Intermetallic Compound with Pronounced Covalency in the Bonding

Feb 5, 2019 - Chemical bonding analysis reveals pronounced covalency of Re–Re, ... structure calculations and by measurements of electrical resistiv...
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ReGa0.4Ge0.6: Intermetallic Compound with Pronounced Covalency in the Bonding Pattern Maxim S. Likhanov,† Valeriy Yu. Verchenko,†,‡ Alexey N. Kuznetsov,†,§ and Andrei V. Shevelkov*,† †

Department of Chemistry, Lomonosov Moscow State University, Moscow 119991, Russia National Institute for Chemical Physics and Biophysics, Tallinn 12618, Estonia § N. S. Kurnakov Institute of General and Inorganic Chemistry, RAS, Moscow 119991, Russia ‡

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S Supporting Information *

ABSTRACT: We report synthesis, crystal and electronic structure, and transport properties of new intermetallic compound ReGa0.4Ge0.6, which was obtained by two-step ampule method from the elements. ReGa0.4Ge0.6 crystallizes in its own structure type (space group I4/mmm, a = 2.89222(3) Å, c = 15.1663(3) Å, and Z = 4) which can be described as a sequential alternation of blocks of rhenium atoms and blocks of gallium and germanium atoms. Chemical bonding analysis reveals pronounced covalency of Re−Re, Re−E, and E−E (E = Ga and Ge) interactions and an interesting bonding pattern that includes many variations of localized bonding within a single compound, including pairwise homo- and heterometallic bonding, three-centered homometallic and four-centered bonding, and possibly even more delocalized bonding, which is not often encountered in such a simple intermetallic compound. Metallic behavior is confirmed by electronic structure calculations and by measurements of electrical resistivity.

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INTRODUCTION Intermetallic compounds formed by a combination of transition metals and p-block metals and/or semimetals are a large family of compounds with extreme diversity of crystal and electronic structures and properties.1,2 Among such compounds, it is relatively easy to find examples of systems with various types of magnetic ordering,3−7 superconductivity,8−11 thermoelectric activity,12−18 and so on. However, despite the vastness of the class of binary intermetallics, the use of a combination of two p-elements with different numbers of valence electrons and a transition metal may lead not only to the formation of simple solid solutions but also to the emergence of new structure types and occasionally to the formation of completely unique ones.6,7,19−25 For example, ferromagnetic MnAlGe with its own structure type has large magnetic anisotropy and high coercivity,6 whereas Fe3‑δGeTe2 is a uniaxial van der Waals intrinsic ferromagnet with abnormally high magnetocrystalline anisotropy.7 Fe32+δGe33As2 represents a very rare two-dimensional intergrowth phase with unusual field-dependent antiferromagnetic-like transition.20 TiSnSb is considered an efficient negative electrode for Liand Na-ion batteries.26 Semiconducting Fe3Al2Si3 demonstrates high thermoelectric performance.27 Finally, the properties of many compounds such as Ni5Ga3Ge2,25 Ni13Ga3Ge6,28 Fe3Al2Si4,23 and FeAl3Si2,24 possessing new and unique crystal structures, have not yet been studied. Predictions of such behavior (formation of a new or already known structure types) remains a rather complicated task, and quite often rely © XXXX American Chemical Society

on the a priori knowledge or an educated guesses of the type of chemical bonding in said intermetallics and their assignment to a certain class. This is far from a simple task since despite the high interest in the problem of understanding chemical bonding in such intermetallic compounds and the existence of well-established lucid rules based on the valence electron count for certain types of intermetallic systems, such as the Zintl29 and Hume−Rothery30 phases including the emerging new attractive concepts like the 18-n rule31 which has been gaining general character lately, this area is still not fully understood and is far from being generalized. Therefore, there is no universal and reliable way to unequivocally predict the type of the structure and bonding in a given intermetallic compound based just on its chemical composition, especially when d-block metals are involved; as a consequence, the discovery of new compounds with the desired properties frequently originates from the exploratory synthesis.32 In general, a combination of two p-elements with a transition metal is an attractive playground for finding new compounds with welcome properties and intriguing bonding patterns. This stems from both the different structure of valence shells of interacting atoms and their slightly different electronegativity that ensures incomplete charge transfer. In this paper, we explore the combination of two p-elements, Ga and Ge, with Re and synthesize a new compound, Received: December 13, 2018

A

DOI: 10.1021/acs.inorgchem.8b03468 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

ELK code34 and (ii) a pseudopotential projector augmented wave method (PAW) as implemented in the Vienna ab initio Simulation Package (VASP).35,36 In the first approach, PBESol exchangecorrelation functional37 of the GGA-type was utilized. The Brillouin zone sampling was performed using a 17 × 17 × 7 k-point grid (1071 irreducible k-points), the muffin-tin sphere radii for the respective atoms were (Bohr): 2.46 (Re), 2.29 (Ga), 2.29 (Ge), and the maximum moduli for the reciprocal vectors kmax were chosen such that RMTkmax= 10.0. In the second, pseudopotential approach, a Monckhorst-Pack k-point mesh38 of 16 × 16 × 8 (144 irreducible kpoints) was employed, and the energy cutoff was set at 500 eV. The SCAN exchange-correlation functional of the meta-GGA-type, augmented with nonlocal correlation part from the rVV10 vdW density functional,39 was used in the PAW-based calculations. The convergence of the total energy with respect to the k-point sets was checked. Experimental unit cell metrics and coordinates of atomic positions were taken as starting points for calculations. In both FP-LAPW and PAW approaches, two ordered models of gallium and germanium distribution were considered (see Figure 1): (i) the model with 50/50

ReGa0.4Ge0.6, which crystallizes in its own structure type derived from close packing of atoms. This compound exhibits a rather remarkable pattern of localized chemical bonds, from classical pairwise homo- and heteroatomic interactions to multicenter bonding involving different number of atoms, yet features electron transport properties typical for a metal rather than an essentially covalent solid.

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EXPERIMENTAL SECTION

Synthesis and Characterization. For the synthesis of polycrystalline samples of ReGa1−xGex (x = 0.25, 0.3, 0.4, 0.45, 0.5, 0.525, 0.55, 0.575, 0.6, 0.65, 0.7, and 0.75), rhenium powder (99.99%, Sigma-Aldrich), germanium chips (99.999%, Sigma-Aldrich), and gallium ingots (99.9999%, Sigma-Aldrich) were used as starting reagents. Standard ampule technique was employed for obtaining the samples. Evacuated and flame-sealed fused silica ampules with a mixture of elements in the desired stoichiometric ratio were annealed at 950 °C for 2 days. Then, the temperature was reduced to 750 °C, and the samples were annealed for 5 more days. Afterward, the samples were cooled down, ground into powders, pressed into pellets, and annealed at 750 °C for 1 week. X-ray powder diffraction analysis of the products was performed using a Huber G670 Guinier Camera (Cu Kα1 radiation, Ge monochromator, λ = 1.5406 Å). A scanning electron microscope JSM JEOL 6490-LV equipped with an energydispersive X-ray (EDX) analysis system INCA x-Sight was used for the analysis of chemical composition and its possible variation across the samples with different value of x = 0.25, 0.5, 0.55, 0.6, and 0.75. The melting point temperature of ReGa0.4Ge0.6 was determined by differential scanning calorimetry analysis with the heating rate of 10°/ min at temperature between 300 and 1300 K in an argon atmosphere using a STA 409 PC Luxx thermal analyzer (Netzsch). The product obtained after heating in thermal analyzer was investigated by the PXRD analysis. Crystal Structure Determination. A single-phase powder sample with the ReGa0.4Ge0.6 nominal composition was used for the crystal structure determination. X-ray powder diffraction patterns were recorded using a BRUKER D8 Advance diffractometer, Cu Kα1,2 radiation. The crystal structure was solved using the Superflip option implemented in Jana2006 package and subsequently refined using the same program package.33 Crystallographic data as well as structure solution and refinement details are presented in Table 1. Electronic Structure Calculations. Electronic structure calculations were performed on the Density Functional Theory (DFT) level using two approaches: (i) an all-electron full-potential linearized augmented plane wave method (FP-LAPW) as implemented in the

Figure 1. Two ordered models of Re2GaGe: one with mixed Ga−Ge dumbbells (top, O1) and the other with homoatomic dumbbells (bottom, O2).

gallium to germanium ratio where only heteroatomic dumbbells exist (O1 model), i.e., Ga atoms have only Ge atoms at the bonding distances, and vice versa, and (ii) the model with 50/50 gallium to germanium ratio with all dumbbells being homoatomic (O2 model). A third model, representing statistical disorder of the original unit cell through the Virtual Crystal Approximation (VCA), was also used in the FP-LAPW calculations. For that purpose, a fractional atom imitating 60% Ge and 40% Ga occupancy of the same atomic position, with a nuclear charge of +31.6, was created using the internal routine of the ELK program and used to represent the p-block elements in the structure. For the O1 and O2 models, we have also performed atomic coordinate relaxation within fixed unit cells and unconstrained structural optimization, both using VASP package and PBESol functional. In order to accommodate unconstrained structural optimization and relaxation, all the structures were described in the calculations by space group P1, with all atomic positions independent. The results are shown in Table 2, with “relaxed” denoting fixed experimental cell metrics and atomic relaxation, and “optimized” means unconstrained optimization. Atomic charges in the direct-space analysis were calculated according to Bader’s QTAIM approach.40 The electron localizability indicator (ELI-D) was calculated according to the literature41−43 using DGrid package.44 Bonding analysis in the orbital space was performed based on the Crystal Orbital Hamilton Populations (COHP)45−47 using LOBSTER 3.0.0 program package.48 Atomic charges from the orbital space data were calculated according to the Mulliken and Löwdin schemes as implemented in the LOBSTER

Table 1. Crystallographic and Refinement Parameters for ReGa0.4Ge0.6 formula formula weight (g·mol−1) crystal system space group a (Å) c (Å) V (Å3) Z ρcalc (g·cm−3) temperature (K) radiation, λ (Å) 2θ range (deg) R1 wR2 GoF Rprof wRprof

ReGa0.4Ge0.6 257.66 tetragonal I4/mmm 2.89222(3) 15.1663(3) 126.865(4) 4 13.494 293 Cu Kα, 1.540593, 1.544427 8.00−120.0 0.0564 0.0751 1.56 0.0793 0.1080 B

DOI: 10.1021/acs.inorgchem.8b03468 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Table 2. Structural and Energetic Parameters for the Experimental and Calculated Structures of Re2GaGe parameter

experimental

O1 relaxed

O1 optimized

O2 relaxed

O2 optimized

a, Å c, Å Etot, eV ΔE, kJ/mola

2.89222(3) 15.1663(3) −70.6573 0 2.630(2) 2.89222(6) 2.487(6)

2.89222 15.1663 −70.6772 -2.27 2.6122 2.8922 2.4712

2.87749 15.2362 −70.6949 -3.63 2.6114 2.8775 2.4713

2.89222 15.1663 −70.3551 +29.16 2.62935 2.89222

2.87753 15.2344 −70.3717 +27.56 2.6268 2.8775

Re−Re, Å Ga−Ge, Å Ga−Ga, Å Ge−Ge, Å Re−Ga, Å Re−Ge, Å

2.673(3) 2.673(3)

2.6973 2.6774

2.4898 2.4701 2.7201 2.6321

2.7212 2.6313

2.4906 2.4707 2.7212 2.6313

−ΔE = (Etot − Etot(experimental)) × F.

a

Table 3. Atomic Charges for the O1 and O2 Ordered Models of Re2GaGe, Calculated According to Various Partitioning Schemes Re method QTAIM/FP-LAPW QTAIM/PAW Mulliken Löwdin

O1 −0.12 −0.12 −0.11 −0.25

Ga O2a −0.05 −0.13 −0.08 −0.13 −0.06 −0.16 −0.24 −0.28

(Ge) (Ga) (Ge) (Ga) (Ge) (Ga) (Ge) (Ga)

Ge

O1

O2

O1

O2

+0.24

+0.13

0.00

+0.05

+0.27

+0.16

−0.03

+0.05

+0.12

+0.12

+0.10

+0.10

+0.34

+0.32

+0.16

+0.20

a

Symbols in the parentheses denote neighboring atoms for the O2 model.

Figure 2. X-ray diffraction patterns of the ReGa1−xGex samples with x = 0.25, 0.5, 0.6, and 0.7. Resistivity Measurements. For resistivity measurements, dense pellets were prepared by spark plasma sintering (SPS) using a Labox625 machine. Densification was performed in 10 mm graphite dies by heating the sample to 973 K at 70 K/min under a pressure of 60 MPa in vacuum, keeping it at this temperature for 7 min, and then cooling down to room temperature. The relative density of the sample of approximately 95% was achieved. Electrical resistivity was measured on parallelepiped-shaped pellets with typical dimensions of 0.8 × 0.3 × 0.2 cm3 cut out of the pellet using the Resistivity option of a

package. Atomic charges according to various schemes are summarized in Table 3. The calculations were performed using the Intel Core-i7-based laboratory cluster and the MSU Lomonosov supercomputer. Structure visualization and topological analysis of the electron localization indicator were performed using VESTA 3.4.4 and ParaView 5.2.0 packages, respectively.49,50 The results of the VASP and LOBSTER calculations were visualized using wxDragon package.51 C

DOI: 10.1021/acs.inorgchem.8b03468 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Physical Property Measurement System (PPMS, Quantum Design) at temperatures between 4 and 400 K in zero magnetic field.

Table 4. Atomic Coordinates and Thermal Displacement Parameters for the ReGa0.4Ge0.6

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RESULTS AND DISCUSSION Synthesis, Homogeneity Range, and Crystal Structure. ReGa0.4Ge0.6 was synthesized in a phase-pure form by a two-step ampule synthesis. The compound possesses a relatively narrow homogeneity range (Figure 2). According to the X-ray powder diffraction data (XRPD), increasing the Ge content (x > 0.6) leads to the formation of Re3Ge7 as an admixture.52 Increasing the Ga content in ReGa1−xGex (x ≤ 0.5) results in another side product, which could be identified as a phase of the IrIn3 structure type53 with the estimated composition ReGa3‑yGey where y ≈ 1. This admixture is visible only as three extra peaks of very low intensity at x = 0.5; the intensities of the peaks substantially increase with increasing the Ga content. Besides, rhenium is present as an impurity on diffraction patterns when x > 0.6 and x < 0.5. The unit cell parameters of ReGa1−xGex vary linearly in the range of x between 0.5 and 0.6 and are constant when x > 0.6 and x < 0.5 (Figure S1). These data are in perfect agreement with the results of the EDXS analysis of the samples pressed into pellets, according to which the composition of the new phase ranges from Re 0 . 9 8 ( 3 ) Ga 0 . 4 9 ( 3 ) Ge 0 . 5 3 ( 4 ) at x n o m = 0.25 to Re0.99(2)Ga0.40(1)Ge0.61(2) at xnom = 0.75 (Table S1). From the PXRD and EDXS data, we assume that the homogeneity range spreads from x = 0.6 almost to x = 0.5 but does not include the ReGa0.5Ge0.5 composition. According to the DSC analysis, ReGa0.4Ge0.6 melts incongruently at 1202(5) K. According to the crystal structure solution (Figure 3), ReGa0.4Ge0.6 crystallizes in the tetragonal crystal system, space

atom

Wyckoff site

x

y

z

Uaniso, Å2

occupancy

Re1 Ga1 Ge1

4e 4e 4e

0 0 0

0 0 0

0.30451(18) 0.0820(3) 0.0820(3)

0.0235(3) 0.0273(10) 0.0273(10)

1 0.4a 0.6a

a

Fixed according to the sample composition.

Figure 4. Block representation (a) and unit cell (b) of the ReGa0.4Ge0.6 crystal structure and its comparison with the CuZr2 (c), and MoB (d) crystal structures.

two layers of a body centered cubic structure. These blocks alternate along the c direction of the unit cell in the way that each atom of rhenium is located above the void between two pelement atoms. Such an arrangement causes a shift of gallium/ germanium layers relative to each other toward the (110) direction by a half of the translation. Thus, the layers of rhenium atoms can also be considered as an fcc structure, since the rhenium atom has cuboctahedral coordination by nearest 8 atoms of Re and 4 p-atoms. It is interesting to compare the new crystal structure with that of CuZr2.54 In the latter, zirconium atoms form blocks similar to those of rhenium atoms in the structure ReGa0.4Ge0.6. However, unlike the ReGa0.4Ge0.6 structure, copper atoms in CuZr2 form a monolayer and not a double layer as gallium and germanium in ReGa0.4Ge0.6. Comparison of both structure types is given in Figure 4. It should also be noted that Re2Al crystallizes in the CuZr2 structure type and rhenium atoms occupy the same positions as in the ReGa0.4Ge0.6 crystal structure.55 Thus, when one extra layer of the p-elements is added between the rhenium layers in Re2Al structure, the ReGa0.4Ge0.6 structure is obtained. We also note that according to similarity of the space group unit cell metrics and the ratio of d/p elements the title crystal structure resembles that of MoB (Figure 4d); however, the latter shows different arrangement of atoms. Importantly, boron atoms form zigzag chains alternating in the a and b directions of the unit cell.56 In addition, it should be noted that ReGa0.4Ge0.6 is formally isotypic to the Hg2X2 (X = F, Cl, Br, I) crystal structure.57 However, the difference in the c/a ratio, 2.97 (Hg2F2) and 5.24 (ReGa0.4Ge0.6), shows that despite the congruous Wyckoff positions the two structures are completely different. The Hg(I) halides exhibit almost independent Hg− Hg dumbbells, whereas in the title compound, two sorts of layers can be subtracted (Re and Ga/Ge). Analysis of the interatomic distances (Table 5) reveals two notable features. First, the distance between p-atoms of 2.49 Å is close to the distance in the Ga−Ga dumbbell (2.48 Å),58 which is a structural unit of the α-Ga and is comparable to length of the Ge−Ge dumbbell in some intermetallic

Figure 3. Powder X-ray diffraction pattern of ReGa0.4Ge0.6. The upper black line represents the experimental diffraction pattern, the black ticks show peak positions, and the lower black line is the difference between the experimental and calculated patterns.

group I4/mmm (#139). There are two unique crystallographic sites: One of them is occupied by rhenium atoms, and the other is jointly populated by two p-elements. For the latter position, the Ga/Ge ratio was fixed in the refinement as 0.4:0.6 in accordance with the experimental composition of the sample. Final anisotropic refinement led to the atomic parameters listed in Table 4. The crystal structure of ReGa0.4Ge0.6 (Figure 4) can be described as a sequential alternation of blocks consisting entirely of p- or d-metal atoms, where the arrangement of gallium and germanium atoms in the block of p-elements represents an α-polonium primitive crystal structure slightly oblate along the c axis, so that a system of p-element−pelement dumbbells is formed, whereas rhenium atoms form D

DOI: 10.1021/acs.inorgchem.8b03468 Inorg. Chem. XXXX, XXX, XXX−XXX

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compounds such as OsGe2 (2.37 Å),59 Re3Ge7 (2.45 Å),52 CoGe2 (2.54 Å),60 and NiGe1.67Zn0.33 (2.55 Å).61 Isolated Ga−Ga dumbbells almost never occur in the intermetallic compounds of this family, except for orthogonal bonds of Ga− Ga in Fe3Ga4 (2.60 Å),62 Ni3Ga7 (2.59 Å),63 and Pt3Ga7 (2.87 Å).64 Second, there is a bond between two rhenium atoms with a length of 2.63 Å, which is much shorter than the Re−Re bond in metallic rhenium (2.74−2.77 Å),65 but at the same time too long to regard this bond as multiple (2.20−2.50

Table 5. Selected Interatomic Distances for the ReGa0.4Ge0.6 atom Re1 E1a

atom

distance, Å

Re1 (×4) Re1 (×4) E1 (×4) E1 (×4) E1 (×1)

2.89222(6) 2.630(2) 2.673(3) 2.89222(6) 2.487(6)

a

E = 0.4 Ga + 0.6 Ge.

Figure 5. Total and projected l-resolved DOS near the Fermi level for the O1 (top), O2 (middle), and VCA models (bottom) from the FP-LAPW all-electron DFT calculations. E

DOI: 10.1021/acs.inorgchem.8b03468 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Å).66−68 Nevertheless, such an unusual small distance between rhenium atoms became the reason to initiate a detailed study of the electronic structure and analysis of the bonding pattern in the new compound. In fact, the distance of 2.63 Å is close to the sum of the covalent radii of rhenium (2.56 Å),69 which may indirectly indicate the preferential covalent nature of the bonding in the new compound, which will be discussed later. Electronic Structure and Chemical Bonding. Calculated total (TDOS) and projected (PDOS) densities of states near the Fermi level from the FP-LAPW calculations are shown in Figure 5. We note that the results of both approaches are in very good agreement (for the PAW-based DOS plots, please see the Supporting Information). Also, the DOS plots for the O1, O2, and VCA models are very similar, and the differences between them are miniscule and purely quantitative. As seen from the plots, the region near the Fermi level (both below and above) is dominated by the contribution from rhenium 5dstates, which is rather typical for intermetallics rich in d-metal. These d-metal states are not completely filled, and partial splitting can be observed, with the formation of a pseudogap. However, the Fermi level does not fall directly into this pseudogap but rather sits ca. 1 eV below, where the DOS is higher, so the overall behavior of the compound is expected to be metallic. Gallium and germanium 4p-states also contribute to the same energy range as rhenium; however, their contributions are significantly smaller. The presence of a pseudogap raises a question of how many electrons are needed to move the Fermi level into this pseudogap and which composition such a compound would have. According to the generalized 18-n electron count rule,31 the ReGa0.4Ge0.6 compound is electron-poor, while the electron-precise, supposedly the most stable one, would have the ReGe composition and the Fermi level in the pseudogap. We have modeled such hypothetical compound and found out that while the Fermi level for hypothetical “ReGe” does move into the pseudogap, the minimum point of said gap corresponds to the ReGa0.2Ge0.8 composition, which is outside the compositional range where the compound exists; thus, it appears that the stability of ReGa0.4Ge0.6 is not governed by 18n rule. Further details are provided in the respective section of the Supporting Information. Electron energy dispersion plots (band structure) for the three models (Figure 6) are consistent with 3D metallic behavior of the compound, whichever model is used for calculations. Band dispersion does differ somewhat along the kpath, and there are regions around the N and X points where bands do not cross the Fermi level at all, but this is not enough to assume any pronounced anisotropic character for the structure. Calculated QTAIM atomic charges for the O1 and O2 models are given in Table 3. The trend is well-reproduced in both approaches and shows a small degree of electron transfer from gallium to rhenium atoms, while germanium effectively remains neutral. The O1 model, featuring heteroatomic dumbbells, naturally has more even charge distribution than the O2 one, yet the differences are almost negligible. Thus, from the charge density analysis we can deduce the lack of strong ionic interactions in the compound, suggesting that the bonding is likely of the covalent nature. The comparison between the two ordered models of the structure, O1 and O2, shows a strong similarity in the description, with some quantitative differences. Nevertheless, energy-wise, the O1 model appears to be the preferred one.

Figure 6. Band structure near the Fermi level for the O1 (top), O2 (middle), and VCA models (bottom) of Re2GaGe from the FPLAPW all-electron DFT calculations.

Total energy difference between the O1 and O2 models is ca. 26.2 kJ/mol in favor of the O1 according to the FP-LAPW calculations, and 39.5 kJ/mol according to the PAW ones from the calculations based on the experimental structures. Atomic relaxation and full structural optimization do not alter this picture qualitatively (see Table 2). Thus, we can assume that the model with less order is favored for this structure. Unfortunately, the differences in the cell metrics and structural parameters for the O1 and O2 models are too small to serve as distinguishing features, thus experimental proof that the O1 model is preferred is hard to obtain. However, it has to be noted that there is a way in which mixed occupancy of Ga/Ge sites can be achieved on average, while retaining homoatomic dumbbells: it is mixing of the Ga−Ga and Ge−Ge dumbbells. Considering the closeness of the atomic scattering factors, F

DOI: 10.1021/acs.inorgchem.8b03468 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 7. ELI-D localization domains corresponding to different kinds of interatomic interactions in the descending order of localizability indicator for the O1 model: pairwise Ga−Ge interactions (Ω1); ϒ = four-centered 2Ga+2Re interactions (Ω3), Re−Ge delocalized five centered interactions (Ω4), Re−Re pairwise (Ω5) and three-centered interactions (Ω6 and Ω6′).

Figure 8. ELI-D localization domains corresponding to different kinds of interatomic interactions in the descending order of localizability indicator for the O2 model: pairwise Ga−Ga (Ω1) and Ge−Ge (Ω2) interactions; four-centered 2Ga+2Re interactions (Ω3), Re−Ge five-center delocalized bonds (Ω4), Re−Re pairwise (Ω5) and three-centered interactions (Ω6 and Ω6′).

In order to gain an insight into the nature of chemical bonding and bonding patterns in O1 and O2, we have performed topological analysis of the electron localizability indicator (ELI-D).40−42 This is performed in the same spirit as the analysis of the well-known ELF function, by scanning a certain range of function parameters and assigning chemical meaning to the features observed in isosurfaces. The ELI-D

there would likely be no measurable effect upon the cell metrics, and the situation would be nigh indistinguishable from mixing gallium and germanium in the same position. Such pattern requires large supercell and is difficult to model accurately, yet, we cannot totally rule out a possibility of homoatomic dumbbell formation, so this case also needs to be considered. G

DOI: 10.1021/acs.inorgchem.8b03468 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 9. Projected COHP (pCOHP) for Re−Re (red lines), Re−Ga (green lines), Re−Ge (blue lines), Ga−Ge (orange lines), Ge−Ge (violet lines), and Ga−Ga (gray line) interactions in the O1 and O2 models.

isosurfaces for the decreasing ϒ parameter for the O1 and O2 models are shown in Figures 7 and 8, respectively. For the O1 model, where all the dumbbells are heteroatomic, the first nonatomic attractors to appear are the disc-shaped localization domains corresponding to the pairwise Ga−Ge interactions (Ω1 bonding basins, see Figure 7a). The integration of the electron density over basins gives the basin population of 2.53 electrons. This is slightly more than a classic σ 2-center 2-electron bond, suggesting that a certain degree of π-interaction might also occur. The intersection of Ω1 by charge density basins of Ga and Ge shows the electron partitioning of ca. 35:65, which means that the bond shows a certain polarity and the electrons are shifted (with respect to the perfect 50:50 ratio) toward germanium atom, which is reflected by an asymmetric shape of the respective domain in the ELI-D isosurface (see Figure 7). As we decrease the ϒ parameter, the next arising features are tetrahedra-shaped localization domains that correspond to the four-centered 2Ga +2Re interactions (Ω3 tetrasynaptic bonding basins, see Figure 7b). The integration gives the basin population of 1.98 e−, and basin intersection shows electron partitioning of ca. 61:39 shifted toward gallium. Further lowering of the ϒ parameter reveals what appear at first to be four localization domains corresponding to the three-center 2Ge+Re bonds (Ω4 bonding basins, see Figure 7b). However, further investigations show that no evident boundaries exist between the basins corresponding to these ELI-D maxima. Either this is due the very flat shape of the basins near the boundary and we have four basins of three-centered 2Ge+Re interactions with the population of ca. 0.51 e− each, or as we are inclined to believe, this is in fact one bonding basin corresponding to the fivecentered 4Ge+Re interaction with the population of 2.04 e−.

The last features to appear in the ELI-D topology (see Figure 7c) are Re−Re pairwise interactions (Ω5 bonding basins, population of 0.51 e−) and Re−Re three-center bonds (Ω6 and Ω6′, population 0.28 and 0.26 e−, respectively). Bonding pattern derived from the ELI-D topology for the O2 model, featuring homoatomic dumbbells, is pretty similar (see Figure 8). The main difference is that we observe two separate basins for homoatomic pairwise Ga−Ga (Ω1) and Ge−Ge (Ω2) interactions with the population of 2.14 and 2.53 e−, respectively (see Figure 8a). Basin intersection for both Ω1 and Ω2 gives almost perfect 50:50 partitioning, confirming the nonpolar covalent nature of the respective bonds. Tetrasynaptic Ω3 basins corresponding to the 2Re+2Ga interactions are populated by 1.95 e−, almost identical to the 1.98 e− for the O1 model (see Figure 8a). The Ω4-type basins do not appear as a separate maxima in ELI-D at all, like they do at first for the O1 model, but rather as a continuous doughnut-shaped maximum, supporting the interpretation as a single five-center interactions basin populated by 2.08 e− (see Figure 8b). Finally, disynaptic (Ω5) and trisynaptic (Ω6, Ω6′) basins corresponding to the pairwise and three-centered interactions between rhenium atoms arise, populated by 0.49, 0.25, and 0.30 e−, respectively (see Figure 8c). To gain another prospect of the bonding pattern, we have complemented our direct-space analysis with Crystal Orbital Hamilton Populations (COHP) analysis, which evaluates bonding or antibonding character of interactions between pairs of atoms based on the Hamilton matrix elements contributing to the overlap of the projected local atomic orbitals. The corresponding set of local orbitals is reconstructed from the plane-wave wave functions calculated by the VASP code. H

DOI: 10.1021/acs.inorgchem.8b03468 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Projected COHP (pCOHP) for the O1 and O2 models is displayed in the Figure 9, which shows that Re−Ga and Re− Ge interactions in both models are quite well-optimized, featuring bonding character (positive−pCOHP) below the Fermi level and antibonding character (negative−pCOHP) above it. Re−Re interactions in both cases show only minor antibonding character at the Fermi level, but mostly bonding character below it. In the O1 model, Ga−Ge interactions below the Fermi level are of the bonding nature, and also there is a small amount of bonding states above the Fermi level, but not enough to regard it as a source of Ga−Ge bond instability due to poor bonding optimization. Nevertheless, this could be used as an explanation for the Ga/Ge ratio in the compound slightly shifted toward Ge from perfect 50:50 ratio, as the excess of Ge provides more electrons to the band near the Fermi level. For the O2 model, however, the situation is quite different. In this model, instead of Ga−Ge interactions we have two pairs of homoatomic bonds. While Ge−Ge pairwise interactions appear to be quite well optimized, with just a few bonding states above the Fermi level, for Ga−Ga pair there is a visible portion of bonding states above the Fermi level (Figure 8, gray line). This suggests that more electrons are necessary to stabilize the Ga−Ga bond. This might be the source of the excessive total energy of the O2 model as compared to the O1 one. Partial COHPs, integrated up to the Fermi level (IpCOHP), which can be used as a relative indicator of bond strengths, are −3.50 eV/bond (Re−Re), −2.93 eV/bond (Re−Ga), −3.09 eV (Re−Ge), and −4.96 eV/bond (Ga−Ge) for the O1 model and −3.48 eV/bond (Re−Re), −2.91 eV/ bond (Re−Ga), −3.07 eV/bond (Re−Ge), −4.56 eV/bond (Ga−Ga), and −4.90 eV/bond (Ge−Ge) for the O2 model. These figures agree well with significant degree of covalency in the bonding pattern of Re2GaGe. Also, from the IpCOHP data we can see that the Ga−Ga homoatomic bonds are relatively weaker than either Ge−Ge or Ga−Ge bonds, which agrees with lesser stability of the O2 model. Atomic charges, calculated from orbital projections, are given in Table 3. As expected, the Mulliken scheme somewhat underestimates bond polarity, nevertheless, qualitative trends in charge transfer are reproduced and overall match the results of Bader charge density from the direct-space analysis, with the main difference being a slightly larger positive charge on germanium as compared to the respective Bader charges. Thus, in both structural models we observe pronounced covalency and a variety of homo- and heteroatomic bonds of different type, indicating prominently localized nature of bonding in the compound. Such a variety of localized bonds within one compound with a rather simple crystal structure appears quite interesting and, perhaps, a bit unexpected, particularly due to the fact that the compound in question is clearly metallic in terms of electric conductivity, for which high degree of electron delocalization is normally expected.70 Transport Properties. Our resistivity measurements confirm the metallic nature of ReGa0.4Ge0.6, in line with the calculated electronic structure. Electrical resistivity increases almost linearly in the temperature range of 4 to 400 K (Figure 10).

Figure 10. Temperature dependence of electrical resistivity for ReGa0.4Ge0.6.

structure can be represented as a sequential alternation of blocks consisting entirely of rhenium atoms and those of gallium and germanium ones along the c direction of the unit cell. Electronic structure calculations indicate metallic character of the new compound, which is confirmed by experimental data. Chemical bonding analysis reveals pronounced covalency in the bonding pattern in general, including an unusually wide variety of localized bond types for a single compound, and, in particular, the localization of electronic density between the rhenium atoms, in the form of two- and three-center Re−Re bonds, which is directly connected with the relatively short distance of a rhenium−rhenium bond with a length of 2.63 Å.

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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.8b03468. Dependence of unit cell volume of ReGa1−xGex upon composition; results of EDX analysis and PAW DFT calculations; description and results of the DFT calculations modeling the hypothetical “ReGe” compound (PDF) Accession Codes

CCDC 1868227 contains 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]. ORCID

Maxim S. Likhanov: 0000-0002-4683-8197 Andrei V. Shevelkov: 0000-0002-8316-3280

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Funding

CONCLUSIONS A new compound, ReGa0.4Ge0.6, which is the first ternary phase in the Re−Ga−Ge system, was synthesized as a single-phase powder. It crystallizes in its own structure type; its crystal

The work is supported by the Russian Science Foundation, Grant No. 17−13−01033. Notes

The authors declare no competing financial interest. I

DOI: 10.1021/acs.inorgchem.8b03468 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

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ACKNOWLEDGMENTS We thank Dr. S. S. Fedotov for his help with the PXRD experiments, A. S. Tyablikov for helping with preparation of dense pellets, S. A. Vladimirova for carrying out DSC analysis, and Dr. A. A. Tsirlin for discussion. We acknowledge the use of a Labox-625 SPS machine purchased under the Lomonosov MSU program of development. The computations were carried out using the equipment of the shared research facilities of the HPC computing resources at Lomonosov Moscow State University.

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