Lithium intercalation into TiS₂ cathode material: phase equilibria in a Li–TiS₂ system

Abstract

Lithium-intercalated titanium disulfide Li _x TiS₂ had been extensively studied as prototypical cathode material for high-energy-density reversible lithium batteries with moderate voltage. Today, this phase is one of the leading candidates for all-solid-state lithium batteries with durable high energy and high rate performance. However, fundamental knowledge of Li⁺ insertion into TiS₂ is still incomplete; available information on the phase diagram of the Li–TiS₂ system is limited by x = 1 due to difficulties in preparing lithium-rich equilibrated samples. The goals of this work were to re-examine Li _x TiS₂ single phase boundaries and to clarify the existence of lithium-rich intercalates with x > 1. А new preparation technique was developed to obtain 1T-Li _x TiS₂ samples as good-quality equilibrated products with desirable lithium content. Phase equilibria in a quasibinary Li–TiS₂ system were studied by X-ray diffraction, emf measurements (25 °C) and thermal analysis (25–350 °C) over a wide range of Li:Ti ratios (0 to 4).

Introduction

Layered dichalcogenides with the general formula MX₂ (M = transition metal, X = S, Se, Te) form a group of materials that can be intercalated with a wide range of both organic and inorganic materials without undergoing major structural modifications [1–3]. The intercalation reaction is driven by charge transfer from the intercalant to the host layered compound conduction band; thus, electron-donating species can take part in such a reaction. Lithium-intercalated dichalcogenides Li _x MX₂ have been extensively studied as cathode materials for high-energy-density reversible lithium batteries, and TiS₂ is the prototypical cathode material, demonstrating all of the desired characteristics except for overall cell voltage, 1.7–2.5 V [1, 4–7]. Exxon combined TiS₂ with a LiAl anode and an organic-based electrolyte to create safe, rechargeable cells in 1977–1979 [4, 5]. Today, transition-metal-based cathode materials such as LiCoO₂, LiNi _x Co _y Mn _z O₂, LiNi_0.53Co_0.3Al_0.17O₂, LiMn₂O₄ and LiFePO₄ are the most commonly used in commercial lithium-ion cells [4, 8–10]. Nevertheless, TiS₂-based systems having favourable intercalation kinetics and high energy density (which have still not been exceeded by systems such as LiCoO₂ and LiMn₂O₄ [5]) are currently considered attractive candidates for high-power lithium batteries. Recently, it was demonstrated that titanium disulfide is a particularly interesting cathode material in conjunction with a metallic lithium anode in all-solid-state cells [11–14] or with lithiated silicon anode in Li-ion cells comprising modified liquid electrolyte [15]. Moreover, TiS₂ was incorporated as a second active component in sulfur–carbon cathodes of Li–S cells; serving as active reaction sites during cycling, TiS₂ suppresses agglomeration of sulfur and facilitates better ionic/electronic transport within the cathode structure [16, 17]. In addition to their practical importance, the Li–TiS₂ system has attracted considerable attention from theorists because the TiS₂ host provides an important model for elucidating lithium diffusion mechanisms and the structural, elastic and electronic effects of lithium intercalation [18–25].

The goal of the present work was to investigate phase equilibria in the Li–TiS₂ system up to a Li:Ti ratio of 4 in order to re-examine Li _x TiS₂ single phase boundaries and to clarify the existence of lithium-rich phases with x > 1. Lithium-intercalated compounds Li _x TiS₂ were obtained by a new preparation technique based on direct reaction between Li metal and TiS₂ that does not set limits on the composition range. Because the structure of the titanium disulfide host remains essentially unchanged during lithium intercalation, X-ray data were combined with thermodynamic emf studies of phase equilibria. To evaluate thermal behaviour of the Li _x TiS₂ intercalates, DSC measurements were carried out over the range of 25–350 °C.

Lithium-intercalated titanium disulfide

Structure of titanium dichalcogenides TiX₂

Titanium disulfide, diselenide and ditelluride are isomorphous members of a group of compounds that crystallise in a characteristic 1T-CdI₂ layer structure (P$\overline{3}$ m1 space group) [1]. Their structures (Fig. 1(a)) consist of stacked composite layers, each layer comprising two sheets of hexagonally close-packed chalcogenium atoms sandwiching a sheet of metal atoms. Because the primary valency is saturated within the sandwich X–Ti–X structure, adjacent layers are held together only by relatively weak van der Waals forces. The sandwich layers therefore form extended sheets running through the lattice, forming a strongly anisotropic structure. Thus, the crystals are characterised by a platy habit, with extended growth and pronounced cleavage perpendicular to the trigonal c-axis [1, 23, 26–28]. When intercalation occurs, the intercalant Li enters the van der Waals gaps between the X–Ti–X layers. The system can then be considered to be more three-dimensional [29]. Because the transfer of charge (electrons) from the intercalant Li atoms to the host TiX₂ lattice occurs, the relatively weak van der Waals forces are replaced by stronger Coulomb interactions, and the lattice does not expand very much along the c direction normal to the layers.

Fig. 1

Structure of h-TiX₂ (X = S, Se, Te) (а) and sequential lithium filling of octahedral (b) and tetrahedral (с) sites in van der Waals gap

In Fig. 1(b, c), the three interstitial sites available for Li intercalation in the van der Waals gap are shown: one octahedral, which is surrounded by six chalcogen atoms, and two tetrahedrals, which lie in the projections below and above the chalcogen atoms [1, 28]. Thus, from structural considerations, the overall limiting value of intercalated lithium in the TiX₂ structure can reach x = 3.

Lithium intercalation into TiS₂

It is generally accepted that the reaction between lithium and titanium disulfide is the perfect intercalation reaction, with the reactant and product having the same structure over the entire range of the reaction, 0 ≤ x ≤ 1, in Li _x TiS₂ [1, 4, 5, 27, 30–36]. This single phase is characterised by only a 10 % expansion of the crystalline lattice along the c-axis (perpendicular to the basal plane) and approximately 1 % along the a-axis [27, 30, 34] which is typical for solid solutions. More recently, a single phase was not excluded for a wider range, at least, up to x = 1.24 [37]. In addition to the likely extension of this solid-solution region, the results regarding the charge–discharge profiles of Li/TiS₂ cells [38–40] make it possible to propose formation of a lithium-rich compound with x > 1. The range of 1 ≤ x ≤ 2, with a low-voltage plateau (near 0.5 V vs. Li/Li⁺) in the discharge profile, had been suggested to be a region where LiTiS₂ (accepted now as the end member of Li _x TiS₂ solid solution) and hypothetical stoichiometric Li₂TiS₂ coexist [38–41]. The intercalation process for the range 0 ≤ x ≤ 2 is reversible [38, 39, 41] while electrochemical intercalation up to x = 3 results in hysteresis [39]. It should be noted, however, that all attempts to prepare the lithium-rich Li₂TiS₂ phase to study its physical properties have been unsuccessful [38, 40]; the proposed XRD pattern of Li₂TiS₂ was obtained ex situ for electrochemically intercalated samples [38]. In contrast, Li _x TiS₂ solid solutions with 0 ≤ x ≤ 1 have been repeatedly synthesised and studied [1, 27, 34, 42, 43].

Thus, it is valid to say that despite numerous studies on lithium intercalation into TiS₂, the phase diagram of the Li–TiS₂ quasibinary system clearly requires further investigation. This is particularly true for Li:Ti ratios greater than 1, for which very poor previous information (mainly, charge–discharge profiles) is available. It seems that a key problem on this way is synthesis of lithium-rich intercalate samples.

Li _x TiS₂ preparation methods

Commonly used electrointercalation in Li/TiS₂ cells with a non-aqueous electrolyte [1, 22, 30, 44–46] inevitably yields a composite product, Li _x TiS₂, with a polymer binder, acetylene black, electrolyte, etc. Therefore, a number of chemical intercalation techniques using non-aqueous solutions of lithiating reagents have been proposed to prepare pure Li _x TiS₂ intercalate compounds with a preset Li:Ti ratio. One such technique is the treatment of parent TiS₂ with a solution of lithium in liquid ammonia at low temperatures followed by heat treatment at 250 °C in vacuo to remove NH₃ molecules inserted between the S–Ti–S layers [1, 42, 47, 48]. In addition to ammonia co-intercalation, this technique is characterised by obvious experimental difficulties. Therefore, the most frequently used chemical intercalation technique to date remains the immersion of TiS₂ powder in the appropriate amount of n-butyllithium solution in hexane (or other simple hydrocarbons) for a few days [1, 18, 31, 37, 47–54]. The procedure is carried out at ambient temperatures. After the filtration and washing of the solid with hexane, vacuum drying is used to remove residual solvent. It is a “clean” method: only lithium penetrates between the layers, the butyl radicals combining to yield n-octane, which is easily eliminated together with the solvent. It is worth noting, however, that this method allows the maximum possible reaction product of one lithium per titanium [34], i.e. only Li _x TiХ₂ with 0 < x ≤ 1, to be obtained in such a way. Only two pure intercalate samples with x greater than one, Li_1.24TiS₂ and Li_1.49TiS₂, have been reported in the literature [37]. A more vigorous preparation technique was used in this case; specifically, a lithium naphthalide solution in tetrahydrofuran was used as the Li source, and longer equilibration times were used during preparation (2 weeks).

The most common chemical intercalation technique using n-butyllithium solutions allows for good-quality Li _x TiS₂ products suitable for the measurement of physical properties to be obtained. However, such procedure without subsequent long-term heat treatment can yield inhomogeneous products due to the non-uniform distribution of intercalated Li. The direct intercalation path from the crystal surface through the X–Ti–X sandwich into the van der Waals gap is hindered by a high-energy barrier (3.81 eV for TiSe₂ [55, 56]). Therefore, the intercalation reaction occurs predominantly at the edge of the crystalline platelets, and the filling of the edges is faster than the propagation of the diffusion front into the solid [28, 53, 54, 56–58]. This leads to a bottleneck at the edges [58]. The blocking effect of intercalated lithium leads to the characteristic appearance of the Li concentration profile. This phenomenon was demonstrated by direct measurements of Li concentration profiles on titanium disulfide single crystals [54]. At room temperature, the homogenisation process is inhibited during the initial phase because the lattice has to be stretched along the stacking direction (c-axis) by the first lithium ions that enter. Therefore, it is necessary to homogenise the lithium distribution by heating the samples for a few days at elevated temperatures before studying the Li _x TiS₂ intercalate properties [58]. It is crucial to note that the majority of structure and physical properties investigations described in literature were performed on the Li _x TiS₂ samples not subjected to heating.

Another way to prepare Li _x TiS₂ intercalate compounds is solid-state reactions at elevated temperatures which provide equilibrated lithium distribution. As it was shown [38, 59], Li _x TiS₂ intercalates can be synthesised from Li₂S, Ti and S as starting materials. Reagents were mixed together and placed in a carbon-coated quartz tube that was then sealed under vacuum and heated at 750 °C for 3 days, cooled slowly to 250 °C and subsequently quenched in air. This procedure was repeated again after grinding and pressing the samples. Unfortunately, lithium-deficient product relative to the desirable intercalate composition was obtained: Li _z TiS₂ (z ≈ 0.8) instead of the set composition of LiTiS₂ [38]. When a stoichiometric mixture of the same starting materials in a sealed evacuated silica glass tube was heated at 800 °C for 2 weeks and then rapidly quenched to ambient temperature, the 3R-LiTiS₂ polymorph of LiTiS₂ was obtained instead of the 1T phase [60]. Compared to the 1T type, the 3R type shows a different stacking sequence of the sulfide layers, and the unit cell of the 3R phase is nearly three times that for the 1T phase [60, 61]. Solid-state reaction of TiS₂ with Li₂S and Ti powders at 500 to 900 °C in a sealed glass tube [61] or graphite ampoule under an argon atmosphere [62] leads to the same result: 3R-Li _x TiS₂, 1T-Li _x TiS₂ or their mixture was obtained depending on synthesis conditions and cooling rate. Samples prepared from Li₂CO₃ and TiS₂ under the same conditions (500–900 °C, argon atmosphere) showed similar phase compositions (3R-Li _x TiS₂, 1T-Li _x TiS₂ or their mixture) and the presence of some oxygen-containing impurity compounds [62]. It is evident from the above that solid-state synthesis at 500–900 °C makes it possible to obtain the metastable 3R-Li _x TiS₂ polymorph instead of the desired 1T-Li _x TiS₂ phase and does not guarantee a preset composition of the intercalate. Recently, ambient temperature and pressure solid-state mechanochemical lithiation technique was proposed to obtain nano-LiTiS₂ [11]; a stoichiometric mixture of TiS₂ and Li₃N was used as starting material. The resulting product had poor crystallinity.

All the studies cited above (except for [37]) suffer from the fact that lithium content in the synthesised Li _x TiS₂ intercalate samples does not exceed x = 1. Thus, an alternative preparation technique is clearly required to re-investigate the phase diagram of the Li–TiS₂ system. Such a technique must allow obtaining equilibrated samples with the desirable lithium content over a wide range of Li:Ti ratios without any limitations and exclude formation of metastable 3R-Li _x TiS₂ intercalates.

Experimental

The TiS₂ powder (both Aldrich (99.9 %) and home-made) and lithium metal (99.9 %, Novosibirsk Chemical Concentrates Plant) were used as starting materials for the synthesis of the lithium intercalate samples with Li:Ti ratio 0.05 to 4. Before use, lithium metal was subjected to additional purification from its degradation products by refusion. Home-made polycrystalline TiS₂ was prepared from the elements titanium (after iodine purification, 99.96 %) and sulfur (OSCh 16-5, 99.999 %) (Petersburg Krasnij Khymik Plant). The appropriated amounts of titanium and sulfur with a small excess (~3 wt%) of the latter were sintered at a temperature of 800 °C for 10–12 days in a sealed quartz ampoule evacuated down to 10⁻⁵ Torr. Then, the ampoule was cooled, transferred into a glove box with inert argon atmosphere and opened. The charge was ground into powder, pressed, placed into a quartz ampoule together with the same excess of sulfur (for homogenising and saturation by chalcogen), evacuated down to 10⁻⁵ Torr and annealed again for 10–12 days at 600 °C. After cooling, the ampoule was opened within the glove box and the charge was ground into powder. The homogeneity and a phase uniformity of the resulting product TiS₂ were tested by X-ray analysis (ICDD-ICPDS card no. 15-853). The concentration of excess titanium in the TiS₂ product thus obtained was estimated as 1 %. Online Resource 1 illustrates TiS₂ structure and morphology for home-made and Aldrich products (Figs. A1 and A2, respectively).

X-ray patterns of starting titanium disulfide and their lithium-intercalated products were obtained using Rigaku D-MAX-2200V diffractometer with a vertical goniometer (Cu Kα ₁ radiation, 2θ = 5–90°). The powdered samples were placed into a sample holder of the diffractometer which was sealed with 15 μm Al foil or 30 μm Kapton tape to insulate air-sensitive samples; the foil or tape was tightly glued using two-sided scotch tape along the perimeter of the cell. The cells for XRD measurements were assembled under an argon atmosphere within a UNILAB MBRAUN glove box. The lattice parameters of TiS₂ and lithium-intercalated products Li _x TiS₂ were determined using FPEAK and/or ASTM software.

To control the lithium content in the lithium-intercalated products Li _x TiS₂, quadrupole mass spectrometer ELAN 9000 (PerkinElmer SCIEX) was used. The ionisation is carried out by means of micro-wave plasma. The plasma jet is fed with fine aerosol of sample solution. Fine aerosol was obtained by pneumatic dispersion of the solution and subsequent separation of the raw aerosol in a temperature-stabilised Scott chamber. Sample solutions for ICP/MS analysis were obtained by dissolution of ~15 mg of Li _x TiS₂ powder in 50 ml of HCl/HNO₃/HF = 0.5:1:1 (vol.) mixture of 0.1 M acids followed by dilution with bidistilled water by 20 times. The relative error of the x value determination by ICP/MS analysis was about 1–2 %.

The morphology of the starting TiS₂ powders and Li _x TiS₂ samples was observed using a 3 LMU (Tescan) scanning electron microscope.

Thermal behaviour of the Li _x TiS₂ intercalates was studied by differential scanning calorimetry (DSC 204 F1 Phoenix, NETZSCH). For DSC measurements, the powder Li _x TiS₂ samples were placed and compacted into high-pressure stainless steel crucibles; then, the crucible was thoroughly screwed by the lid with gold seals. The manipulations were carried out in a dry argon atmosphere UNILAB MBRAUN box. The DSC measurements were performed in the temperature range from 25 to 350 at a heating rate of 10 °C/min and subsequent cooling in the same temperature range; the sample cell was purged with argon at a rate of 30 ml/min. The measurements for each sample were repeated at least three times. The data obtained were processed using the NETZSCH Proteus software.

The open-circuit voltage for lithium-intercalated samples with nominal composition of Li _x TiS₂ was measured at 25 °C in hermetically sealed two-probe test cells Li│SPE│Li _x TiS₂. Solid polymer electrolyte (SPE) used was elastomeric random copolymer of butadiene and acrylonitrile (PBAN), 60 and 40 wt% of each monomer, respectively, containing LiClO₄ [63]. The SPE conductivity at room temperature was about 10⁻³ Sm cm⁻¹. The Li _x TiS₂ electrodes were prepared by pressing powdered samples into a Ni grid (current collector). The area of the cathode/electrolyte interface used in the cells was about 0.5 cm². The anode was the freshly scraped 1-cm-diameter lithium disc with 1 mm thickness pressed into the Ni grid. For contact improvement in the electrode/electrolyte interfaces, the assembled cells were subjected to short-term heating up to 45 °C (30 min) and then were stored at 25 °C for several days for equilibration before emf measurements. All sample preparation procedures and assembling of test cells were carried out within the dry box. A V7-34A voltmeter and P-8S Elins potentiostate with large internal resistance were used for emf measurements.

Results and discussion

The ampoule synthesis of intercalate compounds

A novel preparation technique was developed in the present work to obtain lithium-intercalated disulfide samples at a Li:Ti ratio of up to 4. To get the best results, two different preparation schemes were applied.

TiS₂ powder and Li metal were used as starting materials to synthesise samples with integer values of x (1, 2 and 3) as well as samples with Li:Ti ratios exceeding 3 (see Table 1). The precise stoichiometric amounts of the starting materials were placed in a BeO crucible (inert in respect of lithium) such that lithium metal granules measuring approximately 0.3–0.5 cm in diameter were uniformly distributed in a disulfide powder; the reaction mixture was then manually compacted to improve the contact between reagents. The BeO crucible with the reaction mixture was then placed in a Pyrex ampoule, which was evacuated to 10⁻⁵ Torr and sealed. The regime of the following thermal treatment for each reaction mixture is presented in Table 1 for stage 1. After the first stage of annealing (when Li metal was fully transformed), the ampoules were cooled, transferred into a glove box with an inert argon atmosphere and opened. The charges were ground into powder for homogenisation, pressed into pellets and placed into Pyrex ampoules, evacuated to 10⁻⁵ Torr, and annealed again at the same temperatures (Table 1, stage 2). The stage 2 operations were repeated until the diffractogram of the product stopped changing; the overall durations of the thermal treatment are presented in Table 1.

Table 1 Synthesis conditions and resulting lithium content for Li _x TiS₂ intercalate samples with integer-valued Li:Ti ratios and Li:Ti > 3 (scheme 1)

Since we have proposed here a novel preparation technique for the Li _x TiS₂ intercalates, it is of interest to consider a sequence of chemical reactions, occurring in the reaction mixture during thermal treatment. An example of changes in XRD patterns during thermal treatment is shown in Fig. 2(a, b) for reaction mixture of Li metal and TiS₂ with a Li:Ti ratio of 3. The resulting chemical processes may be schematically summarised as follows:

$$ x\mathrm{L}\mathrm{i}+\frac{x}{4}{\mathrm{TiS}}_2=\frac{x}{2}{\mathrm{Li}}_2\mathrm{S}+\frac{x}{4}\mathrm{T}\mathrm{i}; $$

(1)

$$ \frac{x}{2}{\mathrm{Li}}_2\mathrm{S}+\left(1-\frac{x}{4}\right){\mathrm{TiS}}_2+\frac{x}{4}\mathrm{T}\mathrm{i}={\mathrm{Li}}_x{\mathrm{TiS}}_2. $$

(2)

Fig. 2

XRD patterns for the reaction mixture of Li metal and TiS₂ with different Li:Ti ratios after annealing at 235 °C: a thermal treatment for 28 days (intermediates for Li:Ti = 3); b thermal treatment for 42 days (Li_3 − δTiS₂ as a final product); c thermal treatment for 42 days (equilibrium products for Li:Ti = 3.4); d thermal treatment for 49 days (nearly equilibrium products for Li:Ti = 4). The dashed grey bar at the abscissa indicates the reflections from the sample holder sealed with Al foil

Equation (1) describes the reaction which is the main content of stage 1 of the synthesis process while Eq. (2) relates to the interaction which proceeds mainly during stage 2. Intermediates in such a way are Li₂S and h-Ti metal (incorporation of excess titanium into the van der Waals gap of TiS₂ also cannot be excluded). It is easy to see that stage 2 is chemically identical to the process used in some solid-state preparation techniques [38, 59–62] described above in Section “Li_xTiS₂ preparation methods” but occurs at a much lower temperature due to fine h-Ti intermediate (for this reason, h-Ti peaks are hardly distinguishable in XRD patterns; see Fig. 2(a)) or excess Ti in Ti_1 + y S₂.

Because the sample preparation technique employed can influence the experimental results (as it was shown in Section “Li_xTiS₂ preparation methods”), it is necessary to specify some of the details of the thermal treatments. A muffle furnace with a uniform distribution of temperature along vertically placed ampoules was used to prevent a violation of stoichiometry due to the deposition of chalcogen vapour on the cooler end of the ampoules. After each thermal treatment was completed, the ampoules were slowly cooled together with the muffle furnace to room temperature to prevent the quenching of the high-temperature phases. In all cases, any deposits on the ampoule walls or their turbidity due to chemical interactions with lithium vapour were absent. Therefore, it was reasonable to propose that the resulting product composition was similar to the preset value. To be confident in the composition for the intercalates obtained, the lithium content for samples with nominal compositions of LiTiS₂, Li₂TiS₂ and Li₃TiS₂ was analysed by ICP/MS, as described in Section “Experimental”. The results are presented in Table 1. One can see that the uncertainty in composition associated with ampoule synthesis was approximately 1–7 %.

Li _x TiS₂ intercalates with fractional х values less than 3 were synthesised as follows. Powdered TiS₂ and synthesised products with nominal compositions of LiTiS₂, Li₂TiS₂ and Li₃TiS₂ were used as starting materials (Table 2) to minimise the error in the preset x values, which is extremely important if taking into account a small increment in the lithium composition Δх = 0.05–0.20. Stoichiometric amounts of the reagents were homogenised, pressed into pellets, placed into Pyrex ampoules, evacuated to 10⁻⁵ Torr and then annealed at 235 °C (Table 2). These operations were repeated until the diffractograms of the products stopped changing.

Table 2 Synthesis conditions for intercalates with nominal composition of Li _x TiS₂ and fractional x values less than 3 (scheme 2)

After completing the synthesis, all lithium-intercalated products were stored in an argon glove box for 0.5–1 year at room temperature for equilibration.

Phase composition of lithium-intercalated products

XRD patterns of the samples with Li:Ti ratio 0 to 3 are shown in Fig. 3. The formation of 1T phase with a nominal composition of Li _x TiS₂ without any impurities of the starting materials or foreign phases (including 3R-Li _x TiS₂) was observed for all samples with x < 3. The sample with nominal composition of Li₃TiS₂ contained trace amounts of Li₂S, and the result was reproduced on repeated syntheses irrespective of the starting TiS₂, Aldrich or home-made. For samples with higher lithium contents (Li:Ti > 3), titanium metal and Li₂S were found together with Li _x TiS₂ phase, and the intensity of the Ti and Li₂S peaks increased with the Li:Ti ratio (Fig. 2(c, d)). It is reasonable to conclude that the limiting intercalated lithium content in the TiS₂ structure can be really close to the expected value of x = 3 (see Section “Structure of titanium dichalcogenides TiX₂ ”). Intercalated lithium content in this sample may be expressed as x = 3 − δ, with δ < 0.2 taking into account Δx value (see Table 2). For the sample with Li:Ti = 4 (for which XRD patterns did not stop to change for the time of the thermal treatment and, therefore, which failed to reach the equilibrium state), the lithium-intercalated phase tended to disappear (Fig. 2(d)). Because of this, Ti and Li₂S must be equilibrium products; this conclusion is consistent with thermodynamic estimations of stable two-phase lines in isothermal ternary cross section of the Li–Ti–S system [37].

Fig. 3

XRD patterns for TiS₂ and lithium-intercalated disulfide samples with varied Li:Ti ratios (indicated on the left). The dashed grey bar at the abscissa indicates the reflections from the sample holder sealed with Al foil

XRD data (Fig. 3) indicate the minor changes of the Li _x TiS₂ diffraction profiles with lithium content over the entire range of the lithium intercalation, 0 ≤ x ≤ 3. Figure 4 gives the details of the variation of (001) Bragg peak (one of the most sensitive to c-axis expansion) as a function of Li content. One can see that the magnitudes of the shifts in the peak positions that occur upon intercalation are very small and become zero at x ≥ 1; no noticeable splitting of the (001) peak is observed over the whole concentration range 0.05 ≤ x ≤ 3.0. Because the structure of the TiS₂ host remains essentially unchanged during lithium intercalation, the distinction between coexisting intercalate phases within two-phase regions (if this is the case) can hardly be detected by XRD. Therefore, XRD alone is not an appropriate tool to establish the exact phase composition of the intercalate samples with a nominal Li _x TiS₂ composition, i.e. for x ≤ 3. Consequently, thermodynamics studies have to be performed as a more precise tool in the investigation of phase equilibria in this very specific Li–TiS₂ system. In the present work, emf data were used to construct the phase diagram.

Fig. 4

Variation of (001) Bragg peak as a function of x in Li _x TiS₂

Emf measurements

The emf technique is known to be an excellent tool of solid-state chemistry that allows for direct measurements of the thermodynamic parameters of the intercalation process [1, 25, 64–67]. For studies of lithium intercalation into titanium disulfide host, a simple reversible two-electrode test cell Li│electrolyte│Li _x TiS₂can be used, in which the negative electrode (lithium metal), which exhibits a constant voltage, also serves as a reference electrode. The equilibrium voltage difference between the two electrodes separated by a Li⁺-conducting electrolyte in an open-circuit is the electromotive force of the cell, V(x). At a fixed temperature, emf is a function of lithium content x in a chemically formed intercalate with a nominal composition of Li _x TiS₂ and depends on the difference in the Li chemical potential between the anode and cathode according to the Nernst equation [6, 25, 65]:

$$ V(x)=-\frac{\mu_{\mathrm{Li}}^{\mathrm{cathode}}(x)-{\mu}_{\mathrm{Li}}^{\mathrm{anode}}}{zF}=-\frac{\varDelta \overline{G}(x)}{zF}. $$

(3)

μ ^cathode_Li (x) is the Li chemical potential in Li _x TiS₂, μ ^anode_Li is the Li chemical potential in the lithium metal anode, F is the Faraday constant and z = 1 is the charge (in electrons) transported by lithium in the electrolyte. It is clear that the cell emf under isothermal and isobaric conditions is defined by the lithium chemical potential in a Li _x TiS₂ sample only. The value of V(x) at a given temperature measures the change in the molar Gibbs free energy of intercalation $\varDelta \overline{G}(x)$ in the reversible reaction

$$ x\mathrm{L}\mathrm{i}+{\mathrm{TiS}}_2={\mathrm{Li}}_x{\mathrm{TiS}}_2. $$

(4)

Therefore, the composition dependence of emf provides direct thermodynamic information about phase equilibria in the Li–TiS₂ system. As Li is intercalated, its chemical potential in the cathode increases, leading to a decrease in the cell voltage. The continuous decrease in emf with increasing x is characteristic of a single-phase system and indicates solid-solution behaviour. Coexisting phase regions (first-order phase transformation) appear as plateaus in emf vs. x plots because the chemical potential of Li in coexisting phases is equal. Second-order phase transitions that do not involve two-phase domains can even be detected, as they lead to changes in the slope of the voltage curve [1, 25, 64, 65, 67–70].

The critical issues encountered in emf investigations are as follows. It is necessary to prevent any foreign chemical processes from occurring on the electrode/electrolyte interfaces to eliminate any “parasitic” contribution to the measured open-circuit voltage (OCV) value. Thus, a solvent-free Li⁺-conducting solid polymer electrolyte [63] chemically stable in contact with lithium metal was used in our experiments. Emf measurements were carried out under isothermal conditions (25 °C) for long durations (up to 1–3 days) until the cell OCV stopped changing; the final value was accepted as the emf. To verify the reproducibility of the emf results, a series of electrochemical cells (from 2 to 6) was assembled for each Li _x TiS₂ intercalate sample. Moreover, a repeat synthesis with different TiS₂ hosts, Aldrich and home-made, was performed for some samples (Li _x TiS₂ with x = 1 and 3) to verify the reproducibility of the results. To test the results obtained for equilibrium, cell OCV measurements were carried out at 25 °C as described above before and after thermal treatment at 50–95 °C. Finally, it should be particularly emphasised that the intercalated samples under investigation were prepared such that the equilibrium lithium distribution was guaranteed.

The emf vs. х dependencies for intercalates with nominal compositions of Li _x TiS₂ (0 ≤ x ≤ 3) as well as for three-phase samples with Li:Ti > 3 are shown in Fig. 5(a), where all emf values obtained are presented. One can see that the reproducibility of the emf measurements is rather good in spite of the different starting TiS₂ for Li _x TiS₂ synthesis, home-made or Aldrich. Therefore, we can conclude that the careful control described above made it possible to obtain thermodynamic emf results that truly characterise phase equilibria in the Li–TiS₂ system.

Fig. 5

Concentration dependencies of emf (a) and lattice parameters c (b) and a (c) for lithium-intercalated titanium disulfide at 25 °C. 1—emf concentration dependence obtained in this work; 2—discharge profile of Li/TiS₂ cell at room temperature [39]. Lattice parameters are shown for sample series prepared from TiS₂ (Aldrich). The solid bar at the abscissa indicates the intercalation limit of x = 3 for Li _x TiS₂; the shaded areas correspond to solid-solution regions

Phase equilibria in the Li–TiS₂ system

The emf vs. x dependence for the Li–TiS₂ system at 25 °C (Fig. 5(a)) can clearly be divided into five different regions that reflect changes in phase composition with lithium content. Regions I (0 ≤ х ≤ 0.30) and III (0.80 ≤ х ≤ 1.4), where a decrease in emf is observed must be attributed to solid-solution behaviour. Region II (between x = 0.30 and x = 0.80), with a constant emf of approximately 2.30 V, can be associated with two-phase system behaviour corresponding to the coexistence of the end members of these two solid-solution series. The voltage plateau at ~1.95 V between x = 1.4 and x = 3.0 (region IV) is indicative of the coexistence of two phases as well and suggests the formation of a lithium-rich intercalated compound with nominal composition of Li₃TiS₂. The existence of the Li₂TiS₂ phase proposed previously [38–41] lacks support from the emf vs.x dependence obtained in our work. When the Li:Ti ratio exceeds the proposed upper lithium intercalation limit of 3, a sharp decrease in emf is observed within three-phase region V, composed of lithium-rich Li₃TiS₂ phase, Li₂S and Ti metal.

Figure 5(b, c) shows the variation in the lattice parameters a and c as a function of x for the lithium intercalation range 0 ≤ x ≤ 3 together with the emf (Fig. 5(a)). The characteristics of the a and c dependencies agree with the emf results, but it is easily observed that the lattice parameters alone do not provide reliable information on phase equilibria in the Li–TiS₂ system due to the small amplitude of the structure changes (see also Fig. 4).

Li _x TiS₂ single phase within the 0 ≤ х ≤ 0.30 range is clearly based on the parent TiS₂ structure. Lithium intercalation is accompanied by a linear increase in the c lattice parameter but does not cause any changes in a (Fig. 5(b, c)). Such behaviour is known to be caused by preferential Li insertion into the octahedral sites of the van der Waals gap, which follows from NMR and neutron diffraction results as well as theoretical calculations [18, 25, 31, 34, 71]. The characteristic feature of single-phase Li _x TiS₂ within the range 0 ≤ х ≤ 0.30 is the abrupt change in the slope of the emf vs. x curve in the vicinity of x = 0.10 (Fig. 5(a)), which may be indicative of a second-order phase transition.

The next solid-solution range extending from x = 0.80 to 1.4 can be regarded as a continuous, homogeneous region of LiTiS₂ phase. For x = 1, all octahedral sites must be occupied, but a small percentage of Li ions might reside in tetrahedral sites also [34, 36]. The intercalation energy was established to be larger at the octahedral positions than at the tetrahedral ones, but the difference between the two positions decreases as x increases [18]; therefore, tetrahedral sites become energetically attractive as well. Because there is only one octahedral site for Li per TiS₂ unit, tetrahedral positions have to be populated for 1 < x ≤ 1.4 as well. As shown in Fig. 5(b), the c parameter stops changing and a plateau is observed when all octahedral sites become filled at x = 1. Thus, the partial filling of tetrahedral sites does not cause any increase in the c lattice parameter, whereas the a parameter appears to be sensitive to lithium insertion into tetrahedral sites and increases with x, although very slightly (~1 %, Fig. 5(c)). An increase in the a parameter within continuous LiTiS₂-based solid-solution range (region III) results from Coulomb repulsion between ionised Li atoms intercalated into TiX₂ crystal lattice [47, 72]. Since Δa is very small, it is reasonable to propose that the effect of Coulomb repulsion is small. An increase in the value of a within two-phase region IV, between x = 1.4 and x = 3 (Fig. 5(c)), must be attributed to the poor resolution of reflections from LiTiS₂-based solid solutions (see Fig. 3).

In a stoichiometric phase of Li₃TiS₂, both octahedral and tetrahedral sites in the van der Waals gap of the host TiS₂ lattice would have been fully occupied by lithium. Since Li₂S traces were detected for all XRD patterns of the samples with the nominal composition of Li₃TiS₂ at repeated syntheses (see Figs. 2(b) and 6), we had proposed that the real lithium content in this phase corresponds to 3 − δ (as discussed in Section “Phase composition of lithium-intercalated products”). This result seems to be quite reasonable, because the more completed the octa- and tetrahedral sites are, the more difficult it becomes for lithium to intercalate into the compound structure. Therefore, Li₃TiS₂ corresponds to the limiting phase composition, which is unlikely to be achieved in a real synthesis procedure. The filling of two tetrahedral sites after octahedral ones does not cause any increase in the c lattice parameter relative to that measured for LiTiS₂ (Fig. 5(b)), whereas the a lattice parameter increases by 1.4 % and reaches its maximum at x = 3 (Fig. 5(c)). More detailed characterisation of synthesised samples with nominal composition of Li₃TiS₂ is given in Online Resource 2. In order to establish real lithium content and Li atom distribution in the structure of this new Li-rich phase obtained for the first time, high-resolution neutron diffraction measurements are obviously needed. This will be done soon and described in a forthcoming paper.

Fig. 6

XRD pattern of sample with nominal composition of Li₃TiS₂ prepared from home-made TiS₂

It is appropriate to correlate the composition dependencies of the emf and lattice parameters obtained in the present work with other data sets available from the literature and also presented in Fig. 5. In making this comparison, it should be recalled following sample preparation features. Firstly, home-made TiS₂ powders with distinct deviations from stoichiometry were used as starting materials in all cited works; secondly, different sample preparation techniques were applied to obtain Li _x TiS₂ products. Therefore, the discrepancy in the lattice parameters of Li _x TiS₂ (Fig. 5(b, c)) seems to be inevitable. The discrepancy in the emf values also is not surprising since they are very sensitive to lithium distribution. All literature data (Fig. 5(a)) were collected from samples lithiated chemically using n-butyllithium near room temperature without annealing [1, 27, 31, 34, 37, 43] or electrochemically [22, 30]. An inhomogeneous lithium distribution in samples thus obtained was particularly noted by Dahn et al. [34] and Hibma [72] and more recently discussed in detail by Winter and Heitjans [58] and Schwarzburger et al. [54]. Our results, in contrast, were obtained from equilibrated Li _x TiS₂ samples. It is worth noting, however, that the emf values within the first solid-solution range (0 ≤ x ≤ 0.3) are nearly identical despite the differences in the preparation technique employed. Moreover, this part of emf vs. x dependence is almost identical to the corresponding part of the discharge curve on lithium insertion into TiS₂ [39] (Fig. 5(a), curve 2). This observation may be attributed to the lack of first-order phase changes over 0 ≤ x ≤ 0.3 composition range and therefore the fast homogenisation of the lithium distribution and equilibration of such samples irrespective of the Li _x TiS₂ preparation technique. In contrast, a more complicated non-equilibrium phase composition must be proposed for all samples prepared chemically with a higher lithium content of 0.3 < x ≤ 1.49 (Fig. 5). One can readily see from Fig. 5(a) that the published emf values for intercalates with a nominal stoichiometry of LiTiS₂ [1, 27, 37] are very similar to those of the hypothetical phase Li_3 − δTiS₂ obtained in our work. This result seems to be quite reasonable because Li_3 − δTiS₂ may be precisely the phase responsible for the “blocking effect” (see Section “Li_xTiS₂ preparation methods”) under lithium-rich conditions due to deficiency of lithium vacancies available for Li motion in its structure.

Phase boundaries in the Li–TiS₂ system is one more subject to be discussed in relation to information available in the literature for a nominal stoichiometry of 0 ≤ x ≤ 1. It must be noted that the limits of the two solid-solution series established in our work agree with the profile of the composition dependence of magnetic susceptibility obtained for chemically lithiated and annealed (250 °C) Li _x TiS₂ samples for x ranging from 0 to 1 [42]. The correlation between several phase regions existing in Li _x TiS₂ and changes in the degree of lithium ionisation is also worth noting. It was established that the ionisation of the first Li atoms entering the TiS₂ host is essentially complete due to the donation of Li-conducting electrons to the lattice, while above x = 0.80, electron transfer from Li to TiS₂ is not complete, with 10–20 % of the valence electron density remaining in the vicinity of the lithium atoms in LiTiS₂ [20, 24, 31, 32, 36, 42, 71]. Finally, two series of Li _x TiS₂ solid solutions definitely differ in their ability to exist as 3R-polymorph. So, TiS₂-based solid solutions (0 ≤ x ≤ 0.3) correspond to composition range where formation of 3R-Li _x TiS₂ was not observed at high-temperature solid-state synthesis, and all diffraction peaks were well indexed to the 1T structure [61]. It is interesting that electrochemical delithiation of 3R-LiTiS₂ resulted in a non-reversible transformation to the 1T phase at x ≤ 0.4 [62]. It is likely, therefore, that the 3R phase is a polymorph of the LiTiS₂-based solid solutions only (0.80 ≤ х ≤ 1.4).

The correlation between phase boundaries established in the present work and the results obtained by the incremental capacity technique [30, 44, 45] also merits discussion. A principal feature of this peculiar data collection scheme proposed by Thompson [44, 45] is that both kinetic and thermodynamic data can be collected during the same measurement. Although the voltage vs. composition curves for Li/Li _x TiS₂ cells [30, 44, 45] are not identical to our thermodynamic emf results, the peaks in the −Δx/ΔV vs. x dependencies at x = 1/9, 1/4 and 6/7 are very similar to our phase boundary values. The reason for such correlation is still unclear, taking into account the inevitable effect of kinetics during incremental capacity measurements. The peaks at these fractional compositions are usually interpreted by assuming that ordered superlattices exist for the Li ions and vacancies [30, 44, 45]; lattice-gas theory was used to justify this assumption. It is possible that superlattice formation is actually the cause of the first- and second-order phase transitions in Li _x TiS₂ intercalates, but a more detailed study is beyond the scope of this work.

Li–Ti–S isothermal ternary section

New results regarding phase equilibria in the quasibinary Li–TiS₂ system at 25 °C allow for the clarification of the isothermal ternary section Li–Ti–S proposed previously by Johnson and Worrell [37]. The resulting fragment of the Li–Ti–S isothermal section is presented in Fig. 7; the data concerning phase equilibria in constituent binary systems [73–75] were also taken into account. The Li–Ti–S diagram indicates that for Li:Ti ratios greater than 3, there is three-phase region composed of Li₂S, titanium metal and Li_3 − δTiS₂. For Li:Ti = 4:1, two-phase equilibrium between Li₂S and titanium metal was established. A further increase in the Li:Ti ratio results in three-phase equilibrium between Li₂S, titanium metal and lithium metal.

Fig. 7

Fragment of the isothermal section of the Li–Ti–S ternary system at 25 °C

Thermal behaviour of the Li _x TiS₂ intercalates

To investigate thermal stability of lithium-intercalated compounds, single-phase samples from different regions of the phase diagram (Fig. 7) were selected: Li_0.15TiS₂, Li_0.25TiS₂, LiTiS₂ and the sample with nominal composition of Li₃TiS₂. DSC curves for all samples are presented in Fig. 8. It can be seen that the DSC curves do not demonstrate any effects associated with phase transitions. These data were well reproduced in repeated measurements. It is evident from the results that all intercalates studied are thermally stable in the temperature range of 25–350 °C. This is true for both TiS₂-based (0 ≤ x ≤ 0.3) and LiTiS₂-based (0.8 ≤ x ≤ 1.4) solid solutions as well as for hypothetical lithium-rich Li_3 − δTiS₂ compound. A small deviation of the DSC curves above 240–300 °C may be caused by disturbance of the stoichiometry of the host lattice due to intensive reversible vaporisation of sulfur [76]. Therefore, we ought to propose authenticity of the isothermal section of the phase diagram of the ternary system Li–Ti–S, which is shown in Fig. 7 for 25 up to 350 °C.

Fig. 8

DSC curves of the Li _х TiS₂ samples measured in hermetically sealed high-pressure stainless steel crucibles

Conclusion

A novel preparation technique based on direct reaction between Li metal and TiS₂ allowed obtaining a good-quality equilibrated product with a desirable lithium content over a wide range of Li:Ti ratios (0 to 4). This technique made it possible to overcome the limit of х~1.5 previously reached for pure Li _x TiS₂ compounds and to get for the first time a lithium-rich phase with proposed composition of Li_3 − δTiS₂. The results of re-investigations of phase equilibria in the quasibinary Li–TiS₂ system provide grounds to revise the current accepted view of the single-phase Li _x TiS₂ over the entire composition range of 0 ≤ x ≤ 1 where two series of solid solutions were found.