NMR studies of lamellar intercalation compounds

107 NMR STUDIES OF L A M E L L A R I N T E R C A L A T I O N COMPOUNDS C. B E R T H I E R , Y. C H A B R E and P. S E G R A N S A N Laboratoire de Spectrom~trie Physique, associd au CNRS, USMG, BP 53X, 38041 Grenoble Cedex, France Invited paper W e present a review of recent N M R investigations of lamellar intercalation compounds. W e first give a general discussion of the various information that N M R can shed on these systems: the symmetry of the sites occupied by the intercalated species, their degree of ionization, the change in the electronic and magnetic properties of the host matrix, and the dynamics of the intercalated species. A s far as this last point is concerned, we underline the importance of the two-dimensional character of the atomic diffusion in the interpretation of N M R data. Experimental data in various lamellar intercalated c o m p o u n d s - transition metal dichalcogenides, transition metal p h o s p h o r u s trichalcogenides, and graphite - are first considered from the point of view of charge donation and change in the electronic properties of the host matrix. Finally, N M R studies of the dynamic of intercalated species are reviewed, in particular in the case of cathode materials.

1. Introduction Transition metal dichalcogenides (TX2) [1, 2] and graphite [3] are the most famous examples of lamellar compounds subject to intercalation; the first ones only accommodate electronic donors, like alkali metals or Lewis basis, and LixTiS2 is the prototype of cathode materials. On the other hand, graphite can be intercalated with acceptor species (like protonic or Lewis acids) as well as with donors. Intercalated lamellar compounds have the following features in common: (1) The absence of noticeable structural modification of the host matrix, in the sense that the structure of the lamellar units of the parent h o s t - [XTX] in TX2, hexagonal carbon planes in g r a p h i t e - a r e nearly unchanged. (2) A relatively weak interaction between the host and the intercalated species; as a consequence, the planar mobility of atoms or molecules intercalated between two layers of the matrix can be very high and this is one of the basic properties required for cathode materials. Nevertheless, these interactions are far from negligible, since they can alter the stacking sequence of lamellar unit of the parent compounds like in LixZrS2, Na, TiS2 and graphite compounds. (3) A large modification of the electronic and magnetic properties of the host matrix can occur with intercalation; for example semiconductors or semi-metals can become metallic, and sometimes superconductors like M o S 2 . In the case of graphite, the conductivity and its anisotropy can be increased and in some TX2 compounds like 2H-TaS2, the superconductivity is enhanced.

Physica 99B (1980) 107-116 (~ North-Holland

Nuclear Magnetic Resonance (NMR) techniques have been extensively used in the study of intercalation compounds. They provide some structural information on the configuration of intercalated molecules or on the symmetry of the sites occupied by the guest atoms. However, the main interest of N M R is to give a microscopic insight in the changes of the electronic properties of the host matrix as well as the degree of ionization of the guest on one hand and on the dynamics of the intercalated species on the other hand. These two points will be respectively discussed in sections 3 and 4 of this paper, in which we review recent experimental data. In section 2, we review basic N M R theory. 2. Introduction to NMR in lamellar intercalated compounds Let us consider a hypothetical solid A x B , , B ' , where the A atoms are the intercalated species (they can be part of a molecule) which have a high mobility, while the B atoms belong to the host matrix and are static. Provided the A atom has a nuclear magnetic m o m e n t /tN = "yhl A, application of a magnetic field H0 will allow the observation of resonant absorption of a radio-frequency field around the Z e e m a n frequency UL= yH0. Let us first suppose that the A atoms also are static.

2.1. Knight shift, chemical shift If I A = 1/2, the nuclei will only be sensitive to magnetic interaction with environment, that is dipole--dipole interaction with the other nuclear

108 magnetic moments in the crystal, which will give a finite linewidth for the resonance, as well as magnetic hyperfine coupling with the electrons in the crystal. This last interaction shifts the resonance from its bare value u0 by an amount Au0 proportional to H0, which reflects the local electronic susceptibility. The contributions to this relative shift coming from localized and delocalized electrons are respectively called the chemical shift and the Knight shift [4]. It is often a difficult task to relate experimental values of AHo/Ho = K - o" to the electronic structure of the intercalated compounds; but in principle, it gives information on the degree of ionization of the intercalated species. Provided one of the B nuclei is observable, the measure of AHo/Ho will yield valuable information on the change in the electronic properties of the host matrix [5, 6, 7]. These two points will be analyzed in more details in section 3.

2.2. Quadrupolar couplings If I A is larger than 1/2 the A nuclei will also be sensitive to electric interaction with the local environment (A and B atoms) and will experience a quadrupolar coupling which strongly depends on the local symmetry. This quadrupolar coupling will split the nuclear resonance line into 2I distinct lines whose separation depends on the magnitude of the electric field gradient (EFG) tensor, its symmetry and the direction of its principal axis with respect to H0 [4]. Careful studies of the quadrupolar spectra of single crystals (or even of powders) can give information on the local symmetry (axial or non axial) of the sites occupied by the A atoms and (or) give evidence for occupation of different sites submitted to different EFG. Quadrupolar couplings experienced by VLi have been measured in graphite [7, 8] and a number of transition metal dichalcogenides [5, 9, 10]. The (e2qO/h) values usually lie in the range 10-50 kHz, showing no marked dependence on the chalcogene environment. In the case of 23Na, quadrupolar couplings are much stronger [10, 11], due to a larger polarizability of the sodium core electrons. One usually does not observe first order satellites, but rather a splitting of the (1/2, - 1 / 2 ) transition due to second order perturbation [4] (fig. 1). Unfortunately, accurate theoretical calculation of E F G are very difficult,

4G t

I

Fig. 1. Second order quadrupolar splitting of the central line in Na~l.TZr03In07S2 at u0 = 15 MHz giving (e2qO/h)= 0.69 MHz.

and little information can be extracted from these measurements. Nevertheless, the variation of quadrupolar couplings with the intercalant concentration can be meaningful. In NaxTiS2 [11], the (e2qO/h) values strongly differ from sites of octahedral or trigonal coordination. NMR-results [12] for x = 0.7 indicates a two-phase system corresponding to the superposition of the two types of spectra (fig. 2). The variations of quadrupolar couplings experienced by nuclei of

Fig. 2. Evidence of a two-phase system in Na0 7TiS2 considering the shapes of the derivatives of the central lines in c.w. experiments versus x. The two values of the quadrupolar coupling correspond to different structures with sites of octahedral and trigonal prismatic symmetries for the intercalated Na atoms.

109 host matrix have also been used to determine the charge transfer in intercalated compounds like NbS2 (pyridine)l/2 [13] and Ga, In, TI, Sn and Pb in NbS2 and NbSe2 [14]. Structural phase transitions, charge density waves [15] can also be probed on a microscopic scale through the variation of quadrupolar couplings [16, 17], and a detailed study of the influence of intercalation on these phase transitions in compounds like LixVSe2 remains yet to be done. Let us now suppose that the A atoms become mobile with a thermally activated jump rate

u = uo e x p ( - E A / k T ) .

(1)

This motion will randomly modulate the various interactions which the A spins undergo (this is also partially the case for the B spins). Here we restrict these interactions to the A atoms only, the A atom motion has several consequences.

2.3. Motional narrowing The A spin needs a time of the order of w ?~ to sense an interaction of strength h00in t. If the hopping time r of the A atom is shorter than to~nlt(c.Oint'/"< 1) the A nuclei will see an average value of this interaction. Particularly the dipolar interaction, which gives rise to the second m o m e n t (dw~) in the rigid lattice limit, will be averaged and the linewidth due to spin-spin interaction will become in the limits (A(.o2)l/2'T <~ 1, w07 >> 1, (T2)-' = (A~o~)r,

of translational diffusion. Such a situation has been encountered in TaS2(NH3) [18]. Another consequence of the motional narrowing is the averaging of quadrupolar interaction experienced by the A nuclei on different type of sites, leading to a unique average E F G tensor when the hopping rate is larger than these interactions. For example, the EFG tensor experienced by the A nuclei will result from interactions with the host matrix only, contributions from neighbouring A atoms being averaged to zero.

(2)

where Tz, the spin-spin relaxation time, is the correlation time of the transverse nuclear magnetization. Consequently, a measurement of 7"2 as a function of temperature allows the determination of the activation energy of a diffusion process and gives an idea of the hopping time since Awdr ~ 1 at the onset of the motional narrowing. However, formula (2) has been established in the three, dimensional case, and is not valid for two-dimensional diffusion, which is the case for lamellar intercalated compounds. This point will be discussed further below. When the A nuclei belong to molecules like NHs for example, the intra-molecular dipolar couplings can be averaged due to the spinning of the molecule which usually occurs before the onset

2.4. Effect on the spin-lattice relaxation rate The random modulation of the various interactions experienced by the A nuclei will also affect their spin-lattice relaxation time (SLRT) 7"1 which is the time constant of the recovery of the longitudinal nuclear magnetization. Components of the spectral density J ( w ) of random processes near the L a r m o r frequency w0 = yH0 will induce transitions between the Z e e m a n levels. If we call (o~,t) the mean quadratic value of the strength of the modulated interaction, the spin-lattice relaxation rate T1Z can be written T ; t = (toi2nt)lJ1(tOo)+ (toiznt)2Je(2to0),

(3)

where we have separated the interactions producing Am = 1 and Am = 2 transitions. Such an expression was proposed as early as 1948 by Bloembergen, Purcell and Pound (BPP) [19] who replaced J ( w ) by the Lorentzian function J ( w ) = r[1 + w2rz] -l, where ~- is the correlation time of the random process. In the case of the dipoledipole interaction this leads to the well-known formula for a powder average 1 Tl

(Am2)[~'[1 + °J°2~'2]-1+ 4~-[1 + 4o~02~'2]-']

(4)

and Ta = 7"2 in the high temperature regime w0r "~ 1. The BPP formula predicts a minimum of T1 for ~Oor~l, T11 ~ w62r -1 for w0~'<~l and T~ ~ ~ ~- for ~o0r'~ 1. Considerable efforts have been made to calculate J ( w ) by more elaborate models of diffusion [20, 21, 22] in three dimensional (3D) solids, which confirm the general feature of the BPP model. In the case of 2D diffusion which is pertinent to the case of intercalated species in lamellar compounds, the spec-

110 tral density is drastically modified and diverges as In co0~"in the limit co0~"~ 1. Such a behaviour, which was first realized for spin diffusion in 2D magnetic compounds [23], was also seen in the case of atomic diffusion by Silbernagel and Gamble [24] in TaS2(NH3). It is a consequence of the long time behaviour (t ~> ~-) of the radial part of the correlation function of the dipolar interaction R (t) = (r~3(t)r~3(O)), where rij is the interatomic distance, which decays as t -t instead of t -3/2 in 3D. Using a continuous diffusion model, Avogadro and Villa [25] have obtained an analytical expression of the long time expansion of R ( t ) and numerically calculated J(co), which behaves as In cot in the limit coy~ 1. Unfortunately, the continuous diffusion model cannot lead to the correct result in the limit co~'>> 1 where one expects ( I / T 0 0~ (1/coaT) whatever the dimensionality. Thus a good approximation for T~ in 2D systems would consist of replacing the Lorentzian in equation (4) by ~- In(1 + 1/co2r 2) [26, 27]. As a consequence of the divergence of J(~o) for low frequency, usual expression of T2 involving J(0) can no longer be used and the calculation of the correlation function of transverse magnetization becomes much more difficult. Qualitatively, one expects at least T~ ~ larger, and different from T i t in the range co0~"~ 1, instead of T1 = T2 for dipolar relaxation in 3D. From the above consideration, we see that the determination of the temperature dependence of T t - i n the range co0~-~->1 - a l l o w s the determination of the activation energy of the motion process, as well as an estimation of the hopping time if one observes the T~ minimum which occurs when 0.5
above give hopping times, not diffusion coefficients; as N M R is sensitive to any kind of motion, local as well as long-range, the selfdiffusion coefficients determined from this technique have to be compared to those determined from ionic conductivity, tracer, or electrochemical techniques. On the contrary, the so-called pulsed field gradient method [31] allows the direct determination of the self-diffusion coefficient D* by NMR, but requires D* values larger than 10-9-10 -8 cmRs ~. Comparison of D* determined by the pulsed field gradient method and r obtained from T1 measurement on the same sample and in the same temperature range allowed Zogal and Cotts [32] to determine directly the length of the jump and so the diffusion mechanism. Secondly, the effects of atomic motion on the nuclear spin relaxation rates ( T 0 -~ and (7"2)-1 can be strongly modified by the presence of a small amount of paramagnetic impurities [27, 33]. These can produce a frequency dependence of (T1)-t which strongly depart from the co-2 behaviour expected in the range toy>> 1 and in some cases lead to an apparent activation energy [33, 34]. Anomalous frequency dependence of T1 can also result from a distribution of jump frequencies corresponding to a distribution of activation energies. Such an explanation was proposed by Walstedt et al. [35] to explain an asymmetric peak of log T~ as a function of the inverse temperature l I T in Na-/3 alumina. Finally, let us imagine the possible consequences of collective atomic motions on nuclear spin-lattice relaxation. This point has never been considered in detail. One has to note that in the presence of collective motion, the cross-correlation functions between two different pairs of s p i n s - o f the type (r~3(t)r~3(O)) - c a n no longer be neglected; they can give rise to non-exponential recovery of the longitudinal nuclear magnetization [36], with a very long tail which can lead to an apparent loss of signal. Such effects have been observed in LixTiS2 and in Na-/3alumina and could be due to correlated atomic motion.

3. NMR investigation of the electronic structure of intercalated layer compounds The ideal approach to the comprehension of the electronic structure of intercalated corn-

111 pounds, at least for stoichiometric ones like LiC6, LiTiS2, would be the comparison between band structure calculations and experimental measurements like specific heat, magnetic susceptibility, N M R properties of the host and guest atoms. Unfortunately, the difficulties of band structure calculations severely increase with the number of atoms in the unit cell, and at present time, the only available band structure calculation of intercalated compounds are for LiC6 [37, 38] and KC8 [39]. In the case of the transition metal dichalcogenides, a large number of band structure calculations exist as far as the parent compounds are concerned, but none of intercalated compounds. In some cathode materials, like the transition metal phosphorus trichalcogenides [40, 41] or transition metal oxyhalides [42], the situation is still worse since no calculation at all are available. This absence of band structure data renders rather difficult the interpretation of the shift of the nuclear resonance of intercalated atoms, especially when they are small. As far as the shift of the nuclei belonging to the host matrix are concerned, more information can be drawn, at least in a qualitative way. In the case where the host matrix is a semiconductor, one expects the electrons given up by the intercalant to go into the conduction band of the matrix, at least for large enough concentration; so one should be able to follow the variation of the (partial) density of states at the Fermi level. But for low enough concentration, one can expect a metal insulator transition as observed in the sodium tungsten bronzes [43]. We shall now try to illustrate these points from available N M R data in various intercalated layer compounds.

3.1. Graphite compounds Knight shifts of the guest nuclei have been measured in LiC6 [44], RbC8 [45] and CsC8 [46] (table I). One can reasonably assume that in these compounds the Knight shift is mainly due to contact interaction with the " n s " electrons at the Fermi level (n = 2, 5, 6 for Li, Rb, and Cs, respectively) and can be expressed [4] as: K = ~-~ c~([~Pk(0)]2)F)t/P, where a = 11.2,


(5) is the averaged

nuclear contact density at the Fermi level (expressed in e/(a.u.) 3) and Xp is the Pauli susceptibility (in e.m.u, cgs/mole). In absence of band structure calcination, one could take for PF the same values as for Li, Rb and Cs metals, that is respectively 0.0743, 2.8512, 2.8125 [48], which lead to X~" values of 6 x 10-6, 5.4 × 10 -6 and 11 x 10-6e.m.u./mole respectively; here g~" would be the contribution to the total Pauli susceptibility of a partially filled conduction band constructed from the " n s " wavefunctions of the alkali atoms. In such an approach, we neglect any possible hybridization between these wavefunctions and those forming the ~rz bands of the pure graphite. These latter also are partially occupied and contribute to the total Pauli susceptibility, but not to the alkali atom Knight shift. However, a recent band structure calculation in LiC6 [38] indicates that in this compound the conduction band constructed from Li 2s wavefunctions is empty; but, at the Fermi level, the 7rz wavefunctions of the carbon are slightly hybridized with the Li 2s wavefunctions; the corresponding PF value is 0.01 which has now to be multiplied by the total Pauli susceptibility, Taking the value given by Delhaes et al. [50], and applying formula (5), Holzwarth et al. [38] found a good agreement with K value measured by Conard and Estrade [441. In spite of the academic character of this discussion, it illustrates the difficulties encountered in the interpretation of N M R data, in particular when the measured shifts are small and of the order of chemical shifts. Very recently, Lauginie et al. [7] reported measurements of the 13C shift in a number ¢3f donors graphite compounds including II, III a,:d IV stages. A calculation of the core-polarization hyperfine field for ¢rz electrons of the carbon in graphite would be of great help in further interpretation of these data. Table I Knight shifts of 7Li, STRb and ~33Cs in first stage intercalated graphite compounds (from refs. 44, 45, 46) and in the corresponding alkali metals (from ref. 47).

K (%) Kmetal

LiC6

RbCs

CsCs

0.0042 0.026

0.145 0.651

0.29 1.49

112 As far as acceptor graphite compounds are concerned, E b e r t and Selig [50, 51] have been able to determine the oxidation degree of some acceptor molecules from 19F chemical shifts. On another hand, ~3C resonance in some acceptors compounds [7] confirm the general picture that charge transfer is rather small compared to donors compounds.

Q~

-

~

. . . .

-O.05L ,./

k _o,.1L0

~

3.2. Transition metal dichalcogenides 3.2.1. Alkali metals intercalates The shift of 7Li resonance has been measured in most of the transition metal disulphides and diselenides [5, 52]. Silbernagel's study [5] of fully lithiated Li~TX2 transition metal dichalcogenides shows that the 7Li shifts lie between 10 and 3 0 p p m , which is small. Their detailed interpretation would require the knowledge of the Pauli susceptibility of these compounds as well as band structure calculations as discussed above in the case of LiC6. These results nevertheless imply a large charge transfer from the lithium atoms to the host conduction band, and a very small admixture of the Li 2s wavefunctions with the wavefunctions of the TX2 conduction band at the Fermi level. Silbernagel [52] also m e a s u r e d the shift of 7Li as a function of x in Li~TiS2, which he found to increase linearly with x in LixTiS2; he interpreted this as a consequence of a decrease of ionization with increasing x, but according to formula (5) this can as well be explained by a linear variation of XP (or N(EF)) with x. Such a variation departs from the free electrons predictions, but was also observed in sodium tungsten bronzes [53, 54] and in Li~ZrSe2 as discussed below. 775e r e s o n a n c e has been observed in the LiITSe2 (T = Ti, Zr, V, Nb, Ta, Hf) c o m p o u n d s [5]. The striking feature is that whatever the 77Se shift in the parent c o m p o u n d s is, depending on its metallic, semi-metallic or semiconductor character, the value obtained after intercalation is about the same. Further investigation of 778e shift as a function of the intercalant concentration are needed to understand this puzzling result. Such a variation has been measured in the case of Li~ZrSe2 [55]; the 778e shift has been found nearly constant up to x = 0.4 and then to vary linearly with x up to x = 1 (fig. 3). H o w e v e r , t h e 77Se spin-lattice relaxation time is shorter in

I

_ o.1 s t _ _

I

t

o

;

0.5 x

in

LixZrSe

I 2

Fig. 3. Shift of 77Se in LixZrSe2 versus x (H2SeO3 was taken as reference); O P. S6gransan et al. m e a s u r e m e n t s [55]; • Silbernagel m e a s u r e m e n t s [5].

the intercalated c o m p o u n d s than in the pure matrix, as also observed by Silbernagel [5] (even for x < 0.4). These data could indicate a metal-insulator transition occurring around x = 0.4 in this system, but this question needs further investigation. One can notice that the shift of 7Li in LixTiS2, those of 23Na and 183W in Na~WO3 and the one of 77Se in LixZrSe2 for x > 0.4 are all linear with x, while a rigid band model and a simple 3D free electrons picture would predict a x I/3 behaviour.

3.2.2. Transition metals intercalates Although the parent c o m p o u n d VS2 cannot be directly prepared, V~S8 has been considered as an intercalation c o m p o u n d with the chemical formula [V0.z5VS2] , in which vanadium atoms occupy one fourth of the octahedral sites in the Van der Waals gap between VS2 layers. 51V N M R [56] indeed reveals that those vanadium between the layers bear localized electronic moments, while those inside the layer exhibit a metallic character. This different nature of vanadium atoms inside and between the layers can justify the denomination of intercalation c o m p o u n d for VsS~.

3.2.3. Post transition metals intercalates TaS2, NbS2 and NbSez intercalated with post transition metals like Ga, In, T1, Sn, Pb have been studied by N M R [57, 14]. Intercalation

113 compounds only exist for definite composition (x = 1, 2/3 and 1/3) in contrast with the situation encountered in alkali metal A~TX2 intercalates, where the concentration x can usually be continuously varied from x = 0 to 1. In Sn~TaS2, where the Sn-Sn distance is close to that observed in metallic tin, Gossard et al. [57] measured a Sn Knight shift larger than in metallic tin; this indicates the existence at the Fermi level of a conduction band constructed from the wavefunctions of the intercalated atoms. However, in Sn~/3TaS2 where the Sn-Sn distance is much larger, they observed a sharp decrease of the Sn shift and its ratio to the metallic one is comparable to those observed in alkali intercalates.

3.2.4. Molecules intercalates Most of the N M R studies of intercalated molecules in transition metal dichalcogenides concern their orientation and their motion, and not the electronic structure of these compounds. Charge transfer to the conduction band has nevertheless been studied in the NbS: (pyridine)l/2 through the variations of the E F G experienced by the 93Nb nuclei [13]. Proton N M R in TaS2(pyridine)~/2 has also been investigated [58].

3.2.5. Transition metals cogenides

phosphorus trichal-

The MPX3 compounds (M = Ni, Fe, Mn, X = S, Se) can be intercalated with lithium [40, 41] either chemically or electrochemically without any observable expansion of the lattice parameters. The change in the electronic and magnetic properties of the host matrix due to intercalation have been studied through the N M R of the 31p nuclei [6, 59], which experience a transferred hyperfine interaction from the local m o m e n t of the 3d ions. Curiously, one observes no modification of the magnetic properties (antiferromagnetism) in the selenium compounds through the whole intercalation concentration range. Quite different is the behaviour of the sulfides (NIPS3, FePS3): as soon as one third of the Li octahedral sites are occupied, a second phase appears, in which the 3d ions have lost their magnetic moments, and grows at the expense of the first one; this can be seen from the coexistence of two sip lines having different

B

A

Fig. 4. 31p resonance in LixNiPS3. The B line has the same position as in CdPS3 and corresponds to a second phase with x = 1.5 in which the Ni atoms have lost their magnetic moments

16, 591. shifts and T1 (fig. 4). No evidence of conduction electrons could be found by NMR. This review of N M R data on the electronic structure of lamellar intercalated compounds is not exhaustive; we would like to conclude this section with one remark. The usual way of extracting information on the electronic structure from N M R in metallic compounds is to combine Knight shift and spin-lattice relaxation data which have to verify the well-known Korringa relation [4]. When the conduction electrons have " p " or " d " character, one has to write separate Korringa relations for the contact, corepolarization and dipolar terms, and take into account orbital shift and relaxation rate which do not verify the Korringa relation [60]. (In contrast to the other contributions in the Knight shift, the orbital one is not proportional to the density of states at the Fermi level.) The reasons we have principally discussed resonance shifts are: (1) In the case of intercalates like alkali metals, or molecules, the effects due to atomic motion usually dominate the spin-lattice relaxation, or are of the same order of magnitude as the electronic contributions. (2) In the case of the host matrix, precise TI measurements (which require a better signal to noise ratio than shift measurements) do not exist for most of the intercalated compounds which we have discussed here.

114 Nevertheless, examples of such type of analysis can be found in refs. 14, 53 and 54.

4. Dynamics studies N M R techniques have been widely used to investigate the motion of intercalated species in lameilar compounds. These studies can be roughly classified according to three subjects of interest: (1) The problems related to the two-dimensional character of the diffusion of the intercalated species, which is specific of lamellar compounds. (2) The details of the complex motion of intercalated molecules. (3) The determination of self-diffusion coefficient and activation energy of cations in cathode materials like LixTiS> 4.1. Two-dimensional diffusion As noted in section 2, the main consequence of the two-dimensional character of atomic diffusion is the logarithmic divergence of the spectral densities of the spin-correlation function for o) ~ 0. Evidence for this divergence was given by Silbernagel and Gamble [24] who studied the 1H resonance in TaS2(NH3) and by Avogadro and Villa [25] who studied the ~H resonance in graphite intercalated with nitric acid. This divergence of the spectral density also affects the spin-spin relaxation time /'2; 7Li N M R in LixTiS: [61] shows that (T2)-l is an order of magnitude larger than (7"1)-~ at the T1 minimum. Furthermore, (T2)-1 in the motional narrowing regime will no longer be simply proportional to the hopping time r and corrections have to be applied for a proper determination of the activation energy of the diffusion motion [26]. 4.2. Intercalated molecules In the case of intercalated molecules, several types of motion have to be considered. If the molecule has a many fold symmetry axis (NH3, metallocenes), one expects spinning of the molecule around this axis, and reorientation of this axis (partial or isotropic), in addition to translational diffusion. In any case, one expects at least two types of motion, reorientation and translation. The separation between these different types of motion from N M R data is far

from being obvious. An example of detailed NMR investigation of molecular motion can be found in the work of Silbernagel et al. [18, 24, 62, 63] in TaS2 and TiS2 compounds intercalated with NH3 and ND3. As far as intercalated compounds of graphite are concerned, the readers are referred to refs. 25, 51 and 64. 4.3. Cathode materials A high mobility of the intercalated alkali ions is one of the conditions required to get a good mixed conductor suitable for battery application like Li,TiS2 ]65]. As explained in section 2, the self-diffusion coefficient D* and its activation energy EA can be deduced from N M R measurements, provided one correctly takes into account the effects of low-dimensionality. These parameters have to be compared to those deduced from electrochemical measurements, that is the chemical diffusion coefficient /9 and Aix(c), the energy of intercalation versus composition [66]. D* and / ) are related by the Darken relation / ) = D*(0 In a/a In c), where a is the activity of the alkali ions and (,9 In a/O In c) can be deduced from A/x(c)= A/z°+ R T In a. 4,3.1. Lithium intercalates of transition metal dichalcogenides A NMR survey of the LixTS2 compounds [5] has revealed a much higher mobility in LiIVSe2 and in the group IV b compounds than in those of group V. Inside the IV b group, the activation energies have been found substantially higher in LixZrS2 than in LixTiS2 [67], reflecting a more ionic character of the host matrix. The variation of D* and EA versus composition has also been measured in LixTiS2 (table II) [33, 67]. Ea was determined from the temperature dependence of In 7"1 as a function of the inverse temperature 1/T, in the low temperature side of the T~ minimum. This is the most reliable procedure in presence of two-dimensional diffusion. The rapid variation of EA from x = 0 to about 0.5 seems to be correlated to the expansion of the c parameter, which has the same qualitative behaviour. it is important to notice the very low value of the prefactor 1,0 in the hopping rate expression u = Vo e x p ( - E A / k T ) which is usually of the order of optical phonon frequencies (1012 Hz), a situation often encountered in superionic conductors

115

Table 11 Activation energy, prefactor v0 and self-diffusion coefficients of 7Li in Li~TiS2compounds x

0.16

0.38

0.57

0.72

0.86

Ea (eV) v0 (Hz)a D~00~(cm2s-l)

0.20 3.5 × 109 4.5× 10-l°

0.14 1.1 x 109 1.4×10 9

0.13 6.7 × 108

0.10 <3 x 108 ~10-9

0.10 ~<3× 108 ~10-9

a v0 is determined assuming t O 0 " r N M R D* is taken equal to a2/(4~-at).

:

2 × 10-9

I at T1 minimum, 7 = "roexp(Ea/kT) and

[68]. T h e r e m a r k a b l e a s p e c t of t h e s e d a t a is t h a t t h e g o o d a g r e e m e n t b e t w e e n t h e s e self-diffusion coefficients and the chemical diffusion coefficients m e a s u r e d in LixTiS2 b y e l e c t r o c h e mical t e c h n i q u e s [65, 69]; i m p l i e s t h a t t h e s e low v a l u e s of v0 a r e n o t an a r t i f a c t of N M R m e a s u r e m e n t s . This c o u l d b e an e v i d e n c e for a d e v i a t i o n f r o m t h e a b s o l u t e r a t e t h e o r y of E y r i n g , as p r o p o s e d b y H u b e r m a n a n d B o y c e [68].

4.3.2. Sodium intercalates of transition metal dichalcogenides N M R d a t a o n t h e s o d i u m m o b i l i t y in t h e TX2 c o m p o u n d s a r e m u c h less n u m e r o u s t h a n for l i t h i u m i n t e r c a l a t e s , a n d t h e o n l y existing d a t a [67, 70] a r e f o r i n s u l a t o r m a t e r i a l s like NaxZrl-xMxS2 [71] w h e r e M = In, Y in a t r i v a l e n t metal.

4.3.3. Lithium intercalates of transition metal phosphorus trichalcogenides T h e l i t h i u m m o b i l i t y in t h e LixNiPS3 c o m p o u n d s has b e e n i n v e s t i g a t e d b o t h b y N M R [6, 59] a n d e l e c t r o c h e m i c a l t e c h n i q u e s [72]. F r o m dipolar spin-lattice relaxation time measurem e n t s , self-diffusion coefficients o f t h e o r d e r of 10-13cmEs -l h a v e b e e n d e d u c e d . T h e m o d e of p r e p a r a t i o n o f t h e s a m p l e s , c h e m i c a l o r elect r o c h e m i c a l , s e e m s to p l a y n o role. T h i s c o n t r a s t s with c h e m i c a l diffusion coefficients o f t h e o r d e r o f 10 -1° f o u n d in o n e of t h e d o m a i n of e l e c t r o a c tivity o f t h e s e c o m p o u n d s [72]. Such a disc r e p a n c y is n o t y e t fully u n d e r s t o o d , b u t c o u l d b e d u e to a n i n c r e a s e o f t h e diffusion coefficients in p r e s e n c e o f l a r g e e l e c t r i c field. S u c h a situation, in w h i c h N M R i n d i c a t e s a low ionic m o b i l ity, in s p i t e of a g o o d e l e c t r o c h e m i c a l activity, h a s also b e e n s e e n in LixV6013 [73].

"/'NMR =

7at/2.

T h e a u t h o r s a r e i n d e b t e d to M. M i n i e r for critical r e a d i n g of t h e m a n u s c r i p t a n d G . O u v r a r d , R. B r e c , A . L e M e h a u t e , L. T r i c h e t a n d J. R o u x e l for s a m p l e s p r e p a r a t i o n a n d c h a r a c t e r i z a t i o n , a n d h e l p f u l discussions.

References [1] F.R. Gamble and T.H. Geballe, Treatise on Solid State Chemistry, Vol. 3, N.B. Hannay, ed. (Plenum Press, New York, 1976) p. 89. [2] J. Rouxel, in "Intercalation Compounds", Vol. 5, F. Levy, ed. (D. Reidel, Dordrecht, 1979). [3] Intercalation Compounds of Graphite, F.L. Vogel and A. H6rold, eds., Mat. Sci. Eng. 31 (1977). [4] A. Abragam, Principles of Nuclear Magnetic Resonance (Clarendon Press, Oxford, 1961). [5] B.G. Silbcrnagel, Sol. State Comm. 17 (1975) 361. [6] C. Berthier, Y. Chabre, M. Minier and G. Ouvrard, Sol. State Comm. 28 (1978) 327. [7] P. Lauginie, J. Conard, H. Estrade, D. Guerard, M. El Makhini, P. Lagrange, H. Fuzelier, G. Furdin and R. Vasse, Proceedings of the 14th Biennial Conference on Carbon, Pennsylvania University, June 1979, to be published. [8] J. Conard and H. Estrade, Mat. Sci. Eng. 31 (1977) 173. [9] B.G. Silbernagel and M.S. Whittingham, J. Chem. Phys. 64 (1976) 3670. [10] B.G. Silbernagel and M.S. Whittingham, Mat. Res. Bull. 12 (1977) 853. [11] B.G. Silbernagel and M.S. Whittingham, Mat. Res. Bull. 11 (1976) 29. [12] C. Berthier, M. Minier and L. Trichet, unpublished results. [13] E. Ehrenfreund, A.C. Gossard and F.R. Gamble, Phys. Rev. B 5 (1972) 1708. [14] N. Karnezos, L.B. Welsh and M.W. Sharer, Phys. Rev. B 5 (1975) 1808. [15] J.A. Wilson, F.J. Di Salvo and S. Mahajan, Adv. Phys. 24 (1975) 117. [16] C. Berthier, D. Jerome and P. Molinie, J. Phys. C, Solid State Phys. 11 (1978) 797. [17] A.H. Thompson and B.G. Silbernagel, B.A.P.S. 21 (1976) 260. [18] B.G. Silbernagel, M.B. Dines, F.R. Gamble, L.A. Gebhard and M.S. Whittingham, J. Chem. Phys. 65 (1976) 1906.

116

[19] N. Bloembergen, E.M. Purcell and R.V. Pound, Phys. Rev. 73 (1948) 679. [211] M.C. Torrey, Phys. Rev. 95 (1953) 962, 96 (1954) 960. [2l] M. Eisenstadt and A.G. Redfield, Phys. Rev. 132 (1963) 635. [22] D. Wolf, Z. Naturforsh 26a (1971) 1816; Phys. Rev. B 15 (1977) 37 and refs. therein. [23] P.M. Richards, Proceedings of the International School of Physics E. Fermi, Course LIX, K A . Muller and A. Rigamonti, eds. (North-Holland, Amsterdam, 1976). [24] B.G. Silbernagel and F.R. Gamble, Phys. Rev. Left. 32 (1974) 1436. [25] A. Avogadro and M. Villa, J. Chem. Phys. 66 (1977) 2359. [26] P.M. Richards, Sol. State Comm. 25 (1978) 11119. [27] P.M. Richards, in: Current Topics in Physics, Superionic Conductors, M.B. Salamon, ed. (Springer Verlag, Berlin) to be published. [28] M. Goldman, Spin Temperature and Nuclear Magnetic Resonance in Solids (Oxford Univ. Press, London, 1970). [29] C.P. Slichter, Principles of Magnetic Resonance (Springer Verlag, Berlin, 1978). [30] C.P. Slichter and D.C. Ailion, Phys. Rev. 135 (1964) A 1099. [31] R.M. Cotts, Ber. Bunsenges, Phys. Chem. 76 (1972) 76/t. [32] O.J. Zogal and R.M. Cotts, Phys. Rev. B 11 (1975) 2443. [33] C. Berthier, Proc. of the Intern. Conf. on Fast Ion Transport in Solids, Lake Geneva, 1979 (to be published). [34] L. Shen, Phys. Rev. 172 (1968) 259. [35] R.E. Walstedt, R. Dupree, J.P. Remeika and A. Rodriguez, Phys. Rev. B 15 (1977) 3442. [36] R.L. Hilt and P.S. Hubbard, Phys. Rev. 134 (1964) A 392. [37] N.A.W. Holzwarth, S. Rabii and L.A. Girifalco, Phys. Rev. B 18 (1978) 5!90. [38] N.A.W. Holzwarth, L.A. Girifalco and S. Rabii, Phys. Rev. B 18 (1978) 5206. [39] T. Inoshita, K. Nakao and H. Kamimura, J. Phys. Soc. Jpn 43 (1977) 1237. [40] A.H. Thompson and M.S. Whittingham, Mat. Res. Bull. 12 (1977) 741. [41] A. Le M6haut~, G. Ouvrard, R. Brec and J. Rouxel, Mat. Res. Bull. 12 (1977) 1191. [42] P. Palvadeau, L. Coic, J. Rouxel and J. Portier, Mat. Res. Bull. 13 (1978) 221. [43] N.F. Mott, Phil. Mag. 35 (1977) 111 and refs. therein. [44] J. Conard and H. Estrade, Mat. Sci. Eng. 31 11977) 173. [45] Y. Chabre, P. Segransan and J.E. Fischer, private communication.

[46] G.P. Carver, Phys. Rev. B 2 (1970) 2284. [47] G.C. Carter, L.H. Bennett and D.J. Kahan, Progress in Mat. Sci. 20 (1971)). [48] S.D. Mahanti and T.P. Das, Phys. Rev. B 3 11971) 1599. [49] P. Delhaes, J.C. Rouillon, J.P. Manceau, D. Guerard and A. H6rold, J. Phys. Lett. Paris 37 (1976) L127. I50] L.B. Ebert and H. Selig, Mat. Sci. Eng. 31 (1977) 177. [51] H. Selig and L.B. Ebert, to be published in Adv. lnorg. Chem. Radiochem. [52] B.G. Silbernagel and M.S. Whittingham, J. Chem. Phys. 64 (1976) 3670. [531 D.P. Tunstall, Phys. Rev. B 11 (1975) 2821. [54] B.R. Weinberger, Phys. Rev. B 17 (1978) 566. [55] P. S6gransan, Y. Chabre, C. Berthier and L. Trichet, to be published. [56] B.G. Silbernagel, R.B. Levy and F.R. Gamble, Phys. Rev. B 11 (1975) 4563. [57] A.C. Gossard, F~J. Di Salvo and H. Yasuoka, Phys. Rev. B 9 (1974) 3965. [58] S. Wada, H. Alloul and P~ Molinie, J. Phys. Lett. 39 (1978) 243. [59] Y. Chabre, P. S6gransan, C. Berthier and G. Ouvrard, Proc. of Intern. Conf. on Fast Ions Transport in Solids, Lake Geneva (1979). [6{/] J. Winter. Magnetic Resonance in Metals (Clarendon, New York, 1971). [61] C. Berthier et al., to be published. [62] B.G, Silbernagel and F.R. Gamble, J. Chem. Phys. 65 (1976) 1914. [63] F.R. Gamble and B.G. Silbernagel, J. Chem. Phys. 63 (1975) 2544. [64] A. Avogadro and M. Villa, J. Chem. Phys. 70 (1979) 109. [65] M.S. Whittingham, in Solid Electrolytes, P. Hagenmiiller and W. Van Gool, eds. (Academic Press, New York, 1978) p. 367. [66] B.C.H. Steele, in Superionic Conductors, G.D. Mahan and W.L. Roth, eds. (Plenum Press, New York, 1976) p. 47. [67] C. Berthier, Y. Chabre, M. Minier, L. Trichet and G. Ouvrard, Proc. of the 2nd Intern. Meeting on Solid Electrolytes, St, Andrews (1978). [68] B.A. Huberman and J.B. Boyce, Sol. State Comm. 25 (1978) 759. [69] S. Basu and W.L. Worrell, Proc. of the Intern. Conf. on Fast Ion Transport in Solids, Lake Geneva (1979). [70] L. Trichet et al., to be published. [71] L. Trichet and J. Rouxel, Mat. Res. Bull. 12 (1977) 345. [72] A. Le M6haut6, C.R. Acad. So. 287 (1978) Serie C, 309. [73] R.E. Walstedt, D. Murphy and F.J. Di Salvo, private communication.