In this paper, we show how the thermoelectric properties can be modified in crystallographic structures based on the CdI2 type layer, by changing the block layers between these CdI2 type layers or by going from oxides to selenides and sulfides. In the case of oxides, the unique properties generated in these structures will be demonstrated in Bi-based misfit compounds. By combining Hall effect, resistivity, and Seebeck coefficients in single crystals of this family, the importance of doping and of spin and orbital degeneracy term on the Seebeck coefficient will be shown. From this single crystal investigation, the power factor at 300 K is found to be unexpectedly constant as a function of doping. To further enhance the power factor and thus ZT, it is necessary to modify either the block layer or to perform anionic substitutions. By going from oxides to selenides and sulfides, the decrease of the ionic character can induce a decrease of electrical resistivity. Compared to oxides, the properties can generally be described in a more classical way using Boltzmann transport theory. For these materials, the critical parameter is then thermal conductivity and this quantity can be decreased as shown here by intercalating Cu between the layers (CuxTiS2), or by making solid solution such as TiS2 − xSex. These two approaches will be described here, leading to ZT close to 0.5 and 0.4, at 800 and 700 K, respectively.
Since 1997 and the discovery of a large thermopower in the metallic NaxCoO21, the search for new thermoelectric oxides has been very active. Moreover, the complex properties of these layered cobaltates, with Co sitting on a triangular lattice, have stimulated many theoretical studies to better understand the electronic properties and their link to the band structure 2, the Co valence and spin states, the spin and orbital degeneracy 3, the electronic correlations and the triangular lattice 4. Layered cobaltates containing CdI2-type layers, made of edge shared CoO6 octahedra, are very interesting materials in the strongly correlated electron systems from both physical and technological points of view.
The original properties of these layered cobaltates can be found as well in the misfit family 5, 6. The difference between NaxCoO2 and the misfit layered cobaltate is the separating block layer: a randomly filled layer of Na+ in the case of NaxCoO2, and a rock-salt type layer in misfits, with 2, 3, or 4 separating layers. One important point in this family is that the thermopower can be described by models typically used for localized carriers, such as the generalized Heikes formula 7, 8, while the resistivity presents a metallic behavior.
To understand in more details this discrepancy, we have investigated the transport properties of single crystals belonging to the 4 rock-salt layers, a family which can be described as (A = Ca, Sr, Ba), with the misfit ratio b1/b2 varying between 1.69 and 1.98. b1/b2 is the ratio between the two b parameters of the monoclinic lattices of the rock-salt type and of the CoO2 layers. By combining resistivity, thermopower and Hall effect experiments in these single crystals, we probe here the carrier density influence on the thermoelectric properties, the carrier density being tuned through the b1/b2 ratio.
In these families of oxides, as shown here, the power factor does not depend on the carrier density, so that no enhancement of ZT can be expected from this carrier density tuning. The limiting factor for ZT in these oxides remains the too large electrical resistivity. To obtain larger ZT, other layered compounds are currently under investigation, with related crystallographic structures such as TiS29, misfit sulfides 10, or selenides 11. To compare these sulfides and selenides with oxides, we present here the transport properties of layered sulfides from the CuxTiS2 family, and of TiS2 − xSex. We will emphasize here the differences between these three families and show the peculiar behavior of each family and how to enhance ZT in these different families.
2 Experimental details
Single crystals of misfit cobaltates [Bi2A2O4]RS[CoO2]p (A = Ca, Sr, and Ba, 1.69 ≤ p ≤ 1.98) were grown using K2CO3KCl fluxes. In the first step, polycrystalline samples were prepared by a solid state reaction method. Stoichiometric amounts of Bi2O3, BaCO3, SrCO3, CaCO3, and Co3O4 were mixed, and the mixtures were heated at 1123 K for A = Ca, 1073 K for A = Sr and Ba crystals. Then the prepared powder samples and a 4:1 ratio of K2CO3KCl mixture were mixed in a ratio of 1:30 and loaded in an aluminum crucible. The powder-flux mixture was kept at 1073 K for 20 h, cooled to 973 K at the rate of 1 K h−1, then to 873 K at the rate of 5 K h−1 and finally to room temperature at a rate of 100 K h−1. Crystals with a thin plate-like shape of 2 × 2 × 0.008–0.02 mm3 were obtained. These crystals were collected from the solidified materials by dissolving the flux in water.
The CuxTiS2 dense ceramics were synthesized in a two steps process. First TiS2 powder was synthesized in sealed silica tube from the stoichiometric mixture of pure elements. Then, this powder was ground and mixed with Cu in stoichiometric amounts. Details can be found in Ref. 12. The Ti(S, Se)2 compounds have been prepared directly from stoichiometric mixture of pure elements (titanium powder, sulfur powder, and selenium shots), loaded in fused silica ampoules 13. The series of compounds TiSxSe2 − x is stable in air at room temperature and the synthesis of large polycrystalline batches of the title compounds is rather straight forward although it has been reported that single crystals grown via iodine vapor transport exhibit very different low temperature electrical resistivity depending on the temperature used for their preparation 14. However, in the same report, it is also stated that below a temperature of synthesis of 700 °C, the deviation from the 1:2 stoichiometry falls within the measurement uncertainty and also that the use of iodine as transport agent is favorable to the presence of up to 0.3 at.% of iodine in the samples. Thus, using a temperature of 650 °C and no iodine (useless for preparing polycrystalline sample), the substitution of selenium by sulfur is easy to realize and indeed a full solid solution exist between TiS2 and TiSe2. Scanning electron microscopy and electron dispersive spectroscopy were performed on every sample and confirmed the absence of impurity phase and also the relative ratio of the elements in all the members of the solid solution.
Densification of these intermetallic compounds was then performed using Spark Plasma Sintering (SPS), as described in Refs. 12, 13.
These materials have all been characterized by X-ray diffraction and transmission electron microscopy. The single crystal oxide samples were characterized by single crystal X-ray diffraction (four circle diffractometer) using Mo Kα radiation with a Bruker Kappa CCD diffractometer. Energy dispersive X-ray spectroscopy measurements have confirmed the compositional ratio. All crystals show the specific diffraction pattern of layered misfit oxides, with two independent lattices. The structure of [Bi1.7Sr2O4 − δ]RS[CoO2]1.82 and [Bi1.7Ca2O4 − δ]RS[CoO2]1.69 have already been refined 15, 16. The misfit ratio of [Bi2Ba1.3K0.7O4 − δ]RS[CoO2]1.98 could be refined to a value very close to 2 (1.98). For [Bi2Ba1.3K0.7O4 − δ]RS[CoO2]1.98, the large mosaicity did not allow us to determine a satisfactory set of integrated intensities, but lattice parameters and crystal symmetry could be determined from digitally reconstructed precession images, generated from the measured data by EVALCCD software 17.
The in-plane resistivity of single crystals was measured by a four-probe method from 2.5 to 400 K using physical properties measurement system (PPMS, Quantum Design). Four contact terminals were made by Ag paste (Dupont 6838) and gold wire with a diameter of 20 µm on a surface of the crystal with a thickness of 8–12 µm. The in-plane thermopower was measured using a steady-state technique with a small temperature gradient of about 1 K cm−1 detected by 2 chromel-constantan thermocouples from 5 to 320 K using PPMS. The in-plane Hall coefficient measurement was performed using PPMS by applying −5 to 5 T. As shown in the inset of Fig. 4(b), 6 terminals made by gold wire and Ag paste are put on the crystal with a thickness of 8–12 µm. Typical signal of ΔRxy was 3–50 mΩ and a clear linear line of ΔRxy(H) was obtained. A small extra contribution to ΔRxy(H) due to misalignments of the terminals was carefully subtracted by using the equation of (ΔRxy(H) − ΔRxy(−H))/2. Due to an inhomogeneous thickness of the sample, resistivity, and Hall coefficient have error bar of ±10%.
For SPS prepared samples of TiS2 and Ti(S,Se)2, due to the induced texture of the materials during the SPS process, the measurements of S, ρ, and κ were all performed along the average (ab) planes. The electrical resistivity ρ and Seebeck coefficient S were measured in a Ulvac – Riko ZEM3 system from 300 to 825 K. Hall effect experiments have been performed at 300 K in PPMS (Quantum Design), with a maximum magnetic field of 9 T.
3 Hall effect as a probe of the thermoelectric properties in crystals of misfit layered cobalt oxides [Bi2A2O4][CoO2]p (A = Ca, Sr, and Ba, 1.69 ≤ p ≤ 1.98)
The common parameters of NaxCoO2 and misfit cobaltates is the presence of CoO2 layers of edge shared CoO6 octahedra which favor the stabilization of low spin states Co3+ and Co4+. In the so-called “misfits”, the CoO2 layers are separated by 2 18, 3 5, 6, or 4 15 RS-type layers, while in NaxCoO2, depending on x, a layer of randomly filled or ordered Na+ separates the CoO2 layers 19. In misfits, the two different sublattices (CoO2 and NaCl-like layers) are alternately stacked along the c-axis (see Fig. 1), which causes the “misfit” ratio p (p = b1/b2, where b1 and b2 represent b-axis parameters of the two incommensurate monoclinic sublattices RS layer and CoO2 layer, respectively).
In Na0.7CoO2, large thermopower S (100 µV K−1 at 300 K), low resistivity ρ (200 µΩ cm at 300 K) 1 and also reduced lattice thermal conductivity κ20 are observed, leading to the high thermoelectric performance defined by the figure of merit Z = S2/ρκ21. The misfit cobaltates possess similar properties, with large thermopower (between 60 and 200 µV K−1 at 300 K) and metallicity observed for T > 100–200 K. Only four misfits have been shown so far to be metallic in the whole T range, from 2 to 400 K, as Na0.7CoO222–25. However, in all misfit cobaltates, the Seebeck coefficient presents a common evolution as a function of T: a rapid increase at low T followed by a plateau for T > 100–150 K. The coexistence of these two classically antagonistic properties (large S and metallic behavior) has stimulated a lot of interest for this class of materials.
Two models have first been proposed to explain the large thermopower in these materials. A high temperature limit of S has been calculated from the Hubbard model, taking into account the large spin and orbital degeneracy associated to Co3+ and Co4+ in low spin states 8. This is the so-called generalized Heikes formula which states that
with x the Co4+ concentration, and g3 and g4 the spin and orbital degeneracy associated to Co3+ and Co4+. For low spin states Co3+ and Co4+, g3 = 1 and g4 = 6. This formula reproduces well the large values of S observed at 300 K and above, even if the g3/g4 term has been questioned and should be reduced to 1/2 26. This localized picture is however difficult to reconcile with the origin of metallicity in these oxides.
From band structure calculations 2, the importance of the rhombohedral symmetry has been evidenced. This symmetry induces a lifting of the t2g degeneracy into two orbitals, the broad band responsible for metallicity and a narrow a1g band responsible for large Seebeck coefficient, due to the large derivative of the density of states (DOS) at the Fermi level. With this model, the classical Mott equation is used to calculate the thermopower (S ∼ (dlnσ(E)/dE)E=EF, with σ(E) = n(E)µ(E) where n(E) is the DOS and µ(E) the mobility), and correlation effects are not considered.
More recently, Sriram Shastry and coworkers have examined a t–J model to explain the complex transport properties of NaxCoO2 system, combining the Heikes formula and a diffusive term for S27. They show that the Heikes term is dominant in a wide range of temperature and (t, J) values. The same conclusion has been obtained by LDA + DMFT calculations 28, which shows that the Heikes formula can be a good approximation at high T in the incoherent regime.
Depending on the (t, J) values, the Heikes formula could thus be valid even at room temperature in this metallic system. Furthermore, the doping should play a major role in tuning S and we have decided to investigate this effect in the misfit layered-cobalt oxides [Bi2A2O4]RS[CoO2]p (A = Ba, Sr, and Ca, 1.65 ≤ p ≤ 2) 15, 16, 29–31 family. These compounds were also found to be good thermoelectric materials. Especially, the whisker crystal of BiSrCoO was shown to exhibit a large dimensionless-figure-of-merit ZT > 1 at 973 K 32. In misfit cobaltates, the [CoO2]p mono layer with Co triangular lattices is separated by a block of four RS-type layers with square lattice. In this system, the magnitude of the thermopower changes from 90 to 150 µV K−1 according to A cation (Ba2+, Sr2+, and Ca2+) at 300 K 16, 29, 31. Since the oxidation state of the A ion is always 2+, there is in principle no doping effect by changing A. However, the A ion causes a modification of the misfit ratio p because of different ionic radii of A ions. As a result, the change of the misfit ratio affects carrier concentration 33. Indeed, due to electroneutrality between the two block layers, the formal Co valency in the CoO2 planes can be written as
with α the positive charge in the NaCl-like layers. A systematic combination of thermopower and Hall coefficient measurements performed on single crystals of these three different misfits has been used to investigate the importance of both misfit ratio p and doping on the thermoelectric properties.
Figure 2 shows in-plane resistivity ρ for A = Ba, Sr, and Ca crystals. (Hereafter we denote A = Ca, Sr, and Ba crystals by BCCO, BSCO, and BBCO, respectively.) At 300 K, the values for BBCO, BSCO, and BCCO are 4.1, 8.4, and 10.1 mΩ cm, respectively. With increasing p, ρ systematically decreases in the whole T range. The 8.4 mΩ cm for BSCO is consistent with other data for crystals 30, 31, 34. The 10.1 mΩ cm for BCCO is also similar to other data for crystals though temperature dependence is rather different 26. The 4.1 mΩ cm for BBCO is very close to the behavior reported in Ref. 29. BCCO and BSCO exhibit metallic conduction above = 202 and 78 K, respectively. The most interesting feature is no upturn of the resistivity in BBCO at low temperatures, as previously reported in Ref. 29, with a residual resistivity below 1 mΩ cm. As shown in the inset of Fig. 2, the resistivity of BCCO at 2.5 K is 7 orders of magnitude larger than that of BBCO, and the resistivity of BSCO is 2 orders of magnitude larger than that of BBCO. The metallic behavior observed for BBCO is completely suppressed at low T in BCCO and BSCO, and replaced by a strongly localized behavior: the larger dρ/dT is obtained for the smaller p. It must be noticed that in the case of misfits, only a few metallic compounds have been reported so far 22–25. In NaxCoO2, metallicity is observed down to low temperatures except for x = 0.5, where charge ordering is observed 35. In misfits as well, the block layer might play a role on the localization observed at low T.
Figure 3 shows the in-plane thermopower S as a function of temperature. Even if strong differences of ρ(T) are observed at low T between the three different crystals, the three S(T) exhibit the same trend. The temperature dependence is metallic-like (dS/dT > 0) at low temperatures, with a large slope, and a very small T dependence is observed for T > 200 K. At 300 K, the slope dS/dT is almost zero for BCCO, and increases as p increases. The magnitude of S for BBCO, BSCO, and BCCO is 94, 123, and 149 µV K−1 at 320 K, respectively. With increasing misfit ratio p, S systematically decreases. The value is almost the same as that of polycrystalline samples 16, 29. In BBCO crystals, S is smaller than in Ref. 34, with 94 µV K−1 to be compared to 110 µV K−1.
Figure 4(a) shows in-plane Hall coefficient RH as a function of temperature. For BSCO, the magnitude at 300 K is 1.3 × 10−2 cm3 C−1, which is almost the same as the previously published data 30, 31. The magnitude for BCCO and BBCO is 0.7 and 2.6 × 10−2 cm3 C−1, respectively. According to the equation of RH = 1/ne, where n and e represent carrier concentration and unit of charge, respectively, we estimated n value in Fig. 4(b). BBCO crystal shows the largest carrier concentration in the whole temperature range, which is consistent with the low magnitudes of the resistivity and thermopower. Compared to previously reported data, the value of RH is larger (7 × 10−3 cm3 C−1 to be compared to 5 × 10−3 cm3 C−1 in Ref. 34). All the samples exhibit linear-like temperature dependence above 100–200 K, the larger linear regime being observed for the smaller p, and BCCO and BSCO exhibit upturn below 90 K, while BBCO does not show such an upturn. We do not observe here the low T increase of RH reported in other BBCO crystals 34, it rather saturates at low T in our crystals. Finally, it should be noted that in the case of BCCO, there is a downturn of RH, with a maximum at T ∼ 300 K, a behavior which is not observed in BSCO and BBCO.
The resistivity, Hall effect and Seebeck coefficient measurements show that when p decreases, ρ, RH and the thermopower increase (see the data at 320 K plotted in Fig. 5a and b). In a first approach, the change of p has only a quantitative effect on S, with a similar S(T) dependence and only a shift of the values in the whole T range. On the other hand, it has a much more drastic impact on the resistivity, with strong variations of ρ(T) observed at low T, and a metallic-to-insulator behavior when going from BBCO to BCCO below 100–200 K. This localized behavior also strongly modifies Hall effect at low T. Let us focus on the results obtained at high temperature, i.e., for T > 200 K.
Using the simple classical equation RH = 1/ne, the Co valency can in principle be extracted. From the values measured at 200 K, in the linear T regime above the upturn, vco increases from 3.06 to 3.08 and 3.15 for BCCO, BSCO, and BBCO, respectively. This means that as the Co valency increases by the p increase, S decreases, as expected in classical materials. From Eq. (2), the modification of the misfit ratio directly tunes the formal Co4+ content, thereby inducing a change in S. The larger S will thus be obtained for the smaller Co valency, i.e., the smaller p.
From Fig. 4a, it is obvious that this analysis of RH is too simple as RH is not constant. Compared to a classical material, RH exhibits a strong T dependence in the whole T range, with a linear behavior at high T. This characteristic shape has also been observed in NaxCoO236 and different models developed for a triangular lattice can reproduce the high T linear dependence 37–39. The importance of the triangular lattice geometry being at the origin of this linear behavior is emphasized in Ref. 38. In these models, a linear slope is observed for T > t, and the slope depends on the carrier concentration. Using the t–J model enables a direct comparison with Na0.68CoO236. In the t–J model 37,
where a is a CoCo bond length, d the interlayer distance, |e| the magnitude of the electronic charge, t the hopping amplitude, and x is the doping away from half-filling. As parameters, we use a = 2 Å and d = 15 Å for each crystal. The positive slope of RH(T) shows that t is negative in these misfits as in NaxCoO2 with x ∼ 0.7 36.
To further analyze Hall effect, the x values of doping have to be extracted from other experiments. For exactly the same set of crystals, angle resolved photoemission spectroscopy (ARPES) measurements have been performed by Brouet et al. 40. A cylinder-like Fermi surface which has a1g band characteristic has been observed in BBCO crystal as seen in NaxCoO2. The Fermi wave vector kF of BBCO is almost the same as kF of Na0.7CoO2. Thus, of BBCO is estimated to be +3.3 ± 0.05 40. Then using Eq. (2) with vCo = +3.3 ± 0.05 of BBCO and misfit ratio p = 1.98, α is estimated to be 1.386 ± 0.1 for BBCO. Supposing this α value is the same for BSCO and BCCO, s are estimated to be +3.24 ± 0.055 and +3.18 ± 0.06 for BSCO and BCCO, respectively. These values are larger than the ones obtained from Hall effect, but are consistent with the ones obtained by a TEP scaling analysis on similar misfit polycrystals investigated by NMR 41. With the cobalt valence estimated to be 3.3+, 3.24+, and 3.18+ (x = 0.7, 0.76, and 0.82) from ARPES data, obtained t is 13, 21, and 41 K for BCCO, BSCO, and BBCO, respectively. It can be noted that another analysis of thermopower taking into account the magnetic field dependence of thermopower gave a doping level of 3.3 for BCCO 42. This would result in t = 10 K for BCCO, not far from 13 K. The main result here is therefore that, even if there is some uncertainty on the x values, the obtained t values are very small, with t smaller than 50 K. The increase of t as p increases is consistent with the fact that the smaller resistivity is observed in BBCO and also that this linear regime of RH is evidenced at higher T in BBCO than in BCCO, as Eq. (3) should be valid only for T > t. The value of 41 K for BBCO with x = 0.7 is not so far from t = 50 K estimated for Na0.68CoO2 with x = 0.68 by the same way 36. Also, the estimated t is of the same order as the one (8–12 meV) in NaxCoO2 estimated by ARPES 43, 44, which shows that our result is reasonable. However, the t in misfits and NaxCoO2 is much smaller than the value (130 meV) estimated by band calculation in NaxCoO22 implying strong electron correlation, which is consistent with rather large γ20, 29. This very small t value might come from disorder within the separating planes 45.
The t value is thus very small in these compounds. According to the numerical calculation for thermopower based on t–J model on the triangular lattices performed by Peterson et al. 27, thermopower systematically increases when the carrier concentration increases, and the thermopower shows high-temperature limit (i.e., Heikes formula or generalized Heikes formula) at around T ∼ 5t–6t. Indeed we have observed almost constant thermopower around this temperature range, for T > 200 K, as shown in Fig. 3 (since t is 13–41 K, the limit T ∼ 5t–6t is reached at 65–205 K < T < 78–246 K). This means that the high temperature limit of the Heikes formula can easily be reached in this family of oxides, even at 300 K. These reduced energy scales explain why an almost constant Seebeck coefficient is observed as soon as T > 200 K. This had already been evidenced in BCCO 43 and this study shows that t is not strongly modified by a change of p, with a small increase of t when p increases.
It can be noted that RH seems to saturate at T ∼ 300 K in BCCO. Such a maximum of RH has already been observed in thin films of [Ca2CoO3][CoO2]1.6246 coexisting with a maximum of resistivity, and interpretated as a transition to incoherent excitations. This is not observed, at least for T ≤ 300 K, in the two other misfits and in NaxCoO2. Also, for BCCO, the maximum of RH does not coexist with a maximum of resistivity in this range of T.
By using the experimental S values and vCo obtained from ARPES experiments, the spin and orbital degeneracy term g3/g4 of the Heikes formula can be estimated. We obtain g3/g4 = 0.78/0.76/0.8 for BBCO, BSCO, and BCCO respectively, closer to 1/2 than to 1/6. As previously emphasized by Pollet et al. 26, this larger value is induced by the modification of the orbital filling of Co3+ and Co4+ due to trigonal distortion 47. For Co3+, g3 is always equal to 1, all the t2g orbitals are filled. On the other hand, for Co4+, due to the splitting of the t2g orbitals in a1g and , there is only one hole in the a1g orbital and the orbitals are filled so that g4 = 2. The enhancement of S by spin and orbital degeneracy is thus not so large as compared to the prediction of Koshibae et al. 8.
Finally, as shown in Fig. 5(c), the obtained power factor defined by PF = S2/ρ is estimated to be ∼2 × 10−4 Wm−1 K−2 for all the crystals. This is, however, not expected in degenerated semiconductor thermoelectrics which show a bell-shape curve in PF = f(vCo) 48. For this range of doping ∼1020–1021 cm−3, the slope of PF as a function of doping is very large. This shows that this classical description of PF in thermoelectric materials is not valid in these strongly correlated systems.
By combining resistivity, Hall effect, and thermopower measurements on the same crystals of misfit cobaltates of the family [Bi2A2O4][CoO2]p (A = Ca, Sr, and Ba, 1.69 ≤ p ≤ 1.98), the thermoelectric properties of these crystals have been investigated. As shown by the variation of RH, the modification of p modifies the charge transfer between the block layers, and an increase of p induces an increase of the formal Co valency in the CoO2 plane. The RH coefficients exhibit a complex evolution, with a linear high T dependence for T > 150–200 K. This linear dependence is characteristic of triangular lattices and has been interpretated using the t–J model developed by Kumar and Sriram Shastry 37. The t parameters are very small (13–41 K) and this justifies why the generalized Heikes formula can be used even at relatively low T. t increases as p increases, consistently with the better metallicity observed in BBCO. Also, compared to BSCO and BCCO, the linear regime of RH and the almost constant Seebeck coefficient are observed at higher T due to the larger value of t in BBCO. Using the Co valency extracted from ARPES experiments and the S values, the enhancement of S induced by the spin and orbital degeneracy term g3/g4 is found to be closer to 1/2, due to the splitting of the t2g orbitals in a1g and , as previously reported in Ref. 26.
These measurements on single crystals actually show that the power factor S2/ρ remains constant for this range of doping, close to 2 × 10−4 Wm−1 K−2. This is not expected as a strong dependence of PF on the carrier content is classically observed for this range of doping. This demonstrates that the classical approach followed for the search of new thermoelectric materials has to be completely modified in strongly correlated materials. To obtain larger values of power factor, one strategy is now followed by different groups 9, 10: by going from oxides to selenides or sulfides, the decrease of the ionic character could lead to a reduction of the electrical resistivity.
4 Layered TiS2-based compounds
Transition metal dichalcogenides belong to the layered compounds of the type TX2, where T symbolizes an early transition metal of group IV (Ti, Zr, Hf), V (V, Nb, Ta), or VI (Cr, Mo, or W) of the periodic table and X is one of the chalcogenides S, Se, or Te. They are built up by three atomic sandwich layers, which are stacked on top of each other. Each sandwich consists of a hexagonally ordered sheet of transition metals that is surrounded by two hexagonal layer planes of chalcogen atoms. Although all transition metal dichalcogenides are built up in a similar way, they still differ in their crystallographic description. The transition metal can be coordinated by the nearest chalcogen atoms in two different ways: in the 1T structure (symmorphic space group ), the chalcogen atoms form a regular octahedron forming a CdI2 type layer, similar to CoO2 layer found in NaxCoO2 or misfit cobaltites. The unit cell contains one sandwich layer in the c direction. The unit cell of the 2H structure is extended over two sandwich layers. In one layer the chalcogen atoms are situated above each other. It is rotated by 60° with respect to the neighboring layers.
The bonds within one sandwich are of strong covalent and ionic character, while the interaction between different sandwich layers is rather weak and van der Waals like. Due to their electronic structure and the degree of filling of d bands 49, each transition metal group induces different electrical, magnetic and optical character to the material. For example, the transition metals of IVb group are in a d0 configuration, so the dz2 band stays unoccupied and the respective materials are generally semiconductors. This electronic structure offers particularly interesting thermoelectric properties in TiS2-based compounds 50, 51, with high thermopower and relatively low electrical resistivity.
Of particular interest of the TiS2 (and most of TX2 chalcogenide compounds) is the possibility to intercalate foreign atoms or molecules into the van der Waals gap between the host layers. This method of modifying the physical properties and in particular the electronic structure was widely studied and discussed in view of practical applications (batteries). It is for instance possible to achieve semiconductor-to-metal transitions (or vice versa). The occurring changes are ascribed to a charge transfer from the introduced species to the host lattice. They are simply described in terms of the rigid band model in which it is assumed that the band structure of the host material is not changed except for the filling of the conduction band due to charge transfer 49.
These structural changes can then modify the charge carrier concentration and modify the electronic properties of the compounds. In the context of searching for efficient thermoelectric compounds, the Seebeck coefficient and the electrical conductivity of the TiS2 layered compounds can be then optimized through intercalation and change in charge carrier concentration, so the power factor can be optimized in a specified temperature range.
Moreover, as discussed on misfit cobaltates, it is believed that the ideal thermoelectric material would have regions of the structure composed of a high-mobility semiconductor that provides the electron-crystal electronic structure, interwoven with a phonon-glass. The phonon-glass region would be ideal for housing dopants and disordered structures without disrupting the carrier mobility in the electron-crystal region. This principle can be considered for layered TiS2-based compounds, where the CdI2 layers form a high-mobility semiconductor, whereas the intercalated layer can create disorder and phonon scaterring. This effect has been recently shown in misfit based sulfide, (MS)1 + x(TiS2)2 (M = Pb, Bi, Sn) where, through the intercalation of MS layer between the TiS2 slabs, the charge mobility is maintained while the phonon transport is significantly suppressed owing to the reduction in transverse phonon velocities 52, 53. Another way to reduce the lattice thermal conductivity is to add some disorder on the anionic site, this is possible for instance by substituting sulfur by selenium in TiX2 structures.
Based on these ideas, we have recently revisited the intercalation of Cu in TiS2 compounds and studied their thermoelectric properties 12 and also studied the solid solution TiSxSe2 − x13.
The crystal structure of CuxTiS2 compound is shown in Fig. 6. For x ≤ 0.1, X-ray data were well refined in the trigonal space group of the TiS2 host structure (). For higher Cu content (x > 0.1), traces of the CuTi2S4 spinel are systematically observed which indicates that using our synthesis route the limit of solubility is close to x = 0.1.
Within the solution, as Cu atoms are added, they occupy randomly the octahedral positions in the van der Waals gap. This was evidenced by means of Rietveld refinements and by using high resolution electron microscopy which reveals extra rows in the TiS2 contrast correlated to the presence of the copper ions (Fig. 7). This intercalation results in a systematic expansion of the stacking cell axis. Moreover, electron diffraction patterns containing this axis exhibit elongated dot reflections confirming the statistic mode of intercalation which leads to disorder phenomena in successive layers.
The structural observations can be well correlated with thermal conductivity data. The temperature dependence of the thermal conductivity, presented in Fig. 8, shows that κ increases slightly from x = 0.02 to 0.1 according to the increase in charge carrier concentration (see below). The TiS2 compound (x = 0) has a different temperature dependence with comparable or higher κ values (especially over 650 K) as compared to the Cu intercalated compounds. Although the electronic contribution of the thermal conductivity (κe) increases with x due to charge carriers doping, the Cu intercalation between the TiS2 layers generates disorder and phonon scattering even for small Cu content. As shown in Fig. 8, the lattice part (κph) of the thermal conductivity (κtotal) decreases significantly with Cu intercalation. As reported recently by Wan et al. in (MS)1 + x(TiS2)2 (M = Pb, Bi, Sn) misfit layer compounds 52, the decrease in the lattice thermal conductivity may be linked to the weak interlayer bonding and disruption of periodicity of TiS2 layers in the direction perpendicular to the layers by the intercalated Cu layers. Li et al. 54, 55 also proposed that Nd or Bi intercalation into TiS2 gives rise to substantial enhancement of phonon-drag effect. This phenomenon would result from the low-frequency vibrations (or “rattling”) of metal atoms in the van der Waals gap, which provides additional phonon scattering to the charge carriers (electrons) in the slabs of the TiS2 host. The magnitude of the κph reduction (∼50% in the present study) through Cu intercalation is also in good agreement with reported data in intercalated (SnS)1.2(TiS2)253 and Nd0.025TiS254 compounds which exhibited substantial decrease of 50 and 30%, respectively. It definitely suggests that the creation of an intermediate layer even composed of few intercalated metal cations is efficient to decrease the lattice part of thermal conductivity as compared to TiS2.
The electrical resistivity ρ and the Seebeck coefficient S of CuxTiS2 compounds are shown in Fig. 9. All compounds show a typical metallic behavior. As x increases, it is found that the ρ and values decrease showing that electron charge carriers are created by the Cu intercalation. For TiS2, an electron concentration of n = 6.5 × 1020 cm−3 is measured with a corresponding ρ = 1.5 mΩ cm value of the resistivity at 300 K. These values can be well compared to those reported for in-plane measurements in Ti1 + xS2 crystals, as for n = 6.7 × 1020 cm−3 carrier concentration, a ρ(300 K) value of 0.9 mΩ cm was reported 56. This result, for as-prepared SPS TiS2, shows the existence of a nonstoechiometry written as Ti1 + xS2. The Cu intercalation allows to increase n from 6.5 × 1020 to 3.67 × 1021 cm−3. Correspondingly, for T = 800 K, ρ and decrease from 8.4 mΩ cm and = 276 µV K−1 for TiS2, down to 1.9 mΩ cm and = 142 µV K−1 for x = 0.1. The temperature dependence of the power factor (PF = S2/ρ) shows different behavior according to the copper content with PF ∼ 1 mW mK−2 above 600 K for all compositions (Fig. 10). Interestingly, TiS2 compound exhibits high power factor value of 1.7 mW mK−2 at 325 K, whereas the magnitude of PF in Cu0.02TiS2 remains relatively high on the full temperature range, varying from 1.5 mW mK−2 (300 K) to 1.1 mW mK−2 (800 K). The first relevant point is the possibility to synthesize by SPS dense CuxTiS2 ceramics for which, the electrical properties are rather close to those of nonstoichiometric TiS2 crystals.
The figure of merit, ZT (T = 800 K), slightly increases from 0.37 to 0.45 with Cu intercalation. The temperature dependence of ZT shows a constant increase up to 800 K (Fig. 11). As observed on the PF(T) curves (Fig. 10), pristine TiS2 and Cu0.02TiS2 exhibit highest ZT values on the low temperature range (RT-600 K).
In conclusion, the improvement of the thermoelectric properties in Cu intercalated TiS2 compounds could be ascribed to two combined effects: (1) a slight increase in the power factor through a tuning in the carrier concentration in dense textured SPS-prepared CuxTiS2 ceramics and (2) a substantial decrease in the lattice thermal conductivity presumably caused by the disorder of Cu atoms in the van der Waals gaps of TiS2.
Although the thermal conductivity of layered CuxTiS2 compounds is relatively large compared to other “PGEC” thermoelectrics, most of it comes from the reducible lattice component especially for small x values, with moderate carrier concentrations. Thus, two-dimensional intercalated metallic TiS2 could be a good thermoelectric if the intercalated layer would scatter more efficiently the heat-carrying phonons. The Ti and S atomic frameworks can also be chemically substituted, and this would presumably dominate the band structure and modify the electronic transport properties. Finally, it is worthwhile to note that sulfur and titanium are all largely abundant and hence relatively cheap. These elements are non-toxic and moreover they both are relatively light (3.25 g cm−3 against 8.16 g cm−3 for PbTe). Indeed, when considering transport application, low density is a criterion that is definitely decisive. These characteristics make them extremely attractive candidates for being utilized in future thermoelectric converters at low or medium temperatures.
4.2 Solid solution TiSxSe2 − x
TiSe2 and TiS2 are known to exhibit the same trigonal crystal symmetry related to the layered CdI2 structure type, thus, the structures of the series TiSxSe2 − x (x = 1, 1.25, 1.5, and 2) can be well refined in the aristotype space group P-3m1, which implies a statistic distribution of the sulfur and selenium atoms over the same crystallographic site (Ti 1a: 0, 0, 0 and S/Se 2d: 1/3, 2/3, Z). Furthermore, the existence of this solid solution is confirmed by the linear evolution of cell parameters (Fig. 12) that follow Vegard's law with x varying from 0 to 2. Indeed, between the two end members the variation of the volume of the cell is close to 11% with a variation of about −4% within and between planes for x varying from 0 to 2 (ionic radii: 1.84 Å for S2− and 1.98 Å for Se2−). This evidently implies that the spacing separating the TiX6 layers is larger in the selenide than in the sulfide.
Electronically, TiSxSe2 − x can be simply viewed as made of Ti4+ cations and of two divalent counter-ions, xS2− and (2 − x)Se2−. However, the difference of electronegativity between S and Se leads us to intuitively envisage differences in term of physical and chemical properties. Indeed, the more electronegative sulfur renders the structure of TiS2 more ionic than that of TiSe2, so that a larger electrical resistivity is expected for the sulfide, together with a larger Seebeck coefficient. Behind that rather “chemical” view, lays the question of the respective band gaps of TiS2 and TiSe2, and according to the numerous reports on that topic, the question is still not firmly resolved, although band gaps have been attributed for both compounds 57–61.
Indeed, these underlined differences are reflected on the transport properties. In Table 1 are reported the transport properties at room temperature and at 700 K of all TiSxSe2 − x with x = 0, 0.5, 1, 1.5, and 2. The positive sign of the Seebeck coefficient of TiSe2 is reminiscent of a p-type material while TiS2 is clearly n-type (Fig. 13). Moreover, the amplitude and the slope of the Seebeck coefficient data also indicates a pronounced degree of metallicity of the selenide as reported before, while the large thermopower of the sulfide is rather providing evidences for its semiconducting behavior (Fig. 13). It is worth noticing that the room temperature thermopower reported in this paper (−153 µV K−1), compares very well with the value reported in a previous study 62. Throughout the solid solution, the values of the Seebeck coefficient are expected to fall in between the values measured for the two end-members. It is indeed the case as the n-type behavior is reinforced by the substitution of selenium by sulfur. This can very simply be attributed to the fact that sulfur is a much “better” anion than selenium, so that it provides more electrons to the structure, hence behaving like an n-type dopant. In Fig. 13, it is also noticeable that the compound TiS0.5Se1.5 behaves somewhat differently than the sulfur-richer member of the solid solution as its Seebeck coefficient seems to reach a peak value around 570 K before decreasing, whereas all the other compounds have strictly monotonically increasing thermopower with temperature (in absolute value).
Table 1. Seebeck coefficient, electrical resistivity, thermal conductivity, power factor, and thermoelectric figure of merit at 300 and 700 K for the compounds TiSxSe2 − x with x = 0, 0.5, 1, 1.5, and 2 (from Ref. 13).
resistivity (mΩ cm)
Seebeck (µV K−1)
power factor (mW mK−2)
thermal conductivity (W mK−1)
The electrical resistivity of all the compounds increases monotonically with increasing temperature, feature typical of (semi)-metal or heavily doped semiconductors. Indeed while TiS2 shows a resistivity ranging from 1.63 to 6.56 Ω cm from room temperature to 700 K, the more metallic TiSe2 has a lower resistivity that furthermore has little variation with temperature as shown on Fig. 14.
The thermal conductivity (Fig. 15) of TiS2 and TiSe2 is varying as a function of T−x and decreases from 3.4 and 5.5 W mK−1 at room temperature to 2.1 and 4.8 W mK−1 at 700 K for the sulfide and the selenide, respectively. Except for TiS0.5Se1.5, the other members of the solid solution have lower thermal conductivity than TiS2, due to the disorder generated by the mix occupancy of S and Se. Figure 16 represents the lattice thermal conductivity at 300 K of TiSxSe2 − x as a function of x. As expected from the theory, the minimum thermal conductivity is obtained for TiSSe corresponding to an equimolar ratio of anions. The lattice thermal conductivity of each compound at 700 K is also shown in Fig. 16, it is lower than at room temperature and with a value of 1.1 W mK−1, TiS1Se1 has the lowest thermal conductivity of all. Here again, the somewhat “different” transport properties behavior of TiS0.5Se1.5 should be stressed out. In order to validate these data and erase any doubt concerning the actual stoichiometry and purity of this particular sample, the same composition has been synthesized and analyzed several times and undoubtedly the same composition and measured data were obtained each time. This rather peculiar variation of properties with temperature may be due to the fact that this compound might be situated just at the border of the two different regimes observed for TiS2 and TiSe2 that show an n-type and a p-type character, respectively. Band structure calculations might be useful to clarify this behavior. This “anomalous composition” is also very different from the other compositions in term of figure of merit, as it is the only one that passes through a maximum value at about 600 K while the other compounds have monotonically increasing ZT over the all range of temperature (Fig. 17). TiSe2 has a very low ZT owing to its semi-metallic character while a maximum figure of merit of about 0.4 is obtained for TiS1.5Se0.5 mostly because of its low thermal conductivity compared to the other compounds while they all have about the same power factor at 700 K (except for TiSe2) as indicated in Table 1.
Within the large family of AX2 compounds, two main structure-types coexist depending on the nature of the component, CdI2 with hexagonal coordination and MoS2 with prismatic coordination. Moreover, some compositions do not exist without the presence of an intercalated species filling the interlayer spacing, for example, CrSe2 is not stable while AgCrSe2 consist of CdI2 layers of CrSe2 with silver atoms between the layers. The title compound indeed exists without intercalated species but can also accommodate numerous chemical entities. Such a variety of possible combination is indeed an attractive playground for seeking adequate transport properties and eventually tuning them into efficient thermoelectric properties. Our present report shows that the “empty” structures along the solid solution TiSxSe2 − x (no species within the interlayer spacing) have reasonable thermoelectric properties with a maximum ZT of about 0.4 at 700 K. Moreover, the fact that the power factor is higher at the lower temperature implies that more effort should be dedicated to lower the thermal conductivity of these layered structures around the ambient. If this can be achieved, transition metal layered lighter chalcogenides might represent a replacement solution to the long known and used bismuth telluride that seems to suffer from the somewhat erratic price of the tellurium, but also from its relatively high density.
The unique properties of materials based on CdI2 type structures have been reviewed here. In oxides, this structure generates complex transport properties, with a metallic behavior coexisting with large thermopower. The low T resistivity behaviors (metallic or strongly localized) do not affect the shape of the S(T) curves. Moreover, a strong dependence of the Hall effect as a function of temperature is observed, which cannot be explained by standard transport Boltzmann theory. These oxides are thus very interesting from a physical point of view, and reach power factor close to 2 × 10−4 Wm−1 K−2. By going from oxides to sulfides and selenides, the covalency increases and smaller resistivities are obtained, leading to larger power factor of 10−3 Wm−1 K−2. Also, due to the great flexibility of this structure, lattice part of thermal conductivity can be strongly modified by inserting cations between the CdI2 type layers or by anionic substitutions. By these two mechanisms, large ZT values are obtained, up to 0.5 in the case of CuxTiS2.
We would like to thank V. Brouet and J. Bobroff (LPS Orsay) and P. Limelette (LEMA, Tours) for fruitful discussion, and Y. Klein for technical support of thermopower measurement. We also thank CNRS for a postdoctoral fellowship, and ANR OCTE for financial support.