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Physical properties of graphite lamellar compounds with alkali metals and halogens
225
Materials Science and Engineering, 31 (1977) 225 - 234 © 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
Physical Properties of Graphite Lamellar Compounds with Alkali Metals and Halogens
P. D E L H A E S
Centre de Recherches Paul Pascal, CNRS, Domaine Universitaire, Universitd de Bordeaux I, 33405 Talence C~dex (France)
SUMMARY
The binary and ternary lamellar compounds with alkali metals, which are electron donors, and with halogens, electron acceptors, are reviewed. The following physical properties of crystal compounds of graphite are analysed: (a) transport properties: increase of electrical conductivity and metallic behavior; (b) magnetism: the static measurements show a fundamental difference between the donor compounds which are paramagnetic, and the diamagnetic acceptor compounds. Electron spin resonance confirms the existence of Pauli paramagnetism in the donor lamellar compound group; (c) specific heat: these experiments are compared with magnetism results: (d) superconductivity: the occurrence at very low temperature of first stage alkaline compounds is discussed. The nature of bonding in these materials is discussed in relation to structure and thermochemistry. Following Hennig's work [ 1] these compounds must be considered as charge transfer complexes with a partial charge transfer: a critical analysis of this point will be presented.
(a) propri~t~s de transport: accroissement de la conductivit~ ~lectrique mettant en ~vidence un comportement m~tallique; (b) magn~tisme: les mesures en m~thode statique montrent une difference essentielle entre les compos~s avec les donneurs qui sont paramagn~tiques et les compos~s avec les accepteurs diamagn~tiques. Les ~tudes en r~sonance paramagn~tique ~lectronique confirment l'existence d'un paramagn~tisme de Pauli dans le premier groupe des compos~s lamellaires; {c) chaleur sp~cifique: les premieres mesures aux basses temperatures sont analys~es en liaison avec le magn~tisme present; (d) supraconductivit~: l'apparition d'un ~tat supraconducteur ~ tr~s basse temperature darts les compos~s du ler stade avec les alcalins est discut~e. L'analyse de ces r~sultats montre que ces compos~s sont des complexes de transfert de charge ~ taux de transfert partiel. Les travaux d'Hennig (Progress in Inorganic Chemistry, Vol. 1, {1959) p. 25) sont analys~s et completes. En liaison avec les considerations structurale et thermodynamique, ils conduisent ~ appr~cier le taux de transfert de charge dans les divers compos~s ~tudi~s.
1. I N T R O D U C T I O N RESUME
General background Les compos~s lamellaires, binaires et ternaires, avec les ~l~ments alcalins, donneurs d'~lectrons, et les halog~nes accepteurs d'~lectrons sont rappel~s. La stochiom~trie de ces compos~s est li~e ~ la d~finition du stade d'insertion dont la distance interplanaire est la caract~ristique structurale fondamentale. Les propri~t~s physiques suivantes de ces mat~riaux sont pass~es en revue:
A variety of atoms or molecules in the liquid or vapor state react with hexagonal graphite to form compounds in which the reactant enters between the carbon layers, while the graphitic character of the layer planes is preserved [1 - 6]. Graphite exhibits an amphoteric character which means that two kinds of compounds are formed: ones which transfer
226
electrons to graphite, and others which receive electrons from graphite. Among the substances which are donors or acceptors of electrons (respectively, n type and p type compounds) we shall be interested in alkali metals and halogens only. They constitute the best known family of lamellar compounds of graphite on which several investigations of physical properties have been carried out.
(a) Donor compounds with alkali metals M = Li(Na), K, Rb, Cs In principle a crystal compound can be formed if the ionization potential (ID) is smaller than the electron affinity (EA) o f graphite (see Table 1). At first sight Li and Na are not possible intercalating elements, however Li can be intercalated with a different stoichiometry. TABLE 1 Possible intercalating elements with graphite [ 7 ] Alkali metals
Ionization potential I D (eV)
Li Na K Rb Cs
5.39 5.14 4.34 4.18 3.89
Halogens
Electron affinity EA (eV)
F C1 Br I
3.58 3.75 3.55 3.29
Graphite
Ionization potential, I D = 4.39 eV LElectron affinity, EA = 4.39 eV
(b) Acceptor compounds with halogens and pseudo-halogens X2 = C12, Br2; BrF3, IF~. In principle, the electron affinity of halogens has to be larger than the ionization potential of graphite (Table 1). This is not true, except with iodine, the halogens form intercalation compounds with graphite. But, it must be pointed out that it is the molecular species which enter into graphite and it is this electron affinity which is important.
Stoichiometry and crystallographic structure The structure of these lamellar compounds is known [1 - 6] ; in a first approximation, the distance between the carbon layers which contain the reactant increases, but the interplanar carbon-carbon distances remain constant. Several stoichiometries are known which are defined by different stages. A stage is defined as the ratio of the number of layers of carbon to those of the other constituent. The usual terminology [6] is therefore: C~n- 1)aCaR, with n = c o m p o u n d stage, a = number of mole of carbon per mole o f reactant, R = reactant, M or X.
(a) Alkali metal compounds a =8 M K, Rb, Cs: the first stage compounds CsM were discovered some time ago. Higher stages have also been synthesized C24M(n =3), C36M(n = 4), C4~M(n = 5) [1 - 3]. Even ternary compounds with couples of these alkali metals have been prepared [19] *
t
a
lM
=6
Li: the first and second stage compounds have been characterized [ 1 1 ]. Similar lamellar compounds have been prepared with alkali-earth metals such as barium or calcium.
(b) Halogen compounds a = 16 X = C12, Br2 CleX2 or CsX: Electronic diffraction studies [13] show that the bromine forms a second stage compound. A similar behaviour must occur for the chloride compound which is quite unstable. Ternary compounds with iodine, bromine and chlorine have also been prepared [14]. In Part 2, we will present the electronic and thermal properties of these lamellar compounds which have been examined in order to compare the different results and their consistency. In Part 3, we shall analyze these data and compare them with the theoretical calculations. The main point that we shall develop is the problem o f the a m o u n t of
*First stage compounds with a different stoichiometry, C10M (M = Cs, Rh), have been reported [10] but they will not be considered here.
227
charge transfer between graphite and donors or acceptors. To conclude this Section, two remarks must be made: First, all these compounds are more or less unstable and reactive to air; therefore special care is necessary to examine their physical properties. Second, phase transitions in several higher stage compounds (C24M) have been discovered at low temperatures [15] ; they are not considered in this study.
2. PHYSICAL PROPERTIES OF LAMELLAR COMPOUNDS OF GRAPHITE
Electronic transport properties The lamellar compounds of graphite with alkali metals and with halogens exhibit metallic behaviour. They have been called synthetic metals by Ubbelohde [16] who, with his coworkers, was the first to study their electronic transport properties. We will examine, first, the electrical resistivity and, later, we will review the other transport properties.
(a) Electrical resistivity The electrical resistivity has been measured by d.c. and a.c. (at low frequency) methods on essentially artificial pyrolytic graphites which offer larger size samples than the natural single crystals. The quality of the parent crystal is, therefore, crucial. In Table 2, a summary of the electrical resistivity along the graphitic planes is presented: the first column gives the ratio, at 295 K, between the resistivity of the lamellar compound (p) and the parent graphite (P0). The two other columns indicate the thermal variation ratios at liquid nitrogen and liquid helium temperatures, respectively. The two kinds of lamellar compounds exhibit metallic characteristics; however, it appears that with acceptors the increase of conductivity at 78 K is larger than for donors. In addition, it is interesting to note that the resistivity decreases very quickly with the amount of halogen; for example, the residue compound C20oBr behaves as a metal already [19]. Along the C axis, for the few cases known, the behaviour is opposite; for donors, the resistivity ratio (p/p 0) decreases more than for
TABLE 2 Electrical resistivity of lamellar compounds along the graphitic planes Lamellar compounds
(~op,) T = 295 K
p77
p4.2
p295
p295
With donors CsK C24 K C36K
t [171 [18]
[17] I [17] CsRb [181 C24Rb [18] C36Rb I [17] CsCs [18] C24Cs C36Cs [18] C6Li [11]
0.25 0.23
0.10 0.10
0.135 0.26 0.22 0.16
0.13 0.12 0.26
0.24 0.22
0.13 0.13
0.17 0.17
0.16 0.25
0.01
0.13
With acceptors CsBr CsC1
[19] [20]
0.05 ~0.10
*The electrical resistivity of graphite in the graphitic planes is PO -~ 4.5 × 10-5 ~ cm at 295 K [17].
the acceptors, whereas the anisotropy remains higher than in graphite [19].
(b) Other transport properties These are essentially the thermoelectric, the Hall effect and the magnetoresistance. The first investigations [3, 17, 19] have been supported by the simple model of n or p type compounds. The alkali metal atoms inject electrons in the n conduction band, and the halogen molecules empty the ~ valence band of graphite. However more recent studies [18, 21, 22] have shown that two carrier behaviour occurs for stages 1 and 2 alkali metal compounds. This work is done in relation to theoretical band calculations for the first stage compounds.
Magnetism (a) Static measurements These are generally carried out with magnetic balances using the Gouy method for the older experiments [5], and the Faraday method for more recent determinations [14]. PolycrystaUine samples obtained from flakes of natural graphite in a glass vessel sealed under vacuum are usually used. Mainly due to
228 TABLE 3 Magnetic susceptibilities of lamellar compounds Lamellar compounds
× 106 (emu c.g.s./g) (at T -~ 295 K)
Xd X 106 (emu c.g.s./g)
Xc × 106 (emu c.g.s./g)
With acceptors CSK C24K C36K C48K CsRb C24Rb C36Rb C48Rb CsCs CsLi
f f
[23 ] [24 ] [14] [23] [23] [23 ] [23] [24] [14] [23] [23] [23] [ 14 ] [25]
+0.617 +1.04 +0.83 +0.718 +0.67 +0.39 +0.23 +0.36 +0.62 +0.34 +0.39 +0.49 +0.31 +0.67
[26] [27, 28] [14] [26] [14]
--0.30 -0.46 --0.63 --0.46 -0.66
--0.385 -0.39 -0.40 --0.40 --0.330
--0.338 --0.37
+1.002 +1.425 +1.215 +1.108 +1.07 +0.79 +0.56 +0.69 +0.95
+0.65 +1.04
With donors CsBr CsC1
f
--0.425 --0.444
the experimental conditions, the accuracy of the experiments is not very good and several discrepancies exist. The main results are quoted in Table 3, and several comments must be made. - - T h e measured physical quantity is the mean value of the total susceptibility given per gram of c o m p o u n d (see first column). It is well known that the large diamagnetic anisotropy of graphite disappears as soon as some atoms or molecules are intercalated [1, 5]. Comparison of these values shows that those of Furdin [14] are always larger than those o f Riidorff and Schulze [23] for donors and o f Juza et al. [26] for acceptors (in absolute value). It is n o t e w o r t h y that the stoichiometries given by the latter authors are not exactly the standard ones that we have defined in Part 1. The relation between departure from stoichiometry and magnetic susceptibility is not known. Besides, some first stage ternary compounds have been investigated (CsM~_xM x with M,M' = K, Cs, Rb) and they exhibit anomalies o f para-
-
+0.12 --0.04 --0.20 --0.01 --0.22
magnetism at a critical concentration, which are not completely explained [9]. -- The main result is that the lamellar compounds with alkali metals and with halogens are paramagnetic and diamagnetic, respectively. A few thermal variation studies have been made, down to liquid nitrogen temperature by Furdin [14], and one in liquid helium by Delhaes e t al. [25], but each time a temperature independent magnetism has been found. The experimental values are broken down into two terms: the ionic contribution due to the inner electrons, and the valence contribution which, in a metal, is subdivided into two terms: Pauli paramagnetism (×p) and Landau diamagnetism ()/L). Before looking for the latter terms, we have calculated the intrinsic diamagnetism related to the orbital motion of core electrons (see column 2 of Table 3). In order to make this calculation, using the usual additive law, we have chosen: -- for the halogens, the Pascal constants as quoted by Furdin [14] (for Br 2 the highest value given for the gaseous state has been selected);
229
method [ 33] ; it is, nevertheless, interesting to note that the ratio A/B is of the order of 2.7 - 4.5 in CaM compounds [ 3 1 ] , b u t is larger for the C6Li material where A/B 1 0 - 15 [25]. The g-factor and line-width anisotropies are very weak as compared with standard results for a single crystal of graphite; this behaviour is in agreement with the disappearance of diamagnetic anisotropy. Furthermore, the EPR confirms that the observed paramagnetism is related to conduction carriers, and a similarity with CESR in alkali metals is apparent [34]. On a qualitative basis, the gfactor anisotropy and the intrinsic line-width (the scattering by impurities is neglected) increases with the spin-orbit coupling. The spin-orbit coupling parameter is proportional to the atomic number [31]. Therefore, as in pure alkali metals, the small g-factor anisot r o p y and the line-width increase from Li to Cs. For the heaviest elements, the EPR lines of first stage lamellar compounds have n o t been detected. Using nuclear magnetic resonance, information about the electronic paramagnetism has been obtained [35, 36]. Carver [36] has investigated the C la and Cs la3 NMR is powdered samples of the cesium-graphite compounds of each stage (n = 1 - 5) between 1.3 and 4.2 K. In addition, a nuclear spin dynamic study of the CS133 Knight shift has been determined. The Knight shift is proportional to the square of the wave-function density at the nucleus and to the electronic suscepti-
for the alkali ions, values obtained by applying the formula of Stoner [29] ; for carbon the value Xd = --0.4 × 10 -6 emu c.g.s, because, it appears, from magnetic anisotropy measurements on bromine compounds [ 3 0 ] , that the residual anisotropy is always of order 0.3 × 10 -6 emu c.g.s./g with ×± = 0.3 X 10 -6 emu c.g.s./g. This choice assumes that the Landau diamagnetism of graphite is completely destroyed without any alteration of the bonds of carbon atoms. Finally, by adding the two first columns of Table 3 the second term ×c = ×p + ×L is evaluated. -
-
-
-
(b) Dynamic measurements: EPR and NMR The first c o m m e n t is to point o u t that, up to now, no EPR lines have been detected on halogen compounds. This observation confirms the presence of Pauli paramagnetism, as concluded from static measurements. Concerning the alkali metal compounds, initial experiments have been carried out by Muller and Kleiner [31] and extended by other authors. All the experiments on single crystals were carried out with spectrometers operating at 3.2 cm wavelength and are given in Table 4. For each c o m p o u n d a Dysonian line due to a skin effect is observed. The line shape is characterized b y the asymmetric parameter A/B as currently defined [33]. The linewidth and g values presented in Table 4 are corrected following the standard TABLE 4
Electron spin resonance results on donor lamellar compounds (11 and ± means that the C-axis is parallel and perpendicular to the static magnetic field) Donor lamellar compounds
295 K CsK at T
78 K
1.2K 295 K C24K at T 78K 295 K C24Rb at T 78 K 295 K C 6 Li at T 78K C8Rb, CsCs and C24Cs
g factor
Line width (gauss)
gH
g±
~/ll
[31] [321
2.002 3
2.003 7
[311
2.002 2
2.003 1
14.3 12.5 5.6 5.1 5.0 3.9 3.0 28.7 19.7
[321 [321
[311 [311 [25] [31]
2.002 4 2.003 2.002 1 2.003 2.005 2.006 2.003 1 2.004 2.002 1 2.003 2.002 1 2.003 no resonance line
2 1
0 0
~t
0.80 0.32
0.57 0.285
230
bility [34]. From the experiments, this author concluded that the cesium is partially ionized in CsCs and completely ionized in the cesium-poorer stages. The only previous investigation [35] is in disagreement with these results. We may see that it is not clear in these papers how the Pauli paramagnetism of such compounds has been accounted for (see Table 4).
Specific heat Among the thermal properties, only the specific heat has begun to be studied if we exclude thermal dilatation measurements around room temperature on CsM compounds [37]. Recent measurements of two series, with potassium and cesium as intercalated reagents, have been undertaken in the helium temperature range by Mizutami, Kondow and Massalski [38]. Following these authors we define a molar quantity, m, as: m-
xAc
+ AM
l+x
where Ac, AM are the atomic weights of carbon and alkali metal, and x is the number of carbons per atom of reactant. In Table 5, we have reported the electronic specific heat which we can compare with the observed paramagnetism, as we shall show in the final part of the paper. Two further comments can be made about these results: (i) The electronic heat coefficient increases similarly for the two series; in addition, a
Schottky-type anomaly which is not explained has been observed in all compounds with cesium. If we compare this coefficient with values known for alkali metals [39, 40], they are of about the same order, but much larger than in graphite [41]. (ii) The lattice specific heat coefficient allows us to calculate the Debye temperature. For each compound the Debye temperature is smaller than in graphite because of a stronger binding energy (see column 1, Table 5). When the alkali metal quantity decreases for the higher stage compounds the Debye temperature must increase and tend towards the graphite value; however this is true for the potassium series only [38].
Superconductivity Superconductivity has been discovered in first stage intercalation compounds of graphite with the alkali metals K, Rb, Cs by Hannay et al. [42]. Their results are reported in Table 6 where we see that the superconductivity onset and the critical magnetic field seem to depend on stoichiometry. However, this result has not been confirmed by Poitrenaud [32] who has studied by EPR and magnetic induction at low frequency the potassium lamellar compound. This negative result, however, might be due to the quality of the parent pyrographite. In order to have a better understanding of this phenomenon we may make two observations:
TABLE 5 Low temperature electronic specific heat coefficients. Comparison between calculated (Xp0) and measured (Xp(exp)) Pauli paramagnetism Lamellar compounds
C8K
•
C24K
C36K CsCs
[38]
C24Cs C36Cs C48Cs C6Li [25] Natural graphite [41]
Debye temperatures 190 (K)
Electronic specific heat coefficient 7(m) j/mole K 2)
~0
235
0.697
+9.3
373 385 341 284 300 319 590 413
0.241 0.189 0.63 0.25 0.19 0.16 0.43 0.014
+3.2 +2.5 +8.4
6 pem c.g.s./mole)
+5.9 +0.018
Xp(exp.) (X 10 ~'/.tern c.g.s./mole) 15.05 19.05 15.98 13.63 16.54
[23] [14] [23] [27] [24]
11.74 [15]
231 TABLE 6 S u p e r c o n d u c t i v i t y in d o n o r lamellar c o m p o u n d s of graphite Lamellar c o m p o u n d s
CsK CsK CsRb CsCs
stoichiometric K in excess
Second stage c o m p o u n d s
Tc (K)
Hc. II(gauss)
Hc2 J_(gauss)
( a t ' T = 0.32 K)
(at T = 0.32 K)
0.39 0.55 0.023 - 0.151 0.020 - 0.135
250 730
25 160
no superconductivity at T/> 0.011 K
T c is the critical t e m p e r a t u r e magnetic field at which shielding currents are observed (1 and II means, respectively, H perpendicular and parallel to the C-axis).
H% is the
(i) No superconductivity has been found in Li, Na, and K at temperatures down to 0.08 K [8]. (ii) In m o l y b d e n u m disulfide (MoS2), which is a transition metal dichalcogenide with a lamellar structure, the intercalation of the entire alkali metal group has been realized and superconductivity has been found [43]. A similarity of behaviour is difficult to demonstrate, b u t we may note that the critical temperature is constant for the alkali metals K, Rb, Cs in MoS2 with a large critical magnetic field. This is not in accord with the results obtained by Hannay et al. [42].
3. R E L A T I O N B E T W E E N P R O P E R T I E S AND CRYSTAL BINDING
Analysis o f the physical properties We shall discuss the donor lamellar compounds which are reasonably well known. From the transport and the optical properties [22] (not included in this work), it appears that the effective mass of free charge carriers is of the order of unity [46]. Recent investigations on first stage c o m p o u n d s show that two kinds of carriers exist, as announced from a preliminary theoretical band calculation on CsK [45], and therefore the effective mass calculations are not straightforward. We use this argument to assume that the Pauli paramagnetism must be larger than the Landau diamagnetism. Within this approximation we can compare the experimental values found after taking account of the intrinsic diamagnetism (see column 3, Table 3) and the calculated values from the elec-
tronic specific heat term (Table. 5). For the simplest model, a 3D free electronic gas, the following relations are well known: 2 7?
2
a = - - k N(EF) 3 Xpo = p2N(EF) where a is the electronic specific heat component, ×p0 the Pauli paramagnetism at zero Kelvin, N(EF) the density of states at Fermi level EF, and h and/~B Boltzmann constant and Bohr magneton, respectively. A comparison is given in Table 5 for a reduced mole as previously defined. A systematic discrepancy is found. In each case the experimental value is at least twice as large as the calculated one. More elaborate models can be involved to explain this difference: If the e l e c t r o n - p h o n o n interaction is predominant, as we can assume for CsM compounds which have been found to be superconductors, an enhancement of the electronic specific heat must occur while the paramagnetism stays at the classical value because the interaction is n o t spin dependent. Mizutami et al. [38] have given an evaluation of the e l e c t r o n - p h o n o n enhancement factor utilizing McMillan's formula ()~ -~ 1/3). But this correction will increase the observed difference. If magnetic effects exist with a paramagnon model, which anticipates the approach of an itinerant ferromagnetism, an exchange enhanced paramagnetism is found [46]. Such a model would support the experimental facts b u t is is without any physical meaning.
232 These results appear, therefore, not to be consistent, but before any further interpretation the experimental data must be confirmed. The chemical preparation and the experimental conditions for physical measurements are not easy; furthermore, several factors such as stoichiometry and homogeneity of the material might play a role. Actually, the analysis of magnetic properties shows that the electronic properties are similar to those observed on pure alkali metals. This fact is essential for analysing the nature of bonding and the dimensionality of the system. The first stage lamellar compounds, either CsM or C6M, do not seem to behave as 2D systems even for superconductivity [47, 48]. The observation of spin waves [34] could give further information on this similarity. Concerning the dimensionality of a material, the difference between magnetic, electronic and lattice properties must be noted; as observed in quasi-lD systems, a distinct behaviour can be detected. The electronic properties of these compounds appear to be definitely anisotropic (see the electrical conductivity) but essentially 3D, for example, charge density waves which are typical of low dimensional systems have not been detected. Actually, however, no conclusion can be proposed for the higher stage lamellar compounds where superstructures can exist [51].
Nature of bonding and amount of charge transfer The bonding in these compounds involves ionic, metallic and van der Waals forces. The cohesive energy is therefore difficult to evaluate; from the Debye temperature we conclude that it is larger than in graphite. The fundamental parameter is the a m o u n t of charge transfer (p) which has been evaluated by some authors from different physical properties:
1 CsX (X = ~ Br2)
p -~ 0 [1]
CsM (M = K, Rb, Cs)
p -~ 0.3 - 0.4 [1, 3]
C(,_l)sCs M
p
CsM (M = Li)
p -~ 0.1 [25]
~
1 [1, 10]
The structural investigations furnish other information for the donor compounds: (i} The c a r b o n - m e t a l - c a r b o n distance is independent of stage but characteristic of the ionic character of the reactant. Except for Li, using the ionic radii of alkali metals, and assuming that the van der Waals radii of the carbon layers is the same as in pure graphite, the calculated interlayer spacing is correct [49]. (ii) The expansion of the carbon-carbon bond length has been found to be proportional to the stage of intercalation [50] but with a different relationship for CsM and CsM compounds [52]. These results are consistent with the existence of a specific electron transfer for each series. As concluded by some authors, it appears difficult to attribute a full charge transfer for these compounds. In particular, the steric factors and the possible bonding between metals must be taken into account. The thermodynamic approach is the most rigorous. As proposed by Hennig [1] the free energy of formation, AF, for these compounds must be calculated:
AF=ID --EA +EM +Ed + U + ~12 Ad where I D is the ionization energy of the donor, Z A the electronic affinity of graphite, E M is the electrostatic or Madelung energy, Ed is the energy of delocalization, U is the van der Waals energy, and ~n Ad is the displacement of Fermi energy (correction on EA). A complete calculation is very difficult to carry out but several remarks may be made. The first three terms are predominant; therefore, in first approximation two cases exist: "IEMI ~> ]/'D - - E A I. A full charge transfer occurs, an ionic ground state is formed with a large enthalpy of formation. "IEMI < lid - - E A I . There is no charge transfer and we have a neutral ground state with a low enthalpy of formation. It is necessary to calculate the Madelung energy [7] ; Hennig has proposed a model [53], but the evaluation is difficult because of the choice of an effective dielectric constant and the unknown distribution of the positive charge on carbon layers (supposed
233
uniform in the absence of charge density waves). In the general case, an intermediate situation with a partial charge transfer (0 < p < 1) might be found. It would be necessary to calculate E M ( P ) and to find the free energy minimum as a function of p. One other point concerns the mechanism and the kinetics of insertion. It seems to us that the overall reaction can be broken down in two steps: (i) Insertion of ionized species, which are M ÷ or X2, if the initial electrostatic conditions are fulfilled (see Table 1: ID < EA). (ii) Formation of the reactant sheets, especially with alkali metals, with a back charge transfer. In other words, the amount of charge transfer, p, is decreasing with the concentration dependence until one of the given stoichiometries is obtained. In conclusion, the nature of the bonding is not well known b u t this analysis of physical properties observations suggests that the amount of charge transfer might always be quite small.
ACKNOWLEDGEMENTS
The author thanks Dr. J. Woollam for his critical reading of the manuscript.
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11 D. Oudrard and A. H6rold, Carbon, 13 (4) (1976) 337; D. Gu6rard, Ph.D. Thesis, Univ. Nancy, 1974. 12 D. Gudrard and A. Hdrold, C.R. Acad. Sci., Ser. C, 279 (1974) 455; Ser. C, 280 (1975) 279. 13 W. T. Eeles and J. A. Turnbull, Nature (London), 198 (4889) (1963) 877. 14 G. Furdin, Ph. D. Thesis, Univ. Nancy, 1974. 15 G. S. Parry and D. E. Nixon, Nature (London), 216 (1967) 909; J. Phys. D, 1 (1968) 291. 16 A. R. Ubbelohde, Carbon, 14 (1976) 1. 17 J. J. Murray and A. R. Ubbelohde, Proe. R. Soc. London, Ser. A, 312 (1969) 371. 18 D. Gu~rard, G. M. T. Foley, M. Zanini and J. E. Fischer, Nuovo Cimento, 38B (1977) 410. 19 L. C. F. Blackman, J. F. Matthews and A. R. Ubbe|ohde, Proe. R. Soc. London, Ser. A, 258 (1960) 339. 20 G. R. Hennig, J. Chem. Phys., 20 (1952) 1443. 21 J. E. Fischer, J. G. Onn and G. M. T. Foley, Bull. Am. Phys. Soc., March, 1977, communication GB 6, p. 421. 22 J. E. Fischer, Mater. Sci. Eng., 31 (1977) 211. 23 W. Riidorff and E. Schulze, Z. Anorg. Allg. Chem., 277 (1954) 156. 24 W. Sprissler, Ph. D. Thesis, Univ. Tiibingen, 1960. 25 P. Delhaes, J. C. Rouillon, J. P. Manceau, D. Gudrard and A. Hdrold, J. Phys. (Paris), Lett., 37 L (1976) 127. 26 R. Juza, H. Liibbe and L. Heinlein, Z. Anorg. Allg. Chem., 258 (1949) 105; R. Juza, P. S. Schmidt, A. Schmeckenbecker and P. Jonk, Naturwissenschaften, 42 (1955) 124. 27 F. R. M. McDonnell, R. C. Pink and A. R. Ubbelohde, J. Chem. Soc., (1951) 191. 28 M. Goldsmith, J. Chem. Phys., 18 (1950) 523. 29 C. M. Hurd and P. Coodin, J. Phys. Chem. Solids, 28 (1967) 523. 30 A. Marchand and J. C. Rouillon, personal communication. 31 K. A. Muller and R. Kleiner, Phys. Lett., 1 (3) (1962) 98. 32 J. Poitrenaud, Rev. Phys. Appl., 5 (1970) 275. 33 G. Feher and A. F. Kip, Phys. Rev., 98 (1955) 337. 34 J. Winter, Magnetic Resonance in Metals, Clarendon Press, Oxford, 1971. 35 V. Jensen, D. E. O'Reilly and T. Tsang, J. Chem. Phys., 47 (1967) 1195. 36 G. P. Carver, Phys. Rev. B, 2 (7) (1970) 2284. 37 D. Billaud and A. H6rold, Bull. Soc. Chim. Fr., II (1974) 2407. 38 U. Mizutami, T. Kondow and T. B. Massalski, to be published. 39 W. de Sorbo and G. E. Nichols, J. Phys. Chem. Solids, 6 {1958) 352. 40 J. D. Filby and D. L. Martin, Proc. R. Soc. London, Ser. A, 278 (1964) 83. 41 B. J. C. van der Hoeven, P. H. Keesom, J. W. McClure and G. Wagoner, Phys. Rev., 152 (2) (1966) 796. 42 N. B. Hannay, T. H. Geballe, B. T. Matthias, K. Endres, P. Schmidt and D. Macnair, Phys. Rev. Lett., 14 (7) (1965) 225. 43 J. A, Woollam and R. B. Somoano, Phys. Rev. B, 13 (9) (1976) 3843.
234 44 G. R. Hennig, J. Chem. Phys., 43 (4) (1965) 1201. 45 H. Kamimura, T. Inoshita and K. Nakao, Bull. Am. Phys. Soc., Communication GD4, March, 1977. 46 J. R. Schrieffer, J. Appi. Phys., 39 (1968) 642. 47 F.J. Salzano and M. Strongin, Phys. Rev., 153 (2) (1967) 533. 48 B. T. Matthias, Phys. Lett. A, 37 (3) (1971) 249. 49 R. Setton, Ph.D. Thesis, Orleans, 1971.
50 D. E. Nixon and G. S. Parry, J. Phys. C, 2 (2) (1969) 1732. 51 G. S. Parry, MSE 1363; G. Dresselhaus, M. S. Dresselhaus and D. D. L. Chung, MSE 1370. 52 D. Gu~rard, C. Zeller and A. H~rold, C.R. Acad. Sci., Set. C, 283 (1976) 437. 53 G. R. Hennig, Proc. 1st and 2nd Conf. Carbon, Buffalo, Pergamon, Oxford, 1956, p. 103.
Materials Science and Engineering, 31 (1977) 225 - 234 © 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
Physical Properties of Graphite Lamellar Compounds with Alkali Metals and Halogens
P. D E L H A E S
Centre de Recherches Paul Pascal, CNRS, Domaine Universitaire, Universitd de Bordeaux I, 33405 Talence C~dex (France)
SUMMARY
The binary and ternary lamellar compounds with alkali metals, which are electron donors, and with halogens, electron acceptors, are reviewed. The following physical properties of crystal compounds of graphite are analysed: (a) transport properties: increase of electrical conductivity and metallic behavior; (b) magnetism: the static measurements show a fundamental difference between the donor compounds which are paramagnetic, and the diamagnetic acceptor compounds. Electron spin resonance confirms the existence of Pauli paramagnetism in the donor lamellar compound group; (c) specific heat: these experiments are compared with magnetism results: (d) superconductivity: the occurrence at very low temperature of first stage alkaline compounds is discussed. The nature of bonding in these materials is discussed in relation to structure and thermochemistry. Following Hennig's work [ 1] these compounds must be considered as charge transfer complexes with a partial charge transfer: a critical analysis of this point will be presented.
(a) propri~t~s de transport: accroissement de la conductivit~ ~lectrique mettant en ~vidence un comportement m~tallique; (b) magn~tisme: les mesures en m~thode statique montrent une difference essentielle entre les compos~s avec les donneurs qui sont paramagn~tiques et les compos~s avec les accepteurs diamagn~tiques. Les ~tudes en r~sonance paramagn~tique ~lectronique confirment l'existence d'un paramagn~tisme de Pauli dans le premier groupe des compos~s lamellaires; {c) chaleur sp~cifique: les premieres mesures aux basses temperatures sont analys~es en liaison avec le magn~tisme present; (d) supraconductivit~: l'apparition d'un ~tat supraconducteur ~ tr~s basse temperature darts les compos~s du ler stade avec les alcalins est discut~e. L'analyse de ces r~sultats montre que ces compos~s sont des complexes de transfert de charge ~ taux de transfert partiel. Les travaux d'Hennig (Progress in Inorganic Chemistry, Vol. 1, {1959) p. 25) sont analys~s et completes. En liaison avec les considerations structurale et thermodynamique, ils conduisent ~ appr~cier le taux de transfert de charge dans les divers compos~s ~tudi~s.
1. I N T R O D U C T I O N RESUME
General background Les compos~s lamellaires, binaires et ternaires, avec les ~l~ments alcalins, donneurs d'~lectrons, et les halog~nes accepteurs d'~lectrons sont rappel~s. La stochiom~trie de ces compos~s est li~e ~ la d~finition du stade d'insertion dont la distance interplanaire est la caract~ristique structurale fondamentale. Les propri~t~s physiques suivantes de ces mat~riaux sont pass~es en revue:
A variety of atoms or molecules in the liquid or vapor state react with hexagonal graphite to form compounds in which the reactant enters between the carbon layers, while the graphitic character of the layer planes is preserved [1 - 6]. Graphite exhibits an amphoteric character which means that two kinds of compounds are formed: ones which transfer
226
electrons to graphite, and others which receive electrons from graphite. Among the substances which are donors or acceptors of electrons (respectively, n type and p type compounds) we shall be interested in alkali metals and halogens only. They constitute the best known family of lamellar compounds of graphite on which several investigations of physical properties have been carried out.
(a) Donor compounds with alkali metals M = Li(Na), K, Rb, Cs In principle a crystal compound can be formed if the ionization potential (ID) is smaller than the electron affinity (EA) o f graphite (see Table 1). At first sight Li and Na are not possible intercalating elements, however Li can be intercalated with a different stoichiometry. TABLE 1 Possible intercalating elements with graphite [ 7 ] Alkali metals
Ionization potential I D (eV)
Li Na K Rb Cs
5.39 5.14 4.34 4.18 3.89
Halogens
Electron affinity EA (eV)
F C1 Br I
3.58 3.75 3.55 3.29
Graphite
Ionization potential, I D = 4.39 eV LElectron affinity, EA = 4.39 eV
(b) Acceptor compounds with halogens and pseudo-halogens X2 = C12, Br2; BrF3, IF~. In principle, the electron affinity of halogens has to be larger than the ionization potential of graphite (Table 1). This is not true, except with iodine, the halogens form intercalation compounds with graphite. But, it must be pointed out that it is the molecular species which enter into graphite and it is this electron affinity which is important.
Stoichiometry and crystallographic structure The structure of these lamellar compounds is known [1 - 6] ; in a first approximation, the distance between the carbon layers which contain the reactant increases, but the interplanar carbon-carbon distances remain constant. Several stoichiometries are known which are defined by different stages. A stage is defined as the ratio of the number of layers of carbon to those of the other constituent. The usual terminology [6] is therefore: C~n- 1)aCaR, with n = c o m p o u n d stage, a = number of mole of carbon per mole o f reactant, R = reactant, M or X.
(a) Alkali metal compounds a =8 M K, Rb, Cs: the first stage compounds CsM were discovered some time ago. Higher stages have also been synthesized C24M(n =3), C36M(n = 4), C4~M(n = 5) [1 - 3]. Even ternary compounds with couples of these alkali metals have been prepared [19] *
t
a
lM
=6
Li: the first and second stage compounds have been characterized [ 1 1 ]. Similar lamellar compounds have been prepared with alkali-earth metals such as barium or calcium.
(b) Halogen compounds a = 16 X = C12, Br2 CleX2 or CsX: Electronic diffraction studies [13] show that the bromine forms a second stage compound. A similar behaviour must occur for the chloride compound which is quite unstable. Ternary compounds with iodine, bromine and chlorine have also been prepared [14]. In Part 2, we will present the electronic and thermal properties of these lamellar compounds which have been examined in order to compare the different results and their consistency. In Part 3, we shall analyze these data and compare them with the theoretical calculations. The main point that we shall develop is the problem o f the a m o u n t of
*First stage compounds with a different stoichiometry, C10M (M = Cs, Rh), have been reported [10] but they will not be considered here.
227
charge transfer between graphite and donors or acceptors. To conclude this Section, two remarks must be made: First, all these compounds are more or less unstable and reactive to air; therefore special care is necessary to examine their physical properties. Second, phase transitions in several higher stage compounds (C24M) have been discovered at low temperatures [15] ; they are not considered in this study.
2. PHYSICAL PROPERTIES OF LAMELLAR COMPOUNDS OF GRAPHITE
Electronic transport properties The lamellar compounds of graphite with alkali metals and with halogens exhibit metallic behaviour. They have been called synthetic metals by Ubbelohde [16] who, with his coworkers, was the first to study their electronic transport properties. We will examine, first, the electrical resistivity and, later, we will review the other transport properties.
(a) Electrical resistivity The electrical resistivity has been measured by d.c. and a.c. (at low frequency) methods on essentially artificial pyrolytic graphites which offer larger size samples than the natural single crystals. The quality of the parent crystal is, therefore, crucial. In Table 2, a summary of the electrical resistivity along the graphitic planes is presented: the first column gives the ratio, at 295 K, between the resistivity of the lamellar compound (p) and the parent graphite (P0). The two other columns indicate the thermal variation ratios at liquid nitrogen and liquid helium temperatures, respectively. The two kinds of lamellar compounds exhibit metallic characteristics; however, it appears that with acceptors the increase of conductivity at 78 K is larger than for donors. In addition, it is interesting to note that the resistivity decreases very quickly with the amount of halogen; for example, the residue compound C20oBr behaves as a metal already [19]. Along the C axis, for the few cases known, the behaviour is opposite; for donors, the resistivity ratio (p/p 0) decreases more than for
TABLE 2 Electrical resistivity of lamellar compounds along the graphitic planes Lamellar compounds
(~op,) T = 295 K
p77
p4.2
p295
p295
With donors CsK C24 K C36K
t [171 [18]
[17] I [17] CsRb [181 C24Rb [18] C36Rb I [17] CsCs [18] C24Cs C36Cs [18] C6Li [11]
0.25 0.23
0.10 0.10
0.135 0.26 0.22 0.16
0.13 0.12 0.26
0.24 0.22
0.13 0.13
0.17 0.17
0.16 0.25
0.01
0.13
With acceptors CsBr CsC1
[19] [20]
0.05 ~0.10
*The electrical resistivity of graphite in the graphitic planes is PO -~ 4.5 × 10-5 ~ cm at 295 K [17].
the acceptors, whereas the anisotropy remains higher than in graphite [19].
(b) Other transport properties These are essentially the thermoelectric, the Hall effect and the magnetoresistance. The first investigations [3, 17, 19] have been supported by the simple model of n or p type compounds. The alkali metal atoms inject electrons in the n conduction band, and the halogen molecules empty the ~ valence band of graphite. However more recent studies [18, 21, 22] have shown that two carrier behaviour occurs for stages 1 and 2 alkali metal compounds. This work is done in relation to theoretical band calculations for the first stage compounds.
Magnetism (a) Static measurements These are generally carried out with magnetic balances using the Gouy method for the older experiments [5], and the Faraday method for more recent determinations [14]. PolycrystaUine samples obtained from flakes of natural graphite in a glass vessel sealed under vacuum are usually used. Mainly due to
228 TABLE 3 Magnetic susceptibilities of lamellar compounds Lamellar compounds
× 106 (emu c.g.s./g) (at T -~ 295 K)
Xd X 106 (emu c.g.s./g)
Xc × 106 (emu c.g.s./g)
With acceptors CSK C24K C36K C48K CsRb C24Rb C36Rb C48Rb CsCs CsLi
f f
[23 ] [24 ] [14] [23] [23] [23 ] [23] [24] [14] [23] [23] [23] [ 14 ] [25]
+0.617 +1.04 +0.83 +0.718 +0.67 +0.39 +0.23 +0.36 +0.62 +0.34 +0.39 +0.49 +0.31 +0.67
[26] [27, 28] [14] [26] [14]
--0.30 -0.46 --0.63 --0.46 -0.66
--0.385 -0.39 -0.40 --0.40 --0.330
--0.338 --0.37
+1.002 +1.425 +1.215 +1.108 +1.07 +0.79 +0.56 +0.69 +0.95
+0.65 +1.04
With donors CsBr CsC1
f
--0.425 --0.444
the experimental conditions, the accuracy of the experiments is not very good and several discrepancies exist. The main results are quoted in Table 3, and several comments must be made. - - T h e measured physical quantity is the mean value of the total susceptibility given per gram of c o m p o u n d (see first column). It is well known that the large diamagnetic anisotropy of graphite disappears as soon as some atoms or molecules are intercalated [1, 5]. Comparison of these values shows that those of Furdin [14] are always larger than those o f Riidorff and Schulze [23] for donors and o f Juza et al. [26] for acceptors (in absolute value). It is n o t e w o r t h y that the stoichiometries given by the latter authors are not exactly the standard ones that we have defined in Part 1. The relation between departure from stoichiometry and magnetic susceptibility is not known. Besides, some first stage ternary compounds have been investigated (CsM~_xM x with M,M' = K, Cs, Rb) and they exhibit anomalies o f para-
-
+0.12 --0.04 --0.20 --0.01 --0.22
magnetism at a critical concentration, which are not completely explained [9]. -- The main result is that the lamellar compounds with alkali metals and with halogens are paramagnetic and diamagnetic, respectively. A few thermal variation studies have been made, down to liquid nitrogen temperature by Furdin [14], and one in liquid helium by Delhaes e t al. [25], but each time a temperature independent magnetism has been found. The experimental values are broken down into two terms: the ionic contribution due to the inner electrons, and the valence contribution which, in a metal, is subdivided into two terms: Pauli paramagnetism (×p) and Landau diamagnetism ()/L). Before looking for the latter terms, we have calculated the intrinsic diamagnetism related to the orbital motion of core electrons (see column 2 of Table 3). In order to make this calculation, using the usual additive law, we have chosen: -- for the halogens, the Pascal constants as quoted by Furdin [14] (for Br 2 the highest value given for the gaseous state has been selected);
229
method [ 33] ; it is, nevertheless, interesting to note that the ratio A/B is of the order of 2.7 - 4.5 in CaM compounds [ 3 1 ] , b u t is larger for the C6Li material where A/B 1 0 - 15 [25]. The g-factor and line-width anisotropies are very weak as compared with standard results for a single crystal of graphite; this behaviour is in agreement with the disappearance of diamagnetic anisotropy. Furthermore, the EPR confirms that the observed paramagnetism is related to conduction carriers, and a similarity with CESR in alkali metals is apparent [34]. On a qualitative basis, the gfactor anisotropy and the intrinsic line-width (the scattering by impurities is neglected) increases with the spin-orbit coupling. The spin-orbit coupling parameter is proportional to the atomic number [31]. Therefore, as in pure alkali metals, the small g-factor anisot r o p y and the line-width increase from Li to Cs. For the heaviest elements, the EPR lines of first stage lamellar compounds have n o t been detected. Using nuclear magnetic resonance, information about the electronic paramagnetism has been obtained [35, 36]. Carver [36] has investigated the C la and Cs la3 NMR is powdered samples of the cesium-graphite compounds of each stage (n = 1 - 5) between 1.3 and 4.2 K. In addition, a nuclear spin dynamic study of the CS133 Knight shift has been determined. The Knight shift is proportional to the square of the wave-function density at the nucleus and to the electronic suscepti-
for the alkali ions, values obtained by applying the formula of Stoner [29] ; for carbon the value Xd = --0.4 × 10 -6 emu c.g.s, because, it appears, from magnetic anisotropy measurements on bromine compounds [ 3 0 ] , that the residual anisotropy is always of order 0.3 × 10 -6 emu c.g.s./g with ×± = 0.3 X 10 -6 emu c.g.s./g. This choice assumes that the Landau diamagnetism of graphite is completely destroyed without any alteration of the bonds of carbon atoms. Finally, by adding the two first columns of Table 3 the second term ×c = ×p + ×L is evaluated. -
-
-
-
(b) Dynamic measurements: EPR and NMR The first c o m m e n t is to point o u t that, up to now, no EPR lines have been detected on halogen compounds. This observation confirms the presence of Pauli paramagnetism, as concluded from static measurements. Concerning the alkali metal compounds, initial experiments have been carried out by Muller and Kleiner [31] and extended by other authors. All the experiments on single crystals were carried out with spectrometers operating at 3.2 cm wavelength and are given in Table 4. For each c o m p o u n d a Dysonian line due to a skin effect is observed. The line shape is characterized b y the asymmetric parameter A/B as currently defined [33]. The linewidth and g values presented in Table 4 are corrected following the standard TABLE 4
Electron spin resonance results on donor lamellar compounds (11 and ± means that the C-axis is parallel and perpendicular to the static magnetic field) Donor lamellar compounds
295 K CsK at T
78 K
1.2K 295 K C24K at T 78K 295 K C24Rb at T 78 K 295 K C 6 Li at T 78K C8Rb, CsCs and C24Cs
g factor
Line width (gauss)
gH
g±
~/ll
[31] [321
2.002 3
2.003 7
[311
2.002 2
2.003 1
14.3 12.5 5.6 5.1 5.0 3.9 3.0 28.7 19.7
[321 [321
[311 [311 [25] [31]
2.002 4 2.003 2.002 1 2.003 2.005 2.006 2.003 1 2.004 2.002 1 2.003 2.002 1 2.003 no resonance line
2 1
0 0
~t
0.80 0.32
0.57 0.285
230
bility [34]. From the experiments, this author concluded that the cesium is partially ionized in CsCs and completely ionized in the cesium-poorer stages. The only previous investigation [35] is in disagreement with these results. We may see that it is not clear in these papers how the Pauli paramagnetism of such compounds has been accounted for (see Table 4).
Specific heat Among the thermal properties, only the specific heat has begun to be studied if we exclude thermal dilatation measurements around room temperature on CsM compounds [37]. Recent measurements of two series, with potassium and cesium as intercalated reagents, have been undertaken in the helium temperature range by Mizutami, Kondow and Massalski [38]. Following these authors we define a molar quantity, m, as: m-
xAc
+ AM
l+x
where Ac, AM are the atomic weights of carbon and alkali metal, and x is the number of carbons per atom of reactant. In Table 5, we have reported the electronic specific heat which we can compare with the observed paramagnetism, as we shall show in the final part of the paper. Two further comments can be made about these results: (i) The electronic heat coefficient increases similarly for the two series; in addition, a
Schottky-type anomaly which is not explained has been observed in all compounds with cesium. If we compare this coefficient with values known for alkali metals [39, 40], they are of about the same order, but much larger than in graphite [41]. (ii) The lattice specific heat coefficient allows us to calculate the Debye temperature. For each compound the Debye temperature is smaller than in graphite because of a stronger binding energy (see column 1, Table 5). When the alkali metal quantity decreases for the higher stage compounds the Debye temperature must increase and tend towards the graphite value; however this is true for the potassium series only [38].
Superconductivity Superconductivity has been discovered in first stage intercalation compounds of graphite with the alkali metals K, Rb, Cs by Hannay et al. [42]. Their results are reported in Table 6 where we see that the superconductivity onset and the critical magnetic field seem to depend on stoichiometry. However, this result has not been confirmed by Poitrenaud [32] who has studied by EPR and magnetic induction at low frequency the potassium lamellar compound. This negative result, however, might be due to the quality of the parent pyrographite. In order to have a better understanding of this phenomenon we may make two observations:
TABLE 5 Low temperature electronic specific heat coefficients. Comparison between calculated (Xp0) and measured (Xp(exp)) Pauli paramagnetism Lamellar compounds
C8K
•
C24K
C36K CsCs
[38]
C24Cs C36Cs C48Cs C6Li [25] Natural graphite [41]
Debye temperatures 190 (K)
Electronic specific heat coefficient 7(m) j/mole K 2)
~0
235
0.697
+9.3
373 385 341 284 300 319 590 413
0.241 0.189 0.63 0.25 0.19 0.16 0.43 0.014
+3.2 +2.5 +8.4
6 pem c.g.s./mole)
+5.9 +0.018
Xp(exp.) (X 10 ~'/.tern c.g.s./mole) 15.05 19.05 15.98 13.63 16.54
[23] [14] [23] [27] [24]
11.74 [15]
231 TABLE 6 S u p e r c o n d u c t i v i t y in d o n o r lamellar c o m p o u n d s of graphite Lamellar c o m p o u n d s
CsK CsK CsRb CsCs
stoichiometric K in excess
Second stage c o m p o u n d s
Tc (K)
Hc. II(gauss)
Hc2 J_(gauss)
( a t ' T = 0.32 K)
(at T = 0.32 K)
0.39 0.55 0.023 - 0.151 0.020 - 0.135
250 730
25 160
no superconductivity at T/> 0.011 K
T c is the critical t e m p e r a t u r e magnetic field at which shielding currents are observed (1 and II means, respectively, H perpendicular and parallel to the C-axis).
H% is the
(i) No superconductivity has been found in Li, Na, and K at temperatures down to 0.08 K [8]. (ii) In m o l y b d e n u m disulfide (MoS2), which is a transition metal dichalcogenide with a lamellar structure, the intercalation of the entire alkali metal group has been realized and superconductivity has been found [43]. A similarity of behaviour is difficult to demonstrate, b u t we may note that the critical temperature is constant for the alkali metals K, Rb, Cs in MoS2 with a large critical magnetic field. This is not in accord with the results obtained by Hannay et al. [42].
3. R E L A T I O N B E T W E E N P R O P E R T I E S AND CRYSTAL BINDING
Analysis o f the physical properties We shall discuss the donor lamellar compounds which are reasonably well known. From the transport and the optical properties [22] (not included in this work), it appears that the effective mass of free charge carriers is of the order of unity [46]. Recent investigations on first stage c o m p o u n d s show that two kinds of carriers exist, as announced from a preliminary theoretical band calculation on CsK [45], and therefore the effective mass calculations are not straightforward. We use this argument to assume that the Pauli paramagnetism must be larger than the Landau diamagnetism. Within this approximation we can compare the experimental values found after taking account of the intrinsic diamagnetism (see column 3, Table 3) and the calculated values from the elec-
tronic specific heat term (Table. 5). For the simplest model, a 3D free electronic gas, the following relations are well known: 2 7?
2
a = - - k N(EF) 3 Xpo = p2N(EF) where a is the electronic specific heat component, ×p0 the Pauli paramagnetism at zero Kelvin, N(EF) the density of states at Fermi level EF, and h and/~B Boltzmann constant and Bohr magneton, respectively. A comparison is given in Table 5 for a reduced mole as previously defined. A systematic discrepancy is found. In each case the experimental value is at least twice as large as the calculated one. More elaborate models can be involved to explain this difference: If the e l e c t r o n - p h o n o n interaction is predominant, as we can assume for CsM compounds which have been found to be superconductors, an enhancement of the electronic specific heat must occur while the paramagnetism stays at the classical value because the interaction is n o t spin dependent. Mizutami et al. [38] have given an evaluation of the e l e c t r o n - p h o n o n enhancement factor utilizing McMillan's formula ()~ -~ 1/3). But this correction will increase the observed difference. If magnetic effects exist with a paramagnon model, which anticipates the approach of an itinerant ferromagnetism, an exchange enhanced paramagnetism is found [46]. Such a model would support the experimental facts b u t is is without any physical meaning.
232 These results appear, therefore, not to be consistent, but before any further interpretation the experimental data must be confirmed. The chemical preparation and the experimental conditions for physical measurements are not easy; furthermore, several factors such as stoichiometry and homogeneity of the material might play a role. Actually, the analysis of magnetic properties shows that the electronic properties are similar to those observed on pure alkali metals. This fact is essential for analysing the nature of bonding and the dimensionality of the system. The first stage lamellar compounds, either CsM or C6M, do not seem to behave as 2D systems even for superconductivity [47, 48]. The observation of spin waves [34] could give further information on this similarity. Concerning the dimensionality of a material, the difference between magnetic, electronic and lattice properties must be noted; as observed in quasi-lD systems, a distinct behaviour can be detected. The electronic properties of these compounds appear to be definitely anisotropic (see the electrical conductivity) but essentially 3D, for example, charge density waves which are typical of low dimensional systems have not been detected. Actually, however, no conclusion can be proposed for the higher stage lamellar compounds where superstructures can exist [51].
Nature of bonding and amount of charge transfer The bonding in these compounds involves ionic, metallic and van der Waals forces. The cohesive energy is therefore difficult to evaluate; from the Debye temperature we conclude that it is larger than in graphite. The fundamental parameter is the a m o u n t of charge transfer (p) which has been evaluated by some authors from different physical properties:
1 CsX (X = ~ Br2)
p -~ 0 [1]
CsM (M = K, Rb, Cs)
p -~ 0.3 - 0.4 [1, 3]
C(,_l)sCs M
p
CsM (M = Li)
p -~ 0.1 [25]
~
1 [1, 10]
The structural investigations furnish other information for the donor compounds: (i} The c a r b o n - m e t a l - c a r b o n distance is independent of stage but characteristic of the ionic character of the reactant. Except for Li, using the ionic radii of alkali metals, and assuming that the van der Waals radii of the carbon layers is the same as in pure graphite, the calculated interlayer spacing is correct [49]. (ii) The expansion of the carbon-carbon bond length has been found to be proportional to the stage of intercalation [50] but with a different relationship for CsM and CsM compounds [52]. These results are consistent with the existence of a specific electron transfer for each series. As concluded by some authors, it appears difficult to attribute a full charge transfer for these compounds. In particular, the steric factors and the possible bonding between metals must be taken into account. The thermodynamic approach is the most rigorous. As proposed by Hennig [1] the free energy of formation, AF, for these compounds must be calculated:
AF=ID --EA +EM +Ed + U + ~12 Ad where I D is the ionization energy of the donor, Z A the electronic affinity of graphite, E M is the electrostatic or Madelung energy, Ed is the energy of delocalization, U is the van der Waals energy, and ~n Ad is the displacement of Fermi energy (correction on EA). A complete calculation is very difficult to carry out but several remarks may be made. The first three terms are predominant; therefore, in first approximation two cases exist: "IEMI ~> ]/'D - - E A I. A full charge transfer occurs, an ionic ground state is formed with a large enthalpy of formation. "IEMI < lid - - E A I . There is no charge transfer and we have a neutral ground state with a low enthalpy of formation. It is necessary to calculate the Madelung energy [7] ; Hennig has proposed a model [53], but the evaluation is difficult because of the choice of an effective dielectric constant and the unknown distribution of the positive charge on carbon layers (supposed
233
uniform in the absence of charge density waves). In the general case, an intermediate situation with a partial charge transfer (0 < p < 1) might be found. It would be necessary to calculate E M ( P ) and to find the free energy minimum as a function of p. One other point concerns the mechanism and the kinetics of insertion. It seems to us that the overall reaction can be broken down in two steps: (i) Insertion of ionized species, which are M ÷ or X2, if the initial electrostatic conditions are fulfilled (see Table 1: ID < EA). (ii) Formation of the reactant sheets, especially with alkali metals, with a back charge transfer. In other words, the amount of charge transfer, p, is decreasing with the concentration dependence until one of the given stoichiometries is obtained. In conclusion, the nature of the bonding is not well known b u t this analysis of physical properties observations suggests that the amount of charge transfer might always be quite small.
ACKNOWLEDGEMENTS
The author thanks Dr. J. Woollam for his critical reading of the manuscript.
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