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Graphite intercalation compounds are a new class of electronic materials that are classified as graphite-based host gues

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Graphite Intercalation Compounds and Applications
 9780195351842, 9780195128277

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Graphite Intercalation Compounds and Applications

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Graphite Intercalation Compounds and Applications

Toshiaki Enoki Masatsugu Suzuki Morinobu Endo

OXFORD UNIVERSITY PRESS

2003

OXFORD UNIVERSITY PRESS

Oxford New York Auckland Bangkok Buenos Aires Cape Town Chennai Dar es Salaam Delhi Hong Kong Istanbul Karachi Kolkata Kuala Lumpur Madrid Melbourne Mexico City Mumbai Nairobi Sao Paulo Shanghai Taipei Tokyo Toronto

Copyright © 2003 by Oxford University Press, Inc. Published by Oxford University Press, Inc. 198 Madison Avenue, New York. New York, 10016 www.oup.com Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Enoki, Toshiaki. Graphite intercalation compounds and applications / Toshiaki Enoki, Masatsugu Suzuki. Morinobu Endo p. cm. Includes bibliographical references and index. ISBN 0-19-512827-3 1. Graphite. 2. Clathrate compounds. I. Suzuki. Masatsugu. II. Endo. Morinobu. III. Title QD474.E56 2003 541.2'2—dc21 2002074850

9 8 7 6 5 4 3 2 1 Printed in the United States of America on acid-free paper

Preface

Graphite intercalation compounds (GICs) are typical layered compounds featuring graphite-based host-guest systems. Since the 1980s they have been a target of intensive studies in chemistry, physics, materials science, and electronic and electrical engineering because of novel features in their structures and electronic properties. Their extremely high electrical conductivity (the value almost reaches that of copper) has attracted people who are interested in applications of GICs to electrical engineering. Physicists have been interested in the novel features of two-dimensional electronic structures in which superconductivity is occasionally present. GICs have provided typical examples of twodimensional magnets, which contribute to the understanding of low-dimensional magnetic systems. Host-guest structures of GICs featuring in-plane guest superstructures and a unique stacking manner (called staging) have been an important issue not only in structural chemistry but also in phase transition phenomena in statistical physics. Catalytic and gas adsorption activities, which have features considerably different from those of other materials such as zeolite and activated carbons, are of great interest in chemistry. From an application viewpoint, GICs are important building blocks of batteries. In current development of lithium ion secondary batteries, not only actual materials but also a basic knowledge of GICs are indispensable. Since the first discovery, in 1841, of potassium GICs, the efforts of chemists have produced hundreds of GICs with a large variety of intercalate species, donors, and acceptors. Even now, new compounds have been successively produced. The large family of GICs has been providing essential materials in chemistry, physics, and applications as mentioned above.

vi

Preface

The discoveries of fullerenes and carbon nanotubes since 1985 have opened a new aspect in carbon science and stimulated surrounding areas involving nanomaterials science. In understanding the properties of these newcomers to the carbon family, knowledge accumulated in the study of GICs has been strongly contributing as an indispensable component. So far there have been several review articles on GICs. Comprehensive reviews were provided by Herold (1979) and by Dresselhaus and Dresselhaus (1981), and books titled Graphite Intercalation Compounds I and II were edited by Zabel and Solin (1990, 1992). As far as the authors know, there have been no major comprehensive reviews since 1992, in spite of recent progress in research on the chemistry and physics of GICs. This is the impetus for writing a book that features current developments in GICs. Recently developed areas of carbon science and technology, such as the Li ion battery, fullerenes, carbon nanotubes and related materials, have been requiring comprehensive scientific concepts for understanding the new phenomena and achieving a technical breakthrough, in which GIC science has an important potential to contribute to developing such frontiers. This book has been written for those who want to study the chemistry, physics, and applications of GICs. It is appropriate also as a textbook for graduate students in chemistry, physics, materials science, and electrical engineering. We discuss comprehensively a wide range of issues extending from chemistry and physics to applications in relation to GICs. We cover current developments in GIC studies, part of which is relevant to the areas of lithium batteries, fullerenes, and carbon nanotubes. We are convinced of the importance of this book as a resource of comprehensive knowledge related to GICs and also to expanding related areas. The present authors are all Japanese. In Japan a number of researchers in the fields of chemistry, physics, and applied science have studied GICs since the mid1970s. We believe that much pioneering work in GICs has been done by Japanese chemists and physicists. Despite their contributions, unfortunately there has been only one progress report (Tanuma and Kamimura, 1985) on the physics of GICs. One of the authors (T. E.) has been involved in research on the physical chemistry of GICs since the beginning of the 1980s, being based at the Institute of Molecular Science, Okazaki, Japan. In collaboration with Professors Hiroo Inokuchi, Mizuka Sano, and Seiichi Miyajima, he has discovered novel electronic properties of hydrogenated alkali metal GICs in which a two-dimensional metallic hydrogen layer is accommodated. In 1984, he stayed at the Massachusetts Institute of Technology to collaborate with Professor Mildred S. Dresselhaus and Dr Gene Dresselhaus. This collaboration led to his extending his interests from ordinary GICs to unconventional intercalation systems with novel intercalates and host carbons such as activated carbon fibers. Since 1987, at the Tokyo Institute of Technology, he has been interested in physical properties of intercalation systems in nano-sized carbon materials. In 1999, he chaired the 10th International Symposium on Intercalation Compounds held in Okazaki, Japan, in collaboration with M. E. as vice-chairman. M. S. joined in the Special Distinguished Research Project: The Study of Graphite Intercalation Compounds (principal investigators Professors Sei-ichi

Preface

vii

Tanuma and Hiroshi Kamimura), which was supported by a grant-in-aid from the Ministry of Education, Science, and Culture from April 1981 to March 1983. Since then his interest has been focused on the physical properties, in particular, various kinds of magnetic and structural phase transitions in GICs. In 1984-1985 he stayed at the University of Illinois at Urbana-Champaign and collaborated with Professor Harmut Zabel on the discommensuration domain structure of high-stage alkali metal GICs, the structure of graphite bi-intercalation compounds, and magnetic neutron scattering of stage-2 CoCl2 GIC. Since 1986, at the Physics Department, State University of New York at Binghamton, he has been studying the spin frustration effects occurring in GICs such as random mixture GICs. M. E. joined the GIC research field in 1977, working on graphite fiber-based materials from the application point of view. He has developed specific carbon fibers, vapor-grown carbon fibers (VGCF), which are obtained by hydrocarbon pyrolysis using the catalytic effect of ultra-fine metal particles as small as 100 A. He has also studied mesophase pitch-based carbon fibers. He has used various kinds of carbon and graphite fibers to form GIC and evaluated their electronic and electric properties for applications. This background has contributed to the development of a new type of secondary battery, the Li ion secondary battery, and he has established some promising anode materials of carbon, carbon fibers, and VGCF for a practical commercial cell. M. E. thinks that the Li ion battery should be developed on the basis of established GIC science. He is also studying carbon nanotubes based on the VGCF technique, called pyrolytic carbon nanotubes. He organizes the research projects Carbon Alloy (With Prof. Ei-ich Yasuda) and Nanocarbon for Energy Storage Applications (JSPS, Research for Future Program). The authors would like to thank all those who have contributed to the subject matters of this book: in particular (in alphabetical order), Prof. Noboru Akuzawa, Prof. Mildred S. Dresselhaus, Dr Gene Dresselhaus, Prof. Peter C. Eklund, Prof. Yasuo Endoh, Dr Nicole Grobert, Dr Takuya Hayashi, Prof. Hitoshi Homma, Dr Seong Hwa Hong, Prof, (the late) Hironobu Ikeda, Prof. Michio Inagaki, Prof. Hiroo Inokuchi, Prof. Hiroshi Kamimura, Prof. Hikaru Kawamura, Dr Chan Kim, Dr Yoong Ahm Kim, Prof. H. W. Kroto, Dr Keiko Matsubara, Prof. Seiichi Miyajima, Prof. Motohiro Matsuura, Prof. Naoto Metoki, Prof. Simon C. Moss, Dr Youichi Murakami, Prof. Tsuyosi Nakajima, Dr Dan A. Neumann, Prof. Hironori Nishihara, Prof. Ryusuke Nishitani, Dr Nicholas Rosov, Prof. Mizuka Sano, Prof. Hirohiko Sato, Prof. Ralph Setton, Prof. Hiroyuki Shiba, Prof. Hiroyoshi Suematsu, Prof. Ko Sugihara, Dr Itsuko S. Suzuki, Prof. Youichi Takahashi, Prof. Seiichi Tanuma, Prof. Mauricio Terrenes, Prof. Hidekazu Touhara, Prof. Noboru Wada, Prof. Nobuatu Watanabe, Prof. M. Stanley Whittingham, Dr David G. Wiesler, Prof. Yasusada Yamada, Prof. Ei-ichi Yasuda, and Prof. Hartmut Zabel. We are also grateful to Dr Itsuko S. Suzuki, Ms Tomoko Kuroiwa, Mr Toshiaki Kasai, and Mrs Chie Aoki for their help in preparing some of the manuscripts and figures. We would like to express our gratitude to the publishers for their help in many ways.

vi ii

Preface

References Herold, A. In Physics and Chemistry of Materials with Layered Structures, Vol. 6; Levy, F. Ed.; Reidel: Dordrecht, 1979. Dresselhaus, M. S.; Dresselhaus, G. Adv. Phys. 1981, 30, 139. Tanuma, S.; Kamimura, H. Graphite Intercalation Compounds; Tanuma, S., Kamimura, H., Eds.; World Scientific: Philadelphia, 1985. Zabel, H.; Solin, S. A., Eds. Graphite Intercalation Compounds I; Springer-Verlag: Berlin, 1990. Zabel, H.; Solin, S. A., Eds. Graphite Intercalation Compounds II; Springer-Verlag: Berlin, 1992.

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Contents

1

Introduction, 3

References, 7 2

Synthesis and Intercalation Chemistry, 9

2.1 Donor Intercalation Compounds, 9 2.2 Ternary Intercalation Compounds, 16 2.3 Acceptor Intercalation Compounds, 31 2.4 Bi-intercalation Compounds, 44 References, 50 3

Structures and Phase Transitions, 56

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11

Overview and Definition, 56 Liquid State in Stage-2 Alkali Metal GICs, 62 Phase Transition in Stage-2 Alkali Metal GICs, 65 In-Plane Structure Model in High-Stage Alkali Metal GICs, 73 Liquid-Solid Transition in K GIC, 80 Two-Dimensional Melting in Stage-1 Rb GIC, 84 Staging Structure, 88 Hendricks-Teller Stage Disorder, 94 Fractional Stage, 99 Stripe Domain Phase in Br2 GIC, 103 Phase Transition in SbCl5 GIC, 107

x Contents

3.12 Ordering Kinetics, 110 References, 115 4

Lattice Dynamics, 118

4.1 Phonon Dispersion in Alkali Metal GICs (Theory), 118 4.2 Phonon Dispersion in Alkali Metal GICs (Experiment), 122 4.3 Raman Scattering, 127 4.4 Donor-Acceptor Graphite Bi-intercalation Compound, 135 4.5 Intercalate Diffusion, 136 References, 141 5

Electronic Structures, 143

5.1 Band Structure of Graphite, and Tight Binding Model for GICs, 143 5.2 Acceptor GICs, 155 5.3 Alkali Metal GICs, 164 5.4 GICs with Novel Intercalates, 178 References, 186 6

Electron Transport Properties, 190

6.1 In-Plane Electron Transport Process, 190 6.2 c-Axis Conduction Process, 198 6.3 Weak Localization, 206 6.4 Transport Properties of Magnetic GICs, 213 6.5 Superconductivity, 219 References, 232 7

Magnetic Properties, 236

7.1 Overview, 236 7.2 Stage-2 CoCl2 GIC, 238 7.3 Stage-2 MnCl2 GIC, 254 7.4 Stage-2 CuCl2 GIC, 266 7.5 Stage-2 FeCl3 GIC, 273 7.6 Stage-1 Eu GIC (EuC6), 283 7.7 Magnetic Ternary (Quaternary) GICs, 289 References, 290 8

Surface Properties and Gas Adsorption, 294

8.1 8.2 9

Gas Physisorption in Alkali Metal GICs, 294 Surface Properties and Monolayer, 317 References, 332

GICs and Batteries, 336

9.1 9.2

Application of Intercalated Graphite in Primary Battery System, 336 Secondary Battery Applications as Li Ion Battery, 354 References, 384

Contents 10

Highly Conductive Graphite Fibers, 388

10.1 10.2 10.3 10.4 10.5 10.6 11

Introduction, 388 Structure and Staging, 389 Intercalate-Induced Enhancement of Conductivity, 390 Stability of Intercalated Graphite Fibers, 394 Fluorine-Intercalated Graphite Fibers with Ionic Bonding, 395 Conclusions, 398 References, 400

Exfoliated Graphite Formed by Intercalation, 403

11.1 11.2 11.3 11.4 11.5 11.6 12

xi

Introduction, 403 Structural Variation after the Exfoliation Process, 404 Exfoliation Process, 406 Exfoliated Graphite Fibers, 407 Applications, 408 Conclusions, 412 References, 412

Intercalated Fullerenes and Carbon Nanotubes, 414

12.1 Introduction, 414 12.2 Preparation and Structure of Pristine and Intercalated Fullerenes, 416 12.3 Preparation and Structure of Intercalated Carbon Nanotubes and Potential Applications, 422 12.4 Conclusions, 428 References, 429 Index, 433

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Graphite Intercalation Compounds and Applications

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I Introduction

There are two important features in the structure and electronic properties of graphite: a two-dimensional (2D) layered structure and an amphoteric feature (Kelly, 1981). The basic unit of graphite, called graphene is an extreme state of condensed aromatic hydrocarbons with an infinite in-plane dimension, in which an infinite number of benzene hexagon rings are condensed to form a rigid planar sheet, as shown in Figure 1.1. In a graphene sheet, ^-electrons form a 2D extended electronic structure. The top of the HOMO (highest occupied molecular orbital) level featured by the bonding jr-band touches the bottom of the LUMO (lowest unoccupied molecular orbital) level featured by the ?r*-antibonding band at the Fermi energy Ep, the zero-gap semiconductor state being stabilized as shown in Figure 1.2a. The AB stacking of graphene sheets gives graphite, as shown in Figure 1.3, in which the weak inter-sheet interaction modifies the electronic structure into a semimetallic one having a quasi-2D nature, as shown in Figure 1.2b. Graphite thus features a 2D system from both structural and electronic aspects. The amphoteric feature is characterized by the fact that graphite works not only as an oxidizer but also as a reducer in chemical reactions. This characteristic stems from the zero-gap-semiconductortype or semimetallic electronic structure, in which the ionization potential and the electron affinity have the same value of 4.6 eV (Kelly, 1981). Here, the ionization potential is defined as the energy required when we take one electron from the top of the bonding 7r-band to the vacuum level, while the electron affinity is defined as the energy produced by taking an electron from the vacuum level to the bottom of the anti-bonding ;r*-band. The amphoteric character gives graphite (or graphene) a unique property in the charge transfer reaction with a 3

4

Graphite Intercalation Compounds and Applications

Figure I.I The structure of graphene.

Figure 1.2 The electronic structures of graphene (a), graphite (b), donor GICs (c), and acceptor GICs (d), where D(E) is the density of states and £F is the Fermi energy.

Introduction

5

Figure 1.3 The structure of graphite, formed by the AB stacking of graphene sheets.

variety of materials: namely, not only an electron donor but also an electron acceptor gives charge transfer complexes with graphite, as shown in the following reactions:

(1.1) (1.2) where C, D, and A are graphite, donor, and acceptor, respectively. In the charge transfer reactions, the layered structure of graphite plays an important role. Reacted donor or acceptor species are accommodated in the galleries of graphite layers, since the reaction proceeds by expanding the intersheet distance against the intersheet interaction. The reaction described above is termed an intercalation reaction, where the donor or acceptor is called intercalate. The charge transfer complex with graphite obtained in the intercalation reaction is called graphite intercalation compound, which is abbreviated to GIC (Brandt et al., 1988; Dresselhaus and Dresselhaus, 1981; Zabel and Solin, 1990, 1992). The first discovery of GICs was made with potassium more than 160 years ago (Schaffautl, 1841). In the long history of research on GICs, a great number of GICs have been yielded with a large variety of donors and acceptors, in which alkali metals, alkaline earth metals, transition metal chlorides, acids, and halogens are involved as typical intercalates. The graphitic galleries having intercalates are very active chemically, so that they are attractive agents for investigations of catalytic reactions, gas adsorption phenomena, and so on. From the electronic structure aspect, the electron transferred from donor to graphite occupies the anti-bonding jr*-band in donor GICs, while the charge transfer from graphite to acceptor empties the top of the bonding rr-band in acceptor GICs. The electronic structures thus produced in donor and acceptor GICs are represented in Figure 1.2c and d, respectively. The increase in the

6

Graphite Intercalation Compounds and Applications

number of electrons or holes around the Fermi energy EF that follows the charge transfer between intercalate and graphite makes GICs metallic, in remarkable contrast to the semimetal or zero-gap semiconductor structure of host graphite or graphene. Therefore, GICs can indeed be called synthetic metals. Actually, GICs have 2D metallic structures. In donor GICs, the electrons added to the anti-bonding jr*-band behave as carriers having electron nature, while the vacancies appearing in the bonding 7r-band produce hole carriers in acceptor GICs. The 2D-featured metallic electronic structures of GICs have been intensively investigated as attractive targets in the physics of low-dimensional electronic systems. A combination of graphitic jr-electrons and the electrons in the intercalates brings about a variety of novel electronic structures and related electron transport phenomena. In some of the donor GICs, superconductivity appears, having unconventional features. Magnetism is also among the highlighted subjects in the research on GICs, as many of intercalates possess localized magnetic moments. The arrangement of localized magnetic moments features a 2D magnetic lattice. The magnetic structures and the dynamical properties of magnetic phase transition in GICs provide important aspects of the physics of 2D magnetic systems. The structures of GICs also provide basic issues in structural chemistry and lattice dynamical properties. Intercalates accommodated in the graphitic galleries form a 2D superlattice, which is commensurate or incommensurate with respect to the host graphite lattice depending on the electronic and structural properties of the intercalates. One of the most remarkable structural features in GICs is a unique c-axis periodicity of the graphitic galleries in which intercalates are accommodated. Intercalates occupy graphitic galleries periodically in the c-axis direction, giving a regular sequence in the c-axis stacking structure. This is called a staging phenomenon. When intercalates occupy every graphitic gallery, we call this a stage-1 structure. Stage-n is defined as the structure in which intercalates are accommodated regularly in every «th graphitic gallery. The stage number dependence of c-axis lattice spacing 7C is given in the following equation: / c (A) = 4 + 3.35(n-l)

(1.3)

where n is the stage-number, and 4 is the sandwich thickness, representing the distance separating two graphitic layers between which an intercalate layer is sandwiched. For stage-1 GICs, ds = Ic. The effective thickness of the intercalate (intercalate thickness) rf; is obtained by subtracting the interlayer distance of host graphite dG — 3.35 A from ds. It is very interesting that we can have upto stage-8 GICs, which have an extremely long periodicity of over 30 A. Staging occurs very generally regardless of the superlattice that intercalates take in the graphitic galleries. The electronic and structural properties of GICs depend on the host graphite. In the investigation of physical properties, well crystallized graphite is required for obtaining physical parameters that can be used in quantitative discussion with no ambiguity. Among crystalline graphite forms, we have natural single crystal flakes where the dimensions are ~ 1 mm in in-plane size and only several hundredths of a millimeter in thickness. The limited sizes of the flakes make natural graphite less useful in physical investigations. In addition, the presence of magnetic impurities

Introduction

7

is sometimes unavoidable, and this works against precise magnetic measurements. In actual investigations, highly oriented pyrolitic graphite (HOPG) is a useful host graphite, which is artificially synthesized at high temperature and high pressure (Moore, 1973). We can take samples large enough to investigate most of the physical quantities for comprehensive understanding of solid-state properties, although the layer plane consists of a randomly ordered collection of crystallites of ~ 1 fjim in average in-plane size. Kish graphite is also an important host graphite which has a well ordered crystalline structure. Exfoliated graphite, such as grafoil, is also an important host graphite. Grafoil, which is made by rolling exfoliated graphite into foil, can be easily intercalated with most intercalate species. We can use it in gas adsorption experiments. Carbon fibers are another type of host graphite. Although these fibers have defects that make them less useful in physical investigation, applications of GICs can be carried out effectively using carbon fibers, producing a lightweight conductor. GICs are important and useful materials in many applications. High electrical conductivity makes them applicable in electrical wiring since the conductivity becomes as high as that of copper (Vogel et al., 1977). We have Li ion secondary batteries, in which the intercalation reaction is an important contributor. Using different types of graphite hosts, many efforts have been made to improve the performance of batteries. Since the discovery of the soccer-ball-shaped molecule C60, fullerenes having TTelectron systems have attracted intensive interest in carbon science and related research areas (Dresselhaus et al., 1996). Carbon nanotubes, which were discovered later as a molecule-size tube made of a cylindrical carbon-hexagon network, are another type of carbon-based ^--electron system. From the aspect of intercalation, fullerenes and carbon nanotubes can be classified into graphite analogs whose electronic structures are discussed similarly to those of GICs on the basis of charge transfer between fullerenes or carbon nanotubes and guest species. Thus, the chemistry and physics of intercalated fullerenes and carbon nanotubes have a common background with those of GICs, and information on GICs is of importance in clarifying the properties of fullerenes and carbon nanotubes. Finally, we summarize the issues that will be discussed in each chapter as follows: Chapter 2, Synthesis and Intercalation Chemistry; Chapter 3, Structures and Phase Transitions; Chapter 4, Lattice Dynamics; Chapter 5, Electronic Structures; Chapter 6, Electron Transport Properties; Chapter 7, Magnetic Properties; Chapter 8, Surface Properties and Gas Adsorption; Chapter 9, GICs and Batteries; Chapter 10, Highly Conductive Graphite Fibers; Chapter 11, Exfoliated Graphite Formed by Intercalation; and Chapter 12, Intercalated Fullerenes and Carbon Nanotubes.

References Brandt, N. B.; Ponomarev, S. M.; Zilbert, O. A. Semimetals-Graphite and its Compounds; North Holland: Amsterdam, 1988. Dresselhaus, M. S.; Dresselhaus, G. Adv. Physics 1981, 30, 139.

8

Graphite Intercalation Compounds and Applications

Dresselhaus, M. S.; Dresselhaus, G.; Eklund, P. C. Science of Fullerenes and Carbon Nanotubes; Academic Press: San Diego, 1996. Kelly, B. T. Physics of Graphite; Applied Science Publishers: London, 1981. Moore, A. W. Chemistry and Physics of Carbon, Vol. 11; Waker, P. L., Thrower, P. A., Eds.; Dekker: New York, 1973; p 69. Schaffautl, P. /. prakt. Chem. 1841, 21, 155. Vogel, F. L.; Foley, G. M. T.; Zeller, C.; Falardeau, E. R.; Gan, J. Mater. Sci. Eng. 1977, 57,261. Zabel, H.; Solin, S. A. Graphite Intercalation Compounds I; Springer-Verlag: Berlin, 1990. Zabel, H.; Solin, S. A. Graphite Intercalation Compounds II; Springer-Verlag: Berlin, 1992.

2

Synthesis and Intercalation Chemistry

2.1 Donor Intercalation Compounds

2.1.1 Alkali Metal, Alkali Earth Metal, and Rare Earth Metal GICs Alkali metal GICs are the best known donor type GICs, since they are easily prepared and their brilliant gold color for stage-1 GICs has attracted scientists working in intercalation chemistry. They have therefore been targets of intensive and detailed studies of their solid-state properties on the basis of the employment of highly oriented pyrolytic graphite (HOPG). There are several intercalation methods, which are classified basically into vapor-phase reaction, reaction of the mixture of graphite and alkali metal, high pressure reaction, electrochemical reaction, and reaction in a solvent. Among these methods, vapor-phase intercalation reaction is the most popular. The two-zone method can easily give alkali metal GICs with well-defined singlestage phases. The vapor pressure of the alkali metal becomes high enough to obtain a satisfactory reaction rate for intercalation reaction in the temperature range 200-550°C, at which we can use a Pyrex glass tube as a reaction chamber. Figure 2.1 shows a typical two-zone method, where graphite and alkali metal are maintained at different temperatures, TG and T{, respectively, in a vacuum-sealed glass tube placed in a two-zone furnace. Changing T\ controls the vapor pressure of the alkali metal. Figure 2.2 presents the conditions of intercalation reaction with potassium, where single-stage phase samples with stages 1 to 8 are obtained by changing the temperature difference TQ — 7"K (Nishitani et al., 1983). Typical 9

10

Graphite Intercalation Compounds and Applications

Figure 2.1 Two-zone method for the preparation of alkalimetal GICs. Tc and T\ are the temperatures of graphite and alkali metal. The intercalation reaction is carried out in the condition Tc > T,.

experimental conditions are given in Table 2.1 for the preparation of K, Rb, and Cs GICs (Dresselhaus and Dresselhaus, 1981). The intercalation reaction is again carried out by heating a mixture of graphite and alkali metal in a vacuum-sealed glass tube. In this case, the reaction becomes considerably more rapid owing to direct contact of molten alkali metal with graphite, although the reaction takes place in a similar manner to the vapor-phase reaction. A stainless steel tube is used for the intercalation of lithium since lithium vapor degrades a glass tube because of its high chemical activity. Alkali metal can be intercalated into graphite when the alkali metal is solvated in liquid ammonia or an organic solvent such as dimethylsulphoxide (DMSO). In this case, the solvent tends to be included as part of the intercalate. Electrochemical reaction is also applied to alkali metal intercalation. Using potassium and potassium iodide dissolved in DMSO solution, potassium GICs with DMSO have been prepared electrochemically (Okuyama

Figure 2.2 The intercalation condition of potassium intercalation into graphite in the vapor-phase reaction, where TG and TK denote the temperatures of graphite and potassium (Nishitani et al., 1983).

Synthesis and Intercalation Chemistry

II

Table 2.1 Intercalation reaction conditions for alkali metal GICs in the two-zone method. Tc and T\ are the temperatures of graphite and alkali metal, respectively (Dresselhaus and Dresselhaus, 1981). K Stage Number 1 2

3

T, = 250°C

TG ( C)

255-320 350-400 450-480

Rb 7, = 208° C TG ( C)

215-330 375-430 450-480

Cs T, = 194"C TG ( C)

200^25 475-530 550

et al., 1981). We will discuss such solvent-including alkali-metal ternary GICs in Section 2.2.2. Alkali metal GICs thus obtained are extremely active in the atmosphere, resulting in rapid decomposition. It is hard to synthesize sodium GICs. Only high-stage Na GICs are reported, where the composition is described by NaC8n with stage numbers n = 4-8 (Metrot et al., 1979/1980). The reason for the difficulty in the synthesis of Na GICs consists in two competing factors: ionization potential and the size of the alkali metal. The ionization potential increases from 3.893 eV to 5.390 eV as we go from Cs to Li in the series of alkali metal elements in the periodic table. The ionic diameter decreases from 4 A to 2 A. The lower the ionization potential, the more easily are electrons transferred to graphite. Consequently, the energy gain upon the charge transfer becomes smaller in the order of Cs > Rb > K > Na > Li. This is why low-stage Na GICs are not well stabilized; at the same time, this seems to be inconsistent with the presence of Li GICs. This fact can be explained by the smallness of the ionic diameter of Li. Small Li ions can be accommodated in the graphitic galleries in spite of their large ionization potential. Sodium, which comes between potassium and lithium, is at a disadvantage not only from its ionization potential but also from its ionic diameter. The stage-1 GICs with heavy alkali metals K, Rb and Cs form a 2 x 2 intercalate superlattice whereas stage-1 Li GIC forms a \/3 x V3 intercalate superlattice. These facts reflect the differences in ionization potentials and ionic diameters, as will be mentioned later. Alkali earth elements are intercalated into graphite similarly to alkali metal elements. Calcium, strontium, and barium are the elements known to give intercalated graphite. However, their high ionization potentials make the intercalation reaction rather difficult for alkali earth species. In addition, the low vapor pressures of these elements in comparison with alkali metal elements require rather higher reaction temperatures (typically 400-500°C) (Guerard et al., 1980, Akuzawa et al., 1985). A stainless steel tube is also required for heat treatment in the vapor-phase reaction. Some of the rare earth metal elements, such as Eu, Sm, and Y, have been reported to be intercalated into graphite (Makrini et al., 1980a). The high ionization potentials and low vapor pressures impose similar restraints to those of alkali earth metal elements.

12

Graphite Intercalation Com pounds and Applications

Crystal structures of alkali metal, alkali earth metal, and rare earth metal GICs depend on the ionic size of the intercalates and the stage numbers. In the case of heavy alkali metal species such as K, Rb, and Cs, the graphite to alkali metal composition ratio is described by MC8 for stage-1 GICs, while that for higher stage GICs is described by MC12n where M = K, Rb, or Cs, and n is the stage number. The in-plane alkali metal structure of stage-1 MC8 is formed with a 2 x 2 superlattice in the graphitic galleries. The higher stage system MC| 2n has a less dense intercalate layer whose in-plane density is 2/3 that of stage-1 GICs. Figure 2.3a gives the in-plane 2 x 2 structure of the intercalates for stage-1 MC8, where the lattice constant of the superlattice is estimated as 4.92 A. Alkali metal ions are considered to form a 2D triangular close-packed structure. The structure of the intercalates in higher stage GICs has a superstructure with structural discommensuration, the details of which will be discussed in Chapter 3. GICs with small-size donors such as Li, alkali earth metal, and rare earth metal have the composition of MC6n, where a V3 x V3 superstructure is formed with the lattice constant of 4.26 A as shown in Figure 2.3b. The c-axis lattice constant reflects the size of the alkali metal species. Table 2.2 presents the sandwich thickness of the donor GICs discussed in this section, where the sandwich thickness ds is defined as the intergraphene layer distance for adjacent graphene layers between which an intercalate layer is inserted. ds is equivalent to the c-axis lattice constant 7C for a stage-1 compound. The sandwich thickness in alkali metal GICs increases with the ionic radius in the order of Li < Na < K < Rb < Cs. There is a similar trend for alkali earth GICs. The stacking sequence of graphene sheets, which is described in terms of ABAB stacking for pristine graphite, is converted to AaAft AyAS for stage-1 KCg, where the Greek letters denote the types of intercalate

Figure 2.3 Intercalate superlattices (2 x 2) and (V3 x \/3) for stage-1 M g C (a) and MC6 (b), respectively, where M = alkali metal, alkali earth metal, or rare earth metal. The open circles represent the metal atoms. The dotted line denotes the graphite unit cell with a = 2.46 A, while the solid lines denote superlattices for GICs: (a) a = 4.92 A, (b) a = 4.26 A.

Table 2.2 Structures of alkali metal, alkali earth metal and rare earth metal binary GICs. ds is the sandwich thickness and n is the stage number. Metal Density (g/cm 3 ) [Crystalline Metal]

Compound

0.20 (1) [0.534] — [0.971]

LiC6,, n > 1) \aC6,, n = 4-8)

K Rb MC12,, -(« > 2) - Cs -MC 8 (1)-

2aC6 (1) 5rC6 (1)

BaC6 (1) EuC6 (1) 5mC6 (1)

^C6 (1) LiC2 (1)

NaC 2 _ 3 (1)

0.58(1) [0.862] 1.20(1)

4 (A)

In-Plane Structure

3.706

75x73(1)

Parry et al., 1969

4.60

73 x 73

Metrot et al.,

5.35

2x2(1)

5.65

2x2(1)

Synthesis Condition and Stability Reference

1979/80 Parry et al., 1969

Vapor phase

5.94

2x2(1)

4.60

73x73(1)

1.87 [2.54] 2.76 [3.5] 3.30 [5.24]

4.94

73x73(1)

5.25

73x73(1)

4.8625 73 x 73 (1)

Underbill et al., 1980 Underbill et al., 1980 Guerard et al.. 1980 Guerard et al., 1980 Guerard et al., 1980 Makrini et al..

3.47 [7.52] 2.05

5.025

Makrini et al..

[1.53] 1.77(1) [1.87] 0.92 [1.55]

[4.47] 0.59 [0.534]



reaction

1980a

73x73(1)

1980a

4.5735 75 x 73 (1)

3.71

1x1

7.04

[0.971]

K.C4 (1)

1.15 [0.862]

5.34



RbC4.5 (1)

2.39 (for RbC 4 ) [1.53]

5.63



CsC4 (1)

3.52 [1.87]

5.92

273 x 2

( ): stage number.

13

> 8 kbar 280-300°C Decomposed to Li 7 C 24 35-40 kbar 350-450C'C Decomposed below 20 kbar > 5 kbar 150-170°C Decomposed to KC8 20-25 kbar 20° C Decomposed to Rtc 6.5 below 2 kbar 2 kbar, 20°C Metastable

Makrini et al.. 1980a Nalimova et al., 1995

Avdeev et al., 1990b

Avdeev et al., 1990a

Nalimova et al., 1991

Avdeev et al., 1990a

14

Graphite Intercalation Com pounds and Applications

layers since there are four possible ways of forming intercalate layer superlattices (see Figure 3.2). High-pressure synthesis is applied for the preparation of highly dense alkalimetal GICs, which can give alkali metal densities exceeding considerably the maximum value for GICs prepared by traditional methods. A large change in volume, induced by the application of pressure, was first reported to give a highdensity potassium GIC KC6 at 19 kbar from KC8 (Fuerst et al., 1981). Later, this technique was applied to ultra-high-density alkali metal GICs at high pressures up to 60 kbar using anvil-type or piston-cylinder-type apparatus, where alkali metal elements impart high-density phases (Avdeev et al., 1990a; Belash et al., 1987; Nalimova et al., 1991; Nalimova, 1998; Semenenka et al., 1983; Syassen et al., 1989). Table 2.2 lists all of the high-density alkali metal GICs ever prepared. Intercalation reactions under pressure proceed very rapidly. The synthesis time is in the order of minutes or even seconds for heavy alkali metals, whereas reactions with lithium and sodium are completed in 0.5 to 4 hours. Using high-pressure synthesis for heavy alkali metal elements, high-density phases with a composition of MC4 are yielded, where the volume change in the reaction reaches 40 to 48% of the volume of starting materials, graphite and alkali metal. These phases are fairly stable in comparison with Li and Na high-density phases, and CsC4, especially, can be stabilized as a metastable phase even after the pressure is released. Lithium gives the highest density phase LiC2 among the high-pressureinduced high-density phases or even all of the reported alkali metal carbon compounds except carbide. In this case, the pressure-induced volume change goes even beyond 50%. LiC2 is decomposed into less dense phases Li n C 2 4 -> Li9C24 -> Li7C24 successively as the pressure is released (Guerard and Nalimova, 1994; Nalimova et al., 1995). Li7C24, which has a still higher lithium density than the ordinary LiC6, is stabilized even at ambient pressure. The high-density lithium GICs are interesting from the aspect of high capacity batteries. Researchers in electrochemistry have been making efforts to increase the lithium content in relation to the structure favorable for incorporation with lithium. Sodium, which does not give stage-1 GICs in the normal preparation technique, forms NaC2.3 under high pressure; this is decomposed into graphite and sodium below 20 kbar. An interesting feature is that the alkali metal density is higher than that of pristine crystalline alkali metal in spite of the coexistence of carbon atoms with compositions of 2 to 4 carbon atoms per 1 metal atom. In the case of LiC2, the density is 10% higher than that of lithium metal. The ratio of the density of the GIC to that of pristine metal increases as we go down the row of the periodic table. The density for CsC4 becomes as much as 85% high in comparison with that of pristine cesium metal. It is interesting that CsC4 is the most stable of the high-density GICs even in such a condition that is far from equilibrium at ambient pressure. The structure of the highest alkali metal density phase LiC2 consists of a lithium monolayer with a sandwich thickness of 3.7 A in every graphitic gallery. The in-plane structure is formed by locating lithium atoms at the center of every carbon hexagon ring or by occupying all the hexagon centers by lithium atoms. The Li-Li interatomic distance of 2.49 A is equal to the length of the in-plane unit cell and is indeed 0.6 A shorter than that of pristine lithium metal. The release

Synthesis and Intercalation Chemistry

15

of pressure induces successive structural changes LiC2 -> LinC24 -> Li9C24 ->• Li7C24 accompanied by decrease in the lithium density, as mentioned above. The final product Li7C24, following the release of pressure, has a hexagonal Li7cluster-based in-plane structure as shown in Figure 2.4a, where the superlattice is given by 2^3 x 2>/3 with a = 8.63 and c = 11.1 A (3/c) (Nalimova et al, 1995). The structures of the intermediates LinC24 and Li9C24 are formed by adding additional lithium atoms at carbon hexagon centers which bridge adjacent Li7 clusters as exhibited in Figure 2.4a, while the superlattice with Li7 clusters remains unchanged. The presence of lithium clusters, which are considered to be stabilized with the formation of covalent Li-Li bondings and have been reported in other chemical systems, is the consequence of the application of pressure. The origin of the cluster formation will be discussed in Section 5.3.4 in relation to the electronic structures. NaC2 6 is reported to form three-layer intercalates in the graphitic galleries, giving an interplanar distance of 7.04 A, in contrast with the monolayer intercalate of super-dense Li GICs (Avdeev et al., 1990b). No information on the inplane structure has been reported for this GIC. Super-dense heavy alkali metal GICs have monolayer intercalates similar to those of Li GICs. In the structure of CsC4, having a superlattice of 2\/3 x 2, a Cs linear chain structure is formed as shown in Figure 2.4b by occupying every center of a hexagon ring in the hexagonedge-sharing direction, where an interatomic Cs-Cs distance is estimated at 2.48 A and adjacent chains are one hexagon ring apart from each other with an interchain distance of 4.28 A. In relation to superdense alkali metal GICs prepared by the high-pressure technique, similar high-density heavy alkali metal GICs are known to be prepared by a traditional technique when we add a trace of oxygen to potassium in the vapor phase intercalation reaction (Herold et al., 1994). Details will be shown in Section 2.2.1 for these GICs.

Figure 2.4 (a) In-plane superstructures of high-density alkali metal GICs: (a) Li7C24 (closed circles), Li9C24 (closed circles + open circles), Li,,€24 (closed circles + open circles + triangles); (b) CsC4 (Nalimova, 1998).

I6

Graphite Intercalation Compounds and Applications

2.2 Ternary Intercalation Compounds

2.2.1 Alkali Metal with Third Elements Hydrogen, oxygen, sulfur, selenium, tellurium, mercury, bismuth, and arsenic are incorporated into intercalates in the presence of alkali metals, giving alkali metal ternary GICs. Moreover, sodium hydroxide, chloride, bromide, and iodide are intercalated in the graphitic galleries, and these may also be categorized as ternary GICs. In alkali metal GICs, the Coulomb attractive force working between positively charged alkali metal intercalate and negatively charged graphene sheet plays an important role in their stabilization. Hence, the introduction of a third element or the ensuing intercalate structure, which destabilizes fatally the Coulomb energy balance, does not result in ternaries. As a consequence, most of the ternaries that include an alkali metal have a multilayer sandwich intercalate in which the electronegative element is inserted between positively charged alkali metal double layers, so that the Coulomb attraction between alkali metal and graphite layers is not seriously affected. Here, we discuss alkali metal ternaries on the basis of this general trend, with various families of elements intercalated as the third species. Alkali metal-hydrogen ternaries were well known at the primitive stage of GIC research. There are two methods of synthesis for alkali metal-hydrogen ternary GICs. Hydrogen adsorption into potassium and rubidium GICs results in corresponding alkali metal hydride GICs at room temperature, where hydrogen gas at 1 atm pressure gives KH0.67C8 (Herold and Lagrange, 1977; Saehr and Herold, 1965) and RbHa05C8 (Colin and Herold, 1971) from stage-1 KC8 and RbC8, respectively. For the rubidium counterpart, the application of hydrogen pressure enhances the hydrogen content, giving RbHo.6yC8 at over 100 atm, which is almost the same composition to that of potassium hydride GIC. CsC8 does not accept hydrogen at ambient conditions. These findings suggest that hydrogen adsorption activity is lowered in the order of K > Rb > Cs in heavy alkali metals. Lithium and sodium GICs do not adsorb hydrogen. Direct reaction of metal hydride with graphite is also available for obtaining alkali metal hydride GICs for almost all alkali GICs. Reaction with KH (Guerard et al., 1983) in a furnace gives a series of potassium hydride GICs with various stage numbers n, KH0.8C4n, where stage-1 prefers a temperature range of 250300°C and stage-2 300^t50°C for heat treatment. Rubidium and cesium hydride GICs are prepared similarly with direct intercalation of RbH and CsH, where the reaction is carried out at 300-500°C (Guerard et al., 1989). The compositions are given as RbH 08 C 3 . 6 and RbH 0 . 8 C 8 1 for stage-1 and stage-2 RbH GICs, respectively, while we obtain CsH 08 C 8 for stage-1 CsH GIC. Sodium hydride GICs are also prepared by direct intercalation with NaH at 300-500°C (Guerard et al., 1985, 1987). The compositions are described as NaHC(2.5_4.5)n for stages n = 1-11. It is interesting that stage-1 sodium hydride GIC is stabilized in spite of the absence of low-stage sodium GICs; this suggests an important role of hydrogen in the stabilization. The same technique gives quarternary hydride GICs with Li and K, K^LiHC^ with stages « = 1-4. It is worth noting that the hydrogen content is larger in the direct intercalation of alkali metal hydrides than in hydrogen chemisorption. In particular, the hydro-

Synthesis and Intercalation Chemistry

17

gen-to-sodium ratio becomes almost unity in the case of NaH GICs. Moreover, the NaH intercalate concentration is very high in NaH GICs irrespective of its stage numbers, and is almost doubled in comparison with the intercalate concentration of KH GICs. Alkali metal hydride GICs, whose color is dark blue for low stage and black for high stage compounds, are relatively stable in the air, in contrast to alkali metal GICs. Table 2.3 summarizes the structures of alkali metal hydride GICs prepared by the direct intercalation of alkali metal hydrides. The sandwich thickness ds, which is equivalent to the c-axis repeat distance for stage-1, is reasonably understood on the basis of the sum of atomic radii of alkali metal ions and hydride ions. It should be noted that the sandwich intercalate of metal+-hydride~-metal+ composite is a favorable structure for energy stabilization, since negatively charged graphene sheets in donor GICs can be proximate to positively charged alkali metal layers and apart from negatively charged hydride layers. Figure 2.5 shows a cross-sectional view of the structure of KH GICs. The KH intercalate forms triple atomic layers of K-H-K sandwiches in the graphitic galleries, where the hydrogen anion H" has a considerably large diameter of 3.0 A due to the repulsion between two electrons surrounding a proton nucleus, in contrast to the diameter of a neutral hydrogen, 1 A. Mercury and thallium, which belong respectively to the 2B and 3B families in the periodic table, also give ternaries having triple atomic layer intercalates of alkali metal-Hg/Tl-alkali metal. These ternaries are prepared by reactions between graphite and binary alloy of alkali metal-Hg/Tl, where potassium and rubidium compounds are reported (Makrini, 1980; Makrini et al., 1980b; Ouitti et al., 1994). Table 2.4 gives information on the synthesis and structure of the MHg and MT1 ternary GICs for M = K and Rb. The general composition is described with reference to MHgC^ for stage-1 and stage-2 MHg GICs, while MT1 GICs have MT1, 5 C 4n with an amount of thallium 50% larger than that of alkali metal. The sandwich thickness ds for the MHg ternaries is explained well by sandwiched triple atomic layer intercalates. The MT1 ternaries have several polymorphs, as shown in Table 2.4. The a-phase, having a thick sandwich thickness, has five layered intercalate sheets of K-T1-T1—Tl—K, and the /3-phase, having a larger sandwich thickness, includes excess thallium in the intercalates. The y-phase

Table 2.3 Structures of alkali metal hydride GICs prepared by direct intercalation of alkali metal hydride. 4 is the sandwich thickness and n is the stage number (Guerard et al., 1989). Intercalate

Formula

LiH + K

K 2 LiHC 8n NaHC(2.5-4.5),, KH ( )8C 4 ,, RbHo 8 C 3 6 RbHojC-K, RbH 0 8 C 8 ] CsH0.gC5

NaH KH RbH CsH

ds

Stage

In-Plane System

a (A)

b(A)

8.90 7.30-7.60 8.53 9.03 10.16 9.42 10.05

1-4 1-11 1-3 la

hexagonal orthorhombic orthorhombic orthorhombic quadratic

4.95 12.79 8.57 38.32 12.83

9.85 12.39 36.6

orthorhombic

21.3

12.33

iy

20

18

Graphite Intercalation Compounds and Applications

Figure 2.5 Cross-sectional view of the structure for K.H GICs (Enoki et al., 1990).

forms a sandwiched triple atomic layer intercalate of M-T1-M, giving a considerably thinner sandwich thickness. It should be noted that the intercalates in these GICs feature with binary alloys having metallic structures, which contrasts with the M+-H~-M+ intercalate in MH GICs having ionic features. The in-plane structures are characterized by a 2 x 2 superlattice for KHg GIC (Lagrange et al., 1983), while a square lattice with a = 10.995 A is suggested for a-phase KTl!.5c4n (Makrini, 1980). There exists alkali metal ternary GICs with elements in the nitrogen family P, As, Sb, and Bi, except for N, which exhibit similar triple layer intercalates to those of alkali metal-hydrogen GICs, in which their electronegativities work effectively in structural stabilization. Stage-1 KP GIC is prepared by heat treatment of graphite with liquid potassium containing 1 atomic percent of phosphorus at 390°C. It is a blue product KP 03 C3 2, which is greatly stable against air and water (Herold et al., 1998). The data for the KP GIC is summarized in Table 2.5. There are no reports on phosphorus-containing alkali metal ternaries for other alkali metal elements. Arsenic gives alkali metal ternaries with heavy alkali metal elements under similar reaction conditions (Assouik, 1991; Assouik and

Table 2.4 Syntheses and structures of alkali metal mercury and alkali metal thallium ternary GICs. ds is the sandwich thickness, and n is the stage number. GIC

Composition

MHg

KHgC4n

4 (A)

In-Plane Structure

10.16-10.76

2x2

(n=1-3) RbHgC4n

10.76

KTl.sQ,,

12.1 OH

KT10.67C4 (1)

10.76[y]

RbTl,. 5 C 4n

12.65[a] 13.40L6]

(n=1.2)

MT1

(n=1.2)

(n=1.2)

square a= 10.995 A

Synthesis

Reference

200°C (1) liquid KHg alloy copper pink (1) 200°C (1) liquid RbHg alloy copper pink (1) 400°C (1) liquid KT1 alloy 350°C (1) liquid KT1 alloy 400°C liquid RbTl alloy

Makrini et al., 1980b

( ): stage number. Greek letters in the brackets denote the types of polymorphs.

Makrini, 1980

Makrini, 1980; Outti et al., 1994

Outti et al., 1994

Table 2.5 Structures and reaction conditions of alkali metal ternaries with nitrogen group elements. rfs is the sandwich thickness. Compound

Stage

KP(uC3.2

1

8.86

K|.o-l.4Aso.6-|.oC4n

1-2

9.50-10.45

Rb0.8-1.oASo.6-l.oC4,,

1-2

9.87-10.65

4 (A)

(n=l,2) (n=l,2)

Cso.g-i.oAs06-i.oC4n (n = 1-3)

CsSb0.5.o.6C4 (1)

1-3

1-4

10.50-11.10

10.45-10.96

In-Plane Structure

Reaction

Reference

hexagonal, a = 4.30 A commensurate hexagonal, a = 8.52 A commensurate (stage-2 KAsC8) hexagonal, a = 8.52 A commensurate (stage-2 RbAsCg)

390°C, liquid K + P (1 atom %), blue 570-630°C, liquid alloy K + As (20-38 atom %) green (1), blue (1) 610-640°C, liquid alloy Rb + As (32-53 atom %) blue green (1), blue (2), gray (2)

Herold et al., 1998

hexagonal, a= 13.84 A incommensurate (stage-2 Rb0.gAsC8) hexagonal, a = 8.52 A commensurate (stage-2 CsAsCg) hexagonal, a= 13.96 A incommensurate (stage-2 Cso.8AsC8) rectangular hexagonal

KBi0.6C4,, (« = 2-5) RbBi 06 C 4n (n = 1 , 2 ) CsBi0.53-i.oC4n

(n=l,2)

( ): stage number.

2-5

9.87-10.86

1-7

10.09-10.52

\-4

10.60-11.50

hexagonal oblique oblique hexagonal oblique

Assouik, 1991; Assouik and Lagrange, 1992 600-650°C, liquid alloy Cs + As (32-50 atom %) vermilion (1), dark blue (1), gray (2)

530-600°C liquid alloy Cs + Sb (25-50 atom %) gray, gray blue liquid alloy K + Bi violet (1), blue (2) liquid alloy Rb + Bi violet (1), blue (2) liquid alloy Cs + Bu violet (1), blue (2)

Essaddek and Lagrange, 1989; Essaddek et al., 1989 Bendriss-Rerhrhaye et al., 1988

Lagrange et al., 1985

20

Graphite Intercalation Compounds and Applications

Lagrange, 1992). Intercalation reactions are carried out at 600-650°C for K, Rb, and Cs in alkali metal-arsenic liquid alloy. The structure of KP GIC is characterized by a triple atomic layer intercalate of K-P-K with an interplane spacing of 8.86 A, in which the concentration of phosphorus, having an electronegativity of 2.1, is in the same range as that of chalcogenide elements having stronger electronegativity in alkali metal chalcogenide GICs. The in-plane structure is determined as being hexagonal with a = 4.30 A, which is commensurate with the underlying graphite lattice. Heavy alkali metal arsenic ternaries have various polymorphs with different intercalate atomic compositions As/M = 0.43-1.0, 0.6-1.3, 0.6-1.3 for M = K, Rb, Cs, respectively, as shown in Table 2.5. Hence the sandwich thickness ds varies depending on the compositions: 9.50-10.45 A, 9.87-10.65 A, and 10.5011.10 A for K, Rb, and Cs, respectively. ds increases as the As/M ratio is elevated. The intercalate having a smaller As/M ratio is structured with a triple atomic layer intercalate of M-As-M, while an increase in the ratio modifies the layered structure in such a way that arsenic becomes mixed with alkali metal in the alkali metal layer. At the same time, the in-plane structure varies. For As/M = 1, MAs GICs have a commensurate hexagonal in-plane structure with a = 8.52 A, whereas for As/M = 1.3, the in-plane structure becomes incommensurate with a = 13.84 and 13.96 A for M = Rb and Cs, respectively. The in-plane structure of As/M = 0.6 is not well characterized. For antimony-including GICs, only CsSb alloys are reported to give stage-1 to -4 ternary GICs with various in-plane structures and sandwich thicknesses, as summarized in Table 2.5 (Essaddek and Lagrange, 1989; Essaddek et al., 1989). Intercalation is carried out by the reaction between graphite and a liquid alloy of cesium and antimony at 530-600°C. The formula of the ternaries is described in terms of CsSbo.s-o.6C4 for stage-1 GIC. There are four polymorphs with different in-plane structures and interlayer spacings. The in-plane structures are reported to vary, depending on samples: rectangular, hexagonal, and so on (Essaddek and Lagrange, 1989). Judging from the thickness of the interlayer spacing ds = 10-11 A, the intercalate is considered to form a polylayer structure similar to MAs GICs, though the stacking of metal atoms and the in-plane structures are more complicated than those of other ternaries. Bismuth forms ternary GICs with all the heavy alkali metal elements, in which several polymorphs are reported (Lagrange et al., 1985). Intercalation reactions are performed with a liquid alloy of alkali metal and bismuth. The GICs produced are stable against air. They have a triple atomic layer intercalate of M-Bi-M, as with many other alkali metal ternaries. It is reported that two types of intercalate structure exist with different in-plane structures and interlayer spacings, although the details remain unsolved (Bendriss-Rerhrhaye et al., 1988). The sandwich thicknesses vary from 9.87-10.86 A for K to 10.60-11.50 A for Cs. It should be noted that, in the order of P > As > Sb > Bi, the ionicity of the intercalate tends to decrease. The intercalate can be described in terms of a binary alloy between alkali metal and an element of the nitrogen family. Next, we discuss alkali metal chalcogenide GICs. The most well known among them is alkali metal oxide GICs. It was believed that oxygen, having high reactivity with alkali metal, cannot be intercalated into alkali-metal-containing GICs.

Synthesis and Intercalation Chemistry

21

However, recent studies have discovered alkali metal oxide GICs in addition to the fact that the presence of oxygen promotes new high-density alkali metal GICs such as KC4, as mentioned in Section 2.1. Alkali metal oxide GICs are prepared by heat treatment-induced direct reaction of graphite with partly oxidized liquid alkali metal, alkali metal peroxide, or alkali metal hyperoxide. These products are stable in air since they are treated with oxygen in the reaction process. Graphite is reacted with liquid sodium, partly oxidized or mixed with a very small amount of sodium peroxide at 470°C, giving a blue sodium-oxide GIC with a composition of stage-2 NaOo.44C5.84, as summarized in Table 2.6 (Gadi et al., 1994, 1997). The structure of the compound, investigated by X-ray, features a five-layer intercalate of Na-O-Na-O-Na with the oaxis lattice constant of Ic = 10.8 A, as shown in Figure 2.6. The in-plane structure has a hexagonal superlattice with a = 6.36 A and a tilting angle of 0.7° with respect to the graphite unit cell. This structure is explained in terms of the sliced aft-plane of sodium peroxide Na2O2 (a = 6.21 A) with a small modification, where oxygen forms O2 ions. Heavy alkali metal also gives alkali metal oxide GICs through a similar reaction. Moreover, high-density alkali metal GICs are produced in the same process; these are similar to super-dense alkali metal GICs. Heat treatment at 300-600°C with slightly oxidized potassium or KO2 gives K.C4 with a composition the same as that of the high-pressure K GIC phase having monolayer intercalates. However, structural investigation suggests the presence of double

Table 2.6 Structure of alkali metal chalcogenide GICs Compound

Stage

NaO0.4C5.8.

2

KO0.07 C4

1

KX)2C4

1

K02C8

2

KC 3 So 25 C 3

1

KC 3 Se 0 .,C 3

1

RbO0.i-0.25C4

1

Rb00.3C3.9 Rb00.2C8

1 2

CsOo,-o6C 4 CsO,.2C8

1 1

CsO05C|8

2

/c (A) 10.80

Synthesis Condition Color

470°C, oxidized Na blue 8.40-8.90 370°C, K + KO2 purple 8.21 8.21-8.44 360-370°C, K or KC8 + KO 2 bright violet 11.62-11.72 11.62 360-370°C, K or KC8 + KO2 bright violet 8.75 340-450°C, K + S(< 1%) purple 8.71 400°C, K + Se(< 1%) purple 8.82- 9.20 350^20°C, RbO2 red 9.20 420°C, Rb0 2 purple 12.52 450-500°C, RbO2 blue 9.60 400°C, CsO2 9.84 180^00°C, Cs3O dark blue 13.19 180^K)0°C, Cs3O dark blue

Reference Gadi et al., 1997 Heroldet al., 1994 Yamashita et al., 1996 Yamashita et al., 1996 Goutfer-Wurmser et al., 1998 Goufter-Wurmser et al., 1998 Lagrange et al., 1996 Lagrange et al., 1996 Lagrange et al., 1996 Lagrange et al., 1996 Mordkovich et al., 1996 Mordkovich et al., 1996

22

Graphite Intercalation Compounds and Applications

Figure 2.6 Structure of stage-2 NaO GIC with five-layer intercalate of Na-O-Na-O-Na. Cross-sectional view (upper panel) and x-ray electron density profile along the c-axis (Gadi et al., 1997).

potassium layer intercalates, giving interlayer distances of 8.40-8.90 A depending on different polymorphs, as shown in Figure 2.7 and Table 2.6. The double potassium layer with positive charge is considered to be stabilized by the presence of a trace of negatively charged oxygen atoms (O/K = 0.07) sandwiched between adjacent potassium layers. Isostructural systems with Rb and Cs are also obtained, although the oxygen concentration is higher than that for the potassium analog as summarized in Table 2.6 (Lagrange et al., 1996). The double layer intercalate system KO_VC4 obtained with the aid of oxygen is, interestingly, converted to super-dense monolayer K GIC with the same com-

Synthesis and Intercalation Chemistry

23

Figure 2.7 Structural model of highdensity RbC4 having rubidium double intercalates. KC4 and CsC4 have the same structure (Lagrange et al., 1996).

position by the application of pressure, accompanied by a considerably large reduction in volume (Lagrange et al., 1996). This is induced by a large volume change in the pressure application process. Increasing the oxygen content works against the conversion. Alkali metal oxide GICs having stoichiometric compositions are obtained under almost similar experimental conditions for heavy alkali metals. Reacting KC8 with peroxide KO2 provides bright violet stage-1 and blue stage-2 semistoichiometric KOT GICs having compositions of KC^C^, (n — 1, 2), where 7C are estimated at 8.44 and 11.72 A for stage-1 and stage-2, respectively (Mordkovich et al., 1994, Yamashita et al., 1996). The reaction of Cs3O with graphite gives dark blue stage-1 CsOv GICs having a composition of CsOi 2C8 with /c = 9.84 A (Mordkovich et al., 1996). The structures of heavy alkali metal oxide GICs feature a four-layer intercalate of M—O-O-M (M = K, Cs). The positive ion/negative ion sandwiched structure commonly observed in alkali metal oxide GICs is favorable for ionic energy stabilization, similar to alkali metal hydride GICs. Sulfur and selenium, members of the chalcogenide family are also intercalated to give alkali metal sulfur/selenium ternary GICs (Goutfer-Wurmser et al., 1998), although the electronegativities (2.5) of these two elements are considerably lower than that of oxygen. This means that a triple atomic layer intercalate, in which negatively charged chalcogen atoms work to bind two positively charged alkali metal layers, is expected to be less stabilized for sulfur/selenium than for oxygen. These phases are prepared by immersing graphite in liquid potassium containing a small amount of sulfur or selenium (< 1% atomic). The reaction is carried out in a sealed stainless steel tube at 350-450°C, where the reaction with sulfur is faster than that with selenium. In these reactions, purple stage-1 compounds with compositions of K2S0.5C6 and K2Se0.2C6 are obtained. The amount of sulfur is larger than that of selenium. The GICs obtained are very stable against air and water. The structures of these GICs are summarized in Table 2.6. The c-axis repeat distances 7C are estimated as 8.75 and 8.71 A for sulfur and selenium respectivel The in-plane structure is characterized with a super-structure of ^/3 x \/3 as shown in Figure 2.8, similar to LiC6 for KS GIC. Potassium atoms form positively charged double layers, between which negatively charged sulfur atoms are

24

Graphite Intercalation Compounds and Applications

Figure 2.8 Structure of KS GIC with an in-plane structure of (a)V3 x -s/3 and (b) 3 x 3 . Small closed, large closed, and gray circles denote C, K, and S atoms, respectively. Half of the potassium atoms form an upper potassium sheet, while the remainder form a lower sheet. Sulfur atoms forming a sheet are sandwiched between the two potassium sheets (Goutfer-Wurmser et al., 1998).

inserted. Here, sulfur atoms are located at the centers of an octahedral environment of potassium atoms. Each potassium layer resembles the Li intercalate in LiCg, different from KgC, so that the in-plane potassium density is 1/3 higher than that of binary KCg. The sulfur atoms statistically occupy one-half of the octahedral sites, giving the atomic ratio of S/K = 1/4. Another KS GIC having a different structure is reported; this has a 3 x 3 hexagonal superstructure with a = 7.4464 A in spite of its similarity of atomic arrangement to the former compound. KSe GIC has a hexagonal structure similar to that of KS GIC, in which the inplane lattice and the c-axis parameters are given by a = 7.439 and c = 2/c = 17.42 A, respectively. Alkali metal halides are reported to give GICs when molten alkali metal in presence of its halide is reacted with graphite sealed in a stainless steel tube with an argon atmosphere (Herold et al., 1995). The intercalation reaction for sodium takes place with NaCl and NaBr at 550-600°C, whereas with Nal it takes place at 450°C. Stage-3 NaX0.5C10, yielded in the reaction for X = Cl and Br, has sandwich thicknesses of ds = 7.56 and 7.71 A for X — Cl and Br, respectively, which suggests the presence of triple layer intercalate of Na+-X~-Na+ in the graphitic galleries. Their in-plane superstructure features with a hexagonal structure with \/3 x V5 as shown in Figure 2.9. For iodide, there are four different stage-2 polymorphs having compositions of NaI018_0.27C5.!_6 with hexagonal -v/3 x \/3, orthorhombic with a = 6.65 and b = 3.80 A, and incomensurate superstructures, where the sandwich thicknesses ds range from 7.62 to 7.74 A for a triple sandwich atomic layer intercalate of Na+-I~-Na+. Alkali metal hydroxide GICs (M = Na, K) are prepared by heat treatment of a mixture of molten alkali metal and its hydroxide with graphite (Herold et al., 1991). We obtain blue stage-1 NaOH GIC with a composition of Na(OH)o.89Ho.o45C2.i2 in a molten Na-NaOH mixture at 350°C over several hours. Similarly, KOH GICs are prepared with a mixed K-KOH liquid at 404°C, resulting in the formation of a mixture of stage-1 to 3 compounds (purple to black). These products are very stable against water. The structure of stage-1 NaOH GIC is characterized by 7C = 9.21 A and a square in-plane superlattice

Synthesis and Intercalation Chemistry

25

Figure 2.9 In-plane superstructure of NaX GICs (X = Cl, Br) (Herold et al., 1995).

with a = 3.41 A, incommensurate with graphite sheets. The intercalate forms a unique double layer in which each layer consists of Na + and OH~ ions alternately positioned on a planar lattice as shown in Figure 2.10. A double layer of pristine NaOH sliced by the £-plane roughly represents this; namely, the in-plane lattice constant a and the thickness of the intercalate (9.21 - 3.35 = 5.86 A) correspond to a = 3.397 A and b/2 = 5.66 A, respectively. Interestingly, according to the composition, the presence of an excess amount of H + ion gives a positive net charge to the intercalate, so that the intercalate can work as a donor to graphite, resulting in the stabilization of the intercalate structure. KOH analogs are considered to form a similar intercalate structure. 2.2.2 Alkali Metal and Rare Earth Metal with Ammonia and Organic Molecules Donor GICs with alkali metal, alkali earth metal, and rare earth metal accept organic compounds and ammonia as part of the intercalates, giving ternary systems. Ammonia or organic molecules are incorporated with donor metal species

Figure 2.10 Structure of the NaOH intercalate of NaOH GIC (Herold et al., 1991).

26

Graphite Intercalation Compounds and Applications

in the intercalates. Ternary GICs with ammonia are prepared mainly by reactions of graphite in liquid ammonia in which alkali metal, alkali earth metal, or rare earth metal is dissolved (Herold et al., 1965; Riidorff, 1965; Riidorffet al., 1955). Another preparation method is that donor binary GICs are reacted with the liquid or gas phase of ammonia; in this method the content of donor species becomes less than that of the starting binary GICs in the case of the reaction with liquid ammonia (York and Solin, 1985). Using the same technique, other nitrogen-containing bases can be introduced to give similar ternaries. Electrolysis of graphite in a solution of metal iodide in liquid ammonia is used for ternaries with Be, Mg, Al, Sc, Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Eu, and Lu (Alheid et al., 1994; Craven and Ostertag, 1966; Stumpp et al., 1996). All the stage-1 GICs are blue, while stage-2 GICs are grayish-blue. Table 2.7 summarizes the compositions and structures of ammonia-including ternaries. The sandwich thicknesses are roughly independent not only of the metal species and their concentration but also of the ammonia concentration, ranging around ds — 6.6 A. This suggests that the size of NH3 molecules governs the sandwich thicknesses in the intercalates. However, a systematic investigation proves that the sandwich thickness increases slightly from 6.5 to 6.6 A with increasing ammonia concentra-

Table 2.7 Structures of metal ammonia ternary GICs (Setton, 1990, revised). Compound Li(NH 3 ),. 6 C, 0 . 6

Na(NH 3 ) 2 ,C, 6 _ 5

K(NH 3 ),,C, 2 ., K(NH3)4.,,C23.6 Rb(NH,),,C 1 1 9 Rb(NH 3 ) 41 C 23J Cs(NH 3 ) 22 C ]2 . 8 Cs(NH,), 65 C 2 ,. 5 Li(MeNH2),.8C12.9 Li(NH 2 CH 2 CH 2 NH 2 )C 28

Li(HMPT)C32

Na(HMPT)C27

K(K222)C 36

K(NEt 3 ) 041 C 36

Stage

/c (A)

1 1 1 1 1 1 1 1 1 2 2 1 1 1

6.62 6.64 6.56 6.62 6.58 6.64 6.58 6.67 6.66 2 x 9.95 11.85 4 x 7.48 4 x 7.63 15.50

1

Be(NH3)0.77C6.,

3

12.40 12.24

Mg(NH 3 ) 2 _,C 32

4 1 1 1

15.95 6.62 6.36 6.36

Ca(NH 3 ) 2 2 C, 2 1 Sr(NH,), 4 C u ,

Ba(NH3)25C,0.9 Eu(NH 3 ), 31 C ]7 . 5 A1(NH3), ,.,. 6 C g _, 0

Yb(NH 3 ), 9 H 0 .,C 2 , 6

2 4 2?

9.80 16.0

Reference Schulze, 1954 Schulze, 1954 Schulze, 1954 Solin et al., 1985

Riidorffet al.. 1955 Solin et al., 1985 Rudorff et al., 1955 Solin et al., 1985 Schulze, 1954 Riidorffet al., 1965 Ginderow, 1971 Ginderow, 1971 Merle et al., 1978; Setton et al., 1983 Merle et al., 1978 Craven and Ostertag, 1966; Riidorffet al., 1965 Riidorffet al., 1965 Riidorffet al., 1965 Rudorff et al., 1965

Rudorff et al., 1965

Craven and Ostertag, 1966 Craven and Ostertag, 1966 Craven and Ostertag, 1966

HMPT: (NMe,),P0 4 ; K222: N(CH 2 CH 2 OCH : CH 2 OCH 2 CH,(H,),N.

Synthesis and Intercalation Chemistry

27

tion in stage-1 K-NH3-GICs (York and Solin, 1985). There is a difference in the compositions, depending on the preparation methods. For heavy alkali metalammonia GICs, the reaction in alkali metal-solvated liquid ammonia gives a composition of M(NH 3 ) 2 .i-2.2Ci 1.2-12.8 (M = K, Rb, Cs) for stage-1 (Riidorff et al., 1955), whereas M(NH3)3.7_4.3C23.3_23.6 is obtained from the gas phase reaction (York and Solin, 1985). The low alkali metal concentration in the sample prepared from liquid ammonia is associated with the expulsion of alkali metal from the intercalate to liquid ammonia. The intercalate structure investigated in detail by Fan and Solin (1987), Tsang et al. (1987a), and Resing et al. (1985) suggests that potassium ions coordinated coplanarly by four ammonia molecules (K(NH3)|) are in a 2D liquid state in the graphitic galleries, where the threefold axes of the NH 3 molecules are oriented parallel to graphene planes or slightly tilted from them to the c-axis (Depondt et al., 1992). Similar NH3-coordinated structures are reported for Cs- and Mg-NH 3 GICs (Depondt et al., 1992; Stumpp et al., 1996). The NH 3 molecules rotate freely with respect to their threefold axes (Depondt et al., 1992; Stumpp et al., 1996; Tsang et al., 1987b). Figure 2.11 displays the structure of the K(NH3)4 intercalates and their liquid state. According to the composition K(NH3)4.3C.24 for stage-1, excess NH 3 molecules (0.3) exist as free molecules between K(NH3)4 units which have bound NH 3 molecules. The reason why the interplanar distance is independent of the donor species and ammonia concentration can be explained by the size of ammonia molecules, which is larger than that of donor ions and governs the interlayer distance, as shown in Figure 2.11. Aromatic hydrocarbons, aliphatic hydrocarbons and their oxygen derivatives are known to be organic molecules that can be intercalated in the presence of alkali metal, similarly to ammonia. There are several preparation methods for the

Figure 2.11 Structure of K(NH 3 )4 intercalates and their liquid structure in K-NH3 GIC. (a) NH 3 molecule between graphitic planes; (b) K(NH 3 ) liquid structure. Closed circles and open (hatched) circles represent potassium ions and bound (free) ammonia molecules respectively (Fan and Solin, 1987).

28

Graphite Intercalation Compounds and Applications

ternaries: (1) direct reaction of graphite with metal complex in solution (Co-MinhDuc et al., 1970); (2) electrolysis (Besenhard et al., 1980); and (3) reaction of the organic molecule with metal-binaries (Hamwi et al., 1980). Tables 2.8-2.10 summarize the alkali metal-organic molecule ternary GICs that have been prepared so far. Benzene is easily intercalated into stage-2 KC24 at a temperature just above room temperature through reaction of KC24 with benzene vapor, giving stage-2 K(Bz)! 2C24, as is evidenced by an increase in the c-axis lattice constant from 7C = 8.8 to 12.6 A (Blumenfeld et al., 1983; Hamwi et al., 1980). When the temperature of KC24 is slightly higher than that of benzene, stage-1 K(Bz)2.2C24 with Ic = 9.24 A is obtained (Jegoudez et al., 1983; Merle and Beguin, 1980). Stage-2 GICs with other heavy alkali metal species form similar ternaries. There is no appreciable change in the interlayer distance among K, Rb, and Cs, suggesting the important role of benzene in the formation of the intercalate structure; that is, the intercalate thickness is larger than the sizes of the alkali metal ions. Interestingly, stage-1 alkali metal GICs do not accept benzene or some other organic molecules as intercalate (Jegoudez et al., 1983). This suggests that organic molecules can be accommodated only in the case that there is enough space in the interstitial between alkali metal ions in the graphitic galleries, judging from the fact that the in-plane alkali metal ion density of stage-2 alkali GICs having a composition of MC24 is two-thirds of that of stage-1 MCg. Toluene and o-xylene are similarly intercalated in alkali metal binary GICs as the third constituents. The ternaries thus produced are similar in composition to the benzene-including ternaries, although the interlayer distances are varied (Besenhard et al., 1983; Isaev et al., 1983). Aliphatic molecules include methane (Pilliere et al., 1992), ethane, ethylene, acetylene (Pilliere et al., 1993, 1994; Takahashi et al., 1991, 1992), «-hexane (Goldmann et al., 1989), and some other alkanes (Beguin et al., 1990), which Table 2.8 Ternary graphite intercalation compounds containing aromatic hydrocarbons (Setton, 1990, revised). Stage

/ C (A)

K(Bz) 28 _ 3 C 24 -26

1

9.27-9.31

K(BzU2C24

1

9.27-9.30

K(Bz),,C48 K(Bz),.2C24

2 2

12.6 12.2-12.6

K(Bz'V 6(H C 24 Rb(Bz),,C24 Cs(Bz),.C24 K(Tol)3C24 K(Tol),.2C24 K(Tol),.C,, K(Tol)0.7Cn K(Tol),,Cn K(Tol)0.7C24

2 2 1 1 1 2 2 3 4

12.2 12.6 9.29 9.08

Compound

9.14

12.37 12.3 15.72 19.01

Reference Blumenfeld et al., 1983; Bonnetain et al., 1977; Hamwi et al., 1976 Beguin et al., 1980; Hamwi et al., 1980; Jegoudez et al., 1983; Merle and Beguin, 1980 Co-Minh-Duc et al., 1970; Hamwi et al., 1976 Blumenfeld et al., 1983; Hamwi et al., 1980; Tabony and Korb, 1985 Blumenfeld et al., 1983; Merle and Beguin, 1980 Bonnetain et al., 1977 Bonnetain et al., 1977 Besenhard et al., 1983 Isaev et al., 1983 Besenhard et al., 1983 Isaev et al., 1983 Besenhard et al., 1983 Besenhard et al., 1983

Bz: benzene; Bz': compounds derived from benzene; Tol: toluene.

Synthesis and Intercalation Chemistry

29

Table 2.9 Ternaries of alkali metals with organic molecules (Setton, 1990, revised). Compound

Na(DMSO),.C24

K(DMSO),,C,4 K(DMSO) 5 ,C 48 K(DMSO) 64 C 7 ,_ 75 K(DMSO),.C% Rb(DMSO)6C24 Cs(DMSO)6C24

NMe 4 (DMSO) 6 C 24 KFu 0 . 76 C 8

Stage

/c(A)

Reference

1 1 2

15.81 14.93 18.24 21.61 25.00 14.98

Besenhard, Besenhard, Besenhard, Besenhard, Besenhard, Besenhard, Besenhard,

3 4 1 1 1 1

K.Fll| 44^24

2

KFu117CM KFu2J4C48

3

KFU 2 2 8C 6 0

KFu 2J5 C 72 RbFu0i9,,C8

2 4

5 1

15.82 15.82 8.78 12.12 12.16 15.48 18.85

22.30

9.00

1980 1980 1980 1980 1980 1980 1980

Besenhard, 1980 Jegoudez, 1986 Jegoudez, 1986

Jegoudez, 1986 Jegoudez, Jegoudez, Jegoudez, Jegoudez,

1986 1986 1986 1986

DMSO: dimethylsulfoxide; Fu: furan.

are reported to form ternaries with Cs GICs (stage higher than 1). Ethylene intercalated in stage-2 CsC24 leads to stage-1 Cs(C2H4)1.2_2C24 with a sandwich thickness of 6.85 A, in which the intercalation reaction takes place at low temperatures below 250 K through the physisorption of ethylene, accompanied by a warming-up process to room temperature. Intercalation at high temperatures above room temperature gives a stage-2 ternary with a different composition Cs(C2H4)0 3C24. Oligomerization of ethylene molecules taking place above room temperature makes the ternary greatly resistant to air and water; the details will be discussed in Section 8.1 in connection with the physisorption phenomenon of etlylene molecules at low temperatures. «-hexane is stabilized in the physisorbed state in the intercalate in the ternary Cs(«-hexane)0.44C24. Ternaries with DMSO (dimethylsulfoxide) are mainly prepared by electrolysis (Besenhard et al., 1980; Okuyama et al., 1981). Furan gives well qualified ternaries with various stages n = 1-5 (Jegoudez et al., 1986). Finally, we discuss the structures of the ternaries mentioned above. In the intercalate of alkali metal-benzene GIC, the molecular plane of benzene is tilted by 60° with respect to the graphene plane, where the alkali metal ion is accommodated in a cavity created by two benzene rings tilted toward each other as shown in Figure 2.12 (Beguin et al., 1980; Reikel et al., 1983). Benzene molecules are rotated freely with respect to the sixfold axis down to 77 K (Beguin et al., 1980). In contrast, there are two phases in alkali metal-THF (tetrahydrofuran) GICs having different orientations of the THF molecular plane, reflecting the difference in their compositions. In the low THF concentration phase with THF/K ~ 1.2, the mean plane of THF molecules is parallel to the graphene plane, giving a sandwich thickness of 7.2 A. In contrast, the high concentration phase with THF/K ~ 2.5 has the molecular plane perpendicular to the graphene

30

Graphite Intercalation Compounds and Applications Table 2.10 Ternaries and quaternaries of alkali metals with oxygencontaining organic molecules (Setton, 1990). Compound

Stage

7 C (A)

Reference

7.24 12.53 12.44 12.45

Nomine and Bonnetain, 1967 Beguin et al., 1985 Beguin et al., 1985 Beguin et al., 1985 Nomine and Bonnetain, 1967 Nomine and Bonnetain, 1967 Nomine and Bonnetain, 1967 Beguin and Setton, 1975 Quinton et al., 1986 Marcus et al., 1986 Beguin and Setton, 1975 Quinton et al., 1986 Beguin and Setton, 1975 Setton et al., 1982 Marcus et al., 1986 Marcus et al., 1986 Quinton et al., 1986 Marcus et al., 1986 Marcus et al., 1986 Marcus et al., 1986 Beguin et al., 1970 Bouat et al., 1983 Marcus et al., 1986 Beguin et al., 1970 Beguin et al., 1988 Goldmann et al., 1988 Goldmann et al., 1988 Merle et al., 1978 Merle and Gole, 1976 Co-Minh-Duc et al., 1972 Co-Minh-Duc et al., 1972 Co-Minh-Duc et al., 1972 Ginderow, 1971 Ginderow, 1971 Beguin and Setton. 1976 Hamwi et al., 1984

Li(THF), 2,C20, Li(THF), 4C6 Li(THF) 23 C l2 Li(THF) 34 C l8 Na(THF)35,C32 Na(THF),C 64 K(THF) M6 C 24 -3 7

2 1

7.15-7.18

K(THF), M 7 C 48 _ 495

2

10.56

K(THF) 2 _ 25 C 24

1

8.84-8.89

K(THF)2.15C24.28

2

12.12-12.27

Rb(THF) M C 24 Rb(THF)_ 2 C 24 Rb(THF)_2C24 Rb(THF) 2 _,C 24

2 1

7.24

1 ") L

11.12

7.16 10.43 8.89

8.90-8.95

Rb(THFK 2 C 24 Cs(THF)3C24 Cs(THF), 75C24

") Z.

1 1

8.95 7.046

Cs(THF) v C 24 K(DOX) 09 ,C M K(DOX).C,7 Li(DME) 28 C 33 Na(DME) 28 C 32 K(DME) 21 C 3 , K(DME)C 32 Li 2 (BzN)(THF), 5C54 K(THF) 04 (Bz) 037 C 8 K(THF)v(Bz)yC24

2 1 2 1 1 1 1 1 1 1

10.192 7.30 8.9 7.32 7.26 7.28 7.24 7.44

12.17

9.00 9.00

THF: tetrahydrofuran; DOX: dioxan; DMF: dimethoxycthane; BzN: bcnzonitrile.

plane, resulting in a large sandwich thickness of 8.9 A. The in-plane structure of the low concentration phase is shown in Figure 2.13 (Facchini et al., 1980). Since the THF molecule has a dipole, the interaction between the dipole and the positive charge of K + plays an important role in the structure, so that the molecular motions of THF molecules are quenched by the strong ion-dipole interaction. In the high concentration phase, the THF molecules, whose oxygen ions protrude to the graphene plane, rotate freely with respect to the twofold axis perpendicular to the graphene plane, suggesting an unfavorable structure for the ion-dipole interaction. The lithium-THF ternaries have a considerably large sandwich thickness

Synthesis and Intercalation Chemistry

3I

Figure 2.12 Intercalate structure of K(Bz)2C24 (Beguin et al., 1980; Reikel et al., 1983). ranging from 12.4 to 12.5 A, which is independent of the THF/Li ratio which varies from 1.4 to 3.5. This suggests the formation of a tetrahedral structure of THF molecules surrounding a central Li+ ion ([Li(THF)4]+), where the THF molecules have a fairly high rotational degree of freedom at room temperature (Beguin et al., 1983). 2.3 Acceptor Intercalation Compounds

2.3.1 Chloride GICs Following early work by Riidorff et al. (1963), transition metal chloride GICs have been the most extensively investigated acceptor GICs in many kinds of

Figure 2.13 Intercalate structure of K(THF)C 24 . Hatched circles represent potassium atoms (Facchini et al., 1980).

32

Graphite Intercalation Compounds and Applications

aspects in basic science and applications, such as chemical properties, structures, electrical and magnetic properties, and applications for batteries and catalysts (Dresselhaus and Dresselhaus, 1981; Dresselhaus et al., 1990; Flandrois, 1982; Herold, 1979). Several preparation methods are known for the preparation of chloride GICs, in which vapor phase synthesis and liquid phase synthesis are most commonly used. In vapor phase synthesis, vaporized metal chloride is reacted with graphite in the presence of chlorine gas or vaporized A1C13 in the temperature range at which the metal chloride is in the gas phase. Chlorine gas or A1C13 works to supply negatively charged chloride ions, which are considered to be accommodated in the graphitic galleries in metal chloride GICs, as shown in the following reaction scheme:

where n is the stage index for the produced GIC. Figure 2.14 shows a typical reaction system for the preparation of transition metal chloride GICs (Dresselhaus and Dresselhaus, 1981). There are several exceptional cases in which the presence of C12 gas is not required. Metal chlorides such as FeCl3, CuCl2, AuCl3, and SbCl5, whose auto-dissociation provides chlorine gas, are involved in these cases, as shown in the following reaction:

Figure!. 14 Synthesis system of FeCl3 GICs: (a) preparation of dried FeCl3 with C12 gas; (b) A sealed glass tube with graphite, FeCl3, and C12 gas is heat-treated in an electrical furnace, in which the temperatures of graphite flakes and FeCl3 are independently determined depending on the stage of the GIC (Dresselhaus and Dresselhaus, 1981).

Synthesis and Intercalation Chemistry

33

The role of A1C13 in the intercalation reaction is the formation of an intermediate complex which makes the intercalation process possible as follows (Stumpp and Nietfeld, 1969);

where the reaction can be processed effectively for rare earth (Ln) chlorides. Figure 2.15 shows the isotherm of the graphite-SbCls system where an SbCls GIC sample is held at a constant temperature (Melin and Herold, 1975). The temperature difference between SbClj and SbCls GIC is maintained below about 20°C for the preparation of stage-1 C|2SbCl5. As the difference increases, higher stage GICs are successively obtained. An intercalation reaction in solvent is carried out mainly with SOC12 (Boeck and Riiddorff, 1973), SO2C12 (Stumpp, 1977), CC14 (Lalancette et al., 1976), or CH3NO2 (Hooley, 1972) as solvent. SOC12 or SO2C12 generates C12 gas, which allows the intercalation reaction to proceed, while reaction with CCU takes place in the coexistence of C12 gas. The electrophilic reagent CH3NO2 is known to give various metal chloride GICs, although the solvent is occasionally co-intercalated in addition to the metal chloride. Electrolytic intercalation in the molten state is also employed for the preparation of several metal chloride GICs such as A1C13 GIC (Fouletier and Armond, 1979), BiCl3 GICs (Stumpp and Wloka, 1981), and so on.

Figure 2.15 Dissociation isotherm of the graphite-SbCls system. The temperature (r comp ) of an SbCl5 GIC sample is held at rcomp = 217°C. Tt is the temperature of the SbCl5 (Melin and Herold, 1975).

34

Graphite Intercalation Compounds and Applications

Judging by the large number of researches that have been carried out, almost all metallic elements in the periodic table give chloride GICs. Table 2.11 shows elements whose chlorides give metal chloride GICs in relation to the periodic table (Ohhashi, 1986). These metal chloride GICs are classified as acceptor-type GICs, except for alkali metal chloride GICs that behave as donor-type GICs as already explained in Section 2.2.1. Although, in alkali earth families, only a small number of elements such as Be and Mg form GICs, most of the elements belonging to the IIIA-VIIA, IB-VB, and VIII families commonly give GICs where the element takes the most stable valence state. It is also known that the chlorides of lanthanide and actinide elements form GICs. Unpaired electrons in the transition metal or rare earth metal bring about localized spin-featured magnetism in the chloride GICs, this has been intensively studied as 2D magnetism as will be discussed in Chapter 7. The intercalate-to-graphite composition ratio and the lowest stage that can be obtained in the intercalation reaction depend on the chemical activity of the metal chlorides, the graphite hosts, and the intercalation methods. For example, the vapor pressure of the metal chloride is an important factor in the case of vapor phase reaction. The intercalate-to-graphite composition ratio is not uniquely determined, unlike that of aklali metal GICs where the ratio depends only on the stage number. Even for stage-1 compounds, the composition ratios vary from 5 to 30, depending on the size and chemical features of the intercalates. Most metal chloride GICs are stable in the air, unlike other GICs such as alkali metal GICs. Metal bromides tend to have similar chemical activities to corresponding metal chlorides. Therefore, some metal bromides can be intercalated in graphite, where the properties and crystal structures of the metal bromide GICs are analogous to their metal chloride counterparts. However, no metal iodide GICs have ever been reported except for Nal GICs, which are donor-type GICs as discussed in Section 2.2.1. From the structural features of intercalates, metal halide GICs are classified into two groups. In the first group, in which 3d-transition metal chloride GICs are involved, intercalates form a chemically bonded infinite 2D network in the graphitic galleries, whereas the second group consists of isolated intercalate molecules. The structure of FeCl3 GIC, which is a typical metal chloride GIC in the first group, is shown in Figure 2.16. In the intercalate, chlorine atoms form a close-packed double layer lattice, the octahedral interstitials of which are occupied by Fe atoms. This structure is almost identical to the structure of pristine FeCl3 crystal sliced parallel to the c-plane. Consequently, the properties of the metal chloride intercalate are not so diferent from those of the pristine compound. The sandwich thicknesses of the metal chloride GICs in this group are in the range of 9.2-9.8 A, which is evidence for the presence of C1-M-C1 triple layer intercalate in the graphitic galleries. The thickness of the intercalate is almost the same, irrespective of metal species. ReCl5 GIC has an exceptionally large sandwich thickness ranging around 11.8 A, which is explained by the presence of a thick intercalate layer Cl-Re-Cl-Re-Cl (Steinwede and Stumpp, 1980). In the second group with isolated molecular intercalates, SbCl5 GICs and AuCl3 GICs are known as typical examples. In SbCl5 GICs, a disproportionation

Table 2.11 Metal chloride GICs. Arabic figures and Roman numerals represent composition ratios C/(MClm) and stage numbers, respectively (adapted and revised from Ohhashi, 1986). IA 2 Li

3 NaCl05 10 III 4 K

II A

BeCl, III MgCl, 11 I Ca

III A

IV A

VIII

FeCl3 6.11 CoCl2

IB

V

YC1

ZrCl 14 HfCl 46 III

NbCl5 40 II TaCl5 25 II

MoCl5 18.6 II WC16 70V

Tc

ReCl 13 I

FeCl2 5.6 I 4.71 RuCl3 RhClj II 119 OsCl3 IrCl4 12.2 II 111

Pm

SmCI3 35

EuCl, 37.1 III

GdCl3 TbCl3 DyCl3 23 III 18.7 III 18 III

Sr

6 Cs

Ba

28.6 II III Laa

7 Fr

Ra Ce

Ac" Pr

Nd

Th

Pa

UC15 19 I

UC14

25 Sodium chloride gives a donor GIC. Lantanoid. b Actinoid.

d

CrCl3 21 II III

VII A

TiCL, 321

5 Rb

b

VI A

ScCl3

21 III

a

VA

MnCl 2

6.61

NiCl, 11.311

CuCl,

4.9 I

PdCl2 Ag 14.8 III AuCl3 PtCl4 12.61 42 III

HoCl3 20.3 II

VB

II B

III B

C

N

Si

P

ZuCl2 16.5 III

BC13 28 III A1C13 8.41 GaCl3 8.41

Ge

As

CdCl2 6.7 I HgCl2 20 III

lnC!3 14 II TiCl3 8.5 I

Sn

SbCl4 12 I BiCl4 18

ErCl3 23.3 II III

TmCl3

YbCl3 25.1 III

23.7 III

IV B

Pb

LuCl, 34.8 IV

36

Graphite Intercalation Compounds and Applications

Figure 2.16 Structure of stage-1 FeCl3 GIC (Dresselhaus and Dresselhaus, 1981).

reaction takes place in the intercalates as given by the following equation (Clarke et al, 1982): 3SbCl5+2e~ -> 2SbCl^+SbCl3

(2.5)

where SbQ3 and SbClg having trigonal pyramid and octahedral shapes, respectively, coexist as isolated molecular species in the graphitic galleries. The c-axis lattice constant 9.42-9.50 A for stage-1 is governed by the size of the SbCl," octahedron. Similar disproportionation in the intercalate is known in AsF5 GICs, as discussed later in Section 2.3.2. AuCl3 GIC (C 13 . 5 ^ 14 AuCl 3 ) has the shortest sandwich thickness 6.8 A for stage-1 (Ishii et al., 1995), where the dimerized unit Au2Cl6, having a planar shape, forms a (2^/7 x 2V?)R 19.1° superlattice. The molecular plane is oriented parallel to the graphene sheets. 2.3.2 Fluoride GICs A large number of fluoride intercalation compounds have been reported among metal fluorides, halogen fluorides, boron fluoride, hydrogen fluoride, and rare gas fluorides as summarized in Table 2.12 (Amine et al., 1991; Nakajima, 1995; Nakajima and Watanabe, 1991; Tressaud et al., 1992). Metal fluoride GICs are mainly classified into four groups depending on the coordination numbers of metal fluorides used as intercalates: trifluorides, tetrafluorides, pentafluorides, and hexafluorides. Most fluorides are intercalated spontaneously (Falardeau et al., 1978; Selig and Ebert, 1980) or by intercalation in an oxidative atmosphere such as fluorine, chlorine, a mixture of F2 and HF, CrO3, or chromyl fluoride

Synthesis and Intercalation Chemistry

37

Table 2.12 Fluoride GICs. The composition represents that estimated for a stage-1 compound. In cases when a stage-1 compound is not obtained, it is deduced from the compositions of higher stage compounds (Amine et al., 1991; Nakajima, 1995; Tressaud et al., 1992) Intercalate (X) Monofluoride Trifluoride

HF

BF,

GIF, BrF,

RhF, Tetrafluoride Pentafluoride

AuF, TiF4 SiF4 GeF4 NbF, TaF5"

PF5

Hexafluoride

AsF5 SbF5 IPs MoF 6 WF 6 OsF6 lrF6 PtF6 UF 6

Composition x CVX 2-3 (X = H(HF) 0>0 5) 7 X = RhF 3 3 (HF 2 ), 3 7 12 8.3-8.6 7.5-8.8 12 (X = PF5.5) 8

6 8.7 11

14(X = WF 6 (HF) V ) 8 8 12 -

Sandwich Thickness ds (A) 5.5-6.4

7.7 -

7.87 8.08 8.4 7.94

-

8.41 8.41-8.44 7.65 8.10 8.46 8.42 8.35 8.10 8.05 7.56 8.55

(Hamwi et al., 1977; Mouras et al., 1987). Intercalation in liquid HF (Touhara et al., 1987b), chemical reduction, and electrochemical intercalation are also employed. Intercalation of most MF6 hexafluorides (M = Mo, Os, Ir, Pt, U) and pentafluorides MF5 (M = As, Sb, Ru, Os) into graphite occurs spontaneously, while oxidative intercalation is employed for tetrafluorides such as TiF4 as well as for hexafluorides and pentafluorides, in which the intercalation reaction is enhanced by the oxidative atmosphere. Among metal fluoride GICs, AsF5 and SbF5 GICs are the best known and have been the target of intensive studies. According to an x-ray absorption study (Bartlett et al., 1979/1980), intercalate AsF5 is subjected to the following disproportionation reaction through charge transfer from graphitic layers: similar to SbCl5 GICs (see Section 2.3.1). AsFs GICs are therefore formulated as Ci 2n (AsF 6 )~ • (l/2)AsF 3 in place of C8wAsF5, where n is the stage number. The introduction of additional fluorine converts AsF3 to AsF^, resulting in the formation of Cg~AsF^~. Crystal structure analysis suggests that the stage-1 compound has a hexagonal structure with lattice parameters a = 4.92(2) and c — 7.86(2) A (McCarron and Bartlett, 1980). Vacuum treatment induces desorption of AsF6,

38

Graphite Intercalation Compounds and Applications

giving the less dense GIC Cj^AsFg with a sandwich thickness of ds = 8.04 (2) A. The in-plane structures of C^AsF^" and Cf^AsF^ are shown in Figure 2.17 (Bartlett and McQuillan, 1982). The AsF6 octahedral intercalates form a triangular lattice in the graphitic galleries in Cg"AsF^", while the disappearance of onethird of the intercalates leads to the formation of a honeycomb lattice in C^AsFg , accompanied by an increase in the c-axis repeat distance due to the diminution of the Coulomb attractive force between positively charged graphitic layers and negatively charged AsF^~ intercalate layers. In SbF5 GICs, a similar structural feature appears with disproportionation between SbFg" and SbF3 (Facchini et al., 1982). Octahedrally coordinated MF6 structures are generally found in metal fluoride GICs. In C 20 RuF 45 , octahedral RuF6 intercalates form (RuF4)« chains in the graphitic galleries, where the intercalate superlattice, with the oblique unit cell having a 7.8 A edge and 42° angle, is incommensurate with the graphite lattice (Flandrois et al., 1988). In C V VF 6 , VF6 intercalates are well separated from each other in a large hexagonal lattice with the lattice constant of a = 8.868 A, where the unit cell direction differs by 14° with respect to that of graphite (Nakajima et al., 1988).

2.3.3 Acid GICs: HNO3, H2SO4, etc. Acids work as acceptors to graphite, giving acceptor-type GICs. In the intensively oxidative condition with acid, graphite is converted to graphite oxide, where oxygen breaks the graphite ;r-bonds, resulting in the formation of an oxygenbridged corrugated sheet of carbons at the expense of jr-bonds (Ubbelohde, 1960). On the other hand, a moderate condition gives acid GICs. These are prepared by oxidant-assisted intercalation or electrochemical intercalation as given by the following reactions, respectively:

Figure 2.17 In-plane structures of (a) C^AsF6 and (b) Cj"2,,AsF6 (Bartlett and McQuillan, 1982).

Synthesis and Intercalation Chemistry

39

where HA is the acid intercalated in the graphitic galleries. Several oxidants are known to have been used in the intercalation reactions: HNO3, CrO3, KMnO 4 , (NH4)2S2O8, PbO2, MnO2, HC1O4, MeClO4, As2O5, Na2O2, H2O2, and N2O5. In the reactions, acid HA is intercalated, generally accompanied with A~ anion. H2SO4 GICs are typical acid GICs prepared by both electrochemical and oxidant-assisted intercalation reactions. Figure 2.18 shows the variation of cell potential during galvanostatic oxidation of highly oriented pyrolytic graphite (HOPG) in 96% H2SO4 for electrochemical intercalation. During the passage of time in the electrochemical cell, giving a step-like increase in the cell potential, H2SO4 GICs with lower stage indices are developed (Metrot and Fischer, 1981). Stage-1 H2SO4 GIC, in which graphite is most oxidized, is prepared at a cell potential just below the potential of electrolyte decomposition. In contrast to H 2 SO 4 -GICs, HNO3 is easily intercalated into graphite in a gas-solid reaction without the aid of oxidant since HNO3 itself works as an oxidant. In addition to GICs with HNO 3 (Fuzellier et al., 1977) and H2SO4 (LopeGonzalez, 1969), it is known that acid GICs are formed with H3PO4 (LopeGonzalez et al., 1969), H3AsO4, HF (Mallouk and Bartlett, 1983), H2SeO4, H4P207 (Lope-Gonzalez et al., 1969), HC1O4 (Nixon et al., 1964), CF3COOH, HS03F (Touzain, 1978), HIO4, H5IO6, HAuCl 4 (Griebel, et al., 1992), and H2PtCl6 (Griebel, et al., 1992). Table 2.13 presents the c-axis repeat distances and compositions of those acid GICs that have been investigated. The compositions of most stage-1 acid-GICs are described as C24_26+X~ (X = intercalate), while the c-axis repeat distances of stage-1 GICs are in the range of 7.7-8.2 A except for HAuCl4 GIC. The small c-axis repeat distance of HAuCL, GIC results from the planar shape of the intercalate, similar to AuCl 3 GICs which have been discussed in Section 2.3.1.

Figure 2.18 Variation in cell potential during galvanostatic oxidation of HOPG in 96% H2SO4. A-B: stage-2; B-C: mixture of stages 1 and 2; C-E: stage-1; E-F: no further change; beyond F: the electrolyte decomposes with copious evolution of gas (Metrot and Fischer, 1981).

40

Graphite Intercalation Compounds and Applications

Table 2.13 Compositions and c-axis repeat distances of stage-1 acid GICs. In cases when a stage-1 GIC is not obtained, that with the lowest stage obtained is presented. Acid

Composition

HNO3 HNO 3 H,SO4 H,P04 H4P207

Cj,NO^ • 3HNO, C16 • HN03 C^HSOJ • 2H2SO4

HF

H2SeO4 HC104 HSO,F HS03C1 CF3COOH HSO3CF3 BF3(CH3COOH)2) H 2 Au 2 Cl 6 H2PtCl6

/c (A)

-

Cn • HF2~ Cj4HSeO4 • xH2SeO4 CJ,C1C>4 • 2HC1O3 C5HSO3F C + v CISOJ • yHSO3Cl C^CF^COQ- -xCF 3 COOH Cj,CF3S0^.1.63HS03CF3

-

C 2 5 HAuCl 1 9 .0.4H 2 0 C48H2PtCl6 • 3.9H20

7.8-7.85 9.90 (stage-2) 7.98-8.01 11.38 (stage-2) 11. 54 (stage-2) 18.89 (stage-2) 8.25-8.26 7.73-7.95 8.04 8.03 8.19 8.036 8.10 6.78 12.53 (stage-2)

Reference Nixon et al., 1966 Fuzellier et al., 1977 Lope-Gonzalez et al., 1969 Lope-Gonzalez et al., 1969 Lope-Gonzalez et al., 1969 Mallouk and Bartlett, 1983 Riidorff and Hoffmann, 1938 Nixon et al., 1964 Touzain, 1978 Bartlett et al., 1978 Rudorff and Siecke, 1958 Horn and Boehm, 1977 Ubbelohde et al., 1963 Griebel et al., 1992 Griebel et al., 1992

Among the acid GICs, HNO3 and H2SO4 GICs have been most intensively investigated, not only from the structural aspect but also from that of the electronic structure. In H2SO4 GICs, in which HSO^ ions and H2SO4 molecules coexist with the composition of t^SC^/HSOJ = 2.4—2.5, tetrahedral SC>4~ ions are networked by hydrogen bonds, giving a 2 x 2 superstructure in the intercalate layer (Aronson et al., 197la). Tetrahedral SO^ ions are in rotational motion at room temperature, where the presence of water molecules decelerates the rotational motion because of the strengthening of hydrogen bonding (Bindl, 1986). It is worth noting that the density of the intercalate, 1.94 g/cm3, is larger than that of liquid sulfuric acid, 1.82 g/ cm3, suggesting the presence of a considerably condensed 2D sulfuric acid layer in the graphitic galleries (Aronson et al., 1971b). In contrast, HNC>3 molecules, having triangular planar shaped NO^~ ions, are in a liquid state in HNO3 GICs, where planes of NOf ions are randomly oriented. A liquidsolid phase transition taking place at 250 K considerably reduces the c-axis repeat distance; this is accompanied by the ordering of NO^ ions in the low temperature phase (Bottomley et al., 1964).

2.3.4 Halogen GICs: F, Cl, Id, Br Graphite forms intercalation compounds with all halogen species except iodine. In addition, mixed halogen species such as IC1 and IBr are intercalated. It is worth noting that iodine is not intercalated in graphite, although it forms charge transfer complexes with condensed polycyclic aromatic carbons such as perylene and pyrene. The intercalation mode of fluorine is considerably different from that of

Synthesis and In te real at ion Chemistry

41

other intercalate species, because fluorine has strong chemical reactivity. First, we discuss the fluorine GICs and related materials. When graphite reacts with fluorine gas, two types of product are obtained which are classified as fluorinated and fluorine-intercalated graphite. The former comprises only sp3 bonds, whereas fluorine atoms are intercalated in graphitic galleries in the latter. At high temperatures, strongly active fluorine gas breaks the ^•-bonds in the graphite structure, resulting in the formation of fluorinated graphite (Nakajima, 1995; Nakajima and Watanabe, 1991; Touhara et al., 1987a; Watanabe and Takashima, 1971). In the temperature range around 380°C a dark gray compound with the composition of C/F = 2 is obtained, whereas treatment at higher temperatures produces a white compound with C/F = 1 where the reaction that produces the compound is completed at around 600°C. In milder conditions in the presence of metal fluoride, fluorine GICs are produced (Nakajima et al., 1986; Nakajima, 1995). Fluorinated graphite compounds (CF)« and (C2F)n with the compositions of C/F = 2 and 1, respectively, have layered structures consisting of stacked armchair-form corrugated sheets (Nakajima and Watanabe, 1991; Touhara et al., 1987a), as shown in Figure 2.19. In (CF),,, the individual layer is formed with a 2D condensed cyclohexane network where the connected fluorine atoms protrude perpendicularly from the layer plane. The bond distances are given as C —F = 1.41 A and C-C — 1.53 A. The interlayer distance is estimated as 5.85 A. (C2F)n has a double-layer structure where two layers facing each other are coupled by C-C bonds. The inter-double-layer distance is given as 8.1-8.2 A. Fluorinated graphite is an electrical insulator. Fluorine-intercalated graphite is one of the ordinary acceptor-type GICs that have metallic properties (Mallouk and Bartlett, 1983; Nakajima, 1995; Palchan et al., 1983). The introduction of fluorine into graphitic gallaries expands the c-axis lattice spacing Ic by 2.5-2.7 A, and the stage-number dependence of 7C is given by eq (1.3), where the sandwich thickness ds is estimated at 6.0 A. In the graphitic galleries, the intercalated fluorine is considered to be in the ionic state (Nakajima, 1991). Details of the electronic properties will be discussed in Section 5.4.3. Next, we discuss other halogen GICs. Halogen intercalate species such as C12, Br2, BrCl, IC1, IBr, BrF5, and IF5 are considered to consist of molecular species since they are in pristine states. The specific features in the synthesis of halogen GICs are that the reaction temperature is quite low, ranging around room temperature, and it is difficult to obtain stage-1 GICs even in saturated vapor pressure. Figure 2.20 shows the sandwich thickness ds of halogen GICs including mixed halogen intercalates (Furdin et al., 1970; Sasa et al., 1971; Selig et al., 1978; Setton, 1965). It is suggested that the sandwich thickness is roughly proportional to the size of the halogen species as reasonably understood. The c-axis lattice constant of stage-« GIC is also given by eq (1.3), where ds is estimated as the value given in Figure 2.20. The compositions are described as C7,,XX' or Cg,,XX' as a function of stage number n for XX' = IC1, Br2, BrCl, and C12. The in-plane structures have been well investigated, though mainly for Br GICs and IC1 GICs. Figure 2.21 shows the in-plane structure of C7nBr2 with stage n = 2-4 (Eeles and Turnbull, 1965; Erbil et al., 1983;

42

Graphite In te real at ion Com pounds and Applications

Figure 2.19 Structures of fluorinated graphite: (a) (CF),, showing stacking sequence A/A' and (b) (C2F)« showing possible stacking sequences a/AB/B'A'/ and b/AA'/AA'/ (ah is a mirror plane) (Nakajima and Watanabe, 1991).

Synthesis and Intercalation Chemistry

43

Figure 2.20 Sandwich thickness ds of halogen GICs, including mixed halogen intercalates.

Ghosh and Chung, 1983; Kortan et al., 1982). The intercalate lattice forms a (\/3 x 7) rectangular superlattice with four Br2 molecules whose structure is the same as that in the pristine state. The area per Br2 molecule, 1.833 A2, is smaller than that of the pristine state which is 1.953 A2. Consequently, the Br2 molecule is tilted by 13-21° with respect to the graphitic plane. The low intercalate density materials C gn Br 2 have an incommensurate structure, in contrast with the structure of C7,,Br2. ICI GIC has a similar in-plane molecular arrangement with the superlattice (a = 4.92 A, b = 19.2 A, y = 93.5) (Culik and Chung 1979; Leung et al., 1981; Wortmann et al., 1988), which involves four ICI molecules. The intra-molecular atomic distance I-C1 is elongated by 10% from that in the

Figure 2.21 In-plane structure of C 7n Br 2 with stage n = 2-4 having a (i/3 x 7) rectangular superlattice. The dash-dotted line shows the primitive cell (Erbil et al., 1983).

44 Graphite Intercalation Compounds and Applications

pristine IC1 molecule (2.36 A) under the effect of interaction with the graphitic layers. Because of the weakness of the interaction between intercalates and graphitic planes, a variety of phase transitions take place related to commensurate-incommensurate transition and melting transition (Chung, 1978; Culik and Chung 1979; Erbil et al., 1983; Kortan et al., 1982; Tashiro et al., 1978). The details will be discussed in Section 3.10. 2.3.5 Other Acceptor GICs Other materials are reported to give acceptor GICs. Among these, CrO3 GICs are well known; these are obtained by refluxing a mixture of graphite and CrO3 in glacial acetic acid (Platzer and Martiniere, 1961). Another interesting system is acceptor GICs in which organic molecules are co-intercalated. For a typical example, a second intercalate of organic molecules is co-intercalated with halide into graphite in some cases when a solution reaction is employed. FeCl3 dissolved in nitromethane (CH3NO2) yields the co-intercalation compound C24FeCl3(CH3NO2)o.73 through direct reaction with graphite (Hooley, 1972). Electrochemical intercalation of PF(~ and AsF 1 2 -» 1 4 -* 1?

11.00 11.27 13.80 14.15 14.45 14 .47 28.6?

4^2 6-^2 4-* 2 2-> 1 2-* 1 2^ 1 2-* 1 2->- 1

24.74 18.80 18.93 18.94 18.60 18.95

York et al., 1983 York et al., 1983 Lagrange et al., 1974 Lagrange et al., 1974 Lagrange et al., 1974 Lagrange et al., 1974 Freeman, 1974 Stumpp and Wageringel, 1979 Stumpp and Wageringel, 1979 Wageringel and Stumpp, 1980 Nadi, 1985 Nadi, 1985 Hachim, 1984 Suzuki et al., 1984 Hachim, 1984 Stumpp, 1981 Hachim, 1984 Hachim, 1984 Nadi, 1985 Stumpp et al., 1988 Niess and Stumpp, 1978

1

2-*- 1

solution reaction

2^ 1 2-* 1 2^ 1 2 —» 1 2^ 1

19.11 19.2 18.9 16.34 19.66

Mixed

C v BiCl 3 • (AuBr v ), C v BiCl 3 • (AuBr v ) r • (T1C13), C,6lnCl3., • (H2S04), C 23 BiCl 32 .(H 2 S0 4 ) r C v BiCl 3 • (AuBr v ) r • (TIC!,) • (H2SO4)r C v (HNO 3 ) r • (H2SO4), Ci0CuCl2 • (1C1)06 C,(FeCl3),-(lCIj, C|06CoCl2 • (K) CvCoCl2 • KC ]2 C13.9CdCl2 • (Na)

4^2

2-> 1

23.35 29.93 17.23 25.38 33.34 7.91 16.56 16.53 14.71 14.65 13.80

C )39 CdCl 2 • (K)

2-* 1

14.90

C13 9CdCl2 • (Rb)

2-»- 1

15.25

C l3 . 9 CdCl 2 .(Cs)

2^ 1

15.10

C,CuCl2 • (K) CvCuCl • (K)

2-> 1 2-> 1

14.70 12.55

electrochemical reaction liquid phase reaction vapor phase reaction

2-> 4/3 2^ 1 3-* 1 4/3-* 1

2^ 2-> 2-» 2^ 2->

Tol: toluene. The change in stage number due to the bi-intercalation process is shown as two numbers connected by an arrow.

Scharffet al., 1988 Scharffet al., 1988 Scharffet al., 1988 Scharffet al., 1988 Scharffet al., 1988 Scharff, 1992 Avdeev, 1992 Avdeev, 1992 Hachim, 1984 Suzuki et al., 1985 Furdin et al., 1985; Hachirn, 1984 Furdin et al., 1985; Hachim, 1984 Furdin et al., 1985; Hachim, 1984 Furdin et al., 1985; Hachim, 1984 Sokolova et al., 1994 Sokolova et al., 1994

48

Graphite Intercalation Compounds and Applications

Successive intercalation of two different halides, carried out in vapor phase reaction, is commonly used for producing halide bi-intercalation compounds. In this case, the second halide is introduced in the free graphitic galleries after the first halide intercalate is accommodated. The heat treatment temperature with the second halide should be lower than the temperature above which the first intercalate becomes de-intercalated. Using this method, several halide bi-intercalation systems have been prepared, as summarized in Table 2.14. Mixed bi-intercalation systems are most interesting since novel electronic features associated with the heterostructures are expected to come about through competition in the charge transfer process. Namely, when two kinds of intercalate are of opposite types (donor and acceptor), one can obtain compounds having microscopically alternating p- and n-type layers. In the mixed bi-intercalation compounds, only alkali metal-transition metal chloride biintercalation compounds are reported, as summarized in Table 2.14 (Avdeev, 1992; Furdin et al., 1985; Murakami et al., 1989; Suzuki et al., 1985). Stage-2 CoCl2, CuCl2, and CdCl2 binary GICs are converted to bi-intercalation compounds with alkali metal by the reaction of the binary with alkali metal vapor. The c-axis stacking sequence is described in terms of -G-AM-G-MC12-, where AM = Na, K, Rb, Cs and MC12 = CoCl2, CuCl2, CdCl2. The c-axis lattice constant can be explained by the sum of the interlayer distances of alkali metal and chloride intercalates. The kinetics of the transformation from stage-2 binary to stage-1 heterostructure can be understood by the movement of K atoms through Dumas-Herold domains (Suzuki et al., 1985). Sequential intercalation of potassium with high-stage transition metal halide binary GICs is a clue to understanding the intercalation mechanism. Figure 2.22 shows the time evolution of the (001) x-ray diffraction profiles in the process of potassium intercalation into stage-4 MoClg GIC, where potassium and the GIC are held at the same temperature of 105°C (Murakami et al., 1989, 1990). The x-ray spectra correspond to those of a pure stage-4 MoCl5 GIC at time t — 0, stage-4 lK-MoCl 5 GIC at 284 h, and stage-4 2K-MoCl 5 GIC at / = 382 h, respectively; IK and 2K mean that the GBICs include one and two K layers per c-axis repeat distance, respectively. In the case of stage-3 MoCl5 GIC the intercalation reaction of K atoms occurs at 130°C. The (001) x-ray diffraction spectrum of the product corresponds to that of stage-3 IK-MoClj GIC. The c-axis structural changes during the sequential intercalation of K atoms into stage-3 and stage-4 MoClj GICs are schematically shown in Figure 2.23. For stage-4 1KMoCl5 GIC there are two possible structures: (a) the K layer is inserted into the graphite gallery next to an MoCl5 layer; and (b) the K layer is inserted into the graphite gallery away from an MoCl5 layer. The calculated spectrum for (a) reproduces the experimental data very well. Similarly, in stage-4 2K-MoCl 5 GIC two K layers are inserted into the two graphite galleries neighboring the Mods layers. Thus one can conclude that in the sequential intercalation K atoms preferentially enter the graphite gallery next to MoCls layers. This behavior can be explained in terms of the attractive Coulomb interaction between the negatively charged MoCl5 layer and the positively charged K layers.

Figure 2.22 Time evolution of (001) x-ray diffraction spectra during the sequential intercalation of K into stage-4 '.MoCl 5 GIC at 105°C: (a) from stage-4 MoCl55 GIC to stage-4 !K-MoCl5 GIC; (b) from stage-4 IK-MoCIs GIC to stage-4 2KMoCl5 GIC (Murakami et al., 1990).

Figure 2.23 Proposed processes for the sequential intercalation of K into stage-3 and stage-4 MoCl5 GIC (Murakami et al., 1990).

50 Graphite Intercalation Compounds and Applications

The average in-plane C — C bond length (A^c-c) relative to that of pristine graphite is closely related to the charge transfer, as will be discussed in Section 5.2. The Adc-c value of pure MoCl5 GIC is negative, as is usual in acceptor GICs. The sequential intercalation of K atoms leads to an increase of Adc-c: Ad c _ c of stage-4 2K-MoCl5 GIC becomes positive. References Akuzawa, N.; Ogima, M.; Amemiya, T.; Takahashi, T. Tanso 1985, 121, 65. Alheid, H.; Schwarz, M.; Stump, E. Mol. Cryst. Liq. Cryst. 1994, 244, 191. Amine, K.; Tressaud, A.; Imoto, H.; Fargin, E.; Hagenmuller, P.; Touhara, H. Mater. Res. Bull. 1991, 26, 337. Aronson, S.; Lermont, S.; Weiner, J. Inorg. Chem. 1971a, 10, 1296. Aronson, S.; Frishberg, C.; Frankl, G. Carbon 1971b, 9, 715. Assouik, J. Ph.D. Thesis, Universite de Nancy I, 1991. Assouik, J.; Lagrange, P. Mater. Sci. Forum 1992, 91-93, 313. Avdeev, V. V. Mater. Sci. Forum 1992, 91-93, 63. Avdeev, V. V.; Nalimova, V. A.; Semenenko, K. N. High Pressure Res. 1990a, 6, 11. Avdeev, V. V.; Nalimova, V. A.; Semenenko, K. N. Synth. Metals 1990b, 38, 363. Bartlett, N.; McQuillan, B. W. In Intercalation Chemistry, Whittingham, M. S., Jacobson, A. J., Eds.; Academic Press: New York, 1982, p 19. Bartlett, N., Biagioni, R. N.; McQuillan, B. W.; Robertson, A. S.; Thompson, A. C. J Chem. Soc. Chem. Commun. 1978, 200, 1978. Bartlett, N., McCarron, E. M.; McQuillan, B. W.; Thompson, T. E. Synth. Metals 1979/ 1980, /, 221. Beguin, F.; Setton, R. Carbon 1975, 13, 293. Beguin, F.; Setton, R. J. Chem. Soc., Chem. Commun. 1976, 1976, 611. Beguin, F.; Setton, R.; Hamwi, A.; Touzain, P. Mater. Sci. Eng. 1970, 40, 167. Beguin, F.; Setton, R.; Facchini, L.; Legrand, A. P.; Merle, G.; Mai, C. Synth. Metals 1980, 2, 161. Beguin, F.; Estrade-Szwarckopf, H.; Conard, J.; Laguinie, P.; Marceau, P.; Guerard, D.; Facchini, L. Synth. Metals 1983, 7, 11. Beguin, F.; Gonzalez, B.; Conard, J.; Estrade-Szwarckopf, H.; Guerard, D. Synth. Metals 1985, 12, 187. Beguin, F.; Laroche, C.; Gonzalez, B.; Goldmann, M.; Quinton, M. F. Synth. Metals 1988, 23, 155. Beguin, F.; Pilliere, H.; Goldmann, M. Extended Abstract of International Symposium on Carbon, Tsukuba, Japan, 1990, Vol. 5B08, p 110. Belash, I. T.; Bronnikov, A. D.; Zharikov, O. V.; Palnichenko, A. V. Solid State Commun. 1987, 64, 1445. Bendriss-Rerhrhaye, A.; Lagrange, P.; Rousseaux, F. Synth. Metals 1988, 23, 89. Besenhard, J. O.; Fritz, H. P. Naturforsch. 1972, 27B, 1294. Besenhard, J. O.; Mohwald, H.; Nickl, J. J. Carbon 1980, 18, 399. Besenhard, J. O.; Kain, I.; Klein, H. F.; Mohwald, H.; Witty, H. Mater. Res. Symp. Proc. 1983,20,221. Billaud, D.; Metrot, A.; Willmann, P.; Herold, A. In Proceedings of International Carbon Conference, Baden-Baden, 1980, p 140. Billaud, D.; Chemti, A.; Metrot, A. Carbon 1982, 20, 493. Bindl, M. Thesis. TU Miinchen, 1986.

Synthesis and Intercalation Chemistry

5I

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Guerard, D.; Chaabouni, M.; Lagrange, P.; El Makrini, S.; Herold, A. Carbon 1980, 18, 257.

Guerard, D.; Takoudjou, C.; Rousseaux, F. Synth. Metals 1983, 7, 43. Guerard, D.; Elalem, N. E.; Takoudjou, C.; Rousseaux, F. Synth. Metals 1985, 72, 195. Guerard, D.; Elalem, N. E.; El Hadigui, S.; Ansari, L.; Lagrange, P.; Rousseaux, F.; Estrade-Szwarchkoph, H.; Conard, J.; Lauginie, P. J. Less-Common Metals 1987, 131, 173. Guerard, M.; Elansari, L.; Elalem, N. E.; Mareche, J. F.; McRae, E. Synth. Metals 1989, 34, 27. Hachim, L. Thesis, Nancy, 1984. Hamwi, A.; Touzain, P.; Bonnetain, L. In Proceedings of 2nd. International Carbon Conference, Baden-Baden, 1976, p 143. Hamwi, A.; Touzain, P.; Bonnetain, L. Mater. Sci. Eng. 1977, 31, 95. Hamwi, A.; Touzain, P.; Riekel, C. Synth. Metals 1980, 2, 153. Hamwi, A.; Touzain, P.; Bonnetain, L. C. R. Acad. Sci. 1984, 299/7, 1385. Hark, S. K.; York, B. R.; Solin, S. A. J. Chem. Phys. 1985, 82, 921. Herold, A. In Physics and Chemistry of Materials with Layered Structures', Levy, F., Ed.; Reidel: Dordrecht, 1979, vol. 6, p 323. Herold, A.; Lagrange, P. Mater. Sci. and Eng. 1977, 31, 33. Herold, A.; Setton.; R.; Platzer, N. Les Carbones (Masson Paris) 1965, vol. 2, 513. Herold, A.; Lelaurain, M.; Mareche, J.-F.. C. R. Acad. Sci. Paris Ser. II1991, 312, 361. Herold, A.; Lelaurain, M.; Mareche, J.-F.; MacRae, E. C. R. Acad. Sci. Paris Ser. II1995, 321, 61. Herold, C.; El Gadi, M.; Mareche, J.-F.; Lagrange, P. Mol. Cryst. Liq. Cryst. 1994, 244, 41. Herold, C.; Goutfer-Wurmzer, F.; Mareche, J.-F.; Lagrange, P. Mol. Cryst. Liq. Cryst. 1998, 310, 57. Hooley, J. G. Carbon 1972, 10, 155. Horn, D.; Boehm, H. P. Mater. Sci. Eng. 1972, 31, 87. Isaev, Y. V.; Novikov, Y. N.; Vol'pin, M. E.; Rashkov, I.; Panayotov, I. Synth. Metals 1983, 6, 9. Ishii, T.; Shibayama, Y.; Enoki, T.; Bandow, S.; Shirotani, L; Sugihara, K. /. Phys. Soc. Jpn. 1995, 64, 4748. Jegoudez, J.; Mazieres, C.; Setton, R. Synth. Metals 1983, 7, 85. Jegoudez, J.; Mazieres, C.; Setton, R. Carbon 1986, 24, 747. Kortan, A. R.; Erbil, A.; Birgeneau, R. J.; Dresselhaus, M. S.. Phys. Rev. Lett. 1982, 49, 1427. Lagrange, P.; Metrot, A.; Herold, A. C. R. Acad. Sci. C 1974, 278, 701. Lagrange, P.; El Makrini, M.; Bendriss, A. Synth. Metals 1983, 7, 33. Lagrange, P.; Bendriss-Rerhrhaye, A.; Mareche, J. F.; McRae, E. Synth. Metals 1985, 72, 201. Lagrange, P.; Herold, C.; Nalimova, V. A.; Sklovsky, D. E.; Guerard, D. J. Phys. Chem. Solids 1996, 57, 707. Lalancette, J.M.; Roy, L.; Lafontaine, J. Can. J. Chem. 1976, 54, 2505. Leung, S. Y.; Dresselhaus, M. S.; Underbill, C.; Krapchev, T.; Dresselhaus, G.; Wuensch, B. J. Phys. Rev. B 1981, 24, 3505. Lope-Gonzalez, J. D.; Rodriguez, A. M.; Vega, F. D. Carbon 1969, 7, 583. McCarron, E. M.; Bartlett, N. J. Chem. Soc., Chem. Commun. 1980, 1980, 404. Makrini, M. El. Carbon 1980, 18, 374. Makrini, M.; Guerard, D.; Lagrange, P.; Herold, A. Physica 1980a, 995, 481. Makrini, M. El; Lagrange, P.; Guerard, D.; Herold, A. Carbon 1980b, 18, 211. Mallouk, T.; Bartlett, N. /. Chem. Soc., Chem. Commun. 1983, 1983, 103.

Synthesis and Intercalation Chemistry 53 Marcus, B.; Touzain, P.; Hamwi, H. Carbon 1986, 24, 403. Melin, J.; Herold, A. Carbon 1975, 13, 357. Melin, J.; Furdin, G.; Fuzellier, H.; Vasse, R.; Herold, A. Mater. Sci. Eng. 1977, 31, 61. Merle, G.; Gole, J. Bull. Soc. Chim. Fr. 1976, 1976, 1082. Merle, G.; Beguin, F. Carbon 1980, 18, 371. Merle, G.; Lotoffe, J. M.; Rashkov, I. B.; Clandy, P. J. Therm. Anal. 1978, 13, 293. Metrot, A; Fischer. J. E. Synth. Metals 1981, 3, 201. Metrot, A.; Guerard, D.; Billaud, D.; Herold, A. Synth. Metals 1979/1980, 1, 363. Mordkovich, V. Z.; Ohki, Y.; Yoshimura, S.; Hino, S.; Yamashita, T.; Enoki, T. Synth. Metals 1994, 68, 79. Mordkovich, V. Z.; Baxendale, M.; Ohki, Y.; Yoshimura, S.; Yamashita, T.; Enoki, T. J. Phys. Chem. Solids 1996, 57, 821. Mouras, S.; Hamwi, A.; Djurado, D.; Cousseins, J. C. Rev. Chem. Miner. 1987, 24, 572. Murakami, Y.; Kishimoto, T.; Suematsu, H. Synth. Metals 1989, 34, 205. Murakami, Y.; Kishimoto, T.; Suematsu, H. J. Phys. Soc. Jpn. 1990, 59, 571. Nadi, N. Thesis, Nancy, 1985. Nakajima, T. Fluorine-Carbon and Fluoride-Carbon Materials—Chemistry, Physics and Applications. Marcel Dekker: New York, 1995. Nakajima, T.; Watanabe, N. Graphite Fluorides and Carbon-Fluorine Compounds; CRC Press: Boca Raton, FL, 1991. Nakajima, T.; Kawaguchi, M.; Watanabe, N. Bull. Chem. Soc. Jpn. 1981, 54, 2295. Nakajima, T.; Kameda, I.; Endo, M.; Watanabe, N. Carbon 1986, 24, 343. Nakajima, T.; Matsui, T.; Motoyama, M.; Mizutani, Y. Carbon 1988, 26, 831. Nalimova, V. A. Mol. Cryst. Liq. Cryst. 1998, 310, 5. Nalimova, V. A.; Chepurko, S. N.; Avdeev, V. V.; Semenenko, K. N. Synth. Metals 1991, 40, 267. Nalimova, V. A.; Guerard, D.; Lelaurain, M.; Fateev, O. V. Carbon 1995, 33, 111. Niess, R.; Stumpp, E. Carbon 1978, 16, 265. Nishitani, R.; Uno, Y.; Suematsu, H. Phys Rev. B 1983, 27, 6572. Nixon, D. E.; Parry, G. S.; Ubbelohde, A. R. Proc. Roy. Soc. London 1966, 291 A, 32. Nixon, D. E.; Parry, G. S.; Ubbelohde, A. R. Proc. Roy. Soc. London 1964, A291, 324. Nomine, M.; Bonnetain, L. C. R. Acad. Sci. C 1967, 264, 2084. Ohhashi, K. In Graphite Intercalation Compounds; Watanabe, N., Ed.; Kindai-HenshuSha: Tokyo, 1986; p 165 (in Japanese). Okuyama, N.; Takahashi, T., Kanayama, S.; Yasunaga, H. Physica 1981, 705B, 298. Outti, B.; Clement, J.; Herold, C.; Lagrange, P. Mol. Cryst. Liq. Cryst. 1994, 244, 281. Palchan, L; Davidov, D.; Selig, H. /. Chem. Soc., Chem. Commun. 1983, 1983, 657. Parry, G. S.; Nixon, D. E.; Lester, K. M.; Levene. B. C. J. Phys. C 1969, 2, 2156. Pilliere, H.; Soubeyroux, J. L.; Goldmann, M.; Beguin, F. Mater. Sci. Forum 1992, 97-93, 331. Pilliere, H.; Takahashi, Y.; Yoneoka, T.; Otosaka, T. Synth. Metals 1993, 59, 191. Pilliere, H.; Takahashi, Y.; Yoneoka, T.; Otosaka, T.; Akuzawa, N. Mol. Cryst. Liq. Cryst. 1994, 245, 201. Platzer, N.; de la Martiniere, B. Bull. Soc. Chim. Fr. 1961, 7967, 177. Quinton, M. F.; Legrand, A. P.; Beguin, F. Synth. Metals 1986, 14, 179. Reikel, C.; Hamwi, A.; Touzain, P. Synth. Metals 1983, 6, 265. Resing, H. A.; York, B. R.; Solin, S. A.; Fronko, R. M. In Extended Abstracts of the 17th Carbon Conference, American Carbon Society: Lexington, 1985; p 192. Rudorff, W. Chimia 1965, 79, 489. Rudorff, W.; Hoffmann, U. Z. Anorg. Allg. Chem. 1938, 238, 1. Rudorff, W.; Shulze, E.; Rubisch, O. Z. Anorg. Allg. Chem. 1955, 282, 232.

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Rudorff, W.; Siecke, W.-F. Chem. Ber. 1958, 91, 1348. Riidorff, W.; Stumpp, E.; Spriesseler, W.; Siecke, F. W. Angew. Chem. Int. Ed. Engl. 1963, 2, 67.

Saehr, D.; Herold, A. Bull. Soc. Chim. Fr., 1965, 7965, 3130. Sasa, T., Takahashi, Y.; Mukaibo, T. Carbon 1971, 9, 407. Scharff, P. Mater. Sci. Forum 1992, 91-93, 23. Scharff, P.; Stumpp, E.; Ehrhardt, C. Synth. Metals 1988, 23, 415. Schlogl, R.; Bohm, H. P. Synth. Metals 1988, 23, 407. Schulze, E. Thesis, Tubingen, 1954. Selig, H.; Ebert, L. B. Adv. Inorg. Chem. Radiochem. 1980, 23, 281. Selig, H.; Sunder, W. A.; Vasile, M. J.; Stevie, F. A.; Gallagher, P. K.; Ebert, L. B. Fluorine Chem. 1978, 12, 397. Semenenko, K. N.; Avdeev, V. V.; Mordkovich, V. Z. Dokl. AN. SSSR 1983, 277, 1402. Setton, R. In Les Carbones, Vol. 2; Pacault, A., Ed.; Masson: Paris, 1965; p 645. Setton, R. In Graphite Intercalation Compounds I, Zabel, H.; Solin, S. A., Eds.; SpringerVerlag: Berlin, 1990, p 305. Setton, R.; Beguin, F.; Jegoudez, J.; Mazieres, C. Rev. Chim. Miner. 1982, 19, 360. Setton, R.; Beguin, F.; Facchini, L.; Quinton, M. F.; Legrand, A. P.; Ruisinger, B.; Bohm, H. P. /. Chem. Soc. Chem. Commun. 1983, 1983, 36. Skowronski, J. M. Synth. Metals 1995, 73, 21. Sokolova, T. Y.; Nalimova, V. A.; Fateev, O. V.; Avdeev, V. V.; Semenenko, K. N.; Guerard, D. Mol. Cryst. Liq. Cryst. 1994, 244, 35. Solin, S. A.; Fan, Y. B.; Qian, X. W. Synth. Metals 1985, 12, 181. Steinwede, K.; Stumpp, E. Z. Anorg. Allg. Chem. 1980, 469, 101. Stumpp, E. Mater. Sci. Eng. 1977, 31, 53. Stumpp, E. Physica 1981, 7055, 9. Stumpp, E.; Nietfeld, G. Z. Anorg. Allg. Chem. 1969, 456, 261. Stumpp, E.; Wageringel, K.-D. Extended Abstracts, 14th Biennial Conference on Carbon, 1979. Stumpp, E.; Wloka, K. Synth. Metals 1981, 3, 209. Stumpp, E.; Hummol, H. J.; Ehrhardt, C. Synth. Metals. 1988, 23, 441. Stumpp, E.; Alheid, H.; Shwarz, M.; Janssen, J.; Muller-Warmuth, W. J. Phys. Chem. Solids 1996, 57, 925. Suzuki, M.; Oguro, I.; Jinzaki, Y. J. Phys. Chem. 1984, 77, L575. Suzuki, M.; Chow, P. C.; Zabel, H. Phys. Rev. B 1985, 32, 6800. Syassen, K.; Sonnenshein, R.; Hanfland, M.; Beister, H. J. Synth. Metals 1989, 34, 293. Tabony, J.; Korb, J. P. Mol. Phys. 1985, 56, 1281. Takahashi, Y.; Oi, K.; Terai, T.; Akuzawa, N. Carbon 1991, 29, 283. Takahashi, Y.; Oi, K.; Terai, T; Otsuka, T.; Akuzawa, N. Mater. Sci. Forum 1992, 97-93, 113. Tashiro, K.; Saito, M.; Tsuzuku, T. Carbon 1978, 16, 292. Touhara, H.; Kadono, K.; Fujii, Y.; Watanabe, N. Z. Anorg. Allg. Chem. 1987a, 544, 7. Touhara, H.; Kadono, K.; Imoto, H.; Watanabe, N.; Tressaud, A.; Grannec. J. Synth. Metals 1987b, 18, 549. Touzain, P. Carbon 1978, 16, 403. Tressaud, A.; Amine, K.; Mayorga, S. G.; Fargin, E.; Grannec, J.; Hagenmuller, P.; Nakajima, T. Eur. J. Solid State Inorg. Chem. 1992, 29, 947. Tsang, T.; Fronko, R. M.; Resing, H. A.; Qian, X. W.; Solin, S. A. Solid State Commun. 1987a, 62, 117. Tsang, T.; Fronko, R. M.; Fronko, H. A.; Qian, X. W.; Solin, S. A. Solid State Commun. 1987b, 63, 361.

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3

Structures and Phase Transitions

3.1 Overview and Definition

3.1.1 Overview Graphite intercalation compounds (GICs) have unique layered structures where intercalate layers are arranged periodically between graphite layers. This phenomenon is known as staging, and the number of graphite layers between adjacent intercalate layers is known as the stage number n. As the stage number n increases, the separation between adjacent intercalate layers becomes larger. So the interlayer interactions between intercalate layers become weak, leading to a crossover of dimensionality from three-dimensional (3D) to two-dimensional (2D). Because of their intrinsic anisotropy, GICs exhibit a great variety of structural orderings such as staging, in-plane ordering of intercalate layers, and stacking ordering of both graphite and intercalate layers. The stable stage and in-plane ordering of the intercalate layers depend on the relative strength of the intercalate-graphite interaction to the intercalate-intercalate interaction. At low temperatures the intercalate layers form a variety of 2D superlattices resulting from the competing interactions. At elevated temperatures the superlattice undergoes a transition to a 2D liquid. The migration of intercalate atoms is restricted to the 2D gallery between graphite layers. The critical temperature below which the stacking order appears is equal to or lower than the critical temperature below which the in-plane order appears. In this chapter, we review the subject of structures, phase transitions, and kinetics for donor and acceptor GICs. The subject matter of this chapter is 56

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organized as follows. Section 3.1 deals with the general structural characteristics of GICs. Sections 3.2 and 3.3 are respectively devoted to descriptions of liquid state and phase transitions of stage-2 alkali metal GICs. Section 3.4 deals with the discommensuration domain model for high-stage alkali metal GICs. Sections 3.5 and 3.6 are devoted to descriptions of liquid-solid transitions in stage-1 K and Rb GIC. In Sections 3.7-3.9, we describe the stage transition, Kirczenow's model, Hendricks-Teller-type stage disorder, and fractional stage. In Sections 3.10 and 3.11 we describe the phase transitions of acceptor-type GICs (Br2 GIC and SbClj GIC). Section 3.12 treats the ordering kinetics in K GIC and SbCl5 GIC. There are several excellent reviews (Dresselhaus and Dresselhaus, 1981; Herold, 1979; Kirczenow, 1990; Moret, 1986; Moss and Moret, 1990; Zabel and Chow, 1986) that provide a good deal of structural background for our discussion. In particular, many topics that were studied up to the late 1980s were extensively reviewed by Moss and Moret (1990).

3.1.2 Graphite and Intercalate Layers Pristine graphite is one of many layered materials that can host layers of foreign atoms, called intercalates. In Chapter 1, Figure 1.3 shows the structure of pristine graphite. The in-plane carbon-carbon bond length is 1.42 A with a layer separation of 3.35 A. It is because of the strong sp carbon-carbon bonding within a layer and weak van der Waals bonding between adjacent layers that the carbon hexagonal net can maintain its own layer integrity and at the same time host any of a number of metal atoms, gas atoms, or molecules. In each graphite layer carbon atoms form a hexagonal net with a unit cell defined by the fundamental in-plane lattice vectors bj and b2, where |b] = |b2| = ao = 2.46 A and the angle between bj and b2 is 120°. There are two carbon atoms per unit cell. Pristine graphite has two types of stacking structure: a hexagonal graphite (Figure 1.3) and a rhombohedral graphite. The planes are stacked ABAS for the hexagonal graphite and ABCABC for the rhombohedral graphite. The inplane positions of the carbon atoms in the B- and C-layers are related to those of the carbon atoms in the A layer by the fundamental translation vectors A g and — A g (or 2A g ) as shown in Figure 3.1, where A g = (2b[ + b 2 )/3 with |A g = 1.42 A. The rhombohedral graphite is metastable and is transformed into hexagonal graphite by heating at high temperature or by formation of an intercalation compound followed by its dissociation (Herold, 1979). There are two kinds of graphite sample used for studying GICs: single crystal and highly oriented pyrolytic graphite (HOPG) as discussed in Chapter 1. Small single crystals are available from coal mines in Ticonderoga, New York, and Madagascar, and from blast furnaces for steel production. In the walls of the furnaces are deposited small single-crystal graphite flakes called kish graphite, from the German word Kiesel which means gravel. For most of the studies on GICs, HOPG is used. This material consists of many crystallites with a common, well-defined c-axis direction, but whose b} and b2 axes point randomly in the plane of the layers, forming a two-dimensional (2D) powder. The best material available has a c-axis mosaic spread of about 0.2° (Zabel and Chow, 1986).

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Figure 3.1 Hexagonal network and 2D unit cell of graphite, where b, and b2 are the in-plane lattice vectors of the graphite layer. |bj| = |b2| = ac = 2.46 A. A, = (2b,+b 2 )/3.

The staging is the most distinctive type of ordering in GICs. The stage number of a GIC is the number n of graphite layers separating successive intercalate layers. It is often possible to relate the structure of the intercalate layer to that of the graphite layer. We consider the in-plane structure of the intercalate layer in alkali metal (AM) GICs. There are two C atoms per unit cell of graphite layer and one AM atom per unit cell of AM layer. For GICs having a stoichiometry of MCS per one AM layer and one graphite layer, the AM layer is expected to form an inplane structure of (A/s/2 x */s/2) (Dresselhaus and Dresselhaus, 1981). For stage1 AM GIC having the stoichiometry of MC8 (M = K, Rb, Cs), M atoms form a triangular lattice with a side twice as large as the unit cell length of graphite: p(2 x 2)RO°, which is a structure commensurate with that of the graphite layer. Here the notation R(#) means that the fundamental lattice vector of the intercalate layer is rotated by 6 with respect to that of the graphite layer. In contrast, stage-1 Li GIC (LiC6) has a/>(v / 3 x \/3)R30° commensurate structure. The commensurate p(2 x 2)RO° structure is shown in Figure 3.2. There are four equivalent intercalate sites, labeled a, ft, y, and F(ri) and F(n + 1) > F(ri). The interval of chemical potential over which the stage-« structure is stable is given by where A/i' = A/u. Since A/z > 0 or the stable stage-n structure, V(n) should be repulsive and is a function of n with concave curvature.

3.7.2 X-ray Scattering Studies Among GICs the alkali-metal (AM) GICs, in particular K GICs, have been the subject of most structural studies. The results are compared with theoretical predictions. AM GICs can usually be prepared by means of the two-zone furnace, in which the temperature of host graphite (7g) and the temperature of alkali metal (TM) are independently controlled. The theory behind the twobulb technique is simple. The graphite sample is immersed in an environment of alkali vapor. In thermal equilibrium, the chemical potential of the alkali in the vapor phase fj,M equals that of the intercalated atoms within graphite layers ju: fj. = fj.M = kBTGln(PM) + constant, where PM is the vapor pressure and is related to TM via In PM = A/TM + S, with the constants A and B depending on the species of M. Usually GICs can be prepared by keeping the temperature of host graphite (TG) and changing the temperature of AM (TM). The vapor pressure (PM) of AM is uniquely related to the temperature TM. The intercalation occurs in thermal equilibrium when the chemical potential of the GIC /LI is equal to /ZM . The staging structures of GIC during the synthesis can be directly observed by in situ (OOL) xray diffraction. The phase diagram of K GIC and Rb GIC is shown in Figure 2.2 (Nishitani et al., 1983ab), where TM is varied with TG held constant. The j-axis of this figure is the reciprocal of stage number n (= 1, 2, 3,...), while the x-axis is the temperature difference (TG - TM), which is related to the vapor pressure PM or chemical potential /z. The main features of Figure 2.2 are as follows: (1) only pure stage states are observed; (2) The stable region of A//(«) becomes narrower as the

Structures and Phase Transitions 91

stage number increases; (3) the transitions between stages are reversible. From the stage-stable region of TK,one can evaluate the stability of a stage n as the range of chemical potential, A/u.(«), by the relation where PM( ( > ' + 1) is the vapor pressure of the intercalate at which the stage transition occurs from stage / to / + 1. The experimental values of AM(«) are almost independent of TG within the measured temperature ranges: Aju.(2) = 0.1 50 ± 0.005 eV, A/43) = 0.070 ± 0.005 eV, A^(4) = 0.038 ± 0.005 eV, and A/45) = 0.02 ± 0.005 eV (jTG = 660.65 K) for K GICs; and A/42) = 0.154 eV, A/43) = 0.076 eV, and A/44) = 0.048 eV (TG = 764.65 K) for Rb GICs. The value of A/4«) is almost independent of TG. These values of A/u,(«) are in good agreement with theoretical results by Safran and Hamann (1982) for the ionicity/(= 1/2), which is different from a result derived from electronic studies that / = 1 for heavy AM GICs. Here the degree of charge transfer is characterized by the ionicity / corresponding to the transfer of / electrons per intercalate atom. A fit of experimental data [A/4«) vs. n] to eq (3.25) with V(ri) proportional to Vf)[Ic(n)]~a yields the results of a = 1.55 and K0 > 0 for K GICs, where 7c(n) is the c-axis repeat distance. These results indicate that the interlayer interaction between intercalate layers is repulsive and strongly screened out. Similar measurements were carried out for the acceptor GICs (Yosida et al., 1986). Figure 3.25 shows the stage isotherm for SbCl5 GICs as a function of rsbc,5, indicating discrete steps in each of which a single stage is stable. The value' of A/4«) for SbCl5 GICs is roughly one-half of that for K GICs, and is in agreement with the Safran-Hamann theory for 1/4 < / < 1/2.

Figure 3.25 Phase diagram of stage number vs. rsbci5 in SbCls GICs. The lower diagram was taken when 7"sbCi5 was decreased (note that the upper one is shifted upward to avoid confusion of data points). Stage number is indicated. The overlapping regions at the stage transition, indicated by open circles and triangles, constitute the two-phase region (Yosida et al., 1986).

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3.7.3 Kinetics The kinetics of stage transition have been experimentally studied by in situ x-ray diffraction. Figure 3.26 shows the time dependence of the (OOL) x-ray diffraction pattern for K GIC, taken during the transition from stage 3 to stage 2 with TG being constant (TG = 485°C). At time t = 0 the temperature difference (TG - TK) was changed from 195°C, corresponding to the equilibrium condition for stage 3, to 190°C for stage 2. The reflection peaks for stage 2 grow and those for stage 3 decrease. Note that the system was swept through the stage transition without equilibration because of its dynamic nature. So far we have considered a classical model of staging in which every gallery between the host layers is either uniformly populated with intercalate or empty. The dynamic process of the stage transition result cannot be explained by such a picture. As an alternative, it is qualitatively understood in terms of a model proposed by Daumas and Herold (1969). In order to explain the fact that stage transitions occur without the intercalate passing through host layers and without intercalate atoms having to leave the system in order to vacate some entire galleries and fill others, Daumas and Herold assume that the intercalate in a high-stage (n > 2) GIC is present in every graphite gallery but condenses into domains. Every domain has a stage-« structure, but in different domains the intercalate occupies galleries between different pairs of host layers. The host layers are elastically deformed at the domain boundaries. Within a gallery, the intercalate consists of 2D islands, each island belonging to a particular domain. The stage-tt GIC consists of n different domains. Stage transitions in which the stage number n changes to n ± 1 can then occur by 2D diffusion of intercalate from domain to domain.

Figure 3.26 Time dependence of the (OOL) x-ray diffraction pattern during the transition from stage 3 to stage 2, where time t is measured after TK is changed from the equilibrium condition for stage 3 to that for stage 2 (Nishitani et al., 1983b).

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Nishitani et al. (1983b) have explained their result as shown in Figure 3.26 in terms of the Daumas-Herold model. In a pure stage 3 there are three different domains (Figure 3.27a). The stage transition starts at the sample surface, and stage-2 domains evolve and proceed toward the inner region of the sample in a 2D diffusion such that the inner domains of stage 2 are pushed into the inner region by outer domains of stage 2, as indicated by the arrows in Figure 3.27c. In this picture there may be a possibility of an intermediate state with an overlapping of different domains of stage 3 at the front of the stage transition (Figure 3.27b) unless the excess intercalate islands of stage 3 are expelled from the sample. In order to complete the stage transition from stage 3 to stage 2 at the phase boundary region (Figures 3.27b and c), three different domains of stage 3 must be transformed to two domains of stage 2. If the phase boundary region is transformed into two domains of stage 2 and the above mentioned 2D diffusion motion occurs (Figure 3.27c), the front of the stage transition proceeds towards the inner region, as shown in Figure 3.27d. On the other hand, the overlapping of the domains (Figure 3.27b) may cause the c-axis disorder more or less to settle the proper two domains of stage 2. However, the fact is that no appreciable evidence of the intermediate state has been observed during the stage transition.

Figure 3.27 Daumas-Herold model for the stage structure and kinetic processes of a stage transition from stage 3 to stage 2 in K GIC: (a) stage-3 domains; (b) possible intermediate structure in the transformation from stage 3 to stage 2; (c) diffusion motion of stage-2 domains—the phase boundary region in the intermediate state (b) is ordered into stage-2 domains; (d) the subsequent intermediate structure. The phase boundary region has proceeded toward the inner region of the sample (Nishitani et al., 1983b).

94 Graphite Intercalation Compounds and Applications 3.8 Hendricks-Teller Stage Disorder

3.8.1 Overview The staging structure of GICs is characterized by the stage number, which refers to the number of graphite layers separating adjacent intercalate layers. HendricksTeller (HT)-type (Hendricks and Teller, 1942, Kakinoki and Konura, 1952) stage disorder is a random arrangement of packages with different stages along the c-axis, where the package with stage i refers to an intercalate layer plus i graphite layers. A simple equilibrium theory of staging structure in GICs is proposed by Kirczenow (1985, 1990). The theory shows that HT stage disorder is a direct thermodynamic consequence when the Daumas-Herold domain model is taken into account. A typical result is shown in Figure 3.28, where the fraction/ of the stage-/ unit in the disordered domain is plotted as a function of chemical potential [i. For large \JL, f\ — 1 and the system is pure stage 1. With decreasing /x, f\ decreases continuously to zero over a very narrow range of /u,, while /2 increases from zero to 1 and the system becomes pure stage 2. Similar continuous transitions through stage-disordered states are also found between successive higher stages. For high stages, pure stages can no longer exist in thermodynamic equilibrium. Kirczenow (1985, 1990) has found a scaling law that provides a framework for understanding the HT stage disorder of donor and acceptor GICs. The scaling law indicates that the degree of HT stage disorder is related to (i) domain size in intercalate layers, (ii) charge transfer, (iii) filling factor, and (iv) temperature. The in-plane order of the intercalate layer is not related to stage disorder. The HT stage disorder is measured as the fraction of stage-/ unit that is approximated by a Gaussian distribution with a peak at the dominant average stage denoted by (/). The width of the Gaussian distribution

Figure 3.28 A typical plot of the fraction/ of stage-/ units in a stage-disordered DaumasHerold domain at equilibrium vs. chemical potential (Kirczenow, 1985).

Structures and Phase Transitions 95

is a measure of stage disorder, where T is temperature, jV0 is domain size of the intercalate layer, that is, the in-plane dimension of intercalate islands, x is the filling factor of domains, and M,- is the interlayer repulsive interaction of the form Uj = v0ra, where v0 and a are constants. The scaling law indicates the importance of the repulsive interlayer interaction u{. The degree of HT stage disorder increases as stage (/> and temperature increase and as domain size and filling factor decrease. The value of v0 is a measure of charge transfer, so the degree of stage disorder increases as charge transfer decreases. The charge transfer of acceptor GICs is smaller than that of donor GICs, as will be discussed in Chapter 5. The intercalate layers of acceptor GICs are known to be formed of small islands whose periphery provides an acceptor site for the charge transferred from the graphite layers. The size of these islands is much smaller than the domain size of donor GICs. The scaling law explains well the experimental evidence that acceptor GICs exhibit more stage disorder than donor GICs. Up to now most of experimental studies (Cajipe et al., 1989; Fischer et al, 1983; Huster et al., 1987; Kim et al., 1986; Meisenheimer and Zabel, 1985) on HT stage disorder have dealt with donor GICs such as alkali metal GICs. In contrast, there have been few systematic studies on the stage disorder of acceptor GICs (Hohlwein and Metz, 1974; Metz and Hohlwein, 1975; Suzuki and Suzuki, 1991). The (OOL) x-ray diffraction pattern of GICs with HT stage disorder is characterized by (i) full-width at half-maximum (FWHM) of Bragg reflections, which depends on the index L; and (ii) peak shift (PS) of Bragg reflections from that of the pure stage, which also depends on the index L. Fischer et al. (1983) have carried out (OOL) x-ray diffraction of a donor K GIC sample consisting of a random mixture of 76% stage 7 and 24% stage 8 packages, and have found that the peak shift of the Bragg reflections from the ideal stage 7 as a function of the index L shows an oscillatory behavior. Metz and Hohlwein (1975) have also found a characteristic HT stage disorder-induced broadening and peak shift of xray Bragg reflections for an acceptor FeClj GIC.

3.8.2 In Situ X-ray Studies Experiments on stage disorder were performed by Meisenheimer and Zabel (1985) on K GIC. The high-resolution in situ x-ray data show stage disorder, in thermal equilibrium, for stage n (> 2). The stage disorder is found to increase close to the transition between successive stages. Figure 3.29a shows a plot of the scattering intensity versus wavenumber Qc for (005) stage-5 reflection at TG = 455°C and TK = 230°C. As the temperature TG is lowered with TK held constant, this reflection is seen to shift continuously toward lower Qc values and to broaden. At each temperature, the measurement is made after thermal equilibrium is reached. At TG = 450°C, corresponding to the transition region, the (004) stage-4 reflection

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appears (Figure 3.29b) at the expense of the stage-5 reflection. A dramatic increase in the peak width is noticed. At TG = 444°C the (004) stage-4 reflection is seen to shift continuously to lower Qc, toward its ideal stage-4 position, and to become narrower (Figure 3.29c). The solid lines in Figures 3.29a and c are fits using the Hendricks-Teller theory, assuming disordered mixtures of stage-4 and stage-5 units. As the stage transition is approached and the degree of stage disorder increases, the disordered stage-5 reflection moves towards the stage-4 position because of the change in the average stage of the sample. Figure 3.29b shows broadened and shifted stage-4 and stage-5 lines together, indicative of the coexistence of disordered stage-4-rich and stage-5-rich regions in the system during part of the transition. Figure 3.30 shows the fraction /„ of stage-« units as a function of chemical potential. The stage-1 compounds are always purely staged ones throughout the stability region, containing only stage-1 packages. The stage-2 compounds reach pure-stage order near the stage-1 transition, but show some HT stage disorder with stage-1 and stage-3 packages close to the stage-2 and stage-3 transition. The minority stages present are 2 and 4 with increasing fractional amounts as either the stage-3 to 2 or the stage-3 to 4 transition is approached.

Figure 3.29 Scattering intensity vs wavenumber Qc for (OOL) reflections taken in situ at constant chemical potential in K GIC at JK = 230°C: (a) stage 5 (005) at Tc = 455°C; solid line is a fit using HT theory, convoluted with instrumental resolution; (b) superposition of two reflections in the transition region to stage 4 at TQ = 450°C; with time the lower Qe reflection grows at the expense of the higher; (c) stage 4 (004) at TG = 444°C; Solid line is again a fit using HT theory. Q corresponds to Qc in the text. Note the shift and broadening of the two reflections in (b) in comparison with (a) and (c) (Meisenheimer and Zabel, 1985).

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Figure 3.30 Fraction /„ of stage-« packages as a function of the chemical potential at constant sample temperature in K GIC. Arrows on top of the figure indicate the stability region of a stage-« compound and dashed lines the stage transition. Fractional staging is indicated by: x, stage 1; O, stage 2; •. stage 3; and A; stage 4 (Meisenheimer and Zabel, 1985).

Qualitatively these experimental results are in good agreement with Kirczenow's staging model (Kirczenow, 1985, 1990). HT disorder is seen to be a fundamental ingredient of the staging phase diagram. The composition of a mixed stage varies continuously across the stability region of the dominant stage. All staging transitions measured show a discontinuous change in the fractional amount of the dominant stage packages, characteristic of a first-order transition and in contrast to the prediction of a continuous staging transition. The discontinuity follows from the coexistence of two sets of reflections in the transition region from dominantly stage-« and stage-(n + 1) regions. This coexistence may be described as a miscibility gap in the maximum allowed mixture of stage-n and stage-(n + 1) packages. The gap size decreases with increasing stage number and the staging transition becomes more continuous. The miscibility gap may result from domain-domain interactions, which are neglected in the theory.

3.8.3 Fractional Probability In GICs with HT stage disorder, the alternation between graphite and intercalate layers is no longer periodic and statistical analysis of the x-ray data is required to obtain a detailed microscopic description of the stacking sequence. Suzuki and Suzuki (1991) have presented a simple method to determine the fractional probability of each stage from the Bragg index (L) dependence of the HT stage-disorder induced peak shift and full-width at half-maximum. The HT stage disorder-

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induced peak shift Ap$(L) for GICs consisting mainly of stage-« packages is theoretically predicted by the formula

where fr is the probability of a package being stage-r (fr = 0forr < 0) and is much smaller than /„ and Q(f = (2n/I^n))L of the pure stage-H GIC with the c axis repeat distance I("\ When stage-(n - 2), n-\, n, n + l, and n + 2 packages with the probabilities of fn_2, /«-i, /«, /«+i> and/ n+2 are randomly arranged along the c-axis, A^(L) can be approximately described by a sum of first and second harmonics,

With

Suzuki and Suzuki (1991) have made model calculations of the (OOL) x-ray intensity for CoCl2 GIC with HT stage disorder and have found that the peak shift and full-width at half-maximum of the Bragg reflections oscillate as a function of the Bragg index L, as shown in Figure 3.31. Here we show an experimental result on a (OOL) x-ray scattering profile for MoCl5 GIC (Suzuki et al., 1996), where the Bragg peaks are well indexed to stage-4 reflections with 44) = 19.396 ±

Figure 3.31 Model calculations of (a) full-width at half-maximum (FWHM) and (b) peak shift (PS) for the CoCl2 GIC system with a random mixture of stage 2 (/"2) and stage 3 (f3), as a function of the Bragg index of stage 2, L: /2 = 0.8 and/3 = 0.2. The exact values of FWHM and PS are denoted by closed circles and the first-order approximation is denoted by solid lines. Note that the solid line of the PS coincides with the A ps = 0 line (Suzuki and Suzuki, 1991).

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0.014 A. Figure 3.32 shows the L-dependence of the peak shift APS of the (OOL) Bragg reflection from the average position Q(^ of the pure stage 4. The peak shift ApS sinusoidally oscillates with the Bragg index L around APS = 0. The data of Ap S versus L fall on the solid line described by eq (3.29) with RbC gx6 . The behavior of stage-1 KC8 deserves special attention. KC8 (s = 8) is thought to be the high-density or hard sphere limit for K atoms in graphite. A stage transition in KC8 would imply densification to a smaller discrete value of s. Figure 3.33 shows a (OOL) neutron scattering scan of KC8 at 16.5 and 20 kbar (Fuerst et al., 1983). The pressure dependence of the integrated intensity for stage 1, fractional stage (3/2), and stage 2 in KC8 is shown in Figure 3.34. The fractional stage (3/2) with a CKCCKCKCCK... stacking sequence (the repeat distance is 13.61 A) is observed together with stage 1 between 15 and 19 kbar and is replaced by stage 2 above 19 kbar. A scheme that is consistent with this behavior is the series of transitions where KC 6xl (s = 6) is a superdense stage-1 with a/?(\/3 x \/3)R30° superlattice, K 2 C 8x3 (s = 8) is the fractional stage (3/2), and KC 6x2 (s = 6) is a superdense stage-2. The existence of /»(\/3 x V3)R30° superlattices at high pressure has been directly confirmed from single-crystal x-ray film experiments using the diamond anvil technique by Bloch et al. (1985). These authors have also shown that the p(2 x 2)RO° andXV3 x y3)R30° superlattices coexist in an intermediate pressure

Figure 3.33 (OOL) neutron diffraction profile of KC8 at room temperature under a hydrostatic pressure P. A fractional stage (3/2) with a CKCCKCKCCK... sequence is observed for 15 < P < 19 kbar. n(L) denotes the (OOL) Bragg reflection of stage n (Fuerst et al., 1983).

Structures and Phase Transitions

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101

Figure 3.34 Integrated intensity vs. pressure for the phases observed in KC8. At 19 kbar stage (3/2) disappears and stage 2 appears. Stage 1 is unaffected (Fuerst et al, 1983).

range which, however, is found to be much broader (10-23 kbar) than the stable region of stage (3/2) (15-19 kbar). 3.9.2 Devil's Staircase The guest atoms (I atoms) are periodically intercalated into the graphite galleries. This structure is ideally regarded as a one-dimensional (ID) chain along the caxis. We consider the phenomenological model of Safran (1980), a lattice gas model, in which each lattice site of the ID chain is occupied by either an I atom or a C atom. The interaction between I atoms at the rth and j'th sites is given by a repulsive interaction Vy. If the interaction is attractive, the I atoms tend to condense, forming no periodic structure. The Hamiltonian of this system is described by

where fj, is a chemical potential and the variableCT,to each lattice site i is equal to 1 if the I atom is present and 0 if the C atom is present. The repulsive interaction Vy depends only on the distance (s = \i-j\) between two lattice sites i and7: Vy = Vs for convenience. Bak and Jensen (1984) have pointed out that eq (3.31) is equivalent to an Ising model with long-range antiferromagnetic interaction in an exter-

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nal magnetic field H if /u, and Vy are replaced by H and exchange interaction, respectively. In this case one would expect that a stage transformation between integer stages takes place through an infinite number of fractional stages, forming a devil's staircase. The stable configuration {crj is obtained by minimizing /u, subject to the constant p, where p is the ratio of site occupied by atoms to the total of atom sites. The ground state configuration for p < 1/2 is described as follows. If p = 1/2, 1 / 3 , . . . , (reciprocal of stage number), the lowest energy configuration is that in which all the I atoms are equally spaced n neighbors apart. This is the ID analog of the staging structure of GICs, where the strong screening condition is satisfied: repulsion between two guest atoms i and j is effectively screened out by any intervening guest atom. In a more general situation p = m/n, where m and « are irreducible integers (m < n), the ground state has a periodic configuration with period n containing m guest layers in each period. For a given rational number p, it is mathematically proved that the ground state can be obtained by the following procedure (Hubbard, 1978). First, we define the integers k,, n0, nlt..., nk by the following equations: l/p = n0+r0, |l/r 0 | = n, + r b . . . , \\/rk_2 = «*_i + rk^, and \\/rk\ = n/f'. —1/2 < YJ < 1/2 for ally (the sequence must terminate for rational r). Next we define the sequences Xl, X2,..., Xk and Y\, Y2,..., Yk by X\ = n0, Y{ — n0 + a0, Xi+i = (X,y"-lY,, and YM = (Xi)"'^'1 Y,, where a, = r ( y|/v|. Then XM gives the ground state configuration. For example, we consider the case of p = 7/12, «0 = 2, «, = 3, «2 = 2, «0 = -1, and a, = 1, X} = 2, 7, = l,X2 = X\Y} = 22 • 72 = X\7, = 23 • 1, and X3 = X2Y2 = (22 • 1)(23 • 1). Here the superscripts indicate the numbers of repetitions: the ground state configuration X3 can be also written as Z3 = 2 • 2 • 1 • 2 • 2 • 2 • 1, where the 2s and 1 s indicate the spacing between successive I atoms (or stage 1 and stage 2) in each period. When p — 1/3, 2/5, 3/7, and 5/12, the ground state configuration can be expressed the forms 3, 3 • 2, 2 • 2 • 3, and 2 • 3 • 2 • 2 • 3, respectively. Thus it is concluded that the ground state configuration for a rational p can be expressed by the combination of two fundamental structures X\ and Y\ (= Xl + 1 or Xl - 1). Now we discuss the stability of ID superlattice gas. For simplicity we consider the three cases: p = 1/3, 5/12, and 1/4. We define A £/(+!) and AC/(-l) as fo lows: A £/(+!) is the energy required to form the structure p = 5/12 by adding on I atom to the structure p = 1/3, and A U(—\) is the energy required to form th structure p — 5/12 by adding one I atom to the structure of p = 1/4. When onl the interactions between adjacent I atoms are taken into account, A£/(+!) = —/x +3F 2 -2F 3 and Af/(-l) = /u, + 3F4 - 4F3. The range of M over which the configuration p= 1/3 is stable is obtained from the inequalities A [/(+!) > 0 and A£/(+!) >0: 4F3 - 3F4 < /* < 3F2 - 2V3 or AM(/O = 1/3) = 3[(F2 + F4) -2F3]. When A/4p = 1/3) > 0 the structure with p = 1/3 is stable. In general, the range of stability of /j, for the structure p — m/n is described as Afj,(p = m/n) = n(Vn_i + Vn+\ - 2Vn) + (higher order terms)

(3.32)

The value of A/z(p = m/n) is dependent only on n. When Vn is a function of n such that Vn+\ + Vn_\ - IVn > 0, the value of A/a(p = m/n) is positive for any m and n, indicating that the structure with p — m/n becomes stable.

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If the staging is indeed described by the Safran (1980) model, there should exist fractional staging in addition to the integer stages. In GICs we find experimentally that (i) only integer stage numbers n(= l/p) are observed, and (ii) A,u for each stage number becomes narrower as the stage number increases. For p = 2/3, corresponding to fractional stage (3/2) observed in KC8 under high pressure, the period is 3 with 2 I atoms in each period, n0 = 1, n\ = 2, aQ — 1, X\ = \, and 7] = 2. The ground state configuration is X2 = X\ Y{ = 1 • 2, indicating that stage-1 and stage-2 structures are alternately stacked along the c-axis. For p = 3/4, corresponding to fractional stage (4/3) observed in K(THF) (potassium solvated tetrahydrofuran) GIC (Marcus et al., 1988), the period is 4 with 3 I layers in each period, «0 = 1, n\ = 3, ot0 = \, X\ = 1, and Y\ = 2. The ground-state configuration is X2 = I 2 • 2, indicating that two stage-1 and one stage-2 structures are included CICICICCIC...). Integral stages require only a short-range interaction between nearest-neighbor intercalate layers. The stage (3/2) as an equilibrium phase implies second-neighbor layer interactions over a relatively short distance. It is significant that one cannot observe stage (4/3), K 3 C 6x4 , which is directly accessible from KC8 without phase separation: 3KC8 ->• K 3 C 6x4 . The stage (4/3) would require correlations among third-neighbor K layers. Whether any of these considerations might help to explain the observation of stage (4/3) K(THF) GIC is unclear. 3.10 Stripe Domain Phase in Br2 GIC

The structure of stage-4 Br2 GIC (C28Br2) with the largest in-plane density C 7 Br 2 has been extensively studied using single-crystal x-ray diffraction and high-resolution synchrotron diffraction (Erbil et al., 1983; Kortan et al., 1982; Mochrie et al., 1984). In this compound the Br2 molecules form a centered (\/3 x 7) commensurate superlattice structure with the sevenfold axis oriented along the graphite (110) direction: each unit cell contains four Br2 molecules (see Figure 2.21). In the sample as a whole, three sets of equivalent domains are observed, corresponding to the three (110) directions. The c-axis stacking sequence is described by AlABABIB with the c-axis repeat distance It. = 17.07 ± 0.01 A. A partial correlation between adjacent I layers is found: one I layer is translated by Q.25b with respect to the nearest-neighbor intercalate layer in the sevenfold direction. This correlation in the stacking of bromine I layers disappears above 325 K. Above 325 K the I layers are completely uncorrelated and the Br2 layers form essentially 2D systems. Correspondingly, the pure bromine Bragg reflections exhibit Bragg rods at Br(h, k) with the wavevector //a* + kb* in the reciprocal lattice plane, where h + k = In (n is an integer) (see Figure 3.35). The Bragg rods, which are oriented in the c* direction, indicate the absence of long-range order in the c direction. Those reflections that have indices k that are a multiple of 7 lie at the positions of the normal graphite (hkQ) reflections. The Br2 layers exhibit a commensurate-incommensurate transition at Tc — 342.20 ± 0.05 K. The Bragg rods relative to the 2D bromine structure shift along the k direction only, that is along the sevenfold direction as indicated

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by arrows in Figure 3.35. This result indicates that the Br2 layer has a stripe domain (SD) structure which is commensurate in the \/3 direction and incommensurate in the sevenfold direction. The (V3 x 7) commensurate structures are separated by domain walls running in the \/3 direction. The original Bragg reflection at Qy = kb* shifts to k\ (2n/L), where k{ is an integer and L is the sum of domain wall separation (Nb) (N: integer) and domain wall thickness (?). The shift of Bragg reflection A(£, r) from the commensurate reflection Br(h, K) can be described as

where r = k\— kN (integer) and d = b/t. The choice of t as 2b/7 (= 2aG) leads to the shift A(&, r) given by A(fc, r) = e(7r/2 - k), where the incommensurability e is defined as e = 4n/lL. Then, in the SD phase, the Bragg reflections denoted as Br[h, (k, r)] appear at the wavenumbers Qx = ha* and Qy = kb* + A(fc, r), where A(/c, r) = -€ for Br[l, (1,0)], 5e/2 for Br[l, (1, 1)], 3e/2 for Br[0, (2, 0)1, -e/2 for Br[0, (4, 1)], e/2 for Br[l(3, 1)J, -3c/2 for Br[l, (5, 1)], 2e for Br[l, (5, 2)], -5c/2 for Br[0(6, 1)], e for Br[0, (6, 2)], -3e/2 for Br[0, (12, 3)], and 2e for Br[0, (12,4)]. Figure 3.36 shows the shifts of the principal peak positions as a function of reduced temperature for Br[0, (4, 1)], Br[l, (1,0)], and Br[l, (5, 1)]. The experimental points are well fitted by a power-law form € = €o(T/Tc — 1)^, with ft = 0.50 ± 0.02 near Tc. This power-law fit starts deviating from the experimental points above 348 K and € reaches its saturation value at about 355 K. At saturation, the domain walls are separated by about 130 A, which is approximately 7.56. These results are well explained in terms of the theory of Pokrovsky and Talapov (1979, 1980) developed for a 2D system having commensurate-incommensurate transition in only one direction: the domain-wall density p (= 1/L) and hence the incommensurability € should initially rise as (T — Tc)1/2 but should saturate as the domain-wall density increases. With increasing domain wall density the repulsive

Figure 3.35 (hkO) reciprocal plane of a Br2 sublattice. Circles correspond to Bragg rods originating from the 2D Br2 super-lattice. Triangles represent 3D graphite and bromine peaks. Arrows at each Br2 peak show the directions of the principal peak position shifts during the transition at Tc. Bragg rods, represented by the open circles, solid circles, and half-filled circles, exhibit shifts of Aqy = e/2 e, and 3e/2, respectively, from their commensurate peak positions. qx and qy correspond to Qx and Qv in the text (Erbi et al., 1983).

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Figure 3.36 Shifts of the principal peak positions as a function of reduced temperature for the Br[0, (4, 1)], Br[l, (1, 0)], and Br[l, (5, 1)] peaks in a stage-4 Br2 GIC. Solid curves show the power-law fits as described in the text (Erbil et al., 1983).

interaction between the domain walls becomes large so that it hinders the creation of the domain walls. The line shape of the Bragg reflections in the SD phase near Tc has been studied with a high-resolution synchrotron x-ray experiment (Mochrie et al., 1984). In a 2D solid one expects a power-law line shape of the form IQ - Qo\~2+r>, corresponding to an algebraic form of the correlation function [c(r) ^ r'l], where Q0 is the reciprocal lattice vector of Br[/z, (k, r)] in the SD phase. The exponent rj(k, r) depends on both the order of the peak and the temperature: r)(k, r) ^ TA(k, r}2/K, where K is an elastic constant (Jancovici, 1967). Figure 3.37 shows typical scattering profiles in the sevenfold direction from the commensurate (C) phase at 329.75 K, and the SD phase at 348.25 K. The further a peak is displaced from the C position, the greater is the ratio of the intensity in the tail to the intensity at the peak: increasing ij(k, r) has precisely the effect of increasing this ratio. Mochrie et al. (1984) have shown that the line shapes for the five reflections, each having different k and r indices, are well described by the power-law form if the scaling of ri(k, r) with [A(fc, r)]2 is satisfied,

which is independent of temperature. Using this relation, the value of r](k, r) is estimated as q(k, r) = 2/49 = 0.041 for Br[0, (4, 1)], 0.163 for Br[0, (6, 2)], 0.367 for -3c/2 for Br[0, (12, 3)], and 0.653 for Br[0, (12,4)]. These results strongly support the algebraic decay of the correlation in the SD phase in the 2D uniaxial commensurate-incommensurate transition. As predicted by Schultz (1980), the

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Figure 3.37 Diffraction profiles of

various peaks in the commensurate (•) and incommensurate (O) phases at 56.6°C and 75.TC, respectively, in a stage-4 Br2 GIC. The dashed lines are fitted commensurate line shapes and the solid lines are power-law fits calculated from the SD model (Mochrie et al., 1984).

exponent rj can be described by r\n = 2n2/p2, where p (= 7 for C28Br2) is the periodicity of the commensurate structure relative to the reference lattice and n is the harmonic number. This exponent is independent of temperature, wall density, and the microscopic elastic constants. The Br2 layers exhibit an unusual melting transition at Tm (— 373.41 ±0.10 K). The diffraction profile of the Bragg reflection at Br[0, (4, 1)] evolves continuously from a power law to an anisotropic Lorentzian form on passing Tm. The ratio of correlation length ^ in the -v/3 direction to t-y in the sevenfold direction changes from 2.5 very near Tm to a value less than 1 at a temperature 0.4 K above Tm. This result suggests the existence of an anisotropic melting in the 2D bromine layers: a substantial order is maintained in the \/3 direction even in the fluid phase.

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3.11 Phase Transition in SbCI5 GIC

3.11.1 X-ray Scattering Studies Homma and Clarke (1985) have undertaken an extensive study of the ordered structure and phase transition of SbCIs GICs, using x-ray scattering. For all stages the graphite stacking sequence is ABABAB..., which is the same as pristine graphite stacking. The stage-1 stacking sequence is AaBftAa showing a partial 3D stacking coherence, where a and ft layers of intercalate differ by an inplane shift. For n = 2 the interplanar interaction between adjacent intercalate layers is weaker than that for n = 1. However, there is still a weak 3D correlation. For higher stages (n > 3) there is no 3D correlation. The in-plane structure of SbCl5 layers in SbCl5 GICs is complicated because a disproportionation of the SbCl5 molecules occurs during the intercalation process: 3 SbCl5 + 2e~ -» 2SbClg + SbCl3 as discussed in Section 2.3.1 (Boolchand et al., 1981; Friedt et al., 1984; Hwang, 1990; Hwang et al., 1984). The SbClg species form a commensurate structure of p(\fi x A/7)R19.11° with one SbClg" molecule per \/7 x \/7 unit cell, which is stable up to at least room temperature (RT) for any stage n. The SbCl^" molecule has one Sb atom, three Cl atoms located in a trigonal plane below the Sb atoms, and three Cl atoms located in a trigonal plane above the Sb atoms so that the molecule forms trigonal prisms, where the trigonal axes are normal to the graphite layer (Homma and Clarke, 1985). The Sb atom is located at the center of the triangle formed by three Cl atoms. The close packing of SbClg molecules leads to a spacing between Sb atoms of 2\/3rC| (= 6.24 A), where r^\ is the ionic radius of free Cl~ (= 1.80 A). This distance is close to the commensurate spacing of 6.51 A (= -Jla.^, where a^ (= 2.46 A) is the in-plane lattice constant of graphite. For n = I the SbCl3 species form a /?(\/39 x \/39)R16.r superlattice which is stable up to at least RT. For n > 2 the SbCl3 species are in the fluid-like disordered state at RT and undergo first-order phase transitions near 200-230 K into a p(V39 x \/39)R16.r superlattice. The spacing is actually approximately 2% compressed relative to the commensurate V39 periodicity. Figure 3.38 shows the temperature dependence of the x-ray peak intensity for the (200) Bragg reflection of the XV39 x V39)R16.1° structure in stage-2 SbCl5 GIC (Homma and Clarke, 1985). The transition is strongly hysteretic around 200-230 K. In some stage-2 samples a small residual x-ray intensity is observed at the V39 x -v/39 reciprocal-lattice point, at temperatures above the transition temperature. Further indications of residual \/39 x -v/39 superlattice ordering up to RT in stage-2 samples were observed in the heat capacity measurement (Bittner and Bretz, 1985), No evidence for the persistence of \/39 x \/39 superlattice ordering above the transition temperature is observed for n > 3. This suggests that interlayer interactions may enhance the stability of the in-plane ordering in SbCl3 molecules. In the intercalate layer SbCl3 molecular species form two kinds of trigonal prisms: one Sb atom and three Cl atoms located in a trigonal plane below the Sb atom, and another Sb atom and three Cl atoms located in a trigonal plane

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Figure 3.38 Thermal hysteresis of (200) x-ray peak intensity

superlattice in stage-2 SbQ5 GIC (Homma and Clarke, 1985).

above the Sb atom (Homma and Clarke, 1985). The energy of this molecule is the same for the two possible positions of the Sb atoms. It is well known that the pristine SbCl3 molecule has a rather large electric dipole moment \i = 3.9D (D = 10 esc cm) with its direction pointed away from the Sb atom and perpendicular to the plane of the Cl atoms. This dipole moment fi, at the site / is assumed to be coupled with the nearest-neighbor moment \LJ at the site7 through a dipole-dipole interaction (Suzuki et al., 1997)

where Ry is a position vector connecting between the locations of n, and n;. When both ft, and (iy- are perpendicular to the position vector R,y, this interaction favors a configuration of dipole moments with the direction of ji, being antiparallel to that of ]ij. The distance between nearest-neighbor electric dipoles is 7.64 A. The dipoledipole interaction U can then be estimated as 3.41 x 10~14 erg, where T = U/k^ = 244 K, which is close to the upper critical temperature Tcu (= 223-231 K), as will be defined in Section 3.11.2. This dipole-dipole interaction favors an antiparallel configuration for the nearest-neighbor SbCl3 molecules. The SbCl3 molecular species form a p(Vl9 x ->/3^)R16.1° commensurate structure because of these directions. For nearest-neighbor interactions there are four antiparallel couplings and two parallel couplings. This is also true for next-nearest-neighbor interactions. The competition between these interactions gives rise to a frustration effect inside the system. This situation is similar to that of the 2D Ising antiferromagnet on the triangular lattice with spin frustration effects arising from competing intraplanar exchange interactions.

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3.11.2 Electric Dipole Fluctuations The c-axis resistivity pc. of SbCl5 GICs with 3 < n < 9 is influenced by enhanced fluctuation due to the electric dipole moments of SbCl3 molecules. Figure 3.39 shows the temperature dependence of pc for stage-6 SbCl5 GICs (Suzuki et al., 1997), where pc(T 4.) and pc(T t) are the resistivity obtained in cooling and heating processes, respectively. The value of pc returns to the same room temperature (RT) value after each thermal cycle. The value of pc below 180 K does not depend on the detail of the thermal cycle, indicating that both the 2D ordered state below 180 K and the disordered state at RT are thermodynamically reversible states. The strongly hysteretic characters of the transition between the ordered state and disordered state are related to the nature of in-plane structural order of SbCl3 species in the intercalate layers. The critical temperatures of SbCl5 GICs with 3 < n < 9 are defined from temperatures where pc(T t) has local minima. These compounds undergo two kinds of phase transition at Tc\ (= 196-211 K) and Tcu (= 223-231 K). The value of Td tends to decrease with increasing stage number (3 < n < 7), while the value of Tcu is less weakly dependent on the stage number (3 < n < 9). This result suggests that the 2D and 3D long-range dipole orders appear at rcu and Td, respectively. Well above Tca the system of SbCl3 molecules is in a structurally disordered state. The 2D structural correlation length drastically increases on approaching Tcu from the high-temperature side, giving rise to the enhancement of intraplanar correlation between dipoles of SbCl3 molecules in each SbCl5 layer. A 2D long-range dipole order is established below Tm.

Figure 3.39 Temperature dependence of c-axis resistivity p, for stage-6 SbCl5 GIC measured during the cooling (T 4.) and heating (T t) processes. The detail of pc(T f) vs. T near the critical temperatures is shown in the inset. In the inset the temperatures corresponding to local minima of pc are denoted by arrows (Suzuki et al., 1997).

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The effective interplanar interaction between dipoles of SbCl3 is a driving force for the 3D ordering process of dipoles. The interaction is determined by a product of very weak interplanar interaction between dipoles and a square of intraplanar dipole correlation length, in analogy with effective interplanar interactions between spins in stage-2 CoCl2 GIC (Suzuki and Suzuki, 1998), as will be discussed in Chapter 7. The growth of the intraplanar dipole correlation length is limited by the size of SbCl3 -forming islands in the SbCl5 layer. A 3D long-range dipole order appears below Tc[ a little lower than Tcu, because of the suppression of divergence in the effective interplanar interactions between dipoles around Tcu. 3.12 Ordering Kinetics

3.12.1 Overview In recent years there has been renewed interest in the non-equilibrium kinetics of first order phase transitions. A key concept in the modern understanding of these phenomena is that, with proper scaling of both space and time, the pattern of grain growth in the quenched phase is reduced to a universal form. This scaling behavior appears in the time evolution of various physical quantities such as the fraction of transformed volume, average domain size, and the domain-size distribution function. These quantities are directly related to the integrated intensity of Bragg reflection I(t), the linewidth, and the structure factor 5(q, t). Note that the kinetic process of the first-order phase transition generally consists of two successive processes, namely, nucleation growth (NG) and domain growth (DG). The nucleation of the stable phase and the growth of these nuclei in the metastable phase matrix occur at an early stage of the transition; this process is driven by the free energy gain. After the system is completely transformed into the stable phase, the DG process starts and the stable phase domains grow in size by merging with other domains. This process is driven by the gain of interface energy between domains. The commensurate in-plane superlattice in GICs has equivalent ground states depending on the symmetry. A wide range of degeneracy (p) can be achieved in GICs: p — 3(-/3 x A/3 ordering in LiC6), p = 4 (^/2 x V2 ordering in RbC8), and p = 7 (A// x A/7 ordering in SbCl5 GIC). When these systems undergo a first order phase transition, they provide model systems for studying the kinetics in the NG and DG process of quenched phase. In general, a degenerate system with higher p exhibits slow kinetics because such a system has lower probability in finding domains of the same superlattice out of many other degenerate ones. 3.12.2 2D Kinetics: Stage-4 SbCl5 GIC The SbClg" species in stage-4 SbCls GIC form an commensurate in-plane structure with theX\/7 x VT) R19.ll 0 superlattice below the melting temperature Tm (— 450 K) (Homma and Clarke, 1984). The ground state of this system is degenerate, with a degeneracy of p = 7. Hernandez et al. (1987) have studied the kinetics of ordering in stage-4 SbQ5 GIC using a high-resolution synchrotron

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I II

radiation technique and parallel data acquisition via a position-sensitive detector (PSD). They observed the time dependence of the (100) diffraction peak of the p (\/7 x \/7)R19.11° superlattice after quenching the sample from the high-temperature disordered state to the low-temperature ordered state below the melting temperature Tm. Figure 3.40 shows a series of time-resolved PDS diffraction profiles from a stage-4 SbCl5 GIC, based on single crystal graphite when it is quenched from 480 K (disordered phase) to Tq = 260 K. The superlattice peak grows rapidly and saturates within the first minute. Thereafter, the diffraction intensity increases very slowly. The line width of the peak is quite narrow even at short times (~ 1 s) after quenching, implying that the \/7 x -Jl correlations are long range even though the ordering process is far from complete. The growing process during the transition is the DG process. The line shapes of Figure 3.40 are found to be fitted to a Lorentzian 5(q, i) = [K2(f) + (q - q 0 ) 2 ]~' convoluted with a

Figure 3.40 (100) diffraction peak of stage-4 SbCl5 GIC based on single-crystal graphite at various times (units of seconds) after quenching from T = 480 K to 260 K. The integration time for each data set is 1 s (Hernandez et al., 1987).

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Gaussian instrumental function, where q0 is the wavevector of the (100) Bragg reflection and K is the inverse in-plane correlation length. Figure 3.41 shows the time dependence of the in-plane correlation length (f = K~I). It shows a powerlaw form of £ % f (t is time) with « = 0.43 ± 0.05 in the early stage of the transition. The exponent n is close to the classical value (1/2) (Nakashima et al., 1989). In the inset of Figure 3.41 the time dependence of the peak intensity S(q0) is shown. The initial rise of S(q0) is fitted by a power law. The long-time behavior of S(q0) is well described by ln(?) after t = 50 s. This ln(;) behavior is due to thermal domain-wall roughening. 3.12.3 ID Kinetics: Stage-1 K GIC Stage-1 Rb GIC undergoes a first order phase transition when the K vapor pressure P is equal to the critical vapor pressure at the fixed low sample temperature TG (= 378°C). The c-axis stacking sequence changes from aft to aftyS as the vapor pressure decreases, while the in-plane structure (2 x 2) remains unchanged. Figure 3.42 shows the time dependence of the x-ray diffraction spectra along the (10L) direction in RbC8 during the transition from aftyS to aft phase (Metoki et al., 1989, 1990). The spectra kinetics were obtained by rapidly changing the vapor pressure of Rb (P) from an initial pressure Pj stabilizing the aftyS phase to a final pressure Pf stabilizing the aft phase: AP = Pf - Pj = -1.6 Pa (< 0). Note that the transition occurs from aft phase to aftyS phase for AP > 0. In Figure 3.42 the (103) and (104) peaks correspond to the Bragg reflections of aftyS and aft phases respectively. The peak intensity of the (104) Bragg reflection increases with time, whereas the peak intensity of the (103) Bragg reflection decreases. The (104)

Figure 3.41 Plot of the inverse inplane correlation length K as a function of time after quenching. The solid-line fit in the early stage of the transition is described by a power-law form. The inset shows the time dependence of the peak intensity 5(q0, t). The initial rise is fitted to a power-law form (denoted by a dashed line) and the long-time behavior by a ln(0 dependence (denoted by a solid line) (Hernandez et al., 1987).

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Figure 3.42 Time dependence of the (10L) diffraction spectra for RbCg after the Rb vapor pressure is quickly changed by A/> Rb = -1.6 Pa at t = 0, corresponding to the transition from aftyS to a/8 phase; TG = 378°C. The (103) and (104) peaks correspond to the Bragg reflections of afiyS and a$ phases respectively. Horizontal bars indicate the resolution (Metoki et al., 1990).

spectrum has a sharp peak profile characteristic of a squared Lorentzian S(q, t) = [K2(t) + (q - q0)2r2 rather than Lorentzian or Gaussian. No diffuse scattering is observed throughout the transition. This is true for the case even in the earliest stage of t = 1.2 min immediately after quenching. The nucleation of the aft phase occurs in the matrix of the aftyS metastable phase with a finite cluster size, enough to give rise to the Bragg reflection. The (104) diffraction is fitted well to a squared Lorentzian. The stable and metastable phases are separated by a sharp boundary without a disordered state. Thus the growing process in this period is the NG process. The integrated intensities around (104) and (103) reflections are proportional to the numbers of Rb atoms contributing to the aftyS and aft phase respectively. Since there is no change in the stage number and the in-plane density during the transition, the total number of Rb atoms remains unchanged, implying that the sum of the two integrated intensities is constant. The volume fraction of the growing phase, X(t), has a characteristic time dependence, X(i) = I(i)/I0, where I(f) is the integrated intensity around the (104) Bragg reflection, and 70 is the saturation value in thermal equilibrium. Note that the growing phase is aft for AP < 0 and aftyS for AP > 0. For different AP, X(t) has a different time dependence. However, as shown in Figure 3.43, X (t, AP) obeys a simple scaling relation by a scaling function of characteristic time

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Figure 3.43 Time dependence of the volume fraction of the growing phase: aftyS phase for AP Rb > 0 and cc/J phase for AP R b < 0. The data are plotted as a function of the normalized time t/ti/2, ?i/2 being the time that the volume fraction of the growing phase grows to onehalf of that at the completion of the transition. For comparison, the results of the phenomenological theory of Avrami, described by I/I0 = 1 - exp[-(//? I/2 ) rf+l ], are shown for ID (solid line), 2D (dashed line), and 3D (dotted line) (Metoki et al., 1990).

dependent on AP, where /,/ 2 (A/ > ) is the time when X(i) grows to onehalf the intensity at the completion of the transition. In Figure 3.43 the results of the phenomenological theory of Avrami (1939, 1940, 1941) for the NG process in a system with J-dimension are also shown: X(T) = 1 - exp(-rrf+1). The calculated function for d = 1 is in good agreement with the experimental results except for small A P. The system size Rap(t) of the growing aft phase for AP < 0 is determined from the inverse of the line width corrected by the experimental resolution. As shown in Figure 3.44 Rap(t) shows a remarkable time dependence from critical size (~ 60 A) to final size (~ 300 A). However, the observed time dependence is far from a linear function. The straight line in Figure 3.44 indicates that Rafl(t) is proportional to \n(t). According to Metoki et al. (1989, 1990), the stacking sequences apafi and aflyS are equivalent to ferromagnetic and antiferromagnetic states, respectively, when the two-layer packages aft (= A) and yS (= B) are regarded as spin-up state and spin-down state, respectively. Furthermore, the order parameter is not conserved, since the number of the growing phase changes with time. Thus the system belongs to a universality class of ID non-conserved order parameters (NCOP) with degeneracy p = 2 for the oaxis stacking order, instead of p = 4 for the (2 x 2) in-plane ordering. For the DG process in the ID NCOP (p = 2) system, Kawasaki and Nagai (1986) have theoretically obtained a nearly squared Lorentzian for S(q, f) and a logarithmic time dependence of domain size R(t). On the other hand, there has been no theory for the NG process. These results may indicate the possibility that the DG process, as well as the NG process, occurs in the early stage of transition in RbC 8 .

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I I5

Figure 3.44 Time dependence of grain size Rap(t) of the growing aft phase at various APRb. The origin is vertically shifted for each A/5, for clarification (Metoki et al., 1990).

References Avrami, M. J. Chem. Phys. 1939, 7, 1103. Avrami, M. /. Chem. Phys. 1940, 8, 212. Avrami, M. J. Chem. Phys. 1941, 9, 177. Bak, P.; Domany, E. Phys. Rev. 1979, B 20, 2818. Bak, P.; Jensen, M. H. In Multicritical Phenomena; Pynn, R., Skjeltorp, A., Eds.; Plenum: New York, 1984; p 237. Bittner, D. N.; Bretz, M. Phys. Rev. 1985, B 31, 1060. Bloch, J. M.; Katz, H.; Moses, D.; Cajipe, V. B.; Fischer, J. E. Phys. Rev. 1985, B31, 6785. Boolchand, P.; Bresser, W. J.; McDaniel, D.; Sisson, K.; Yen, V.; Eklund, P. C. Solid State Commun. 1981, 40, 1049. Cajipe, V. B.; Heiney, P. A.; Fischer, J. E. Phys. Rev. 1989, B 39, 4374. Chow, P. C.; Zabel, H. Phys. Rev. 1987, B 35, 3663. Clarke, R.; Caswell, N.; Solin, S. A.; Horn, P. M. Phys. Rev. Lett. 1979, 43, 2018. Clarke, R.; Wada, N.; Solin, S. A. Phys. Rev. Lett. 1980, 44, 1616. Clarke, R.; Gray, J. N.; Homma, H.;Winokur, M. J. Phys. Rev. Lett. 1981, 47, 1407. Daumas, N.; Herold, A. C.R. Acad. Sci. Ser. 1969, C 268, 273. Dicenzo, S. B. Phys. Rev. 1982, B 26, 5878. Dresselhaus, M. S.; Dresselhaus. G. Adv. Phys. 1981, 30, 139. Ellenson, W. D.; Semmingsen, D.; Guerad, D.; Onn, D. G.; Fischer, J. E. Mater. Sci. Eng. 1977, 37, 137. Erbil, A.; Kortan, A. R.; Birgeneau, R. J.; Dresselhaus, M. S. Phys. Rev. 1983, B 28, 6329. Fischer, J. E.; Fuerst, C. D.; Woo, K. C. Synth. Metals 1983, 7, 1. Friedt, J.M., Poinsot, R.; Soderholm, L. Solid State Commun. 1984, 49, 223.

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Fuerst, C. D.; Fischer, J. E.; Axe, J. D.; Hastings, J. B.; McWhan, D. B. Phys. Rev. Lett. 1983, 50, 357. Hastings, J. B.; Ellenson, W. D.; Fischer, J. E. Phys. Rev. Lett. 1979, 42, 1552. Hendricks, S.; Teller, E. J. Chem. Phys. 1942, 10, 147. Hernandez, P.; Lamelas, F.; Clarke, R.; Dimon, P.; Sirota, E. B.; Sinha, S. K. Phys. Rev. Lett. 1987, 59, 1220. Herold, A. In Physics and Chemistry of Materials with Layered Structures, vol. 6\ Levy, F., Ed.; D. Reidel: Dordrecht, 1979; p 323. Hohlwein, D.; Metz, W. Z. Kristallogr. 1974, 139, 279. Homma, H.; Clarke, R. Phys. Rev. Lett. 1984, 52, 629. Homma, H.; Clarke, R. Phys. Rev. 1985, B 31, 5865. Hubbard, J. Phys. Rev. 1978, 577, 494. Huster, M. E.; Heiney, P. A.; Cajipe V. B.; Fischer, J. E. Phys. Rev. 1987, B 35, 3311. Hwang, D. M. In Graphite Intercalation Compounds I; Zabel, H., Solin, S. A., Eds.; Springer-Verlag: Berlin, 1990; p 247. Hwang, D. M.; Qian, X. W.; Solin, S. A. Phys. Rev. Lett. 1984, 53, 1473. Jancovici, B. Phys. Rev. Lett. 1967, 19, 20. Kakinoki, J.; Komura, Y. J. Phys. Soc. Jpn. 1952, 7, 30. Kawasaki, K.; Nagai, T. J. Phys. 1986, C 19, L551. Kim, H. J.; Fischer, J. E.; McWhan, D. B.; Axe, J. D. Phys. Rev. 1986, B 33, 1329. Kirczenow, G. Phys. Rev. 1985, B 31, 5376. Kirczenow, G. In Graphite Intercalation Compounds I, Zabel, H., Solin, S. A., Eds.; Springer-Verlag: Berlin, 1990, p 59. Kortan, A. R.; Erbil, A.; Birgeneau, R. J.; Dresselhaus, M. S. Phys. Rev. Lett. 1982, 49, 1427. Lee, C. R.; Aoki, H.; Kamimura, H. J. Phys. Soc. Jpn. 1980, 49, 870. Marcus, B.; Touzain, Ph.; Soubeyroux, J. L. Synth. Me!. 1988, 23, 13. Meisenheimer, M. E.; Zabel, H. Phys. Rev. Lett. 1985, 54, 2521. Metoki, N.; Suematsu, H. Phys. Rev. 1988, B 38, 5310. Metoki, N.; Suematsu, H.; Murakami, Y. Synth. Met. 1989, 34, 323. Metoki, N.; Suematsu, H.; Murakami, Y.; Ohishi, Y.; Fujii, Y. Phys. Rev. Lett. 1990, 64, 657. Metz, W.; Hohlwein, D. Carbon 1975, 13, 87. Millman, S. E.; Kirczenow, G. Phys. Rev. 1982, B 26, 2310. Minemoto, H.; Suematsu, H. Synth. Met. 1985, 12, 33. Mitani, H.; Niizeki, K. /. Phys. 1988, C 21, 1895. Miyazaki, H.; Horie, C.; Watanabe, T. /. Phys. Soc. Jpn. 1984, 53, 3843. Mochrie, S. G.; Kortan, A. R.; Birgeneau, R. J.; Horn, P. M. Phys. Rev. Lett. 1984, 53, 985. Moret, R. In Intercalation in Layered Materials, Dresselhaus, M. S., Ed.; Plenum Press: New York, 1986, p 185. Mori, M.; Moss, S. C.; Jan, Y. M.; Zabel, H. Phys. Rev. 1982, B 25, 1287. Mori, M.; Moss, S. C.; Jan, Y. M. Phys. Rev. 1983, B 27, 6385. Moss, S. C.; Moret, R. In Graphite Intercalation Compounds I, Zabel, H., Solin, S. A., Eds.; Springer-Verlag: Berlin, 1990, p 5. Moss, S. C.; Reiter, G.; Robertson, J. L.; Thompson, C.; Fan, J. D. Phys. Rev. Lett. 1986, 57, 3191. Moss, S. C.; Kan, X. B.; Fan, J. D.; Robertson, J .L.; Reiter, G.; Karim, O. A. In Competing Interactions and Microstructure: Statics and Dynamics LeSar, R., Bishop, A., Heffner, R., Eds.; Springer-Verlag: Berlin, 1988; Springer Proc. Phys. 27. Nakashima, K.; Nagai, T.; Kawasaki, K. /. Stat. Phys. 1989, 57, 759.

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Nishitani, R.; Uno, Y.; Suematsu, H. Phys. Rev. 1983a, B 27, 6572. Nishitani, R.; Uno, Y.; Suematsu, H. Synth. Met. 1983b, 7, 13. Nishitani, R.; Uno, Y.; Suematsu, H.; Fujii, Y.; Matsushita, T. Phys. Rev. Lett. 1984, 52, 1504. Nishitani, R.; Suda, K.; Suematsu, H. J. Phys. Soc. Jpn. 1986, 55, 1601. Parry, G. S. Mater. Sd. Eng. 1977, 31, 99. Pokrovsky, V. L.; Talapov, A. L. Phys. Rev. Lett. 1979, 42, 65. Pokrovsky, V. L.; Talapov, A. L. Zh. Eksp. Tear. Fiz. 1980: 78, 269. Sov. Phys.-JETP 1980, 51, 134. Reiter, G.; Moss, S. C. Phys. Rev. 1986, B 33, 7209. Rousseaux, F.; Moret, R.; Guerard, R. D.; Lagrange, P.; Lelaurain, M. J. Phys. Lett. 1984, 45, L - l l l . Rousseaux, F.; Moret, R.; Guerard, D.; Lagrange, P.; Lelaurain, M. Ann. Phys., Colloque

1986,2: 11: 85.

Rousseaux, F.; Moret, R.; Guerard, D.; Lagrange, P. Phys. Rev. 1990, B 42, 725. Safran, S. A. Phys. Rev. Lett. 1980, 44, 937. Safran, S. A; Hamann, D. R. Phys. Rev. 1982, B 22, 606. Salzano, F. ).; Aronson, S. J. Chem. Phys. 1966, 45, 4551. Schultz, H. ]. Phys. Rev. 1980, B 22, 5274. Suematsu, H.; Suzuki. M.; Ikeda, H. J. Phys. Soc. Jpn. 1980, 49, 835. Suzuki, I. S.; Suzuki, M. J. Phys. Condensed Matter 1991, 3, 8825. Suzuki, M. Phys. Rev. 1986, B 33, 1386. Suzuki, M.; Suematsu, H. J. Phys. Soc. Jpn. 1983, 52, 2761. Suzuki, M.; Suzuki, I. S. Phys. Rev. 1998, B 58, 840. Suzuki, M.; Suzuki, I. S.; Matsubara, K.; Lee, C.; Niver, R.; Sugihara, K. J. Phys. Condensed Matter 1997, 9, 10399. Suzuki, M.; Ikeda, H.; Suematsu, H.; Endoh, Y.; Shiba, H.; Mulchings, M. T. J. Phys. Soc. Jpn. 1980, 49, 671. Suzuki, M.; Ikeda, H.; Suematsu, H.; Endoh, Y.; Shiba, H. Physica 1981, 105B, 280. Suzuki, M.; Lee, C.; Suzuki, I. S.; Matsubara, K.; Sugihara, K. Phys. Rev. B 1996, 54, 17128. Wada, N. Phys. Rev. 1981, B 24, 1065. Winokur, M. }.; Clarke, R. Phys. Rev. Lett. 1985, 54, 811. Winokur, M. ).; Clarke, R. Phys. Rev. 1986a, B 34, 4948. Winokur M. J.; Clarke, R. Phys. Rev. Lett. 1986b, 56, 2072. Wu, F. Y. Rev. Mod. Phys. 1982, 54, 235. Yamada, Y.; Naiki, I. J. Phys. Soc. Jpn. 1982, 51, 2174. Yosida, Y.; Sato, K.; Suda, K.; Suematsu, H. J. Phys. Soc. Jpn. 1986, 55, 561. Zabel, H.; Moss, S. C.; Caswell, N.; Solin, S. A. Phys. Rev. Lett. 1979, 43, 2022. Zabel, H.; Chow, P. C. Comments Cond. Mat. Phys. 1986, 12, 225.

4

Lattice Dynamics

4.1 Phonon Dispersion in Alkali Metal GICs (Theory)

Pristine graphite crystallizes according to the Dgh space group. There are twelve modes of vibration associated with the three degrees of freedom of the four atoms in the primitive cell. The hexagonal Brillouin zone and the phonon dispersion curves of pristine graphite, calculated by Maeda et al. (1979), are shown in Figure 4.1. The zone-center (F point) modes are labeled as three acoustic modes (A2u + E l u ), three infrared active modes (A2u + E lu ), four Raman active modes (2E2g), and two silent modes (2B lg ). The first calculation of phonon dispersion for the stage-1 compounds KC8 and RbC g was presented by Horie et al. (1980) on the basis of the model of Maeda et al. (1979) for the lattice dynamics of pristine graphite. Although the calculated phonon energies do not agree well with the experimental data, the model has most of the ingredients for describing the lattice dynamics of stage-1 GICs. A simple review of their work is presented as follows. The primitive cell of KC8 (Figure 4.2a), having a p(2 x 2)RO° superlattice, contains 16 carbon atoms and two K atoms. Note that only an aft stacking sequence is assumed here (see Section 3.6.1). The primitive translation vectors are given by ?, — (0, a, 0), t2 = (-V3a/2, a/2, 0), and r3 = (—v/3a/4, -a/4, c), where a = 2aG = 4.91 A and c = 5.35 x 2 = 10.70 A. The corresponding Brillouin zone is shown in Figure 4.2b. The phonon dispersion for KC8 has been calculated by Horie et al. (1980) on the basis of the Born-von Karman force constant model. This dispersion curve is compared with that of pristine graphite by folding the dispersion curves of graphite into the first Brillouin zone of KC g . Since the side of the Brillouin zone in KC8 is not flat 118

Lattice Dynamics

119

Figure 4.1 (a) Hexagonal Brillouin zone of pristine graphite; (b) phonon dispersion relations of pristine graphite (Maeda et al., 1979).

in two directions, as shown in Figure 4.2b, it is a little difficult to transfer the information on the dispersion curves in the first Brillouin zone of graphite into the Brillouin zone of KC8. For simplicity, nevertheless, we assume that the side of the Brillouin zone in KC8 is flat like that of graphite. Figure 4.2c shows

I 20 Graphite In te real at ion Com pounds and Applications

Figure 4.2 (a) Primitive cell of KC8; (b) first Brillouin zone of KC8 (bold lines); (c) schematic diagram for the explanation of zone-folding at k, = 0. The solid line denotes the Brillouin zone of graphite and the dotted line denotes the approximate Brillouin zone of KC8, having a p(2 x 2)RO° in-plane structure and a/3 stacking (Horie et al., 1980).

Lattice Dynamics

I 21

Figure 4.2 (continued)

the 2D cross-section of the Brillouin zone of graphite (denoted by solid line) and KC8 (denoted by dotted line) with k, = 0. The edge point M in the Brillouin zone of graphite is brought to the F point by folding. There are 18 x 3 = 54 modes, corresponding to 18 atoms per unit cell. When the phonon dispersion curves for graphite folded in the Brillouin zone of KC8 are compared with the phonon dispersion curves of KC8, it is clear that for KC8 there are six new optical modes in the low-frequency region, originating from vibrations of two K atoms in a primitive cell. The frequency of these modes is almost independent of wavenumber (dispersionless) because of weak coupling between K atoms. The remaining modes are associated with vibrations of carbon atoms and exhibit a definite correspondence with the folded dispersion relation for graphite. When the oscillating modes of K atoms and carbon atoms have the same polarization vector, mixing modes are generated near the wavevector where two dispersion curves merge because of the strong interactions. In the mixed modes the vibration of K atoms is predominant in the wavenumber region where noticeable phonon dispersion exists. The phonon dispersion curves obtained for RbC8 are qualitatively similar to those for KC8. The only difference is that the modes associated with vibrations of carbon atoms have a tendency to shift upwards, whereas those associated with vibrations of Rb shift downwards because of the heavier mass of Rb. The model of Horie et al. (1980) is limited to the symmetry of stage-1 GICs, and a simple extension to higher stage compounds is not possible. A more general model was proposed by Leung et al. (1981) and, in a refined version, later by Al-Jishi and Dresselhaus (1982). The dispersion curves for all GIC stages can be obtained from those of pristine graphite by carrying out a &.-axis zone folding of the graphite dynamical matrix and replacing carbon layers with intercalate layers. Al-Jishi and Dresselhaus have used the dispersion of the graphite layers with a stacking sequence ABABAB For simplicity they assume that the stacking sequence is AIAIA ... for stage 1, ABIABIABI... for stage 2, ABAIABAIABAI... for stage 3, and ABABIABABIABABIABAB... for stage 4. The unit cell of stage-« GIC (IC,^) is taken to include n graphite layers and one intercalate layer (I). There are two carbon atoms and one I atom per area (\/3flG/2) of graphite layer, where the effective mass of the I atom is (2/£)M), where M\ is the real mass of the I atom. Furthermore, the distance between

I 22 Graphite Intercalation Compounds and Applications

Figure 4.3 Phonon dispersion curves along the c* axis in stage-1, 2, 3, and 4 Rb GICs. The open circles represent the experimental points. Heavy lines (light lines) represent calculated dispersions of the layer shear modes (layer breathing modes) (Al-Jishi and Dresselhaus, 1982).

adjacent graphite layers is assumed to be equal to that between adjacent graphite and intercalate layers. The oaxis periodicity results in the well-known effect of zone folding of the graphite phonon dispersion curves so that no-zone-center phonons of graphite are mapped back to the zone center in the GIC. The Brillouin zone along the c* direction is reduced by a factor 2 / ( n + l ) as compared to pristine graphite with the ABAB stacking sequence: the component of reciprocal lattice vector along the c* axis is 2n/(2da) = n/dG for graphite and 2n[(n + l)dG] for stage-« GIC. The agreement between the calculated and observed values is very good in spite of the simplification in the model. Such good agreement is due in part to the use of an accurate model for the phonondispersion relations for pristine graphite and the symmetry of the crystal structure. The phonon dispersion thus obtained can be applied to various stages and compounds merely by adjusting the effective intercalate masses. Figure 4.3 shows the phonon dispersion curves of low-frequency interlayer modes in Rb GICs along the c* axis, obtained by Al-Jishi and Dresselhaus (1982). 4.2 Phonon Dispersion in Alkali Metal GICs (Experiment)

4.2.1 Inelastic Neutron Scattering in Alkali Metal GICs The vibrational modes observed in GICs may be classified as high-frequency intraplanar modes and low-frequency interlayer modes. The low-lying modes consist of the [OOg] longitudinal (L) mode (the so-called layer breathing mode) and the [00