The physical properties of layered dichalcogenides and their intercalation compounds

281

Materials Science and Engineering, 31 ( 1 9 7 7 ) 2 8 1 - 2 8 8 © Elsevier S e q u o i a S.A., L a u s a n n e - - P r i n t e d in t h e N e t h e r l a n d s

The Physical Properties o f Layered Dichalcogenides and their Intercalation Compounds

B. G. S I L B E R N A G E L

Corporate Research Laboratories, Exxon Research and Engineering Company, Linden, N. J. 07036 (U.S.A.)

LAYERED DICHALCOGENIDES& INTERCALATIONCOMPOUNDS

1. I N T R O D U C T I O N

0

IA

A major recent theme in solid state chemistry and physics has been the relationship between the structural dimensionality of a material and its physical and chemical properties. Extensive studies of materials like the one-dimensional charge transfer salts (e.g., TTF-TCNQ) and such two
•

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IIIA~VA

IItB IVB VB VIB VIIB

~

VIIIB ~

IB

VA VIA

IIB i

il T

Formone or more Layered Dichaicogenides

Form NH3 Inte~calation Complexes

~

FormLithi~m Intercalation Compounds

Fig. 1. T h e o c c u r r e n c e o f layered dichalcogenides.

varying electronic properties, from semiconductors like M o S 2 and H f S 2 to superconducting metals like NbSe 2. This layered structure facilitates the inclusion of atomic and molecular species in the spaces between the basic dichalcogenide units (commonly called the van der Waals gap region) in a phenomenon known as intercalation. A wide variety of molecular species, alkali metal atoms and transition and posttransition metals, is known to occur as guests [3]. The last few years have marked the beginning of the study of such materials by solid state physics techniques and the present paper is a topical review of these studies. Four major areas will be examined: (1) The current understanding of the electronic structure of the layered dichalcogenides as inferred from experimental observations and theoretical band structure calculations. (2) The cooperative lattice distortions, known as Charge Density Waves, which are observed in many layered dichalcogenides and which are related to their electronic properties.

282

I I

i

I I i

I-T TaS2

B

I I

2-H TaS2 Trigonal Prism

Octahedron

Y t 2g "///////////72-~

(O)

d z2

(TP)

Fig. 2. (a) The two metal atom site symmetries,octahedral, and trigonal prismatic, consistent with the layered structures. (b) Band structures proposed by valence bond theory analysis for metal atoms in octahedral and trigonal prismatic sites. (3) An overview of the physical properties o f in tercalation compounds. (4) A report of detailed studies of two systems, lithiated dichalcogenides and vanadium sulfides, to illustrate the interplay of synthesis, macroscopic, and microscopic observations required to provide a clear picture of the material. 2. LAYERED DICHALCOGENIDES

(a) Electronic structure The layered dichalcogenides exhibit a regular alternation of semiconducting and metallic properties for cations from Groups IV(b), V(b) and VI(b) of the Periodic Table. With metals from Groups IV(b) and VI(b), semiconductors (or at best semimetals) are formed, while elements from Group V(b) form metallic, sometimes superconducting, materials. Application of valence bond theory explains this general feature in terms of the site symmetry and electronic character of the metal atom. As illustrated in Fig. 2(a), two types of metal atom sites axe consistent with

the atomic packing: octahedral (O) and trigonal prismatic (TP) forms. Disulfides and diselenides with Group IV(b ) metals adopt the O form while those of Group VI(b) have the TP one. Both site types occur for Group V(b) metals. The preferred site symmetry depends on the covalent character of the metalchalcogen bond [4] and is quantitatively correlated with the ionicities of the constituents [5]. Different site symmetries produce different arrangements of the metal d orbitals as shown in Fig. 2(b). Bonding occurs via the eg orbitals in the O case and by the dxz and dyz orbitals in the TP case. The non-bonding t2~ orbitals are degenerate in the O case, while the TP crystalline field causes the dz~( 3 Z 2 - r 2) orbital to lie at lower energies than the dxy and dx~-y~ orbitals. For IV(b) materials, the eg orbitals are filled, the higher-lying t2g orbitals are empty and the materials are semiconductors. The d~z, dyz and dz~ orbitals are filled for VI(b) materials, and in the absence of overlap between d~ and dxy, dx~-y~ levels, semiconducting properties would also be expected. As indicated in Fig. 2(b), V(b) materials would be metallic in either case. Preliminary tight binding band structure calculations supported this picture [6]. More important, "first principles" band structure calculations also verify these simple ideas and extend them by providing detailed information about the electron wave functions and densities of electronic states. For example, the "dz~" orbital in MoS 2 is, indeed, found to be narrow (~1 eV wide) and "split off" from the "dxy", d~-v~" orbitals by 1.2 eV [7]. Photoemission [8 - 10] and soft X-ray [11] observations confirm the relative band position and state densities of the band structure calculations. Recent de Haas-van Alphen measurements support the details of the band structure in 2H-TaSe2 [12]. Changes in electronic properties with applied pressure are also consistent with the band picture [13, 14]. However, such band structure calculations are limited in their ability to probe fine details of specific materials, as illustrated by the case of TiS2. While a standard (in this case KKR-"muffin tin" potential) calculation of TiS2 reproduces the general features reasonably well, calculations of the relative positions of the conduction and valence bands

283 predicted a gap of ~1.5 eV and semiconducting properties [15], while experiments indicated semimetallic behavior [ 1 ]. The disagreement between theory and experiment has been ascribed to materials problems, since metal-rich TiS2 compositions are easily formed and since a common defect in TiS2 involves a displacement of a Ti atom from the metal layer of the basic structural unit into the van der Waals gap [16]. Both effects could produce defect conductivity in what would otherwise be a semiconductor. Thus, establishing the intrinsic properties of TiS2 is both a synthetic and a theoretical challenge: to produce and characterize stoichiometric defect-free TiS2, and to determine the relative positions of the valence and conduction bands with high precision. Thompson et al. [17 ] show that the composition TiS2 is the limit of the Ti-S phase diagram in this region and that compositions within +0.05% of that value are obtained by low temperature (~600 °C) synthesis techniques. Precision Xray and Seebeck coefficient data place deviations from stoichiometry at less than 0.1%, and intercalation studies place the maximum number of defect Ti atoms in the van der Waals gap at a similar value. These defect-free, stoichiometric materials are still semimetallic: improving crystal perfection or purity increases the resistance ratio, R (300 K)/R (4.2 K) and the Hall constant is nearly temperature independent from 1.7 - 300 K. Further, the magnitudes of the magnetic, transport and optical properties would require deviations from stoichiometry of ~1 - 2% if TiS2 were a semiconductor -- an order of magnitude larger than encountered in these materials. The original band structure calculations predict a direct gap of 2.0 eV and an indirect gap of 1.4 eV [15]. Attempts to vary the calculation parameters to minimize the gap suggest a lower bound of ~1 eV. Such calculations are non-relativistic and computational considerations preclude obtaining a self-consistent solution. These limitations are important since self-consistent calculations using the X~ technique indicate a marked reduction in gap size [18]. A newly developed computation scheme employing self-consistent basis set LCAO's also indicates significant reductions: a direct gap of 0.8 eV and an indirect gap of 0.2 - 0.3 eV are found [19]. This latter gap is so small that small changes (possi-

bly relativistic effects) could result in the band overlap required to explain the observed semi-metallic properties. Conversely, this small gap could be destroyed by structural effects which produce band tailing and semimetallic behavior. Thus, theory and experiment appear to be converging even in this delicate case. (b) Charge density waves Many layered dichalcogenides exhibit sharp variations in their electronic [20] and magnetic [21] properties with changing temperature. Recent electron diffraction studies show that these changes are accompanied by displacements of atoms from their high temperature position in the unit cell [22]. These coupled electronic and structural changes have become known as Charge Density Waves (CDW) [23]. At high temperatures the diffraction pattern typical of the ideal solid is observed, while additional diffraction spots appear as the temperature is lowered, suggesting superlattice formation. In many cases the initial atomic displacements are incommensurate with the underlying lattice structure. At still lower temperatures a superlattice commensurate with the high temperature unit cell is usually formed. Although it has long been thought that such lattice distortions could be driven electronically, attempts to observe such distortions in alkali metals were unsuccessful [24]. However, the Fermi surface topology in these two dimensional materials is especially favorable for inducing such distortions, and three pieces of experimental evidence suggest that electronic effects are involved. First, these lattice distortions are associated exclusively with the metallic dichalcogenides. Second, the incommensurate lattice vectors are simply related to Fermi surface topology [22]. Finally, the dimensions of the superlattice can be varied by alloying [25] in ways anticipated from the known shape of the Fermi surface. These distortions produce gaps in the Fermi surface, modifying the character and number of Fermi surface electrons. The CDW phenomenon has been probed microscopically by NMR. The Knight shift and quadrupole coupling of 51V nuclei in VSe2 begin to change with the onset of an incommensurate CDW (for T ~ 120 K), and a change in the 51V hyperfine field occurs at

284 the commensurate transition (T ~ 70 K) [26]. In NbSe 2 the incommensurate CDW occurring at 33.5 K produces no deviation from the normal NMR spin-lattice relaxation (T1) behavior, but the lineshape is modified [27]. In TiSe2, NMR studies of the 77Se anions show a change in lineshape and a dramatic increase in Tz below the 202 K transition to the commensurate state, but no change in the 77Se hyperfine field [28]. This suggests that the CDW destroys residual Fermi surface selectron character, but does not affect the electrons' contribution to the 77Se hyperfine field. MSssbauer studies of Fe substituted 1TTaSe 2 reveal three electronically inequivalent metal sites below 473 K, and differences in isomer shifts suggest CDW wave amplitudes of an appreciable fraction of an electron per atom [29]. ESCA measurements in 1T-TaS2 also reflect a difference in local electron density of as much as one electron between inequivalent Ta sites [30]. The symmetry and onset of charge density wave states in •2H-NbSe2 and 2H-TaSe 2 have been examined by tracing the development of the superlattice peaks using neutron diffraction and optical techniques [ 31]. Initial attempts to describe the CDW mechanism [22] suggested electronically driven instabilities caused by large nesting regions of the Fermi surface and leading to a divergence of the electronic susceptibility •(q) [24]. Other Fermi surface features, notably saddle points, can produce similar instabilities [32]. Attempts to evaluate ×(q) directly from the calculated band structure have met with qualitative success [33]. Applying the Landau theory to these transitions predicts the two transition, normal, uncommensurate, commensurate behavior often observed [34]. The relationship of CDW's to Mott metal-insulator transitions has also been explored [35]. This theory can presently explain the driving mechanism for CDW's, the qualitative changes in physical properties, and the relation to the band structure. However, the present theories are not quantitative and cannot predict onset temperatures or detailed temperature dependences. This situation will almost certainly be clarified as more of the CDW materials are examine~ n detail. One valuable clue is the observed correlation between structure,

ionicity, and electronic properties which has recently been discovered [36].

3. INTERCALATES

(a) Introduction The variety of the dichalcogenides is compounded by the existence of their many atomic and molecular intercalation compounds [3]. Lewis base molecules, especially aliphatic and aromatic amines, are facile intercalators [37]. Organometallic complexes like metallocenes (e.g., cobaltocene, Co(~C5H5)2) intercalate most of the Group IV(b) and V(b) disulfides and diselenides [38] and more elaborate bisbenzene and bisaryl species have been intercalated in ZrS2 [39]. All alkali metals form such intercalation compounds [40]. Transition- [41] and post transition metals [42] have also been routinely included. In many instances, the detailed solid state chemistry of these intercalates is not completely determined, but enough is known from systematic observations to identify general trends. Further, specific systems have been examined in considerable detail and the resulting observations are the basis for the first quantitative analysis of the intrinsic properties of intercalates. Synthesis, chemical, and structural analyses provide information about the composition of the intercalates. For molecules the intercalation reaction usually proceeds to completion, the van der Waals gap region being filled to the closepacking limit with guests. Partial loading often leads to the staging phenomenon common to graphite materials [37]. By contrast, broad ranges of composition are observed for alkali metal intercalates, especially for the lighter Li and Na species [40]. For transition and especially post-transition species, discrete fractional layer loadings often occur [41, 42]. The chemistry and energetics of intercalation in the dichalcogenides are becoming better understood. By contrast to the amphoteric character of the graphite hosts, the layered dichalcogenides function as acceptors, and intercalation involves charge donation to the host layers. While the charge transfer question may be delicate for Lewis base molecules [43], inclusion of alkali metal atoms [44, 45]

285 TABLE 1 Structure and NMR parameters of lithiated dichalcogenides* Host

TiS2 TiSe2 ZrS2 ZrSe2 HfS2 HfSe2 VSe 2

2H-NbSe2 2H-TaS2 1T-TaS2 2H-TaSe 2

Metal site symmetry

Lattice constants c axis

a axis

(h)

(h)

1 × 6.195 1 × 6.480 3 × 6.25 1 × 6.648 3 × 6.375 1 × 6.642 1 × 6.356 2 × 6.772 2 × 6.475

3.455 3.644 3.604 3.734 3.56 3.715 3.584 3.496 3.340

O

--

--

TP

? x 6.817

3.477

O O O O O O O TP TP

-

~c (A)

Li chemical shift (ppm)

Li quadrupole coupling (kHz)

0.50 0.48 0.42 0.49 0.52 0.48 0.26 0.50 0.44

+12 +10 +15 +13 +11 +17 --27 +30 +20 +20 +11

29.0 33.6 29 24.1 32.8 37.0 31.6 39.0 47.7 39.9 26.8

-

0.47

*From refs. 44 and 48.

and metallocenes [38] involves the transfer of nearly one electron per guest, and inclusion of other guest atoms also involves extensive electron donation, i.e., four electrons per atom for small amounts of Ti between the layers in metal-rich TiS2 [20]. The net energy of intercalation can be determined, being, e.g., ~10 kcal/mole for the TaS2(NH3) intercalation complex [46], and ~50 kcal/ mole for LiTiS2 [47]. However, explicit calculation of such energies involves making simple approximations of a number of imponderables such as energy gained in charge transfer, energy lost in opening up the van der Waals gap region and guest-guest interaction effects. It is striking that the distinction between host and guest remains well preserved. While this might be obvious for the molecular intercalates, it also holds true in alkali metal intercalation compounds where guest-host interactions are found to be extremely weak. Even in cases like the non-stoichiometric vanadium sulfides, guest atoms retain their unique electronic character.

(b) Detailed studies o f intercalation compounds The close relationship between synthesis, structural determination and analysis of physical properties is best demonstrated by example. We first consider lithium intercala-

tion compounds. Synthesizing these materials via reaction with n-butyl lithium [49] produces a homogeneous series of high quality materials which were examined by X-ray and NMR techniques. These studies, summarized in Table 1, provide the following picture. (1) Upon exposure to n-butyl lithium, all disulfides and diselenides of Groups IV(b) and V(b) form intercalation compounds. By contrast, Group VI(b) materials form decomposition products (involving Li2S or Li2Se) as anticipated from t h e r m o d y n a m i c considerations [ 50]. (2) In the presence of excess n-butyl lithium, the composition of the final product (with the exception of VSe2 [49, 51] ) is LiTX2, i.e., one lithium atom per formula unit of the dichalcogenides. This corresponds to complete filling of the octahedral holes in the van der Waals gap between the TX2 layers. (3) X-ray analysis indicates an interlayer (c axis) expansion of ~0.5 • to accommodate the guests, while intralayer (a axis) expansion is generally an order of magnitude smaller [44]. (4) The c axis dilation [44], thermodynamic properties [47], and 71Li NMR shifts [48] suggest nearly complete Li 2s electron donation to the host layers. (5) The 77Se NMR in diselenides reflects changes in the electronic character

286 6.2

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./

•

•

•

•

•

•

FULL LAYER

O

PARTIALLY FILLED LAYER

•

FULLLAYER

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2.4

o~

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O

O

SULFUR

•

•

VANADIUM

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•

•

•

•

•

R

< -J 5.9

2,1 Q

5.8

•

2.2

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2.0

\

Fig. 4. The alternation of filled and depleted vanadium atom layers in non~toichiometric vanadium sulfides reflects the intercalation pattern.

1.9

5.7

I 0.5

1.8 1.0

Li CONCENTRATION (x)

a

20

./

//

4

/// 0 0,0

I 0.5

1.0

Li CONCENTRATtON (x)

Fig. 3. (a) Variation o f crystal structure and thermodynamic properties for partially intercalated LixTiS 2. (b) Intercalation also enhances electrostatic inhomogeneities in the LixTiS 2 system.

of the hosts associated with charge donation [48]. (6) The 7Li NMR quadrupole coupling constants show similar electrostatic environments in the van der Waals gap region of the different dichalcogenides [48]. (7) NMR T1 measurements reveal weak coupling between the guest atoms and the adjacent host layers. Finally, both electrochemical [50] and NMR [48] measurements reveal a high degree of Li ion mobility in these intercalates, particularly for TiS2, TiSe2 and VSe2 hosts. The combination of high mobility and variable composition makes these materials ideal candidates for battery cathode applications [52].

To understand the details of this intercalation process, a series of partially intercalated materials has been synthesized and examined for the system LixTiS2 [45], and the results are shown in Fig. 3(a) and (b). The c axis lattice constant increases rapidly with the initial lithium inclusion reaching the limiting dilation of ~0.5 A for full Li loading. A monotonic decrease in the free energy is observed and, coupled with an increase in the Knight shift, suggests that the charge donation process is less effective as more Li atoms are included between the layers. The electrostatic field gradient also grows with the inclusion of more Li atoms, presumably as a result of polarization of the host and guestguest interactions. These systematic observations provide the basis for present attempts to obtain a quantitative understanding of the intercalation process. These considerations can be extended to the study of systems in which the relationship to intercalation is not immediately obvious -- one example being the nonstoichiometric vanadium sulfides. In the vanadium-sulfur system a broad range of compounds of nearly continuous composition is formed, with sulfur to vanadium ratios varying from 1.0 (VS) to approximately 1.7 (~VsSs) [53]. They possess closely related crystal structures consisting of alternating layers of vanadium and sulfur atoms. Throughout the composition range every second vanadium layer remains completely filled, while the alternating layers are depleted (Fig. 4). In terms of the intercalation picture they might be more properly regarded as V1÷~$2 -= (VS2):V8 where the fraction of atoms in the depleted layer could be viewed as intercalated guests. For certain filling levels the atoms in the depleted layer form

287

well defined superlattices, e.g., for V5Ss (5 = 1/4), the vanadium atoms arrange themselves so that they have no nearest neighbors in the depleted layer [54]. The strong magnetic response for V5Ss suggests that these vanadium atoms retain localized d electrons in spite of the fact that they lie within ~2.9 A of vanadium atoms, with delocalized electrons in the filled layer [55] ! Detailed microscopic studies of the vanadium NMR support the picture presented by the magnetic measurements [56], and a similar situation is found to obtain for the vanadium selenides [57]. Delocalization of these electrons occurs with the inclusion of more atoms between the layers, and the systematics of this loss of magnetic response provides information about the delocalization mechanism [58]. Detailed studies of the phase diagram are currently underway [59].

4. CONCLUSION

The present selection of topics has been chosen to illustrate the great richness and extent of the layered dichalcogenides and their intercalation compounds. Present work reveals the great novelty of these materials associated with their lamellar structure, great variation of electronic properties, and varied relationships between guests and hosts. These materials have proven to be of great technical interest in areas as diverse as advanced battery systems [52] and catalysis, where cobalt molybdenum sulfides are the active materials in conventional catalysts used in hydrogen treating of oil. An adequate treatment of these systems requires a high level of sophistication and a mixture of solid state chemistry and physics, proceeding from synthesis, to a characterization of structural and macroscopic properties, to an understanding of the microscopic properties of a material and, ultimately to a quantitative theoretical understanding. It is useful to survey the four topics discussed here in terms of these four areas. Within the limits of modern band structure theory, the electronic properties of the dichalcogenides are understood and explain most experimental observations. Cooperative phenomena, like charge density waves are qualitatively understood, though many of the details will require further experimental and

theoretical effort. The basic features of intercalation are coming to be understood although in many areas the process of synthesis and analysis are just beginning and the potential for novel discoveries of great scientific and technical importance are high. Finally, for a few selected intercalates, a critical mass of experimental data is being accumulated which should permit the first semi-quantitative attempts at theoretical interpretation. There is much room for further effort in the future.

ACKNOWLEDGEMENTS

I particularly wish to thank F. R. Gamble, H. M. McConnell, J. R. Schrieffer, A. H. Thompson and M. S. Whittingham, whose fruitful discussion and collaboration have taught me much about these intriguing systems. We also thank A. J. Freeman, K. H. Johnson, W. W. Warren and A. Zunger for the communication of their results prior to publication.

REFERENCES 1 J. A. Wilson and A. D. Yoffe, Adv. Phys., 18 (1969) 193. 2 A. D. Yoffe, FestkSrperphysik, XIII (1973) 1. 3 For a recent review, see F. R. Gamble and T. H. Geballe, Treatise on Solid State Chemistry, Vol. 3, Plenum Press, New York, 1976, p. 89. 4 R. Huisman, R. de Jonge, C. Haas and F. JeUinek, J. Solid State Chem., 3 (1971) 56. 5 F. R. Gamble, J. Solid State Chem., 9 (1974) 358. 6 R. A. Bromley and R. B. Murray, J. Phys. C., 5 (1972) 738; R. B. Murray, R. A. Bromley and A. D. Yoffe, J. Phys. C., 5 (1972) 746, 759. 7 L. F. Mattheiss, Phys. Rev. B, 8 (1973) 3719. 8 J. C. McMenamin and W. E. Spicer, Phys. Rev. Lett., 29 (1972) 1501. 9 F. R. Shepherd and P. M. Williams, J. Phys. C., 7 (1974) 4416, 4427. 10 N. V. Smith, M. M. Traum and F. J. Di Salvo, Solid State Commun., 15 (1974) 211; R. Z. Bachrach, M. Skibkowski and F. C. Brown, Phy~ Rev. Lett., 37 (1976) 40. 11 D. W. Fischer, Phys. Rev. B, 8 (1973) 3576; B. Sonntag and F. C. Brown, Phys. Rev. B, 10 (1974) 2300. 12 J. E. Graebner, Solid State Commun., 21 (1977) 353. 13 C. W. Chu, V. Diatschenko, C. Y. Huang and F. J. Di Salvo, Phys. Rev. B, 15 (1977) 1340.

288 14 P. Molinie, D. Jerome and A. J. Grant, Philos. Mag., 30 (1974) 1091. 15 H. W. Myron and A. J. Freeman, Phys. Rev. B, 9 (1974) 481. 16 S. Takenchi and H. Katsuda, J. Jpn. Inst. Met., 34 (1970) 758. 17 A. H. Thompson, F. R. Gamble and C. R. Symon, Mater. Res. Bull., 10 (1975) 915. 18 D. Vvedensky, K. H. Johnson, V. W. Day and A. H. Thompson, Bull. Am. Phys. Soc., 21 (1976) 263. 19 A. Zunger and A. J. Freeman, Phys. Rev. B, 16 (1977) 906. 20 A. H. Thompson, F. R. Gamble and J. F. Revelli, Solid State Commun., 9 (1971) 981. 21 F . J . Di Salvo, B. J. Bagley, J. M. Voorhorve and J. V. Waszczak, J. Phys. Chem. Solids, 34 (1973) 1357. 22 J. A. Wilson, F. J. Di Salvo and S. Mahajan, Phys. Rev. Lett., 32 (1974) 882; P. M. Williams, G. S. Parry and C. B. Scruby, Philos. Mag., 29 (1974) 695. 23 For a recent review, see J. A. Wilson, F. J. Di Salvo and S. Mahajan, Adv. Phys., 24 (1975) 117. 24 A. W. Overhauser, Phys. Rev., 167 (1968) 691. 25 F. J. Di Salvo, J. A. Wilson, B. J. Bagley and J. V. Waszczak, Phys. Rev. B, 12 (1975) 2220. 26 A. H. Thompson and B. G. Silbernagel, Bull. Am. Phys. Soc., 21 (1976) 260. 27 C. Berthier, D. Jerome, P. Molinie and J. Rouxel, Solid State Commun., 19 (1976) 131. 28 R. Dupree, W. W. Warren and F. J. Di Salvo, Phys. Rev. B, 16 (1977) 1001. 29 M. Eibschiitz and F. J. Di Salvo, Phys. Rev. B, 15 (1977) 5181. 30 G. K. Wertheim, F. J. Di Salvo and S. Chiang, Phys. Lett. A, 54 (1975) 304. 31 D. E. Moncton, J. D. Axe and F. J. Di Salvo, Phys. Rev. Lett., 34 (1975) 734; J. A. Holy, M. V. Klein, W. L. McMillan and S. F. Meyer, Phys. Rev. Lett., 37 (1976) 1145. 32 T . M . Rice and G. K. Scott, Phys. Rev. Lett., 35 (1975) 120. 33 H. S. Myron and A. J. Freeman, Phys. Rev. B, 15 (1977) 885. 34 W. L. McMillan. Phys. Rev. B, 14 (1976) 1496. 35 P. Fazekas and E. Tosatti, Proc. Int. Conf. Semiconductors, Bari, Italy, 1976.

36 A. H. Thompson, Phys. Rev. Lett., 34 (1975) 520. 37 F. R. Gamble, J. H. Osiecki, M. Cais, R. Pisharody, F. J. Di Salvo and T. H. Geballe, Science, 174 (1971) 493. 38 M. B. Dines, Science, 188 (1975) 1210. 39 W. B. Davies, M. L. H. Green and A. J. Jacobson, J. Chem. Soc., Chem. Commun., (1976) 781. 40 See, e.g., J. Bichon, M. Danot and J. Rouxel, C.R. Acad. Sci., Ser. C, 273 (1973) 1283. 41 See e.g., M. Danot, J. Bichon and J. Rouxel, Bull. Soc. Chim. Fr., 8 (1972) 3063. 42 F . J . Di Salvo, in K. D. Timmerhaus, W. J. O'Sullivan and E. F. Hammel (eds.), Low Temperature Physics -- LT 13, Vol. 3, Plenum Press, New York, 1974, p. 417. 43 F. R. Gamble and B. G. Silbernagel, J. Chem. Phys., 63 (1975) 2544. 44 M. S. Whittingham and F. R. Gamble, Mater. Res. Bull., 10 (1975) 363. 45 B. G. Silbernagel and M. S. Whittingham, J. Chem. Phys., 64 (1976) 3670. 46 M. B. Dines and R. B. Levy, J. Phys. Chem., 79 (1975) 1979. 47 M. S. Whittingham, J. Electrochem. Soc., 123 (1976) 315. 48 B. G. Silbernagel, Solid State Commun., 17 (1975) 361. 49 M. B. Dines, Mater. Res. Bull., 10 (1975) 287. 50 M. S. Whittingham, Electrochiml Acta, 20 (1975) 575. 51 D.W. Murphy, F. J. Di Salvo, G. W. Hall and J. V. Waszczak, Inorg. Chem., 15 (1976)17. 52 M. S. Whittingham, Science, 192 (1976) 1126. 53 A. B. de Vries and F. Jellinek, Rev. Chim. Miner., 11 (1974) 624. 54 S. Brunie and M. Chevreton, C.R. Acad. Sci., Set. C, 258 (1964) 5847. 55 A. B. de Vries and C. Haas, J. Phys. Chem. Solids, 34 (1973) 541. 56 B. G. Silbernagel, R. B. Levy and F. R. Gamble, Phys. Rev. B, 11 (1975) 4563. 57 B. G. Silbernagel, A. H. Thompson and F. R. Gamble, AIP Conf. Proc., 24 (1974) 380. 58 B. G. Silbernagel and A. H. Thompson, Physica, 88B (1977) 1003. 59 J. P. de Neufville, A. F. Ruppert and B. G. Silbernagel, Bull. Am. Phys. Soc., 22 (1977) 422.