Reliability of the Rigid-Band Model in Lithium Intercalation Compounds

Abstract

Numerous layered structured compounds are interesting materials in which lithium intercalation occurs primarily without destruction of the host lattice. In many cases a rigid band model is a useful first approximation for describing the changes in electronic properties of the host material with intercalation. We observed, nevertheless, that the rigid-band model is not applicable to all of the layered compounds. One may argue that the applicability of the rigid-band model may be taken as a test for the properties most desirable in a good intercalation material. This needs yet to be more extensively documented for their promising applications as insertion electrode in rechargeable lithium batteries. This chapter presents the applicability of the rigid-band model on intercalation compounds with a layered structure namely the transition-metal chalcogenides MX ₂ (X = S, Se) and the transition-metal oxides LiMO₂ (M = Co, Ni) as well.

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

4.1 Introduction

Layered compounds, in particular the transition-metal dichalcogenides (TMDs) and transition-metal oxides (TMOs) , can be intercalated with a wide range of both organic and inorganic materials which may have a profound influence on the physical properties of the host compound [1]. The intercalation reaction in these compounds is driven by charge transfer from the intercalant to the host layered compound conduction band and thus electron-donating species can take place in such a reaction. The reversible ion-electron transfer reaction is classically represented by the scheme:

$$ x{A}^{+}+x{e}^{-}+\left\langle H\right\rangle \iff {A}_x^{+}{\left\langle H\right\rangle}^{x-}, $$

(4.1)

in the usual case where 〈H〉 is the host material, A an alkali metal and x the molar intercalation fraction. The electronic transport plays an important role in such reaction toward the formation of intercalation compounds. It also governs the phase transitions as the parameter expansion of the host structure has an electronic component. Consequently, it is possible to consider three classes of intercalation reaction that correspond to the different steps in the delocalization of the transferred electrons. The level of acceptance can be either a discrete atomic state, or a molecular level of a discrete polyatomic entity existing in the structure, or part of a conduction band.

In this chapter, we present the physical properties of cathodes materials and verify the applicability of the rigid-band model for intercalation compounds with a layered structure namely transition-metal chalcogenides MX ₂ (M = Ti, Ta, Mo, W; X = S, Se) and oxides LiMO₂ (M = Co, Ni) as well. Electrical and optical properties are investigated. For some materials, we observe different degrees of irreversibility in the intercalation process and lattice evolution to the complete destruction of the host. Since the purpose here is the study of the materials in the framework of materials science, all the electrochemical properties reported in this chapter have been recorded at low rate C/12 or C/24 to be close to thermodynamic equilibrium so that they can be related to the physical properties.

4.2 Evolution of the Fermi Level

Let consider the schematic representation of Fig. 4.1 providing an easy way to visualize the energetic levels of the three active components of a lithium battery that are the negative and positive electrodes and the electrolyte. Taking into account the description of physicists, the vacuum refers the zero-energy level . The electronic band structure of a material is characterized by three energies: the work function W that is the minimum thermodynamic energy to remove an electron from the Fermi level of a solid to the vacuum W = E _vac − E _F, the electron affinity E _EA = E _vac − E _cb that is the energy obtained by moving an electron from the bottom of the conduction band to the vacuum and the band gap E _g = E _vb − E _cb is the energy separation between the valence band E _vb and the conduction band E _cb. The negative electrode is lithium metal, which is an infinite reservoir of electrons; so electrons in a metal can be viewed as free electrons in a conduction band with W _(Li) = E _EA(Li) ≈ 1.5 eV. The electrolyte is an electronic insulating medium characterized by a wide band gap E _g > 4 eV, which is the separation between the occupied and unoccupied molecular orbital energies that are HOMO and LUMO level, respectively. The case of the positive electrode is more complex as it is a semiconductor with various locations for the Fermi level that is not necessarily at the position E _F = (E _cb + E _vb)/2. For instance, TiS₂ is a degenerate semiconductor with E _g ≈ 0.2 eV [2], while LiCoO₂ is a p-type semiconductor with E _g ≈ 2.4 eV and W = 4.36 eV that makes the Fermi level 0.4 eV above the top of the valence band [3].

Fig. 4.1

Schematic representation of the electronic structure of the active elements of a lithium battery. E _EA indicates the electron affinity, W represents the work function and E _g is the band gap energy of the materials

The rigid-band model (RBM) is a useful approximation for describing the changes in electronic properties of the host material with intercalation. Sellmyer [4] distinguishes two versions of the rigid-band model for dilute solid solutions, which might be called the electron-gas RBM and the screened-impurity RBM. In the former, described mainly by Jones [5], the valence electrons are regarded essentially as in plane wave states and the only effect of alloying with an element having a valence difference ΔZ, is to change the free electron density to a new value, that obtained simply by scaling the valences of the solvent and solute according to their atomic fractions in the alloy. In this case, the Fermi energy in the material has changed accordingly, but E_BC remains unchanged. In the screened-impurity RBM of Friedel [6], it is recognized that the electron gas cannot support an electric field at long distances from the charge impurity. The reason is that the conduction electrons will redistribute themselves to screen out the Coulomb field, an effect that is measured by the dielectric constant , which is large in conducting materials. In this case, any charged impurity added to a solid will polarize the solid, which generates a Coulomb potential. Therefore, the Fermi energy is unchanged, but the whole conduction band has been shifted by this potential (Fig. 4.2).

Fig. 4.2

Scheme of the Fermi level evolution in the frame of the rigid-band model (RBM). Two situations are considered: case I represents the electron-gas RBM, case II shows the screened-impurity RBM. (B) and (A) mean before and after lithium insertion, respectively. In both cases, the cell voltage V _oc is the same

The concept of rigid-bands implies chemical stability of the system. From the energetic point of view, this means the total energy of the substance is little affected by the addition of intercalated electrons. The consequence is that the structure too is stable, and the only energy band involved in intercalation is the narrow d-conduction band in TMDs. These are precisely the properties most desirable in a good cathode material, which provide features such as stable voltage against aging and mechanical durability [1]. It is most important, therefore, to investigate theoretically and experimentally how well the approximation can apply in a system employed for the lithium battery cathode.

As the potential of an insertion compound-based lithium battery is determined by the difference between the chemical potentials of electrodes (Eq. 1.6), the crystal chemistry of the cathode governs the cell voltage. As an example, Fig. 4.3 illustrates the role of the polyanions , i.e., (PO₄)³⁻ and (P₂O₇)⁴⁻, in iron-containing lithium insertion compounds, for which positions of the iron redox energies relative to Li⁰/Li⁺ changes as a function of the cation environment. This phenomenon has been described as the inductive effect by Goodenough [7]. It depends on the framework connectivity. For instance, the fluorophosphate compounds are expected to exhibit a high cell potential as a result of both the inductive effect of (PO₄)³⁻ group and the electron-withdrawing character of the F⁻ ion.

Fig. 4.3

Position of the iron redox energies to the Li⁰/Li⁺ in various Fe-containing lithium insertion hosts and consequent changes in cell voltages, illustrating the role of polyanions

4.3 Electronic Structure of TMDs

Considerations of the structural and chemical similarities in the layer structure of TMDs led Wilson and Yoffe [8–10] to suggest that the electronic energy band structures of the materials might also be similar and that the range of observed optical and electrical properties results from differences in the filling of band subgroups as the number of valence electrons is changed. While a completely rigid band model of the TMD compounds cannot account for all properties, theoretical calculations and experiments show that the basic view of the materials is probably correct: the character and the order of the various band subgroups remain the same, while their separations and widths vary slightly with changes in the constituents and the type of coordination unit in the crystal structure.

TMDs have a layered structure made up of a sheet of metal atoms M sandwiched between two sheets of chalcogen atoms X (Fig. 4.4). The X-M-X layers are held together by weak van der Waals forces. Each sheet consists of atoms in a hexagonally close-packed network as shown in Fig. 4.4a. This structure allows almost unlimited expansion of the interslab distance upon insertion of electron-donating species in the layer. Although initial interest in these intercalation compounds was driven by their superconducting properties (at very low temperature), these were used as the active electrode of secondary lithium batteries [8]. Three nonequivalent hexagonally close-packed positions are noted A, B, and C. Two types of coordination structure are possible, either one or both can form the basic unit of the crystal. In the trigonal prismatic coordination, the sandwich of X-M-X follows the AbA sequence and in the octahedral coordination it follows the AbC sequence (Fig. 4.4a). Capital letters denote the chalcogen atoms and lower case letters the metal atoms.

Fig. 4.4

(a) The octahedral and trigonal prismatic structures of MX ₂ compounds. A, B, C represent the three nonequivalent positions for a close-packed stacking. In octahedron and tetrahedron, capital letters denote the chalcogen atoms and lower case letters the metal atoms. (b) Elementary unit cell of simple polytypes of TMDs in the <1120> projection

A rational nomenclature adopted for naming the different polymorphs and polytypes proposed Brown and Beerntsen [11] is presented in Fig. 4.4b. In designating the polytypes, one first indicates the number of sandwiches required to obtain a unit cell perpendicular to the plane of the layers, then the overall symmetry of the structure: trigonal T, hexagonal H, or rhombohedral R. Lower case subscripts are used to distinguish polytype otherwise similarly labeled, e.g., 2Ha and 2Hb. Thus the simplest polytype with octahedral coordination, labeled 1T, has a repeat of the sandwich perpendicular to the layer, i.e., this polytype is obtained by piling the sandwich units. In the trigonal symmetry and the simplest trigonal prismatic coordination, polytypes have two sandwich repeats, and are designated 2Ha and 2Hb. The 2Ha structure is adopted by metallic group V materials such as NbS₂ and stocks the metal atoms directly above each other along the c-axis, while in the 2Hb structure, adopted by semiconducting group VI materials such as MoS₂, the metal atoms are staggered. In the 4Hb and 6R polytypes, the coordination within successive sandwiches alternates between octahedral and trigonal prism, i.e., a mixed coordination. The six best known polytypes of transition metal dichalcogenides are shown in Fig. 4.4b. Octahedral interstitial (vacant) sites between sandwiches are represented by square sites, into which intercalation atoms may enter.

The electronic band structure of TMDs have been generally calculated using simplest molecular-orbital arguments [5] and experimentally established from the optical properties for the group IV, V, and VI TMDs. Figure 4.5 shows the schematic band structure of the MX ₂ compounds having octahedral and trigonal prismatic coordination. The basic features of the band model are shown for the regular trigonal prismatic structure (groups VI and V) and the regular octahedral structure (groups IV and V). The chalcogen p states with different degrees of admixture of metal states form the main valence band, while the energy of the chalcogen s states is located 10–15 eV below. The metal d states, with possible admixture of chalcogen states, lie immediately above the p valence band, and the next higher bands are made up of metal s and p states. The d band is subdivided in accordance with the ligand field splitting. The lowest of these sub-bands can hold two electrons and is called the “d _z ²” band after Wilson and Yoffe [8]. The reason is that the d _z ² is split off the d _xy −d _x ²− _y ² band towards lower energy by the trigonal distortion. The same band-labeling scheme is used here in spite of the hybridization between d and p states, and between the various d states. In all the compounds of the group IV to group VI transition metals, the p- and s-valence bands are completely filled, and the variations of the electrical and optical properties are largely accounted for by the gradual filling of the d _z ² band [12].

Fig. 4.5

Schematic band structures for all the TMDs compounds with octahedral and trigonal prismatic coordination. Sketches show the electronic structures before (a) and after (b) lithium intercalation with the respective position of the Fermi level

On the whole the band structure of an octahedrally coordinated material is characterized by greater charge transfer from the metal atom to the chalcogen atom. The p-valence band is relatively narrow (about 2.5 eV wide), while the d _z ² band forms part of the d band manifold which is separated from the p-valence bands by about 2 eV. This is the case for all the group IV compounds and for some of the group V compounds. The band structure of a trigonal prism coordinated material, on the other hand, has a wider p-valence band (about 5 eV wide) and there is more mixing between p and d states, while the d _z ² band lies close to or overlaps with the p bands and is now well separated from the rest of the d band manifold. This is the case for all the regular group VI compounds and the rest of the group V compounds.

The position of the d _z ² band is thus determined by the symmetry of the coordination unit. It is interesting to consider the total energy for a given coordination. This is basically determined by two competing terms: the electrostatic potential energy and the energy of the d _z ² electrons. In the group IV compounds, the d _z ² band is empty and the electrostatic energy term favors octahedral coordination, where the chalcogen atoms on two sides of the metal atoms in a sandwich are staggered, while in the group VI compounds where the d _z ² band is full and the bonding is predominantly covalent, it is energetically advantageous to depress the d _z ² band by adopting the trigonal prism coordination where the chalcogen atoms are in the eclipsed position. In the group V compounds, the d _z ² band is only half full, so it is not surprising that neither term necessarily dominates completely and both coordination units occur.

In the simple picture, during intercalation, the donating-electrons will occupy one of the empty d-bands. The simplest approximation to the band structure of an intercalation compound is just that of the parent host compound with the Fermi level moved up to accommodate the extra electrons.

Many techniques have been used to obtain information on the optical absorption α, the reflectivity R and dielectric constants ε ₁ and ε ₂. Visible and ultra-violet absorption spectroscopy gives us the joint density of states of valence and conduction bands. Soft X-rays and synchrotron radiation give us information on conduction bands, while photoemission experiments (UPS, XPS, ESCA) can tell us about density of states in valence band and give the energies relative to the Fermi level. Typical absorption spectra for the semiconductor MoS₂ (d ², group VI), metal NbS₂ (d ¹, group V), and wide-band gap semiconductor ZrS₂ (d ⁰, group IV) are given in Fig. 4.6. The prominent features A and B for MoS₂ are excitons, while in the metal NbS₂ one observes the characteristic free carrier absorption at about 1 eV.

Fig. 4.6

Absorption spectra of two-dimensional TMDs : (a) 1T-ZrS₂, (b) 2H-NbS₂, and (c) 2H-MoS₂. The prominent features A and B for MoS₂ are excitonic transitions

4.4 Lithium Intercalation in TiS₂

For TMDs, the temperature dependence of the electron mobility is usually formed to be much stronger than expected for acoustic phonon scattering. The resistivity for materials with a temperature independent extrinsic carrier concentration is usually fit by the empirical relation:

$$ \rho ={\rho}_0+A{T}^{\alpha }, $$

(4.2)

where ρ ₀ is the temperature-independent contribution form impurity scattering and A is a constant [13]. The exponent α is found to vary from 2.3 in good-stoichiometry TiS₂ sample (with carrier concentration n = 1.1 × 10²⁰ cm⁻³) to 1.6 in poor-stoichiometry sample (n = 2.9 × 10²¹ cm⁻³); α is found to be as large as 2.2 for ZrSe₂.

In Li _x TiS₂ the magnitude of the Hall coefficient decreases with increasing lithium content, confirming the occurrence of electron transfer from intercalates to the host [6–8]. The electron concentration is TiS₂ before intercalation is 3.1 × 10²⁰ cm⁻³ indicating that this material is of stoichiometry Ti_1.0044S₂ [14]. Upon lithium intercalation we observe a large decrease of the resistivity as well as of the Hall coefficient. The carrier concentration in electro-intercalated samples increases to 5 × 10²¹ and 9.6 × 10²¹ cm⁻³ for x = 0.25 and 0.5, respectively. The Hall coefficient R _H of all the samples is nearly temperature independent, as would be expected for a normal metal.

Klipstein et al. [15, 16] explain this behavior by a model involving the interplay between inter-pocket and intra-pocket scattering of electrons by longitudinal acoustic phonons, whereby the increase in Fermi surface dimensions reduces the restriction on the wave-vector of phonons that may take part in the scattering process, implying that, as the carrier concentration increases, α should tend towards unity, which is the limit for a metal when the resistivity is solely due to a scattering of the electrons by LA-acoustic phonons. Simultaneously, the temperature T _min below which the ln(ρ − ρ ₀) vs. ln(T) curve starts deviating from linearity, should increase, since this deviation originates from incomplete momentum relaxation when the phonon wave-vectors characteristic of these temperatures are too short to span the Fermi surface. This model, which was originally based on studies in pristine TiS₂ with a varying degree of stoichiometry, was later verified to remain valid for higher carrier concentrations, such as in TiS₂ intercalated with lithium via the n-butyllithium technique [16] or intercalated with hydrazine [17].

Electron transfer is also apparent in the optical properties of this system. Figure 4.7 shows the absorption spectra, in the energy range 0.5–6.0 eV of pure and Li-intercalated TiS₂ [18]. In the spectrum of the intercalation complex LiTiS₂, the free carrier absorption is evidenced below 1 eV as it is responsible for the increase of the absorption when decreasing the photon frequency in the vicinity of the plasma frequency ω _p. We also observe interband transitions which are the first direct allowed transitions from the p valence to the d conduction band at the L point of the Brillouin zone. Moving into the spectrum of Li _x TiS₂, the onset of inter-band transitions is seen to have shifted to higher energies and the oscillator strength under the absorption band is roughly halved. Beal and Nulsen [18] argue that this is exactly what one would expect as the d _z ² band is now half-full following saturation of the intercalation complexes.

Fig. 4.7

Room-temperature absorption spectra of TiS₂ and LiTiS₂. The schematic band structure shows that the rigid-band model may be used for the intercalation complexes

Another optical experiment, infrared reflectivity was carried out on Li-electro-intercalated TiS₂ [15]. Figure 4.8 shows the FTIR reflectivity spectra of Li intercalated TiS₂ single crystals as a function of x(Li) in the range 0 ≤ x ≤ 1. We observe a large shift in the plasma edge for Li_1.0TiS₂ with respect to pure TiS₂. According to the free-carrier Drude model (see Chap. 13), the analysis of the dielectric function gives the values as follows. In TiS₂, the plasma edge lies around 1200 cm⁻¹, whereas in LiTiS₂ the plasma edge occurs at about 4000 cm⁻¹ giving plasma frequencies of 1360 and 4100 cm⁻¹, respectively, if we take into account that the high-frequency dielectric constant remains similar to that of the pristine material and if we consider the electron effective mass as obtained by Isomaki et al. [19]. At the L-point of the Brillouin zone, Isomaki et al. estimate m _a  = 0.4 m ₀ along the a-axis. This assumption implies that the optical effective mass m _opt has a value higher than 1.3 m ₀. In the present studies, the Drude analysis gives a carrier concentration of 1.7 × 10²² cm⁻³ for complete intercalation of TiS₂ at x = 1. This is in excellent agreement with the theoretically expected value of 1.75 × 10²² cm⁻³ and very close to the value of 2.2 × 10²² cm⁻³ determined from Hall measurements.

Fig. 4.8

FTIR reflectivity spectra of Li _x TiS₂ as a function of lithium content

We assume in the spirit of the rigid-band model [1] that intercalation changes appreciably neither the effective mass of the conduction band, nor the high-frequency dielectric constant of the host material. The charge transfer Δn from the alkali-metal atoms to the d-conduction band of the host compound can be directly calculated from the difference between ω _p ² before and after intercalation. Here Δn is expressed in terms of the number of electrons transferred per Ti atoms. Using this method we have Δn = 0.9 ± 0.1 electrons. The uncertainty of 0.1 electrons is thought to be a reasonable estimate in view of the assumptions made. It is interesting to note the large increase of the plasma damping factor from 310 to 2160 cm⁻¹ in Ti_1.005S₂ and Li_1.0Ti_1.005S₂, respectively. This increase is observed in the energy-loss function by the broadening of the plasmon peak. The damping factor can be expressed as follows:

$$ \Gamma =1/\tau =q/m*{\mu}_{\mathrm{H}}, $$

(4.3)

where μ _H is the Hall mobility of free carriers. The observed increase of Γ suggests a decrease of the Hall mobility or a modification of the effective mass tin the intercalated sample. In Li_1.0Ti_1.005S₂ the electron mobility measured by Hall effect has a value of 1.9 cm²V⁻¹ s⁻¹ at room temperature [14]. This value can be related with those given in the literature, namely 13.5 and 0.35 cm² V⁻¹ s⁻¹ for TiS₂ and LiTiS₂, respectively [16].

The temperature dependence of the IR reflectivity spectra of the Li_1.0Ti_1.005S₂ sample is similar to those of the pure material. The spectra show a dip close to the plasma frequency ω _p = 4180 cm⁻¹ extracted from analysis of the data using a Drude-like model with a frequency dependent relaxation time, as:

$$ 1/\tau \left(x,T,\omega \right)=x\kern0.5em {\tau}_0+\alpha \left[{(pT)}^2+{\omega}^2\right]. $$

(4.4)

A good fit to the optical data is achieved with the scattering rate given by Eq. (4.4) [20], with p = 13.6, against 2π in the ideal isotropic three-dimensional effective mass model [21], while the second term in ω ² is due to the electron-electron scattering. For Li intercalated TiS₂ sample, the temperature and frequency components of Eq. (4.4) are strongly screened by the first term (xτ ₀) as shown in Fig. 4.9. This may be due to the complete filling of the d-band associated with a very low Hall mobility. In this case, it is difficult to evaluate the optical mobility because the quantity ωτ > > 1 is no longer valid.

Fig. 4.9

Temperature dependence of the damping factor (inverse relaxation time) for TiS₂ and LiTiS₂

Considering that Hall measurements on the Li_1.0Ti_1.005S₂ sample give N _H  = 1.8 × 10²² cm⁻³ and that the Fermi energy obtained by optical reflectivity measurements is E _F  = 4180 cm⁻¹ = 0.52 eV, we may estimate the electron effective mass m* = 0.49 m ₀. This value is very close to the value reported for the pure material by Isomaki et al. [19]. In conclusion, it can be seen from the electrical and optical properties of the Li-intercalated TiS₂ presented above that they all can be explained in terms of the rigid-band model. It is worth mentioning here that optical absorption results by Scholz and Frindt [22] on Ag-intercalated TiS₂ also agreed with this model.

The reliability of the rigid-band model is due to the excellent structural stability of TiS₂. From the electrochemical view point, TiS₂ was considered as the best positive electrode for lithium batteries due to its high electronic conductivity, which avoids carbon additive, and the high mobility of Li⁺ ions into van der Waals planes. Unfortunately, problems came from the anode side. Note that the Li//TiS₂ electrochemical cell was invented by Broadhead and Butherus at Bell Telephone Labs, who filed their patent on 24 July 1972 [23].

4.5 Lithium Intercalation in TaS₂

Among the group-V TMDs, TaS₂ has perhaps been the subject of greatest interest, because of the fascinating structural and electronic properties that this material exhibits. Due to valence electron occupying their d _z ² band, this metallic compound can exist in either 1T-, 2H-, or 4H-structure [24]. As a consequence of the switching from octahedral (Oh) to trigonal prismatic (TP) coordination, the shift of the d _z ² band to lower energies occurs gradually. The absorption spectrum of pure 2H-TaS₂ shows a Drude edge below 1 eV associated with the free-carrier absorption in this material owing to the half-filled d _z ² band. After intercalation, the Drude edge disappears and the first d _z ² → d transition shifts toward lower energy. These changes are attributed to the gradual filling of the d _z ² band by electron transferred from lithium.

The absorption spectrum of 1T-TaS₂ is shown in Fig. 4.10. Near 1.5 eV, the absorption bands are associated with the d _z ² ₁ → d _z ² ₂ and d _z ² ₁ → d transitions, whereas the band above ~3.5 eV owing to p → d _z ² transition. Charge transfer from Li to the host lattice increases the population of the d _z ² band and raises the Fermi level E _F to a new energy, E _F′. The displacement of the strong absorption edge around ~3 eV indicates a considerable lowering of the d _z ² band with respect to its position in the pristine material. The lowering of the d _z ² band is attributed to the filling with electrons donated by Li, as well as the modification of the crystal structure that is an increase of the c/a ratio after intercalation [25]. These results provide further support to the argument that, upon lithium intercalation the rigid-band model is not entirely applicable in 1T-TaS₂.

Fig. 4.10

Absorption spectra of pure 1T-TaS₂ and 1T-Li _x TaS₂. The schematic band structure shows the lowering of the d _z band upon Li intercalation. Reproduced with permission from [24]. Copyright 1986 Kluwer Academic Press

4.6 Lithium Intercalation in 2H-MoS₂

Among the group-VI TMDs, MoS₂ is one of the materials where intercalation reactions induce a transition of the host related to local ligand field modification. In this particular case, molybdenum presents a trigonal prismatic sulfur coordination that changes the octahedral one (TP → Oh transition) [26–28]. The structure modification is accompanied by an increase of the M-X band ionicity in agreement with the respective stability of the new atomic arrangement, the Coulomb repulsion between partially charged ligands favoring the octahedral form. Also, the comparison of the d-band density of states of 2H-MoS₂ and hypothetical 1T-LiMoS₂ shows that the occupied bands, which contain six states, are lower in the case of the Oh phase. This effect corresponds to the glide process between Mo and S atoms. This is a fine example of destabilization through lithium reduction.

Figure 4.11 shows the voltage profile vs. composition x(Li) of the Li//Li _x MoS₂ cell using 1 mol L⁻¹ LiClO₄ in propylene carbonate as electrolyte [29]. The Li-MoS₂ system exhibit three distinct phases in good agreement with the work of Hearing et al. [30]. The discharge reaction of a fresh cell occurs in the range 3.0–0.55 V with two voltage plateaus at 1.1 and ~0.7 V when 3Li are intercalated in the layered MoS₂ lattice. The first discharge curve (phase I) exhibits a plateau in the range 0.25 ≤ x ≤ 1 that corresponds to a two-phase system including both 2H-Li_0.25MoS₂ and 1T-LiMoS₂ structures. For x = 1 the complete transformation from (TP) to (Oh) coordination is attributed to a process, which is driven by a lowering of the electronic energy for the octahedral structure when electrons are donated from Li to the MoS₂ layer upon intercalation. The octahedral transformation starting at x≈0.25 completes around x = 1.0 and is not preserved on subsequent cycling [1, 26, 27]. For x > 1, the phase II is formed, which appears to be reversible in the range 0.75–3.2 V without plateau formation. This phase II is a preferred phase (path D-G in Fig. 4.11) for battery use that requires the so-called battery formation process, i.e., first discharge down to 0.75 V. The phase III (path E-F) occurs at the end of the second plateau. This phase is not suitable because the poor reversibility [30].

Fig. 4.11

Electrochemical profile of the Li-MoS₂ system as a function of the Li content in Li _x MoS₂. Reproduced with permission from [29]. Copyright 2002 Elsevier

Electron diffraction studies on the Li-MoS₂ system have shown that the structural transformation is accompanied by a 2a ₀ × 2a ₀ superlattice formation observed for the composition x≈0.25, which is interpreted as a pseudo-staging on the basal hexagonal lattice (Fig. 4.12) [31]. This superlattice formation was also observed in the incremental capacity dQ/dV obtained from electrochemical measurements [28] and in the Raman scattering spectra of Li_0.3MoS₂ [32, 33]. However, we do expect that the lithiation process is accompanied by the raising of the Fermi level due to the charge transfer from Li intercalation. This is depicted in Fig. 4.13, where the temperature dependence of the electrical conductivity of lithium intercalated MoS₂. Undoped MoS₂ is a n-type semiconductor with σ ~ exp(−E _a/k _B T), where E _a = 0.05 eV, and Li_0.3MoS₂ is a highly degenerate semiconductor with σ ~ T ^−1.4. Here, we must be aware of the limitations of the rigid band model. It is probably non appropriate for Li _x MoS₂ because the fully occupied d _z ² states in the pristine material imply new electrons to enter the next higher d band with a change of the c/a ratio associated with the destabilization of the host lattice.

Fig. 4.12

Li intercalation of MoS₂ in n-butyllithium. (a) After 10 min, defects are created near the edges and in the steps of the specimen denoted by arrows. (b) After 2 h intercalation, superlattice spots appear (denoted by the letter s), which are indexed as (1/201/20). Notice also the splitting of the main spots (denoted by the letter M). (c) A micrograph taken from the same area reveals that the specimen is heavily defected owing to intercalation. (d) Distribution of lithium vs. Distance from the edges of the specimen as revealed by SSNTD images. Reproduced with permission from [29]. Copyright 2002 Elsevier

Fig. 4.13

Temperature dependence of the electrical conductivity of lithium intercalated MoS₂. Reproduced with permission from [29]. Copyright 2002 Elsevier

Following the above structural transformation, phonon spectroscopy offers an excellent way of quantifying the degree of anisotropy not only by distinguishing between inter- and intra-layer normal modes but also by determining the shear moduli in different directions. The Raman spectrum of 2H-MoS₂ at room temperature is shown in Fig. 4.14. It exhibits four Raman-active bands that are the intra-layer A _1g mode at 407 cm⁻¹ involving motion along the c-axis, the intra-layer E _2g mode at 382 cm⁻¹ involving motion in the based plane, the E _1g mode at 286 cm⁻¹ and the rigid-layer (RL) mode at 32 cm⁻¹ of E _2g symmetry. This last mode is of interlayer type involving rigid motion of neighboring sandwiches in opposite phase.

Fig. 4.14

Raman spectra of 2H-MoS₂ natural crystal as a function of Li content lithium

The Raman spectra of Li _x MoS₂ with x ≈ 0.1 and x = 0.3 (Fig. 4.14) display the structural changes from the ß-phase (2H structure) to a α-phase (1T structure) upon Li intercalation [32]. This transformation from trigonal prismatic to octahedral coordination has been attributed to a process which is driven by a lowering of the electronic energy for the octahedral structure when electrons are donated from Li to the MoS₂ layer during intercalation [33]. The octahedral transformation in Li _x MoS₂ starts at x = 0.1 and completes around x = 1. For a degree of intercalation x ≈ 0.1, the Raman intensity is considerably reduced (by a factor 5) and we observe two new bands: a broad peak located at 153 cm⁻¹ (A-line) and a weak peak situated at 205 cm⁻¹ (B-line) and the intensity of the RL mode is reduced. The two pristine intra-layer modes can still be observed, with little shift in frequency, but both of them are split to give weak additional side bands towards lower energies (C- and D-line). These bands are attributed to the Davydov pairs of the optical phonon branches. For x = 0.3, the spectrum of Li _x MoS₂ is modified with respect to the former ones. The RL mode is no longer recorded. All the other lines are still observed. In addition, a small shift in frequency of the lattice modes of MoS₂ can be observed [33].

A simple model has been used to calculate the frequencies of the new modes appearing after Li intercalation. The intercalation mode is given by:

$$ {\omega}_{\mathrm{int}}\left(\mathrm{o}\right)={\left[k\left(2{m}_1+{m}_2\right)/{m}_1{m}_2\right]}^{1/2}, $$

(4.5)

where m ₁ and m ₂ are the masses of the MoS₂ molecule and of the Li atom, respectively, and k is the force constant between the S and Li atoms. We estimate k = 8.23 × 10³ dyn cm⁻¹, which is much smaller than the intra-layer force constants. For a degree of intercalation x = 0.3, we assume that Li _x MoS₂ is a two-phase system. The following changes on the lattice dynamics can be expected. The RL mode disappears because the elementary cell of the 1T-structure contains only one molecular unit (3 atoms per sandwich). The symmetry changes from D _6h to D _3d and the new symmetry allows only the two Raman active A _1g and E _g modes representative of the intra-layer atomic motions. The weak spacing expansion observed upon Li intercalation and the difference of the molybdenum coordination do not modify significantly the frequency of these modes. A simplest calculation gives a change of about 6 % in frequency. Thus, we can trust the validity of the lattice dynamics model using a 2H-structure [33]. Finally, it is obvious that Li intercalation into molybdenum disulfides does not satisfy the concept of rigid-band model.

4.7 Lithium Intercalation in WS₂

Among the TMDs materials, WS₂, which belongs to the group VIb transition metal , crystallizes into a layered structure identical to MoS₂. Two polytypes hexagonal (2H) and rhombohedral (3R) are commonly found among the materials with trigonal-prismatic coordination. Varieties of other polymorphic structures have been described such as o-WS₂ and 2M-WS₂ [34]. Orthorhombic ß-WS₂ (1T-structure) has been prepared by removing Na from Na _x WS₂ [35]. WS₂ is a grey-black indirect-gap semiconductor with a n-type character and an energy gap of 1.35 eV due to electronic transition of the d → d type. In terms of the two-dimensional WS₂ band structure direct low energy transitions at about 1.9–2.5 eV are characterized by A and B exciton pairs and its narrow d _z ² subband is completely filled. The conduction band based on d _x ² _−y ², d _xy orbitals is empty and can thus be populated by electron donors. The observation by Rüdorff [36] that WS₂ forms metal intercalated products when the dichalcogenide is treated with liquid ammonia solutions of alkali metals prompted us to examine more generally the features of electrochemically Li-intercalated WS₂. Somoano et al. [37] have also shown that intercalation compounds are found in the case of tungsten derivatives. Omloo and Jellinek [38] made an attempt to understand the unstability of WS₂ and WSe₂ intercalated by alkali metals and alkaline earths. The electrochemical features of the intercalation-deintercalation reaction of Li _x WS₂ is shown in Fig. 4.15a [39]. The voltage-composition curve displays features as follows: (a) the initial OCV of 3.0 V, (b) the emf decreases smoothly from 3.0 to 2.2 V in the range 0 ≤ x ≤ 0.2 and a break is clearly observed at about x = 0.2, (c) for x > 0.2 the discharge curve occurs with a pseudo-plateau at about 2.1 V, (d) the cell voltage drops to 0.5 V for x = 0.6 giving a specific energy density of 140 Wh kg⁻¹. The incremental capacity −(∂x/∂V) curve recorded at the first discharge (Fig. 4.15b) shows patterns comparable to a double-site energy system [40]. This should be the evidence of either increasing repulsive forces between inserted ions or formation of a new phase. During the insertion process the alkali metal transfers electron to the empty conduction band based on d _x ² _−y ², d _xy orbitals of W. Intercalation with electron donors is expected to populate these higher energy bands and give metallic properties. According to molecular-orbital calculations [25] with the d _z ² band already full and intercalation increasing the d band population from d ² to d ³, the electron energy can be lowered by a trigonal. Indeed, for the W layered compounds, the number of d electrons exceeds d ² during intercalation. The stability of intercalates of WS₂ is clearly related to the ionization potentials of the inserted metals and the affinity of the layer compound [38] and the prismatic coordination is destabilized on addition of lithium ions for x > 0.2. It was suggested that the result is a structural transformation from 3R-WS₂ to 2H-Li _x WS₂ due to the instabilities in the interlayer structure. Later in the discussion it will be demonstrated that upon Li⁺ insertion the interlayer spacing increases with a small expansion [41].

Fig. 4.15

(a) Discharge–charge curves of an electrochemical Li//WS₂ cell using the 3R-WS₂ polymorph as cathode material. (b) Incremental capacity dx/dV vs. composition

Figure 4.16a shows the absorbance spectra recorded at 5 K of pristine WS₂ and Li_0.1WS₂ samples in the energy range 1.4–2.5 eV. In these spectra, we observe absorption edge at 1.9 and 1.7 eV and side-band at 1.93 and 1.88 eV corresponding to the absorption edge and the excitonic peak of WS₂ and Li_0.1WS₂, respectively. The exciton transition at about 1.93 eV is attributed to the smallest direct gap at K (the zone-edge point in the (110) direction) in between the d _z ² valence states and the d _x ² _−y ², d _xy conduction states, split by interlayer interactions and spin-orbit coupling [42]. Upon Li intercalation, modifications in the absorption spectrum are observed, with a red shift of absoption edge and the vanishing of the exciton peak (located at E _ex on the curves) due to free carrier screening. In this process the free carriers arise from band filling above the full d _z ² band. For Li _x WS₂ the donated electrons should go into the empty conduction band based on the d _x ² _−y ², d _xy orbitals. The half width at half-maximum (HWHM) of the exciton of pure WS₂ at 5 K is about 20 meV, whereas one observes a HWHM of 55 meV for Li _x WS₂. The primary phenomenon associated with the lithium intercalation in WS₂ is the donation of x electrons from the guest to the host matrix. The second effect is that the interband absorption edge around 1.9 eV shifts to lower energies with Li insertion (Fig. 4.16b). This result can be understood in terms of a destabilization of the electronic band structure. The shift of the fundamental absorption edge toward lower energies can be attributed to an interaction between the conduction band made up of s and p orbitals and the 2s orbitals of lithium. Thus, the net effect is a decrease of the optical band gap of about 0.22 eV. Optical effects in Li-intercalated WS₂ can be satisfactory interpreted in terms of electron donation but the rigid-band model is essentially inadequate in such a compound. One may note that, in the studied energy range (1.4–2.5 eV), intercalation of Li ions did not give rise to extra absorption bands [42].

Fig. 4.16

(Left) The absorbance spectra recorded at 5 K of pure WS₂ and Li-intercalated WS₂ single crystal containing a small amount of lithium x = 0.1. (Right) Electronic band structure of trigonal prismatic dichalcogenide (i) pure WS₂ and (ii) Li_0.1WS₂

4.8 Lithium Intercalation in InSe

The intercalation of lithium in InSe has been extensively studied. Indium monoselenide is a layered semiconductor in which each layer consists of four close-packed, covalently bounded, monoatomic sheets in the sequence Se-In-In-Se. When material is grown by the Bridgman method, the 3R polytype (γ-InSe) crystallizes in a rhombohedral system with the R3m space group (C ⁵ _6v) with the primitive unit cell containing three layers but only one molecule [43, 44]. The layers are stacked in the sequence CBA□ABC separated by weak interlayer interaction (often referred to as van der Waals-like). The square symbol represents the empty site available for insertion. The interaction of cleaved InSe crystals with lithium was investigated by electrochemical titration, in situ X-ray diffractometry, and by X-ray photoemission spectroscopy showing a competition between intercalation and chemical decomposition reactions expressed as [45–47]:

$$ x\mathrm{L}\mathrm{i}+\mathrm{InSe}\to {\mathrm{Li}}_x\mathrm{InSe}, $$

(4.7)

$$ 2\mathrm{L}\mathrm{i}+\mathrm{InSe}\to {\mathrm{Li}}_2\mathrm{S}\mathrm{e}+{\mathrm{In}}^0. $$

(4.8)

The effect of Li insertion on the electronic structure of InSe has been evidenced by photoluminescence, Raman scattering, and absorption measurements [48, 49]. Upon lithium insertion, one observes different features in the optical spectra of Li _x InSe, which appear to be strongly dependent on the Li concentration. For x ≈ 0.1, a blue shift of the fundamental absorption threshold is due to the destabilization of both the highest valence band and the lowest conduction band. This is attributed to the (s, p _z) character of these energy states which interact with the lithium s-orbital. New broad bands appeared at 1.278 and 1.206 eV in the photoluminescence spectrum of Li_0.1InSe, which were attributed to transitions associated with the lattice deformations introduced by the expansion perpendicular to the basal plane and to those associated with the lithium donor levels, respectively [49].

Figure 4.17 displays the evolution of Raman spectra of Li _x InSe . The structural modification due to lithium insertion is clearly shown from these experiments. The vibrational feature of γ-InSe (C ⁵_3v symmetry) includes six Raman-active modes such as 3A ₁  + 3E [50]. The Raman spectrum displays a low-frequency band at 41 cm⁻¹ (E species), a strong band at 117 cm⁻¹ (A ₁ species), three bands located in the polar phonon domain at 177, 199, and 211 cm⁻¹ (LO and TO modes), and a nonpolar mode at 225 cm⁻¹ (A ₁ species). After intercalation (x≈0.2), the Raman spectrum is drastically modified. It displays vanishing bands of the pristine material and additional broad peaks centered at 95, 174 and 257 cm⁻¹. These bands, which are attributed to the presence of Li₂Se and amorphous Se in the host lattice, respectively, dominate the RS spectrum for x = 0.5. Here, the bending mode, ν(Se-Li-Se), appears at 174 cm⁻¹ in Li _x InSe. At this stage, the crystal is partially decomposed in the presence of Li producing Li₂Se, amorphous Se and In metal. At this stage, we explain these experimental data by the simple schematic band structure presented in Fig. 4.18. At relatively low lithium concentration (x ≈ 0.1), we assume the picture (Fig. 4.18a) where the principal electronic states are grouped into two categories (s, p _z ) and (p _x , p _y ). The electronic lithium-like s-orbital, which is located at the higher position energy into the conduction band, repulses the lower levels of same symmetry (Fig. 4.18b). The effect of Li intercalation on the interband optical transitions is rather weak but nevertheless clearly observable [52]. These results suggesting a decomposition process are in good accordance with the potential-composition curve (not shown) in which the plateau represents the Gibbs free energy ΔG _react = −140 kJ mol⁻¹ for the decomposition reaction of InSe by Li. This means for x > 0.1, a chemical decomposition of InSe occurs with two competitive reactions given by Eqs. (4.1) and (4.2).

Fig. 4.17

Raman scattering spectra of pristine and Li intercalated γ-InSe single crystal. The intercalated samples were prepared by galvanostatic method in lithium cell

Fig. 4.18

Schematic representation of the electronic band structure evolution of InSe upon Li insertion. (a) pristine material, (b) Li _x InSe for x ≤ 0.1, and (c) Li _x InSe for x ≥ 0.1 showing the chemical decomposition

4.9 Electrochemical Properties of TMCs

Figure 4.19 compares the discharge profile of prior nonaqueous rechargeable lithium batteries including lithium metal as anode, 1 mol L⁻¹ LiClO₂ in propylene carbonate (PC) as electrolyte and MX ₂ dichalcogenide as cathode. Such positive electrodes have several advantages: (1) they deliver high voltage, (2) water hydrogen is not liberated by electrolytic reduction, (3) materials exhibit high conductivity, and (4) these electrodes are insoluble in electrolyte solvents such as PC [51]. Note that PC cannot be used with graphitic carbon as negative electrode, but we consider in this chapter only half-cells, i.e., lithium metal is the negative electrode. The change of the cell voltage depends in general on the electronic states of the material. During the runaway, the voltage is also a function of the electrode composition x, which represents the fraction of electrons in the Li _x <H> host. Also, Li–Li interactions play a role in determining the magnitude of the voltage. It is therefore instructive to analyze the dependence of the voltage, V vs. x. Operating voltage of a solid-state redox reaction associated with lithium ions insertion or extraction usually exhibits subtle dependence on the concentration of lithium ions and electrons in a solid matrix, which does not follow the simple Nernst equation. Problems that have limited the usefulness of these batteries are associated to the dendritic growth which eventually generate short circuit between the negative and the positive electrodes.

Fig. 4.19

Discharge voltage curves of the Li intercalation reaction into several TMD frameworks

4.10 Concluding Remarks

In this chapter we have shown that intercalation is a heterogeneous process in layered materials. Consequently, the rigid-band model leaving the electronic band structure of the host mostly unchanged can only be rarely applied. The electronic band structure of transition-metal dichalcogenides of group IV with the octahedral coordination in their X-M-X sandwich is not really affected by the lithium intercalation. There are two main energy terms to be considered in relation to the stability of a given coordination structure. These are the lattice energy term on the one hand which is based on ionicity and the Coulomb interactions between ions (the Madelung energy), and the electronic band energy term on the other, which depends on the energy position of the filled bands, particularly that of the occupied d _z ² band (the lowest lying d sub-band of the d-band manifold).

The striking example is the reactivity of lithium with III-VI layered compounds such as the decomposition of Li intercalated InSe with the formation of lithium selenide, Li₂Se, observed by Raman spectroscopy on specimens prepared by various intercalation methods. The insertion of Li into MoS₂ appears more stable with the occurrence of a superlattice formation at x(Li) ≈ 0.25 but a structural transformation from 2H-MoS₂ (β-phase) to 1T-MoS₂ (α-phase) occurs for x ≈ 1. This process is irreversible but the intercalation-deintercalation reaction is possible with the 1T-MoS₂, which could act as a positive electrode in rechargeable lithium batteries after formation of the cells.