2nv/L where v is an integer.

In the absence of such interlayer interference, the 2nd term in Eq.
(11) is identically zero and one expects to observe, {Run all values of
ql such that q = (alch*) does not intersect a Bragg reflection of the
host graphite structure, a monatonically decreasing intensity on either
side of q0* = 0 due to the a dependent form factor contributing to the
first term ofimL (11). This is exactly what is observed in the q =

0.88 A-1, q scan of K(NH )

0* 3 A.33C2A

particular scan across the "ridge" of the first and most pronounced peak

which is shown in Fig. 1.3. This

in Il(q) traverses a trajectory in q-space which is free from host
lattice Bragg reflections. [Note that the very small peak at qc* == 0.8
A-1 in Fig. 1.3 is a Bragg reflection from a residual contaminent of K08
on the sample surface.] Therefore, we confirm and hereinafter assume
that there is no correlation between the K--NH3 liquid layers in dif-
ferent galleries of the carbon host. These x-ray observations have been
independently confirmuui by (201) c* neutron scattering scans1u which
also show a monotonic decrease about q0* = 0.

In the absence of interlayer correlation, the in-plane structure

function is the same as for a single layer,

, iE-(Sa ~ 3a.)
11(q> = Z rq<q>f;.(q> e . <12)

29

apart from the absolute magnitude. Furthermore, if the positions so
within the layer are disordered, as in a liquid, then Il(q) depends only
on the magnitude of 23. In that case, we may average Il(q) over the

directions of q, with the result

Il(q) = aza'fa(q)f’;,(q) Jo(q|ra - ra,|) . (13)

This is the formula which we use to calculate the structure function in
our model calculations. In those calculations the number of particles
is 500 potassium atoms and 2165 ammonia molecules. This number is found
to be sufficiently large that 11(5), computed from Eq. (133), is almost
independent of the direction of 6. If a smaller collection of particles
is used, then there is some dependence on the direction of 8, because

the close packing of K-NH clusters in our models (see section IV below)

3
creates local ordering on a scale of approximately 50 K--NH3 clusters.
This local ordering produces preferred directions,2nmionly when the
number of particles is sufficient to produce a structure whose scale is

much larger than the scale of the local ordering is the diffracthmu

pattern independent of the direction of 6.

IV. Structural Models

 

In order to model the structure of the K-NH3 liquid in the graphite
galleries, we make several simplifying assumptions whichanwelisted

below:

1. The potassium ions and the NH molecules are treated as hard

3
infinitely thin discs oriented with their planes parallel to

30

the carbon planes and located at the mid-point of the gallery
along the graphite C-axis.

2. The radii of the K+ discs are identical and fixed at a value
which is adjusted to give the best fit to the diffraction
pattern consistent with the charge exchange to the graphite
layer.

3. The radii of the ammonia discs are variable and vary with the
tilt angle a according to a probability distribution that is
related to the tilt angle distribution.

11. Where N ammonia molecules are bound to a K+ ion in the liq-
uid, the N-fold coordinated K-NH3 cluster is symmetric.

Thus, the lines connecting the center of the K+ disc to each

of the NH discs in a cluster make equal angles of 2n/N.

3
5. The computer-generated collection of K-NH3 clusters and free
lHi3 discs is assembled in such a way as to maximize the in-

plane density.

6. The effect of the graphite substrate potential on the struc-

ture of the K-NH3 liquid has been ignored.

Consider now the basis and justifications for these assumptions.
Hard disc models have been applied with reasonable success to ascertain
the structures of 2D disordered systems including the case of a cesium
GIC, 0302“.23 Such models are justified in part because they remove the
horrendous complications attendant to a calculation of the diffraction
from a dynamic, irregularly-shaped 3D charge distribution (e.g. the
diffusing ammonia molecule). In addition, ammonia is a reasonable

candidate for disc representation because ttuali atoms are relatively

invisible to x-rays.

31

3.”.9

We know from other studies that all of the K+ ions are bound

in clusters to NH3 Species. Moreover, there is evidence that the charge
3

exchange parameter, f, is almost unity. Therefore, it is sensible tc>

assign a fixed radius to all the potassium ions. The radius was chosen

as rK+ = 1.A6 A, a value greater than the ionic radius of 1.33 A,2u

confirming that the potassium ion is not fully ionized. Other fixed

values of rK+ gave inferior fits to the experimental results.

As noted in the introduction, the NH molecules in the graphite

3

galleries are simultaneously spinning about their'(3 axes, precessing

3
about the graphite C-axis, and rocking as the tilt angle a fluctuates.

These motions are fast on the NMR time scale, =10-Ssec,25

but infinitely
slow on the x-ray time scale. Therefore, the x-ray pattern represents

the diffraction from an ensemble of K-NH layers, each with its own

3
"frozen" configuratitni<of K and NH3 "discs". The polarization of the
lone pair of electrons on the nitrogen atom of the NH3 molecule by the
positively-charged K+ ion causes the NH molecules to cluster around and

3
tilt towards the ion (i.e. (a) i 0). While at any instant in time the

tilt angle of a particular molecule in the specimen is fixed, there is a

"static" distribution of those tilt angles between the values of “min =
0° and “max = 90°. Corresponding to these are the effective radii of

the NH3 molecule, rmin

2.0A, the radius of the circle inscribing the centers of the three H

= 1.3A, the height of the molecule, and rmax =
atoms.

The distribution function P(r) giving the probability of finding an
NH3 disc of radius r was modeled as a Gaussian with a cut on at rmin and

a cut off at r . Thus
max

2 2
P(r) = A exp[’(r - rmin) /o ] 6(r - rmin) 6(rmax ~ r) (1A)

32

where A is a proportionality constant, 6(x) is a step function [0(x) = 1
if x > 0, 6(x) = 0 if x < 0] and the parameter a is related to the mean

radius <r > by

NH
3
rmax 2 2 rmax 2 2
<rNH3> = i expD-0~-r}un) /o ]rdr / i exp[-(r - rmin) /0 ]dr
min min

(15)

Note from Eq. (1A) that P(r) is peaked at rmin' This reflects the fact
that most of the molecules experience large tilt angles in analogy with

bulk K-NH3 solutions for which the axes of the 6 NH3 molecules all point

through the center of the K+ ion.7 In further analogy to the bulk K-NH

3

solutions which contain symmetric octahedral clusters we have assumed

that the planar K-NH clusters in the graphite galleries are also sym-

3
metric [e.g. item A of our assumptions above].

In any hard Sphere or hard disc model, the assembly procedure
(algorithm) used is designed to maximize the contact between the com-
ponent species.26 This is equivalent to maximizing the areal density
for planar models; accordingly, we designed our structure generation
inoutines to maximize density. In addition, to simplify our procedures
we ignored the substrate potential as noted above. While this approach
cannot be justified a priori, it is retroactively justified by the
results which we obtain.

Using the assumptions specified above, a structural model of the K-
NH liquid layers in graphite was generated as follows. Each model was

3

constructed from 500 K+ discs and 2165 NH3 discs to satisfy the

stoichiometry K(NH3) where 2165/500 = “.33. For an N-fold model

u.33C2u

33

exactly 500N molecules were bound symmetrically to K+ ions to form N-
fold coordinated clusters while the remaining 2165-500N molecules were
assembled as spacer discs.

By way of example, consider the assembly of a A-fold coordinated
structural distribution illustrated in Fig. 1.A. First, a "pot" of 500
A-fold clusters was created by attaching A ammonia discs symmetrically
to each K+ disc. The radii of the A NH3 discs in each cluster were
randomly selected by the computer using the probability distribution

function P(r). A seed cluster was then moved to the center of the

plane. Next, a random number generator made a decision to add either

another A-fold cluster or a single ammonia disc. The initial such

decision was weighted by the factors A99/[2165 - 500(A) + A99] = .75 and
[2165 - 500(A)]/[2165 - 500(A) + A99] = .25, which represent the respec-

tive probabilities of selecting a cluster or a bare NH3 disc from a

combined pot containing A99 clusters and 2165 - 500(A) = 165 bare NH3

molecules. Subsequent decisions were always weighted by the remaining

 

numbers of clusters and NH3 discs in the combined pot so that the rare

NH3 discs were not expended too rapidly.

If a A-fold cluster was chosen from the combined pot, the computer
brought it into contact with the seed cluster through a series of small
translations and rotations. Two kinds of rotation were involved, one
around the center of the plane and the other around the center of the
new cluster (see Fig. 1.A). The newly-added cluster was assembled in
such a position that the distance between the center of the seed and of
new cluster was minimized, to maximize the in-plane density. If, on the
other hand, a single disc was chosen, the computer created a single NH

3

disc with a radius randomly selected using P(r). This newly-generated

34

 

(b)

[’18- 1.11. (a) Schematic representation of mechanism used to computer

generate a fourfold coordinated hard disc K-NH3 liquid (see text).

Arrows indicate the combined translation and rotation of the
clusters which are close packed to the seed cluster. In the case
of the packing of a single NH3 disc, the arrow indicates

translation only. (b) Close packing configuration of two fourfold
clusters. The letters 0, a, b, c, and d indicate positions which
are relevant to the discussion in the text.

35

single NH3 disc was moved in a series of small translations towards the
center of the plane, and positioned in contact with the discs already
assembled so as to maximize the in-plane density. Care was taken to
prevent overlapping of the assembled discs. This procedure is also
depicted in Fig. 1.A, and was repeated until all K+ and NH3 discs had
been assembled. The central part (about one-sixth) of the resulting
structure, which is close-packed and A-fold coordinated, is shown in
Fig. 1.5(a).

Using exactly the same method that was employed to construct the A-
fold structure, we also constructed a 3-fold coordinated structural
distribution which consisted of 500 3-fold clusters and 665 single NH3
discs. This structure is shown in Fig. 1.6(a). A 0-fold
(uncoordinated) structure was also constructed by randomly selecting K+
or NH3 discs from the "pots" of 500 K+ ions and 2165 NH3 molecules

starting with a K+ seed. When subsequent selections yielded an NH3
disc, its radius was randomly selected using P(r) as described above.
Both K+ and NH3 discs were translated to the existing assembly and
placed in locations which maximized the density. The resultant O-fold
structure is shown in Fig. 1.7(a). For the purpose of further dis-
cussion we also show in Figs. 1.5b, 1.6b, and 1.7b the arrangements of
only the K+ ions in the A-fold, 3-fold, and 0-fold coordinated distribu-
tions, respectively.

Equation (13) has been applied to the structures shown in Figs.
1.5a, 1.6a, and 1.7a, and the calculated diffraction patterns Il(q) are
compared with the experimental measurement in Figs. Sc, 60, and 70,
respectively. The only adjustable parameter used for these comparisons

1

was a scale factor to optimize the fit at high q (> 5 A- ).

Fig.

36

 

o o. . o
0.0....o."
O'0...o. .0
9 0" 'oo.
0 .00. .
o o
. O O.
0’ " ‘. 0’
g 0.. O
0 co...
3 9'0...
— 9' o (b)

l.5(a),(b).

37

 
   
  

NITS)
[01000
Iowa
04:00
coo

2.0

11(ELECTRONU
on 63 11‘
on N m
o o o

440

0 ‘1 2 34 567
O—
ql(A1)

Fig. 1.5. (a) Section of the fourfold coordinated computer-generated

distribution for the K-NH ' ' . +
3 liquid in K(NH3)A.33C2A The K ions,

bound NH3 molecules, and bare NH3 molecules are represented by
solid circles, Open circles, and checkered circles, respectively.

(b) Configuration of K+ ions for the distribution shown in (a)
above. (0) Diffuse in-plane x-ray scattering I-L(q) (solid line)

calculated using the fourfold coordinated distribution shown in
(a) above and compared with the experimental measurement Of
l:I-L(<:1)]exp (dots) reproduced from Fig. 1.2. Inset: The

probability distribution P(r) (see text) for NH3 disc radii used

to generate the distribution shown in (a) above. The parameters

USGd P P r' r. I I. 3 8 r'
A. < H” > 1.” A.

3

38

 

Fig. 1.6(a). (b) -

39

 

(ELECTRON UNITS)

'1-

 

Fig. 1.6. Section of the threefold coordinated computer-generated
distribution for (a) the K-NH3 liquid in K(NH3)u 3302“. (b)

together with the resulting distribution of K+ ions, and (c) a
comparison of the corresponding calculated x-ray diffraction
pattern with the experimental measurement Of in-plane diffuse
scattering. See the caption of FIG. 1.5 for an explanation of
the symbols used and a listing of the relevant parameters.

40

 

Fig. 1.7(a).(b)-

41

  
 

 

 

11(ELECTRON UNITS)

Edg. 1.7. Section of the zerofold coordinated computer-generated
distribution for (a) the K-NH3 liquid in K(NH3)u.33C2u, (b)
together with the resulting distribution of K+ ions and (c) a
comparison of the corresponding calculated x-ray diffraction
pattern with the experimental measurement of in-plane diffuse
scattering. Open circles represent bare NH3 molecules. All other

symbols and relevant parameters are the same as those used in Fiso
1.5.

A2

A comparison Of Figs. 1.50, 1.60, and 1.70 reveals that the best
fit is clearly obtained with the A-fold coordinated distribution which
accounts semiquantitatively for all Of the observed features in the
experimental diffraction patttnui, and in particular, the peak at q =
0.88 A-1. This peak is a key, discerning feature Of the diffraction
pattern and can therefore be used as the major test for the model
calculation. Notice that the 0.88 A"1 peak is very weak in tflua calcu-
lated pattern for the 3-fold structure (see Fig. 1.60) and is totally
absent in the calculated pattern Of the 0-fOld structure (see Fig.
1.70). On the other hand, the 3-fold structure does provide the best
(fit for the q > 2.0 A”1 region, but the serious discrepancy at 0.88 A81
is ground for rejecting 3-fold coordination as a dominant structural
feature.

We can acquire a considerable degree of insight into the structural
origins of various features in the experimental and theoretical diffrac-

tion patterns by decomposing the total calculated scattering intensity

. + + +
into three separate contributions from K -K correlaticnus, K -NH

3 cor-
relations, and NH3-NH3 correlations. Thus
1(3): 1 (q) + i (q) + i (q) (16)
l lK+-K+ iK+-NH JLNH -NH
3 3 3
where
. 2
l +(q)= f+() J(r) (17)
lK+—K+ I + + l K q I 0 q
all K —K
pairs
1 (q) = Z 2Re1r +(q>r* (q) J (qr) (18>
lK+-NH + K NH3 J o
3 all K -NH
pairs

‘43

2
(q) = Z IfNH (q)| J0(qr) (19)

_ 3
3 all NH3 NH3

pairs

1
l —
NH3 NH

These individual pair contributions to the total scattering intensity
can be easily calculated from the model structures and are shown for the
A-fold, 3-fold, euni 0-fOld distributions in Figs. 1.8, 1.9, and 1.10,
reSpectively.

It is immediately clear that the peaks in Ii(Q) cannot, in general,
be simply related to particular correlations Of one species to another
'or to itself in the K-NH3 liquid. For instance, it can be seen frmm
Fig. 1.8 that all three pair functions contribute significantly (and in
one case, with negative amplitude) to the resultant peak at q = 2.0 A-1.
Indeed the amplitude, shape, and position of that peak are seriously
affected by even small changes in the relative contributions of the
three constituents from which it is constructed. However, the peak at q

= 0.88 A"1 is dominated by the contribution from ii + + and as a result
K -K

this peak is the most sensitive to cluster structure as can be seen from
Figs. 1.5, 1.6, and 1.7. Notice, for instance, the marked regularity of
the spacings between K+ discs in the A-fold distribution as depicteni in
Fig. 1.5b which shows only those discs. The array Of Fig. 1.5b is
quasi-crystalline and, as a result, yields a very strong peak in 11K+-K+

at q = 0.88 A-1. The K+-K+ pair separations are so regular in the A-

'1
fold distribution that even the 3rd order reflection of the 0.88 A

peak can be seen in 1.1. + +(q) (Fig. 1.8a). The q . 0.88 A”1 peak has
K -K

largely disappeared from Il(q) for the 3-fold coordinated structure

+ +
b(ecause the K -K distances are much more irregular as can be seen from

 

2200
1760
1320

880
(a)

 

440 J

0
1320

ON UNITS)

11(ELECTR

 

 

 

Fig. 1.8. The calculated (solid line) (a) KI-K+, (b) NH3-HH3, and (c)
4.
K ~NH pair contributions [i (q)] + (q)]
A -N
3 l_ K i. VH3 H3
[i

J—(C1)]K+_”H to the in-plane diffuse scattering from the fourfold
3

. , d
_K+. [1 an

coordinated distribution shown in Fig. 1.5(a). The dots are a
plot of 2f (q)f (q)J (qR) with R=2.89 A (see text).
K NH3 0

45

 

01234567
o-1
QLIA)

EFig. 1.9.. Pair contributions to the in-plane diffuse scattering
calculated using the threefold coordinated distribution shown
in Fig. 1.6(a). See the caption Of Fig. 1.8 for an explanation of
the symbols and labels used here.

46

 

2200
1760
1320

880
440

(a)

o
1320
880
440 (b)

880
440

i 1(ELECTRON UNITS)

-440
-880

 

 

Fig. 1.10. Pair contributions to the in-plane diffuse scattering
calculated using the zerofold coordinated distribution shown in

Fig. 1.7(a). See the caption of Fig. 1.8 for an explanation of
the symbols and labels used here.

A7

Fig. 1.6b. This peak is completely absent in the 0-fold coordination
pattern (Figs. 1.7a and 1.10) because there is no dominant pair separa~
tion in the K+-K+ configuration [Fig. 1.7b] for that structure.

The regularity Of the K+-K+ pair separations in the A-fold coor-
dinated structure provides us with the Opportunity to deduce an
analytical expression for the position Of the K+-K+ contribution tn) the
sharp first peak iJ111L(q). As noted above, this peak is dominated by
the the local ordering of K+ positions, which form a quasicrystalline
array over a region Of size approximately 50 clusters. The separation
between K+ ions in this array is the distance od in Fig. 1.A. With the

aid of that figure this distance, r

o + +, can be calculated, with the
K-K

result

2 _.
R + {/ZR + [(2<rNH

K -K 3

2 I 21/2}2]1/2

>) - R J (20)

ml

with

R = r + + <r > (21)
K NH3

4
where rK+ and <rNH > have been defined above. For momentum transfer q
3

along a line parallel to the line Od in Fig. 1.A, there is constructive

. +
interference of the waves scattered from these K ions if

+ _ a 2n
lql - qo ;:—-————. (22)

°K+-K+
In a large sample of liquid there are locally ordered regions with
arbitrary alignment. Therefore, this constructive interference occurs

. -)
for any direction of q. The values Of rK and <rNH > in the computer-

generated sample Of closely packed A-fold K--NH3 clusters are rK+ = 1.116

A8

A and <rNH > 1.A3 A, respectively; the corresponding value of Q0 from
3
Eq. (19) is q0 = 0.98 A“. This is the position at which the sharp

first peak in ii + +(q) occurs, as can be seen from Fig. 1.8, and it is
K-K

this peak which is primarily responsible for the first peak in 11(6) for
the A-fold distribution. Note, however, that the contributions from

(a) and to a lesser extent 1 (q) are sufficient tO cause

i —
3 NH3 NH3
1

a slight downward shift of the first peak in 11(6) to 0.88 A- , the

i
iK+-NH

exact position at which it is Observed experimentally. The next peak in

ii + +(q), which occurs at =(1.9)A-1, is the second harmonic Of the
K -K

interference. It is broader than the lowest peak because the structure
is not crystalline.
A striking feature Of the pair contributions to Il(q) is the

similarity in the K‘I-NH3 contributions shown in Figs. 1.80, 1.90, and

1.100 particularly with regard to the peak at =2.5 A-1. This similarity
results from the fact that the mean radius of the ammonia discs is the
same for each distribution and the NH3 discs have a relatively small
spread in their radii. Therefore, there is a dominant K+--NH3 distance
that manifests itself in each Of the distributions we have addressed.
To illustrate this point further, we show in Fig. 1.80 the Bessel fun0~

tion contribution JO(qRO) to i + from a single pair separation R
ix -NH °

3

(see Eq. 21), where R0 = 2.89 A. Clearly, this function gives a very

good fit to ii + (q) in the range q > 2 11-1 and shows only interfe-
K -NH

3
rence induced deviations from ii + (q) in the region q < 2 A-1.
” 3

This

“9

result confirms the dominance Of the distance RO hitflmeA-fold coor—
dinated distribution. Analogous results for JO(qRO) are obtained from
the 3-fold and O-folcldistributions as can be seen from Figs. 1.90 and
1.100.

We have also studied the case in which all NH3 discs have the same

fixed radius. In this case the distribution function P(r) is given by

P(r) = 6(r - <rNH >) (23)

3
as is shown in the inset of Fig. 1.11, the full panel of which shows the

corresponding calculated Il(q). The form of Il(q) at small q is similar

 

to that for the A-fold coordinated structure with a spread in tilt
angles (i.e. Fig. 1.50). However, the peak at q ~ A.5 A—1 is sig-
nificantly sharper for the case Of a fixed NH3 radius than for a
variable NH3 radius. As can be seen from Fig. 1.12, this high-q feature
is a higher harmonic Of features that appear at low q. The A-fold
coordinated structure with fixed NH3 radius produces a more regular
arrangement than the structures described earlier. For example, the K+r
K+ contribution to Ii(q) (Fig. 1.12a) shows at least five orders of the
0.88 A“1 reflection because the distances between nearest neighbor K+'s
are almost equal if the NH3 radius is fixed. The experimental in-plane
x-ray scattering data [Fig. 1.2] does not have a sharp feature at high-
q. This is clear evidence that the NH3 radius is variable, disrupting
the order of the closely-packed clusters. The structure shown in Fig.
5a, with an NH3 radius that varies by approximately 110%, has a
IDrmmdened peak at q ~ A-5 A—1; however, even that is qualitatively

d ifferent from the smooth behavior Of the experimental data at high q.

50

 

 

    

2.0 I

(ELECTRON UNITS)

'i

012 3 4 5 5 7
q_L(A-1)

Fig. 1.11. The in-plane diffuse scattering (solid line) calculated

+
using a fourfold coordinated distribution in which both the K
radius and the NH3 radius were fixed at 1.116 and 1.A3 A.

respectively. The latter is reflected in the 6 function P(r)

shown in the inset. The dots represent the corresponding
experimental results given in Fig. 1.2.

 

51

 

 

2200
1760
1320
A 880 (a)
g; 440
z , J
D
55 880
o: (b)
E5 440
LLI
_.|
E!
.:'

 
  

 

 

llllilil

01234557
—1

EMA)

trig. 1.12. The pair contributions tO the in—plane diffuse scattering

calculated using the fourfold coordinated distribution whose

parameters are given in the caption of Fig.1.11. See also the
caption of FIG. 1.8.

52

This suggests that the physical variation of the NH radius may be even

3

greater than what we used in our two—dimensional model calculation.

V. Radial Distribution Function

 

One can obtain a measure of the degree Of correlation in the K-NH3
liquid by computing the mean particle-particle radial distribution
function Rpp(r) which is prOportional to the probability of finding any

pair of particles (i.e. K+ or NH ) with a pair separation Of r. The

3
quantity Rpp(r) is defined by
r2 1 N N
R r d = — - -
I pp( ) r N .2 .X 6(r2 rij)e(ri‘j r1). (2A)
r1 i=1 j=1
where
I ’ (25)
rij - |r1 rjl,

+
the indices 1 and j both label all the K ions and NH molecules, and N

3
is the total number of particles in the system.
Figures 1.13a, b, and 0, respectively, show the distribution func-

tions [R for the large

pp(r)]A-fold’ [Rpp(r)J3-fold’ [Rpp(r)]0-fold
computer-generated sample of closely packed A-fold, 3-fold, and 0-fold
coordinated clusters. The existence of sharp spikes at particular
values of r indicates the existence of local ordering. The specific
values Of r where the peaks occur in Fig. 1.13a are associated with
characteristic distances of a closely packed pair of A-fold clusters.
Refer again to Figure 1.A. There the letters label the center points of

the various disks. The distances 0a, 0b, 00, 0d, and so on, are the

Values of
r where [Rpp(r)]A-fold has sharp peaks in Figure 13a. These

53

 

.1.
0|

 

‘oumofii
l

 

.5
0|

(ATOMS/A)
'16

"pp
0 a a: CD

 

 

.s
OI
l

- (c)

 

   

950.121 MOMS/A2

 

oumcofi

 

IIJJLII
1215182124

r (A)

 

O
(A
0)
‘0

Fig. 1.13. The full particle-particle radial distribution function for
the (a) fourfold , (b) threefold, and (c) zerofold coordinated
distributions shown in Fig. 1.5(a). 1.6(a). and 1.7(a).
respectively. The dashed lines are plots of rp where p is the

0

0
mean number density calculated in the manner described in the
text.

 

5A

distances are not precisely equal for all pairs of clusters, because the
clusters form a.lixniid structure, and because in our model we let the

radius of the NH3 disks be somewhat variable. But the close packing of

these A-fold clusters produces sufficient local ordering that the varia-
tion in the distances 0a, 0b, etc. is small. Thus, R(r) has sharp

peaks. The distribution [Rpp(r)] is quite different than

0-fold

[Rpp(r)]A-fold because the uncorrelated discs just form a close-packed
array of particles having approximately equal radii; the peaks in

[Rpp(r)]

0-fold are just multiples Of the near-neighbor hard disc

distance. The distribution [R (r)] is intermediate between the
pp 3-fold
other two cases.
In the liquid state the correlation between particle positions
decreases as r increases. Therefore, the peaks in Rpp(r) broaden and
then disappear as r increases. Ihn'r 2 20A the distribution functions

shown in Fig. 1.13 approach

Rpp(r) ~ 2hr po, (26)

Where pO is the mean particle number density. From Fig. 1.13 we can

A-fold’ (po)3-fold’ and
—2

d’ and we find the values 0.103 A—Z, 0.110 A-2, and 0.121 A ,

calculate the mean number densities (p0)
(po)0—fol

respectively.

+ +
Finally, the K —K correlations can be studied by considering the

+ + . . . .
K -K pair distribution R + +(r) given by

 

K ’K
r2 1 NK+ NK+
f R (r)dr = 2 ) 0(r - r .)0(r.. - r ) (27)
r K+-K+ NK+ i=1 j=1 2 i3 13 1

iij

55

where the sum on the right and side of Eq. (2A) is now computed using

+ K+ particles in the distribution. It is R + +(r) which

only the N K -K

K

illustrates so clearly the distinctions between the three distributions
we have discussed as can be seen from Figs. 1.1Aa, b, and 0. Only Fig.
1.1Aa shows well‘defined "regularly" Spaced peaks characteristic of the
high degree of K+ ordering in the A-fold coordinated distribution,
whereas the 3-fold and 0-fold distributions show little (Fig. 1.1Ab) and
no (Fig. 1.1Ac) K+-K+ correlations respectively.

Recall that the origin Of the peak in Il(q) at q ~ 0.88 A.1 is the
approximate local order of the K+ ions. The K‘I-K+ radial distribution
function in Fig. 1.1Aa indicates that the nature of the ordering is
approximately rhombohedra,. This can also be seen qualitatively by
inspection of the K+ positions in Fig. 1.5a, but it can be made quan-
titative by inspection of the K+-K+ radial distribution function. A
square lattice is a rhombohedral lattice with a rhombohedral angle of
90°; the corresponding radial distribution function has peaks at r = a,
/2a, and 2a (where a is the lattice spacing), each with total area A. A
triangular lattice is a rhombohedral lattice with a rhombohedral angle
of 60°; the corresponding radial distribution function has peaks at
r = a and ./3a, each with area 6. An intermediate rhombohedral lattice
with a rhombohedral angle a, where 90° > a > 60°, has peaks at a, 2a cos
11/2, 2a sin d/2, and 2a, with areas A, 2, 2, and A, reSpectively. The
K+-K+ radial distribution function shown in Figure 1Aa has broad peaks
vwith maxima at 6.8 A and 1A.A A and areas approximately A.5 and 6, and a

plateau in the region 8 A < r < 13 A with area 3.5. This indicates that

the K ions are approximately ordered in an intermediate rhombohedral

 

:L attice, at least over distances of about 20 A.

=-

 

‘m'l'm-

56

 

(a)

 

15
9
6
3
01(11L111

 

OMS/A)

I3“¢kfIIVT

o u 0: co R3 5
-—r'—'1—r'—'l—I'

 

 

 

15

12

91

6

(c)

3

0 111111
0 3691215182124

0
r (A)

Fig. 1.111. The partial K+-K+ radial distribution function for the (a)
fourfold (b) threefold, and (c) zerofold coordinated distributions
shown in Figs. 1.5(a). 1.6(a). and 1.7(a). respectively.

57

VI. Concluding Remarks

 

Although the best fit to the experimental diffraction data was
Obtained with a A-fold coordinated distribution, that:fih:(see Fig.
1.50) must still be characterized as semiquantative» 'The major~ depar-
ture from experiment exhibited by our model structure is in the high q
shoulder to the 2.0 A“1 peak and the larger amplitude of the A.8 A”1
peak, both Of which are absent in the data. These discrepancies could
no doubt be reduced, if not completely eliminated, if we were to intro-
duce additional parameters or equivalently more flexibility into our
model.

'The high q shoulder cuithe 2.0 A—1 peak derives mainly from K-NH

3
and NH3-NH3 contributions both of which could be noticeably perturbed if
we had allowed the angular positions of the NH discs about the K+ ions

3
in a cluster to vary--perhaps according to a distribution function P(e).

Even more fitting parameters could have been added by taking account Of

the dynamic nature of the K-NH liquid and the resultant fact that it

3
will simultaneously contain clusters with differing coordination
numbers. Though the introduction of additional parameters would sharply
improve the agreement between the experimental and calculated diffrac-
tion patterns, we feel that such a procedure is not justified by the
data and that it would mask the essential Structural features-~the
dominance of the A-fold coordinated clusters and the distribution in NH

3

C3 axis tilt angles.
It is not surprising that the model which we have used does not
yield a quantitative fit to the data. Rather, it is very surprising

that such a Simple model produces such a good semiquantitative fit.

58

The reader may wonder why we did not introduce and test clusters
with higher coordination than A. Such clusters are essentially
precluded by the size Of the ammonia discs. While 5 and even 6 such

discs, each of radius rmin = 1.3 A, could just fit symmetrically around

a potassium ion without overlapping, such a configurations are extremely
rare in our computer—generated structures. Moreover, it is not possible
to make a N-fold coordinated distribution with N > A and have all K+

ions exactly N-fold coordinated since for our specimen K(NH3)M 38C2A’

the maximum number of available ammonia molecules, 11.33 per K+ ion, is
less than 5. Thus, configurations with higher than A-fold coordination
(can be ruled out.

The upper bound on cluster coordination in the 2D liquid is
analogous to the situation which obtains in bulk 3D metal-ammonia

solutions.7 In K-NH3 3D solutions, the K+ is octohedrally 6-fold coor-

dinated to the NH3 molecules, the number 6 being determined by the space

available around the ion to pack in NH3 molecules. Thus, in Li-NH3 3D

solutions the coordination is tetrahedral A-fold since Li is smaller
than potassium, whereas the coordination is believed to be 7-fold for

the larger Cs ion in Cs-NH 3D solutions. Also note that the A-fold

3

coordination of the 2D liquid K-NH clusters is a natural consequence of

3

the 6~fold coordination in the 3D liquid. The gallery height in K(NH3

) 1.2.3

A 3302“ is insufficient to accommodate a K(NH3)6 octohedron.

However, this height can naturally accommodate a planar K(NH cluster

3%:

which is derived by removing opposite apical NH3 molecules from a

K(NH3)6 octohedral cluster.
As an additional comment, we would like to address the relationship

between the in-plane areal density of the 2D K-NH liquid, the liquid

3

59

structure, and the layer stoichiometry. Each of the computer-generated

structures which we tested was assembled to satisfy the K-NH3

stoichiometry of our samples, i.e. the ratio Of the numbers of K+ discs

and NH discs was fixed at 1/A.33 independent of the cluster coordina-

3

tion number used. However, the in-plane density was very model-

dependent because the packing fraction depended on cluster coordination.

In fact, only the A-fold distribution which yielded a densitqr().10 A-2

which was equal, wdttun experimental error, to the known in-plane den-

sample, 0.09 1 0.01 A_2. The other

2

Sity of our K(NH3)A.33C2A

distributions resulted in in-plane densities Of 0.11 A- (3-fold

coordinated) and 0.12 A-Z, both of which are significantlyriiigher than
the actual density.
While fitting the experimental in-plane diffraction pattern to the

pattern calculated from the A-fOld coordinated distribution, we dis-

1 1

covered that the relative intensity of the 0.88 A” enni 2.0 A- peaks

was dependent upon the size Of the K+ ion and that the best results were

obtained with rK+ = 1.A6 A. We can use this result to estimate the

charge transfer, f, in the K(NH3)A.33C2A

relationship which has been employed by Enoki, et al.

sample if we adopt the linear

27 to relate charge

transfer to ion size,

f r + (1 - f) r = r . (25)

K+1 K0 K
In Eq. (25) r +1 = 1.33 A is the ionic radius Of singly ionized potas-
sium, r o = 2.38 A28 is the atomic radius of potassium and rK+ is the

K

radius of the partially-ionized Species. Using the value r + = 1.A6 A
K

 

60

in Eq. (25) we find a charge exchange f -- 0.88. This value is grati-

3

fyingly close to the value Of charge exchange determined by x-ray

13

and

other measurements.

VII. Acknowledgments

 

This work is done in collaboration with D.R. Stump, S.A. Solin. We
gratefully acknowledge useful discussions with B.R. York, Y.B. Fan, and
S.D. Mahanti. This work was supported by the NSF LHHNa" grant #DMR82-

1155A.

1.

10.

11.

12.
13.
1A.

15.

61

REFERENCES
W. Ruddrff and E. Schultze, Angew. Chem. 66, 305 (195A).
S.K. Hark,ILJL York, S.D. Mahanti, and S.A. Solin, Solid State
Comm. 59, 5A5 (198A).
B.R. York and S.A. Solin, Phys. Rev. B31, 8206 (1985).
H.A. Resimug, B.R. York, S.A. Solin, and R.M. Fronko, Proc. of the
17th Carbon Conf., Louisville, 1985 (in press).
D.M. Hoffman, A.M. Rao, G.L. Doll, P.C. Eklund, B.R. York, and S.A.
Solin, Mats. Res. Soc. Bull., 198A (in press).
Y.B. Fan and S.A. Solin, Proc. of the 17th Carbon Conf.,
Louisville, 1985 (in press).

J.C. Thompson, Electrons in Liquid Ammonia (Clarendon,Cthrd,

 

1976).
E. Abrahams, P.W. Anderson, D.C. Licciardello, and T.V.
Ramakrishnan, Phys. Rev. Lett. 33, 673 (1979).

X.W. Qian, D.R. Stump, B.R. York, and S.A. Solin, Phys. Rev. Lett.

23, 1271 (1985).

S.A. Solin, in Localization and Metal-Insulator Transitions, ed. by

 

H. Fritzsche and D. Adler (Plenum Press, New York, 1985). P. 393.

P. Hansen, Physical Metallurgy (Cambridge University Press,

 

Cambridge, England, 1978).

S.A. Solin, Adv. in Chem. Phys. Ag, A55 (1982).

R.M. Fronko, H. Resing, Y.B. Fan, and S.A. Solin, to be published.
D. Neumann, H. Zabel, Y.B. Fan and S.A. Solin (unpublished).

Y.Y. Huang, S.A. Solin, and J. Heremans (unpublished).

16.

17

18.

19.

20.

21.

22.

23.
2A.

25.

26.

27.

28.

62

A. Herold, in Proceedings of the International Conference on the
Physics of Intercalation Compounds, edited by L. Pietronero and E.
Tosatti (Springer, New York, 1981) p.7.

H. Herold, Bull. Soc. Chim. Fr., p.999(1955).

R. Clarke, N. Caswell, and S.A. Solin, Phys. Rev. Lett. A2,
61(1979).

H.P. Klug and L.E. Alexander, X-ray Differaction Procedures for
Polycrystalline and Amorphous Materials (Wiley, New York, 197A).
B.E. Warren, X-ray Diffraction (Addison-Wesley, Reeding, Mass.,
1969), pp. 26A-275.

R. Clarke, N. Caswell, S.A. Solin, and P.M. Horn, Phys. Rev. Lett.
“3. 886(1979).

S.A. Solin, in Structure and Excitations of Amorphous Solids
(Williamsberg,1HL” 1976), proceedings of an International
Conference, AIP Conference Proceedings, No. 31, Williamsberg, Va.
1976), edited by G. Lucovsky and F.L. Galeener (AIP, New York,
1976), p. 205.

M. Plischke and W.D. Leckie, Can. J. Phys. 60, 1139 (1982).

L. Pauling, The Nature of the Chemical Bond (Conell, Ithaca, 1960).
T.C. Farrar and E.D. Becker, Pulse and Fourier Transform
NMR(Academic, New York, 1971).

0.8. Cargill III, in Solid State Physics, edited by H. Ehrenreich,
F. Seitz, and.D. Turnbull (Academic, New York, 1957). Vol. 30, p.
227.

T. Enoki, M. Sano, and H. Inokuchi, J. Chem. Phys. 78, 2017 (1983).
N. Glinka, Genaral Chemistry (Gordon and Breach, New York, 1965).

p. 1A6.

63

PART II
The Microstructure-Derived Macroscopic Residual Resistance

of Brominated Graphite Fibers

 

 

OI

lim—

[a

A

”Iv

‘QA
vv'

I l
\Fv

51%.

6A

I. INTRODUCTION

During the past few decades, pitch-based graphite fibers prepared
at high temperature by the graphitization of precursor material such as
mesophase pitch have attracted considerable interest and attention
primarily as a result of potential practical applications which are
based on their novel physical prOperties 1. For instance, it is now
well known that pitch-based graphite fibers are not only light weight
and very strong mechanically as evidenced by a high tensile strength and
high Young's modulus 2 but they also exhibit modest electrical
conductivity 3.
- The relatively recent discovery that the electrical properties of
pitch-based graphite fibers (herein after referred to as PB fibers) can
be greatly modified by the intercalation of guest species without
concomitant degradation of their desirable mechanical peoperties has
further heightened the already established keen interest alluded to
above 3-5. While many chemically distinct types of intercalated PB
fibers have been synthesized in an impirical effort to improve their
electrical properties, the fundamental relationship between the
microscopic distribution of guest species in the fiber and its
macroscopic resistance has, to our knowledge, not been addressed. Yet,
for a given Species of guest its micrOSCOpic distribution in the fiber
critically determines the ultimate conductivity. Accordingly, we report
in this paper a detailed scanning transmission electron microscope
(STEM) study of the distribution Of one selected (see below) chemical
species, Br, inserted into PB fibers. Our experimental results together
unth.a wealth of information on the companion material, Br intercalated

6,7

highly oriented pyrolytic graphite (HOPG) and other graphite

65

intecalation compounds ( GIC's) 8, have provided the irnnit for a
theoretical model which we have deveIOped to deduce the macroscopic
fiber resistance from a knowledge Of the guest species and it's
microscopic distribution.

To date the evidence that Br is actually intercalated irnxa the PB
fiber rather than absorbed on internal surfaces is weak since no
convincing X-ray data in support of intercalation have IKHHT presented.
Whatever the insertion mechanism, the unusual air stability1and
electrical properties of PB fibers clearly warrant investigation by the
method employed here. However we are reluctant to characterize the
(modified fibers as intercalation compounds and hereinafter employ the
descriptive phrase "brominated" to signify the physical alteration
associated with exposure to Br.

Bromine intercalated PB fiber is one of the few fiber GIC's which

5’9’10. (Here a residue

has a stable residue phase in air and in vacuum
compound is one in which desorption of the intercalant species by
reactnwivdth the environment, pumping Off etc. is incomplete. The
residual intercalant may be pinned to defects in tie host graphitic
material.) Thus Br-PB fiber is an ideal material for a STEM study Of
the type reported here. When exposed to and maintained in a Br vapor of
sufficient vapor pressure, PB fibers form a saturated compound with a
typical resistivivity of ~15 uQ-cm. This represents an 18- fold
decrease over the resistivity of the pristine fiber of 253 uQ‘CmL. When
the saturated fibers are removed from the Br vapor and.subsequently
exposed to ambient environment to form a Br deficient residue compound,

their resistivity rises by a factor of three to ~A5 un-cm 11.

 

66

In order to understand the resistivity changes between the
saturated and residual PB fiber we adopted the following approach: First
the micrOSCOpic Br distribution in the residual fiber is determined
using the STIRi . Then a model which relates the local conductivity of
the fiber to the local density of Br is develOped and used to calculate
the resistivities of the residual and saturated fibers. The calculated
results are then compared to experimental results to test tnua validity

of the model.

II. EXPERIMENTAL TECHNIQUES AND JUSTIFICATION

A. Samples and Preparation

 

The pristine PB fibers which were used in this study had a typical

cross-sectional dimension of about 10 um, a density of (1.99 i 0.05)

3

gm/cm and were obtained from Union Carbide Corporation .

Morphologically, they are composed of highly graphitized carbon ribbons
which are bundled together in such a way that on average the carbon

layers align radially outward from the center longitudinal axis of the

fiber 1’11

To achieve bromination PB fibers were exposed to Br vamM‘at a

9,10

pressure in excess of the threshold pressure for reaction The

compounds formed after equilibrium is obtained are referred to as

"saturated", and have a density of (2.39 i 0.05) gm/cm3

a composition of 022 5Br 12. These saturated PB fibers were

subsequently removed from the Br vapor and exposed to air at ambient

temperature 9. The resulting debrominated "residual" fibers which have

3

correSponding to

a density of (2.19 i 0.05) gm/cm corresponding to a composition of

0 Br 3’12

1
”5 were found to be stable in air vis a vis their electrical

67

prOperties and were even stable in a 100% relative humidity envirionment
9’10. It is these residual Br-PB fibers which were the major focus of
this study.

The longitudinal resistance Of each fiber was measuredirrsitu
during each stage of its synthesis using techniques that are described
in detail elsewhere 1C). In‘Table 1. we present the results of these
measurements for seven of the fiber specimens used in this study. It is
interesting to note that the variation in the ratio of the resistance of
(fineresidual fiber to that Of the saturated fiber is partially
correlated with the ratio of the resistance of the pristine fiber to
that of the saturated fiber. For instance, the fiber with the lowest
ratio Rr/Rs (see Table 1) also has the lowest value of Rp/Rs. Since
Rp/Rs is a measure of the degree of bromination of the fiber, and Rr/Rs.
characterizes the degree of debromination, this partial correlathmi
shows that the easier the Br can be inserted, the easier it can be
released. This suggests that bromination of the fiber is a physical
absorption process which depends heavily on the defects of the material.

'To prepare the residual fibers for STEM studies segments ( typical
length 0.5mm) of the single strands that were affixed to a ceramic plate
at four points with the electrically conductive glue used for the
electric resistance measurements were cut from the regions between glue
dots with a razor blade. After cutting, the fiber pieces were floated
Off of the plate onto the surface of doubly distilled deionized water
and picked up with folded copper electron microscope grids (mesh size

200)<fi‘standard dimension 3mm. These grids were mounted to a dual

gimble beryllium nosed tiltable cartridge for microscope studies.

Table 1.

Sample

 

Pristine

Fiber
R (n)
p

68

Saturated

Fiber
RS(Q)

Residual

Fiber
Rr(0)

71.99
59.7A
55.99
79.30
83.AA
88.21

77.02

3.
3.

99

111

.15
.A2
.AA
.29

.83

13.0A
10.95
10.70
16.00
15.57
16.83

1A.A6

R /R
r s

 

3.26
3.21
2.07
2.95

3.5

2.99

Resistances and Resistance Ratios of.Brominated P100 Pitch-
Based Graphite Fiber '

R /R
p s

 

18.
17.
10.
1A.
18.
16.

15.

on
52
87
63
79
67

95

F8
"1

 

he”. 37)-.

g ‘k

(1)

U1

Hg

5?

3T

 

69

B. Apparatus

 

The measurements reported here were made with a 100-kV Vacuum
Generators Model H8501 analytical scanning transmission electron
micrOSCOpe equipped with a field-emission tip, digital tmunn control, a
30-mm2 Li-drifted Si energy-dispersive X-ray (EDX) detechm~vuth an
energy resolution of 157 ev, an annular dark-field detector (collection
half-angle 0, CLJD1 rad S 0 S 0.5 rad), and an energy loss spectrometer
capable of 0.5 eV resolution. The vacuum level in the sample space was

10 and 3-10—9 torr. This instrument is

typically between 7°10-
interfaced with a Tracor Northern Model 2000 computerized detection

system which provides both signal processing and digital beam control.

C. Method and Analysis

 

In Fig. 2.1a the experimental configuration used to ascertain the
Br’distribution in brominated PB fibers is illustrated. The fiber is
oriented with it's axis perpindicular to a 100 kv electron beam which is
tightly focussed to a diameter of approximately 50 A. A beam current of
~1-10n9amp was used and was found to be below the threshold for
radiation damage in our specimens. As is depicted in Fig 2.1a.,
energetic electrons traverse the specimen and in so doing excite Br
atoms in their pathway to emit inner-shell X-ray photons which are
collected by an EDX detector. An example of the X-ray emission spectrum
created by this process is shown in Fig. 2.1b which also shows the
bromine Kc:1 line that is used as a fingerprint of the Br distribution in
the fiber. Notice that for a given lateral position (e.g. horizontal
position in the figure) the integrated X-ray intensity from the entire

beam path traversed is collected. By digitally repositioning the beam

70

 

 

S)
a
O
0

CU Ka‘
CU K02
' Bf KM

100

 

INTENSITY (ARBITRARY um
8
O

"‘ Bf K02

0‘...

C . . . '
~. ‘1... . J ‘ o , .
n. 'éo" f 1'... Go >.~~-..*~u.o \......J

 

.‘-"§-o o“

5.0 7.0 9.0 11.0 13.0 15.0
E (keV)

(b)

Fig. 2.1. (a) A schematic diagram of the experimental configuration.
The circle represents the cross-sect ion of a 10 um PB fiber the

dotted region of which is the volume containing 90% of the
incident electrons whose lateral position of entry into the fiber
is measured along the x axis. The label EDX represents the energy
dispersive X-ray detector. (b) The energy dispersive X-ray
spectrum of the fiber showing the Br K lines from the specimen
and spurious Cu Kc lines from the supporting micrOSCOpe grid.

71

to arunalateral location and again accumulating X-ray signal for a
fixed preset time, the later spatial profile of the X-ray intensity can
be determined. It is this profile which provides quantitative
information on the micrOSCOpic Br distribution in the fiber.

To establish the Br distribution from the above described EDX
measurement we must be able to relate the X-ray intensity to the
electron beam depth profile and range in the specimen. ihn" instance,
the bromine cross-sectional distribution could not be measured by EDX if
the electron beam only penetrated to a depth which was a small fraction
of the fiber radius. Fortunately this is not the case.

When electrons strike a bulk material, they strongly interact with
the material through both elastic and inelastic scattering processes and
as a result their propagation direction deviates from the direction of
the incident beanu UDf these several processes, only the inner shell
excitation which generates the EDX spectrum is of immediate relevance
here.) The path traversed by the interacting electrons in the material,
and in particular those that are capable of generating X-ray photons,
has been extensively studied using both experimental methods 13 and
theoretical Monte Carlo techniques “4. It is found that though the
electrons lose energy and scatter away from the incident direction
during penetration they nevertheless remain confined to a bulbous region
as depicted schematically in Fig. 2.2. For X‘ray generation, the
excitation range R (in um) can be deduced from the following equation
% t (3;.68 _

Here E0 (in keV) is the energy of the incident electrons, Ec (in keV) is

1.68
R - Ec ) (1)

the critical excitation energy for the inner shell X-ray ennission line,

6

t is a constant and is equal to 6.“ x 10- gm/(cmzkeV), p (in gm/cm3) is

72

 

 

 

Fig. 2.2. A schematic scaled diagram of the Br Kc X-ray excitation
region of a bulk Cu Br material by a 100 KeV electron beam. The
dashed circle represents the 10 um diameter fiber cross-section. R
is the excitation range defined in the text.

73

the mass density of the material and R is the mean distance that the
electron travels when it loses energy to a value of EC. Notice that R
is significantly larger than A, the mean free path of an electron where
A is defined by the mean distance the electron can travel between two
subsequent collisions. In contrast, the electron can undergo many
collisions with the atoms before its energy is reduced to Be at which
point it ceases to cause inner shell excitation.

The residual Br—PB fibers studied here have an average mass density

3

of 2.19 i 0.05 gm/cm corresponding to a composition C Br. Also in our

115
case E0 = 100 keV and Ec = 11.911 kev for the Br ka line. Using these

1
values in Eq. 1. we find a value of R s 71 pm. This value is very large
compared to the 10 um diameter of the fiber; thus, the X-ray generating
electron beam completely penetrates the sample.

To determine the Br profile quantitatively it is necessary to know
the detailed path of the electrons through the fiber. We computed this
path using a Monte Carlo calculation program developed by Joy 16. The
results of this calculation are shown in Fig 2.1a. where the dotted
region depicts the volume through which 90% of the incident electrons
pass. The computer-generated cross-sectional radius of the beam, b, can
be expressed empirically as an analytic function of the penetration

depth, 2, using the following equation 17:

1 3/2
b(Z) 8 C 0 W Z (2)
Here 13(2) is the depth-dependent energy of the electron in Kev, b and z
are given in pm, and C is a constant which depends on atomic number,

atomic weight, and fiber density and for the Br-PB fibers studied here

/
has a value of 6.7 keV/(um)1 2. Moreover, it can be shown that for the

711

fibers studied here, the Monte Carlo calculation yields an electron
energy variation with depth which can be empirically written as

8(2) = 8 - Yz (3)

0
for
0 3 z < 10um

where Y = 0.6 keV/pm. In deriving 8qs (2) and (3) we assumed a uniform
density of Br in the fiber corresponding to a composition of CMSBr or
equivalently, an effective atomic number and atomic weight of 6.611 and
13.5, respectively. This assumption is quite reasonable because the
intercalant is so sparsely distributed in the fiber (the average density
.of Br is 0.2 gm/cm3) that the density variation due to Br is negligible.

Having determined the electron beam-path in the fiber, we can now
calculate the X-ray intensity profile. Consider a small excitation
region located at a penetration depth 2 with a lateral position x, an
incremental cross-sectional area ds and a thickness dz (see Fig. 2.1a.).
The incremental X-ray intensity generated by the interacthmicfi‘the

electron beam with this small volume will be

61(x) = const. - 9(E)nepBr(dS)(dZ) (M)

where 0(8) is the Br K-shell ionization cross section, ”e is the

incident electron current density, and pBr is the density of Br only.
, 18

The functional form of 0(8) has been deduced by Powell who finds

1 E
0(8) = const. - 8 1n (EC). (5)

The electron current is of course maintained constant during an x-ray

acquisition scan. Thus
(d8)

—— . (6)
n[b(z)]2

= cons .
ne 1:

75

Now Eqs. (11)-(6) can be combined to yield the total X-ray intensity,
I(x), measured with the electron beam at a lateral posititni, x, in the

fiber

8(2)

E
C

2

J

 

pBr(r(x),z)ln[
(ds)(dz). (7)

 

I(x) = const. - JJ E(z)[b(z)]

The integration ierMq. 67) is carried out over the excitation volume
which contains 90% of the incident electrons as discussed above.

In the derivation of 8q (7) we have justifiably neglected the self
absorption of the Br Ka emission as it exits the fiber. The absorption

‘ 1
length for an X-ray line is given by L = 1/u where u is the mass

absorption coefficient 19. For the Br Kc line of CMSBr, L = 2000pm

l

which is much much greater than the fiber diameter. Therefore self
absorption can indeed be neglected in this case.

One can, irlxmninciple, deduce the Br distribution pBr(P) from Eq.
(7) if I(x) is known. However this is difficult in practice as a result
of the complex integrations involved. Instead, we adOpted a more
tractable proceedure in which a functional form of the Br distribution
is first assumed and then tested by comparing the resultant calculated

profile I(x) with the measured X-ray profile. The application of this

Proceedure will be discussed below.

III. THE FIBER RESISTANCE CALCULATION

In order to calculate the macrosc0pic resistance of the Br-PB fiber
We must know the relation between the Br density and the bulk
Conductivity of a host material homogeniously saturated with bromine.

Since the Br concentration in our fibers is very low even at saturation

 

76

we make the reasonable assumption that the axial conductivity of the
brominated fiber relative to that the pristine fiber is linearly
prOportional to bromine content. This assumption is supported by the
work of Sasa 6 who studied the electrical prOperties of natural graphite
intercalated with Br. He found that for the low concentration range the
composition-dependent relativity conductivity varied as

(8)

o
_ g 1 +
0 up

r
0 B
where 00 is the conductivity of the pristimuaxnaterial, <3 is the
conductivity of the GIC, ‘%h" is the Br density as before, and a is a

coefficient of linearity. Equation (8) is valid in the range 0 -<- 98,. S
0.56 g/cm3 for which the value of a apprOpriate to our case is a = 0.023

(Br/C)-1.

If we assume that the Br density is cylindrically symmetric, i.e.
pBr = pBr(r), then the total conductance of a fiber with radius a and
length l is

39
9.

and the corresponding macrOSCOpic resistance is

G = I: [1 + upBr(r)]2n rdr (9)

R = g [1 +.§% f3 (r) rdr].1 (10)

1130
0

To illustrate the application of this result, suppose that the Br

 

pBr

distribution is Gaussian-like. Then

_2 2
pBP(P) = 008 r /(Ba ) (11)

where p0 is a constant and B is a<3aussian width parameter. (Mi
inserting Eq. (11) into Eq. (10) and carrying out the integration, one
finds a total fiber resistance given by

R g

 

[1 + ap08(1 - {WSW1 . (12)
“3 00

 

77

IV. EXPERIMENTAL RESULTS AND DISCUSSION

A. Intensity Profiles

 

X-ray cross-sectional line profile measurements were carried out on
several different segments along the length of a fiber section using the
STEM. It was found that on most areas examined, the X-ray line profile
had a very round or bell-shape form as shown in Fig. 2.3a. Such regions
always exhibited a relatively high Br content and will therefore be
referred to as Br-rich. A few of the segments examined along the fiber
length yielded X—ray profiles which were Gaussian-like as depicted in
Fig. 2.uau Idoreover, in these Gaussian-like regions the X-ray signals
(are relatively weak indicating a deficiency of Br. Accordingly, the
Gaussian-like regions will be referred to as Br-poor. Note that the Br-
poor regions are very significant because the longitudinal resistance of
the fiber is primarily determined by these regions.

One additional feature of the Br-poor regions warrants attention.
These regions exhibit a marked depletion layer extending radially inward
from the fiber surface to a depth of approximately 1pm. An expanded
scale X-ray line scan of one such depletion layer region is shown in
Fig. 2.5. and reveals a complete absence of Br in the depleted area. It
is probable that the depletion layer results from the fiber morphology
itself. That morphology produces a surface structure with a local
porosity which varies along the fiber length. The most porous areas
'cannot effectively confine residual Br or shield it from reacticniivith
the ambient environment.

Using 8q. (7) derived in the previous section and the assumption of
a Gaussian-like or uniform Br crossectional distribution we have carried

out computer calculations of the X-ray intensity profile for Br K0:
l

—_

78

(a)

 

MAG. 7500

2km

 

 

 

 

 

g 600- (b)

I:

D y-_m".":“‘,-w_o.\.,

E 400- 3:" "it,

< .:/ \-

E -/ '.

3?: 200_/ \.

5 . ‘.

Q .’ 1

== 0 I i 1 1 1 l 1 1 ' ' J
—a 0 a

x

Fig. 2.3. (a) The Br K X-ray intensity profile of a Br-poor region of
a PB fiber superpgsed on the bright field image of the fiber. The
straight and curved dotted lines have the same meaning as in Fig.
2.3(a) above. (b) A plot of the Br K X-ray intensity vs. beam
position (sold dots as in Fig. 2.3(% ).

The dashed lines is the
calculated result from a uniform Br distribution and the solid

line is the calculated intensity from the gaussian distribution

given in panel (c). (c) A plot of the Br density vs. radial
coordinate in the fiber. The dashed line is an uniform

distribution. and solid line is a Gaussian form with B =O.M5.

Fig.

79

2.“. (a) The Br K X-ray intensity profile (curved line of dots)
of a Br-rich regioroi‘ superposed on the bright field image of a PB
fiber the longitudinal axis of which lies in a plane that is
perpindicular to the incident electron beam. The straight dotted
line denotes the lateral position of the electron beam as it is
digitaly scanned across the fiber cross-section. The
magnification scale is indicated in the upper right portion of the
figure. (b) A plot of the Br K X-ray intensity vs. the lateral
position of the incident beam a8 indicated by the straight line of
dots in (a) above. The solid dots represint the experimental data
points waNn (a) and the dashed line is the calculated intensity
from a uniform Br distribution,

80

(a)

 

 

 

(b)

 

 

 

6
atz: >m<mtmm<1xz

 

Fig. 2.4.

 

(c)

 

 

l
5

 

 

.—
atz: >m<m=mm<zt

m
m
Q

I' (p.111)

81

 

Fig. 2.5. The Br KG X-ray intensity profile of a region near the edge
of a PB fiber superposed on the bright field image of the fiber.
See also the caption of Fig. 2.3(a).

82

radiation and compared our results with the above described experimental
measurements. These comparisons are shown in Figs. 2.3b and 2.11b. As
can be seen, the agreement between theory and experiment in Fig. 2.36 is
excellent and provides direct confirmation of the uniformity of the Bm'
distribution in the Br-rich regions. Most revealing about Fig. 2.3b is
the fact that the rounded shape of the X-ray profdjxa, if not prOperly
analyzed, could easily be misconstrued to represent a Br density which
decreases with increasing radial distance from the fiber axis. In fact
the real cause of the observed profile is the reduced thickness of the

fixer sampled by the electron beam as its lateral distance from the

(fiber axis is increased.

In Fig. 2.11b the measured X-ray intensity profile of a Br- poor
region is compared with calculations in which both a uniform
distribution and a Gaussian distribution were used in Eq. (7). Clearly
the Gaussian distribution yields a much better fit although marked
discrepancies between theory and experiment can be noted at the edges of
the profile which correspond to the surface of the fiber. In that area,
the theoretical results give a significant excess intensity relative to
experiment. This discrepancy is a direct manifestation of the Br
depletion layer.

As previously noted, we also measured the Br distribution along the
length of a fiber section. The results of this measurement, in which
the electron beam was laterally aligned to pass through the fiber axis,
are shown in Fig. 2.6 which clearly reveals a distinct inhomogeniety

characterized by extended Br-rich regions interspersed with short Br-

poor regions.

83

MAG. 2000

 

Fig. 2.6. The Br K 1 X-ray intensity variation along a PB fiber
superposed on ghe bright field image of the fiber the axis of
which is perpindicular to the incident electron beam and
horizontal in the figure. See also the caption of Fig. 2.3(a).

8U

B. Fiber Resistance

 

We now address the change in resistance which occurs when saturated
Br-Pb fibers transform to residual fibers upon prolonged exposure to
air. Assume that in the saturated fiber, Br is uniformly distributed
across1flmafiber with a density ps while the Br distribution in the
residual fiber is taken as Gaussian radially but uniform longitudinally.
This latter assumption is supported by the fact that the overall
resistance of the fiber is largely determined by the Br-poor regions in
which the conductivity is low, and in these regions the Br‘distribution
_is Gaussian. With the just noted assumptions and 8qs. (9)-(12) we find

the ratio of the residual fiber resistance, R to the saturated fiber

r.’
resistance, R3, to be

5: 1 + a ps
Rs 1 + up 8(1 - e
r

(13)

 

”I/B)

In deriving Eq. (13) the very small change in fiber radius engendered by
the transition from saturated to residue form has been neglected.

From the measured densities of the parent saturated fibers and the
daughter residue fibers used in this study we find the coresponding Br
densities to be p8 = 0.u0 : 0.05 g/cm3 and pr = 0.20 i 0.05 g/cm’,
respectively. Using these values together with a value of B =- 0.115
deduced from Fig. 2.N. we find from Eq. (13) a calculated value of Rr/Rs

- 3.2. THUS result is in fortuitously good agreement with the

corresponding measured value of 3.02 -_t 0.16 deduced from the data of

Table 1.

85

V. CONCLUDING REMARKS AND SUMMARY

1T9 excellent agreement between the theoretical and experimental
values of Rr/Rs is, we believe, encouraging but as noted probably
fortuitous given the fact that there are at least three major sources of
discrepancy iritnue calculation. First, it is impossible to obtain an
extended three-dimensional map of the Br distribution using the STEM
because the sample stage has a relatively small translation range and
because such a map would require extended acquisition times during which
the microscope would be unavailable for other pressing experimental
studies. As a result, the volume fraction of Br-poor regions is unknown

and we are forced to overestimate the role played by these regions in

limiting the macrOSCOpic conductivity of the fiber. Second, the in-situ
Br density distribution of the saturated fiber cannot be directly
measured because the Br vapor pressure required to stablilze the
saturated compound is incompatible with the ultra high vacuum
environment of the STEM. Third, the linear relation between
conductivity and Br composition given in Eq. 8 was based on measurements
of natural graphite which was pitch-bound and heat-treated to 3000°C.
This material is electrically distinct from PB fibers and in pristine
form has a considerably larger resistivity of 1100 uQ-cm compared to 253
nil-cm. Thus any attendant nonlinearity in the conductivity-density
relation of Eq. (8) would contribute to an error in the calculated value
of Rr/Rs°

We could, in principle have measured the absolute Br density
profile of our fiber Specimens. But such a measurement is frought with
<HJTiculty in practice and involves a detailed knowledge of many

GXperimental parameters such as detector collection efficiency, detector

86

window absorption, the takeoff angle for collection, the detailed X-ray
line shape, the absolute electron beam current at the sample, etc.
Fortunately, these factors which are presumed to be constant do not
affect the relative intensity measurements which we have carried out
here.

Additional comments on the measurement method used here are ha
order. Equation (2) shows that the beam broadening inside the material
is inversely proportional to the energy of the electrons. This is the
reason we used the maximum excitation energy available in the STEM to
generate the X-ray Spectrum. Obviously, the smaller the sample volume
probed by the electron beam for a given lateral position, x, the higher
is the Spatial resolution of the X-ray profile measurement. Thus the
use of a higher voltage microscope such as the commercially available
NOOkV machines would Significantly improve the resolution. Furthermore,
at higun'energies the relative energy loss of the electron will be
small and the ionization cross section 0(8) in Eq. (7) can be treated as
energy independent. As a result the task of extracting pBr, from I(x)
would be greatly simplified.

Finally we note that the Significance of the results reported here
lies with the proceedure outlined for relating the macroscopic relative
resistance of the fiber to the microscopic distribution of the inserted
Br. In principle, the accuracy of our proceedure is limited only by the

detail of the X-ray intensity profile.

 

87

VI. ACKNOWLEDGEMENTS

This work is done in collaboration with S.A. Solin and.J.R. Gaier.
We thank D.M. Hwang for several useful discussions and for providing a
copy of the Monte Carlo program. We are also grateful to D. Jaworski
for helpful comments and to V. Shull for valuable technical assistance.
IWUS work was supported by the National Aeronautics and Space
Administration under grant #NAG-3-595. Partial support by Michigan
State University through its internally funded Analytical Electron
Microscope Laboratory, and by the the National Science Foundation under

grant #DMR 85-17223 is also acknowledged.

 

88

References
1. L.S. Singer and I.C. Lewis, Carbon 16, “09(1978).

2. J.B. Donnet and R.C. Bansal, Carbon Fibers (Marcel Dekker. New York

 

and Basel, 1989).
3. J.B. Gaier and D. Marino, NASA TM-87016, 1985.
A. C. Herinckx, R. Perret and W. Ruland, Carbon 19, 711(1972).
5. J.G. Hooley and V.R. Diets, Carbon 16, 251(1978).
6. T. Sasa, Bull. Chem. Soc. Japan 35, u3(1970).
7. M.S. Dresselhaus and G. Dresselhaus, Adv. in Phys. 39, 130(1980).
.8. S.A. Solin, Adv. Chem. Phys. A9, “55(1982).
9. J.B. Gaier, NASA TM-86859, 198A.
10. J.R. Gaier and D.A. Jaworske, NASA TM-87025, 1985.
11. J.R. Gaier, NASA TM-87275, 1986.
12. J.B. Gaier, in Proceedings of the Materials Research Society
Meeting, ed. by M.S. Dresselhaus, G. Dresselhaus and S.A. Solin
(Boston, 1986).

13. v.8. Cosslett and R.N. Thoms, in The Electron MicrOprobe, edited by

 

K.F.J. Heinrich and D.B. Wittry, (Wiley, New York, 1966).
1A. L. Curgenven and P. Duncomb, Tube Investments Lab Reports, 303
(1971).

15. J.I. Goldstein, in Practical Scanning Electron Microscope, ed. by

 

J.I. Goldstein and H. Yakowitz, Ch.3, (Plenum Press, New York and
Landon, 1975).
16. D.C. Joy, unpublished.

17. J.I. (hxldstein, in Introduction to Analytical Electron Microscopy,

 

edited by J.J. Hern, J.I. Goldstein and D.C. Joy. (Plenum Press, New

York and Landon, 1979).

89

18. C.J. Powell, NBS Special Publication A60, edited by K.F.J. Heinrich,

97(1976).

19. Intenational Table for X-ray Crystallography, edited by C.H.

 

Macgillavry and 0.0. Rieck, v.3, 162(1962).

90

APENDICES

VOLUME 53, NUMBER 15

PHYSICAL REVIEW LETTERS

8 OCTOBER 1984

Physics and Chemistry of Spatially Resolved Microdomains
in SbCls-Intercalated Graphite. _

D. M. Hwang")
Department ofPhysics. University of Illinois at Chicago, C hicago. Illinois 60680

and

X. W. Qian and S. A. Solin
Department of Physics and Astronomy. Michigan State University, East Lansing. Michigan 48824
(Received 5 June 1984)

We report on the first spatially resolved study of the chemical and electronic properties of
microdomains in molecular monolayers. Analytical electron-microscope measurements of
stage-4 SbCls-intetcalated graphite show Sb-tich islands of lateral dimension 500-1000 A.
Energy-loss spectra yield a 6-eV graphite 1r plasmon modulated by the domain structure. but
the ZS-eV 71' + a plasmon and the carbon core excitations are spatially invariant. The derived
island and background compositions are (SbCl,)m(SbCl.' 11m and (SbCl,)m.(SbCl.' )gm.

PACS numbers: 61.16.Di, 71.45.Gm, 82.65.-i

The study of the properties of quasi-two-
dimensional (quasi-20) molecular or atomic mono-
layers in the presence of a rigid substrate potential
constitutes a fundamental problem of considerable
current interest.‘ To date primary attention has
been focused on the multiphase-multidomain struc-
tures and associated order-disorder phenomena2
which such monolayers often exhibit. For many
systems, and in particular the acceptor-type graphite
intercalation compounds (GIC‘s), the microsc0pic
chemical and physical properties can play a critical
role in domain formation. Those properties have
not yet been explored because conventional probes
do not provide sufficient spatial resolution to exam.
inc individual domains direCtly. We report here the
first analytical electron-microscope study of the
physical and chemical pr0perties of directly ob-
served microdomains in quasi-20 molecular mono-
layers.

SbCls-intcrcalated graphite was chosen for this
study for several reasons. lt is the most air stable of
the GIC‘s known to date.3 Therefore, SbCls-
intercalated graphite has been examined by a
myriad of conventional techniques‘ and is easily
transferred into an electron microscope. Diffrac-
tion studies5 show that SbCls-intetcalated graphite
forms novel, in-plane microdomain structures. one
of which is a glass phase.“

It has been proposed7 that $00; behaves chemi-
cally like AsF,‘ upon intercalation into graphite,
and disproportionates into (SbCls).-,(SbC13),/3-
(SbCl; )h/J, 0$X$L The SbCIs and SbCl;
species apparently form a complex in which the Cl'
ion is dynamically exchanged.’ There is also evi-
dence for an SbClI disprOportionation product.9

The uniformity of the distribution of these molecu-
lar species in the graphite galleries has nor been es-
tablished. Obviously, the microscopic homogeneity
of disprOportionation may affect both domain for-
mation and the bulk electronic properties.

Stage-4 SbCls-intercalated graphite was prepared
from highly oriented pyrolytic graphite by the two-
bulb technique. The samples were intercalated at
an extremely low rate over a period of two months
to avoid exfoliation and to maximize homogenei-
ty.‘° 'X-tay diffraction indicated that the stage puri-
ty‘was greater than 99%. Specimens were cleaved
from the bulk, glued to a glass slide with water
soluble glue, thinned with adhesive tape, floated
off , and then picked up with microgrids. The mea-
surements reported here were made with a lOO-kV
Vacuum Generators Model H8501 analytical scan-
ning transmission electron microscope (STEM)
equipped with a field-emission tip, digital beam
control, a 30-mm2 Liodrifted Si energy-dispersive
x-ray detector, an annular dark-field detector (col-
lection half-angle 0, 0.01 radS9$005 rad), and
an energy-loss spectrometer capable of 0.5-eV reso-
lution. Spectrometer instability as determined by
the variation of the width of the zero-loss peak of
single short scans (<400 ms) and summed multiple
short scans (total acquisition time ~S min) was
less than 0.2 eV.

A typical dark-field image of stage-4 SbCIs-
intercalated graphite is shown in Fig. l and clearly
exhibits high-density islands of dimension 500-
1000 A. Essentially identical bright-field images of
the same region were also obtained. The islands oc-
cupied (1112)% of the total imaged area. En-
ergy-dispersive xoray (EDX) 5mm of the island

© 1984 The American Physical Society 1473

VOLUMES}. NUMBERIS PHYSICAL REVIEW LETTERS 80croaax198-t

 

 

 

 

 

 

(a)
(b) 50 _
4.0 .. i _
§ 3 “i [i
K .0 l- J lb —
‘0 M . i ' . .
lg- 20 :1 \a- — 3°»- .J—oa-Z O
o ,3 ,_ 3 E
0 _ ea. .9 "
1.0 .. U y. (I) 8 ..
\6 (i r'
O 0 9"".an .0
. 1 . l i l i
4.0 5.0 6.0

2.0

.‘r’
o

ENERGY (Kev)
. FIG. 1. (a) Dark-field STEM image of stage-4 SbCl,—
lntercalated graphite. (b) Energy-dispersive x-ray spectra

of the island (open circles) and background (closed cir-
cles) regions.

and background regions (beam spot size a 50 A)
are shown in Fig. No) in the range which incor-
porates the Cl K lines and the Sb L lines. We have
used these lines to deduce the Sb1Cl ratio in the is-
land and background regions following standard
thin-specimen analysis procedures.” The composi-
tion in the island region is SbCl“ :0.J~ while that of
the background regiOn is SbClmno. The uncer-
tainty In composition arises from the variation from
island to island and background region to back-
ground l'Csion and from a statistical fluctuation as-
socnated with the relatively low count levels engen'
deer blf the need to limit sample contamination
during Signal acquisition. Note that our specimens
have a nominal thickness of 500 A, which is less
than the electron mean free path. Therefore struc-
tural differences of the island and background re-
gions (see below) have a negligible effect on the
EDX anaii’sis. Moreover, the data reported here
were acQuired with a convergent electron beam
(20 a 17 mrad) that generated many Brass reflec-
1474

 

 

 

(a)
(b)
...ii.‘.‘-l‘-liillil..-.-- a,
g
E eitlii‘tiiiii‘rtii'n‘m;

 

POSITION
FIG. 2. (a) Bright-field image showing an island. the
surrounding background, and a scan line (denoted by ar-
rows). (0) Sb Him and Cl Kmne integrated x-ray in-
tensities along the scan line.

tions. Thus the modulations in EDX signals or
channeling effects associated with individual Bragg
reflections observed with collimated incident beams
were averaged out.ll Accordingly we recorded
STEM images that were insensitive to sample tilt
angle” and the error in EDX analysis attributable to
channeling was also negligible.

We propose that the islands are composed of Sb-
rich SbClJSbCl.‘ ~like material whereas the back-
ground consists of Sb—del‘lcient SbClJSbSlg-like
material. To further verify this we refer to Fig. 2
which shows a digital-beam-control line scan across
an island and the relative Sb L-line and Cl K-line
signals acquired from such a scan. Note that Cl
yields a constant signal and is thus uniformly distri-
buted over the line of scan. whereas the Sb signal
doubles in the region of the island. These observa-
tions are additionally confirmed by two-dimensional
x-ray mapping studies of SbCl, GIC‘s.”

Preliminary microdiffraction studies'1 show that
the islands are disordered and yield diffuse rings.
whereas the background exhibits a pattern which
can be associated with a (J7XJ7)R19.1° structure
and some as yet unindexed additional spars. These
results indicate that the island and background re-
gions extend through the (uniform) thickness of
the sample with the former adopting an irregularly

VOLUME 53, NUMBER 15

shaped columnar structure which gives rise to the
highcontmst dark- and bright-field images of Figs.
1 and 2, respectively. This columnar structure
Which might be directly imaged with crossssectioned
samples can be attributed to a nucleation process
which is driven by the dipole strain field" associat-
ed with the intercalate intraplane and interplanar in-
teraction. The nucleation density, the equilibrium
of dispr0portionation, and «fees intrinsic to the
graphite itself all influence island formation. The
interaction between these several effects is ex-
tremely complex and difficult to quantify.

By examining the demon energy-loss spectra
(EELS).we have probed the effect of chemical
segregation on the electronic band structure of
Stage-4 SbCls-intercalated graphite. The EELS ob-
. tamed from selected spots in the island and back-
ground regions with momentum transfer 4 z 0 are
shown in Fig. 3. In the 0-10-eV range these spec-
tra are very similar to the EELS calculated by Ek-
lund er al. '5 from optical measurements of the com-
plex dielectric function of stageo4 SbCls-intercalated
graphite. We have observed, but not resolved. the
intraband plasmon at a 1 eV. ‘

As can be seen from Fig. 3, the broad 1r + o elec-
tron peak at a 25 eV is essentially independent of
the acquisition region whereas the 1r plasmon peak
at =§6 eV shows a 17% intensity decrease and a
possible slight energy upshift for the island region
relative to the background. This upshift, though
small. is nevertheless observable as a relative
change in EELS patterns which are themselves
internally referenced to the zero-loss peak. (The 1r

 

 

COUNTS x103

 

 

 

 

 

0 20 40 ‘ 60 so
ENERGY (eV)
FIG. 3. Plasmon electron energy-loss spectra of the is-

land’lsolid line) and background (dashed line) regions
acqmrcd with a spectrometer resolution of 1 eV.

PHYSICAL REVIEW LETTERS

8 OCTOBER 1984

and n+0 plasmon peaks occur at 7 and 25 eV.
respectively, in pristine graphite.) Moreover. the
EELS of islands ranging in lateral size from 500 to
1000 A were indistinguishable. Therefore. the
analyzed regions of our specimens were sufficiently
thick and uniform to tender negligible config-
uration-effect contributions" to the 17% variation
of the 6-eV plasmon intensity. Note also that the
spectra of Fig. 3 show no trace of the n+0
plasmon multiple-scattering peak at z 50 eV which
is usually seen in thicker specimens. We have also
recorded carbon 15-core-excitation EELS from the
island and background regions.u These specrra are
indistinguishable and exhibit a broad peak at 289 eV
and a weak, sharper peak at 281 eV. Such features
are typical of acceptor GIC‘s.”

The gross downshif t and marked intensity reduc-
tion in the 6-cV plasmon of GIC‘s relative to pris-
tine graphite is due to the reduction in oscillator
strength of the 4.5-eV 1r-° n' transition associated
with the reduced number of carbon layers per unit
volume in the intercalated material." The reduced
intensity of the 6-eV plasmon of the island relative
to the background evidenced in Fig. 3 has a more
subtle origin related to the detailed energy band
Structure of different intercalant domains.

Any intercalant interband transition of lower en-
ergy than 4.5 eV will lower the intensity of the 6-eV
plasmon. This effect is more pronounced if the
transition is close in energy to 4.5 eV and/or has a
larger oscillator strength. We expect the interband
transitions closest to but lower in energy than the
4.5.eV transition to derive from SbCh/SbCl.‘ since
these molecules are more tightly bound than
SbClSISbClg'. Therefore. the 6-eV plasmon of the
island should be less intense than the corresponding
plasmon of the background. In contrast, the a
demons of graphite are much more localized and
more tightly bound than the it electrons. They are
less perturbed by the intercalant and the n+0
plasmon is insensitive to the chemical differences
between the island and background regions.

The spatial invariance of the carbon 15 core exci-
union}2 particularly with regard to the intensity of
the 281-eV satellite peak indicates that. within our
experimental accuracy, the island and background
regions have the same Fermi energy shift with
respect to the rigid carbon electronic bands and thus
the same carbon layer charge density. This charge
delocalization in conjunction with the island area
occupancy of 11% and the uniform Cl distribution
leads'2 to a unique intercalant macroscopic chemi-
cal composition (SbCIfll/“SDCI:11,32ISbCltio/tb‘
(5130; )9/32- The microscopic stiochiometnes are

VOLUME 53, NUMBER 15

then SbClu in the islands and SbCl,” in the back-
ground, and the degree of the disproportionation is
0.44. The charge transfer per SbCl, molecule is
0.31 (0.0055 hole per carbon atom based on the
composition of C.,,,.SbCls), well within the range
of reported values?“ N0te that the derived chem-
ical composition is in reasonable agreement with
Mossbauer studies of the Stage-2 compound which
give SbCl.’ :SbCl, and SbC1{:SbC13 ratios of 0.25
and 1.9, respectively, but indicate a higher degree
of disproportionation.

We are grateful to P. Eklund for providing optical
data prior to publication and for useful conversa-
tions. The technical assistance of V. Shull was in-
valuable. We thank A. W. Moore of Union Carbide
for providing pyrolytic graphite. This research has
been supported by the National Science Foundation
through Grant No. DMR83-11154, by Michigan
State University through its internally funded
Analytical Electron Microscope Laboratory. and by
the Research Board of the University of Illinois at
Chicago.

("Present address: Bell Communications Research.
Murray Hill, NJ. 07974.

ISee. e.g.. Ordering in Two Dimensions. edited by S. K.
Sinha (Elsevier-North-Holland. New York. 1980).

2S. A. Solin, Adv. Chem. Phys. 49, 455 (1982).

3V. R. K. Murthy. D. S. Smith. and P. C. Eklund.
Mater. Sci. Eng. 45. 77 (1980).

‘See for example “Graphite Intercalation Com-
pounds," edited by S. Tanuma and H. Kamlmura, sum-

1476

PHYSICAL REVIEW LETTERS

8 OCTOBER 1984

mary report of project No. 56122027 of the Ministry of
Education. Science, and Culture. Japan. Match 1984
(unpublished).

sR. Clarke. M. Elzinga. J. N. Gray. H. Homma. D. T.
Morelli. M. 1. Winokur. and C. Uher. Phys. Rev. B 26.
3312 (198).

“G. Timp. M. S. Dresselhaus. L. Salamanca-Riba.
A. Erbil. L. W. Hobbs. G. Dresselhaus. P. C. Eklund.
and Y. lye. Phys. Rev. B 26.2323 (1982).

7L. B. Ebert. D. R. Mills. and J. C. Scanlon, Mater.
Res. Bull. 18. 1505 (1983).

8N. Bartlett. R. N. Biagioni. B. W. McQuillan. A. S.
Robertson. and A. C. Thompson. J. Chem. Soc. Chem.
Commun. 1978. 200.

9P. Boolchand, W. J. Bresscr. D. McDaniel. K. Sisson.
V. Yeh. and P. C. Eklund. Solid State Commun. 40. 1049
(I981).

'00. M. Hwang and G. Nicolaidcs. Solid State Com-
mun. 49. 483 (1984).

”Introducrlon to Analytical Electron Microscopy. edited by
J. .I. Hren. J. 1. Goldstein. and D. C. Joy (Plenum. New
York. 1979). Also. D. Cherns. A. Howie. and M. H.
Jacobs. Z. Naturforsch. 28A. 565 (1973); P. Duncumb.
Philos. Mag. 7. 2101 (1962).

”D. M. Hwang, X. W. Quan. and S. A. Solin. to be

.publlshed.

”D. M. Hwang and J. Cowley. unpublished.
1‘S. A. Saffran and D. P. Hamann, Phys. Rev. Lett. 42.
1410 (I979).

lsP. C. Eklund. D. M. Hoffman. G. L. Doll. and R. E.
Heinz. to be published.

“’P. E. Batson. in Proceedings o/‘tlie Thtrryofighrh Annual
Electron Microscopy Society of America Meeting. edited by
G. W. Baily (Claitor‘s. Baton Rouge. 1980), p. l24; P. 5,

. Batson and M. M. J. Treacy. ibid, p. 126.

17.1. .1. Ritsko and E. J. Mele. Synth. Met. 3. 73 (1981).
"R. E. Heinz. G. Doll. P. Charron. and P. C. Eklund.
Mat. Res. Soc. Symp. Proc. 20. 87 (1983).

 

VOLUME 54. NUMBER 12

PHYSICAL REVIEW LETTERS

25 MARCH 1985

Molecular Clustering in a Two-Dimensional Metal-Ammonia Solution

X. W. Qian, D. R. Stump, B. R. York,” and S. A. Solin
Department of Physics and Astronomy. Michigan State University, East Lansing, Michigan 48824
(Received 21 November 1984)

We have measured the in-plane x-tay diffraction pattern of the two-component K’-NH; liquid
layers in the ternary graphite intercalation compound K(NHJ). ”C“. The measured pattern is in
semiquantitative agreement with the scattering calculated for a random distribution of coplanar
hard K" and NH, disks, provided that the K' ions are bound symmetrically to four NH,
molecules. We show that the K-NH; layers consutute the two-dimensional strucrural analog of the
well-known bulk three-dimensional K-NH, metal-ammonia solutions.

PACS numbers: 61.25.Em. 61.10.-i

During the past decade there have been numerous
studies of the structures and structural phase transi-
tions of atomic, ionic, and molecular monolayers
which have been either adsorbed' on or intercalated
, between2 the layers of graphite. Much attention has
been dev0ted to solid-liquid transitions in the quasi-
twodimensional guest layer and to novel disordered
phases such as the liquid states associated with melt-
ing‘3 and wetting.J The twoodimensional (2D) liquid
state has usually been inferred from the temperature.
pressure, and/or coverage dependence of the width
and shape of selected diffraction peaks.H In only one
case (KC;.).‘ to our knowledge. has a complete 20
liquid scattering intensity been calculated and com-
pared with experiment. The calculated pattern rcpto-
duced some of the experimental features but was
based on a structure which is n0t consistent with re-
cent diffraction studies.5 In this Letter we present a
successful calculation of the full diffraction pattern
from a 20 liquid, the two-component K-NH, solution
Which occupies the galleries between graphite layers in
the stage-1 ternary graphite intercalation compound
(GIC) K(NH3)4,”C24. The K-NH; layers in
K(NH3103C1. constitute the 20 structural analog of
the heavily studied bulk metal-ammonia solutions.‘
Furthermore. their 2D liquid scattering intensity is
surprisingly sensitive to the formation of particular
lyrics of K-NH, clusters.

Samples of K(NH3)4_;;C,. were prepared by expos-
ing stage-2 KC}. (derived from highly oriented pyro-
IYtic graphite) to NH; vapor at a pressure as 10 atm.
Details of sample preparation and of the x-ray ape
Paratus used for the measurements reported here are
liven elsewhere"

The in-plane qLC diffuse scattering intensity for
K(NHg). ”C1. is shown as a dotted line in Fig. 1. This
pattern, I ,(q), has been corrected' for the Lorentz-
polarization factor, absorption, and for all background
effects. The ordinate scale in Fig. l was established in
the usual way by fitting the diffraction profile at high q
to the calculated sum of the Compton and coherent
scattering contributions.‘ Also the intense Bragg re-

flections of the graphite host layers have been re-

© 1985 The American Physmal Society

moved from [1(a) for clarity. As can be seen from
Fig. l, I L ( q)°is characterized by a relatively sharp peak
at 4-088 A'| followed by aobroad asymmetric in-
tense peak centered at q --o 2.07 A"I and anOther broad
weak feature at q a 4.24 A' '.

We now discuss a structural model which semiquan-
titatively accounts for the in-plane scattering intensity
of the K-NH, 2D liquid intercalant in K(NH,).,JC2..
We assume that the NH, molecules and the K’ ions
can be represented as coplanar hard disks. If r... is the
position of the center of the mth particle (i.e., NH, or
K+ disk) and 1., its o-dependent scattering factor.
where fuu,(0)- 10 and fx.(0)-18, then the scat-

tered intensity for any distribution of disks will be

I(q)- Zf,exp(itt°t.)2f.'exp( -iq-r,,). (I)

Let there be L layers of K-NH; in the scattering
volume with N particles (disks) in each layer. Then if

 

to
at
a
O

2200
1760

 

1320
880

lflELECTRON UNITS)

 

440

 

 

 

FIG. I. The calculated (solid line) in-plane diffraction
patterns of the K-NH; liquid in K(NH,).;,C1. scaled at
q -0.88 A to the measured room-temperature (dotted linel
pattern. The calculated pattern was deduced by applying Eq.
(4) of the text to the fourfold coordinated distribution
shown in the inset which depicts K’ ions (circles with
plusses) bound to four NH, ions (circles) and unbound Mli
ions (circles with dots). The parameters used were
r...- 2.00 A. rm- 1.30 A. ar-0.23 A. and r“. - 1 in A

1271

 

\KHUMESQ NUHWERIZ

 

4400 i-
3960
3520 -

U

 

aoao (I)

(O)
2640

2200 g
(0)

1760 ‘
(O)
1320

080

lb)
(e)

i‘tELecrnou umrst

440

 

o L L J— 1

1 2

3 4 5 6 7
alt-t)

FIG. 2. The (a) K’-K‘. (b) NH,-Nl~l,. and (c) K’-NH,
in-plane pair-scattering functions calculated using the
parameter set given in the caption of Fig. 1. Eq. (4), and the
distribution shown in the inset of fig. 1. The dots are a plot
of J.(q x (R...- 2.89 Al) (see text).

The total calculated in-plane scattering intensity is

the sum of the pagflscatterin'g-Np'rofiles, i.e., qu)
-if’*’(q)+if"’ ’(q)+i,_ ’(q). These indi-

vidual pair contributions are quite revealing as can be
seen from Fig. 2. The sharp peak in IL(q) at 0.88-
A" results from the dominance of the K’-K* contri-
bution over the K*-NI-13 contribution of opposite sign
at that q value. The former results from the fan that
the K’ -l(" nearest-neighbor distances show little vari-
ation in the fourfold coordinated distribution as is evi-
dent from the inset of Fig. 1.. The sharp negative K‘-
NH, contribution at 0.88 A" results from the fact
that the ammonia and potassium disks have roughly
the same diameter. Also note from Fig 2(c) that the
K+ oNH, contribution consists of. correlations super-
posed on Jo(qx (R_-2.89 A)). This Bessel-
function background results from the presence of
many lU-Nl'h near-neighbor pairs separated by 2.89
A in the fourfold coordinated distribution. It is evi-
dent from Fig. 2(c) that the Bessel-function contribu-
tion is responsible for the enhanced amplitude of
1.,(q) at thechigh-q shoulder of the 2.07-A”I peak and
at the 4.24-A" peak. These enhancements represent
a minor deficiency in our model which we associate
with its oversimplified structural character.

The physical size of the NH, molecules limited to
four the number which could be symmetrically bound
to potassium in a planar configuration. Therefore, as
noted above we tried to fit the data of Fig. l with dis-
tributions having it < 4. Two such distributions with

PHYSICAL REVIEW LETTERS

25 MARCH 1985

 

2200

 

1760
1320
880
440

 

2200
1760

IflELECTRON UNITS)

1320
880

 

 

 

 

 

FIG. 3. The calculated in-plane diffraction patterns for
the threefold coordinated K-NH,.distributions 1(a) and in-
set) with parameter; ram-2.00 A. r...- 1.30 A, 5r-0.30

, and r‘. - 1.33 A and the zerofold coordinated, free am-
monia. distribution ((b). and inset! with parameters
r...- 2.oo A. ,M- 1.30 A, 8r-0.30 A. and r‘. - 1.33 ft.
The symbols used for the insets are the same as in Fig. l.

n - 3 and n -O are shown together with their corre-
sponding best fits in Figs. 3(a) and 3(b). respectively.
It is obvious from Fig. 3 that these Other distributions
yield fits inferior to the n -4 (it, particularly with re-
gard to the sharp peak at 0.88 A", and that the ob
served diffraction pattern is quite sensitive to the clus
ter coordination.

The real 20 KoNl-l, liquid is dynamic and almost
certainly contains K-NH, clusters with differing coor-
dination number. We could have accounted for this
effect by introducing several additional fitting parame-
ters to characterize the probability Hit) of finding an
n-fold coordinate cluster in the liquid. Even more
parameters could have been introduced to model
asymmetries in the angular distributions of the NH,
molecules about the K‘ cores. While such procedures
would improve the fit to the data of Fig. 1, they would
also tend to mask the essential structural features of
the 2D K-NH, liquid. These are the predominance of
the symmetric fourfold coordinated cluster and the
distribution in tilt angles for the C 3 axes of the NH,
molecules. It is not surprising that the simple model
we have employed does nOt yield a fully quantitative
fit to the data of Fig. 1. But it is significant that this

model produces as good a semiquantitative fit as IS ob
served.

1273

 

VOLUME“. NUMBER 12 PHYSICAL REVIEW LETTERS 25 MARCH 1985

a, is the C axis repeat distance and r. - R“; + Sa,k for the S th layer, Eq. (I) can be rewritten as

N . N L ' .
I(q)-LZffiféeXpliq-(Rfl-RgH-i-E 21.5]; expliq-(R‘s-R‘Hexpliq-(S-S')a,k1 (2)
‘. .

““3— S‘

which for in-plane scattering with q - qi‘t becomes

N N L
IL(q)-L2f,‘f.}expliq(x.5-x.5)l+2 2 1.5./2.. expliq(x..5-xfi.)]. (3)
“.

“US-15'
If there is no interlayer correlation, i.e., x“; and

15's., are uncorrelated, the second term in Eq. (3) is r fold coordinated distribution each K" disk was in con:
equal to zero. We have verified the lack of interlayer tact with n NH, disks such that the lines of centers
correlation in K(NH,)._,,C;. by recording “flat” (hk between the K‘ and NH, disks make equal angles of
-const, I) c' x-ray scans.’ For a sufficiently large sys- 2"/ "-
tem which is amenable to cylindrical averaging, the An n-fold coordinated distribution was generated as
first term in Eq. (3) can be recast in the familiar‘ form “HOV“: A seed C105!” was nucleated "000“ a K+ by
N symmetrically attaching it NH, disks with different ra-
1&(4)-sz.f;10(qg_). (4) dii randomly selected from a Gaussian distribution
can (see below). Then a K" or NH, disk was randomly
_ __ . . selected from the remaining collection of 499 K"
Engage-“Jag hifl'digggeg‘:h:°’s:‘:s§$f’:efii disks and 2165- n hm, disks. If the selection yielded
second term in Eq. (3), which has been omitted in pre- .' K duk‘ " NH’ m“? were 9““th to it ”d the “3'
vious treatments of “Hm” diffuse scattering,‘°-” can id cluster. was moved. in a series of small translational
significantly influence both the calculated 11“,)" and and rotational steps. towards the seed cluster until the
the pair correlation function deduced from the Bessel distance between theK. centers of the seed and the
transform of the observed [110) .0 if interlayer corre- added cluster was minimized. .If the next randomly
lations are non-negligible. Such correlations may be selected particlewas an NH’ Li's." u was moved m a
present in a lattice :85 model” of GIC struCture and in series of translational Steps until it was as close as pos-

 

. system that is about to undergo a 2D-3D order- sible to the center of the seed cluster. The above

disorder transition} described process was repeated until all of the particles
In order to account for the observed diffraction pat- baa biesenkzss‘embllfggn NMR u

tern I L( q) shown in Fig. l we have applied Eq. (4) to o n measurements that at

several computer generated structural distributions of room temperature the NH’ molecules spin rapidly
Kand NH; disks. Because K+ ions can effectively po- about their C’ axes mm" ,m turn ("3 ""ed W1”)
larize and bind up to six NH; molecules‘ we concen- "sped 'to the graph“ C “'5; The "'1 “8‘3 varies
trated on distributions of symmetric planar n-fold “1’1“" .m "me such that at any "‘s‘a’“ ”I": isadistri-
coordinated clusters. For reasons which will be made bution .m "I.“ orientations of the NH! m°'¢°“l¢5. Thus
clear below, ns4. In order to satisfy the stoichi- I!” cylindrical pr°’°°"°“5' °f the surfaces 01' revolu-
ometry of our speCimens, each distribution contained :gseaabzrs‘u‘igttg; ainersagi?‘3h"h; graphite basal plane,
+ - - w
exactly 500 K disks and 2165 NH, disks. In an n-J the basis of NMR measurements”; ave modeled on

P(r)¢exp( - (r- rMY/(brVI -epr - (rw- rm“)2/(5r)’l.

where rm,-2.00.A, e.g.-1.30 A. rminSrsrm“, I _
and OsbrsOJ A. The radii of all K+ ions in a dis- inset of Fig. 1 yielded the best in (solid line) to the
tribution were fixed at a value r“. approximately data. Notice that the amplitudes. positions. and widths
equal to the ionic radius of potassium. For each ri-fold 0‘ the features 0f ")3 measured Il.(q) are reasonably
coordinated distribution the parameters hr and r . accounted for. the only exceptions being the shoulder
were varied to achieve the best fit to the data of Fig. l on the high-q side of the 2.07-Rm peak and the peak
using Eq. (4). The fits obtained were quite sensitive at §414 A". Also note that the theor r l

‘0 'p and n. b‘“ were relatively insensitive ‘0 "‘3 0“)- density calculated from the distribution shzw‘iia inflict:1|
er parameters and were size independent, i.e., macro- inset of Fig. l is equal, within experimental error 1:
scapic, for distributions containing more than 50 K’ the experimentally determined density. This is not the
disks.

“5" {0' example, for the distribut' ’ l
The fourfold coordinated distribution shown in the even though the same stoichiometry 0'83 1:: Fig. 3th
1272

 

VOLUME 54, NUMBER 12

The success of the n-4 distribution is in part a
manifestation of the structure of JD metal-ammonia
solutions.‘ For bulk K-NH; liquids. the K’ ion is oc-
tahedrally (sixfold) coordinated to NH}. But the gal-
lery height in K(NH3)4_33C1. is such that only a mono.
layer of NH, molecules can occupy the interlayer
space.7 The resultant fourfold coordinated planar K‘-
NH, cluster is derived from the octahedron by the re-
moval of two apical ammonia molecules. Thus it is
evident that the K-NH, layers in K(NH,).73,C;. do
indeed constitute the 20 structural analog of a bulk
K-NH; solution.

As a final point, we note that to date the structures
of all 20 “liquids“ intercalated into graphite have
been dominated by the host potential.5 The ZD liquid-
like character was a minor feature in comparison to the
role played by substrate-induced registry. modulations,
etc. In contrast, the K-NH; layers intercalated into
graphite are essentially simple 20 liquids at room tem-
perature. Substrate effects. though no doubt present,
are of secondary importance.

We thank S. D. Mahanti and Y. B. Fan for useful
discussions and kindly thank A. W. Moore of Union
Carbide Corporation for providing graphite. This work
was supported in part by the National Science Founda-
tion under Grant No. DMR82-11554.

1274

PHYSICAL REVIEW LETTERS

25 MARCH 1985

("Present address: IBM San Jose Research Laboratory.
San Jose. Cal. 95114.

lOrdering in Two Dimensions. edited by S. K. Sinha
(North-Holland. New York. 1980).

2S. A. Solin, Adv. Chem. Phys. 49, 455 (1982).

JM. Wortis, R. Pandit. and M. Schick. in Melting. Locali-
zation. and Chaos. edited by R. Kalia and P. VashiSta (El-
sevier. Lausanne. 1982), p. 13.

‘M. Plischke and W. D. Leckie, Can. .1. Phys. 60. 1139
(1982).

5R. Clarke, J. N. Gray. H. Homma. and M. .1. Winokur.
Phys. Rev. Lett. 47, 1407 (1981).

‘J. C. Thompson. Electrons in Liquid Ammonia (Claren-
don, Oxford, 1976).

78. R. York. S. K. Hark. and S. A. Solin, Solid State Com-
mun. 50. 595 (1984); B. R. York and S. A. Solin. Phys. Rev.
B (to be published).

"I. P. Klug and L. E. Alexander. X-Ray Dijfracnon Pro-
“dWfl for Polycrystalline and Amorphous Materials (Wiley.
New York. 1974).

’D. Stump. X. W. Qian, B. R. York. and S. A. Solin. to be
published.

10R. Clarke. N. Caswell. S. A. Solin. and P. M. Horn. Phys.
Rev. Lett. 43, 2018 (1979).

”H. Zabel. Y. M. Jan, and S. C. Moss. Physics (Utrecht)
99B. 453 (1980).

12H. Resing, B. R. York, and S. A. Solin. Bull. Am. Phys.
Soc. 29, 294 (1984). and to be published.

 

Synthetic/Metals. 12(1985) 181—186 181

ION SIZE EFFECTS IN ALKALI-AHMONIA TERNARY GRAPHITE INTERCALATION COMPOUNDS

S.A. SOLIN, Y.B. FAN and X.W. QIAN

Department of Physics and Astronomy. Michigan State University. East Lansing,
MI 118824-1116 (U.$.A.)

ABSTRACT

The dependence of the composition and sandwich thickness of H(NH )xczlh .
H - K. Rb. Cs. stage-1 alkali-ammonia ternary graphite intercalation c mpounas

on ion size has been determined using (009.) x-ray diffraction measurements
together with both gravimetric and volumetric measurements of NH weight uptake.
The measured compositions can be quantitatively accounted f r with a three-
dimensional (3D) "volume available" model similar to the Setton model for the
molecular composition dependence of K(molecule) C provided a packing fraction
is is introduced. lie find that c D - 0.35 ahdzlthat the effective ammonia
r331.» is rA - 1.50 A. A two-dimetisional (20) model fails to yield reasonable
results.

INTRODUCTION

Ternary alkali-ammonia graphite intercalation compounds (GICs) were first
prepared by Ruddrff and coworkers1 about four decades ago. but only recently
have these materials attracted the attention of physicists and physical
chemists. This attention was stimulated primarily by two factors. First and
foremost. it was suspected that alkali-ammonia GICs would be the 20 structural

analogues of bulk 30 metal-ammonia solutions.2'3

This suspicion has recently
been confirmed in the case of potassium-ammonia GICs.u Bulk metal-ammonia
solutions are the classic systems for the study of the metal-insulator
transition.5 Thus, the alkali-ammonia GICs may constitute a novel system for
the study of the metal-insulator transition in 20. The second stimulus for
interest in alkali-ammonia GICs was the realization that the intercalant layer
may represent a simple 20 liquid in the graphite gallery,"6 in contrast to the
much more complex disordered structures exhibited by binary alkali GICs.7 This
second stimulus has also been Justified by recent x-ray diffraction studies of

ti
potassium-ammonia GICs.

0379-6779/85/33.30 © Elsevier Sequoia/Printed in The Netherlands

182

Ruddrff and coworkers apparently concluded from their early studies of
alkali-ammonia GICs that their (structural) preperties. e.g. the sandwich
thickness of the galleries, were determined by theNH3 species and that the
alkali metal was incidental.1 Preliminary x-ray8 and NMR9 studies of the K, Rb.
and Cs metal-ammonia GICs indicated the contrary. Accordingly. in this paper
we report the results of x-ray diffraction studies of the metal ion size effects
in ternary metal-ammonia GICs. Collaterally. the work which we report here
represents the first study of cation size effects in any ternary GIC system
whereas molecular size effects in potassium-molecular ternary GICs have been
extensively studied by Setton and coworkers.10

EXPERIMENTAL

Pure stage-l alkali-ternary GICs of K. Rb. and Cs were prepared by
exposing the HOPG-derived (Highly Oriented Pyrolytic Graphite) stage-2 binary
compounds "C24+A' -2.5{5_A.§_O.6 to pure NH3 vapor at a pressure of -8.5 atm.
The value of A J O was measured by direct weighing of the binary compound and is
indicative of its non-stoichiometric character. The x compositions of the
ternary compounds HtNH ) C

3 x Zlad'
gravimetric and volumetric techniques using the apparatus shown schematically in

H - K. Rb. Cs were determined by both

Fig. 1 [here x equals the moles of NH3 absorbed by the binary compound per mole
of potassium]. In the former method. a quartz spring (spring constant -1
mgm/mm) HcBain balance“ was used in conjunction with a Cathetometer to obtain an
absolute accuracy of 20 ugm corresponding to an x accuracy of a 0.05. Further

details of the HcBain balance measurement are given elsewhere.6

 

 

 

 

 

 

 

wswe 10601
I
HmmMmb l g—]
Hatfiesue :
kl m : blloSKU iont
. El T
m WN‘ ' ' T: w :
ftflhdwfl l g
mmmtug- ’ I §
_ _ _. I w_ {I
Smwnw-h T 9"”.1
: can
tmmiei-fl‘ 1 we" W...
“fin
Comma
unpuaue
bah Caretaneter

Fls- 1. Schematic diagrams of the apparatus for gravimetric (left panel) and

volumetric (right panel) measurements of x in K(NH )xc240A alkali-ternary GICS-

3

183

g The apparatus shown schematically on the right of Fig. 1 was used for the
volumetric .measurement of x and also for the (001) x-ray determination of the
sandwich thicknesses d5. To determine x volumetrically. the change in height of
liquid NH3 in the precision bore tubing was determined when the binary GIC was
exposed to NH3 vapor. Correction was made for the height change associated with
the NH3 gas»that fills the sample space. From the measured change in height of
the NH3 liquid. its known density and the bore size of the capillary tube, the
value of x in K(NH3)XC2am could be determined to an accuracy of 20.1.

RESULTS AND DISCUSSION

The results of our measurements of x, A. and ds for M(NH3)XC2M6 are given

in Table 1. The values for the latter will be discussed in detail elsewhere,13
but show a clear. if small. systematic dependence of da on ion size. These
results are qualitatively compatible with recent NMR studies13 which relate the
change in as to the orientation of the NH3 molecules in the graphite gallery.

He now focus our attention on the variation of x with the alkali-metal
ionic radii which are tabulated in the row 1abeled r". in Table l. Setton and
coworkers have shown that the approximate value of x for potassium-molecular
ternary GICs K(moleculelxczu can be deduced from a very simple model10 and that

this model is remarkably successful for a large variety of molecules.

Table 1. Parameters of the 30 "volume available“ and 20 "area available" models
for ternary alkali-ammonia GICs M(N ) C2“. . The parameters x. (A). and d
(at ZO'C) ire experimentally measu ed. V lues for r * were obtained from th
literature and r . the effective radius of the ammonia molecule. a. the
packing fraction. and cc. the correlation coefficient of the least-squares fits

to Eqs. (4) and (6). were deduced using the models described in the text

 

 

K Rb Cs
x 4.33:0.05 4.1010.05 3.6510.05
(A) '0.6 '0.7 '0.5
da (6.620t0.005)A (6.64010.005)A (5.67110.005)A
r". 1.33 1.46 1.67
2
r". 1.77 2.13 2.79
7’3” 2.35 3.11 11.66
20 Model 30 Model
”A 1.22 A 1.50 A
a 0.91 0.35

cc 0.99986 0.99995

 

184

Specifically. Setton showed that if V is the volume available for al

1 —_

intercalant species in a gallery of height d3 and crossection corresponding to
(24+A) carbon atoms. then I

a___2/§[

- (zuoii - 3.3sJi3 (i)

where a - 2.46 A is the lattice parameter of graphite and 3.35 A is the
Van der Haals radius of a carbon atom. Now in Setton's model

vi ' VK ‘ xvmolecule (2)

‘where VK is the volume of the potassium ion which depends on its ionic radius

and vmolecule is the effective volume of the molecule. Finally. by establishing

vmolecule independently (e.g. from the density of the molecular liquid) the
value of x in K(molecule)xC2n could be deduced from a combination of Eqs. (1)
and (2)

V - V
‘-—L——K-— (3)

vmolecule

For our case in which the molecule NH3 is kept fixed and the metal ion is
varied. the equivalent form of Eq. (2) of Setton's 3D model is

030 (29+d) a 2Jim - 3.35) - E-flrB + x(£ Hr

3
3 M+ 3 ‘ ) ». (4)

where °3D is a packing fraction (assumed - 1 by Setton). r is the ionic radius

[44

of the singly ionized metal and r is the effective radius of the intercalated

ammonia molecule. If in addition t6 the assumption of complete charge exchange
we make the reasonable approximations <A> - 0 and (d8) - 6.65 A. then a plot of
r3. vs. x [see Table 1] should be linear and should yield the values of °3D and
r‘. Such a least-squares plot is shown in the lower panel of Fig. 2. This plot

is clearly linear and the deduced value of r - 1.50 A is in excellent agreement

A
with the effective ammonia radius of 1.48 A deduced from diffuse in-plane x-ray
diffraction studies of K(NH3)~ 33 CZ”.

a - 0.31 is quite reasonable since Setton' s model

Moreover. the deduced packing fraction
10

underestimates V1 by not
including the cavity volume available in the lateral spaces between carbon atoms
in the same layer.

The effective ammonia radius found in the x-ray studies cited above“ was
based on a two-dimensional planar disc model for the structure of the 20
potassium-ammonia liquid. It is therefore appropriate to test the 20 analogue
of Setton's 3D model. This 20 version can be simply written as equations (5)

and (6) which follow:

‘i ' AM. . xAmolecule (S)

 

185

 

20 Model

 

 

(A’)

.35

r.

3.1

2.7

 

 

 

23 l I l l l I .
3.6 3.7 3.8 3.9 41% 4.1 42 4.3 4.4

 

Fig. 2. Least-squares fits (solid lines) of the data of Table 1 to Eq. (11) (30
model. lower panel) and to Eq. 6 (20 model. upper panel) of the text.

where A1. Aw. and Amolecule are the areas available for all intercalants. the

metal ion and the molecule. respectively. Then

2
a J3 _ 2 2

A ) (6)

where a is the 20 packing fraction. With the assumption that (A) - 0. Eq. (6)

20

predicts a linear variation of x with r3.

variation is indeed observed as can be seen from the least-squares fit shown in

(see Table 1 for values) and this

186

the upper panel of Fig. 2. Thus. the 20 and 3D models cannot be distinguished
on the basis of linearity alone since their correlation coefficients are
essentially the same [see Table 1]. However. both the ammonia radius and the
packing fraction deduced from the 2D model are much too small and are well

outside the range of experimental uncertainty. Therefore. the 3D model is the
most appropriate. '

CONCLUDING REMARKS

The simple “volume available” Setton approach to the determination of the
composition of ternary GICs works extremely well for variations of both the
molecular and metal ion species provided that a packing fraction is introduced
to calculate the volume occupied by intercalant species. Moreover. the size of
the metal ion has a noticeable effect on the amount of a given molecule'which
can be cointercalated into an alkali binary GIC. Finally. the composition of
alkali-ammonia ternary GICs is dominated by the above described ion-size/volume
effects and not by the tendency to form H-(NH3) n-fold clusters. e.g.
K(NH3)u.u'6 If cluster formation dominated the composition. the larger the ion.
the larger would be the corresponding x value in contrast to observation.

ACKNOHLEDGHERTS
We are grateful to B.R. York. S.D. Mahanti, H.R. Resing, and R. Fronko for

useful discussions. This work was supported by the 0.8. National Science
Foundation under grant DHR-82-1155l.

REFERENCES

1 H. Ruddrff and E. Schultze, Angew. Chem. 66. 305 (1954).

2 J.C. Thompson. Egectrons in Liquid Ammonia (Clarendon Press. Oxford. 1976).

3 J. Jortner and R.R. Kester. editors. Electrons in Fluids: Thegggture of
Metal-Ammonia Solutions (Springer-Verlag. New York. 1973); J.C. Thompson.
Rev. Mod. Phys. 50. 7044(1968).

4 X.W. Qian, D.R. Stump. B.R. York, and S.A. Solin. Phys. Rev. Lett. 54. 1211

(1985).

H.P. Hott and S.A. Davis. Electronic Processes in Non-Crystalline Materials

(Clarendon Press. Oxford. 1971).

B.R. York and S.A. Solin. Phys. Rev.. in press; B.R. York. S.K. Hark. and

S.A. Solin. Solid State Comm. 50. 595 (198A).

S.A. Solin. Adv. Chem. Phys. 49, 455 (1982); R. Clarke. J.M. Gray. H.

Homma. and H.J. Hinokur. Phys. Rev. Lett. 47. 1407 (1981).

B.R. York and S.A. Solin. Bull. Am. Phys. Soc. 0. 284 (1985).

ILA. Resing, B.R. York. S.A. Solin, and R.M. Fronko, Proc. of the 17th

Carbon Conference. Louisville. 1985. in press.

1C) R. Setton. F. Beguin. J. Jegondez, and C. Hazieres. Rev. Chim. Miner. 19.
360 (1982).

11 J.“. HcBain and A.M. Baker. J. Am. Chem. Soc. 48, 690 (1926).

12 R.D. Shannon. Acta. Cryst. A32. 751 (1976).

13 Y.B. Fan. S.A. Solin. R. Fronko, and B.R. Resing, to be published.

£09400!

 

Synthetic Metals. 12 (1985) 73-78 73

APPLICATION OF MICROSCOPIC PROBES TO THE STUDY OF GRAPHITE INTERCALATION
we

D.M. HWANG '
Bell Communications Research, Murray Hill, NJ 07974, (U.S.A.)

R. LEVI-SETTI, G. CROW, Y.L. WANG, N.w. PARKER' and R. MITTLEMEN
The Enrico Fermi Institute and Department of Physics,
The University of Chicago, Chicago, IL 60637, (U.S.A.)

x.w. QIAN and S.A. SOLIN
Department of Physics and Astronomy
Michigan State University, East Lansing, MI 48824, (U.S.A.)

ABSTRACT

Ion and electron microprobes with the highest spatial resolution available
today were used to investigate the nature of graphite intercalasgon_compounds
with multiphase multidomain structures. Secondary ion maps of Cl from
freshly cleaved surfaces of SbCl intercalated graphite were obtained using a
scanning ion microprobe capable 3f 20 nm lateral resolution. The maps exhibit
discrete features of nearly parallel lines and bead-like domains. The sample-
dependent lines are attributed to the accumulation of SbCl along the surface
defects. The bead-like domains have a typical dimension - 00 nm and are
interpreted as the Daumas-Herold domains one graphite monolayer underneath the
surface. Specimens of -50 nm thickness for analytical scanning transmission
electron microsc0pic studies were cleaved from the same bulk materials. Lateral
distribution of elements integrated through the specimen thickness was obtained
using energy dispersive x-ray spectroscopy. It is found that Cl distributes
uniformly, while Sb forms high concentration islands of typical dimension -70
nm. Electron energy loss spectra indicate that the low energy plasmons are
modulated by the island structure while the carbon core excitations are
spatially invariant. He suggest that the islands consist of an SbCl /SbC1;-like
material while the background consists of an SbCls/SbClg-like material.

INTRODUCTION

Many graphite intercalation compounds are synthesized at elevated
temperatures at which the in-plane structures are disordered. Any in-plane
phase transition occurring during cooling would result in a multiphase
multidomain structure owing to the constraint of maintaining a constant average
in-plane density. The nature of the resulting heterogeneous compounds is
difficult to characterize using traditional diffraction probes. In general. the
observed diffraction patterns are superpositions of patterns from several
coexisting phases and the domain sizes exceed the limitation of diffraction
line-width analysis [1]. Microscopic probes. with the probe beam size smaller

 

*Present address: MicroBeam Inc.. 1077 Business Center Dr., Newbury. CA 91320.

0379-6779/85/5330 © Elscvier Sequoia/Printed in The Netherlands

74

than the domain size. are indispensable tools for establishing the physics and
chemistry of individual microdomains. The probe beam can be rastered across the

sample while monitoring various induced signals for constructing two-dimensional
images.

A scanning ion microprobe (SIM) can focus an ion beam to 20 nm in diameter
[2]. Because of the shallow escape depth of the induced secondary electrons and
secondary ions (-0.5 nm). only the top few surface layers are probed. The ion-
induced secondary electron (ISE) images exhibit topographic and channeling
contrast. The channeling contrast is raised by the preferred channeling
directions of the primary ion beam in crystalline materials and reveals
information about the crystalline orientation [3]. The secondary ions can be
energy and mass filtered, yielding a secondary ion mass spectrometric (SIMS) map

which represents the lateral distribution of the selected isotope on the sample
surface.

An electron beam can be focused down to 0.3 nm in diameter. Various electron
induced secondary particles are used for sample characterization, such as
elastic scattered electrons for electron diffraction and dark field imaging,
energy-loss electrons for electron energy loss spectroscopy (EELS), x-rays for
x-ray emission spectrosc0py (XES) including energy dispersive x-ray spectroscopy
(EDS), and visible light for cathodoluminescence. Because of the deep
penetration depth of the primary electrons and the long escape length of the
secondary particles, high spatial resolution is achieved only by using electron
transparent thin samples so that the multiple-scattering broadening of the
primary electron beam is minimized. Therefore, the sample thickness should be
less than the electron mean free path in the material which is in the order of
50 nm for 100 keV electrons. In scanning transmission electron microscopy
(STEM). images with lateral resolution of 0.3 nm can be obtained. For
structural determination (convergent beam electron diffraction) and chemical
analysis (EDS and EELS), the resolution is also limited by the instrument
stability and the electron beam is usually defocused to reduce possible electron
beam induced damage. The information obtained with STEM is integrated through
the sample thickness.

SbCl5 intercalated graphite was chosen in this study for its stability in air
and in vacuum. as well as for its vast variety of structural phase transitions
reported in the literature [4-8]. Above -180 C. the in-plane structure is
disordered. At room temperature. it consists of at least a disordered phase and
an ordered phase. The ordered phase has been identified as /7'x J7'and/or (39 x
V39'commensurate superlattices. There are several phase transitions observed
below room temperature [4-8]. Evidence for the disproportionation of SbCls into
SbCl3. SbCl', and SbCl; has been reported [9.10].

75

Recently. we have characterized the structural and chemical properties of
stage-2 and stage-4 SbCl5 intercalated graphite using ion and electron
microprobes [11,12]. In this article, detailed morphology of the multiphase
multidomain structures of SbClS-graphite deduced from these observations is

presented and its implications on the nature of graphite intercalation compounds
are discussed. ' -

EXPERIMENTAL

Stage-2 and stage-4 SbCl5 intercalated graphite samples were synthesized by
the conventional two-temperature technique with a very slow intercalation rate
[8] from highly oriented pyrolytic graphite (HOPG). For SIM studies, the
samples were cleaved to expose fresh surfaces before inserting into the SIM
chamber which was then evacuated to 10'6 Torr within 30 minutes. later to 10'9
Torr. STEM samples were prepared by repeated cleaving with adhesive tape and
then mounted on copper or titanium supporting grids.

The high resolution SIM used in this study was developed jointly by the
University of Chicago and Hughes Research Laboratories [2]. This instrument can
focus a 40 keV beam of Ga+ ions from a liquid metal source to a spot of 20 nm in
diameter. Secondary electrons and ions are collected for imaging of surface
topographic, crystallographic. and chemical contrast. A high transmission
secondary ion energy analyzer and transport system. coupled to an RF quadrupole
' mass filter. is used to perform SIMS. An ion current of 1.5 pA was used for
high resolution SIMS imaging and approximately half a graphite monolayer was
sputtered away in taking each elemental map [12].

Analytical STEM studies were performed with a Vacuum Generators Model H8501
100 keV dedicated STEM equipped with a field-emission tip, an energy-dispersive
x-ray detector. and an electron energy loss spectrometer of 0.5 eV resolution.
Bright and dark field images were recorded with 0.3 nm resolution. An electron
beam of -5 nm diameter was used for EDS and EELS analysis.

RESULTS AND DISCUSSION
A typical 35Cl' SIMS map of stage-4 SbCl5 intercalated graphite is shown in
Fig. l. The map indicates that the distribution of chlorine (and presumably
intercalant) is highly discrete. The chlorine concentration in the bead-like
domains and the sample-dependent lines is -10 times that of the background. The
bead-like domains distribute randomly and occupy -252 of the total area. except
that the bead density is usually depleted on one side of the lines. Stage-2
SbCls-graphite yields similar SIMS maps except for a higher bead and line

density and a lower peak to background ratio (-3).

Fig. 1. 35Cl' secondary ion mass
spectrometric map of a freshly
cleaved surface of stage-4 SbCl -
graphite. The lines and bead-ITke
domains have a Cl concentration -10
times that of the background.

 

Sequential SIMS mapping of the same SbClS-graphite surface indicates the loss
of intercalant as expected since the sputtering yield of Cl compounds is much
higher than that of graphite. He also noticed that the line pattern diminishes
before the bead-like domains do [12]. indicating that the bead-like domains are
underneath the line pattern. Therefore. we suggest that the beads represent the
Daumas-Hérold domains [13] one graphite monolayer underneath the surface and the
lines represent the accumulation of SbCl5 on surface steps as illustrated in
Fig. 2. Near a surface step. the beads can diffuse toward the step and coalesce
eventually into solid lines.

 

 

 

N
J
xx
2
\

 

 

 

 

 

 

M... _
I \ I \ I \ I \ I
I \ I \ I \ I
_/,_..¥ r \J fl 4 \ J—x—
] \ I \ fl— I \

 

 

Fig. 2. An elaborated version of the Daumas-Herold domain model
which allows for the random nature of the domain size and lateral
distribution. It also shows the depletion of the intercalant near
a surface step.

A STEM dark field image of a stage-4 SbCls-graphite thin flake is shown in
Fig. 3. exhibiting high density islands of typical dimension -70 nm. Two-
dimensional EDS imaging indicates that the Cl distribution is uniform over the
probed area and the high density islands are due to the high concentration of
Sb. Quantitative analysis yields an Sb:Cl ratio of 0.32:0.03 for the islands
and of 0.14:0.04 for the background regions [11]. EELS studies reveal that the
low energy plasmons are modulated by the island structure while the carbon core

77

Fig. 3. Dark field scanning
transmission electron
microscopic image of a stage-4
SbCl -graphite thin flake. It
is f und that Cl distributes
uniformly while Sb has twice the
concentration in the islands
than in the background.

 

excitations are spatially invariant [11]. The later indicates that both the
island and background regions have the same degree of Fenmi level downshift with
respect to the graphite bands, and therefore, have the same degree of charge
transfer. He thus suggest that the island consists of (SbCl3)4(SbCl;), while

the background consists of (SbCl5)2(SbCl;). both having one negative charge per
16 Cl atoms.

Transmission electron diffraction indicates that the dominant phase of our
stage-4 sample is of J7'x/7'structure. consistent with other studies [4—7].
Convergent beam electron diffraction from individual islands exhibits diffuse
rings [14], indicating that the islands are of amorphous structure and the in—
plane structure is correlated along the c-axis. It has been reported that the
ordered phase can be converted into a glassy state by electron bombardment at
low temperatures [7]. Since the glassy state changes back to the ordered phase
at room temperature, that phenomenon is not related to the chemical and
structural segregation observed in our studies.

Note that Fig. I is the Cl distribution on the sample Surface while Fig. 3‘is
the through-thickness mass projection. The unifonn through-thickness Cl
distribution deduced from STEM EDS analysis is consistent with the model shown
in Fig. 2. The typical bead dimension observed in Fig. 1 is -200 nm which is
comparable to the typical island separation observed in Fig. 3. This fact
suggests that the chemical segregation of SbCl3/SbCl4 and SbClS/SbCl6 is limited
to within individual Daumas-Herold domains. i.e.. each Daumas-Hérold domain has
an Sb-rich core of SbCl3/SbCl; which is spatially aligned along the c-axis
through the sample thickness of -50 nm.

78

ACKNOWLEDGMENTS

We would like to thank S. A. Schwarz of Bell Communications Research for
useful discussions and A. M. Moore of Union Carbide for providing the HOPG
material. The work done at the University of Chicago is supported by the
National Science Foundation under Grant No. DMR-8007978 and the Materials
Research Laboratory at the University of Chicago. The work done at Michigan
State University is supported by the National Science Foundation under Grant No.
DMR83-11554 and by Michigan State University through its internally funded
Analytical Electron Microscope Laboratory.

REFERENCES

S. A. Solin. Adv. Chem. Phys. 49, 455 (1982).
R. Levi-Setti. Y. L. Hang. and G. Crow, J. Physique 45. C9 (1984).
a. Levi-Setti. T. a. Fox. and x. Lam. Nucl. Instrum. Methods 205. 299 (1983).

G. Timp. M. S. Dresselhaus. L. Salamanca-Riba. E. Erbil. L. H. Hobbs. G.
Dresselhaus. P. C. Eklund. and Y. lye. Phys. Rev. 826. 2323 (1982).

S R. Clarke. M. Elzinga. J. M. Gray, H. Momma, D. T. Morelli, M. J. Hinokur,
and C. Uher. Phys. Rev. 826. 3312 and 5250 (1982).

6 R. Clarke. in Graphite Intercalation Compounds. ed. P. C. Eklund, M. S.

Dresselhaus, and G. Dresselhaus (Materials Research Society. Pittsburgh.
1984). P. 152.

7 G. Roth. L. Salamanca-Riba. A. R. Kortan. G. Dresselhaus. and R. J.
Birgeneau. in Graphite Intercalation Compounds, ed. P. C. Eklund. M. S.

Dresselhaus. and G. Dresselhausi(Materials Research Society. Pittsburgh.
1984), p. 158.

8 D. M. Hwang and G. Nicolaides. Solid State Commun. 49. 483 (1984).

9 P. Boolchand. H. J. Dresser. D. McDaniel. K. Sisson. V. Yeh, and P. C.
Eklund. Solid State Comun. 40. 1049 (1981).

10 %. B.)Ebert. D. R. Mills. and J. C. Scanlon. Mater. Res. Bull. 18. 1505
1983 .

11 D. M. Hwang. X. H. Qian, and S. A. Solin. Phys. Rev. Lett. 53. 1473 (1984).

12 R. Levi-Setti. G. Crow. Y. L. Hang. N. H. Parker. R. Mittlemen, and D. M.
Hwang. to be published.

13 H. Daumas and A. Hérold. C. R. Acad. Sci. C268. 373 (1969).
14 D. M. Hwang and J. Cowley. to be published.

#wNH

 

MEASUREMENT OF THE MICROSCOPIC DISTRIBUTION 01" BR
IN THE BROMINATED PITCH BASED GRAPHITE FIBERS

X.W. GIANT, S.A. SCI-IN". and J.R. GAIER"

“Department of Physics and Astronomy, Michigan State University, East Lansing.
MI 118821-1116 '

"NASA Lewis Research Center. 21000 Brook Park Road. Cleveland. OH 1111135

Brominated pitch based graphite fibers have been shown to have enhanced
conductivity over that of pristine pitch-based fibers [1]. Two phases of the
brominated fibers corresponding to different compositions exist, i.e. the_
saturated fibers and the residual fibers with the composition of CnBr and
C..Br. respectively. While the saturated fibers have a maximal reduction in
the resistivity relative to that of the pristine material (~18 times) [1].
saturation can only be maintained by constant contact with Br vapor. In
contrast. the residual fibers made by removing the saturated fiber from the
external Br bath are stable in air and even in vacuum [2], but they exhibit a
smaller resistivity decrease relative to pristine fibers (-6 times) than do
the saturated fibers [1]. To understand these resistivity reductions we have
studied the microscopic Br distribution in the fiber compounds and related
that distribution to the macroscopic resistance [3]. In this brief report we
focus on the stable residual fibers.

A field emission scanning transmission electron microscOpe (FESTEM)
equipped with an X-ray energy dispersive spectrometer (EDX) detector was used
to establish the Br distribution. The fiber under examination was illuminated
by a well-focused 100 Kev electron beam (beam diameter ~50A) in such a way
that the direction of the beam was perpendicular to the longitudinal axis of
the fiber. The electrons in the beam excited Br atoms along their pathway
through the fiber. The Br K X-ray emission which resulted from inner shell
excitation of the Br atoms‘1 by the energetic electrons was then collected by
the EDX detector. When the electron beam was digitally controlled to scan
across or along the axis of the fiber. the cross-sectional or longitudinal X-
ray intensity profile could be recorded. Of course, the deduction of the real
Br distribution from the observed X-ray intensity profile critically depends
on the distribution of incident electrons in the fiber. we determined this
distribution by a computer simulation.

A Monte Carlo simulation [3] shows that. as the electrons penetrate a
material with an average composition corresponding to that of the residual
fiber (density 2.2 gm/cm’). they are effectively confined to a conical region
under the impinging point as shown in the inset of Fig. 1. Statistically. as
a result of the multiple scattering process, the energy of the incident
electrons varies linearally with the penetration depth within a range
corresponding to the diameter of our fibers. and the beam radius defined by
the circular cross section of the cone that contains 901 of the incident.
electrons varies with the penetration depth according to a power law with an
exponent of 1.5 [11]. At the penetration depth equivalent to the diameter or
the fiber (~10 um). the electron energy is reduced to 911 Kev and the beam
cross section has increased to 2 pm in radius. With the pathway of the
incident electrons inside the fiber known. we can calculate the cross-
sectional X-ray intensity profile for any assumed Br distributions [3]. when
the calculated intensity profiles are compared with the experimental results.
the Br distribution of the fiber can therefore be deduced.

Experimentally. two distinct cross-sectional X-ray intensity profiles
were measured as indicated in Fig. 1 by dots (-) and crosses (*l which are
associated. respectively with Br-rich and Br-poor regions of the f1ber, The
rounded profile of the Br-rich regions was observed from the vast majority of
cross-sectional areas sampled and is characterized by intense emission at its
peak. In contrast. the Gaussian-like profile of the Br-poor regions was
observed from very few cross-sectional measurements and always exhibited a

210

peak intensity considerably smaller than that of the Br-rich region. In
addition. in the Br-poor regions a Br-free surface depletion layer of typical
thickness 1pm could be detected.

It can be shown [3] using the above cited Monte Carlo computer simulation
that for the configuration and parameters defined in Fig. 2 the X-ray
intensity profile I(x) is given by

E(z)

J
Ec

E(z)[b(z)]2

 

93r[r(x)]ln[

I(x) - const. - (ds)(dz) (1)

i
I

where ds is a cross-sectional area increment. °Br(X) is the bromine density
distribution. E(z) is the electron energy at a penetration depth 2. b(z) is
the beam cross-sectional radius and Ec is the critical excitation energy for
the inner shell X-ray emission line.

If we assume a uniform Br distribution pBr(r) - const. in Eq. (1). we
obtain the excellent scaled fit to the X-ray intensity profile of the Br-rich
region shown as a broken line (-—— - -—- -) in Fig. 1. But a uniform
distribution gives a very poor fit to the profile of the Br-poor region as can
be seen from the dashed line ( ------ ) in Fig. 1. However, if we assume a
Gaussian distribution pBr(r) - exp bra/(0.115 a2)] for the Br-poor region we
obtain the very good fit shown as a solid line (—————————-) in Fig. 1. The

discrepancies in the wings of the Gaussian fit are due to the surface
depletion layer.

ACKNOWLEDGEMENTS
We thank D.M. Hwang and D.A. Jorwoski for useful discussions. This work

is supported by NASA under grant #NAG-3-595.

tExxon Fellow

REFERENCES

. J.R. Gaier. NASA TM-87275. 1986.
. J.R. Gaier. NASA TM-86859. 198D.
X.W. Qian, S.A. Solin. and J.R. Gaier. Phys. Rev.. submitted.

3 U N d
e

..I.I. Goldstein in Introduction to Analytic Electron Microscopy. edited by

J.J. Hern. J.I. Goldstein and D.C. Joy (Plenum Press. New York and London.
1979);

211

 

 

I(x) (ARBITRARY UNITS)

 

 

 

 

Fig. 1. Plots of the Br K X-ray intensity vs. the lateral position (x) of the
incident electron beam. The dots (.) denote the experimental data for the Br-
rich region. and the broken line (— - -— -) was calculated from Eq. (1)
using a radially uniform Br distribution. The crosses (+) represent the
experimental data points in the Br-poor region. and the solid line ( )
[dashed line ( ----- )J was calculated from Eq. (1) using a Gaussian (uniform)
Br distribution. The inset shows an output of the computer simulated paths of
100 keV incident electrons through a 15 um thick slab of brominated fiber.
The dashed circle represents the cross section of the fiber.

 

 

Fig. 2. A geometric designation of the parameters and variables used in Eq.
(1) of the text.

212

:2 h

 

EVIDENCE FOR A Z-DIHENSIONAL HETAL-INSULATOR TRANSITION IN POTASSIUM-

AHMON IA GRAPHITE

Y.Y. Huang. X.W. Qian'. and S.A. Solin

Department of Physics and Astronomy
Michigan State University
East Lansing. MI N882N-1116

J. Heremans and 0.0. Tibbets

Physics Department
General Motors Corporation
Warren. MI “8090-9055

We have studied the ammonia pressure dependence and composition
dependence of the a-axis electrical resistivity of the potassium-ammonia
ternary graphite intercalation compounds K(NH.) C... 0 < x < u.33- Our
results show evidence of the 20 analog of the w’éll-studied bulk 3D metal-
insulator transition [1] in bulk K-NH. solutions.

In order to probe the electrical prOperties of the intercalate layer
in K(NH.) C... we measured the in-plane a-axis resistivity as a function of
ammonia pressure [2]. For convenience, we used a benzene-derived onion
skin-like graphite fiber [3] rather than HOPG. Thus. the fiber axis is
approximately coaxial with the cylindrical graphite planes. From the (001)
x-ray diffraction patterns of a single fiber (see Fig. 1) we determined the
basal spacing of the pristine fiber (d - 3.35A), of stage-2 KC,. potassium
binary GIC (d - 8.7uA) and of the stage-1 ternary GIC K(NH,)u 3C3. (d
6.6UA). 'Thege results indicate that the graphite fiber has thé same Gigbs
phase diagram [u] as HOPG.

A four-probe measurement technique was developed for monitoring the
pressure dependence of the a-axis relative resistance (R/R ) of K(NH.) 02..
using a pressure up-quenching technique. [Here R(RO) is the a-axis
resistance of the ammoniated (KC,.) compound.] The resuIt is plotted in
Fig. 2. Note that the relative resistance ratio remains a constant below
one atmosphere and then starts to increase in the stage-2 to stage-1 phase
transition region at -o.5 atm. [5]. The increasing resistivity in a stage-
2 to stage-1 phase transition is a common feature of binary GIC's [5]. But
when NH. is added to KC... some delocalized electrons in the carbon layer
are back-transferred to the intercalate layer [6] so that the conductivity
of the carbon layers decreases. However. R/R starts to decrease
dramatically at about 3-u atm. at which pressure x s greater than four
[6]. This phenomenon may be a consequence of a 2D metal-insulator
transition. Hhen x u u, there are enough NH. molecules to completely
solvate potassium and form a u-fold coordinated K-NH. clusters [7]. Higher
NH, concentration leads to a sufficient amount of electron back-transfer

33
o
3

00’s...
0000' e ‘.o$. e~ . Ce. ..~.0...

INTENSITY (ARB UNITS)

‘P. 0 "0'00 00......” ouoo~ .-

1 2 3 4 5

 

Fig. 1. The (009.) x-ray diffraction patterns Of (a) a single pristine
cylindrical onion skin-like graphite fiber. (b) the same fiber as in (a)
after intercalation with potassium to form the binary GIC KC... and (c) the
same fiber as in (b) after ammoniation to form the ternary GIC
K(NH.“ C... The diffraction patterns were recorded at room temperature
using MoKi: radiation. The background continuum is diffuse scattering from
the glass envelope and from air in the beam path.

 

n/n.
GANG-hm

 

 

t .) "
PNH3(a m

Fig. 2. The room temperature relative resistance a-axis ratio R/R of
potassium-ammonia-graphite as a function of ammonia pressure. Here R and
R correspond respectively to the resistance of KC.. and K(NH.)XC...

from the graphite layers to the intercalate layers to induce a hopping-type
metal-insulator transition [8]. When there is sufficient solvation to
cause in-plane overlap of the electron wave function. the intercalate layer
starts to conduct in parallel with the carbon layers and the a-axis
resistance draps as is observed in Fig. 2. The study of the composition
dependence of the dielectric constant of K(NH.)XC.. also provides evidence
of a metal-insulator transition at x - u.

ACKNOHLEDGEMENTS

We thank Y.B. Fan for useful discussions. This work was supported by
the National Aeronautics and Space Administration under grant NAG-3-595 and
in part by the U.S. National Science Foundation under grant 85-17223.

’Exxon Fellow

REFERENCES

1. J.C. Thompson. Electrons in Liquid Ammonia (Clarendon. Oxford, 1976).

2. Y.Y. Huang. S.A. Solin. J. Heremans. and 0.0. Tibbets. to be published.

3. J. Tsukamoto. K. Matsumura. T. Takahashi. and K. Sakoda. Synthetic
Metals 13. 255-26“ (1986).

u. Y.B. Fan and S.A. Solin. Proceedings of the Materials Research Society
Meeting. Boston. (1985).

5. M.S. Dresselhaus and G. Dresselhaus. Adv. Phys. 39. 139 (1981).

6. B.R. York and S.A. Solin. Phys. Rev. 831. 8206 (1985).

7. X.W. Qian, D.R. Stump, B.R. York, and S.A. Solin. Phys. Rev. Lett. 2g.
1271 (1985).

8. See reference 1 and references therein.
9. J.M. Zhang, P.C. Eklund. Y.B. Fan, and S.A. Solin. to be published.

A FIELD EMISSION STEM STUDY OF THE B? DISTRIBUTION IN BROHINATED GRAPHITE
FIBERS

X.W. Qian' and S.A. Solin

Department of Physics and Astronomy
Michigan State University
East Lansing. Michigan u882H-1116

J.R. Gaier

NASA Lewis Research Center
21000 Brook Park Road
Cleveland, OH uu135

Brominated pitch based graphite fibers exhibit certain novel
properties and potential applications [1.2]. For example. it has been
observed that an 18 fold reduction of their resistivities of the pitch-
based graphite fibers can be achieved if the pristine fibers are allowed to
fully interact with bromine [3] and even the residual fiber compounds that
are formed by pumping off the bromine from the fully brominated fibers
(saturated fibers), exhibit a five-fold reduction in the resistivities
relative to»that of the pristine fibers [3]. To understand this prOperty.
it is essential to know the Br distribution in such fiber compounds. Here
we focus on the residual fibers that have a density of 2.2 gm/cm'
corresponding to a composition of BrC...

A FESTEM (Field Emission Scanning Transmission Electron Microscope)
was used to study the Br distribution in the residual form of the fiber.
The fiber under examination was bombarded by a well focused 100 Kev
electron beam (beam diameter -50A) in such way that the direction of the
beam was pegpendicular to the longitudinal axis of the fiber. The high
energy electrons penetrate into the material. excite the Br atoms in their
pathway which in turn give off the characteristic K X-rays. A EDX (Energy
Dispersive X-ray) detector collects the X-rays. Nhgn the electron beam is
digitally controlled to scan across the fiber or along the longitudinal
axis of the fiber. the cross-sectional or longitudinal x-ray intensity
profile can be recorded. These X-ray intensity profiles together with a
knowledge of the electron path inside the fiber enabled us to deduce the Br
distributions in the fiber.

The details of the incident electron path are established by computer
simulation. As the electrons penetrate into the material, they strongly
interact with the atoms in the material. They lose energy and are
scattered away from the original direction. Consequently. the electron
beam diameter and the energy vary with the penetration depth [A]. A Monte
Carlo simulation [5] shows that over the range of fiber size (~10 um). the
beam diameter is related to the depth through a power law with an exponent

 

Fig. 1. The Br K X-ray intensity variation (curved line of dots) along a
PB fiber superposéh on the bright field image of the fiber the axis of
which is perpendicular to the incident electron beam. The straight dotted
line denotes the position of the electron beam as it is digitally scanned
along the longitudinal axis if the fiber.

of 1.5, and the energy of the electrons varies linearly with depth with a
rate -0.6 KeV/um. At 10 um depth the beam is broadened to 3 um and the
energy is reduced to 9n Kev. Once the electron paths and energies inside
the fiber are known. the X-ray intensity profile generated from an assumed
bromine distribution can be calculated directly. By comparing the
calculated profile to the experimental profile we can deduce the Br
distribution in the fiber.

Experimentally we find an inhomogeneous Br distribution along the
longitudinal axis of the fiber (see Fig. 1) with two distinct cross-
sectional distributions. i.e. a uniform distribution in the Br-rich region
and a Gaussian distribution in the Br-poor region (See fig. 2). It is
worth noting that a depletion layer of -1 um is found on the surface of
the Br-poor regions. This is attributed to the porous like structure of
the fiber near the surface.

ACKNOWLEDGEMENTS

We thank D.M. Hwang. J.R. Gaier, and D.A. Joworski for their useful
discussions. This work is supported by the National Aeronautics and Space
Administration under grant NAG-3-595.

'Exxon Fellow

REFERENCES
1. J.C. Hooley and V.R. Diets. Carbon 16, 251(1978)
2. J.R. Gaier and D. Marine, NASA TM-87016,1985.

3. .R. Gaier. NASA TM-87275.1986.
A I.

J
. J. Goldstein in Introduction to Analytical Electron Microscopy. edited
b

y J.J. Hern. J.I. Goldstein and D.C. Joy (Plenum Press. New York and
London. 1979).

5. X.W. Qian, S.A. Solin. and J.R. Gaier. Phys. Rev.. submitted.

600

I(x) (ARB UNITS)

/ .- *1 . L "

:ZHEI() /’ .r""’ ‘~“u- ‘
P 1’ 'I “\\ “

II, ‘* \\‘
a- +“’ I

() I. .,«e" " i

 

-a 0 a

Fig. 2. A plot of Br K x-ray intensity vs. the lateral position (x) of
the incident electron beag. The dots (.) denote the experimental data for
the Br-rich region, and the dashed line is the calculated intensity from a
radially uniform Br distribution. The crosses (+) represent the
experimental data points in the Br-poor region, and the solid line is the
r:
calculated intensity from a Gaussian Br distribution. pB (r)-poe 0.u5a’.
where a is the radius of the fiber and r is the distance from the axis of

the fiber. A scaled intensity calculated from a uniform Br-distribution in
the Br-poor region is also shown as a broken line.

ANALYTICAL ELECTRON MICROSCOPIC STUDY OF MICRODOMAIN STRUCTURES IN ANTIMONY
PENTACHLORIDE INTERCALATED GRAPHITE

D. M. HWANG. ' X. W. QIAN. " AND S. A. SOLIN"

“Bell Communications Research. Murray Hill, NJ; "Michigan State University.
East Lansing. MI.

It has been reported‘ that at room temperature SbCls intercalated
graphite exhibits multiphase multidomain inplane structures with Sb-rich
islands in an Sb- difficient background. In this paper. we will show that the
islands consist of SbCl, /SbCl. -like material, while the background _is
SbCl ./SbCl:-like. We report a unique molar ratio of SbCl, :SbCl.:SbCl.: SbCl. -
u:1:18:9 in stage-A SbCl,-graphite.

‘Bulk stage-u SbCl.-graphite was prepared from HOPG by the standard two-,

bulb technique and then x-ray characterized. Transmission electron
microscopic specimens were cleaved from the bulk. thinned with adhesive tape,
and mounted on copper supporting grids. A Vacuum Generators Model H8501
analytical scanning transmission electron microscope equipped with a field
emission tip was used to obtain the bright field and dark field images. the
energy dispersive x-ray spectra, and electron energy loss spectra.

Typical bright and dark field images obtained from stage-A SbCl.-graphite
thin flakes of thickness ~500A are shown in Figs. 1 and 2. respectively. Both
reveal the existence of high density islands. Similar multi-domain images
have also been observed on the fresh surface of bulk stage-2 SbCl,-graphite
with a scanning ion microscope.

 

Fig. 1. Bright field micro-image of stage-u SbCl.-graphite.

Typical energy dispersive x-ray spectra from island and background
regions obtained with an electron beam size of -50A are shown in Fig. 3.
Following standard x-ray microanalysis procedures.’ the chemical composition
in the island region is found to be SbCl3.1:O.3' while the background region

7.012.0. By monitoring the x-ray intensity of the Cl
K-line and the so L-line signals as a function of probe position on the
specimen while scanning the electron beam in one or two dimensions. it is
found that Cl atoms are distributed uniformly throughout the imaged area.
while the Sb concentration is almost doubled in the island region compared to
that in the background region.

has a composition of SbCl

The riigh contrast of the multidomain images and the distinct Sb:Cl ratio
in the island and background regions suggest that the inplane domain
structures are strongly correlated along the c-axis. i.e. the high density
domains in each intercalant layer stack directly on top of each other over the
specimen thickness of ~500A. A preliminary electron microdiffraction study‘
confirms this conclusion. In addition to the graphite diffraction pattern.
the islands give amorphous halos, while the background gives extra spots some
of which could be indexed to the (I? x J7)R19.l° superlattice.“

It has been proposed5 that uppn intercalation into graphite, SbCl.
disproportionates into SbCl. and SbCl.. and the latter species is rgsponsible
for the charge transfer. Our observation suggests that the so and Sb
species are spatially segregated.

If SbCl,. SbCl.. and SbCl. are the only molecular species present. then
the island region should contain only SbCl.. which is electrically neutral.
Consequently. the graphite layers adjacent to the island regnnishould be
neutral. while those adjacent to the background region. would be positively
charged. This point is checked using electron energy loss spectroscopy.‘
Although the graphite 6eV t-plasmon peak shows significant differences between
the island amui background regions. the carbon ls core excitation edge
indicates the same shift of the Fermi level relative to the valence band.
Therefore, the charge in the graphite layers must be delocalized as must the
charge in the intercalant layers. _

We propose that the islands consist of SbCl./SbCl. complexes. while the
background-consists of SbCl,/SbCl. complexes. Ebert. et al.3 have proposed
that SbCl. is also a disportionation product if SbCl. when it is intercalated
into graphite. Given the conditions that (1) The average chemical composition
is SbCl.; (2) The charge is completely delocalized; (3) The C1 atoms are
uniformly distributed; and (A) The island region occupies 11% of the_total
area; we derived the unique chemical formula of (SbCl.) (SbCl.)

_ 1/8
(SbCl.)9,16 (SbCl.)

1/32
9/32' '

ACKNOWLEDGEMENTS

We would like to thank A.W. Moore for providing pyrolytic graphite and V.
Shull for technical assistance. We are grateful to J. Fischer, P. Eklund. J.
Cowley, and R. Levi-Setti for stimulating discussions. This research has been
supported by the NSF under grant DMR83-1155N. by Michigan State University
through its internally-funded Analytical Electron Microscope Laboratory. and
by the Research Board of the University of Illinois at Chicago.

REFERENCES

1. D.M. Hwang and S.A. Solin. Bull. Am. Soc. 32. 293 (198A), and to be
published.

2. W. Parker. R. Levi-Setti. and D.M. Hwang. to be published.

3. Introduction to Analytical Electron Microscopy. ed. by Hren. Goldstein.
and Joy (Plenum. New York. 1979).

A. D.M. Hwang and J. Cowley. unpublished.
S. L.B. Ebert. D.R. Mills. and J.C. Scanlon. Mat. Res. Bull. 18. 1505 (1983).

 

 

Fig. 2. Dark field micro-image of stage-II SbCl. graphite.

 

5.0 _

4.0 — _

!\ _
M a“); a...
2.0 009‘? 0 09090060433 : O

1.0-

COUNTS x102

 

 

L. CI Ka1

‘3'...“le O
1
I 1

I L
. 3.0 4.0 5.0 6.0
ENERGY (KeV)
(b)

Fig. 3. Energy dispersive x-ray spectra from island (0) and background (0)
regions in stage-ll SbCl.-graphite.

 

0.0
2

1H NMR Study of NH3 Orientation and Difgusion in

Te a onia Alkali Meta -Gra hite

R. M. Fronko and H. A.
Code 6120

ntercalation Com ounds

Resing

Naval Research Laboratory
Washington, D. C. 20375-5000

T. Tsang

Department of Physics and Astronomy
Howard University
Washington, D. C. 20059

and Code 6120

Naval Research Laboratory
Washington, D. C. 20375-5000

X. W. Qian* and s. A.

Solin

-Department of Physics and Astronomy
Michigan State University
East Lansing, Michigan 48824-1116

*Exxon Fellow

 

 

ABSTRACT

 

For the first stage ternary graphite compounds (TGIC) I((Nlia),+ 302“
RbINH3)4.1024 and Cs(NH3)3.7CZu derived from_highly oriented
pyrolytic graphite. the 1H NMR spectra have been studied at various

temperatures and orientations. The spectra consist of three sets of

triplet resonance lines due to the 1H-1H and 1H-1uN dipolar interactions.

The simple spectral features and narrow spectral lines indicate fast
diffusion and reorientations of NH3 molecules in the graphite gallery.
The CB-axes of NH3 molecules are oriented nearly perpendicular to

the crystallographic c-axis of the T010. The molecules are situated g'h

 

near the bottoms of potential wells with barrier heights of N0.2 eV.
The HNH bond angle of 10?0 is very close to the gas phase value. The

1“N quadrupolar coupling constant of 3.7 MHz is

indirectly measured
intermediate between the gas and solid NH3 values of 4.1 and 3.2 MHz.
The NMR results are consistent with a rather mobile and liquid-like
layer of planar M(NH3): ions (where M denotes K. Rb or OS) in between
the carbon layers. These ions are the two-dimensional analogues of
the M(NH3)2 ions commonly observed in alkali metal-ammonia solutions.

There is relatively weak partial solvation of the electronic charge

on the carbon layers by the co-intercalation of NHB'

 

.L INTRODUCM

By various oxidation and reduction reactions. graphite inter-
calation compounds (GIC) may be formed from many different types of
graphite. such as natural crystals. highly oriented pyrolytic
graphite (HOPG). and graphite fibers.1'3 A universal feature of
these topotactic reactions is that monatomic or molecular ions open
and enter the space between the carbon layers of the graphite crystal. 4
The entry of the intercalant species is accompanied by the deposit rfr
of counter-charge on the carbon layers. The electrical charge

deposited on the planar carbon layers are highly mobile and give 5’:

 

the GIC's very high electrical conductivities. often highly anisotropic
and comarable to the noble metals. The high strength to weight ratio
of graphite fibers is only slightly diminished by the intercalation
process. Because of these unusual characteristics. the 010's have
many potential applications in power transmission. batteries. chemical
catalysis. etc. i

In donor compounds. the carbon layers are reduced by intercalation
with alkali metals (denoted as M) such as K. Rb and Cs or other metals.
The alkali metal (M) atom donates its outer s-electron to the carbon
layer and enters the gallery or interlayer space as a monatomic ion
withfsingle positive charge. The staging phenomenon is exhibited by
all these compounds. where the intercalate layers are periodically
arranged in a matrix of carbon layers. The GIC's are classified by
a stage index. n. denoting the number of carbon layers between the
adjacent intercalant layers. This number n is not an average. but
indicates the real periodicity of the crystal along the c-axis of the
GIC. Thus several different compounds may be formed. For instance.

the GIC compositions MCB’ M024 and M036 corresponds to n=1.2. and 3.

In acceptor compounds. the carbon layers are oxidized by
intercalation with highly reactive compounds such as Bra. H250“.
HNOB. AsFS. etc. There are mobile holes in the valence bands of
the carbon layer due to the removal of the electrons. Staging
phenomena are also exhibited by the acceptor GIC's. However.
small fractional charge transfers are common for the acceptors and
the stoichiometry is no longer a clear indicator of the chemistry
that has taken place. For instance“. in CBnASFS where n is the
stage index. there are 0.26 holes generated per AsFS for n=1 but
0.50 holes generated per AsFS for n=2. This implies variable ratios
among the equilibrium concentration of the "intercalated" species
which are believed to comprise AsFé'. AsFS and AsFB. Here. the
latter two species play the part of neutral "spacers". Hence the
chemistry of the acceptor GIC's appears to have more variability.
which can be manipulated by sample preparation.

Neutral "spacers" such as tetrahydrofurans and benzene6 may
co-intercalate the donor compounds as well. The ammonia molecules
(NHB) co-intercalate the alkali metal donor GIC's also.7"'9 However.
liquid ammonia itself is a solvent for alkali metals. where the metal
atom gives its outer s-electron to be solvated by the liquid NHB'
The fundamental questions for these ternary GIC's are: (a)what are
the HHB molecular geometries. orientations and motions in the
graphite galleries. and (b) whether the co-intercalated NH3 molecules
are only neutral "spacers” or compete with the carbon layers for
the electrons given up by the alkali atoms.

In our present study. we have used 1H nuclear magnetic resonance
(NMR) spectroscopy of the co-intercalated NH3 molecules to seek
answers to the first question. We have studied the first stage

ternary alkali metal ammonia GIC's. “(NH3)xCZ#’ where x is approxi-

- 2 -

 

 

mately equal to h for M=K. Rb and Cs. These ternary compositions
are reached by the subsequent intercalations of the corresponding
second-stage binary GIC's M024 with gaseous NH3 at room temperature
and a pressure of 9.5 atmospheres. There has been considerable recent
work on these ternary GIC's.(TGIC)8"11 since the existence of M(NH3)x
layers have been shown to be two—dimensional analogue of the
alkali metal-ammonia solutionslz'13 and ate A liquid-like in the
graphite gallery. The binary GIC's M02“ are obtained by the inter-
calation of alkali metal vapors into HOPG. The c-axes of the indivi-
dual crystallites of HOPG are well—aligned (within a spread of 12°)
while there is considerable disorder in the ab-plane of the carbon
layer. Once the TGIC is formed. the sample behaves much like a
single crystal. '

In our present work. the experimental details are described in
Sec. II. Typical experimental 1H NMR spectra are given in Sec. III.
The general features of these spectra are nine resonance lines forming
a triplet of triplets. These features are somewhat more complicated
than the three-line spectra observed by Miller etal.1u for AsF3
co-intercalated into the graphite gallery. These spectra have been
used to deduce the preferred orientations and the rapid motions (with
correlation times shorter than 10-5 sec) of NH3 molecules in the
TGIC. These spectra have been interpreted in terms of the dipolar
splittings due to the 1H-1H and 1H-laN interactions. We have found
that the molecular geometry of NH3 in the TGIC to be very similar to
the geometry of NH3 observed in the gas phase.15 We have also shown
that the uneven spacing of the central triplet is due to the 1“N
quadrupole moment. The temperature dependences of 1H NMR spectra

are presented in Sec. IV. These temperature dependences have been

used to infer that molecular C3-axes of NH3 are nearly perpendicular

.'3-

 

 

to the crystallographic c-axis of the TGIC. In Sec. V. the 1H NMR

results are compared with the previous X-ray and neutron scattering

results.8'11 The results are consistent with a simple liquid-like

intercalant layer of K(NH3)u ions in these TGIC's.

. . , , .
The compOSitions of the TGIC s are R(NH3)u.3024. Rb(Nh3)u.102u

and Cs(NH3)3.7024. The experimental data for these TGIC's are

QUite similar t0 93°“ other. hence only the results for the K-compound {“4
will be discussed in detail.

It has been proposed by us16 that the 13C NMR spectra and

chemical shift may be used to seek answers to the second question.

 

The 13C NMR chemical shift and charge transfer to the carbon layers
of the TGIC will be presented in a separate paper.17

II. EXPERIMENTAL

The TGIC's have been prepared by the exposure of the second
stage binary GIC MCzu (from the reaction of alkali metal vapors with

HOPG) t0 the vapor from liquid ammonia at room temperature (9.5 atm.
vapor pressure) for several hours.8’9 However. a large pool of

excess liquid NH3 would remain in the TGIC sample tube.

The excess
NH

3 is undesirable for many NMR experiments. By using the apparatus

shown in Fig. I. the problem of excess NH3 was circumvented by sealing

the GIC with sufficient NH3 to give the required composition and an
atmosphere of NH3 at 9.5 atm. pressure external to the GIC. The GIC
and liquid NH3 are contained in separate chambers which may be isolated

from each other by teflon stopcock T.

The total volume of the specimen
chamber is V.

The final volume of the sealed GIC sample is V'. The
binary GIC (M024) is exposed to the vapor from a pool of liquid NH3

(from the vacuum line on the other side of the stopcock T'. not shown

-1..-

 

in Fig. 1) for a minimum of 5 hours to reach the fully loaded TGIC

as confirmed by a X-ray diffraction pattern: We then calculate the
amount of NH3 required to fully load the TGIC and to maintain the

9.5 atm. pressure in the volume V'. After closing the stopcock T'.
the resorvoir A is cooled slowly (to prevent exfoliation of the TGIC)
to a pre-determined temperature such that the calculated amount of

NH3 would be present in the TGIC sample and in the vapor phase of the
volume V. After the pre-determined temperature is reached. stopcock T
is closed and the specimen chamber is slowly cooled to liquid nitrogen
temperature to condense all NH3 into the sample chamber; The sample is
then sealed off at the point S to give the volume V'. Upon warming

to room temperature. the TGIC composition is confirmed by a X-ray
diffraction pattern. The TGIC does not contain pool of excess liquid
NHB' Only a slight and non-obscuring amount of NHS is adsorbed on

the TGIC surface.

For the potassium compound K(NH3)Q.3C24 (KTGIC). the X-ray
rocking curve is shown in Fig. 2 for the (002) reflection using
MoKd1.2 radiation (0.71 A wave length). The X-ray intensity is
plotted vs. the angle 6) between the X-ray beam and the GIC surface.

There appears to be about :30 misalignments of the various crystallites

within the GIC.

1

The H NMR spectra were obtained on a JEOL type FX60Q Fourier

transform spectrometer operating at 59.75 MHz using 27 us (90°)
pulses. The TGIC approximates a single crystal and all NMR spectra
will depend only on the angle at between TGIC crystallographic c-axis
and the magnetic field. The orientation «=0O is determined by
maximizing the satellite line splittings of the NMR spectra.

For low temperature spectra. the probe was cooled by passing
nitrogen from a pressurized tank through a cooling coil immersed in

-5-

 

a dewar containing liquid nitrogen. The temperature at the probe
was maintained and measured with a JEOL NMVT-3C temperature controller
using a thermocouple fixed at the bottom of the sample in the probe.

1

III. H NMR SPECTRA AND MOLECULAR MOTION

In Fig. 3, the room temperature spectra at 60 MHz and ot=0° are
shown for the K. Rb and Cs compounds. These spectra are quite similar
to each other. Because of this similarity. only the results of the
K-compound (KTGIC) will be discussed in detail. In Fig. u. the room
temperature spectra of KTGIC at 60 MHz are shown for various angles
' of cx between the magnetic field 50 and the crystallographic c-axis
of the KTGIC. The spectral lines at o(=0° are numbered as 1-9 from
left to right (from higher frequency to lower frequency). The general
spectral feature is three triplets. We will refer to them as the
central triplet and the outer triplets. The spectral line positions
in (m=1 to 9) in KHz are plotted vs. o< in Fig. 5. The splittings

between the spectral lines m and n may be denoted as an = ‘7m - \7

n
The room temperature spectrum at 300 MHz is shown as Fig. 6 for

a =90°. The splittings between the spectral lines are similar to

the values obtained at 60 MHz for o(=90o as shown in Fig. 4.

These experimental spectra may be used to deduce the molecular
orientations and motions of the intercalated NHB. We will now proceed
to calculate the theoretical NMR spectra and then compare with the

experimental spectra: For NH3 molecules. it is necessary to consider

1

three H nuclear spins with Il=Iz=IB=% (forming an equilateral

triangle) and one 1“N spin with 5:1. The complete spin Hamiltonian H

. . 18
is given by:

3‘ ”Huozi Iiz“ ”unosfzij Aij‘li’ij'3lizljz)*zi 31(‘211252)*HQ

(1)

 

where H0 is the magnetic field along the Z-axis.‘7H and ‘YN are the

1H and 1“N gyromagnetic ratios. and HQ is the 1“N quadrupolar

Hamiltonian. The first term is the proton Zeeman term with summation

over i = 1.2.3. The second term is the 1“N Zeeman term. The third

term is the 1H-lH dipolar coupling where zij denotes summation

over ij = 12.23.31. If H. Ho and 1' are expressed in units of Hz.

Gauss. and Hz/Gauss respectively. then we have

- 2 -3 2
A13 "'11 hrij (3cos Vin-1V2 (2)
for pairs of like spins. where rij is the 1H-1H internuclear distance.
h is Planck's constant and tkij is the angle between the internuclear

vector Sij and the magnetic field Ho. The fourth term is the luN-lfl

dipolar coupling:

.6

Bj =‘1H7NhrNj'3(3cosz‘PNj-1)/2 (3)

where rNj is the 1“Isl-1H internuclear distance and ‘pNj is the angle

between the internuclear vector 5N3 and the magnetic field Ho. The
last term. Hq. is the 1“N'quadrupolar Hamiltonian.

If the relatively small 1“'1‘! nuclear magnetic moment and HQ are
temporarily omitted. then the NH3 molecule may be regarded as three
interacting spin é nuclei at the vertices of an equilateral triangle.
The theoretical NMR spectra of these triangles have originally been
discussed by Andrew and Bersohn.19 This treatment has been generalized
to a two-dimensional GIC lattice by Miller etal.1u with necessary
modifications. In the GIC lattice. a spherical coordinate system
may be used where the polar axis (the z-axis) is chosen to be the
crystallographic c-axis of the GIC. The instantaneous orientation

of the CB-axis of a particular NH3 molecule may be denoted by the

polar and azimuthal angles. 0 and (t. in the spherical coordinate

 

 

system as shown in Fig. 7. For the entire GIC system with many NH3
molecules intercalated into the graphite galleries. it is expected

that 0 will occupy only a relatively narrow range of angles because

of the constraints of the gallery height. 0n the other hand. several
angles of ¢' distributed evenly over the range 0 to 2n- are accessible
to an intercalated NH3 molecule. If the NH3 molecules are stationary.
then there would be wide distributions in the angles 933 and ‘PNj

for different NH3 molecules when H0 is at angle a! with respect to

the GIC c-axis. Thus the 1H NMR spectrum will resemble a typical
powder pattern. Examples of these powderlike spectra have been given
by Miller etal.11+ The experimentally observed narrow NMR spectral

lines and simple features (shown in Figs. 3. h and 6) imply considerable
motional averaging (with correlation times of less than 10'5 sec.)

due to: (a) fast rotation of NH3 molecules about the C3 molecular
symmetry axis (equivalence of protons). and (b) fast reorientations

of the molecular C3-axes about the GIC c-axis (fast averaging over the
angle ‘¢). These rapid motional averagings imply that A12=A23=A31=A
and B1=B2=B3=B in equation (1). These equalities simplify the calcu-
lations considerably. We may couple the three proton spins of the

NH3 molecule into the total spin. I=I1+I +1 and Iz=Ilz+Izz+I3z.

m2 .3
Thus we have:

213 $1235 = (23.1. ' zi £121.in . (4)
Zij I121.12 = (122 '21 IiZZ)/2 (5)

and their eigenvalues are [I(I+1)/2]-(9/8) and (Izg/2)-(3/8) since

Ii=% and Iiz = 1%. Thus the energy level for the spin Hamiltonian H

of equation (1) is:

2 ,
E(I.IZ.SZ) =YHH°IZ+(A/2)[I(I+1)-3Iz 1+ flNHOSZ - 231232 (o)

- 3 -

 

 

In equation (6). we have temporarily neglected the effect of HQ'

We also note that HQ may also contribute to spectral line broadening.

These effects will be considered later.

The energy levels. as given by equation (6). are shown schema-

tically (not to scale) in Fig. 8 as HZ+HD (Combined nuclear Zeeman

14

and dipolar effects while N quadrupolar effects are omitted). When_

the 14” spin 5 is omitted. the couplings of three spin 1 nuclei would 1r!

2
result in a total spin of I=3/2 (non-degenerate) and I=l/2 (doubly
degenerate). For I=3/2. the energy levels are at (37RH0/2)-(3A/2). w
(VHHO/2)+(3A/2). (~7HHo/2)+(3A/2) and (~31HHO/2)-(3A/2) for IZ=3/2. '

1/2. -1/2 and -3/2. The differences between the adjacent energy

 

levels are vHHo-BA.'7HHO and 7HH0+3A. For I=1/2. the energy levels
are at VHHo/Z and -1HHo/2 for Iz=1/2 and -1/2. TheJdifference is

VHHO. The theoretical NMR spectrum is a three spectral line pattern

at resonance frequencies of‘VHHo-jA.7HHo and 7HH0+3A with 1:2:1

intensity ratio: That is. we have one central component (at frequency

YHHO) and two satellites with frequency shifts of QHH= 23A from the
center. where the subscript HH emphasizes that the frequency shift
(the frequency difference between the central component and one of

the satellite components) comes from 1H-1H dipolar coupling. When we

include the 1“N spin S. then the NMR spectra in the vicinity of the

frequency YHHo would come from transitions between E(I.I
E(I.I

Z.Sz) and
211.82) where the energy levels are given by equation (6) since
the frequency range of ouquMR spectra are much less than VNHO
(~90 KHz vs. ~# MHz) and there would be no flips of 14W spins. There
are three triplets. the central triplet (denoted as 4-6 in spectra A
of Fig. 8) and two satellite triplets (1-3 and 7-9 in spectra A of
Fig. 8). The frequency shifts of the satellite triplets are DHH= 13A

from the central triplet due to the 1H-IH dipolar coupling. Within

- 9 -

each triplet. the differences are DNH= :ZB between adjacent resonance

lines due to the 1H-iuN dipolar coupling. The difference between the

expressions for DHH and DNH (23A vs. 12B) is due to the well-known ‘
factor of 3/2 between like and unlike spin pairs. This theoretical

spectrum is shown as ”A" in the insert of Fig. 8 where the effect

of HQ has been neglected. This theoretical NMR spectrum is in

qualitative agreement with the experimental spectra in Figs. 3.“ and 6.
Certain discrepancies.such as the uneven spacings of lines u-6 in

Fig. 4 when at is away from 00 or 90°. will be shown later as due to ‘

 

the effects of Hq. The central component (near the frequency VHHO)
may also be more intense in the experimental spectrum than predicted

because of the presence of liquid or adsorbed NH3 in the sample tube

in addition to the GIC.

We will now calculate the motionally averaged values of A and B.
We will begin with the latter. A Cartesian coordinate system x.y.z
may be fixed in the GIC crystal with unit vectors i.j.k. The z-axis
is parallel to the crystallographic c-axis. The magnetic field H0

is in the xz-plane and at angle at away from the z-axis. hence its

A

unit vector H0 is:
A A A

Ho=kcosu+isinot (7)

This Cartesian coordinate system may be transformed into the spherical

coordinate system where the unit vectors are:

A A. O A. O C A
er = 1 Sin 9 cos4>+ 3 Sin 9 Sin42+ k cos 0

A A A

30 = i cos 0 cos¢+ j cos 0 sin4>- k sin 0 (8)
A A

34’ = -i sin¢ + j cos¢

The instantaneous orientation of the NH3 molecular C3-axis is given

by the angles 0 and #> as shown in Fig. 7. The unit vector 3r is

- 1o -

parallel to the CB-axis. while the two unit vectors 3; and a; are

perpendicular to the CB-axis. The N-H internuclear vector;Nj is

at a fixed angle 17 from the CB-axis as shown in Fig. 7. For the
A

unit vector rNj. its component parallel to the CB-axis is cos 7

while the perpendicular component is sin‘q. If the perpendicular

component is at angle 6 from the unit vector 39. then we have:

A

A A A . .
rNj - ercoswz+ (eocosfi +e¢s1np)s1n'7 (9)
For any instantaneous orientation of £Nj' we have:

A A

cos\PNj = rNj-Ho (10)

We may substitute equation (8) into (9) to express 9N. in terms of

AAA
i.j.k and then take the scalar product with equation (7).

.9

cos ‘PNj = cosat (cos-7 cos 0 - sin? sin 0 cosfl)

+ simdcosqsinecoscf +sin11cosccosfcos¢ -sinqsinfisin¢>) (11)
We will now take the motional average of the (3cosz‘PNj-1)/2 term.
The average is over both p=0 to 2n' (rapid reorientations of NH3
molecules about their molecular CB-axis) and ¢=0 to 27r (rapid
precessions of molecular C3-axis about the c-axis of the GIC). The
only non-zero averages are (coszfi) = (sinzp) = (cosz¢>= (sin2¢>> =1/2.
while other averages. such as (cosP) .(cospsin P>' etc. are all

zero. After averaging over f and ¢ . the result is:
((3cos2\)Nj-1V2) =[(3cos29-1)/2][(3cosz7-1)/2][(3coszo(-l)/2] (12)
From equation (3). the motionally averaged value of B is:

B: 7H7NhrNj'3 [(3coszc-1)/2][(3coszoz-1)/2]f(3coszac-1)/2] (13)

It is necessary to average over the probability distribution over
the angle 0 between the NH3 molecular CB-axis and the TGIC c-axis.
This probability function will be denoted by P(G). We may introduce

- 11 -

 

 

the order parameter S which is usually identified asll+

S = ((3coszo - 1)/2> (14)

In equation (14) and hereafter. the angular bracket will be used to

denote averaging over the probability distribution of 0:

1r
w'
(110)) = I f(0)P(0)sin0 d0 /J’ P(O)sin0 d0 (15)
O 0
where f(0) may be any function of 0. Thus B is given by:

B = wflthrNj'3s [(3cosz‘7 -1)/2] [(3coszd -1)/2] (16)

For random distributions of the angle 0 (P is a constant and is
independent of 0). then 8:0 and the NMR spectra would collapse to a
single resonance line. This is the case of totally isotropic motion.
However. the experimental result of three sets of triplets for the
TGIC indicates that S#0 and certain angles of 0 are preferred. That
is. the NH3 molecules are situated in a potential well and the angle

0 will vary over a limited range near the bottom of the potential well.

Since the 1H-lH internuclear vector 3.

13
NH3 molecular CB-axis. equation (16) may also be used for the

is perpendicular to the

motionally averaged value of A by setting ‘q=90° and by replacing

‘YN and rNj with “VH and rij' The result is:

A = (THZhrij-3/2)S[(3coszo( -1)/2] (17)
The frequency shifts of the satellite triplets are DHH=3A from the
central triplet due to the 1H-lH dipolar interaction. Using the
H-H distance of 1.624 A from the electron diffraction studies15 of

NH3 molecules in the gas phase. the absolute value of DHH in KHz is:
[13ml = 3IA| = 112.1 Isl

From Figs. b and 5 for KTGIC at room temperature and 60 MHz. it may

(3coszx-1)/2 (18)

 

be seen that the central lines of the triplets (lines 2.5.8) are

- 12 -

 

 

 

evenly spaced. thus either 0E5 or 458 may be identified with DHH‘
This is shown as the lower diagram of Fig. 9. The experimental data

(shown as crosses) clearly display the (3coszd -1)/2 angular depen-

dence and agrees well with the calculated curve from equation (18)

when we choose the order parameter to be [SI =0.hl.

The effect of HQ will now be included. This has no effect on

the H dipolar interaction and on DHH' However. it is now L4#

necessary to consider the effects of both the Zeeman and quadrupolar

interactions on the 1“N nucleus. These interactions will be denoted

. _ .4-
by HN and HQ respectively. where HN -'VNHOSZ. Because of the
combined effects of both HN and Hq. the 1“

 

N nuclear spin S is not

necessarily quantized along the magnetic field Ho (the Z-axis). '

In the crystal coordinate system (x.y.z) of the GIC. then HQ is
axially symmetric along the z-axis because of motional averaging.
The effective quadrupolar coupling constant will be denoted as

eque/h. The standard matrix20 for HQ with spin 5:1 in the principal

coordinate system is:

_ -1 o o
_ 2
MQ - (e gee/uh) o 2 o (19)
o o -1

where the eigenstates are for Sz=1.0 and -1. We have chosen H0

at angle at away from the z-axis in the xz-plane. Using the standard

matrices of Sz and Sx. the Zeeman matrix for HN is:

1 O O O 1 0
MN = (YNHOc) 0 0 ‘ 0 + (2'1/2ynHos) 1 0 1 (20)
0 0 -1 0 1

where cosd and sinot have been abbreviated as c and s.
A similarity transformation R-1MR will be used for the trans-

formation from the crystal coordinate system (x.y.z) to the magnetic

- 13 -

 

field coordinate system (X.Y.Z). The matrix R is chosen such that

R'IMNR is diagonal. Thus we get:

1+(A/2) (1-3c2) 3csA/‘21/2 -3$2/\/2
R’1(MN+MQ)R = (wNHo) 3csA/21/2 A(3c2-1) -3csA/21/2 (21)
—352A/2 -3cs):/21/2 -1+(A/2)(1-3c2)
where the quadrupolar/Zeeman interaction ratio A is defined by “—1
x = eque/(uwaon) <22)
1L: L“

and the eigenstates in (21) are the N spin functions quantized in

 

the direction of the magnetic field go (the Z-axis). These states

will be denoted as 43. 4b. and \P_1 where the subscripts are the

eigenvalues of 52'

We will now diagonalize the matrix given by equation (21). For
small )\ when the quadrupolar effect is weak as compared to the 1MN
Zeeman term. a perturbation calculation can be made to first order
in 1%. Because of the quadrupolar interaction. there is some mixing
among the eigenstates \Pl.\PO and £P_1. The perturbed wave functions

will be denoted by ‘21. Q0 and 'P-1 and are given by:

T1 = 441 +(3csx/21/2) 4’0 - (ash/4) {1
go = we -(BCSX/21/2)(‘("1 + 4’4) (23)
T4 =‘P-1 +(308A/21/2N’0 + (flak/“Ni

Their eigenvalues are given by the diagonal matrix elements of

equation (21). They will be denoted as 51. £0 and €_1.
For the resonance frequencies of the central triplet (lines
h.5.6) of the 1H NMR spectra. we will now consider the complete spin

Hamiltonian given by equation (1) except for the 1H-lH dipolar

-111-

 

interaction. Thus we will use the Hamiltonian
H =‘7HHOIz + WNHOSZ + HQ + H' (24)

1 1h

where H' is the H- N dipolar Hamiltonian. (In the absence of H

Q.
it is given by equations (6) and (16).

H' = -2BIZSZ = -2blz[Sz(3coszo( —1)/2] (25)

where b is a constant and is given by

b = yflthr j'35(3coszrl -1)/2 (26)

where S is the order parameter. In the presence of the 14N
in

quadrupolar interaction. the N spin may be quantized with

non-vanishing components away from the Z—direction. hence it is

necessary to use20

H. = "ZbIZS' (27)

where S' is defined by

S' = [82(3coszd -1)/2] + [SXcosa sinat /2] (28)

‘ .

The resonance frequencies for m=l.0 and -1 are given by

Jm = (12:1/2. 13m|HIIZ=1/2. gm) - (Iz=-1/2. fmlH|IZ=-1/2. SPm>
= [wane/2w 6.. -b<imls'lim>l {two/2mm +b<im\s'l an >]
eqnno - 2b{}m[s'|§m) (29)
Using in given by equation (23). we get
411 =‘1HHO a 2b[(3c082°‘ -1)/2] - g (30)

o + 2s (31)

where g is the extra shift of the NMR spectral lines due to the 1“N

quadrupolar coupling:

g = (9bk/4)sinzzat ' (32)

- 15 -

 

 

 

The frequencies J31 correspond to lines A and 6 in Figs. 4,5 and 8.
while the frequency J0 correspond to line 5.

The energy levels are shown schematically (not to scale) in
Fig. 8. where HD denotes the 1H-lH and the 1H-luN dipolar interactions

and HQ denotes the 1“N quadrupolar interactions. The theoretical 1

H
NMR spectra are shown in the insert. For spectrum A. the effect of
HQ is neglected. The spectral lines of the central triplet are
evenly spaced with A\745 “”756 = 2b(3coszo( -1)/2. This has been
denoted as DNH=ZB where B is given by equation (16) and the subscript
NH emphasizes that the splittings between adjacent spectral lines are
due to the 1H-luN dipolar interactions. In spectrum B. the effects
of HQ have been included by a perturbation calculation to first order
iJ:)A. We have found that spectral lines A and 6 have shifted by g
in the same direction while line 5 has shifted by 2g in the opposite
direction. We note that iJué is independent of g. hence we have

used Danaqué/Z to calculate DNH from the experimental data shown in
the top diagram of Fig. 5. The results are shown as the crosses in
the top diagram of Fig. 9. The (3coszot-1)/2 angular dependence
(shown as the solid curve) may be clearly seen. We also note that HQ

1H-IH dipolar interactions. For both spectra

has no effect on the
A and B of Fig. 8. we may identify either AJZS or; J58 with DHH=3A

given by equation (17).
From the geometry of the NH3 molecule. it may be seen that

= 31/2r

rij stin‘q. From A and B given by equations (17) and (16).

we note that the ratio DNH/DHH = (2B)/(3A) depends on the angle 7
only:

DNH/DHH = 2(31/2)(YN/1H)(1-3cosz'7 )sin3'7 (33)

From Fig. 9. the experimental ratio is DNH/DHH = 0.116 which gives

-16-

 

$7268.10. This is in very good agreement with the value of q7=68.u°
obtained by electron diffraction studies of NH3 in the gas phase.15
From equations (30) and (31). the difference .
g = (v56 - “5V6 = (2.75 - .7“ - ~76)/6 (31+)

should be proportional to A with the angular dependence of the form

of sin22ac. We have used equation (3“) to calculate g from the
experimental data shown in the top diagram of Fig. 5. The results

are shown as the crosses in the upper diagram of Fig. 10. The

sin22« angular dependence may be clearly seen. The experimental

data are in good agreement with the theoretical curve calculated

from equation (32) using 9bA/h=0.195 KHz which gives 1A=0.087.

From the proton resonance frequency of 59.75 MHz. we get ‘yNHO=#.3 MHz.
From equation (22). we have leque/h‘ = 1.50 MHz. ‘This effective
coupling constant is related to the actual coupling constant eZqQ/h

of the NH3 molecule by the order parameter S:

2 2
le qu/hl = Isl le qQ/hl (35)
Using |s| =o.u1, we get Iequ/h) =3.7 MHz. This indirectly deter-
mined 1“N quadrupolar coupling constant is intermediate between the

22

gaseous NH3 value of #.1 MHz and the solid NH value23 of 3.2 MHz.

3
This result for the intercalated NH3 is consistent with the relatively
weak chemical binding of NH3 molecules in the galleries of the T010.
From equations (30) and (31). the average frequency
‘71 = (‘71. + .75 + 6V3 (36)
of the central triplet is independent of both 1u’N-lH dipolar inter-

action and 14N quadrupolar effects. The experimental JA vs.cKl

curve in the lower diagram of Fig. 10 shows the residual chemical

shift effects:

JA = JAzcoszd + VAxsinth (37)

- 17 -

 

 

 

For the solid curve in the lower diagram of Fig. 10. we have chosen \
sz=0.01 and ka=-0.62 KHz. These frequencies give a chemical
shift anisotropy of Sz' 8&210.7 p.p.m. for protons in the KTGIC.
In summary. it may be seen that for the central triplet, we
have transformed V . J3. J6 into DNH=(JQ"%)/2’ g=(2J5-JL-J%)/6

and Jk=(¢h*~g+0%)/3. These parameters are related to the 1H-luN
14

dipolar interaction. the N quadrupolar effect and the 1H chemical

shift. These parameters also show different angular dependences on cg.
From the room temperature KTGIC spectra shown in Fig. A. it may

be seen that there are considerable broadenings of the outer triplets

 

(spectral lines 1-3 and 7—9) when the orientations are away from
«:00 or 90°. This is due to the slight misalignment of the c-axes

of the various crystallites within the TGIC. This angle of misalign-
ment will be denoted as (E. For equation (18). the actual range of

angle is «if when we consider the individual crystallites. The

range of DHH (in KHz) is given by
DHH = 17.2 {[3cosz(a<:§)-1]/2}

=17.2[(3coszc( -1)/2] 1 (255in2u )§ +°°° (38)
where E is expressed in radians and we have used the experimental
value |s|=o.ufror the TGIC. The last term is the extra broadening
due to the crystal misalignment. This broadening increases rapidly
when 0( is moved away from either 00 or 90°. The spectra in Fig. 4
is consistent with our previous estimate of {IVO.05 radians or 3°
from the X-ray rocking curve shown in Fig. 1.

The frequency dependence of the 1H NMR spectra at room tempera-
ture and CX=90° may be seen by the comparison between Fig. A and
Fig. 6. These spectra are taken at 60 MHz and 300 MHz respectively.
The spectral line positions and the values of DHH and D

NH are
quite similar for these two frequencies. For the 300 MHz spectrum.

-18-

1::

the N quadrupolar interaction is overwhelmed by the Zeeman inter-

actions. Except for the partial obscuring of the central line by
adsorbed and gaseous NHB' there is good agreement between the
experimental spectral line intensities and the theoretical
l:1:1:2:2:2:1:1:1 ratio.

Since S ¢ 0. there are potential barriers for the NH3 molecules'
in the galleries of the TGIC. We have studied the temperature
dependence of the 1H NMR spectra in order to determine these
potential barriers. In Fig. 11. the 60 MHz spectra of KTGIC are
shown at various temperatures. We have chosen oc=0o in order to
minimize the spectral line broadening. We have identified DHH as
the frequency difference between the central components of the
central triplet and the satellite triplet. Equation'(18) (with
d :00) is then used to calculate ISI. Very similar results have

also been obtained for the Rb- and Cs-compounds. The experimental

values of [8! at various temperatures have been summarized in

Fig. 12.

1

From the H NMR spectra of KTGIC at 66 MHz and u=o° for

various temperatures shown in Fig. 11. the relaxation effects due
to the 14N quadrupolar interaction may also be inferred. For the
central triplet (spectral lines A to 6 in the notation of Fig. 8).
it may be seen that the line width (LW) at half-maximum is considerably
larger for the satellites (lines a and 6) as compared to the central
peak (line 5). This difference between the satellite and central
peak LW will be denoted as .64. This extra broadening comes from
motional averaging and may be used to deduce the correlation times 7;
for the motions of NH3 through the GIC gallery. For small 7;. then
.AJ (in Hz) is given by:18

wAJ =O'2 Tc (39)

- 19 -

 

 

i.

i‘

 

where a’ is the frequency range (in radians/sec) over which the

motional averaging occurs. The correlation times can usually be

expressed in the Arrhenius form. ‘rc =‘ter/RT where U is the
activation energy per mole. R is the gas constant. T is the

temperature and Tb is the frequency factor. Hence we get:

ln AJ = in(a'2'ro/1r) + (U/RT) (no)

I: -
" I

In Fig. 13. we have plotted lnAJ vs. 1/T using the data from Fig.11.
We found U=3.3 kcal/mole or 0.14 eV and (7216=1.4. Usually. we have

T°~10'1u sec for ammonium compoundszu'zs. hence we have a’/21r~2 MHz ’

 

which is of the same order of magnitude as the 1“N quadrupolar

coupling constant in KTGIC.

The 14N quadrupolar relaxation may be responsible for the

extra LW of lines 4.6 as compared to line 5 and also for extra LW of
lines 7.9 as compared to line'8.' The correlation times “To may be
related to the diffusion of NH3 molecules in the graphite gallery.
The diffusion is both the rotational and translational type. where
the angle ¢ may change by 60° or 120° on jumping from one site to
another site. Because of the threefold symmetry of the NH3 molecule.
rotations about the molecular 03axes do not contribute to the LW.

We also note that the characteristics of the 1“N quadrupolar relaxa-
tion (sharp lines 5 and 8 but broader lines 4.6.7 and 9) are quite
different from the misalignment broadening (lines 4.5 and 6 are quite
sharp but lines 7.8 and 9 are much broader) given by equation (38)

for at away from 0° or 90°. In Fig. 11. spectra are taken at ot=0°

in order to minimize the misalignment broadening.

- 20 -

 

;IVu SPECTRAL TEMPERATURE DEPENDENCE AND POTENTIAL BARRIERS

From theIH NMR spectra. we have deduced the absolute values (but

not the signs) of the order parameter S at various temperatures. The

 

results are shown in Fig. 12. For the motion of NH3 in a potential
energy well defined by the potential function V. then 8 may be
calculated from equations (14) and (15) by using P = e'v/RT.

Because of the layered structure of the TGIC and the symmetry between

+c and -c directions of the TGIC lattice. we can write a Fourier

expansion of V.

 

V(0) = V2cos 20 + Vucos 49 + °°° (41)

_ where V2. V4. etc. are constants. The first term is expected to be
dominant. In the following. we will use V = Vzcos 2G and consider
(A) the case of V2>0 (potential minimum is at 9:909) and 8(0.
and (B) the case of V2<0 (potential minimum is at 0:00) and S>0.
(A)V2>0.S<0.

Except for a constant. we may write V=2V2c0520. By introducing

the new variable u=cos 0. then for f(0)=coszo. equation (15) may be

written as:
I 2 l 2
(00529) =J. u2e-au du /'J. e-au du (42)
-: -I

where a=2V2/RT. For a>)1. then the integration limits may be
changed from (-1. 1) to (-OO.°0). Thus we get (c0529) = (2a)'1 and

[SI = -s = % - % (c0520) =‘% - %%§ (43)

The next term in the expansion is 3(wa)-1/2e-a. which is very small

for a>)1.
The potential minimum is now at 0:00. For the expansion about

this minimum. we have defined u=sin 0 and V: Zlvzlsinze. By using

- 21 -

 

the Taylor's expansion d0 = (1+éu2+"')du. then we get

' 2 I 2
{sin20> = L e-au (u3+ Jg.‘u5<I~---)du / f0 e-au (u+ §u3+---)du (44)

 

where a=2lV2I/RT is chosen to be positive. For a>)1. the integration
limits may be changed from (0.1) to (0.00). Thus we get:

‘8‘ = s = 1 - % (sin20> = 1 - £I§2T (45)

The next term in the expansion is -3/(4a2). which is very small for

a>)1.

 

For TGIC. the experimental value of [S] is 0.41 at room tempera- 1
ture (3000K). For case A with S<:0. the theoretical curve from
equation (43) is shown as the solid line. From the room.temperature
value of ‘8‘. we have found that V2=2.5 Kcal/mole or 0.11 eV. For
case B with S?>0. the theoretical curve from equation (45) is shown
as the dashed line. From the room temperature value of '8‘. we have
found that -v2 = [val = 0.76 Kcal/mole or 0.033 eV. There is a
factor of 7 difference between the slopes of these two theoretical
lines. The experimental data are consistent with the choice of S<10
(case A). thus the molecular CB-axes of NH3 are nearly perpendicular
to the crystallographic c-axis of the TGIC. The potential barrier
height (the difference between the maximum and the minimum values

of V) is 2V2 = 5 Kcal/mole or 0.22 eV.

- 22 -

V. DISCUSSION

In our present work. 1H NMR spectroscopy has been used to study
the first stage TGIC's. M(NH3)XC2u. where xrv4 and M denotes K. Rb
or Cs. The results of these three TGIC's are quite similar to each
other and are consistent with a rather mobile (liquid-like) intercalant
layer of planar M(NH3)Z ions in between the carbon layers. These
ions are the two-dimensional analogues of the M(NH3)2 ions commonly
observed in alkali metal-liquid ammonia solutions.12 This structure
of TGIC agrees well with the recent X-ray diffraction data.26’27 For
rigid M(NH3)Z intercalants. the order parameter S is -O.5 since 9:900.

Experimentally. we have observed S=-0.41 at room temperature due to

the thermal vibrations of NH3 molecules near the minimum of the
potential barrier. The barrier height is rvo.2 eV. ”

The charge transfers in these TGIC's have been studied by 13C
NMR spectroscopy.17 The approximate reaction for the formation of
the TGIC by the co-intercalation of NH3 is:

M+1 2?-1 + “NH3 ___* [M(NH3)4]+O'8uCZu-o‘84
As expected. there is partial solvation of the electronic charge on
the carbon layers by the intercalated NHB' Nevertheless. this solvation
by NH3 is relatively weak. For example. when the TGIC is in contact
with liquid NHB' the liquid phase remains clear without the highly
characteristic colorations of alkali metal-ammonia solutions. While
alkali metal ions in the TGIC may be fluidized by NH3. very little
metal (if any) is extracted by the liquid NH3° This relatively weak
solvation by.NH3 may be contrasted with the much stronger action of
water which would violently decompose the TGIC. This relatively weak

solvation by NH3 is also consistent with the indirectly observed IQN

quadrupolar coupling constant of TGIC (3.7 MHz) which is intermediate

- 23 -

 

between the gaseous (4.1 MHz) and solid NH3 (3.2 MHz) values.

1

In conclusion. the H and 13C NMR spectral studies have provided

answers to the two fundamental questions about the TGIC: (a)what are
the NH3 molecular geometries. orientations and motions in the graphite
galleries. and (b) whether the co-intercalated NH3 molecules are only

neutral "spacers" or compete with the carbon layers for the electrons-

given up by the alkali atoms.

VI . ACKNOWLEDGMENTS
The partial financial supports of National Research Council
Fellowship for R. M. F. at Naval Research Laboratory. of National
Aeronautics and Space Administration grant NAG-5-156 at Howard
University. and of National Science Foundation grant DMR82-11554 at

Michigan State University are gratefully acknowledged.

-21.-

 

 

 

REFERENCES

1. M. S. Dresselhaus and G. Dresselhaus. Adv. Phys. 39. 139 (1981).

2. s. A. Solin. Adv. Chem. Phys. 33. 455 (1982).

3. M. S. Whittingham and A. J. Jacobson. Intercalation Chemistry.

(Academic Press. New York. 1982).

L. Mattix. J. Milliken. H. A. Resing. J. Mintmire and D. C.

Weber. Synth. Metals 10. 193 (1985).

5. A. P. Legrand. L. Facchini. D. Bonnin. J. Bouat. M. F. Quinton
and F. Beguin. Synth. Metals 13. 175 (1985).

6. A. L. Blumenfeld. Y. V. Isaev and Y. N. Novikov. Synth. Metals
12: 193 (1985)-

7. W. Rudorff and E. Schultze, Angew. Chem. 66. 305 (1954).

8. B. R. York and S. A. Solin. Phys. Rev. B 31. 8206 (1985).

9. B. R. York. S. K. Hark and S. A. Solin. Solid State Commun.
52- 595 (1984)-

10. S. A. Solin. Y. B. Fan and X. W. Qian, Synth. Metals 13. 181
(1985).

11. X. W. Qian, D. R. Stump. B. R. York and S. A. Solin. Phys. Rev.
Lett. 54. 1271 (1985).

12. J. C. Thompson. Electrons in Liquid Ammonia (Clarendon Press.

Oxford. 1976).

13. J. Jortner and N. R. Kestner. Electrons in Fluids (Springer-Verlag.

Berlin. 1973).

14. C. R. Miller. M. J. Moran. H. A. Resing and T. Tsang. Langmuir
Z. 194 (1986)-

15. M. T. Weiss and M. W. P. Strandberg. Phys. Rev. 83. 567 (1951).
16. T. Tsang and H. A. Resing. Solid State Commun. 53. 39 (1985).

- 25 -

 

 

17.
18.

19.
20.
21.

22.
23.
24.
25.

26.
2?.

Manuscript in preparation.

C. P. Slichter. Principles of Magnetic Resonance (Springer—Verlag.
Berlin. 1978).

E. R. Andrew and Bersohn. J. Chem. Phys. 18. 159 (1950).

M. H. Cohen and F. Reif. Solid State Physics 5. 321 (1957).

D. L. Vanderhart. H. S. Gutowsky and T. C. Farrar. J. Amer. Chem.
Soc. 82. 5056 (1967).

G. Hermann. J. Chem. Phys. 32. 875 (1958).

S. S. Lehrer and C. T. O'Konski. J. Chem. Phys. 43. 1941 (1965).
D. E. O'Reilly and T. Tsang. J. Chem. Phys. 46. 1291 (1967).

T. Tsang. T. C. Farrar and J. J. Rush. J. Chem. Phys. 42. 4403
(1968).

X. W. Qian, D. R. Stump and S. A. Solin. PMs. Rev. B33. 5756 (1986).

H. Zabel, A. Mageri. A. J. Dianoux and J. J. Rush. Phys. Rev.
Lett. 59, 2094 (1983).

- 25 -

 

 

 

Fig.

Fig.

Fig.

Fig.

Fig.

_Fig.

Fig.

Fig.

FIGURE; CAPTIONS
1. Apparatus for sample preparation: V. total volume of specimen
chamber: V'. final sample volume; 5. sealing point; T and T'.

teflon stopcocks: A. NH3 resorvoir: B. the GIC sample; C.

connection to vacuum line.

2. X-ray rocking curve for the (002) reflection of K(NH3)4.3C2u
using M01011.2 radiation (0.71 A wave length): X-ray intensity
vs. angle C) between X-ray beam and GIC surface.

3. Room temperature 1H NMR spectra at 60 MHz and ¢X=0° for
K(NH3)u.3C2u. Rb(NH3)u.102u and Cs(NH3)3.7czu. Only six
resonance lines (out of 9) are shown.

4. 1H NMR spectra of K(NH3)4.3C2u at 60 MHz and room temperature
vs. angle at between magnetic field Ho and the crystallographic
c-axis of GIC; The resonance lines are numbered 1 to 9 for the
d:=0° spectrum. Low frequency is toward right. Arrow indicates
the position of 1H signal from adsorbed and gaseous NH}.
5. Spectral line positions Jm in KHz vs. angle1a(from spectra

of Fig. 4). The positions of lines 4.5 and 6(the central triplet)

are plotted on an expanded scale in the upper diagram.

6. 1H NMR spectrum of K(NH3)4.302u at 300 MHz. room temperature
and u =90°.

7. Geometry of NH3 molecule intercalated between two carbon planes.
Two of the hydrogen atoms are denoted by i and j. C3 is the .

NH3 molecular symmetry axis. H0 is the direction of the magnetic

field. N is the nitrogen atom. The z-axis is the crystallographic

c-axis of the GIC.
8. Energy levels due to Hz. HD and HQ (Zeeman. dipolar and 1("N
quadrupolar Hamiltonians). Theoretical NMR spectra are shown

in the insert: (A) HQ is neglected; (B) HQ is included.

- 27 -

 

Fig- 9. DHH and DNH in KHz vs. angle “w Crosses are based on the
experimental data for KTGIC at room temperature and 60 MHz from
Fig. 5. The solid theoretical curves are proportional to
(3cosza-1)/2.

Fig. 10. Upper diagram: g = (295-94-J6)/6 in KHz vs. N. Crosses

 

are based on experimental data in Fig. 5 for KTGIC at room
temperature and 60 MHz. The solid line is the theoretical
curve g=0.1955in220< . Lower diagram: JA=(‘74+‘75+J6)/3 in KHz

vs. (1. Crosses are based on experimental data in Fig. 5.

 

The solid line is the theoretical curve from equation (37).
Fig. 11. 1H NMR spectra at 60 MHz and !1=O° for K(NH3)u.3C2u at
various temperatures (T in OC). Only spectral lines 4-9
(in the notation of Fig. 8) are shown. ‘
Fig. 12. Absolute value '5' of the order parameter vs. temperature
T in OK. The crosses. triangles and circles are for the
K-. Rb- and Cs-compounds respectively. The solid line is
calculated from equation (43) for S<TO. The dashed line is
calculated from equation (45) for S>O.

Fig. 13. lnAJ vs. 1000/T (in °k'1) for the KTGIC at 60 MHz and d=0°.

_ 28 _

 

 

 

 

 

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