Structural and Electronic Properties of Cu 3 InSe 4

: Single crystals of a new ternary chalcogenide Cu 3 InSe 4 were obtained by induction melting, allowing for a complete investigation of the crystal structure by employing high-resolution single-crystal synchrotron X-ray diffraction. Cu 3 InSe 4 crystallizes in a cubic structure, space group P 43 m , with lattice constant 5.7504(2) Å and a density of 5.426 g/cm 3 . 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 dis-cussed in light of the ongoing interest in exploring the structural and electronic properties of new chalcogenide materials.

To the best of our knowledge, the synthesis and crystal structure of Cu 3 InSe 4 has not been previously reported. Wei et al. [38] predicted Cu 3 InSe 4 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 Cu 3 InSe 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.

Materials and Methods
Single crystals of Cu 3 InSe 4 were initially obtained in an attempt to prepare CuFe 2 InSe 4 , resulting in FeSe as well as the shiny metallic ternary chalcogenide crystals identified as Cu 3 InSe 4 . This procedure was repeated with a stoichiometric ratio of the starting highpurity 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 Cu 3 InSe 4 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 3d 10 4s 1 , In 4d 10 5s 2 5p 1 and Se 4s 2 4p 4 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].

Results
The crystallographic data and structural refinement results are shown in Table 1. Cu 3 InSe 4 crystallizes in the cubic space group P43m (No. 215) with cell parameter a = 5.7504(2) Å, Z = 1 and density = 5.426 g/cm 3 . The atomic coordinates and equivalent isotropic displacement parameters, U eq , are shown in Table 2. The anisotropic displacement parameters are presented in Table 3. As shown in Figure 1, the structure consists of CuSe 4 (Cu-Se distance of 2.4622(4) Å) and InSe 4 (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 CuSe 4 and InSe 4 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 CuInSe 2 (2.591 Å) [49] and LiInSe 2 (2.57 Å) [50]. It is important to note that the structure of Cu 3 InSe 4 is related to that of sulvanites Cu 3 XQ 4 (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 Cu 3 InSe 4 and Cu 3 XQ 4 , respectively.  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 Cu 3 InSe 4 , 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, electrongas-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 Cu 3 XSe 4 compounds [54] with Cu 3 InSe 4 , the X-Se bonds in the former show a higher degree of covalency as compared with the primarily ionic character for In-Se in Cu 3 InSe 4 . 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, Ef, 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 Ef falls relatively deep in the valence band and will therefore not be of interest for such applications. 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 Cu 3 InSe 4 thus resulting in p-type metallic behavior. Our detailed structural analyses allow for an investigation of the electronic structure of Cu 3 InSe 4 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, Cu 3 InSe 4 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 CuSe 4 tetrahedra therefore play a dominant role in the metallic conductivity of Cu 3 InSe 4 . It is instructive to compare the electronic structure of Cu 3 InSe 4 to that of Cu 3 XSe 4 in light of the fact that the crystal structure of Cu 3 InSe 4 is not isostructural to that of the later compositions. Specifically, for the case of the Cu 3 XSe 4 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 Cu 3 InSe 4 E f falls relatively deep in the valence band and will therefore not be of interest for such applications.

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.

Conclusions
Single crystals of a new ternary chalcogenide Cu 3 InSe 4 were obtained by induction melting, and the structural and electronic properties are reported for the first time. Cu 3 InSe 4 forms in a cubic crystal structure that consists of CuSe 4 and InSe 4 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.