Thermoelectric Properties and Electronic Structures of CuTi2S4

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Thermoelectric Properties and Electronic Structures of CuTi2S4 Thiospinel and Its Derivatives: Structural Design for Spinel-Related Thermoelectric Materials Katsuaki Hashikuni,*,† Koichiro Suekuni,*,†,‡ Hidetomo Usui,§ Raju Chetty,∥ Michihiro Ohta,∥ Kazuhiko Kuroki,§ Toshiro Takabatake,⊥ Kosuke Watanabe,‡ and Michitaka Ohtaki†,‡

Inorg. Chem. Downloaded from pubs.acs.org by UNIV OF WINNIPEG on 01/11/19. For personal use only.

†

Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan ‡ Transdisciplinary Research and Education Center for Green Technologies, Kyushu University, Kasuga, Fukuoka 816-8580, Japan § Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan ∥ Research Institute for Energy Conservation, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japan ⊥ Department of Quantum Matter, Graduate School of Advanced Sciences of Matter, Hiroshima University, Higashihiroshima 739-8530, Japan S Supporting Information *

ABSTRACT: We report the preparations, thermoelectric and magnetic properties, and electronic structures of Cu−Ti−S systems, namely, cubic thiospinel c-Cu1−xTi2S4 (x ≤ 0.375), a derivative cubic and Ti-rich phase c-Cu1−xTi2.25S4 (x = 0.5, 0.625), and a rhombohedral phase r-CuTi2S4. All samples have the target compositions except for r-CuTi2S4, whose actual composition is Cu1.14Ti1.80S4. All of the phases have ntype metallic character and exhibit Pauli paramagnetism, as proven by experiments and first-principles calculations. The Cu and Ti deficiencies in c-Cu1−xTi2S4 and r-CuTi2S4, respectively, decrease the electron-carrier concentration, whereas the “excess” of Ti ions in c-Cu1−xTi2.25S4 largely increases it. For r-CuTi2S4, the reduced carrier concentration increases the electrical resistivity and Seebeck coefficient, leading to the highest thermoelectric power factor of 0.5 mW K−2 m−1 at 670 K. For all of the Cu−Ti−S phases, the thermal conductivity at 670 K is 3.5−5 W K−1 m−1, where the lattice part of the conductivity is as low as 1 W K−1 m−1 at 670 K. As a result, r-CuTi2S4 shows the highest dimensionless thermoelectric figure of merit ZT of 0.2. The present systematic study on the Cu−Ti−S systems provides insights into the structural design of thermoelectric materials based on Cu−M−S (M = transition-metal elements).

1. INTRODUCTION Cu−S-based compounds CuM2S4 (M = transition-metal elements), which crystallize in the cubic spinel structure, show a wide variety of physical properties that make them interesting from the viewpoint of solid-state physics. For example, these compounds exhibit a structural phase transition when M = V,1 ferromagnetism when M = Cr,2 superconductivity when M = Rh,3 and a metal−insulator transition when M = Ir.4 Furthermore, CuM2S4 compounds have been studied for their technological importance. Specifically, they have attracted attention as electrode materials for Li-ion batteries5−7 and as thermoelectric materials, which convert thermal energy directly into electrical energy.8−12 For the M = Ti compound (c-CuTi2S4), the structural, electrical-transport, magnetic, and electrochemical properties have been studied extensively.2,5−8,13−18 In the cubic structure, © XXXX American Chemical Society

which belongs to the Fd3̅m space group, the S ions are arranged in a cubic close-packed lattice, in which the Cu and Ti ions occupy tetrahedral (8a sites) and octahedral (16d sites) voids, respectively (Figure 1a).14,19 Other octahedral voids (16c sites) remain unfilled by cations. A Cu-deficient phase, cCu1−xTi2S4, is formed by either a direct reaction between constituent elements or the oxidative extraction of Cu from the stoichiometric phase, c-CuTi2S4.13,14 Because Li ions can be inserted into c-Cu1−xTi2S4 (and c-Ti2S4), it has been evaluated as a potential electrode material for Li-ion batteries.5−7,14 The stoichiometric c-CuTi2S4 phase with a formal charge of Cu+Ti3.5+2S2−4 is a Pauli paramagnet and exhibits metallic electrical resistivity ρ (∼3 μΩ m) and a negative Seebeck Received: October 17, 2018

A

DOI: 10.1021/acs.inorgchem.8b02955 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

and octahedral 16c sites are partially occupied by Zn ions and “excess” Ti ions, respectively. To the best of our knowledge, the Cu counterpart of this compound has not been synthesized so far. Here, we compare the crystal structure of a Ti-rich phase, c-Cu0.5Ti2.25S4 (Figure 1b), with that of c-CuTi2S4 (Figure 1a). A rhombohedral form of CuTi2S4 (r-CuTi2S4; Figure 1c) was synthesized by a direct reaction of constituent elements, alternatively, by a reaction in KCl/KI flux.19 The rhombohedral structure (R3̅m) is composed of a densely packed S lattice, wherein the Ti ions occupy half of the octahedral voids and the Cu ions fill one-eighth of the tetrahedral voids.19 The charge formulation was postulated to be Cu+Ti4+0.25Ti3+0.25(Ti3.5+)1.5S2−4, which is at variance with the Pauli paramagnetic behavior.19 First-principles electronicstructure calculations predicted that r-CuTi2S4 would exhibit metallic character as in c-CuTi2S4.19 In this work, we prepared polycrystalline samples of cCu1−xTi2S4 (x ≤ 0.375), Ti-rich c-Cu1−xTi2.25S4 (x = 0.5, 0.625), and r-CuTi2S4 by directly reacting constituent elements, followed by heat treatments (without precursors or flux), and we systematically studied their thermoelectric properties. To gain insight into the electronic structure, we performed magnetization measurements and first-principles calculations. Furthermore, we discuss how the thermoelectric properties and electronic structure depend on the Cu deficiency and the structural transformation from the cubic to the rhombohedral phase.

Figure 1. Crystal structures of (a) cubic CuTi2S4, (b) cubic Cu0.5Ti2.25S4, and (c) rhombohedral CuTi2S4. For all of the structures, Cu and Ti ions occupy tetrahedral and octahedral voids in the S sublattice, respectively. For Cu0.5Ti2.25S4 in part b, 16c sites are occupied by “excess” Ti ions.

2. EXPERIMENTAL AND COMPUTATIONAL DETAILS

coefficient S (∼−10 μV K−1) at room temperature.8,16−19 The values of ρ and S were increased by the substitution of Co for Ti as CuCo0.5Ti1.5S4 (Cu2CoTi3S8), leading to the high thermoelectric power factor S2ρ−1 (0.6 mW K−2 m−1 at 650 K).10 Because of the high S2ρ−1 and relatively low thermal conductivity κtot (2.2 W K−1 m−1 at 650 K), the dimensionless figure of merit ZT = S2Tκtot−1ρ−1 reaches 0.2 at 650 K.10 Thus, c-CuTi2S4 has been regarded as a parent compound of thermoelectric materials. The Cu-deficient c-Cu1−xTi2S4 phase (0 ≤ x ≤ 0.93) is also a Pauli paramagnet with metallic or semimetallic ρ,13,14 which is expected to exhibit a high S2ρ−1. In addition to c-Cu1−xTi2S4, two related systems of c-CuTi2S4 described below can be regarded as potential candidates of thermoelectric materials because of their structural similarities. A thiospinel-derivative cubic structure (Fd3̅m) was reported for a Ti−S-based compound, Zn0.25Ti2.25S4 (Zn2Ti18S32), which was synthesized by directly reacting Ti2S3, ZnS, and Ti.20 The Zn0.25Ti2.25S4-type structure consists of the same close-packed lattice of S ions as that of c-Cu1−xTi2S4. The octahedral 16d sites are fully occupied by Ti ions, whereas tetrahedral 8a sites

2.1. Sample Synthesis. We synthesized samples with the following initial compositions: Cu1−xTi2S4 (x = 0, 0.125, 0.25, 0.375, 0.5) and Cu1−xTi2.25S4 (x = 0.375, 0.5, 0.625, 0.75). Hereafter, the values of x are often used to denote the samples. As element sources, we used Cu wire (4 N), Ti powder (4 N), and S powder (4 N) from Kojundo Chemical Lab. The cubic-phase samples were synthesized by the following procedure. First, the elements were enclosed in an evacuated quartz tube. The quartz tube was then heated to 523 K over a period of 2 h, maintained at this temperature for 2 h, and then heated to 1373 K over 8 h. After this temperature was maintained for 24 h, the furnace was switched off. Then, the sample was allowed to naturally cool to room temperature. The product was pulverized and molded into a pellet, which was again enclosed in an evacuated quartz tube. The sample was heated at 1373 K for 50 h to improve the homogeneity. After this heat treatment, the pellet was reground and loaded into a graphite die, which was heated under an Ar atmosphere to a maximum temperature of 1173−1373 K (Table 1) at a rate of 100 K min−1 in a PLASMAN CSP-KIT-02121 pulsed-electric-current sintering furnace (S. S. Alloy, Ltd.). The samples were sintered at the temperatures listed in Table 1 for 1 h at 50 MPa.

Table 1. Initial Value of x, Sintering Temperature Tsint., Relative Density of the Sintered Sample d, Actual Compositions of Cu and Ti with Respect to S Assumed To Be 4, Lattice Parameters a and c, Hall Coefficient RH, Electron Carrier Density n, and Hall Mobility μH for c-Cu1−xTi2S4, c-Cu1−xTi2.25S4, and r-CuTi2S4 phase c-Cu1−xTi2S4

c-Cu1−xTi2.25S4 r-CuTi2S4

x

Tsint. /K

d/%

Cu

Ti

S

a/Å

0 0.125 0.25 0.375 0.5 0.625

1123 1223 1223 1173 1373 1373 823

100 99 98 93 99 99 96

0.982(4) 0.845(9) 0.749(5) 0.645(4) 0.486(4) 0.386(7) 1.14(4)

1.95(1) 1.96(2) 2.00(1) 2.00(1) 2.23(2) 2.23(1) 1.80(4)

4 4 4 4 4 4 4

10.003(1) 9.975(1) 9.950(2) 9.924(1) 9.882(2) 9.854(1) 7.02(1) B

c/Å

RH/10−4 cm3 C−1

n/1021 cm−3

μH/ cm2 V−1 s−1

34.82(3)

−5.39 −6.17 −6.61 −7.23 −0.931 −1.55 −22.9

11.6 10.1 9.45 8.63 67.1 40.3 2.73

3.6 3.5 3.2 2.7 0.24 0.35 2.4


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Inorganic Chemistry

c-CuTi2S4 and r-CuTi2S4.19 Here, we set 2000 k points and RKmax = 7, where R is the smallest value of the muffin-tin radii and Kmax is the cutoff wavevector of the plane-wave basis set. We used muffin-tin radii (bohr) RMT = 2.33 (Cu), 2.47 (Ti), and 1.91 (S) for cubic CuTi2S4 and Cu0.5Ti2S4, RMT = 2.35 (Ti) and 1.81 (S) for cubic Ti2S4, and RMT = 2.32 (Cu), 2.41 (Ti), and 1.90 (S) for rhombohedral CuTi2S4.

To obtain the rhombohedral phase sample, lower temperatures were applied than those for the cubic phases. Specifically, the quartz ampule encapsulating the elements was heated to 523 K over a period of 2 h, maintained at this temperature for 2 h, and then heated to 723 K over 3 h. The maximum temperature was adopted after the condition necessary to obtain r-CuTi2S4.19 After 24 h kept at 723 K, it was cooled naturally to room temperature. The product was powdered and then pelletized. The pellet was enclosed in an evacuated quartz tube and heat-treated at 723 K for 100 h to improve the homogeneity. After this heat treatment, the powdering and pelletizing processes were repeated, followed by heat treatment at 723 K for 50 h. The pellet was reground and loaded into either a graphite die or a tungsten-carbide die, which was placed in the PLASMAN CSP-I-03121 furnace (S. S. Alloy, Ltd.) for sintering in a N2 atmosphere at 1023 K and 50 MPa or 823 K and 250 MPa, respectively. 2.2. Sample Characterization. The phase homogeneity and crystal structure of the samples were examined by powder X-ray diffraction (XRD) using an Ultima IV diffractometer (Rigaku) and a Miniflex diffractometer (Rigaku) equipped with Cu Kα radiation sources. The thermal stability of the powdered samples was examined up to 1023 K in an Ar atmosphere by differential thermal analysis (DTA) with a TG-DTA 2000SA apparatus (Bruker). The chemical composition of the sintered samples was determined by wavelengthdispersive electron-probe microanalysis (EPMA) with a JXA-8200 analyzer (JEOL). The composition was evaluated by averaging 10 data points, and the S content was assumed to be 4. 2.3. Physical Property Measurements. ρ and S were simultaneously measured at 300−670 K by a direct-current fourprobe method and a temperature differential method, respectively, with a ZEM-3 instrument (ADVANCE-RIKO) under a He atmosphere. The thermal diffusivity α was measured at 300−673 K on an LFA-457 instrument (Netzsch) using a laser-flash method under flowing Ar. The data were utilized to calculate κ = αCDPds, where CDP is the Dulong−Petit value of the specific heat and ds is the sample density. The value of CDP (J g−1 K−1) was calculated to be 3NRW−1, where the number of atoms per formula unit N and formula weight W were calculated based on the actual composition obtained by EPMA and R was the gas constant. Notably, the specific heat Cp was measured simultaneously with α using the laser-flash method. The absolute values of Cp were derived from a comparison of the measured values with those for a standard sample of Pyroceram 9606 (Netzsch), which were confirmed to reasonably agree with the value of CDP (Figure S1). The value of ds was estimated from the dimensions and weight of the sample. We measured ρ and S on barshaped samples cut perpendicularly to the pressed axis of the sintered disk, while α was measured on the disk along the pressed axis. We have confirmed the reproducibility of the data of ρ, S, and α upon both heating and cooling for all samples. Therefore, we represent the data taken upon heating in this paper. The Hall coefficient RH was measured at 300 K on a physical property measurement system (Quantum Design) by an alternatingcurrent four-probe method under magnetic fields −5 T ≤ B ≤ +5 T. The Hall voltage VH was collected every 1 T, and RH was calculated from a VH versus B plot using the relationship VH = RHIBd−1 (I = current and d = thickness of the sample) based on a single-carrier model. The magnetization M was measured at T = 2−300 K in a constant magnetic field B = 1 T using a magnetic property measurement system (Quantum Design) equipped with a superconducting quantum interference device. 2.4. First-Principles Electronic Structure Calculations. Firstprinciples calculations were performed to determine the electronic structures of c-Cu1−xTi2S4 (x = 0, 0.5, 1) and r-CuTi2S4 using the WIEN2k code based on density functional theory.21 This code implements the linearized augmented plane-wave and local orbitals method.22 The electronic structures were self-consistently calculated within the generalized gradient approximation proposed by Perdew, Burke, and Ernzerhof and the U method.23 Here, the Hubbard U parameter was chosen to be 2 eV for Cu 3d and Ti 3d. For the calculations, we adopted the crystallographic parameters reported for

3. RESULTS AND DISCUSSION 3.1. Characterization of the Samples. Figure 2a presents powder XRD patterns of the Cu1−xTi2S4 samples subjected to the long (50 h) heat treatment at 1373 K (before sintering). For x = 0, the peak positions and intensities agree

Figure 2. Powder XRD patterns for the samples of (a) Cu1−xTi2S4 (0 ≤ x ≤ 0.5) and (b) Cu1−xTi2.25S4 (0.375 ≤ x ≤ 0.75) after a long heat treatment at 1373 K (before sintering). Simulated patterns for cCuTi2S4, c-Cu0.5Ti2S4, and c-Cu0.5Ti2.25S4 and the peak positions for Cu Kα radiation are also shown. Closed and open circles denote peaks from TiS2 and Ti2S3, respectively. (c) Dependence of the lattice parameter a on Cu deficiency x, where x denotes the actual value evaluated by EPMA. C


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Inorganic Chemistry with those of a simulated pattern based on c-CuTi2S4. Similar XRD patterns were observed for the Cu-deficient samples with x ≤ 0.375. Notably, the XRD patterns remained unchanged after sintering, as shown in Figure S2. With x increasing from 0 to 0.375, the peaks shifted to higher angles (lattice parameter a decreased) and the relative intensities of the 111 and 400 peaks clearly increased (Figure 2a). Such variations in the XRD pattern suggest a decrease in the Cu content.12 In fact, the actual Cu deficiency evaluated by EPMA increased from 0.02 to 0.36, which agrees with the value of x (Table 1). When x was increased to 0.5, a large amount of an impurity phase (TiS2) appeared (Figure 2a). This result accords with the fact that a Cu deficiency in Cu1−xTi2S4 can be introduced into the cubic thiospinel structure up to x = 0.44.13 A much higher degree of Cu deficiency (x ≤ 0.93) can be achieved by a Cu-extraction treatment using I2.14 Alternatively, as was reported for Zn0.25Ti2.25S4, the deficiency of the cation (Zn) at tetrahedral (8a) sites can be increased when the “excess” Ti ions partially occupy the octahedral (16c) sites.20 Therefore, we synthesized samples with starting compositions of Cu1−xTi2.25S4 (0.375 ≤ x ≤ 0.75). Powder XRD patterns for the Ti-rich samples after the long (50 h) heat treatment at 1373 K (before sintering) are shown in Figure 2b. The patterns for the x = 0.375 and 0.75 samples show the Ti2S3 and TiS2 peaks, respectively. On the other hand, for the x = 0.5 and 0.625 samples, the patterns are similar to a simulated pattern based on “c-Cu0.5Ti2.25S4” (Figure 2b) rather than “cCu0.5Ti2S4”, which was left intact after sintering, as shown in Figure S2. Here, these simulated patterns differ in the intensity ratio I(400)/I(311), which is larger for the Ti-rich phase. In fact, EPMA revealed that the Cu deficiency (0.51 and 0.61) and Ti composition (2.23) agree with the starting values (Table 1). From Cu1−xTi2S4 to Cu1−xTi2.25S4, despite modification of the Ti−S framework from “Ti2S4” to “Ti2.25S4” at 0.375 ≤ x ≤ 0.5, the value of a decreased linearly from 10.003 to 9.854 Å with increasing x (Figure 2c and Table 1). This result indicates that the incorporated Cu ion expands the S tetrahedron, whereas the “excess” Ti ion does not. We now focus on r-CuTi2S4. The sample subjected to the long (100 h + 50 h) heat treatments at 723 K was characterized by powder XRD. Almost all of the peaks could be indexed to the rhombohedral structure (Figure 3a).19 Two small peaks at 10 and 33 deg are from TiS3, and the peak at 15 deg is from TiS2. After sintering at 1023 K, the rhombohedral structure transformed into the cubic structure (Figure 3a). In order to evaluate the thermal stability of r-CuTi2S4, DTA was performed on a powder sample up to 953 K. The DTA signal begins to decrease at 823 K and shows an endothermic peak at 925 K, both of which are absent for c-CuTi2S4 (Figure 3b). After cooling, the sample became a cubic phase. Therefore, the endothermic peak at 925 K should indicate a structural transformation. The DTA curve also shows another endothermic peak at 780 K, which may be associated with S sublimation. We then confirmed that a sample subjected to DTA up to 823 K retained its rhombohedral structure. On the basis of the result, we sintered a r-CuTi2S4 powder at 823 K and obtained a dense compact sample composed mainly of the rhombohedral phase (Figure 3a). Our Rietveld analysis of the XRD pattern gave lattice parameters of a = 7.02 Å and c = 34.82 Å. EPMA showed the actual composition of Cu1.14Ti1.80S4, being excess in Cu and less in Ti with respect to the starting composition. The lattice parameters and chemical compositions are in agreement with the reported

Figure 3. (a) Powder XRD patterns for the samples of CuTi2S4 after long heat treatment at 723 K (before sintering) and after sintering at 823 and 1023 K. The simulated patterns for c-CuTi2S4 and r-CuTi2S4 and the peak positions for Cu Kα radiation are also shown. Squares and a circle denote peaks from TiS3 and TiS2, respectively. (b) DTA data for powders of c-CuTi2S4 and r-CuTi2S4 subjected to no sintering process. A baseline of the data was properly subtracted. The dashed lines are drawn at the sintering temperatures.

values.19 As a result, Ti-based impurity phases formed, namely, Ti, TiS2, and TiS3 (Figure 3a), which were identified by XRD measurement and EPMA in the backscattered electron image (BEI; Figure S3). The trace amount of impurities demonstrated by the XRD pattern and BEI may slightly affect the physical properties. Although the crystal structure of r-CuTi2S4 is noncubic, crystallites in the sintered compact have little preferred orientation, as proven by XRD analysis. In fact, there is no significant difference between the XRD pattern for a surface of the sintered disk and that for powders, as shown in Figure S4. Therefore, anisotropy in the thermoelectric properties is expected to be small in our sintered sample even for the noncubic phase. The relative density d (%; Table 1) of the sintered cCu1−xTi2S4, c-Cu1−xTi2.25S4, and r-CuTi2S4 samples was obtained by dividing the measured ds value by the theoretical density. Here, the theoretical density was calculated using the lattice parameter a and the actual chemical compositions. The values of d all reached at least 96%, except for Cu1−xTi2S4 with x = 0.375 (d = 93%). The density/porosity is reflected in the BEI (Figure S3). The grain sizes of all of the samples were several tens of micrometers. 3.2. Thermoelectric Properties. Figure 4 shows the temperature dependence of ρ and S for the c-Cu1−xTi2S4 samples. For the samples with x ≤ 0.375, the negative S indicates that the dominant charge carrier is electrons. Indeed, the sign of RH is negative (Table 1). For x = 0, the values of ρ and S at 300 K were 1.5 μΩ m (Figure 4a) and −6 μV K−1 (Figure 4b), respectively. These values are ∼50% smaller than D


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Inorganic Chemistry

where the Lorenz number L (10−8 W Ω K−2) is 2.18−2.44 depending on the measured value of S (μV K−1) from the relationship L = 1.5 + exp(−|S|/116).24 With increasing x, κel decreased, mainly because of the increase in ρ (Figure 4a). The lattice component κlat = κtot − κel decreased upon heating (Figure 5a), indicating that the Umklapp process dominates phonon scattering. The value of κlat for x = 0.375 was lower than those for x ≤ 0.25 (Figure 5a), which may result from the former sample’s porous structure (lowest d). As a result, the combination of increased S2ρ−1 and reduced κtot increased ZT for the Cu-deficient samples (Figure 5b), which reached 0.07 at 670 K for x = 0.375. The thermoelectric properties of the c-Cu1−xTi2.25S4 samples with x = 0.5 and 0.625 are shown in Figures 4 and 5. For both samples, the values of ρ and S at 300 K were 4 μΩ m and −30 μV K−1, respectively. The weak temperature dependences of ρ and S at 300−670 K led to a constant S2ρ−1 at ∼0.2 mW K−2 m−1 over the whole temperature range (Figure 4). These behaviors are dissimilar to the increases in ρ and |S| upon heating for the c-Cu1−xTi2S4 samples. The values of ρ and |S| for c-Cu1−xTi2.25S4 are comparable to those for c-Cu1−xTi2S4, although the value of n for the former phase is 1 order of magnitude higher than that for the latter phase (Table 1). This result indicates a remarkable reduction in μH for the Ti-rich phase (Table 1). Thus, the “excess” Ti ions in the 16c sites donate electrons to the conduction band and are likely to be responsible for lowering μH. With increasing temperature, κtot gradually increased from 3.5 to 4.5 W K−1 m−1 (Figure 5a). Although the slope of the κtot(T) curves for c-Cu1−xTi2.25S4 is opposite that for c-Cu1−xTi2S4, the values of κlat for both phases are comparable. In the low-temperature region (300−500 K), κlat is slightly reduced for the Ti-rich phase, which is likely due to the “excess” Ti ions. As a result, the values of ZT for the x = 0.5 and 0.625 samples reached 0.03 at 670 K (Figure 5b). The r-CuTi2S4 sample showed metallic n-type character (Figure 6). More specifically, with the temperature increasing from 300 to 670 K, ρ increased from 9 to 17 μΩ m and |S|

Figure 4. Temperature dependence of (a) the electrical resistivity ρ, (b) Seebeck coefficient S, and (c) power factor S2ρ−1 for the sintered c-Cu1−xTi2S4 (circles) and c-Cu1−xTi2.25S4 (triangles) samples.

the reported values,8 which may result from a deviation in the chemical composition. With x increasing from 0 to 0.375, the values of ρ and |S| increased, which is consistent with the decreasing electron-carrier concentration n from 1.2 to 0.86 × 1022 cm−3 (Table 1). Here, n was calculated based on the single-carrier model using the relationship n = |RH|−1e−1, where e is the elementary charge. The Hall mobility μH = |RH|ρ−1 decreased slightly with increasing x (Table 1). The reduced μH for x = 0.375 may be partly due to its low d value. As a result, S2ρ−1 at 670 K increased to 0.37 mW K−2 m−1 at x = 0.375 (Figure 4c). For the c-Cu1−xTi2S4 samples, κtot decreased with increasing temperature and reached 3.5−5 W K−1 m−1 at 670 K (Figure 5a). We estimated the electronic part of the thermal conductivity κel from the Wiedemann−Franz law, LTρ−1,

Figure 5. Temperature dependence of (a) the total thermal conductivity κtot and lattice component κlat and (b) the dimensionless figure of merit ZT for the sintered c-Cu1−xTi2S4 (circles) and cCu1−xTi2.25S4 (triangles) samples.

Figure 6. Temperature dependence of (a) the electrical resistivity ρ, (b) Seebeck coefficient S, and (c) power factor S2ρ−1 for the sintered c-CuTi2S4 (circles) and r-CuTi2S4 (squares) samples. E


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Inorganic Chemistry increased from 40 to 90 μV K−1. The values of ρ and |S| were much higher than those for c-CuTi2S4 (Figure 6a,b), which originates from the r-CuTi2S4 sample’s lower n value of 2.7 × 1021 cm−3. The reduced n can be attributed to the deficiency of Ti demonstrated by EPMA. The value of μH is only slightly lower than that for c-CuTi2S4. As a result, the large |S| results in a high value of S2ρ−1 = 0.5 mW K−2 m−1 at 670 K (Figure 6c). The r-CuTi2S4 sample shows much lower κtot than the cCuTi2S4 sample (Figure 7a); specifically, κel is reduced in the

positive χ originates from the Pauli paramagnetic susceptibility of conduction electrons,19 which is, in principle, proportional to the density of states (DOS) at the Fermi level EF, N(EF). Therefore, decreasing χ with increasing x indicates a reduction in N(EF). The temperature dependence of χ of a Pauli paramagnet can be expressed as É | ÅÄÅ 2Ñ l Ñ o o o π 2 2ÅÅÅ N″(E) ijj N ′(E) yzz ÑÑÑ 2o o o Å χ (T ) = χ0 m + − 1 k j z B Å j N (E) z ÑÑÑÑT } o o ÅÅ N (E) o 6 o o ÅÅÇ k { ÑÑÖ o n ~ E = EF

where χ0 is a constant, kB is Boltzmann’s constant, and N′(E) and N′′(E) are the first and second derivatives of the DOSs, respectively.25 Therefore, a negative temperature coefficient for x = 0 at 50−300 K indicates a negative value of N′′(E) at EF. The variation in the temperature coefficient from a negative value to almost zero with increasing x may originate from a change in the DOS near EF associated with the decrease in n. Details of the electronic structures are discussed in section 3.4. The c-Cu1−xTi2.25S4 samples with x = 0.5 and 0.625 and rCuTi2S4 exhibit χ(T) similar to/lower than that for cCu1−xTi2S4 with x = 0.375, indicating a relatively low N(EF). 3.4. Electronic Structures. The electronic band dispersion curves and DOSs were calculated for c-CuTi2S4, c-Cu0.5Ti2S4, and c-Ti2S4 (hypothetical systems) and for r-CuTi2S4 (Figures 9 and 10). In these figures, EF was set to zero energy. As shown in Figures 9a and 10a, for c-CuTi2S4, the valence and conduction bands overlap at energy E ≈ −0.6 eV, and EF lies deep in the conduction band, which consists mainly of Ti 3d and S 3p orbitals. This band structure agrees with the ntype metallic character proven experimentally (section 3.2). The DOS shows a peak near EF (Figure 10a), which accords with the negative N′′(E) at EF, as indicated by χ(T). When half of the Cu ion in c-CuTi2S4 was removed (i.e., c-Cu0.5Ti2S4), EF slightly shifts to a lower energy by ∼0.1 eV (Figures 9b and 10b). This result agrees with the reduction in n (section 3.2). Notably, the band dispersion curves and DOSs near EF for cCuTi2S4 and c-Cu0.5Ti2S4 reasonably agree with each other (Figures 9a,b and 10a,b). Therefore, the change in the electronic structure from c-CuTi2S4 to c-Cu0.5Ti2S4 exhibits rigid-band-like behavior. On the other hand, for c-Ti2S4, the conduction band is clearly different from those of c-CuTi2S4 and c-Cu0.5Ti2S4 (Figures 9c and 10c). More specifically, a band possessing the minimum energy at the Γ point considerably shifted to a higher energy. This modification decreased the DOS of the conduction band below EF. As for the Ti-rich phase, c-Cu0.5Ti2.25S4, the electronic structure was not calculated in this work because of the structural complexity. Nevertheless, considering the higher n and lower χ [i.e., N(EF)] than those of c-CuTi2S4 (Figure 8), we conjecture that EF for c-Cu0.5Ti2.25S4 is located in the valley of the DOS at ∼0.5 eV (Figure 10b) based on the rigid-band model. At this energy, however, we cannot find any features responsible for lowering μH (Table 1; e.g., weakly dispersive bands), as shown in Figures 9b and 10b. Further investigations are required to understand whether the reduced μH originates from either the band nature or the increased electron scattering. For r-CuTi2S4, EF lies in the conduction band, as in the case of c-CuTi2S4 (Figures 9d and 10d). The electronic structure is characterized by weakly dispersive bands near EF, which form a sharp peak in the DOS. The value of N(EF) is higher than that for c-CuTi2S4 (Figure 10d), which is consistent with previous

Figure 7. Temperature dependence of (a) the total thermal conductivity κtot and the lattice component κlat and (b) the dimensionless figure of merit ZT for the sintered c-CuTi2S4 (circles) and r-CuTi2S4 (squares) samples.

former, but κlat is comparable in the two samples (Figure 7a). This agreement in the κlat values indicates that the structural modification negligibly affects κlat. As a result, the r-CuTi2S4 sample exhibits a ZT value of 0.2 at 670 K, which is the highest value of all of the samples (Figure 7b). 3.3. Magnetic Properties. In order to gain insight into the electronic structure, we measured the magnetization. Figure 8 shows the temperature dependence of the magnetic susceptibility χ = MB−1 at T ≤ 300 K for c-Cu1−xTi2S4, cCu1−xTi2.25S4, and r-CuTi2S4. For x = 0 of c-Cu1−xTi2S4, the

Figure 8. Temperature dependence of the magnetic susceptibility χ for the sintered c-Cu1−xTi2S4 (circles), c-Cu1−xTi2.25S4 (triangles), and r-CuTi2S4 (squares) samples. F


Article

Inorganic Chemistry

Figure 9. Electronic band dispersion curves for (a) c-CuTi2S4, (b) c-Cu0.5Ti2S4, (c) c-Ti2S4, and (d) r-CuTi2S4. The Fermi level EF is set to zero energy.

When the value of x was further increased to 0.5, the Ti-rich phase, c-Cu1−xTi2.25S4, was stabilized. The “excess” Ti ions donated electrons to the conduction band, which decreased S2ρ−1. The r-CuTi2S4 sample had a Cu-rich, Ti-poor composition. The deviation in the Ti composition from the stoichiometric value likely decreased n relative to that of cCuTi2S4. As a result, r-CuTi2S4 exhibited the highest S2ρ−1 of 0.5 mW K−2 m−1 at 670 K among the Cu−Ti−S samples. Both modifications in the crystal structure from “Ti2S4” to “Ti2.25S4” in the cubic systems and from the cubic to rhombohedral form weakly affect κlat at 670 K. As a result, the highest ZT of 0.2 was obtained for r-CuTi2S4. These insights into the physical properties and electronic structures of the Cu−Ti−S systems offer an opportunity to optimize the thermoelectric performance of the Cu−M−S systems and to design thermoelectric materials using spinel-related structures.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b02955. Specific heat, XRD patterns, and BEIs for the sintered samples (PDF)

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AUTHOR INFORMATION

Corresponding Authors

Figure 10. Electronic DOSs for (a) c-CuTi2S4, (b) c-Cu0.5Ti2S4, (c) c-Ti2S4, and (d) r-CuTi2S4. The total and partial DOSs for Cu, Ti, and S ions are individually drawn. The Fermi level EF is set to zero energy. The total DOSs near EF of c-CuTi2S4 (dashed line) and r-CuTi2S4 (solid line) are compared in the inset of part d.

*E-mail: [email protected],. *E-mail: [email protected].

calculations.19 In fact, for our r-CuTi2S4 sample, EF probably shifts to a lower energy because of the decrease in n.

Author Contributions

ORCID

Katsuaki Hashikuni: 0000-0002-3536-8206 Michihiro Ohta: 0000-0002-9093-7117 The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

4. CONCLUSION We systematically studied the crystal structures, thermoelectric and magnetic properties, and electronic structures of cCu1−xTi2S4, c-Cu1−xTi2.25S4, and r-CuTi2S4. All of the Cu− Ti−S systems exhibit n-type metallic character and Pauli paramagnetism. With x increasing to 0.375 in c-Cu1−xTi2S4, decreasing n increased S2ρ−1 within the rigid-band-like scheme.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Y. Shibata for the EPMA performed at the Natural Science Center for Basic Research and Development, G


Article

Inorganic Chemistry

of a New CuTi2S4 Modification in Comparison to the Thiospinel. Inorg. Chem. 2004, 43, 6473−6478. (20) Kawada, I.; Onoda, M.; Saeki, M. Zn2Ti18S32, a new ternary sulfide. Acta Crystallogr. 1985, C41, 1573−1575. (21) Blaha, P.; Schwarz, K.; Madsen, G. K. H.; Kvasnicka, D.; Luitz, J. WIEN2k, An Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties; Vienna University of Technology: Vienna, Austria, 2001. (22) Sjöstedt, E.; Nordström, L.; Singh, D. J. An alternative way of linearizing the augmented plane-wave method. Solid State Commun. 2000, 114, 15−20. (23) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (24) Kim, H. S.; Gibbs, Z. M.; Tang, Y.; Wang, H.; Snyder, G. J. Characterization of Lorenz number with Seebeck coefficient measurement. APL Mater. 2015, 3, 041506. (25) Mohn, P. Magnetism in the Solid State: An Introduction; Springer: Heidelberg, Germany, 2003.

Hiroshima University, and Atsushi Yamamoto for supporting the electrical and thermal transport measurements at Research Institute for Energy Conservation, AIST. This work was supported financially by JSPS KAKENHI Grant JP17H04951 (to K.S.), grant from the International Joint Research Program for Innovative Energy Technology funded by METI, and CREST JST Grant JPMJCR16Q6.

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REFERENCES

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Thermoelectric Properties and Electronic Structures of CuTi2S4

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