Structural and Electronic Properties of Cu₃InSe₄

Abstract

Single crystals of a new ternary chalcogenide Cu₃InSe₄ were obtained by induction melting, allowing for a complete investigation of the crystal structure by employing high-resolution single-crystal synchrotron X-ray diffraction. Cu₃InSe₄ crystallizes in a cubic structure, space group $P\overline{4}3m$, with lattice constant 5.7504(2) Å and a density of 5.426 g/cm³. There are three unique crystallographic sites in the unit cell, with each cation bonded to four Se atoms in a tetrahedral geometry. Electron localization function calculations were employed in investigating the chemical bonding nature and first-principle electronic structure calculations are also presented. The results are discussed in light of the ongoing interest in exploring the structural and electronic properties of new chalcogenide materials.

1. Introduction

Multinary metal chalcogenides consisting of primarily earth-abundant, low-cost, and non-toxic constituents exhibit physical properties that can be tuned via composition, specific bonding scheme, lattice defects or disorder, and have been investigated for a variety of different applications of interest including thermoelectrics [1,2,3,4,5,6], photovoltaics [7,8,9,10], superconductivity [11,12,13], and as potential topological insulators [14,15]. The interest in ternary Cu-based compositions has recently intensified in pursuit of commercially viable solar cells [16,17,18] and thermoelectrics [19,20,21,22]. The ternary Cu-In-Se system is of particular interest [23], with a number of compounds possible along the Cu₂Se-InSe₃ tie-line [24,25] such as CuInSe₂ [26,27], Cu₃In₅Se₉ [28], Cu₇In₁₉Se₃₂ [23], CuIn₅Se₈ [25], Cu₂In₄Se₇ [29] and CuIn₃Se₅ [30]. The crystal structure of CuInSe₂ was reported to be either tetragonal with space group $I\overline{4}2m$ [31,32] or cubic, $F\overline{4}3m$ [23,33], where the latter structure can be considered as two interpenetrating face-centered cubic sub-lattices. In the case of Cu₃MSe₄, where M is V, Ta, Nb or Sb, both cubic [34,35] and tetragonal [36,37] structure types were reported.

To the best of our knowledge, the synthesis and crystal structure of Cu₃InSe₄ has not been previously reported. Wei et al. [38] predicted Cu₃InSe₄ to be metallic, with “holes in the valence band”, however structural information and details of the electronic structure were not reported. Therefore, we have undertaken to synthesize and investigate the crystal structure and electronic properties of Cu₃InSe_4. We employed high-resolution single crystal synchrotron measurements to determine the structure of this previously unascertained ternary compound. The structural features and bonding were investigated in detail, including analyses of calculated electron localization, and the electronic properties were obtained using density functional theory. Our results are compared to that of other ternary chalcogenides.

2. Materials and Methods

Single crystals of Cu₃InSe₄ were initially obtained in an attempt to prepare CuFe₂InSe₄, resulting in FeSe as well as the shiny metallic ternary chalcogenide crystals identified as Cu₃InSe₄. This procedure was repeated with a stoichiometric ratio of the starting high-purity elements, Cu powder (99.9 % purity, Alfa Aesar, Thermo Fisher Scientific, Ward Hill, MA, USA), In shot (99.99 % purity, Alfa Aesar, Thermo Fisher Scientific, Ward Hill, MA, USA) and Se ingot (99.999 % purity, Alfa Aesar, Thermo Fisher Scientific, Ward Hill, MA, USA) [39]. The elements were placed in a silica ampoule and vacuum-sealed inside a quartz tube, then melted via a water-cooled 3-coil induction (Superior Induction, SI-7KWHF) furnace resulting in an agglomeration of gray Cu₃InSe₄ crystals.

Single-crystal synchrotron measurements were carried out at NSF’s ChemMatCARS, Sector 15 of the Advanced Photon Source, Argonne National Laboratory. Data were collected using a Huber 3-circle diffractometer (Huber diffraction, Lancaster, CA, USA) equipped with a Pilatus3X 2M detector (Dectris USA Inc., Philadelphia, PA, USA) using an Oxford Cryojet (American Laboratory Trading, East Lyme, CT, USA). The ω-angle was set at −180°, κ-angle was set at 0° and 30°, with ϕ-angle scanned over the range of 360° using the shutterless mode of the detector. Data integration was performed with the Bruker APEX 3 suite software. The reduction of the data was obtained with the SAINT v.8.38A and SADABS v.2016 programs (Bruker AXS Inc., Madison, WI, USA) that are included in the APEX suite. The structure was solved directly and refined by the full-matrix least-squares method.

Ab initio calculations based on density functional theory, plane-waves basis set, and pseudopotentials were carried out using the Quantum Espresso software package [40]. Projector-augmented waves (PAW) pseudopotentials [41], the generalized gradient approximation of Perdew-Burke-Ernzehof [42,43] plus Hubbard correction [44] (GGA-PBE + U) exchange-correlation functional were applied. A U parameter of 4 eV for the cations was used based on previous studies on Cu-based chalcogenide materials [45,46] that provide for good agreement between calculated and experimental structure values. For the pseudopotentials, Cu 3d¹⁰4s¹, In 4d¹⁰5s²5p¹ and Se 4s²4p⁴ valence configurations were considered. For self-consistent field (SCF) calculations, a k-point mesh of 6 × 6 × 6 was applied to sample the Brillouin zone. The kinetic energy cutoff for wavefunctions and charge density was set to 70 Ry and 300 Ry, respectively, and an energy convergence threshold of 10⁻⁷ eV was utilized. The electron localization function (ELF) distribution was analyzed and visualized using VESTA v.3.5.8 software [47].

CCDC 2172956 contains the supplementary crystallographic data. These data can be obtained free of charge via https://www.ccdc.cam.ac.uk/structures/search?access=referee&pid=ccdc:2172956&author=ng, accessed on 10 September 2022, (or from the CCDC, 12 Union Road, Cambridge CB2 1EZ, UK; Fax: +44 1223 336033; E-mail: [email protected]).

3. Results

The crystallographic data and structural refinement results are shown in

Table 1. Crystal data and structure refinement results.

Empirical formula	Cu3InSe4
Formula weight	621.32
Temperature	100(2) K
Wavelength	0.49594 Å
Crystal system	Cubic
Space group	$P\overline{4}3m$ (No. 215)
Unit cell dimension	a = 5.7504(2)
Volume	190.15(2) Å3
Z	1
Density (calculated)	5.426 mg/m3
Absorption coefficient	11.36 mm−1
Crystal size	30 × 20 × 10 µm3
Theta range for data collection	2.283 to 26.223°
Reflections collected	2237
Independent reflections	251 [R(int) = 0.0945]
Goodness-of-fit on F2	1.190
Final R indices [I > 2σ(I)]	R1 = 0.0375, wR2 = 0.0886
R indices (all data)	R1 = 0.0403, wR2 = 0.0908

. Cu₃InSe₄ crystallizes in the cubic space group $P\overline{4}3m$ (No. 215) with cell parameter a = 5.7504(2) Å, Z = 1 and density = 5.426 g/cm³. The atomic coordinates and equivalent isotropic displacement parameters, U_eq, are shown in

Table 2. Atomic coordinates and equivalent isotropic displacement parameters (Ų). U_eq is defined as one third of the trace of the orthogonalized U_ij tensor.

Atom	Site	x	y	z	Ueq
In	1b	1/2	1/2	1/2	0.009(1)
Se	4e	0.2412(1)	0.2412(1)	0.2412(1)	0.011(1)
Cu	3d	0	0	1/2	0.007(1)

. The anisotropic displacement parameters are presented in

Table 3. Anisotropic displacement parameters (Ų). The anisotropic displacement factor exponent takes the form: −2π²[h²a*²U₁₁ + … + 2hka*b*U₁₂].

	U11	U22	U33	U23	U13	U12
In	0.010(1)	0.010(1)	0.010(1)	0	0	0
Se	0.011(1)	0.011(1)	0.011(1)	−0.002(1)	−0.002(1)	−0.002(1)
Cu	0.007(1)	0.007(1)	0.006(1)	0	0	0

. As shown in Figure 1, the structure consists of CuSe₄ (Cu-Se distance of 2.4622(4) Å) and InSe₄ (In-Se distance of 2.5775(13) Å) tetrahedra connected by corner-sharing Se atoms. Selenium is surrounded by three Cu atoms and by an In atom, as shown in Figure 1a. The CuSe₄ and InSe₄ tetrahedra are illustrated in Figure 1b. The tetrahedron about the In site is a regular tetrahedron with Se-In-Se angles of 109.471(11)°, while that of Cu is somewhat distorted with Se-Cu-Se angles ranging from 105.63(6)° to 111.42(3)°. The Cu-Se distance (2.4622(4) Å) is similar to that reported for sulvanite and adamantine compounds [36,48,49], while the In-Se distance (2.5775(13) Å) is similar to that for CuInSe₂ (2.591 Å) [49] and LiInSe₂ (2.57 Å) [50]. It is important to note that the structure of Cu₃InSe₄ is related to that of sulvanites Cu₃XQ₄ (X = V, Nb, Ta; Q = S, Se, Te) [19,51,52]; however, the Cu atoms occupy different Wyckoff sites in these two different ternary chalcogenides thus resulting in corner sharing and edge sharing tetrahedra for Cu₃InSe₄ and Cu₃XQ₄, respectively.

The electron density distribution was investigated by calculating the ELF, revealing the ionic nature of the bonding in Cu₃InSe₄, as shown in Figure 2. Figure 2 shows the calculated ELF along the (110) plane. ELF values of 0.0, 0.5 and 1.0 represent fully delocalized, electron-gas-like pair probability and perfect localization, respectively [53]. The atomic core regions of the cations have localization domains with ELF values close to unity and low ELF values away from these regions. This suggests electrons transfer from both Cu and In atoms to adjacent Se atoms, indicating ionic bonding. In comparing the Cu₃XSe₄ compounds [54] with Cu₃InSe₄, the X-Se bonds in the former show a higher degree of covalency as compared with the primarily ionic character for In-Se in Cu₃InSe₄.

The oxidation states of Cu, In and Se are 1+, 3+ and 2−, respectively, resulting in 30 electrons per formula unit, or two fewer than required for the tetrahedral bonds in Cu₃InSe₄ thus resulting in p-type metallic behavior. Our detailed structural analyses allow for an investigation of the electronic structure of Cu₃InSe₄ by calculating the energy band structure and density of states (DOS). As shown in Figure 3, the Fermi level, E_f, crosses the valence band in multiple regions, thus, Cu₃InSe₄ is a p-type metal [46,55], confirming the simple charge imbalance argument. This is also in agreement with the early conjecture [38], and corroborated by our room temperature conductivity measurements indicating metallic conduction [56]. The orbital-projected DOS indicates that the valence band maximum has contributions mainly from the Cu 3d and Se 4p orbitals, while the conduction band maximum is mainly composed of In 5s and Se 4p and minor contributions from Cu 3d4s4p, In 5p and Se 4s orbitals. The orbital interactions between the CuSe₄ tetrahedra therefore play a dominant role in the metallic conductivity of Cu₃InSe₄. It is instructive to compare the electronic structure of Cu₃InSe₄ to that of Cu₃XSe₄ in light of the fact that the crystal structure of Cu₃InSe₄ is not isostructural to that of the later compositions. Specifically, for the case of the Cu₃XSe₄ compositions [19,57,58], an energy gap opens between the valence and conduction bands in these materials. These compositions are therefore semiconductors and are being investigated for thermoelectric [19,20] and photovoltaic [59,60] applications, whereas in the case of Cu₃InSe₄ E_f falls relatively deep in the valence band and will therefore not be of interest for such applications.

4. Conclusions

Single crystals of a new ternary chalcogenide Cu₃InSe₄ were obtained by induction melting, and the structural and electronic properties are reported for the first time. Cu₃InSe₄ forms in a cubic crystal structure that consists of CuSe₄ and InSe₄ tetrahedra connected by corner sharing Se atoms. Electron localization function analyses indicated partially ionic bonding between the cations and Se atoms, with highly delocalized electrons in the regions between cation and selenium. Electronic structure calculations reveal this ternary chalcogenide to be metallic. Given that ternary chalcogenide compounds are of interest for potential thermoelectric and optoelectronic applications, our findings will be useful for investigations on new materials for applications of interest. The results and analyses in this work add to our understanding of the structural and electronic properties of ternary chalcogenides.