Thermoelectric properties in the series Ti1-xTaxS2 M. Beaumale, T. Barbier, Y. Bréard, S. Hébert, Y. Kinemuchi, and E. Guilmeau Citation: Journal of Applied Physics 115, 043704 (2014); doi: 10.1063/1.4863141 View online: http://dx.doi.org/10.1063/1.4863141 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/115/4?ver=pdfcov Published by the AIP Publishing

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JOURNAL OF APPLIED PHYSICS 115, 043704 (2014)

Thermoelectric properties in the series Ti1-xTaxS2 ard,1 S. He bert,1 Y. Kinemuchi,2 and E. Guilmeau1,a) M. Beaumale,1 T. Barbier,1 Y. Bre 1

Laboratoire CRISMAT, UMR 6508 CNRS ENSICAEN, 6 bd Mar echal Juin, 14050 CAEN Cedex 4, France National Institute of Advanced Industrial Science and Technology (AIST), AIST Chubu, Nagoya 463-8560, Japan 2

(Received 31 October 2013; accepted 11 January 2014; published online 24 January 2014) Polycrystalline samples in the series Ti1-xTaxS2 with x varying from 0 to 1 were prepared using solid-liquid-vapor reaction and spark plasma sintering. Rietveld refinements of X-ray diffraction data are consistent with the existence of a full solid solution for x  0.4. Transport measurements reveal that tantalum can act as electron donor when substituted in the Ti sites. As a consequence, the electrical resistivity and the absolute value of the Seebeck coefficient decrease with Ta content due to an increase in the carrier concentration. The lattice thermal conductivity being reduced due to mass fluctuation effect, the ZT values in Ti0.95Ta0.05S2 is slightly increased as compared to TiS2. C 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4863141] V I. INTRODUCTION

Thermoelectric materials have enticed much attention in recent years for possible applications as environmentally electric-power generators.1 To qualify the thermoelectric performance of a material, the dimensionless thermoelectric figure of merit, ZT (ZT ¼ S2 T=qj, where S is the Seebeck coefficient, q is the electrical resistivity, j is the total thermal conductivity, and T the absolute temperature) is used. Currently, the best performances for low and medium temperatures range belong to Bi2Te3 intermetallics with optimum ZT values around 1 at 400 K. However, tellurium is toxic, scarce, and expensive and this prevents the use of Bi2Te3 bulk thermoelectric materials for large scale applications. Thus, one of the current main interests in research on thermoelectric materials is to develop new materials with higher efficiency for room and medium temperature range (i.e., below 400  C). Ten years ago, Imai et al. have revealed a large value of thermopower in TiS2 (S ¼ 250 lV/K at 300 K; n-type behavior) and relatively low and metallic-like resistivity (q ¼ 1.7 mX cm at 300 K).2 However, no great efforts have been devoted to this compound in the following years and, only recently, several studies have shown the great potential of this compound for low and medium temperature applications.3–5 TiS2 belongs to the layered transition metal dichalcogenides (TMDCs) MX2 (M is a transition metal atom from the group IVb, Vb, or VIb columns of the periodic table, X ¼ S, Se, or Te), which have been attractive compounds over a long term of years due to the rich variety of the physical properties.6–8 Depending on the structure type and constituting elements, the TMDC compounds can exhibit either insulating (HfS2), semiconductor (ZrS2) or metal like behavior (NbS2, TaS2). A member of the family of TMDC, titanium disulfide (TiS2), is considered as a semiconductor or semimetal (the question is still under debate).9–15 TiS2 has an a)

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anisotropic structure with a trigonal space group, P3m1.6 1 T-TiS2 is known to exhibit the trigonal crystal symmetry related to the layered CdI2 structure type, a ubiquitous prototype for MX2 stoichiometries. The CdI2 layer is constituted of edge-shared octahedral of TiS6 that forms infinite layers perpendicular to the c axis (inset of Fig. 2). In the layers, TiS6 octahedrons are arranged with each other firmly through strong covalent bonds, and each layer stacks weakly by van der Waals force.6 One particular interest of the TiS2 (and for most of layered MX2 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).16–19 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. 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 (P ¼ S2 =q) can be potentially increased in a specified temperature range. Recently, power factor values ranging between 1 and 1.7 mW/mK2 have been obtained in dense bulk TiS2 based compounds.3–5 Nevertheless, because of its large lattice thermal conductivity, maximum ZT values are equal to 0.15 at RT and around 0.4 at 700 K. Accordingly, the reduction of its thermal conductivity is of great requirement in improving its thermoelectric efficiency for practical applications at room or medium temperature. If the CdI2 layers form a high-mobility semiconductor, the intercalated layer in the 1 T-structure can create disorder and phonon scattering. This effect has been recently shown in misfit based sulphide (MS)1þx(TiS2)2 (M ¼ Pb, Bi, Sn),3 where a rock-salt type block-layer is intercalated between the TiS2 layers. Li et al.20,21 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

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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. Similarly, the reduction of lattice thermal conductivity by 50% through Cu intercalation in TiS24 is also effective. It definitely suggests that the creation of an intermediate layer even composed of few intercalated metal cations is efficient to decrease the thermal conductivity in TiS2. Another way to reduce the lattice thermal conductivity is to add some disorder on the anionic and/or cationic sites. This is possible, for instance, by mixed occupancy of the S and Se on the anionic site in TiS2-xSex.22 In addition, the lattice thermal conductivity can be reduced through the substitution of Ti by heavier cations in TiS2 slabs to generate mass fluctuation effect. Preliminary works have been carried out on Ti1-xMxS2 with M ¼ Ta, Mo, V (Ref. 23) with measurements of only the electrical resistivity and Seebeck coefficient. More recently, mass fluctuation effect was shown in Ti1-xNbxS2 solid solution (Ref. 24). Based on the same idea, we have studied the synthesis and thermoelectric properties in the Ti1-xTaxS2 series. II. EXPERIMENTAL SECTION

Ti1-xTaxS2 dense ceramics were synthesized in a two steps process. First, stoichiometric mixtures from pure elements (Alfa Aesar 99.5%) of Ti1-xTaxS2 powders (x ¼ 0, 0.05, 0.1, 0.4, 0.5, 0.6, 0.8, and 1) were synthesized by two successive calcinations in sealed fused silica tubes: a first calcination at 950  C for 48 h followed by a second calcination at 1000  C for 48 h. The agglomerated powder, composed of plate-like grains of 1–10 lm (in the ab plane), was then ground and sieved down to 200 lm. Second, the Ti1-xTaxS2 powders were placed in graphite dies of 15 mm diameter and densified by Spark Plasma Sintering (SPS) (FCT HPD 25) at 800  C for 10 min under a pressure of 50 MPa. The size of the grains is found around 20–30 lm (Fig. 1). The final dimensions of the pellets are around 7 mm in thickness and 15 mm in diameter. The geometrical densities were higher than 95% of the theoretical ones. The structural characterization has been carried out by means of Transmission Electron Microscopy (TEM JEOL 2010 FEG) and X-Ray Diffraction (XRD) using a Panalytical Xpert Pro

FIG. 1. SEM image of 1T-Ti0.9Ta0.1S2 after cross section polisher treatment.

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diffractometer (Cu Ka radiations). The structural Rietveld refinements were performed using FULLPROF program. The electrical resistivity (q) and Seebeck coefficient (S) were measured simultaneously in the temperature range of 300–700 K using a ULVAC-ZEM3 device under partial Helium pressure. For this measurement, sample size is 3.5 mm  3.5 mm  10 mm. Hall effect experiments have been carried out in a Physical Properties Measurements Systems (PPMS, Quantum Design), in a magnetic field up to 9 T. The heat capacity and thermal diffusivity were analyzed using Netzsch STA 449-F3 and LFA-457 models, respectively, with a sample size of 6 mm  6 mm  1.5 mm. The thermal conductivity (j) was calculated using the product of the geometrical density, the thermal diffusivity, and the heat capacity. The lattice thermal conductivity was determined from the Wiedemann-Franz law by subtracting the electronic contribution to the thermal conductivity from the total thermal conductivity (jlattice ¼ jtotal  jelec). The Lorenz number of each sample was deduced based on Boltzmann transport equation, so that variation in scattering parameter and carrier concentration were taken in account.25 All the property measurements were performed on the same puck. XRD patterns show that the crystalline ab-planes are preferentially oriented perpendicular to the applied pressure direction, which was confirmed by the alignment of platelike grains observed on Fig. 1 by Scanning Electron Microscopy (SEM ZEISS Supra 55) after a cross section polisher treatment (JEOL- SM-09010). Accordingly, S, q, and jtotal were all performed along the same direction (i.e., in the plane perpendicular to the pressure direction). III. RESULTS AND DISCUSSION

TiS2 and TaS2 are known to exhibit different crystal symmetries related to the layered MX2 dichalcogenide structure type. While TiS2 crystallizes mainly in the 1T form, TaS2 can adopt several forms, referred as 1T, 2H, 3R, 4H, 6R phases.26 For 1T-TiS2, CdI2 layer is composed of edge-shared octahedra of TiS6 that form infinite layers perpendicular to the c axis. Differently, in 3R-TaS2, metal atoms are in trigonal prismatic coordination typical from some MX2 phases (X ¼ Mo, Nb, Ta).7 All the structure of the series Ti1-xTaxS2 (for x  0.4) were well refined in the aristotype space group P3m1, which implies a statistic distribution of the titanium and tantalum atoms over the same crystallographic site (Ti/Ta 1a: 0, 0, 0 and S 2d: 1/3, 2/3, z). The refined X-ray diffraction pattern of our limit compound (x ¼ 0.4) is given in Fig. 2. Whatever x, any attempts to introduce order between Ti and Ta atoms during the refinement process were unsuccessful. To confirm the lack of Ti/Ta ordering even on a short scale, a detailed TEM study has been performed. For x  0.4 compounds, no extra dots were detected on the electron diffraction patterns apart from the ones corresponding to the P3m1 S.G. The regularity of the expected stacking mode is also highlighted by HRTEM (Fig. 3). In addition, Energy Dispersive X-ray Spectrometry analyses were performed on numerous crystallites of each compound and confirm that within the technique accuracy, our samples are homogeneous.

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FIG. 4. Variation of a and c lattice parameters versus Ta content in the Ti1-xTaxS2 (0  x  0.4) solid solutions. FIG. 2. Rietveld refinement of powder X-ray diffraction profile of 1TTi0.6Ta0.4S2. Inset: crystal structure of 1T-TiS2.

The existence of this Ti1-xTaxS2 solid solution (for x  0.4) is also confirmed by the linear evolution of cell parameters (Fig. 4) that follow Vegard’s law with x varying from 0 to 0.4. Indeed, between the two end members from x ¼ 0 to x ¼ 0.4, the average spacing between TiS2 layers (c ˚ to 5.7815(2) parameter) expands linearly from 5.7046(2) A ˚ A as Ta content increases; correspondingly, the a parameter ˚ to 3.38853(9) A ˚ . These decreases slightly from 3.40728(7) A results confirm the MS6 octahedron distortion along the ˚ for Ti4þ 3-fold axis due to the different ionic radius (0.605 A 4þ ˚ for Ta ), as suggested previously in Ti1-xTaxS2 and 0.68 A

FIG. 3. HREM image of 1T-Ti0.6Ta0.4S2 compound along [110] direction.

solid solution.27–29 Such behaviour of lattice parameters a and c was also previously reported for TixNb1-xS2 (0  x  1)24,28 and MoxW1-xS2 (0  x  1) solid solution.29 For x > 0.5, the XRD pattern can be refined as a mixture of 1T-TiS2 and 3R-TaS2 phases (Fig. 5). The latter phase showing a highly metallic behavior,6,7 the present study focused only on the single phases with x  0.4. The temperature dependence of the electrical resistivity in the Ti1-xTaxS2 series is displayed in Fig. 6(a). The electrical resistivity curves collected from 300 K up to 700 K demonstrate a clear tendency towards more conducting behavior as the Ta content increases. For instance, at 700 K, q decreases from 2.5 mX cm to 0.9 mX cm as x increases from x ¼ 0 to x ¼ 0.4. This more metallic behavior is also confirmed by the decreasing magnitude of the slope of the electrical resistivity as a function of temperature when Ta content increases. Such behavior is explained by the increase of the overlap between the atomic orbitals of the metal, when the titanium atoms are gradually replaced by tantalum

FIG. 5. XRD patterns in the series Ti1-xTaxS2. 3R-TaS2 phase are indicated by diamonds.

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FIG. 6. Temperature dependence of (a) electrical resistivity and (b) Seebeck coefficient in the series Ti1-xTaxS2. Inset: Hall mobility as a function of temperature for Ti0.9Ta0.1S2.

ones. As a consequence, the binding character of the metal/metal interaction increases in the TixTa1-xS2 series when tantalum concentration increases. In addition, Tison et al.27 have clearly shown that energetic dispersion of the t2g levels is higher for TaS2 (4.1 eV) than for TiS2 (2.1 eV), in agreement with the literature.30 This band dispersion can directly be correlated to the binding metal-metal interactions, which takes part in a non-negligible way in cohesion of tantalum disulphide while such metallic bonds are less considered in titanium disulphide. In addition, because of the different electronic configuration of the metal atoms in their sulfur environment (Ti4þ(d0) and Ta4þ(d1)), the conduction band is theoretically empty for TiS2 and partially filled for TaS2 leading to more metallicity in TaS2. Hall effects measurements were also performed to determine the electron concentration at 300 K. In agreement with the existence of the solid solution, the carrier concentration

(reported in Table I) increases linearly with the Ta content, since the substitution of Ti4þ (3d0) for Ta4þ (5d1) implies the addition of electrons in the conduction band. For TiS2, an electron concentration of n ¼ 2.34  1021 cm3 is measured at 300 K with a corresponding electrical resistivity value q ¼ 0.98 mX cm. This carrier concentration value is significantly higher as compared to those reported recently in TiS2 bulk compounds (n ¼ 6.5  1020 cm3 with a corresponding q ¼ 1.5 mX cm value4). The high carrier concentration observed in the present study for TiS2 indicates that drastic sulphur volatilization occurred during the process due to high temperature powder synthesis requested for the formation of the Ti1-xTaxS2 solid solution (i.e., 900–1000  C, see Sec. II, against 650  C elsewhere4). It is well accepted that sulfur volatilization generates excess titanium atoms, which intercalate into the van der Waals gap and generate conduction electrons in the Ti 3d band by charge transfer. The effect of Ti/S non stoichiometry on the thermoelectric properties in Ti1þxS2 compounds was recently discussed by Ohta et al.5 On the other hand, tantalum atom can also be statistically distributed in the interstitial site located between TiS2 slabs, as it was reported in 3R-TaS2 compounds, and may participate to the electron doping by charge transfer.31 However, according to XRD refinements, the change in cell parameters and cationic distances indicates that Ta intercalation between the layers unlikely occurs, or in a small amount. As expected, the Hall mobility decreases with Ta content as seen in Table I. This is in good agreement with the data from Thompson et al., Benda, and Inada et al.32–34 and confirms increased scattering effect due to an increase in charge carrier concentration. The Hall mobility as a function of the temperature was also calculated for the whole series (see inset of Fig. 6(a) for Ti0.9Ta0.1S2) assuming a constant carrier concentration in the full temperature range. For 0  x  0.1, a similar behavior with a T1 dependence characteristic of phonon-electron interactions35 can be observed, while for x ¼ 0.4, a more complex behavior resulting in several types of interactions occurs. The temperature dependence of the Seebeck coefficient is given in Fig. 6(b). The absolute value of Seebeck coefficient decreases with the increase of Ta, as visible on Fig. 6(b) due to an increase in the carrier concentration. This trend remains in good agreement with previous studies.23,32 However, the magnitude of the Seebeck coefficient values on the whole series (60 lV/K for TiS2 and 20 lV/K for Ti0.6Ta0.4S2) is lower than those reported by Thompson et al.32 on single crystals. This difference can be explained according to the additional electron doping due to sulfur vacancies (Ti excess) that increased carrier concentration in

TABLE I. c cell parameter, carrier concentration (n), and mobility (l) at 300 K, electrical resistivity (q), Seebeck coefficient (S), thermal conductivity (j), its electronic (jelec) and lattice (jlattice) components, power factor (PF), and figure of merit ZT at 700K in Ti1-xTaxS2.

TiS2 Ti0.95Ta0.05S2 Ti0.9Ta0.1S2 Ti0.6Ta0.4S2

c parameter ˚) (A

q (mX cm)

S (lV/K)

jtotal (W/mK)

jelec (W/mK)

jlattice (W/mK)

PF (mW/mK2)

ZT

n (300 K) ( 1021 cm3)

l (cm2 V1 s1)

5.7046(1) 5.7139(3) 5.7275(4) 5.7815(4)

2.50 1.97 1.16 0.94

126 122 94 39

1.95 1.92 2.19 2.38

0.68 0.87 1.47 1.83

1.27 1.05 0.71 0.55

0.63 0.76 0.75 0.17

0.23 0.28 0.24 0.05

2.72 3.89 4.85 9.31

2.34 2.09 1.67 1.10

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FIG. 7. Evolution of S at 300 K as a function of n extracted from Hall effect (symbols). The solid line represents a fit considering S  n2/3.

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FIG. 9. Temperature dependence of the thermal conductivity (jtotal, solid line) and its lattice component (jlattice) in the series Ti1-xTaxS2.

our samples, as discussed above. In Ti1þxS2, S has been previously described by a Boltzmann model with a single band 8p2 k2 p 2=3 5,36 Þ . For Ti1-xTaxS2, the evodescription: S ¼ 3eh2B m Tð3n lution of S at 300 K as a function of n, extracted from Hall effect, follows this trend as well, as shown in Fig. 7. The temperature dependence of the power factor for Ti1-xTaxS2 materials is shown in Fig. 8. For all compositions, power factor increases with temperature as it is usually observed in highly doped TiS2.4,5 It can be observed that, for low doping concentration, power factor values are similar to those of TiS2 on the full temperature range with an average value around 0.7 mW/mK2 at 700 K. For x ¼ 0.4, the power factor decreases to 0.1 mW/mK2 at 700 K. Compared to previous studies,4,5 the magnitude of the power factor remains lower due to high carrier concentration caused by Ti/S non stoichiometry. The temperature dependence of the total thermal conductivity jtotal for Ti1-xTaxS2 materials is shown in Fig. 9. It

can be seen that jtotal does not significantly increase with tantalum content, whereas the electronic contribution increases significantly with x due to charge carriers doping (Fig. 10). The Ti0.6Ta0.4S2 compound exhibits different temperature dependence with comparable or higher j values (especially over 450 K) as compared to the first members of the Ti1-xTaxS2 series. The lattice thermal conductivity jlattice was then calculated by subtracting jelec from jtotal (Fig. 9). The Lorenz number of each sample was deduced based on Boltzmann transport equation. It was calculated considering the variation in scattering parameter (r). The variation of scattering parameter was estimated as shown in Fig. 11. To obtain r, we follow the procedure described by Ohta et al.25 Basic assumptions are (a) dominant acoustic phonon scattering (r ¼ 0) at high temperature and (b) parabolic band model near the Fermi level. Finally, Lorenz number (L) was deduced by the following equation:

FIG. 8. Temperature dependence of the power factor in the series Ti1-xTaxS2.

FIG. 10. Temperature dependence of electronic thermal conductivity jelec in the series Ti1-xTaxS2.

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FIG. 11. Temperature dependence of the scattering parameter (r) and Lorenz number (L).

 2 "   # kB ðr þ 3ÞFrþ2 ðnÞ ðr þ 2ÞFrþ1 ðnÞ 2  L¼ : e ðr þ 1ÞFr ðnÞ ðr þ 1ÞFr ðnÞ

(1)

Here, Fr(n) is Fermi-Dirac integral and n is reduced Fermi energy. As expected, deviation of L at x ¼ 0.4 is found to be significant as shown in Fig. 11. It can be seen that jlattice decreases significantly with Ta content. As expected, the partial substitution of heavy elements (tantalum) for constituent elements (titanium) reduces the lattice thermal conductivity. The origin of this behaviour may be due to two principal effects, namely structural disorder/deformation due to octahedral distortion or mass fluctuation effect. For a quantitative and better understanding of this change in lattice thermal conductivity in this system, we have analyzed its temperature dependence by Debye-Callaway model37 which can be expressed as follows:  ð hD T 3Nkv2 xp 4 exp ðexp  1Þ2 dxp ; (2) jlattice ¼ 3 4 ðhD =TÞ 0 AT xp 4 þ BT 5 xp 2 þ v=d xp ¼

hx ; kT

(3)

where N is the number of atoms per unit volume, hD is the Debye temperature, v is the phonon velocity, x is the circular frequency, d is the mean free path of boundary scattering, and É is the Dirac constant. A and B are constants related to impurity and umklapp scattering, respectively. The effect of Ta doping was evaluated by A and B parameters, which were numerically obtained by the least square fitting (see Fig. 9) of the model to the experimental results. Here, v of 3343 m/s (Ref. 3) and hD of 240 K (Ref. 38) were used. d was adjusted to be 33 nm. Fitting result is shown in Fig. 12. The parameter A increased parabolically with Ta content, while B increased stepwise near x ¼ 0.1. Because the former relates with defect scattering, the doping effect of Ta on parameter A is analyzed following the discussion by Klemens.39

FIG. 12. Phonon scattering parameters, A and B, as a function of Ta content, x. The parameters were deduced from the fitting of Debye-Callaway model (Eq. (2)) to the experimentally observed jlattice. The increase in A, DA(C), originating in the atomic mixture between Ti and Ta was also obtained based on Klemens model (Eq. (4)).

The relaxation time for this process is given by si

1

 4 x4 d3 C d3 C k ¼ ¼ T 4 xp 4  DAT 4 xp 4 ; 4pv3 4pv3 h

(4)

where d3 is the average atomic volume, and C for a mixture of two kinds of atoms can be expressed as follows:40 " 2  2 # DM Dd ; (5) C ¼ xð1  xÞ þe M d where x is fractional concentration of the dopant, DM and Dd are the differences in mass and size between host atom and dopant, respectively. M and d are average mass and size. e indicates contribution of strain and a value of 39 (Ref. 40) was adopted in the present analysis. The strain effect was analyzed based on the observed lattice volume change with Ta amount, and was found to be negligible compared with mass effect. Structural disorder/deformation from octahedral distortion,30 as discussed before, in the layers due to the higher tantalum radius compared to titanium radius may be then excluded as a major contribution for the decrease in the lattice thermal conductivity. The calculated C and corresponding increase in A parameter (DA) are shown in Fig. 11. The trend of A with Ta doping reasonably agrees with DA, indicating mass difference between Ti and Ta effectively depresses the jlattice in this system. In addition to that the increase in B term at higher Ta content has an effect to decrease jlattice at high temperature, thus the change in phonon-phonon interaction by the Ta doping is also an important mechanism in the practical application at high temperature. Fig. 13 shows the temperature dependence of the dimensionless figure of merit ZT of the Ti1-xTaxS2 series. The ZT value for all the specimens increases with increasing temperature. The ZT value of Ti0.95Ta0.05S2 is slightly increased compared with TiS2, whereas heavily doped compounds tend to exhibit comparable (x ¼ 0.1) or lower values x ¼ 0.4.

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SEM technical support. E. Guilmeau and T. Barbier thank European Commission (FP7-SME-2012-1) for financial support. 1

FIG. 13. Temperature dependence of the figure of merit ZT in the series Ti1-xTaxS2.

The evolution in the ZT versus tantalum content can be ascribed to two combined effects: (1) a slight increase in the power factor through a tuning in the carrier concentration and (2) a substantial decrease in the lattice thermal conductivity presumably caused by mass fluctuation effect. Nevertheless, the ZT values reported in the whole series remain lower than previous ones4 due to an electron overdoping caused by sulphur vacancies. IV. CONCLUSIONS

Within the large family of MX2 compounds, two main structures coexist depending on the nature of the component, TiS2 (CdI2 type), for example, with hexagonal coordination and MoS2 with prismatic coordination. Titanium disulfide, which belongs to this large family appears as a promising thermoelectric material candidate. TiS2 can host different elements in the structure by intercalation or substitution modifying its thermal and electrical properties. In the present study, we have shown that the partial substitution of heavy elements (tantalum) for constituent elements (titanium) reduces the lattice thermal conductivity through mass difference effect. It leads to slightly improved ZT values compared to pristine TiS2. On the other hand, the fact that the power factor is lower as compared to previous studies due to higher carrier concentration implies that more efforts should be dedicated to control the Ti/S stoichiometry in these compounds through different processing routes. If this can be achieved, transition metal layered chalcogenides might represent a replacement solution to the long known and used Bi2Te3 for room and medium temperature range applications. ACKNOWLEDGMENTS

The authors gratefully thank J. Lecourt for sample preparation, F.-X. Lefe`vre for technical assistance on high temperature measurements, and X. Larose and M. Strebel for

G. A. Slack, in CRC Handbook of Thermoelectric, edited by D. M. Rowe (CRC, Boca Raton, 1995), p. 407. 2 H. Imai, Y. Shimakawa, and Y. Kubo, Phys. Rev. B 64, 241104 (2001). 3 C. Wan, Y. Wang, N. Wang, and K. Koumoto, Materials 3, 2606–2617 (2010). 4 E. Guilmeau, Y. Breard, and A. Maignan, Appl. Phys. Lett. 99, 052107 (2011). 5 M. Ohta, S. Satoh, T. Kuzuya, S. Hirai, M. Kunii, and A. Yamamoto, Acta Mater. 60, 7232–7240 (2012). 6 L. F. Mattheis, Phys. Rev. B 8, 3719–3740 (1973). 7 J. A. Wilson and A. D. Yoffe, Adv. Phys. 18, 193–335 (1969). 8 R. A. Bromley, R. B. Murray, and A. D. Yoffe, J. Phys. C 5, 759 (1972). 9 P. C. Klipstein, A. G. Bagnall, and W. Y. Liang, J. Phys. C 14, 4067–4081 (1981). 10 C. M. Fang, R. A. de Groot, and C. Haas, Phys. Rev. B 56, 4455–4463 (1997). 11 E. M. Logothetis, W. J. Kaiser, and C. A. Kukkonen, Physica B 99, 193–198 (1980). 12 M. S. Whittingham and J. A. Panella, Mater. Res. Bull. 16, 37–45 (1981). 13 A. H. Thompson, F. R. Gamble, and C. R. Symon, Mater. Res. Bull. 10, 915–919 (1975). 14 H. Kobayashi, K. Sakashita, M. Sato, T. Nozue, T. Suzuki, and T. Kamimura, Physica B 237, 169–171 (1997). 15 M. J. McKelvy and W. S. Glaunsinger, J. Solid State Chem. 66, 181–188 (1987). 16 M. S. Whittingham and F. R. Gamble, Mater. Res. Bull. 10, 363–371 (1975). 17 M. S. Whittingham, Prog. Solid State Chem. 12, 41–99 (1978). 18 T. Uchida, K. Kohiro, H. Hinode, M. Wakihara, and M. Taniguchi, Mater. Res. Bull. 22, 935–942 (1987). 19 C. Julien, I. Samaras, and O. Gorochov, Phys. Rev. B 45, 13390–13395 (1992). 20 D. Li, X. Y. Qin, J. Zhang, and H. J. Li, Phys. Lett. A 348, 379–385 (2006). 21 D. Li, X. Y. Qin, J. Liu, and H. S. Yang, Phys. Lett. A 328, 493–499 (2004). 22 F. Gascoin, N. Raghavendra, E. Guilmeau, and Y. Breard, J. Alloys Compd. 521, 121–125 (2012). 23 W. Sams, N. Lowhorn, T. M. Tritt, E. Abbott, and J. W. Kolis, in Proceeding of ICT (2005), pp. 41–45. 24 M. Beaumale, T. Barbier, Y. Breard, B. Raveau, Y. Kinemuchi, R. Funahashi, and E. Guilmeau, “Mass fluctuation effect in Ti1-xNbxS2 bulk compounds,” J. Electron. Mater. (published online). 25 S. Ohta, T. Nomura, H. Ohta, and K. Koumoto, J. Appl. Phys. 97, 034106 (2005). 26 F. Jellinek, J. Less-Common Met. 4(1), 9–15 (1962). 27 Y. Tison et al., Surf. Sci. 563, 83–98 (2004). 28 M. Shimakawa, H. Maki, H. Nishihara, and K. Hayashi, Mater. Res. Bull. 32, 689–699 (1997). 29 S. K. Srivastava, T. K. Mandal, and B. K. Samantaray, Synth. Met. 90, 135–142 (1997). 30 M.-L. Doublet, S. Remy, and F. Lemoigno, J. Chem. Phys. 113, 5879–5890 (2000). 31 Y. Gotoh, J. Akimoto, and Y. Oosawa, J. Alloys Compd. 270, 115–118 (1998). 32 A. H. Thompson, K. R. Pisharody, and R. F. Koehler, Jr., Phys. Rev. Lett. 29, 163–166 (1972). 33 J. A. Benda, Phys. Rev. B 10, 1409–1420 (1974). 34 R. Inada, Y. Onuki, and S. Tanuma, Physica B & C 99, 188–192 (1980). 35 C. B. Vining, J. Appl. Phys. 69, 331–341 (1991). 36 C. A. Kukkonen, W. J. Kaiser, E. M. Logothetis, B. J. Blumenstock, P. A. Schroeder, S. P. Faile, R. Colella, and J. Gambold, Phys. Rev. B 24, 1691–1709 (1981). 37 J. Callaway, Phys. Rev. 113, 1046–1051 (1959). 38 M. Inoue, Y. Muneta, H. Negishi, and M. Sasaki, J. Low Temp. Phys. 63, 235–245 (1986). 39 P. G. Klemens, Proc. Phys. Soc. Sect. A 68, 1113–1128 (1955). 40 B. Abeles, Phys. Rev. 131, 1906–1911 (1963).

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