Low-Temperature Structural Phase Transitions in Thermoelectric

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Cite This: Cryst. Growth Des. 2019, 19, 3979−3988

Low-Temperature Structural Phase Transitions in Thermoelectric Tetrahedrite, Cu12Sb4S13, and Tennantite, Cu12As4S13 Venkatesha R. Hathwar,†,‡ Atsushi Nakamura,§ Hidetaka Kasai,†,§,∥ Koichiro Suekuni,⊥ Hiromi I. Tanaka,# Toshiro Takabatake,# Bo B. Iversen,†,¶ and Eiji Nishibori*,†,§,∥

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†

Division of Physics, Faculty of Pure and Applied Sciences and ∥Tsukuba Research Center for Energy Materials Science (TREMS), University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan ‡ Department of Physics, Goa University, Taleigao Plateau, Goa-403206, India § Graduate School of Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan ⊥ Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan # Department of Quantum Matter, Graduate School of Advanced Sciences of Matter, Hiroshima University, Higashi-Hiroshima 739-8530, Japan ¶ Center for Materials Crystallography (CMC), Department of Chemistry and Interdisciplinary Nanoscience Center (iNANO), Aarhus University, Aarhus 8000, Denmark S Supporting Information *

ABSTRACT: Tetrahedrite (Cu12Sb4S13) and tennantite (Cu12As4S13) crystallize in isomorphous cubic structures (I4̅3m) at room temperature and exhibit phase transitions at 85 and 124 K, respectively. We have investigated how the crystal structures change through the phase transitions using single crystal synchrotron X-ray diffraction data. The low-temperature structure of Cu12Sb4S13 belongs to the I4̅2m space group, which is described by the 2a × 2a × 2c supercell. The distortion of S(2)Cu(2)6 octahedra is found to be responsible for the structural transformation. In contrast, the structure of Cu12As4S13 preserves its cubic symmetry and periodicity below the transition temperature. The low-temperature structure is characterized by positional disorder of S(1) and As(1) atoms along with a significant change in the occupancy of disordered sites of the Cu(2) atom. Besides distinct lowtemperature structures for Cu12Sb4S13 and Cu12As4S13, the structural phase transition is further accompanied by negative thermal expansion of lattices (per formula unit) in both compounds.

1. INTRODUCTION Tetrahedrite (Cu12Sb4S13), tennantite (Cu12As4S13), and their substituted systems Cu12‑xMx(Sb/As)4S13 (M: transition metals) are state-of-the-art and environmentally benign thermoelectric materials which exhibit high dimentionless figure of merit (ZT). 1 Among substituted systems, Cu11.5Fe0.5Sb4S13 and Cu11ZnSb4S13 show a maximum ZT of 1.0 at 720 K.2 Other substituted systems also exhibit high ZT values: e.g., 0.8 at 665 K for Cu10.5Ni1.5Sb4S13,3 0.98 at 673 K for Cu11.5Co0.5Sb4S13,4 and 0.9 at 623 K for Cu11.25Cd0.75Sb4S13.5 The class of tetrahedrite and tennantite compounds has the body-centered cubic structure with I4̅3m space group at room temperature as shown in Figure 1a.6 The crystal structure includes five nonequivalent crystallographic sites: two for Cu, one for Sb/As, and two for S. The Cu(1) atom is tetrahedrally coordinated (CuS4) by four S(1) atoms and the Cu(2) atom is trigonally coordinated (CuS3) by two S(1) and one S(2) atoms. The Sb atoms form a trigonal pyramid (SbS3) with three S(1) atoms. Additionally, the S(2) © 2019 American Chemical Society

atom is centered in an octahedral unit (SCu6) with six Cu(2) atoms (see in Figure 1b). In the cubic structure, the Cu(2) atom has a large atomic displacement parameter (ADP) out of the triangle and it is pointing toward the Sb/As atom (Figure 1c),7 which appears to affect low thermal conductivity in tetrahedrites.8 Two kinds of mechanisms have been proposed for the occurrence of large amplitude vibration of Cu(2). One is a weak out-of-plane bonding between Cu and Sb via the lone pair electrons of Sb.8 The other is chemical pressure inherent in the sulfur triangle, which squeezes out the Cu atom.9 An interesting feature of Cu12Sb4S13 is a metal to semiconductor transition (MST) at TMST = 85 K, which is characterized by a sharp drop in the magnetic susceptibility and a jump in the electrical resistivity.10 The MST is suppressed by the substitution of transition metals at the Cu Received: March 22, 2019 Revised: May 15, 2019 Published: May 22, 2019 3979

DOI: 10.1021/acs.cgd.9b00385 Cryst. Growth Des. 2019, 19, 3979−3988

Crystal Growth & Design

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Figure 1. (a) Molecular structure with thermal ellipsoids of Cu12Sb4S13 at 300 K, (b) the three types of units, and (c) an atomic arrangement of Sb atoms and [Cu(2)S(1)2S(2)] trigonal plane at 300 K.

2. EXPERIMENTAL SECTION

site in tetrahedrites. It has also been shown that the MST is accompanied by a structural change.11 However, different crystal structures have been proposed below TMST.11−13 Tanaka et al.11 suggested a body-centered tetragonal 2a × 2a × 2c supercell of the cubic cell, whereas May et al.12 proposed a tetragonal 2a × √2a × c supercell. Furthermore, Nasonova et al.13 found no symmetry change of the crystal structure (space group and periodicity of cell). Thus, the lowtemperature crystal structure of Cu12Sb4S13 is still controversial. In analogy with Cu12Sb4S13, tennanitite (Cu12As4S13) also shows a phase transition at T ≈ 124 K, where the magnetic susceptibility drops and the electrical resistivity increases; however, the changes are less drastic compared with those in Cu12Sb4S13.11 Studies on the crystal structure of Cu12As4S13 at low temperatures have not been reported yet. Investigation of the relationship between the phase transitions of Cu12Sb4S13 and Cu12As4S13 from the viewpoint of crystal structure is crucial for deep understanding the system and systematic development of high performance thermoelectrics. In this work, we have investigated the temperature dependence of crystallographic parameters of Cu12Sb4S13 and Cu12As4S13 to determine the low-temperature structures and to gain insight into mechanisms of the phase transitions.

2.1. Sample Preparation. Stoichiometric quantities of constituent elements for Cu12Sb4S13 and Cu12As4S13, Cu (wire; 4N), Sb (lump; 6N), As (lump; 6N), and S (powder; 4N), were sealed in an evacuated quartz tube. This tube was heated to 523 K over a period of 2 h, maintained at this temperature for 1 h, heated to 923 K (1003 K) over 4 h, maintained at these temperatures for 3 h, and then cooled slowly (1 K h−1) to 743 K (853 K) for Cu12Sb4S13 (Cu12As4S13), respectively. Finally, the sample was furnace cooled to room temperature. Single crystals were selected from the obtained ingots. 2.2. Variable Temperature Single-Crystal Synchrotron X-ray Diffraction. Single crystals of suitable size were selected from the synthesized samples for X-ray diffraction experiments. Variable temperature single-crystal X-ray diffraction experiments were performed at the BL02B1 beamline of SPring-8 using an Imaging Plate detector.14 The wavelength of the incident X-ray was set at 0.440 Å to reduce the X-ray fluorescence from the Sb atom. The crystal size was ∼20 μm in all dimensions for both compounds. High resolution data were collected up to a resolution d = 0.40 Å. Integration and empirical absorption correction were carried out using the Rigaku RAPID AUTO software. The crystal structure was solved by direct methods in SHELXT15 and structural refinements were performed with SHELXL16 in the OLEX2 suite.17

3. RESULTS 3.1. Variable Temperature Crystal Structure of Tetrahedrite in the High Temperature (HT) Phase. Cu12Sb4S13 crystallizes in the body-centered cubic structure 3980



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Figure 2. (a) Variation of lattice constant with decreasing temperature, (c) − (i) show changes in structural parameters with temperature and (g) plot of U⊥ of the Cu(2) atom with temperature.

with the space group I4̅3m at room temperature, as shown in Figure 1a. Hereafter, we denote the cubic structure above the transition temperature as the high-temperature (HT) structure. The cubic structure contains five independent atomic sites in

the unit cell, namely, 12d for Cu(1), 12e for Cu(2), 8c for Sb, 24g for S(1), 2a for S(2). The atoms form three types of units, namely, [Cu(1)S(1)4] tetrahedron, [Cu(2)S(1)2S(2)] trigonal plane, and [SbS(1)3] trigonal pyramid (Figure 1b). The Cu(2) 3981



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atom faces two Sb atoms (Figure 1c), and the S(2) atom is coordinated by six Cu(2) atoms forming an ideal octahedron (Figure 1b). We confirmed that Cu12Sb4S13 retains the cubic structure from 300 to 100 K, which is consistent with an earlier report.11 Our analysis shows that the lattice constant (a) decreases from 10.3079(6) Å to 10.2759(4) Å with decreasing temperature from 300 to 100 K as shown in Figure 2a and Table S1. Decreases in interatomic distances, Cu(1)−S(1) in the tetrahedron and Cu(2)−S(2) in the triangle (Figure 2b and c), are likely responsible for the lattice shrinkage. The combination of the decrease in Cu(1)−S(1) and nearly constant angles of S1−Cu1−S1 (Figure 2d) upon cooling indicates uniform contraction of the tetrahedron with keeping the similarity of configuration. The Cu(2)−Sb distance also decreases with decreasing temperature (Figure 2e). On the other hand, the distances of Cu(2)−S(1) and Sb(1)−S(1) vary slightly (Figure 2c and f). The atomic displacement parameter (ADP) of the Cu(2) atom perpendicular to the sulfur triangle, U⊥ monotonically decreases from 0.146(1) Å2 at 300 K to 0.112(1) Å2 at 100 K as the temperature is lowered (Figure 2g). Here, U⊥ was calculated by a relation U⊥ = U11 − U12 where U11 and U12 are components of the ADP tensor.9 In the next section, we describe a crystal structure below the transition temperature, namely, low-temperature (LT) phase, which is then compared with the HT phase. 3.2. Structure of Tetrahedrite in the Low Temperature (LT) Phase. Figure 3a,b shows the single-crystal diffraction images of Cu12Sb4S13 at 100 and 70 K, respectively, which manifests a structural transformation and presence of weak superlattice reflections at 70 K. The intensity ratio between the superlattice and fundamental-lattice reflections is approximately 1:2000 as depicted in Figure 3c. The X-ray diffraction data of the LT phase are indexed in a body-centered tetragonal 2a × 2a × 2c supercell. Lattice parameters of the super lattice cell at 70 K are a = b = 20.619(3) Å and c = 20.538(4) Å as given in Table S1. A small increase in the cell volume per formula unit (see in Figure S1) upon cooling from 100 to 70 K is observed, which is consistent with earlier studies.11 The symmetry reduction through the phase transition was previously suggested but the crystallographic parameters have never been determined.11 In the structural analysis of the present study, the resolution of X-ray data is fixed at d = 0.6 Å such that all superlattice reflections have sufficient intensities. To determine a space group for the 2a × 2a × 2c tetragonal body-centered supercell, we have examined all 19 possible space groups. As a result, we narrowed down the candidates to three: I4̅, I4̅2d, and I4̅2m. Analyses based on the space groups I4̅ and I4̅2d gave high reliable factors (R1) of 21.5% and 14.3%, respectively, whereas that on I4̅2m gave a lower R1 = 7.7%. The refined structure model with the space group I4̅2m could reproduce all fundamental-lattice and weak superlattice reflections. The molecular structure with thermal ellipsoids for the LT phase is shown in Figure 3d and corresponding packing diagram with unit cell is given in Figure S2. Due to the symmetry reduction and octuple unit cell volume, there are 17 Cu sites, 6 Sb sites, and 17 S sites in the asymmetric unit. The crystal structure has three independent [SCu6] octahedra with their centering at atoms S(2), S(10), and S(12). The differences between the HT and LT structures are discussed in the section 4. 3.3. Variable Temperature Crystal Structure of Tennantite in the HT Phase. The crystal structure of

Figure 3. Predicted and measured reflections of (a) cubic and (b) tetragonal Cu12Sb4S13. The main Bragg reflection (880) has an intensity of 389 984 counts whereas two superlattice reflections (871) and (781) have intensity counts of 871 and 189, respectively. (d) Molecular structure with thermal ellipsoids for tetragonal Cu12Sb4S13 at 70 K.

Cu12As4S13 is cubic with the space group I4̅3m at room temperature,18 which is nearly isomorphous with Cu12Sb4S13. The Cu(2) site in the HT structure of Cu12As4S13 was found to split into two distinct sites perpendicular to the sulfur triangle and pointing toward the neighboring As atoms.18 However, we found the structural model with two sites for Cu(2)18 to be inadequate to refine our high resolution synchrotron X-ray data with d = 0.40 Å reciprocal resolution in the temperature range from 300 to 150 K. Alternatively, we used a model with multiple sites for Cu(2) and an equal atomic displacement parameter for all sites. We started with a simple structure model with one Cu(2) site and an isotropic displacement parameter was adopted. The refinement showed residual electron density “peaks” near the Cu(2) site. The other Cu atoms were then located at the “peak” position in the subsequent refinements to reduce the reliability factor. Here, the sum of occupancies for each site of Cu(2) was assumed to be 1. In the final structural model, the Cu atoms occupy six independent sites that are shown as Cu2−Cu7 in Figure 4a. The Cu(1), S(1), and As(1) sites do not exhibit any indication of disorder in the HT phase. This structural refinement model for Cu12As4S13 holds for all data down to 150 K. 3.4. Structure of Tennantite in the LT Phase. Our Xray diffraction data on Cu12As4S13 showed neither symmetry reduction from I4̅3m nor superlattice reflections upon cooling from 300 to 90 K and it is visualized in the single-crystal diffraction images as shown in Figure S4. The lattice parameter 3982



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Figure 4. (a) Molecular structure with thermal ellipsoids of Cu12As4S13 at 300 K depicting the six disorder sites for Cu(2) atom. (b) Plot of lattice parameter vs temperature for Cu12As4S13. (c) Molecular structure with thermal ellipsoids of Cu12As4S13 at 100 K depicting the six disordered sites for Cu(2) atom and split sites for As and S(2) atoms.

Figure 5. Drawing of the [SCu6] octahedron at (a) 100 K (in the HT phase) and (b−d) at 70K (in the LT phase) for Cu12Sb4S13. The shift of central S atom from the mean plane of Cu atoms in the octahedra are shown in (b−d).

increases from a = 10.1410(4) Å at 125 K to 10.1475(5) Å at 90 K as shown in Figure 4b and Table S2, indicating negative thermal expansion associated with the phase transition. The refined structure at 90 K was found to be different from that of

the HT phases. In the LT structure at 90−125 K, both As(1) and S(2) atoms split into two positions with an occupancy ratio 60:40 and Cu(2) atoms occupy disordered six sites as described for the HT phase (Figure 4c). The structural 3983



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Figure 6. Structural difference in the HT and LT phases of Cu12Sb4S13. (a) Shift of S atoms from the mean plane of Cu atoms in [SCu6] octahedra. The comparison of the [SCu6] octahedral geometry is compared in (b) and (c) and the [CuS4] tetrahedral geometry in (d) and (e). Changes in the Sb−S distance of the [SbS3] unit are shown in (f).

positions of cuboids made of S(10) along the a axis. These octahedra with S(2) and S(12) are consecutively arranged along the c axis, while the displacement directions (+c or − c) of S(2)’s are alternately. Thus, the [SCu6] octahedra are arranged as a doubly periodic in the a and c directions of the superstructure (see Figure S3). The S atoms are displaced from a mean plane made of four Cu atoms by 0.186(1) Å for S(2), 0.028(1) Å for S(10), and 0.00 Å for S(12), as shown in Figure 5b,c,d, respectively, and which are plotted in Figure 6a. Figure 6 depicts overall structural changes with respect to interatomic distances and bond angles of [SCu6] octahedron, [CuS4] tetrahedron, and [SbS3] motif for the HT and LT structures of Cu12Sb4S13. The Cu−S bond length in the [SCu6] octahedra is 2.2257(3) Å in the HT phase at 100 K (see in Figure 6b). In

modification observed is likely to induce the change in physical properties around 125 K.11 The structural differences between two phases are discussed in the section 4.

4. DISCUSSION The LT structure of Cu12Sb4S13 is characterized by the distortion of the [SCu6] octahedron, which is a regular octahedron in the HT structure as shown in Figure 5a. In the LT structure, there are three independent [SCu6] octahedra centered at S(2), S(10), and S(12). The octahedra with S(10) are arranged with the intervals of ∼10.3 Å along the a and c directions of the tetragonal supercell. The octahedra with S(2) and S(12) are alternately arranged at the body-centered 3984



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Figure 7. Plot of variation of (a) Cu(1)−S(1) and (b) As(1,2)−S(1) bond lengths with temperature for Cu12As4S13. (c) Temperature variations of occupancies for Cu(2) among six sites for Cu12As4S13.

structure. Thus, our accurate structural analyses revealed that the structural modification is mainly attributed to the distortion of [SCu6] octahedra. It should be further examined whether the electronic structure calculated on the basis of our LT structural model is consistent with the complex Cu-NMR spectra19−21 and the reduction in the density of states near the Fermi level.10,11,20,22 We also analyzed three kinds of LT phase structures for Cu12Sb4S13 as determined by three different groups.11−13 Among three different structures, Nasonova et al.13 reported no changes in crystal symmetry during the phase transition. It might be due to the sample preparation condition such that prepared compound does not show any indication of phase transition. At present, we could not give clear explanations for the same. In other two cases, the unit cell of super lattice is different. May et al.12 proposed a tetragonal √2a × √2a × 2c supercell whereas Tanaka et al.11 suggested a body-centered tetragonal 2a × 2a × 2c supercell of the cubic cell. In the present study, the superior quality synchrotron single crystal Xray data provided a reliable supercell structure. The intensity of super lattice reflections are less than 0.1% of fundamental reflections as shown in Figure 3c. It is difficult to detect such super lattice peaks from the powder X-ray data. If the super lattice peaks are ignored, then present X-ray data could be indexed by the √2a × √2a × 2c unit cell. Hence, the sample used by May et al.12 might be similar to the present study. However, this is speculation based on the present study. Additionally, the LT phase transition was suppressed in the transition metal substituted tetrahedrite systems in our previous studies.11 Thus, we could not find the conclusive

the LT phase at 70 K, the Cu−S distances are changed with the largest distortion for the [S(2)Cu6] octahedron. Specifically, the Cu−S distance of 2.129(3) Å along the c-axis of the tetragonal supercell is much smaller than that for the HT phase. Mean deviations of Cu−S distances in the [SCu6] octahedra for the LT phase at 70 K from that for the HT phase at 100 K are about 0.124(3) Å for [S(2)Cu6], 0.061(3) Å for [S(10)Cu6], and 0.052(3) Å for [S(12)Cu6]. Figure 6c shows changes in the Cu−S−Cu angles in the [SCu6] octahedra, where the maximum deviation of the angle between the HT and LT structures is as large as 5.7(1)°. In association with the distortion of [SCu6] octahedra, the thermal displacements for the Cu atoms of [SCu6] becomes smaller than U⊥ of Cu(2) (section 3.1) and are comparable to the thermal displacements of S(1) and S(2) in the HT structure. Such a complicated distortion of the [SCu6] octahedron should lead to a change in the electronic field gradient at the Cu site (in the sulfur triangle), which makes Cu-nuclear magnetic resonance (NMR) spectrum broadening in the LT phase.19,20 In the LT structure, there are eight inequivalent [CuS4] tetrahedral units, whose Cu−S distances reasonably agree with those for the HT structure within the range of ±0.02(1) Å (Figure 6d). The S− Cu−S angles in the [CuS4] tetrahedral units in the LT structure remain unchanged (within ±1.8°) from those in the HT structure, e.g., 111.02(1)° and 106.42(3)° at 100 K, as shown in Figure 6e. Symmetry lowering due to the phase transition also creates six independent [SbS3] units. The Sb−S distances do not vary considerably through the phase transition as demonstrated in Figure 6f. The maximum deviation in the Sb−S bond length is about 0.02(1) Å with respect to the HT 3985



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Cu(2) sites tends to shift from out-of-plane to in-plane with decreasing the temperature in both the HT and LT structure. The other is why the S(2) site split into two, and As as well, below the transition temperature. In any event, we can speculate that the changes in the environment/local structures around the Cu(2) atom are responsible for the structural transformation of Cu12As4S13 and Cu12Sb4S13 and that the structural transformations originate from somewhat distinct mechanisms. Both compounds show negative thermal expansion (NTE) through the transition temperature and that in the LT structure. NTEs were also observed for Cu12Sb4S13 and Zn doped tetrahedrites below 80 K in the previous studies.11,12 Hence, NTE is an intrinsic property of the LT phase. Materials undergoing NTE have attracted attention due to their technological importance. If the detailed mechanism of NTE in Cu12Sb4S13 and Cu12As4S13 can be identified, then it offers an opportunity to design a new class of NTE materials. The crystal structures of Cu12Sb4S13 and Cu12As4S13 are composed of the tetrahedral and octahedral units. It should be recalled that the famous NTE materials with the tetrahedral and octahedral units are ZrW2O8 and related materials such as ZrV2O7. A “rigid unit mode” (RUM),23−25 which is the rotation of polyhedral to prevent them distorting, is considered as a mechanism of the NTE. In the low temperature structures of Cu12Sb4S13 and Cu12As4S13, there are relatively small distortions in the [CuS4] tetrahedral units although there are huge distortions and disorders in SCu6 octahedral units. This fact suggests that the rigid unit mode of [CuS4] units may be related with the NTE of the present systems. First-principles electronic-structure calculation for the LT structure is highly required to understand the mechanism of NTE as well as change in the physical properties through the phase transition.

effect of low-temperature structural phase transitions on thermoelectric properties. The first-principles electronicstructure calculations are required for the LT structure to show the effect of phase transitions on thermoelectric properties. In the HT phase of Cu12As4S13, the bond length Cu(1)− S(1) decreases as the temperature is lowered to 150 K, whereas the Cu(1)−S(1) distance shows an opposite trend for the LT phase at 125−90 K as shown in Figure 7a. These expansion and contraction in the bond length are consistent with the variation of lattice parameter with temperature as shown in Figure 4b. Further, because of the aforementioned splitting of As site over two positions, there are two As−S bond lengths, namely, As(1,2)−S(1), in the LT phase. The As(1)−S(1) distance (2.302(2) Å at 90 K) is longer, while the As(2)−S(1) distance (2.204(1) Å at 90 K) is shorter than the As−S(1) bond length (2.2516(4) Å at 150 K) in the HT phase (see in Figure 7b). Similarly, the S(2) atom occupy two inequivalent sites, namely, S(2) and S(3), in the LT phase. Additionally, an interesting change is noticed in the occupancies of the six disordered sites of the Cu(2) atom in LT phase (see Figure 7c). Upon cooling from 300 to 90 K, the occupancies of Cu(2), Cu(3), and Cu(4) sites are significantly reduced, whereas those of Cu(5) and Cu(6) sites are increased as depicted in the plot of Figure 7c and their positions in the crystal structure are shown in Figure S5. In contrast to the variation of occupancies for these sites, that for the Cu(7) remains unaltered in the entire temperature range. These changes in disordered site occupancy of Cu(2,7) sites might be indication of structural transformation in tennantite around 125 K as observed in the physical property measurements.11 Here we discuss the origins of structural phase transitions in Cu12Sb4S13 and Cu12As4S13 based on the results of physical properties, inelastic neutron scattering, and density functional theory-based molecular dynamics simulations.8−13 Thereby, we take account of the relationship between the structural transformations and changes in electronic structures. The experiments and calculations demonstrated that quasi-localized low-energy optical mode at E = 3−4 meV are associated with the vibration of the Cu(2) atom out of the sulfur triangle. For Cu12Sb4S13, the energy of low-lying optical mode decreases upon cooling, and this mode disappears at around TMST and then reappears at lower energy.12 Furthermore, the structure refinement for the LT phase suggested that some of Cu atoms are displaced away from sulfur triangles in the tetragonal supercell.12 Therefore, displacements of the Cu(2) atoms were thought to be involved in the structural transformation. In our study, it is hard to identify such a displacement of the Cu(2) atom due to the complexity of the LT structure. Instead, we revealed the displacement of S atom in the [SCu6] octahedron in the tetragonal supercell (I4̅2m), consistent with the earlier result on the cubic structure (I4̅3m)13 despite different symmetries of the LT structures. Based on these results, we conjecture that S(2) displaces to release the instability of vibration of Cu(2). Contrary to Cu12Sb4S13, less data on phonon and crystal structures are available for Cu12As4S13. One report showed that a neutron scattering spectrum from optical modes involving out-of-plane vibration of Cu(2) is broader in Cu12As4S13 than in Cu12Sb4S13.9 By combining the results with our structural model, the distribution of Cu(2) atoms among six sites is responsible for the broadening of the spectrum. There are two open questions. One is why the “center of gravity” of the

5. CONCLUSIONS Low-temperature crystal structures of both tetrahedrite and tennantite have been determined using high resolution synchrotron single crystal X-ray diffraction data. The structural phase transition of the tetrahedrite from the HT cubic structure to the LT superlattice unit cell was observed on cooling below TMST and the LT structure was successfully determined in the space group, I4̅2m. We observed distortions of [SCu6] octahedra with the displacement of S atoms and minimal distortions of the CuS4 tetrahedra in the LT phase. On the other hand, the phase transition in the tennantite is quite different in comparison with that of tetrahedrite. In the LT phase, neither symmetry reduction nor superlattice formation occurs. The space group remains unchanged in the LT phase, whereas both S(1) and As(1) are disordered over two sites in the ratio 60:40. Though Cu(2) is disordered over six sites in both HT and LT phases, the occupancies of the disordered sites for the Cu(2) atom drastically change during the structural transformation in tennantite. Even though the LT structures are different for tetrahedrite and tennantite, the changes in the environment/local structure around Cu(2) could be responsible for the structural phase transition. It should be noted that both the tetrahedrite and the tennantite show NTEs associated with the structural phase transitions. The NTEs would be attributed to the rigid unit mode of [CuS4] tetrahedra. 3986



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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.cgd.9b00385. Variation of lattice parameters with temperature in Cu12Sb4S13, low-temperature molecular structure and packing diagram with unit cell of tetragonal Cu12Sb4S13 at 70 K, packing diagram showing three independent [SCu6] octahedra centered at S(2), S(10), and S(12) in the superlattice cell at 70 K, predicted and measured reflections for Cu12As4S13 at 300 and 100 K, description of occupancy changes in the Cu(2) site for Cu12As4S13 during the phase transition, data collection and structure refinement details. Crystallographic information files of variable temperature single crystal synchrotron XRD data for both compounds. (PDF) Accession Codes

CCDC 1904076−1904089 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Telephone: +81-29853-6118. ORCID

Venkatesha R. Hathwar: 0000-0001-9438-417X Koichiro Suekuni: 0000-0002-0515-4864 Bo B. Iversen: 0000-0002-4632-1024 Eiji Nishibori: 0000-0002-4192-6577 Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by JSPS KAKENHI Grant Numbers JP17H05328 (E. N.), 18H04499 (E. N.), JP18K14136 (H. K.), and JP26820296 (K. S.), the JSPS Bilateral Open Partnership Joint Research Projects for 2015−2017 and 2017−2019, the International Education and Research Laboratory Program, the International Tenure Track system of Univ. Tsukuba, the Danish National Research Foundation (DNRF93), the Danish Center for Synchrotron and Neutron Science (DanScatt), and CREST JST Grant No. JPMJCR16Q6. This work was also partly supported by CASIO SCIENCE PROMOTION FOUNDATION. VRH thanks the UGC, India for the assistant professorship under the FRP scheme. The synchrotron experiments were performed at SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2017A0078, 2017B0078, 2018A0078, 2018B0078, and 2019A0159).

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REFERENCES

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Tetrahedrite Cu12Sb4S13: 63,65Cu-Nuclear Magnetic Resonance Studies. J. Phys. Soc. Jpn. 2019, 88, 054710. (21) Ghassemi, N.; Lu, X.; Tian, Y.; Conant, E.; Yan, Y.; Zhou, X.; Ross, J. H., Jr. Structure Change and Rattling Dynamics in Cu12Sb4S13 Tetrahedrite: an NMR Study. ACS Appl. Mater. Interfaces 2018, 10, 36010−36017. (22) Sato, H.; Nagasaki, T.; Suekuni, K.; Tanaka, H. I.; Rousuli, A.; Nakamura, S.; Kawamura, N.; Zheng, X.-G.; Fujii, T.; Takabatake, T. Cu 2p-1s X-ray emission spectroscopy of mineral tetrahedrite Cu12Sb4S13. Radiat. Phys. Chem. 2019, 1 DOI: 10.1016/j.radphyschem.2019.02.007. (23) Mary, T. A.; Evans, J. S. O.; Vogt, T.; Sleight, A. W. Negative thermal expansion from 0.3 to 1050 K in ZrW2O8. Science 1996, 272, 90−92. (24) Pryde, A. K. A.; Hammonds, K. D.; Dove, M. T.; Heine, V.; Gale, J. D.; Warren, M. C. Origin of the negative thermal expansion in ZrW2O8 and ZrV2O7. J. Phys.: Condens. Matter 1996, 8, 10973− 10982. (25) Tucker, M. G.; Goodwin, A. L.; Dove, M. T.; Keen, D. A.; Wells, S. A.; Evans, J. S. O. Negative thermal expansion in ZrW2O8: Mechanisms, rigid unit modes, and neutron total scattering. Phys. Rev. Lett. 2005, 95, 255501.

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Low-Temperature Structural Phase Transitions in Thermoelectric

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