Sb Doping of Metallic CuCr - ACS Publications - American

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Sb Doping of Metallic CuCr2S4 as a Route to Highly Improved Thermoelectric Properties Atta Ullah Khan,† Rabih Al Rahal Al Orabi,‡,§ Amir Pakdel,† Jean-Baptiste Vaney,† Bruno Fontaine,∥ Régis Gautier,∥ Jean-François Halet,∥ Seiji Mitani,⊥,# and Takao Mori*,†,# †

National Institute for Materials Science (NIMS), MANA, 1-1-1 Namiki, Tsukuba 305-0044, Japan Department of Environmental Science and Engineering, Ewha Womans University, Seoul 120-750, Korea § Department of Physics and Science of Advanced Materials, Central Michigan University, Mt. Pleasant, Michigan 48858, United States ∥ Institut des Sciences Chimiques de Rennes, UMR 6226 CNRSUniversité de Rennes 1Ecole Nationale Supérieure de Chimie de Rennes, CS 50837, 35708 Rennes, France ⊥ National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba 305-0047, Japan # Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8577, Japan ‡

S Supporting Information *

ABSTRACT: We report for the first time the thermoelectric properties of CuCr2−xSbxS4 (0.22 ≤ x ≤ 0.5). Although CuCr2S4 has been reported to be a metallic compound, addition of Sb shifts the material toward the semiconductor side. This is confirmed by band structure calculations of CuCr2−xSbxS4 (x = 0, 0.25, 0.5) models. Increasing Sb content enhances the power factor. However, beyond x = 0.3, further Sb addition lowers the electrical conductivity and power factor. A very interesting point is the simultaneous increase of the Seebeck coefficient as well as the electrical conductivity with increasing temperature, which acts like a variable range hopping (VRH) compounds but possesses much better properties than those having VRH. Samples were annealed for 48 h prior to thermoelectric properties measurements to have a reliable dimensionless figure of merit (ZT). An attractive ZT of 0.43 is obtained at ∼650 °C. The attractive thermoelectric properties we discovered by driving a metal compound into a semiconductor make this compound an interesting thermoelectric material especially because of the cheap constituent elements compared to those of typical state-of-the-art thermoelectric materials. Furthermore, this material is stable up to 650 °C at least, a relatively high temperature for sulfides. Additionally, we discovered a miscibility gap in this solid solution close to an Sb content of 0.15; although a detailed study dedicated entirely to this miscibility gap would be required, it will encourage the researchers to further explore this system. efforts are ongoing to find new and more efficient thermoelectric materials.4−7 Efficiency of thermoelectric materials is measured by the dimensionless figure of merit (ZT). It is calculated by the formula ZT = S2σT/κ, where S stands for the Seebeck coefficient, σ represents the electrical conductivity, and κ is the

1. INTRODUCTION With increasing consumption of fossil fuels and a relentless depletion of these resources, it has become very important to convert them more efficiently into usable forms of energy. About two-thirds of the energy of fossil fuels is wasted mainly in the form of waste heat.1 It is possible to convert this waste heat into useful energy by employing thermoelectric materials.2,3 This is why research focused on thermoelectric materials has increased by many folds in recent times and why intense © 2017 American Chemical Society

Received: December 19, 2016 Revised: February 16, 2017 Published: February 17, 2017 2988

DOI: 10.1021/acs.chemmater.6b05344 Chem. Mater. 2017, 29, 2988−2996

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Chemistry of Materials thermal conductivity. S2σ as a whole is termed as the power factor. As obvious from the formula, the power factor should be as high as possible while still keeping the thermal conductivity as low as possible. Different thermoelectric materials are required for different temperature ranges and applications. Most middle or low temperature range materials are chalcogenides or antimonides.5−7 Out of chalcogenides, sulfur is the cheapest and lightest element, which makes sulfides attractive compounds for bulk thermoelectric materials. Moreover, sulfur is one of the byproducts of oil exploration, and its production is far more than its consumption. Companies are piling up sulfur in the forms of pyramids,8 posing a huge potential threat to the environment. Therefore, it is very important to utilize sulfur to make some valuable products such as thermoelectric materials. Indeed, several sulfide compounds have been discovered with good thermoelectric properties.9−13 However, naturally occurring minerals, if suitable for thermoelectric applications, are the best option.11,13,14 In addition to a newly discovered sulfospinel cuprokalininite (CuCr2S4) found from metamorphic rocks in the South Baikal region of Russia,15 another mineral named florensovite with the formula Cu(Cr1.5Sb0.5)S4 is already reported to be found from the Baikal region as well.16 Sbdoped CuCr2S4 has been investigated regarding its interesting magnetic properties: CuCr 1.5 Sb 0.5S 4 is reported to be antiferromagnetic,17 while CuCr2S4 is described as ferromagnetic.18 Moreover, giant magnetoresistance has been reported for CuCr1.6Sb0.4S4.19 However, to the best of our knowledge, thermoelectric properties were not investigated for Sb-doped CuCr2S4. On the basis of these previous reports,17−19 we assume that replacing some Cr by Sb can cause a significant influence on thermoelectric properties. Although CuCr2S4 is reported to be metallic,20−22 a detailed literature survey did not show any report related to the effect of Sb addition on the thermoelectric properties except that CuCr1.5Sb0.5S4 is a semiconductor.17 In this study, for the first time, we systematically and comprehensively investigate the band structure and high temperature thermoelectric properties of CuCr2−xSbxS4 using experimental and theoretical tools. Because undoped CuCr2S4 is a metallic compound with the Fermi level below the top of the valence bands, we show that Sb doping provides extra electrons to fill some of the holes in the valence bands, leading to an enhanced Seebeck coefficient and reduction of the magnetic moment. We also show that the substitution of Sb with Cr atoms in CuCr2S4 leads to a high power factor for x = 0.3. This yields to a high figure of merit ZT equal to 0.43 at T ∼ 650 °C, which is one of the highest values reported for sulfurbased thermoelectric materials.

vacuum. Highly dense (∼97% of the theoretical density) disk-shaped pellets with dimensions of 10 mm diameter and 2 mm thickness were obtained. The obtained pellets were sealed in quartz tube and annealed at 650 °C for 48 h. Powder X-ray Diffraction (PXRD) and High Resolution Transmission Electron Microscopy (HRTEM). Samples were characterized by PXRD with Cu Kα (λ = 1.54056 Å) radiation operated at room temperature using Ultima III (Rigaku corporation, Tokyo, Japan) instrument. Lattice constants, volumes, and theoretical densities were calculated by the Rietveld refinement using the Fullprof Suite software. HRTEM was carried out using a JEM-2100F microscope (JEOL Ltd., Japan) equipped with an energy dispersive spectrometer (EDS). Electronic Transport Measurements. The sintered pellets were cut into ∼1.8 × 2.0 × 8 mm bars for simultaneous measurement of the electrical resistivity and the Seebeck coefficient. Measurements were performed under He atmosphere from room temperature to 873 K using a ULVAC-Riko-ZEM-5 instrument. Thermal Transport Measurements. The sintered pellets were polished into a cylinder shape ∼10 and ∼1.7 mm thick for thermal diffusivity measurements. The thermal diffusivity coefficient (D) was measured with an ULVAC TC-7000 instrument. The heat capacity (Cp) was measured using differential scanning calorimetry (DSC, Netzsch AST 449). The total thermal conductivity, k, was calculated using the formula k = DdCp, where d represents the density of the sample. The electronic thermal conductivity is proportional to the electrical conductivity according to the Wiedemann−Franz law (ke = σLT). The Lorenz number, L, was estimated as a function of temperature from the experimental Seebeck coefficients using the single parabolic band model and assuming that acoustic phonon scattering limits the mobility, as explained in previous literature.23 The electronic thermal conductivity was subtracted from the total thermal conductivity to obtain lattice thermal conductivity. Error bars were determined from measurements of different samples of the same composition. Hall Effect Measurements. The Hall coefficient RH was measured at 300 K on the sample CuCr1.5Sb0.5S4 with the AC transport option of the Quantum Design Physical Properties Measurement System (PPMS). A five-wire configuration was used by attaching Au wires with Ag epoxy onto the sample. The magnetic field was swept between −3 and +3 T. The hole concentration p and Hall mobility μH were estimated from p = (1/e)RH and μH = RH/ρ. The Hall effect could not be measured on the other samples due to parasitic effects owing to the magnetic nature of these latter compounds. First-Principles Calculations. Spin-polarized density functional theory (DFT) geometry optimizations of CuCr2−xSbxS4 (x = 0, 0.25, and 0.5) were carried out with the CASTEP8.0 code24 using the GGA in the parametrization of PBE functional.25 Cell parameters and atomic positions were both relaxed. Because of the presence of localized d electrons, an additional Hubbard-like term was introduced for Cr and Cu. The simplified Dudarev approach26 was used with Ueff = U − J = 3.5 eV for Cu 3d orbitals and 2.5 eV on the Cr 3d orbitals.27 All ultrasoft pseudopotentials were generated using the OTF_ultrasoftpseudopotential generator included in the program. The cutoff energy for plane-waves was set to 500 eV. The electronic wave function was sampled with 30 k-points in the first Brillouin zone using the Monkhorst−Pack method.28 For the electronic band structures, we used the full-potential linearized augmented plane wave (FLAPW) approach, as implemented in the WIEN2K code.29 The PBE+U approach was used with the Ueff values for 3d orbitals of Cu and Cr previously mentioned. A plane wave cutoff corresponding to RMTKmax = 7 was used. The radial wave functions inside the nonoverlapping muffin-tin spheres were expanded up to lmax = 12. The charge density was Fourier expanded up to Gmax = 16 Å−1. Total energy convergence was achieved with a Brillouin zone integration mesh of 500 k-points.

2. EXPERIMENTAL PROCEDURES Sample Preparation. CuCr2−xSbxS4 (0 ≤ x ≤ 0.5) samples were prepared by sealing high purity powders of Cr, Sb, Cu, and S in quartz tubes under vacuum. Tubes were heated from room temperature to 750 °C in 8 h, kept at 750 °C for 15 h, and then slowly cooled. The materials were ground in SiC mortars, compressed in a cold isostatic press (CIP) machine, sealed again in quartz under vacuum, heated to 650 °C, and kept there for 15 h to remove any stress induced during pressurized sintering. The obtained samples of CuCr2−xSbxS4 were ground into fine powders using a mortar and pestle to reduce the grains. The powders were then densified by a spark plasma sintering (SPS, Dr Sinter 1080, SPS-Syntex Inc., Tokyo, Japan) method at 720 °C for 5 min in a 10 mm diameter graphite die under an axial pressure of 80 MPa in

3. RESULTS AND DISCUSSION Powder X-ray diffraction measurements followed by the Rietveld refinement confirmed the crystallinity, single phase 2989


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Figure 1. Rietveld refinement of the XRD pattern of CuCr1.5Sb0.5S4 sample, indicating a single phase material and confirming MgAl2O4-type structure. Reasonably low R factors indicate a good fit of the observed and calculated patterns.

Figure 2. Lattice parameters vs Sb content. Slight deviation from Vegard’s law is observed. Lattice parameters of a sintered pellet having Sb content of 0.17 after annealing showed a clear split (green triangles), indicating the presence of a miscibility gap at 600 °C.

formation, and replacement of Cr by Sb, forming a CuCr2−xSbxS4 solid solution. Figure 1 shows the Rietveld refinement of the XRD pattern of CuCr1.5Sb0.5S4, indicating a single-phase sample. Lattice parameters obtained (a = 1.0001 ± 0.0004 nm) were in good agreement with those reported in the literature (1.0018 nm).30 Figure 2 shows the graph of lattice parameters vs Sb content. Owing to the size of Sb much larger than that of Cr, their covalent radii are equal to 1.40 and 1.22 Å, respectively, it is obvious that the replacement of Cr by Sb will expand the lattice, resulting in an increase in lattice constants. Peaks in the XRD pattern shift to the lower 2θ, in accordance

with the lattice parameters expansion. In general, a slight positive deviation from Vegard’s law is observed. Lattice parameters of a sintered pellet with composition CuCr2−xSbxS4 (x = 0.17) after annealing show a clear split (for XRD pattern, see Supporting Information, Figure S2), indicating the presence of a miscibility gap at 600 °C. This miscibility gap is observed for the first time, as no systematic study is reported on this solid solution. High crystallinity as well as the presence of a miscibility gap were also confirmed by HRTEM. Images obtained by HRTEM, performed on a sample with an Sb content x = 0.3 (Figures 3a− 2990


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Figure 3. HRTEM images of x = 0.3 (a−c), indicating a highly crystalline material and presenting the grain boundaries (a and b). Inset in panel c shows the interplanar distance taken for 10 planes, and an average value produced the interplanar distance for this particular plane. STEM helped us confirm the presence of a miscibility gap in the x = 0.17 sample by EDX analysis of points 1 and 2 (d). EDX spectra of points 1 (e) and 2 (f) clearly showed a variation in Cr and Sb content ratio.

metallic.22 Therefore, we focused mainly on the Sb-rich side of the solid solution. It has been previously reported that Sb possesses a valence state similar to that of Cr (+3) in CuCr2−xSbxS4.32,33 This disagrees with the charge of +3.53 computed for Sb in CuCr1.5Sb0.5S4, which suggests a +5 valence state for the pnictogen. Indeed, Warczewski et al. previously experimentally proposed a +5 state.17 The replacement of Cr by Sb hardly affects the local crystal structure. Moreover, shorter than expected Sb−S distances (Supporting Information, Table S1) indicate a rather strong bond.32 This could be a possible reason for a highly stable Sb-rich side of the solid solution under vacuum. The crystal structure of CuCr1.5Sb0.5S4 is shown in Figure 4. This structure consists of tetrahedra and octahedra made of sulfur. One eighth of the total tetrahedra are filled by Cu, and half of the total octahedra are filled by a Cr/Sb mixture.

c), indicated a highly crystalline, defect-free single-phase material. No intergranular phase was observed. However, scanning transmission electron microscopy (STEM), performed on the sample with Sb = 0.17, helped us to confirm the presence of a miscibility gap in this sample, which was already observed in the X-ray powder diffraction patterns. Energy dispersive X-ray (EDX) analysis (Figures 3e and f) of the two grains unambiguously showed a variation in Cr and Sb content ratio. We decided to focus on the thermoelectric properties of the Sb-rich side of the miscibility gap for two reasons: (a) the decomposition temperature of CuCr2S4 under vacuum is reported to be 445−550 °C.31 TC-7000 runs under continuous pumping and caused the samples with Sb content 0 and 0.075 to decompose partially. (b) CuCr2S4 is already reported to be 2991


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as in the present case may have its role in low lattice thermal conductivity as well. HRTEM images (Figure 3a−c) confirmed that the low thermal conductivity observed in the present study was not a result of processing defects; instead, it is more likely an intrinsic property. Considering the electronic properties, addition of Sb is expected to lower the electrical conductivity compared to that of the metallic CuCr2S4 with a corresponding rise in the Seebeck coefficient. Variation of magnetic properties that suggest ferromagnetic (ferrimagnetic) to antiferromagnetic transition with increasing Sb content was also observed (Supporting Information, Figure S1). Figure 5 shows the measured thermoelectric properties of CuCr2−xSbxS4 (0.22 ≤ x ≤ 0.5). Replacement of Cr with Sb decreases the electrical conductivity and makes it a semiconductor compound. From Figure 5a, it is obvious that the electrical conductivity is inversely proportional to the Sb content at low temperatures and decreases with increasing Sb. Regarding the temperature dependence, generally, the electrical conductivity increases as the temperature increases. CuCr2S4 is metallic at room temperature with only a small Seebeck coefficient of 16 μV/K.22 Although, the mineral florensovite CuCr1.5Sb0.5S4 is reported to be a semiconductor, no information regarding the Seebeck coefficient is given yet.17 In current study, we observed that the addition of Sb improves the Seebeck coefficient significantly (Figure 5b). We investigated the thermoelectric properties of this composition and discovered a large Seebeck coefficient of >200 μV/K. Positive

Figure 4. Representation of the crystal structure of CuCr1.5Sb0.5S4. Pink tetrahedra are filled by Cu, while Cr/Sb occupies the center of the octahedra.

The rest of the tetra- and octahedra are empty. Spitzer34 suggested that the spinel structure, having primarily octahedral coordination and partial filling of the polyhedra, tends to have lower lattice thermal conductivity. Additionally, a large unit cell

Figure 5. Temperature dependence of the thermoelectric properties of CuCr2−xSbxS4 (0.22 ≤ x ≤ 0.5). (a) Electrical conductivity (σ) seems to drop rapidly after a certain Sb content. (b) The Seebeck coefficient is positive in the whole temperature range, pointing toward p-type material with holes as dominant charge carriers. (c) Total thermal conductivity (κ) with similar values at low temperatures but differentiating considerably at high temperatures. (d) Lattice thermal conductivity (κlat). (e) Power factor, which increases initially with increasing Sb content, reaches a maximum, and then decreases. (f) Figure of merit (ZT) with a highest value of 0.43 for Sb = 0.3. 2992


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increase in both conductivity and Seebeck coefficient with temperature, the degenerate semiconductor nature may be playing a role, although systems such as Bi2Te3 often show metallic temperature dependence of the conductivity. The relatively low values of mobility indicate the presence of disorder, which is consistent with the crystal structure features mentioned above and the low thermal conductivity. This may also be affecting the temperature dependence of the conductivity, although it is not likely to be a conventional VRH system. The thermoelectric characteristics are overall attractive, and further investigations on the transport of other systems with high carrier concentration and some degree of disorder are merited. Computing the experimentally measured value would give a high effective mass of 5.9m0 with m0 being the electron mass.23 This value appears unexpectedly high, and a breakdown of the above formulation may be occurring, but an enhanced effective mass could nevertheless justify the combination of the high carrier concentration and the high thermopower. In the case of chalcopyrite, magnetic interaction was proposed as the origin of the heavy effective mass and large Seebeck coefficient (large power factor).11,13 Because the present system is also magnetic, a similar situation may be applicable; however, this case indicates that the ordering itself of the magnetic moments may not be critical because the ordering temperature is significantly lower. The explicit mechanism which can be related to, for example, existence of sizable magnetic moments in the system, spin fluctuations, and magnetic interactions cannot be rigorously proved yet. Probing the detailed linkage between the thermoelectric and magnetic properties remains an intriguing research topic to be pursued further. In any case, a heavy effective mass is indicated, and this is also consistent with the DFT calculations described next. To rationalize these physical measurements, DFT calculations were carried out. As shown by the X-ray diffraction experiments, substitution of Cr by Sb in the compound does not modify the description of the crystal structure in the cubic space group Fd3̅m. However, to model the substitution of Cr by Sb atoms in the compound, the crystal structure of CuCr2−xSbxS4 must be described in a lower symmetrical space group. Among the two rates of substitution of Cr with Sb that have been considered (0.25 and 0.5), several distributions can be envisioned. To easily compare the electronic structure of CuCr2−xSbxS4 (x = 0, 0.25, and 0.5), the monoclinic space group P2/m was considered for all models. As Gupta et al. did to study the electronic structure of CoxCu1−xCr2S4 nanocrystals,27 GGA+U calculations were carried out. Table 2 displays the optimized unit cell parameters and pertinent distances. As expected from the larger size of Sb compared to that of Cr and as observed experimentally, substitution of Cr with Sb increases the volume of the unit cell. The DFT optimized unit cell parameters are slightly larger than those resulting from the X-

values suggest that it is a p-type material. However, it possesses a very low electrical conductivity compared to that of the parent compound CuCr2S4 (1.11 × 105 S/m).22 It indicates that the Seebeck coefficient is quite sensitive to Sb content. Like the electrical conductivity, the Seebeck coefficient shows similar temperature dependence and increases in all cases with rising temperature. The only exception is the sample with the highest Sb content x = 0.5, in which it saturates around 350 °C, stays more or less unchanged up to 500 °C, and then starts decreasing. According to the Boltzmann equation, electrical conductivity and the Seebeck coefficient have an inverse relationship, so an improvement in one will result in a degradation of the other. However, the ideal case would be an enhancement in both properties simultaneously, and among typically studied thermoelectric material, there are not many cases where it is observed that both properties increase.35−38 Some notable examples are the VRH systems such as the higher borides, where both properties increase with increasing temperature.37−41 However, these are materials that are typically only thermoelectrically competitive at high temperatures. The current compound under study also shows this kind of behavior, especially in the case of an Sb content of 0.3 where both electrical conductivity and Seebeck coefficient are increasing almost linearly with increasing temperature. However, in this case, considering the relatively high electrical conductivity, it is unlikely to be a VRH system. Furthermore, the overall thermoelectric properties of the present system appear to be superior compared to those VRH systems, making this compound very attractive for further studies. As discussed above, addition of Sb lowers the electrical conductivity but enhances the Seebeck coefficient, so it is necessary to find a compromise between electrical conductivity and the Seebeck coefficient. A better term to represent is the power factor (S2σ), which should be optimized. Figure 5e indicates that the addition of Sb increases the power factor to a certain value and then starts decreasing. The optimized value of Sb from the graph is found to be x = 0.30. A fairly high power factor of ∼1 mW/mK2 is observed at 643 °C. It must be noted that the properties were measured on annealed samples (annealed at 650 °C after sintering) to remove any stress induced due to pressurized sintering. This kind of stress sometimes results in special properties which dissipate after a few runs. Therefore, our reported properties are supposed to stay more or less the same over multiple runs. The Hall effect was measured for the sample CuCr1.5Sb0.5S4, as interfering magnetic effects in the other compounds would not allow a reliable measurement. The measured Hall coefficient and calculations of the hole carrier concentration and hole mobility values are shown in Table 1. This sample shows a very high carrier concentration at 300 K of 2.41 × 1021 cm−3, a high value consistent with a metallic or degenerate semiconducting nature of the compound properties. The hole mobility of 4.06 cm2/V·s is rather low compared to those of other state of art thermoelectric compounds that can exceed 100 cm2/V·s. Regarding the trend discussed above and the

Table 2. Optimized Cell Parameters and Pertinent Distances (Å) CuCr2−xSbxS4 (x = 0, 0.25, and 0.5) Models

Table 1. Electronic Transport Parameters Obtained by Hall Effect Measurement of CuCr1.5Sb0.5S4 measured Hall coefficient (cm3/C) CuCr1.5Sb0.5S4

0.0025

carrier concentration p (cm−3) 2.41 × 10

21

Hall mobility (cm2/V·s) 4.06 2993

x

0

0.25

0.5

a b=c Cu−S Cr−S Sb−S

9.995 7.051 2.296 2.387

10.012 7.103 2.277−2.347 2.349−2.466 2.545−2.552

10.171 7.185 2.325−2.345 2.364−2.467 2.570−2.597


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Chemistry of Materials ray analysis; this overestimation falls into the range of 1−3% that is often computed with the PBE functional. Substitutions of Cr with Sb lower the symmetry of the crystal structure. In the case of CuCr1.75Sb0.25S4, some Cu−S and Cr−S contacts are slightly shorter than those in the Sb-free phase, whereas some others reach 2.347 and 2.466 Å, respectively. A similar effect is computed for CuCr1.5Sb0.5S4. These distortions in the tetrahedral and octahedral environments of Cu and Cr, respectively, should decrease the thermal conductivity of the materials. Spin-polarized total and atom-projected density of states (DOS) of CuCr2−xSbxS4 (x = 0, 0.25, and 0.5) are sketched in Figure 6. Only ferromagnetic states were computed. DOS of Sb-free phase is similar to the one computed by Gupta et al.27 CuCr2S4 is computed to be metallic and magnetic; the cell moment is about 5.1 μB per formula unit. As shown in Figure 6, substituting Cr with Sb decreases the shift between spin-up and spin-down components of the DOS. This leads to the reduction of the magnetic moment (down to 4 μB for CuCr1.5Sb0.5S4) and qualitatively agrees with the magnetic data (Supporting Information, Figure S1). According to the DOS sketched in Figure 6, a semimetallic behavior is expected for these phases at very low temperature. Moreover, CuCr2−xSbxS4 (x = 0.25 and 0.5) should exhibit electrical conductivity lower than that of the Sb-free phase. Even if CuCr2−xSbxS4 (x = 0.25 and 0.5) phases exhibit semiconducting properties, their resistivity is very low, close to the one measured for semimetals. Moreover, one must keep in mind that our calculations are performed at zero temperature. Some charge-ordering or other charge reorganization among the Cu and Cr ions may occur at higher temperatures, leading to the creation of a semiconducting gap. As the content of Sb increases in the structure, electron filling of the valence band increases. This explains why the Seebeck coefficient increases with the Sb content at low temperature. Heremans et al. pointed out that large Seebeck coefficients can be obtained when the Fermi level is positioned where the DOS has a sharp slope.42 The comparison of the DOS sketched in Figure 6 shows that the DOS is higher at the Fermi level for the CuCr1.75Sb0.25S4 model. Moreover, among the three models, the DOS has the sharpest slope at the Fermi level for this CuCr1.75Sb0.25S4 model. The band structure of this model (Supporting Information, Figure S3), shows the presence of flat bands in the vicinity of the Fermi level. Although exact values cannot be determined from our calculations, these features are consistent with the large effective mass indicated from the transport measurements. Another important factor is the thermal conductivity. Apparently, it has a mixed trend and does not change linearly with Sb content (Figure 5c). Lattice thermal conductivity (Figure 5d) overall also shows a mixed trend. Although, while it is hard to explain this trend, there is a clue in bond lengths (Supporting Information, Table S1). (Cr/Sb)−S distances remain the same for Sb content of 0.22 and 0.3, resulting in similar thermal conductivity, but increase considerably in the case of Sb = 0.5. This increase in bond length seems to relax the structure and results in an increase in lattice thermal conductivity. On the other hand, Cu−S bond distances have a steady growth with increasing Sb content and do not seem to affect the thermal conductivity significantly. Overall, as mentioned above, the spinel structure with primarily octahedral coordination and partial filling of the polyhedra have a trend of lower lattice thermal conductivity34 with further disorder in our case coming from Cr/Sb mixing. Moreover, our effort to create vacancies on the sulfur site through sulfur deficient synthesis

Figure 6. Spin-polarized DFT DOS of CuCr2−xSbxS4 (x = 0, 0.25, and 0.5). No band gap at the Fermi level is observed, indicating that all the compositions are metallic at 0 K.

failed and ended up in multiphase samples. The lattice thermal conductivity shows similar temperature dependence to glassy/ disordered systems,43,44 namely little dependence or an increase with temperature at relatively high temperatures. In some systems, lone pairs have been proposed as a powerful mechanism to engender very low thermal conductivity.45−47 However, the thermal conductivity increasing largely for the heavy Sb doping rules out any dominant effect of the lone pairs in this case. Furthermore, the indication of the +5 valence state for Sb obtained from theoretical calculation rules out the existence of lone pairs. The minimum lattice thermal 2994



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ACKNOWLEDGMENTS Support from CREST, JST is acknowledged. We also thank the CNRS PICS Synthesis and Characterization of New NonOxides Functional Materials (Grant 2012 N°159769) for support of this work.

conductivity (κmin) uses the shortest scattering distance (l) of λ/2, where λ is the phonon wavelength. κmin can be approximated at high temperatures by the following equation:48 1 ⎛⎜ π ⎞⎟ 2⎝6⎠

1/3

κ min =

⎛ V ⎞−2/3 KB⎜ ⎟ (νs) ⎝n⎠

■

where KB is Boltzmann constant, V is the unit cell volume, n is the number of atoms per unit cell, and νs (2632 ms−1) is the average speed of sound.49 Using this formula, κmin is estimated at ∼0.2 W/mK. For all samples, the κlat values are higher than the κmin value, indicating that further reductions to κlat may be possible. Such a lowering might be achieved, for example, by reducing the grain size to enhance the boundary scattering of heat-carrying phonons.50,51 On the basis of all of this data, the dimensionless figure of merit of this series was calculated. It is obvious that the ZT increases with increasing Sb content up to a certain optimum amount of Sb (x = 0.30) and then starts decreasing again (Figure 5f). The highest value for ZT was found to be 0.43 at ∼643 °C, which is the best value among the many other related compounds of this series.22 This value is much higher than that of the other sulfur-based chalcopyrites, e.g., CuFeS2.11,13 It is slightly higher than TiS2, comparable to Cu0.1TiS2,12 but lower than the tetrahedrites.14

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.6b05344. Measured magnetic properties and related text, X-ray diffractograms showing the miscibility gap, spin-up band structure calculations, and a table containing bond lengths (PDF)

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REFERENCES

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4. CONCLUSIONS The CuCr2−xSbxS4 (0 ≤ x ≤ 0.5) series was prepared and characterized. Lattice parameters vs Sb content are reported. A miscibility gap close to the Sb content of 0.15 is observed. Replacement of Cr by Sb lowers the thermal conductivity. We determined that the addition of Sb helps in enhancing the Seebeck coefficient. However, addition of Sb degrades the electrical conductivity. Overall, it helps in improving the power factor, and a high power factor at an Sb content of x = 0.3 is observed, resulting in an attractive ZT of 0.43. A MgAl2O4-type structure is quite common, and many different compounds comprised of this structure type have been reported. This report may further trigger intense research on the thermoelectric properties of this series of compounds because Sbdoped CuCr2S4 may be a serious candidate for consideration in medium temperature power generation where toxic and/or expensive element-free materials are required.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Takao Mori: 0000-0003-2682-1846 Notes

The authors declare no competing financial interest. 2995


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NOTE ADDED AFTER ASAP PUBLICATION This paper was published ASAP on February 28, 2017, with an inclusion of an equation in the Results and Discussion Section that should have been deleted. The corrected version was reposted on March 7, 2017.

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Sb Doping of Metallic CuCr - ACS Publications - American

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