Crystal, electronic structure and hydrogenation properties of the Mg5.57Ni16Ge7.43 cluster phase with a new type of polyhedron

Pavlyuk, N.; Dmytriv, G.; Bondaruk, A.; Ciesielski, W.; Pavlyuk, V.

doi:10.1107/S2053229624003140

research papers

STRUCTURAL
CHEMISTRY

ISSN: 2053-2296

Volume 80| Part 5| May 2024| Pages 159-165

https://doi.org/10.1107/S2053229624003140

Crystal, electronic structure and hydrogenation properties of the Mg_5.57Ni₁₆Ge_7.43 cluster phase with a new type of polyhedron

Nazar Pavlyuk,^a Grygoriy Dmytriv,^a Alina Bondaruk,^b Wojciech Ciesielski ^b and Volodymyr Pavlyuk ^a,^b ^*

^aDepartment of Inorganic Chemistry, Ivan Franko Lviv National University, Kyryla and Mefodiya str. 6, 79005 Lviv, Ukraine, and ^bInstitute of Chemistry, Jan Dlugosz University, al. Armii Krajowej 13/15, Czestochowa 42200, Poland
^*Correspondence e-mail: vpavlyuk2002@yahoo.com

Edited by G. P. A. Yap, University of Delaware, USA (Received 7 March 2024; accepted 11 April 2024; online 24 April 2024)

The ternary germanide Mg_5.57Ni₁₆Ge_7.43 (cubic, space group Fm $[\overline{3}]$ m, cF116) belongs to the structural family based on the Th₆Mn₂₃-type. The Ge1 and Ge2 atoms fully occupy the 4a (m $[\overline{3}]$ m symmetry) and 24d (m.mm) sites, respectively. The Ni1 and Ni2 atoms both fully occupy two 32f sites (.3m symmetry). The Mg/Ge statistical mixture occupies the 24e site with 4m.m symmetry. The structure of the title compound contains a three-core-shell cluster. At (0,0,0), there is a Ge1 atom which is surrounded by eight Ni atoms at the vertices of a cube and consequently six Mg atoms at the vertices of an octahedron. These surrounded eight Ni and six Mg atoms form a [Ge1Ni₈(Mg/Ge)₆] rhombic dodecahedron with a coordination number of 14. The [GeNi₈(Mg/Ge)₆] rhombic dodecahedron is encapsulated within the [Ni₂₄] rhombicuboctahedron, which is again encapsulated within an [Ni₃₂(Mg/Ge)₂₄] pentacontatetrahedron; thus, the three-core-shell cluster [GeNi₈(Mg/Ge)₆@Ni₂₄@Ni₃₂(Mg/Ge)₂₄] results. The pentacontatetrahedron is a new representative of Pavlyuk's polyhedra group based on pentagonal, tetragonal and trigonal faces. The dominance of the metallic type of bonding between atoms in the Mg_5.57Ni₁₆Ge_7.43 structure is confirmed by the results of the electronic structure calculations. The hydrogen sorption capacity of this intermetallic at 570 K reaches 0.70 wt% H₂.

Keywords: crystal structure; electronic structure; clusters; convex polyhedra; intermetallics; hydride; ternary; germanide; hydrogenation.

CCDC reference: 2347669

1. Introduction

Magnesium alloys and intermetallics, in addition to their unique mechanical properties, show great potential for use in various types of energy storage systems. These are in particular as hydrogen sorption materials for storage systems and metal hydride batteries (Edalati et al., 2018 ; Ouyang et al., 2020 ; Hitam et al., 2021 ). Binary alloys of magnesium with transition metals, such as Fe, Co, Ni, Zn and others, as well as ternary alloys with the additional involvement of p-elements, such as Al, Ga, Si, Ge, Sn, rare earth metals and others, have attracted special attention (Kalisvaart et al., 2010 ; Zhang et al., 2011 ; Pavlyuk et al., 2012 , 2022a ; Shtender et al., 2015 ). Due to the complexities of the synthesis of magnesium alloys and the complex nature of the physicochemical interaction of magnesium with other elements, ternary metallic systems are still not sufficiently studied. For example, study of the ternary Mg–Ni–Ge system began more than 60 years ago when the first results of analyzing the structures of MgNi_1.6Ge_0.4 and Mg₆Ni₁₆Ge₇ by the powder Debye–Scherrer method were reported (Teslyuk & Markiv, 1962 ). MgNi_1.6Ge_0.4 (cubic, Fd $[\overline{3}]$ m, a = 6.911 Å) belongs to the cubic Laves phase with the MgCu₂ structure type. For Mg₆Ni₁₆Ge₇ (cubic, Fm $[\overline{3}]$ m, a = 11.532 Å), the Mg₆Cu₁₆Si₇ structure type was proposed. Buchholz & Schuster (1981 ) described the crystal structure of MgNi₆Ge₆ (hexagonal, P6/mmm, a = 5.067 and c = 3.860 Å) with the YCo₆Ge₆-type. The equiatomic MgNiGe phase (orthorhombic, Pnma, a = 6.4742, b = 4.0716 and c = 6.9426 Å) belongs to the TiNiSi-type (Hlukhyy et al., 2013 ). The Mg-rich compound Mg₃Ni₂Ge (cubic, Fd $[\overline{3}]$ m, a = 11.521 Å) crystallizes in the Mn₃Ni₂Si-type (Gennari et al., 2003 ). Subsequently, the crystal structures of the two Laves phases Mg₂Ni₃Ge (R $[\overline{3}]$ m, a = 5.0300 and c = 11.330 Å) and MgNi_2–xGe_x (x = 0.5, P6₃/mcm, a = 8.6946 and c = 7.8127 Å) were investigated using single-crystal X-ray diffraction methods (Siggelkow et al., 2017 ).

During our investigation of Ni-rich alloys of the ternary Mg–Ni–Ge system, we obtained a good-quality single crystal of the Mg_5.57Ni₁₆Ge_7.43 ternary phase and report its crystal structure here.

2. Experimental

2.1. Synthesis and crystallization

The target Mg₂₀Ni₅₅Ge₂₅ species was prepared from the following reactants: magnesium, nickel and germanium (purity of elements is more than 99.99 wt%). Appropriate amounts of Mg, Ni and Ge pure elements were mixed according to the aimed-for stoichiometry of the product and filled into a tantalum crucible in a glove box using a purified argon atmosphere. The Ta crucible was sealed by arc welding under a dry argon atmosphere. The reaction between the elements was carried out in an induction furnace at 1100 °C. After 20 min, the samples were cooled rapidly to room temperature by removing the crucibles from the furnace. The Ta container was placed in an evacuated quartz vial and thermally annealed to obtain good-quality single crystals suitable for structure determination. This heating process was carried out at a rate of 5 °C min⁻¹ to T = 800 °C in a resistance furnace and held at this temperature for 15–20 min with a thermal cycle controller. The sample was then cooled slowly (0.1 °C min⁻¹) to 400 °C and the furnace was switched off. After cooling to room temperature, the sample could be separated from the tantalum container. The alloy is stable in air and includes single crystals, which exhibit metallic luster and could be isolated by mechanical fragmentation.

2.2. Refinement

The structure was solved by direct methods after an analytical absorption correction.

The Mg atom in the 24e site showed a displacement parameter that was different from the others, i.e. the Ni and Ge atoms.

Several important factors indicate that the 24e position is occupied mainly by Mg atoms with a small fraction of germanium (a statistical mixture of Mg/Ge). First, the title compound is isostructural with the Mg₆Cu₁₆Si₇ structure type, where the 24e site is also occupied by Mg atoms. Second, analysis of the interatomic distances indicates that they are typical of the largest atom in this structure, which is magnesium. Thirdly, Fourier difference electron-density maps show the electron density to be associated with the Mg atom. During the first cycles of refinement of the Mg atom in the 24e site, we noticed that, in addition to magnesium, there is also a small proportion of the heavier Ge or Ni atom in this site. The best refinement results are for the Mg/Ge statistical mixture. The refined composition of the compound from single-crystal data correlates well with the energy-dispersive X-ray spectroscopy (EDS) analysis.

Crystal data, data collection and structure refinement details are summarized in Table 1.

Table 1
Experimental details

Crystal data
Chemical formula	Mg_5.57Ni₁₆Ge_7.43
M_r	6454.98
Crystal system, space group	Cubic, Fm $[\overline{3}]$ m
Temperature (K)	293
a (Å)	11.5036 (6)
V (Å³)	1522.3 (2)
Z	1
Radiation type	Mo Kα
μ (mm⁻¹)	33.86
Crystal size (mm)	0.06 × 0.05 × 0.03

Data collection
Diffractometer	Oxford Diffraction Xcalibur3 CCD
Absorption correction	Analytical (CrysAlis RED; Oxford Diffraction, 2008 $[Oxford Diffraction (2008). CrysAlis RED. Oxford Diffraction Ltd, Abingdon, Oxfordshire, England.]$ )
T_min, T_max	0.470, 0.683
No. of measured, independent and observed [I > 2σ(I)] reflections	12619, 131, 120
R_int	0.074
(sin θ/λ)_max (Å⁻¹)	0.668

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.013, 0.028, 1.25
No. of reflections	131
No. of parameters	14
Δρ_max, Δρ_min (e Å⁻³)	0.63, −0.63
Computer programs: CrysAlis PRO (Rigaku OD, 2015 $[Rigaku OD (2015). CrysAlis PRO. Rigaku Oxford Diffraction Ltd, Yarnton, Oxfordshire, England.]$ ), SHELXT2014 (Sheldrick, 2015a ), SHELXL2014 (Sheldrick, 2015b ), DIAMOND (Brandenburg, 2006 ) and SHELX97 (Sheldrick, 1997 ).

2.3. Hydrogenation

The hydrogen absorption and desorption measurements for the Mg_5.57Ni₁₆Ge_7.43 alloy were performed using an IMI–COR (Hiden Isochema) manometric hydrogen-storage analyzer. The Sieverts method, up to a pressure of 12 bar (1 bar = 10⁵ Pa) at a temperature of 573 K, was used.

3. Results and discussion

As part of a systematic study of Mg–Ni–Ge alloys, the ternary Mg_5.57Ni₁₆Ge_7.43 phase was detected in the Ni-rich region. A small irregularly shaped single crystal was selected from the annealed sample by mechanical fragmentation. Intensity data were measured at room temperature on an Oxford Diffraction Xcalibur3 automatic diffractometer with a CCD detector (Mo Kα radiation, graphite monochromator, ω scan).

The title compound crystallizes in a cubic Mg₆Cu₁₆Si₇ structure type (Nagorsen & Witte, 1953 ), which is an ordered superstructure of the Th₆Mn₂₃-type (Florio et al., 1952 ). The unit cell and coordination polyhedra of the crystallographically distinct atoms are shown in Fig. 1. The Mg/Ge atom (site symmetry 4m.m) is surrounded by 16 adjacent atoms, which form a pseudo-Frank–Kasper [(Mg/Ge)Ni₈(Mg/Ge)₄Ge₄] polyhedron. The coordination polyhedra of the Ni1 and Ni2 atoms (.3m symmetry) are icosahedral [Ni1Ge₃Ni₆(Mg/Ge)₃] and pseudo-Frank–Kasper polyhedral (CN = 13) [Ni2Ge₄Ni₆(Mg/Ge)₃], respectively. At (0,0,0), there is a Ge1 atom surrounded by eight Ni atoms, which occupy the vertices of an [Ni₈] cube, and also by six Mg/Ge atoms, which are at the vertices of an [(Mg/Ge)₆] octahedron. The eight Ni atoms and six Mg/Ge atoms which surround the Ge1 atom form a [Ge1Ni₈(Mg/Ge)₆] rhombic dodecahedron with CN = 14. For the Ge2 atom, the polyhedron is a 14-vertex [Ge2Ni₈(Mg/Ge)₆] rhombododecahedron. In addition to octahedra filled by germanium, there are also empty [(Mg/Ge)₆] octahedra, the arrangement of which in the unit cell is shown in Fig. 2. Ni atoms form a three-dimensional network in which [Ni₈] cubes are visible, the vertices of which are joined by eight [Ni₄] tetrahedra, which are also connected to other tetrahedra by one face and three edges, as shown in Fig. 3(a). Instead, the Mg and Ge atoms along the z axis form two types of 3- and 4-ring networks, namely, flat at z = 0 and $[1 \over 2]$ [Fig. 3(b)], and slightly corrugated at z = $[1 \over 4]$ and $[3 \over 4]$ [Fig. 3(c)].

Figure 1
A clinographic projection of the Mg_5.57Ni₁₆Ge_7.43 unit-cell contents and the coordination polyhedra of the atoms.

Figure 2
The packing of empty [(Mg/Ge)₆] octahedra in the unit cell.

Figure 3
(a) Three-dimensional network of Ni atoms, (b) flat 3- and 4-ring networks of Mg–Ge atoms at z = 0 and $[1 \over 2]$ , and (c) slightly corrugated networks at z = $[1 \over 4]$ and $[3 \over 4]$ in the Mg_5.57Ni₁₆Ge_7.43 structure.

The ternary germanide Mg_5.57Ni₁₆Ge_7.43 can also be described as three-core-shell clusters of [GeNi₈(Mg/Ge)₆@Ni₂₄@Ni₃₂(Mg/Ge)₂₄] (see Fig. 4). The [GeNi₈(Mg/Ge)₆] rhombic dodecahedron is encapsulated within the [Ni₂₄] rhombicuboctahedron, which is again encapsulated within a [Ni₃₂(Mg/Ge)₂₄] pentacontatetrahedron. The [Ni₃₂(Mg/Ge)₂₄] polyhedron has vertices V = 56, faces F = 54 and edges E = 108. The Euler characteristic (χ) was classically defined for the surfaces of polyhedra, according to the formula (Richeson, 2012 ):

$[\chi = V - E + F,]$

where V, E and F are, respectively, the numbers of vertices (corners), edges and faces in the given polyhedron. For the title structure, the [Ni₃₂(Mg/Ge)₂₄] polyhedron has V = 56, F = 54 and E = 108, which gives a Euler characteristic χ of 2; therefore, [Ni₃₂(Mg/Ge)₂₄] is a new type of convex polyhedron, namely, a pentacontatetrahedron, with the vertex configuration: 24 (3₂5₂), 24 (345₂) and 8 (5₃). The pentacontatetrahedron is a new representative of Pavlyuk's group of polyhedra based on pentagonal, tetragonal and trigonal faces. In the pentacontatetrahedron are 24 pentagonal, six tetragonal and 24 trigonal faces (Fig. 5). In the title compound, the pentacontatetrahedra exhibits close packing in the unit cell (Fig. 6). Earlier, we described the structure of the cluster phase MgMn₄Ga₁₈ (Pavlyuk et al., 2022b ), for which we discovered a pentacontaoctahedron with V = 40, F = 58 and E = 96, and also a convex polyhedron (χ = 2). We also described previously the formation of clusters in magnesium-containing intermetallics using the example of the quaternary phase Li₂₀Mg₆Cu₁₃Al₄₂ with a 60-atom truncated icosahedron (Pavlyuk et al., 2019 ) and new cubic cluster phases in the Mg–Ni–Ga system (Pavlyuk et al., 2020 ).

Figure 4
The atomic structure of a three-shell cluster [GeNi₈(Mg/Ge)₆@Ni₂₄@Ni₃₂(Mg/Ge)₂₄].

Figure 5
The closed and open faces of the [Ni₃₂(Mg/Ge)₂₄] pentacontatetrahedron.

Figure 6
The packing of [Ni₃₂(Mg/Ge)₂₄] pentacontatetrahedra in the unit cell.

The electronic structure calculations were performed for the ordered structure Mg₆Ni₁₆Ge₇ (the 24e site is fully occupied by Mg) using the tight-binding linear muffin-tin orbital (TB–LMTO) method with the atomic spheres approximation (ASA) in the TB–LMTO–ASA program (Version 4.7; Andersen, 1975 ; Andersen et al., 1984 , 1986 ). Electronic energies were calculated using density functional theory (DFT) based on the local-density approximation (LDA) for the exchange-correlation functional as parameterized by von Barth & Hedin (1972 ). The electronic structure calculations were carried out using the non-spin-polarized approach with a dense k-point mesh in the irreducible Brillouin zones of the crystallographic unit cell (48 irreducible k-points from 512 for NKABC = 8 × 8 × 8). From the calculations, a mapping of the electrons in real space was obtained using the electron localization function (ELF) (Becke & Edgecombe, 1990 ). Visualization of the electronic structure calculation data was achieved using wxDragon (Eck, 2012 ). The ELF is a simple measure of electron localization in atomic and molecular systems (Becke & Edgecombe, 1990).

If we consider the distribution of the ELF, two types of layers of atoms can be distinguished in the title structure [Figs. 7(a) and 7(b)] which are alternately packed along the z axis [Fig. 7(c)]. Layers of atoms at z = 0, $[1 \over 4]$ , $[1 \over 2]$ , $[3 \over 4]$ [Figs. 7(a) and 7(c)] consist exclusively of Mg and Ge atoms. The ELF has the highest values (0.709 eV) around the Ge atoms, which is consistent with its higher electronegativity [Figs. 7(a) and 7(d)]. Slightly corrugated layers of atoms at approximately z = $[1 \over 8]$ , $[1 \over 3]$ , $[2 \over 3]$ and $[7 \over 8]$ [Figs. 7(a) and 7(c)] consist exclusively of Ni atoms. The entire space of this layer has an average value of the distribution of the ELF function of 0.350 eV (indicated in green), which corresponds to delocalized electrons, which are typical for the metallic type of bonding between atoms. The dominance of the metallic bond is also reflected in the density of states (DOS) at the Fermi level, the partial and total DOS are shown in Fig. 8.

Figure 7
Two-dimensional representation of the ELF for layers of atoms at (a) z = 0 and (b) z = $[1 \over 8]$ . (c) Packing layers along the z axis and (d) a three-dimensional representation of the isosurfaces of the ELF around the Ge atoms at the 0.75 level.

Figure 8
Total and partial DOS for Mg_5.57Ni₁₆Ge_7.43 from TB–LMTO–ASA calculations.

The prepared Mg_5.57Ni₁₆Ge_7.43 sample was hydrogenated by hydrogen gas at a pressure up to 12 bar and a temperature of 573 K. The PCT (pressure, composition and temperature) isotherms for the hydrogenation and dehydrogenation processes are presented in Fig. 9. At this condition, Mg_5.57Ni₁₆Ge_7.43 absorbs up to 0.7 wt% H₂. Crystallographic analysis of the structure made it possible to determine the geometrically acceptable coordinates of the sites that can be occupied by hydrogen, namely, 4b ( $[1 \over 2]$ , $[1 \over 2]$ , $[1 \over 2]$ ) and 48h ( $[1 \over 8]$ , $[1 \over 8]$ , 0). These coordinates are the centres of the octahedral voids. In the 4b site, there is an [(Mg/Ge)₆] octahedron, and in the 48h site, there is an octahedron of composition [(Mg/Ge)₂Ni₂Ge₂], which is slightly deformed. In the case of full occupation of these sites with hydrogen, the hydrogen capacity reached 0.81 wt% H₂. A slight difference in the hydrogen content in hydride from experimental data and that calculated from geometric considerations indicates that these positions are partially occupied by H atoms (approximately 86%).

Figure 9
The PCT (pressure, composition and temperature) isotherms for hydrogenation and dehydrogenation processes.

The bulk alloy from which the single crystal was selected was examined by scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDS) and powder X-ray diffraction (PXRD). A scanning electron microscope (TESCAN Vega3 LMU) equipped with an Oxford Instruments energy-dispersive X-ray analyzer (Aztec ONE system) was used to determine the chemical composition of the alloy (Fig. 10). The EDS data from three selected spots give the average composition (in at%) of Mg_19.3 (3)Ni_55.2 (2)Ge_25.5 (1) that correlates well with the PXRD data (Mg_19.21Ni_55.17Ge_25.62).

Figure 10
The secondary electron image and representative EDS spectra for the Mg_5.57Ni₁₆Ge_7.43 sample.

The PXRD analysis of the sample before and after hydrogenation was carried out using a Rigaku Mini Flex D-600 powder diffractometer with Cu Kα radiation. As shown in Fig. 11, the structure of the intermetallic is preserved, and the shift of reflexes for the pattern after hydrogenation indicates an increase of the unit-cell dimension of the crystal lattice from a = 11.5036 (6) Å to a = 11.5753 (6) Å during the incorporation of hydrogen into the structural voids.

Figure 11
(a) Observed (red), calculated (black line) and difference (bottom blue line) PXRD patterns of the Mg_5.57Ni₁₆Ge_7.43 sample after Rietveld refinement. (b) Comparison powder patterns before (blue) and after (red) hydrogenation.

Supporting information

CCDC reference: 2347669

Crystal structure: contains datablocks I, global. DOI: https://doi.org/10.1107/S2053229624003140/yp3234sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2053229624003140/yp3234Isup2.hkl

Computing details top

Magnesium nickel germanide top

Crystal data top

Mg_5.57Ni₁₆Ge_7.43	Mo Kα radiation, λ = 0.71073 Å
M_r = 6454.98	Cell parameters from 131 reflections
Cubic, Fm3m	θ = 3.1–28.3°
a = 11.5036 (6) Å	µ = 33.85 mm⁻¹
V = 1522.3 (2) Å³	T = 293 K
Z = 1	Prism, metallic light grey
F(000) = 3010.1	0.06 × 0.05 × 0.03 mm
D_x = 7.041 Mg m⁻³

Data collection top

Oxford Diffraction Xcalibur3 CCD diffractometer	120 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	R_int = 0.074
ω scans	θ_max = 28.3°, θ_min = 3.1°
Absorption correction: analytical (CrysAlis RED; Oxford Diffraction, 2008)	h = −15→15
T_min = 0.470, T_max = 0.683	k = −15→15
12619 measured reflections	l = −15→15
131 independent reflections

Refinement top

Refinement on F²	14 parameters
Least-squares matrix: full	0 restraints
R[F² > 2σ(F²)] = 0.013	w = 1/[σ²(F_o²) + 35.3811P] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.028	(Δ/σ)_max < 0.001
S = 1.25	Δρ_max = 0.63 e Å⁻³
131 reflections	Δρ_min = −0.63 e Å⁻³

Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Ge1	0.0000	0.0000	0.0000	0.0040 (4)
Ge2	0.0000	0.2500	0.2500	0.00442 (18)
Ni1	0.33129 (4)	0.33129 (4)	0.33129 (4)	0.00491 (19)
Ni2	0.11860 (4)	0.11860 (4)	0.11860 (4)	0.00509 (19)
Mg	0.2959 (2)	0.0000	0.0000	0.0048 (4)	0.929 (4)
Ge	0.2959 (2)	0.0000	0.0000	0.0048 (4)	0.071 (4)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ge1	0.0040 (4)	0.0040 (4)	0.0040 (4)	0.000	0.000	0.000
Ge2	0.0039 (4)	0.0047 (2)	0.0047 (2)	0.000	0.000	0.0002 (3)
Ni1	0.00491 (19)	0.00491 (19)	0.00491 (19)	0.00057 (18)	0.00057 (18)	0.00057 (18)
Ni2	0.00509 (19)	0.00509 (19)	0.00509 (19)	−0.00015 (18)	−0.00015 (18)	−0.00015 (18)
Mg	0.0073 (10)	0.0035 (6)	0.0035 (6)	0.000	0.000	0.000
Ge	0.0073 (10)	0.0035 (6)	0.0035 (6)	0.000	0.000	0.000

Geometric parameters (Å, º) top

Ge1—Ni2	2.3631 (8)	Ni1—Ni1^x	2.6450 (14)
Ge1—Ni2ⁱ	2.3632 (8)	Ni1—Ni1^xii	2.6450 (14)
Ge1—Ni2ⁱⁱ	2.3632 (8)	Ni1—Ge^xx	2.7747 (7)
Ge1—Ni2ⁱⁱⁱ	2.3632 (8)	Ni1—Mg^xxi	2.7747 (7)
Ge1—Ni2^iv	2.3632 (8)	Ni1—Mg^xxii	2.7747 (7)
Ge1—Ni2^v	2.3632 (8)	Ni2—Ge2^xvii	2.5359 (3)
Ge1—Ni2^vi	2.3632 (8)	Ni2—Ge2^xv	2.5359 (3)
Ge1—Ni2^vii	2.3632 (8)	Ni2—Ni1^ix	2.5789 (7)
Ge2—Ni1^viii	2.3485 (1)	Ni2—Ni1^xii	2.5789 (7)
Ge2—Ni1^ix	2.3485 (1)	Ni2—Ni1^x	2.5789 (7)
Ge2—Ni1^x	2.3485 (1)	Ni2—Ni2ⁱⁱ	2.7288 (9)
Ge2—Ni1^xi	2.3485 (1)	Ni2—Ni2^vi	2.7288 (9)
Ge2—Ni2ⁱⁱ	2.5359 (3)	Ni2—Ni2^iv	2.7288 (9)
Ge2—Ni2^xii	2.5359 (3)	Ni2—Ge^xvii	2.8075 (17)
Ge2—Ni2^xiii	2.5359 (3)	Ni2—Ge^xv	2.8075 (17)
Ge2—Ni2	2.5359 (3)	Mg—Ni1^xii	2.7747 (7)
Ge2—Ge^xiv	2.9239 (4)	Mg—Ni1^xxiii	2.7747 (7)
Ge2—Mg^xv	2.9239 (4)	Mg—Ni1^xxiv	2.7747 (7)
Ge2—Mg^xvi	2.9239 (4)	Mg—Ni1^xxv	2.7747 (7)
Ge2—Mg^xvii	2.9239 (4)	Mg—Ni2^vii	2.8075 (17)
Ni1—Ge2^xviii	2.3485 (1)	Mg—Ni2^vi	2.8075 (17)
Ni1—Ge2^x	2.3485 (1)	Mg—Ni2^iv	2.8075 (17)
Ni1—Ge2^xix	2.3485 (1)	Mg—Ge2^xxvi	2.9239 (4)
Ni1—Ni2^x	2.5788 (7)	Mg—Ge2^xxvii	2.9239 (4)
Ni1—Ni2^xii	2.5788 (7)	Mg—Ge2^xv	2.9239 (4)
Ni1—Ni2^ix	2.5788 (7)	Mg—Ge2^xvii	2.9239 (4)
Ni1—Ni1^ix	2.6450 (14)

Ni2—Ge1—Ni2ⁱ	180.00 (4)	Ni1^x—Ni1—Mg^xxi	113.00 (4)
Ni2—Ge1—Ni2ⁱⁱ	70.5	Ni1^xii—Ni1—Mg^xxi	171.56 (5)
Ni2ⁱ—Ge1—Ni2ⁱⁱ	109.5	Ge^xx—Ni1—Mg^xxi	73.5
Ni2—Ge1—Ni2ⁱⁱⁱ	109.5	Ge2^xviii—Ni1—Mg^xxii	69.03 (2)
Ni2ⁱ—Ge1—Ni2ⁱⁱⁱ	70.5	Ge2^x—Ni1—Mg^xxii	69.03 (2)
Ni2ⁱⁱ—Ge1—Ni2ⁱⁱⁱ	70.5	Ge2^xix—Ni1—Mg^xxii	132.71 (6)
Ni2—Ge1—Ni2^iv	70.5	Ni2^x—Ni1—Mg^xxii	122.689 (18)
Ni2ⁱ—Ge1—Ni2^iv	109.5	Ni2^xii—Ni1—Mg^xxii	122.689 (18)
Ni2ⁱⁱ—Ge1—Ni2^iv	109.5	Ni2^ix—Ni1—Mg^xxii	63.13 (5)
Ni2ⁱⁱⁱ—Ge1—Ni2^iv	180.00 (6)	Ni1^ix—Ni1—Mg^xxii	171.56 (5)
Ni2—Ge1—Ni2^v	109.5	Ni1^x—Ni1—Mg^xxii	113.00 (4)
Ni2ⁱ—Ge1—Ni2^v	70.529 (1)	Ni1^xii—Ni1—Mg^xxii	113.00 (4)
Ni2ⁱⁱ—Ge1—Ni2^v	70.5	Ge^xx—Ni1—Mg^xxii	73.5
Ni2ⁱⁱⁱ—Ge1—Ni2^v	109.5	Mg^xxi—Ni1—Mg^xxii	73.51 (7)
Ni2^iv—Ge1—Ni2^v	70.5	Ge1—Ni2—Ge2^xvii	112.187 (17)
Ni2—Ge1—Ni2^vi	70.5	Ge1—Ni2—Ge2	112.187 (17)
Ni2ⁱ—Ge1—Ni2^vi	109.5	Ge2^xvii—Ni2—Ge2	106.624 (19)
Ni2ⁱⁱ—Ge1—Ni2^vi	109.5	Ge1—Ni2—Ge2^xv	112.187 (17)
Ni2ⁱⁱⁱ—Ge1—Ni2^vi	70.5	Ge2^xvii—Ni2—Ge2^xv	106.624 (19)
Ni2^iv—Ge1—Ni2^vi	109.5	Ge2—Ni2—Ge2^xv	106.624 (19)
Ni2^v—Ge1—Ni2^vi	180.00 (6)	Ge1—Ni2—Ni1^ix	143.69 (2)
Ni2—Ge1—Ni2^vii	109.5	Ge2^xvii—Ni2—Ni1^ix	54.658 (12)
Ni2ⁱ—Ge1—Ni2^vii	70.5	Ge2—Ni2—Ni1^ix	54.658 (12)
Ni2ⁱⁱ—Ge1—Ni2^vii	180.00 (4)	Ge2^xv—Ni2—Ni1^ix	104.12 (3)
Ni2ⁱⁱⁱ—Ge1—Ni2^vii	109.5	Ge1—Ni2—Ni1^xii	143.69 (2)
Ni2^iv—Ge1—Ni2^vii	70.5	Ge2^xvii—Ni2—Ni1^xii	54.658 (12)
Ni2^v—Ge1—Ni2^vii	109.5	Ge2—Ni2—Ni1^xii	104.12 (3)
Ni2^vi—Ge1—Ni2^vii	70.5	Ge2^xv—Ni2—Ni1^xii	54.658 (12)
Ni1^viii—Ge2—Ni1^ix	180.0	Ni1^ix—Ni2—Ni1^xii	61.70 (3)
Ni1^viii—Ge2—Ni1^x	111.46 (4)	Ge1—Ni2—Ni1^x	143.69 (2)
Ni1^ix—Ge2—Ni1^x	68.54 (4)	Ge2^xvii—Ni2—Ni1^x	104.12 (3)
Ni1^viii—Ge2—Ni1^xi	68.54 (4)	Ge2—Ni2—Ni1^x	54.658 (12)
Ni1^ix—Ge2—Ni1^xi	111.46 (4)	Ge2^xv—Ni2—Ni1^x	54.658 (12)
Ni1^x—Ge2—Ni1^xi	180.0	Ni1^ix—Ni2—Ni1^x	61.70 (3)
Ni1^viii—Ge2—Ni2ⁱⁱ	63.601 (15)	Ni1^xii—Ni2—Ni1^x	61.70 (3)
Ni1^ix—Ge2—Ni2ⁱⁱ	116.399 (15)	Ge1—Ni2—Ni2ⁱⁱ	54.7
Ni1^x—Ge2—Ni2ⁱⁱ	116.399 (15)	Ge2^xvii—Ni2—Ni2ⁱⁱ	126.587 (8)
Ni1^xi—Ge2—Ni2ⁱⁱ	63.601 (15)	Ge2—Ni2—Ni2ⁱⁱ	57.451 (17)
Ni1^viii—Ge2—Ni2^xii	116.399 (15)	Ge2^xv—Ni2—Ni2ⁱⁱ	126.587 (8)
Ni1^ix—Ge2—Ni2^xii	63.601 (15)	Ni1^ix—Ni2—Ni2ⁱⁱ	102.914 (14)
Ni1^x—Ge2—Ni2^xii	63.601 (15)	Ni1^xii—Ni2—Ni2ⁱⁱ	161.57 (2)
Ni1^xi—Ge2—Ni2^xii	116.399 (15)	Ni1^x—Ni2—Ni2ⁱⁱ	102.914 (14)
Ni2ⁱⁱ—Ge2—Ni2^xii	180.00 (3)	Ge1—Ni2—Ni2^vi	54.7
Ni1^viii—Ge2—Ni2^xiii	63.601 (15)	Ge2^xvii—Ni2—Ni2^vi	126.587 (8)
Ni1^ix—Ge2—Ni2^xiii	116.399 (15)	Ge2—Ni2—Ni2^vi	126.587 (8)
Ni1^x—Ge2—Ni2^xiii	116.399 (15)	Ge2^xv—Ni2—Ni2^vi	57.451 (17)
Ni1^xi—Ge2—Ni2^xiii	63.601 (15)	Ni1^ix—Ni2—Ni2^vi	161.57 (2)
Ni2ⁱⁱ—Ge2—Ni2^xiii	114.90 (3)	Ni1^xii—Ni2—Ni2^vi	102.914 (14)
Ni2^xii—Ge2—Ni2^xiii	65.10 (3)	Ni1^x—Ni2—Ni2^vi	102.914 (14)
Ni1^viii—Ge2—Ni2	116.398 (15)	Ni2ⁱⁱ—Ni2—Ni2^vi	90.0
Ni1^ix—Ge2—Ni2	63.602 (15)	Ge1—Ni2—Ni2^iv	54.7
Ni1^x—Ge2—Ni2	63.602 (15)	Ge2^xvii—Ni2—Ni2^iv	57.451 (17)
Ni1^xi—Ge2—Ni2	116.398 (15)	Ge2—Ni2—Ni2^iv	126.587 (8)
Ni2ⁱⁱ—Ge2—Ni2	65.10 (3)	Ge2^xv—Ni2—Ni2^iv	126.587 (8)
Ni2^xii—Ge2—Ni2	114.90 (3)	Ni1^ix—Ni2—Ni2^iv	102.914 (14)
Ni2^xiii—Ge2—Ni2	180.0	Ni1^xii—Ni2—Ni2^iv	102.914 (14)
Ni1^viii—Ge2—Ge^xiv	117.61 (2)	Ni1^x—Ni2—Ni2^iv	161.57 (2)
Ni1^ix—Ge2—Ge^xiv	62.39 (2)	Ni2ⁱⁱ—Ni2—Ni2^iv	90.0
Ni1^x—Ge2—Ge^xiv	117.61 (2)	Ni2^vi—Ni2—Ni2^iv	90.0
Ni1^xi—Ge2—Ge^xiv	62.39 (2)	Ge1—Ni2—Ge^xvii	81.85 (4)
Ni2ⁱⁱ—Ge2—Ge^xiv	118.60 (4)	Ge2^xvii—Ni2—Ge^xvii	165.96 (5)
Ni2^xii—Ge2—Ge^xiv	61.40 (4)	Ge2—Ni2—Ge^xvii	66.123 (16)
Ni2^xiii—Ge2—Ge^xiv	61.40 (4)	Ge2^xv—Ni2—Ge^xvii	66.123 (16)
Ni2—Ge2—Ge^xiv	118.60 (4)	Ni1^ix—Ni2—Ge^xvii	114.04 (3)
Ni1^viii—Ge2—Mg^xv	117.61 (2)	Ni1^xii—Ni2—Ge^xvii	114.04 (3)
Ni1^ix—Ge2—Mg^xv	62.39 (2)	Ni1^x—Ni2—Ge^xvii	61.84 (4)
Ni1^x—Ge2—Mg^xv	117.61 (2)	Ni2ⁱⁱ—Ni2—Ge^xvii	60.92 (2)
Ni1^xi—Ge2—Mg^xv	62.39 (2)	Ni2^vi—Ni2—Ge^xvii	60.92 (2)
Ni2ⁱⁱ—Ge2—Mg^xv	61.40 (4)	Ni2^iv—Ni2—Ge^xvii	136.59 (4)
Ni2^xii—Ge2—Mg^xv	118.60 (4)	Ge1—Ni2—Ge^xv	81.85 (4)
Ni2^xiii—Ge2—Mg^xv	118.60 (4)	Ge2^xvii—Ni2—Ge^xv	66.123 (16)
Ni2—Ge2—Mg^xv	61.40 (4)	Ge2—Ni2—Ge^xv	66.123 (16)
Ge^xiv—Ge2—Mg^xv	69.2	Ge2^xv—Ni2—Ge^xv	165.96 (5)
Ni1^viii—Ge2—Mg^xvi	62.39 (2)	Ni1^ix—Ni2—Ge^xv	61.84 (4)
Ni1^ix—Ge2—Mg^xvi	117.61 (2)	Ni1^xii—Ni2—Ge^xv	114.04 (3)
Ni1^x—Ge2—Mg^xvi	62.39 (2)	Ni1^x—Ni2—Ge^xv	114.04 (3)
Ni1^xi—Ge2—Mg^xvi	117.61 (2)	Ni2ⁱⁱ—Ni2—Ge^xv	60.92 (2)
Ni2ⁱⁱ—Ge2—Mg^xvi	118.60 (4)	Ni2^vi—Ni2—Ge^xv	136.59 (4)
Ni2^xii—Ge2—Mg^xvi	61.40 (4)	Ni2^iv—Ni2—Ge^xv	60.92 (2)
Ni2^xiii—Ge2—Mg^xvi	61.40 (4)	Ge^xvii—Ni2—Ge^xv	118.025 (17)
Ni2—Ge2—Mg^xvi	118.60 (4)	Ni1^xii—Mg—Ni1^xxiii	163.12 (10)
Ge^xiv—Ge2—Mg^xvi	110.8	Ni1^xii—Mg—Ni1^xxiv	88.766 (14)
Mg^xv—Ge2—Mg^xvi	180.0	Ni1^xxiii—Mg—Ni1^xxiv	88.766 (14)
Ni1^viii—Ge2—Mg^xvii	62.39 (2)	Ni1^xii—Mg—Ni1^xxv	88.766 (14)
Ni1^ix—Ge2—Mg^xvii	117.61 (2)	Ni1^xxiii—Mg—Ni1^xxv	88.766 (14)
Ni1^x—Ge2—Mg^xvii	62.39 (2)	Ni1^xxiv—Mg—Ni1^xxv	163.12 (10)
Ni1^xi—Ge2—Mg^xvii	117.61 (2)	Ni1^xii—Mg—Ni2	55.03 (2)
Ni2ⁱⁱ—Ge2—Mg^xvii	61.40 (4)	Ni1^xxiii—Mg—Ni2	141.85 (8)
Ni2^xii—Ge2—Mg^xvii	118.60 (4)	Ni1^xxiv—Mg—Ni2	96.12 (3)
Ni2^xiii—Ge2—Mg^xvii	118.60 (4)	Ni1^xxv—Mg—Ni2	96.12 (3)
Ni2—Ge2—Mg^xvii	61.40 (4)	Ni1^xii—Mg—Ni2^vii	141.85 (8)
Ge^xiv—Ge2—Mg^xvii	180.0	Ni1^xxiii—Mg—Ni2^vii	55.03 (2)
Mg^xv—Ge2—Mg^xvii	110.80 (9)	Ni1^xxiv—Mg—Ni2^vii	96.12 (3)
Mg^xvi—Ge2—Mg^xvii	69.20 (9)	Ni1^xxv—Mg—Ni2^vii	96.12 (3)
Ge2^xviii—Ni1—Ge2^x	119.970 (1)	Ni2—Mg—Ni2^vii	86.83 (7)
Ge2^xviii—Ni1—Ge2^xix	119.970 (1)	Ni1^xii—Mg—Ni2^vi	96.12 (3)
Ge2^x—Ni1—Ge2^xix	119.970 (1)	Ni1^xxiii—Mg—Ni2^vi	96.12 (3)
Ge2^xviii—Ni1—Ni2^x	164.15 (4)	Ni1^xxiv—Mg—Ni2^vi	141.85 (8)
Ge2^x—Ni1—Ni2^x	61.740 (4)	Ni1^xxv—Mg—Ni2^vi	55.03 (2)
Ge2^xix—Ni1—Ni2^x	61.740 (4)	Ni2—Mg—Ni2^vi	58.15 (4)
Ge2^xviii—Ni1—Ni2^xii	61.740 (4)	Ni2^vii—Mg—Ni2^vi	58.15 (4)
Ge2^x—Ni1—Ni2^xii	164.15 (4)	Ni1^xii—Mg—Ni2^iv	96.12 (3)
Ge2^xix—Ni1—Ni2^xii	61.740 (4)	Ni1^xxiii—Mg—Ni2^iv	96.12 (3)
Ni2^x—Ni1—Ni2^xii	111.970 (18)	Ni1^xxiv—Mg—Ni2^iv	55.03 (2)
Ge2^xviii—Ni1—Ni2^ix	61.740 (4)	Ni1^xxv—Mg—Ni2^iv	141.85 (8)
Ge2^x—Ni1—Ni2^ix	61.740 (4)	Ni2—Mg—Ni2^iv	58.15 (4)
Ge2^xix—Ni1—Ni2^ix	164.15 (4)	Ni2^vii—Mg—Ni2^iv	58.15 (4)
Ni2^x—Ni1—Ni2^ix	111.970 (18)	Ni2^vi—Mg—Ni2^iv	86.83 (7)
Ni2^xii—Ni1—Ni2^ix	111.970 (18)	Ni1^xii—Mg—Ge2^xxvi	135.598 (4)
Ge2^xviii—Ni1—Ni1^ix	107.624 (17)	Ni1^xxiii—Mg—Ge2^xxvi	48.589 (5)
Ge2^x—Ni1—Ni1^ix	107.624 (17)	Ni1^xxiv—Mg—Ge2^xxvi	48.589 (5)
Ge2^xix—Ni1—Ni1^ix	55.73 (2)	Ni1^xxv—Mg—Ge2^xxvi	135.598 (4)
Ni2^x—Ni1—Ni1^ix	59.148 (17)	Ni2—Mg—Ge2^xxvi	110.29 (6)
Ni2^xii—Ni1—Ni1^ix	59.148 (17)	Ni2^vii—Mg—Ge2^xxvi	52.47 (2)
Ni2^ix—Ni1—Ni1^ix	108.43 (2)	Ni2^vi—Mg—Ge2^xxvi	110.29 (6)
Ge2^xviii—Ni1—Ni1^x	55.73 (2)	Ni2^iv—Mg—Ge2^xxvi	52.47 (2)
Ge2^x—Ni1—Ni1^x	107.624 (17)	Ni1^xii—Mg—Ge2^xxvii	135.598 (4)
Ge2^xix—Ni1—Ni1^x	107.624 (17)	Ni1^xxiii—Mg—Ge2^xxvii	48.589 (5)
Ni2^x—Ni1—Ni1^x	108.43 (2)	Ni1^xxiv—Mg—Ge2^xxvii	135.598 (4)
Ni2^xii—Ni1—Ni1^x	59.148 (17)	Ni1^xxv—Mg—Ge2^xxvii	48.589 (5)
Ni2^ix—Ni1—Ni1^x	59.148 (17)	Ni2—Mg—Ge2^xxvii	110.29 (6)
Ni1^ix—Ni1—Ni1^x	60.0	Ni2^vii—Mg—Ge2^xxvii	52.47 (2)
Ge2^xviii—Ni1—Ni1^xii	107.624 (17)	Ni2^vi—Mg—Ge2^xxvii	52.47 (2)
Ge2^x—Ni1—Ni1^xii	55.73 (2)	Ni2^iv—Mg—Ge2^xxvii	110.29 (6)
Ge2^xix—Ni1—Ni1^xii	107.624 (17)	Ge2^xxvi—Mg—Ge2^xxvii	88.132 (16)
Ni2^x—Ni1—Ni1^xii	59.148 (17)	Ni1^xii—Mg—Ge2^xv	48.589 (5)
Ni2^xii—Ni1—Ni1^xii	108.43 (2)	Ni1^xxiii—Mg—Ge2^xv	135.598 (4)
Ni2^ix—Ni1—Ni1^xii	59.148 (17)	Ni1^xxiv—Mg—Ge2^xv	135.598 (4)
Ni1^ix—Ni1—Ni1^xii	60.0	Ni1^xxv—Mg—Ge2^xv	48.589 (5)
Ni1^x—Ni1—Ni1^xii	60.0	Ni2—Mg—Ge2^xv	52.47 (2)
Ge2^xviii—Ni1—Ge^xx	132.71 (6)	Ni2^vii—Mg—Ge2^xv	110.29 (6)
Ge2^x—Ni1—Ge^xx	69.03 (2)	Ni2^vi—Mg—Ge2^xv	52.47 (2)
Ge2^xix—Ni1—Ge^xx	69.03 (2)	Ni2^iv—Mg—Ge2^xv	110.29 (6)
Ni2^x—Ni1—Ge^xx	63.13 (5)	Ge2^xxvi—Mg—Ge2^xv	159.20 (9)
Ni2^xii—Ni1—Ge^xx	122.689 (18)	Ge2^xxvii—Mg—Ge2^xv	88.132 (16)
Ni2^ix—Ni1—Ge^xx	122.689 (18)	Ni1^xii—Mg—Ge2^xvii	48.589 (5)
Ni1^ix—Ni1—Ge^xx	113.00 (4)	Ni1^xxiii—Mg—Ge2^xvii	135.598 (4)
Ni1^x—Ni1—Ge^xx	171.56 (5)	Ni1^xxiv—Mg—Ge2^xvii	48.589 (5)
Ni1^xii—Ni1—Ge^xx	113.00 (4)	Ni1^xxv—Mg—Ge2^xvii	135.598 (4)
Ge2^xviii—Ni1—Mg^xxi	69.03 (2)	Ni2—Mg—Ge2^xvii	52.47 (2)
Ge2^x—Ni1—Mg^xxi	132.71 (6)	Ni2^vii—Mg—Ge2^xvii	110.29 (6)
Ge2^xix—Ni1—Mg^xxi	69.03 (2)	Ni2^vi—Mg—Ge2^xvii	110.29 (6)
Ni2^x—Ni1—Mg^xxi	122.689 (18)	Ni2^iv—Mg—Ge2^xvii	52.47 (2)
Ni2^xii—Ni1—Mg^xxi	63.13 (5)	Ge2^xxvi—Mg—Ge2^xvii	88.132 (16)
Ni2^ix—Ni1—Mg^xxi	122.689 (18)	Ge2^xxvii—Mg—Ge2^xvii	159.20 (9)
Ni1^ix—Ni1—Mg^xxi	113.00 (4)	Ge2^xv—Mg—Ge2^xvii	88.132 (16)

Symmetry codes: (i) −x, −y, −z; (ii) −x, y, z; (iii) −x, −y, z; (iv) x, y, −z; (v) −x, y, −z; (vi) x, −y, z; (vii) x, −y, −z; (viii) x−1/2, −y+1/2, z; (ix) −x+1/2, y, −z+1/2; (x) −x+1/2, −y+1/2, z; (xi) x−1/2, y, −z+1/2; (xii) x, −y+1/2, −z+1/2; (xiii) −x, −y+1/2, −z+1/2; (xiv) −y, −z+1/2, −x+1/2; (xv) z, x, y; (xvi) −z, −x+1/2, −y+1/2; (xvii) y, z, x; (xviii) −y+1/2, z, −x+1/2; (xix) z, −x+1/2, −y+1/2; (xx) y+1/2, z+1/2, x; (xxi) x, y+1/2, z+1/2; (xxii) z+1/2, x, y+1/2; (xxiii) x, y−1/2, z−1/2; (xxiv) x, −y+1/2, z−1/2; (xxv) x, y−1/2, −z+1/2; (xxvi) z, −x, −y; (xxvii) −y+1/2, z−1/2, −x.

Funding information

Funding for this research was provided by: National Research Foundation of Ukraine (grant No. 2022.01/0064).

References

Andersen, O. K. (1975). Phys. Rev. B, 12, 3060–3083. CrossRef CAS Web of Science Google Scholar
Andersen, O. K. & Jepsen, O. (1984). Phys. Rev. Lett. 53, 2571–2574. CrossRef CAS Web of Science Google Scholar
Andersen, O. K., Pawlowska, Z. & Jepsen, O. (1986). Phys. Rev. B, 34, 5253–5269. CrossRef CAS Web of Science Google Scholar
Barth, U. & Hedin, L. (1972). J. Phys. C.: Solid State Phys. 5, 1629–1642. CrossRef Web of Science Google Scholar
Becke, A. D. & Edgecombe, K. E. (1990). J. Chem. Phys. 92, 5397–5403. CrossRef CAS Web of Science Google Scholar
Brandenburg, K. (2006). DIAMOND. Version 3.1e. Crystal Impact GbR, Bonn, Germany. Google Scholar
Buchholz, W. & Schuster, H. U. (1981). Z. Anorg. Allg. Chem. 482, 40–48. CrossRef ICSD CAS Google Scholar
Eck, B. (2012). wxDragon. Version 1.6.6. RWTH Aachen, Germany. http://schmeling.ac.rwth-aachen.de/cohp/download/wxDragon_Windows.zip. Google Scholar
Edalati, K., Uehiro, R., Ikeda, Y., Li, H. W., Emami, H., Filinchuk, Y., Arita, M., Sauvage, X., Tanaka, I., Akiba, E. & Horita, Z. (2018). Acta Mater. 149, 88–96. CrossRef CAS Google Scholar
Florio, J. V., Rundle, R. E. & Snow, A. I. (1952). Acta Cryst. 5, 449–457. CrossRef ICSD IUCr Journals Web of Science Google Scholar
Gennari, F. C., Urretavizcaya, G., Andrade Gamboa, J. J. & Meyer, G. (2003). J. Alloys Compd. 354, 187–192. CrossRef CAS Google Scholar
Hitam, C. N. C., Aziz, M. A. A., Ruhaimi, A. H. & Taib, M. R. (2021). Int. J. Hydrogen Energy, 46, 31067–31083. CrossRef CAS Google Scholar
Hlukhyy, V., Hoffmann, A. V. & Fässler, T. F. (2013). J. Solid State Chem. 203, 232–239. CrossRef ICSD CAS Google Scholar
Kalisvaart, W. P., Harrower, C. T., Haagsma, J., Zahiri, B., Luber, E. J., Ophus, C., Poirier, E., Fritzsche, H. & Mitlin, D. (2010). Int. J. Hydrogen Energy, 35, 2091–2103. CrossRef CAS Google Scholar
Nagorsen, G. & Witte, H. (1953). Z. Anorg. Allg. Chem. 271, 144–149. CrossRef ICSD CAS Google Scholar
Ouyang, L., Liu, F., Wang, H., Liu, J., Yang, X. S., Sun, L. & Zhu, M. (2020). J. Alloys Compd. 832, 154865. CrossRef Google Scholar
Oxford Diffraction (2008). CrysAlis RED. Oxford Diffraction Ltd, Abingdon, Oxfordshire, England. Google Scholar
Pavlyuk, N., Dmytriv, G., Pavlyuk, V., Chumak, I., Indris, S. & Ehrenberg, H. (2022a). J. Phase Equilib. Diffus. 43, 458–470. Web of Science CrossRef ICSD CAS Google Scholar
Pavlyuk, N., Dmytriv, G., Pavlyuk, V., Chumak, I., Indris, S., Schwarz, B. & Ehrenberg, H. (2022b). Acta Cryst. C78, 455–461. CrossRef ICSD IUCr Journals Google Scholar
Pavlyuk, N., Dmytriv, G., Pavlyuk, V. & Ehrenberg, H. (2019). Acta Cryst. B75, 168–174. Web of Science CrossRef ICSD IUCr Journals Google Scholar
Pavlyuk, N., Dmytriv, G., Pavlyuk, V., Rozdzynska-Kielbik, B., Cichowicz, G., Cyranski, M. K., Chumak, I. & Ehrenberg, H. (2020). Acta Cryst. B76, 534–542. Web of Science CrossRef ICSD IUCr Journals Google Scholar
Pavlyuk, V., Marciniak, B. & Różycka-Sokołowska, E. (2012). Intermetallics, 20, 8–15. Web of Science CrossRef ICSD CAS Google Scholar
Richeson, D. S. (2012). In Euler's gem: the polyhedron formula and the birth of topology. Princeton University Press. Google Scholar
Rigaku OD (2015). CrysAlis PRO. Rigaku Oxford Diffraction Ltd, Yarnton, Oxfordshire, England. Google Scholar
Sheldrick, G. M. (1997). SHELXL97. University of Göttingen, Germany. Google Scholar
Sheldrick, G. M. (2015a). Acta Cryst. A71, 3–8. Web of Science CrossRef IUCr Journals Google Scholar
Sheldrick, G. M. (2015b). Acta Cryst. C71, 3–8. Web of Science CrossRef IUCr Journals Google Scholar
Shtender, V. V., Denys, R. V., Zavaliy, I. Y., Zelinska, O. Y., Paul-Boncour, V. & Pavlyuk, V. V. (2015). J. Solid State Chem. 232, 228–235. CrossRef ICSD CAS Google Scholar
Siggelkow, L., Hlukhyy, V. & Fässler, T. F. (2017). Z. Anorg. Allg. Chem. 643, 1424–1430. CrossRef ICSD CAS Google Scholar
Teslyuk, M. Y. & Markiv, V. Y. (1962). Sov. Phys. Crystallogr. 7, 103–104. Google Scholar
Zhang, Y. H., Li, B. W., Ren, H. P., Li, X., Qi, Y. & Zhao, D. L. (2011). Materials, 4, 274–287. CrossRef PubMed Google Scholar

This article is published by the International Union of Crystallography. Prior permission is not required to reproduce short quotations, tables and figures from this article, provided the original authors and source are cited. For more information, click here.

STRUCTURAL
CHEMISTRY

ISSN: 2053-2296

Volume 80| Part 5| May 2024| Pages 159-165

https://doi.org/10.1107/S2053229624003140

Format		BIBTeX
		EndNote
		RefMan
		Refer
		Medline
		CIF
		SGML
		Plain Text
		Text

Format		BIBTeX
		EndNote
		RefMan
		Refer
		Medline
		CIF
		SGML
		Plain Text
		Text

Search IUCr Journals		doi		Advanced search
Author		volume	page

research papers\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)