Magnesium aluminium zinc gallium, Mg61.81Al12.77Zn61.41Ga24

Yu, J.; Fan, C.; Xu, Z.; Wen, B.; Zhang, L.

doi:10.1107/S2414314625007709

inorganic compounds

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ISSN: 2414-3146

Volume 10| Part 9| September 2025| x250770

https://doi.org/10.1107/S2414314625007709

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Magnesium aluminium zinc gallium, Mg_61.81Al_12.77Zn_61.41Ga₂₄

Jingchao Yu,^a Changzeng Fan,^a,^b ^* Zhefeng Xu,^a,^b Bin Wen ^a and Lifeng Zhang ^a,^c

^aState Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, People's Republic of China, ^bHebei Key Lab for Optimizing Metal Product Technology and Performance, Yanshan University, Qinhuangdao 066004, People's Republic of China, and ^cSchool of Mechanical and Materials Engineering, North China University of Technology, Beijing, People's Republic of China
^*Correspondence e-mail: [email protected]

Edited by S. Bernès, Benemérita Universidad Autónoma de Puebla, México (Received 25 June 2025; accepted 29 August 2025; online 5 September 2025)

The title single-crystal was obtained during the synthesis of a Mg–Al–Zn–Ga alloy, which was achieved by subjecting the alloy to elevated pressures and temperatures. The compound crystallizes in the space group Im3 (No. 204), with seven distinct metal-atom sites. One of these is occupied by gallium, two by aluminium and zinc, one by zinc and magnesium, and three by magnesium. The structure model contains a vacancy-centred Bergman cluster and a 26-face polyhedron centred on one of the magnesium sites. The crystal structure framework in this study shows a marked similarity to previously examined frameworks, but also evinces significant differences [Edagawa et al. (1992). Philos. Mag. B 65, 1011–1023].

Keywords: crystal structure; high-pressure sintering; intermetallic; Mg_61.81Al_12.77Zn_61.41Ga₂₄.

CCDC reference: 2483585

Structure description

The Mg–Al–Zn–Ga system can serve as a lead-free brazing material, thus it has been extensively investigated. A quasi-crystalline phase Mg_39.5Al_4.1Zn_40.0Ga_16.4 has been reported in the Mg–Zn–Al–Ga system. The calorimetric and X-ray diffraction studies suggest that the quasiperiodic phase undergoes an exothermic transformation to an approximate crystalline phase (a = 36.93±0.06, b = 22.83±0.04, and c = 22.96±0.04 Å) at 630 K on heating at a rate of 20 K min⁻¹ (Edagawa et al., 1992 ). In another study, the icosahedral phase Mg_39.5Al_14.35Zn_40.0Ga_6.5 transforms to a 1/1 cubic approximant phase with a = 14.21 Å at 653 K (Edagawa et al., 1993 ). It has been established that the two quasicrystalline approximant phases possess identical coordination polyhedra, yet divergent cell parameters.

In the present study, a cubic phase with a = 14.1529 (17) Å in space group Im $[\overline{3}]$ with composition Mg_61.81Al_12.77Zn_61.41Ga₂₄ has been discovered and refined on the basis of single-crystal X-ray diffraction, and its chemical composition is in accordance with the EDX results (see the supporting information). The unit cell is illustrated in Fig. 1. There are seven metal atom sites: one is occupied by gallium, two are co-occupied by aluminium and zinc, another one co-occupied by zinc and magnesium, and three by magnesium. The crystal structure can be described by two kinds of clusters which are a 26-face polyhedron centred at Mg2, and a Bergman cluster centred at a vacancy site. The environments of the Mg2 site is delineated in Fig. 2. The Mg2 is located at a position with site symmetry mm2.. (multiplicity 12, Wyckoff letter e) and is surrounded by eight Zn3/Al3 atoms (1, 48h), three Mg1/Zn4 atoms (mm2.., 12e), two Zn2/Al2 atoms (m.., 24g), and two Mg4 atoms (m.., 24g). The typical shelled Bergman cluster centred at a virtual non-occupied 2a position includes 12 atoms in the first shell, 20 atoms in the second shell, and 12 atoms in the third shell. The environments of the 2a sites are delineated in Fig. 3. The first shell consists of twelve Ga1 atoms (m.., 24g), the second shell of twelve Mg4 atoms (m.., 24g) and eight Mg3 atoms (.3., 16f), and the third shell of twelve Zn2/Al2 atoms (m.., 24g). The crystal structure also can be described by one cluster which is an icosahedral cluster centred at Zn2/Al2. The environment of the Zn2/Al2 site is delineated in Fig. 4. The central Zn2/Al2 site is surrounded by one Ga1 atom (m.., 24g), four Zn3/Al3 atoms (1, 48h), one Mg1/Zn4 atom (mm2.., 12e), one Mg2 atom (mm2.., 12e), two Mg3 atoms (.3., 16f), and three Mg4 atoms (m.., 24g).

Figure 1
The crystal structure of Mg_61.81Al_12.77Zn_61.41Ga₂₄ (one unit cell) in a projection along the body diagonal, with displacement ellipsoids drawn at the 99% probability level.

Figure 2
(a) The environment of the Mg2 site with displacement ellipsoids given at the 99% probability level; (b) the 26-face polyhedron formed around the Mg2 site at the 12e site [Symmetry codes: (iii) z, x, y; (ix) −y + $[{1\over 2}]$ , −z + $[{1\over 2}]$ , −x + $[{1\over 2}]$ ; (xvi) z, −x, −y + 1; (xvii) −y + $[{1\over 2}]$ , z − $[{1\over 2}]$ , −x + $[{1\over 2}]$ ; (xviii) −y + $[{1\over 2}]$ , −z + $[{1\over 2}]$ , x + $[{1\over 2}]$ ; (xix) −y + $[{1\over 2}]$ , z − $[{1\over 2}]$ , x + $[{1\over 2}]$ ; (xx) x, −y, z].

Figure 3
The polyhedra around the 2a site with increasing shell size.

Figure 4
(a) The environment of the Zn2/Al2 atom with displacement ellipsoids given at the 99% probability level; (b) The icosahedron formed around the Zn2/Al2 atom at the 24g site [Symmetry codes: (ii) −z, x, y; (iii) z, x, y; (vi) −x, y, z; (vii) −z + $[{1\over 2}]$ , −x + $[{1\over 2}]$ , −y + $[{1\over 2}]$ ; (viii) z − $[{1\over 2}]$ , −x + $[{1\over 2}]$ , −y + $[{1\over 2}]$ ].

The structure described in this paper shares similarities with two previously reported crystal structures in terms of their basic framework. However, there are also significant differences. To compare with the crystal structure model reported by Bergman et al. (1957 ): (i) There are no atoms occupying the 2a position in the present model, while it is occupied by a vacancy aluminium atom in their model; (ii) in the present model, the 12e position is co-occupied by zinc and aluminium atoms while it is solely occupied by one magnesium atom in the previous model; (iii) a gallium atom occupies a 24g position in the present model, while there is no atom at the same position in Bergman et al.'s model. To compare with another previously reported structure (Montagné & Tillard, 2016 ), the 24g position is jointly occupied by aluminium and zinc atoms, while it is only occupied by a gallium atom in the present refined model, and one aluminium atom occupies one of the 12e positions. However, the structure delineated in this paper deviates from the aforementioned positions in the following ways: firstly, it is devoid of an additional 2a position; secondly, the 12e position is occupied by zinc and aluminium atoms. Additionally, a gallium atom occupies a 24g position. In the previously reported structure (Montagné & Tillard, 2016) the 24g position was jointly occupied by aluminium and zinc atoms. In contrast, in the crystal structure described in this paper, this position is occupied by a gallium atom.

Synthesis and crystallization

High-purity magnesium (99.90% purity; 0.2186 g), aluminium (99.95% purity; 0.0882 g), gallium (99.90% purity; 0.0976 g) and zinc (99.90% purity; 0.5955 g) were mixed evenly and ground well in an agate mortar. Subsequently, the blended powder was placed in a carbide grinding die with a diameter of 5 mm and pressed into a tablet at approximately 4 MPa for one minute. The resulting material was a cylindrical block that exhibited no signs of deformation or cracking. Further details regarding the high-pressure sintering experiment utilizing the 1-hexanol high-temperature and high-pressure apparatus can be found in elsewhere (Liu & Fan, 2018 ). The sample was subjected to a pressure of 4 GPa and heated to a temperature of 1073 K for a period of 30 minutes, before being rapidly cooled to room temperature by the deactivation of the furnace power. A single crystal was selected and mounted on a glass fibre for SXRD measurements.

Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1. Occupancies for atoms sharing the same site were refined: Zn2 and Al2 atoms have site occupancies of 0.833 (15) and 0.167 (15); Zn3 and Al3 atoms coexist in a position with occupancies 0.817 (12) and 0.183 (12); while Mg1 and Zn4 atoms coexist in a position with occupancies 0.818 (16) and 0.182 (16), respectively.

Table 1
Experimental details

Crystal data
Chemical formula	Mg_61.81Al_12.77Zn_61.42Ga₂₄
M_r	7535.29
Crystal system, space group	Cubic, Im $[\overline{3}]$
Temperature (K)	296
a (Å)	14.1529 (17)
V (Å³)	2834.9 (10)
Z	1
Radiation type	Mo Kα
μ (mm⁻¹)	18.75
Crystal size (mm)	0.18 × 0.12 × 0.06

Data collection
Diffractometer	Bruker D8 Venture Photon 100 CMOS
Absorption correction	Multi-scan (SADABS; Krause et al., 2015 )
T_min, T_max	0.496, 0.523
No. of measured, independent and observed [I > 2σ(I)] reflections	7679, 475, 341
R_int	0.152
(sin θ/λ)_max (Å⁻¹)	0.593

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.059, 0.105, 1.14
No. of reflections	475
No. of parameters	42
Δρ_max, Δρ_min (e Å⁻³)	1.31, −0.83
Computer programs: APEX5 and SAINT (Bruker, 2023 ), SHELXT2018/2 (Sheldrick, 2015a ), SHELXL2018/3 (Sheldrick, 2015b ), DIAMOND (Brandenburg & Putz, 2017 ) and publCIF (Westrip, 2010 ).

Structural data

CCDC reference: 2483585

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2414314625007709/bh4098sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2414314625007709/bh4098Isup2.hkl

Supporting information file. DOI: https://doi.org/10.1107/S2414314625007709/bh4098sup3.docx

checkCIF report

Computing details top

Dohexacontamagnesium tridecaaluminium henihexacontazinc tetracosagallium top

Crystal data top

Mg_61.81Al_12.77Zn_61.42Ga₂₄	Mo Kα radiation, λ = 0.71073 Å
M_r = 7535.29	Cell parameters from 2565 reflections
Cubic, Im3	θ = 3.2–27.0°
a = 14.1529 (17) Å	µ = 18.75 mm⁻¹
V = 2834.9 (10) Å³	T = 296 K
Z = 1	Lump, grey
F(000) = 3494	0.18 × 0.12 × 0.06 mm
D_x = 4.414 Mg m⁻³

Data collection top

Bruker D8 Venture Photon 100 CMOS diffractometer	341 reflections with I > 2σ(I)
phi and ω scans	R_int = 0.152
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	θ_max = 24.9°, θ_min = 2.9°
T_min = 0.496, T_max = 0.523	h = −15→16
7679 measured reflections	k = −16→11
475 independent reflections	l = −16→16

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	Primary atom site location: dual
R[F² > 2σ(F²)] = 0.059	w = 1/[σ²(F_o²) + (0.0311P)² + 65.7834P] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.105	(Δ/σ)_max < 0.001
S = 1.14	Δρ_max = 1.31 e Å⁻³
475 reflections	Δρ_min = −0.83 e Å⁻³
42 parameters

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Ga1	0.000000	0.09285 (13)	0.15109 (12)	0.0124 (7)
Zn2	0.000000	0.17895 (15)	0.30668 (15)	0.0127 (8)	0.833 (15)
Al2	0.000000	0.17895 (15)	0.30668 (15)	0.0127 (8)	0.167 (15)
Zn3	0.15792 (11)	0.19038 (10)	0.40335 (10)	0.0134 (6)	0.817 (12)
Al3	0.15792 (11)	0.19038 (10)	0.40335 (10)	0.0134 (6)	0.183 (12)
Mg1	0.4030 (4)	0.000000	0.500000	0.014 (2)	0.818 (16)
Zn4	0.4030 (4)	0.000000	0.500000	0.014 (2)	0.182 (16)
Mg2	0.1989 (6)	0.000000	0.500000	0.019 (2)
Mg3	0.1861 (3)	0.1861 (3)	0.1861 (3)	0.0126 (17)
Mg4	0.000000	0.3005 (4)	0.1170 (4)	0.0104 (14)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ga1	0.0134 (11)	0.0112 (12)	0.0125 (12)	0.000	0.000	−0.0002 (8)
Zn2	0.0151 (14)	0.0119 (14)	0.0109 (13)	0.000	0.000	−0.0025 (10)
Al2	0.0151 (14)	0.0119 (14)	0.0109 (13)	0.000	0.000	−0.0025 (10)
Zn3	0.0108 (10)	0.0152 (10)	0.0142 (10)	0.0009 (7)	−0.0005 (7)	0.0004 (7)
Al3	0.0108 (10)	0.0152 (10)	0.0142 (10)	0.0009 (7)	−0.0005 (7)	0.0004 (7)
Mg1	0.009 (4)	0.020 (4)	0.012 (4)	0.000	0.000	0.000
Zn4	0.009 (4)	0.020 (4)	0.012 (4)	0.000	0.000	0.000
Mg2	0.013 (5)	0.021 (5)	0.022 (5)	0.000	0.000	0.000
Mg3	0.0126 (17)	0.0126 (17)	0.0126 (17)	−0.0002 (17)	−0.0002 (17)	−0.0002 (17)
Mg4	0.009 (3)	0.011 (3)	0.010 (3)	0.000	0.000	−0.002 (2)

Geometric parameters (Å, º) top

Ga1—Al2	2.517 (3)	Al2—Mg2^vii	3.236 (5)
Ga1—Zn2	2.517 (3)	Zn3—Zn3^ix	2.6686 (15)
Ga1—Ga1ⁱ	2.628 (4)	Zn3—Zn3^vii	2.6687 (15)
Ga1—Ga1ⁱⁱ	2.642 (2)	Zn3—Zn3^x	2.736 (3)
Ga1—Ga1ⁱⁱⁱ	2.642 (2)	Zn3—Mg1^vii	2.934 (3)
Ga1—Ga1^iv	2.642 (2)	Zn3—Mg2^vii	3.053 (4)
Ga1—Ga1^v	2.642 (2)	Zn3—Mg2	3.077 (2)
Ga1—Mg4	2.978 (6)	Zn3—Mg3^xi	3.088 (4)
Ga1—Mg3^vi	2.987 (6)	Zn3—Mg3	3.101 (4)
Ga1—Mg3	2.987 (6)	Zn3—Mg4^ix	3.106 (5)
Ga1—Mg4ⁱⁱⁱ	2.991 (5)	Zn3—Mg4ⁱⁱⁱ	3.117 (3)
Ga1—Mg4ⁱⁱ	2.991 (5)	Al3—Mg2^vii	3.053 (4)
Zn2—Zn3^vi	2.6255 (19)	Al3—Mg2	3.077 (2)
Zn2—Zn3	2.6255 (19)	Al3—Mg3^xi	3.088 (4)
Zn2—Zn3^vii	2.684 (2)	Al3—Mg3	3.101 (4)
Zn2—Zn3^viii	2.684 (2)	Al3—Mg4^ix	3.106 (5)
Zn2—Mg1^vii	2.971 (3)	Al3—Mg4ⁱⁱⁱ	3.117 (3)
Zn2—Mg4ⁱⁱ	3.028 (3)	Mg1—Mg1^xii	2.747 (11)
Zn2—Mg4ⁱⁱⁱ	3.028 (3)	Mg1—Mg2	2.888 (10)
Zn2—Mg3^vi	3.1400 (17)	Mg1—Mg2^xiii	3.132 (8)
Zn2—Mg3	3.1400 (17)	Mg1—Mg2^ix	3.132 (8)
Zn2—Mg4	3.188 (6)	Mg1—Mg4^xiv	3.550 (5)
Zn2—Mg2^vii	3.236 (5)	Mg1—Mg4^xv	3.550 (5)
Al2—Al3	2.6255 (19)	Zn4—Mg2	2.888 (10)
Al2—Mg4ⁱⁱ	3.028 (3)	Zn4—Mg2^xiii	3.132 (8)
Al2—Mg4ⁱⁱⁱ	3.028 (3)	Zn4—Mg2^ix	3.132 (8)
Al2—Mg3^vi	3.1400 (17)	Mg2—Mg4ⁱⁱⁱ	3.052 (6)
Al2—Mg3	3.1400 (17)	Mg2—Mg4^xvi	3.052 (6)
Al2—Mg4	3.188 (6)	Mg3—Mg3^xi	3.133 (13)

Al2—Ga1—Ga1ⁱ	118.96 (6)	Mg1^xii—Mg1—Mg2	180.0
Zn2—Ga1—Ga1ⁱ	118.96 (6)	Mg1^xii—Mg1—Zn3^xvii	116.75 (10)
Al2—Ga1—Ga1ⁱⁱ	120.92 (4)	Mg2—Mg1—Zn3^xvii	63.25 (10)
Zn2—Ga1—Ga1ⁱⁱ	120.92 (4)	Mg1^xii—Mg1—Zn3^xviii	116.75 (10)
Ga1ⁱ—Ga1—Ga1ⁱⁱ	60.17 (5)	Mg2—Mg1—Zn3^xviii	63.25 (10)
Al2—Ga1—Ga1ⁱⁱⁱ	120.92 (4)	Zn3^xvii—Mg1—Zn3^xviii	126.5 (2)
Zn2—Ga1—Ga1ⁱⁱⁱ	120.92 (4)	Mg1^xii—Mg1—Zn3^ix	116.75 (10)
Ga1ⁱ—Ga1—Ga1ⁱⁱⁱ	60.17 (5)	Mg2—Mg1—Zn3^ix	63.25 (10)
Ga1ⁱⁱ—Ga1—Ga1ⁱⁱⁱ	108.08 (2)	Zn3^xvii—Mg1—Zn3^ix	55.56 (8)
Al2—Ga1—Ga1^iv	123.86 (6)	Zn3^xviii—Mg1—Zn3^ix	99.22 (13)
Zn2—Ga1—Ga1^iv	123.86 (6)	Mg1^xii—Mg1—Zn3^xix	116.75 (10)
Ga1ⁱ—Ga1—Ga1^iv	108.18 (5)	Mg2—Mg1—Zn3^xix	63.25 (10)
Ga1ⁱⁱ—Ga1—Ga1^iv	60.0	Zn3^xvii—Mg1—Zn3^xix	99.22 (13)
Ga1ⁱⁱⁱ—Ga1—Ga1^iv	107.78 (6)	Zn3^xviii—Mg1—Zn3^xix	55.56 (8)
Al2—Ga1—Ga1^v	123.86 (6)	Zn3^ix—Mg1—Zn3^xix	126.5 (2)
Zn2—Ga1—Ga1^v	123.86 (6)	Mg1^xii—Mg1—Zn2^xvii	112.96 (11)
Ga1ⁱ—Ga1—Ga1^v	108.18 (5)	Mg2—Mg1—Zn2^xvii	67.04 (11)
Ga1ⁱⁱ—Ga1—Ga1^v	107.78 (6)	Zn3^xvii—Mg1—Zn2^xvii	52.79 (6)
Ga1ⁱⁱⁱ—Ga1—Ga1^v	60.0	Zn3^xviii—Mg1—Zn2^xvii	104.69 (12)
Ga1^iv—Ga1—Ga1^v	59.66 (9)	Zn3^ix—Mg1—Zn2^xvii	104.69 (12)
Al2—Ga1—Mg4	70.35 (12)	Zn3^xix—Mg1—Zn2^xvii	52.79 (6)
Zn2—Ga1—Mg4	70.35 (12)	Mg1^xii—Mg1—Zn2^ix	112.96 (11)
Ga1ⁱ—Ga1—Mg4	170.69 (11)	Mg2—Mg1—Zn2^ix	67.04 (11)
Ga1ⁱⁱ—Ga1—Mg4	116.13 (7)	Zn3^xvii—Mg1—Zn2^ix	104.69 (12)
Ga1ⁱⁱⁱ—Ga1—Mg4	116.13 (7)	Zn3^xviii—Mg1—Zn2^ix	52.79 (6)
Ga1^iv—Ga1—Mg4	63.97 (11)	Zn3^ix—Mg1—Zn2^ix	52.79 (6)
Ga1^v—Ga1—Mg4	63.97 (11)	Zn3^xix—Mg1—Zn2^ix	104.69 (12)
Zn2—Ga1—Mg3^vi	68.96 (7)	Zn2^xvii—Mg1—Zn2^ix	134.1 (2)
Ga1ⁱ—Ga1—Mg3^vi	116.22 (4)	Mg1^xii—Mg1—Mg2^xiii	63.99 (11)
Ga1ⁱⁱ—Ga1—Mg3^vi	63.76 (6)	Mg2—Mg1—Mg2^xiii	116.01 (11)
Ga1ⁱⁱⁱ—Ga1—Mg3^vi	170.12 (8)	Zn3^xvii—Mg1—Mg2^xiii	151.87 (3)
Ga1^iv—Ga1—Mg3^vi	63.76 (6)	Zn3^xviii—Mg1—Mg2^xiii	60.85 (6)
Ga1^v—Ga1—Mg3^vi	115.78 (10)	Zn3^ix—Mg1—Mg2^xiii	151.87 (3)
Mg4—Ga1—Mg3^vi	65.85 (4)	Zn3^xix—Mg1—Mg2^xiii	60.85 (6)
Al2—Ga1—Mg3	68.96 (7)	Zn2^xvii—Mg1—Mg2^xiii	99.85 (3)
Zn2—Ga1—Mg3	68.96 (7)	Zn2^ix—Mg1—Mg2^xiii	99.85 (3)
Ga1ⁱ—Ga1—Mg3	116.22 (4)	Mg1^xii—Mg1—Mg2^ix	63.99 (11)
Ga1ⁱⁱ—Ga1—Mg3	170.12 (8)	Mg2—Mg1—Mg2^ix	116.01 (11)
Ga1ⁱⁱⁱ—Ga1—Mg3	63.76 (6)	Zn3^xvii—Mg1—Mg2^ix	60.85 (6)
Ga1^iv—Ga1—Mg3	115.79 (10)	Zn3^xviii—Mg1—Mg2^ix	151.87 (3)
Ga1^v—Ga1—Mg3	63.76 (6)	Zn3^ix—Mg1—Mg2^ix	60.85 (6)
Mg4—Ga1—Mg3	65.85 (4)	Zn3^xix—Mg1—Mg2^ix	151.87 (3)
Mg3^vi—Ga1—Mg3	123.69 (11)	Zn2^xvii—Mg1—Mg2^ix	99.85 (3)
Al2—Ga1—Mg4ⁱⁱⁱ	66.05 (9)	Zn2^ix—Mg1—Mg2^ix	99.85 (3)
Zn2—Ga1—Mg4ⁱⁱⁱ	66.05 (9)	Mg2^xiii—Mg1—Mg2^ix	128.0 (2)
Ga1ⁱ—Ga1—Mg4ⁱⁱⁱ	63.93 (5)	Mg1^xii—Mg1—Mg4^xiv	67.24 (9)
Ga1ⁱⁱ—Ga1—Mg4ⁱⁱⁱ	116.77 (11)	Mg2—Mg1—Mg4^xiv	112.76 (9)
Ga1ⁱⁱⁱ—Ga1—Mg4ⁱⁱⁱ	63.49 (11)	Zn3^xvii—Mg1—Mg4^xiv	154.20 (9)
Ga1^iv—Ga1—Mg4ⁱⁱⁱ	170.08 (8)	Zn3^xviii—Mg1—Mg4^xiv	56.50 (6)
Ga1^v—Ga1—Mg4ⁱⁱⁱ	115.72 (11)	Zn3^ix—Mg1—Mg4^xiv	99.14 (8)
Mg4—Ga1—Mg4ⁱⁱⁱ	123.23 (13)	Zn3^xix—Mg1—Mg4^xiv	100.92 (8)
Mg3^vi—Ga1—Mg4ⁱⁱⁱ	124.42 (13)	Zn2^xvii—Mg1—Mg4^xiv	152.04 (8)
Mg3—Ga1—Mg4ⁱⁱⁱ	65.70 (8)	Zn2^ix—Mg1—Mg4^xiv	54.45 (7)
Al2—Ga1—Mg4ⁱⁱ	66.05 (9)	Mg2^xiii—Mg1—Mg4^xiv	53.91 (9)
Zn2—Ga1—Mg4ⁱⁱ	66.05 (9)	Mg2^ix—Mg1—Mg4^xiv	104.46 (13)
Ga1ⁱ—Ga1—Mg4ⁱⁱ	63.93 (5)	Mg1^xii—Mg1—Mg4^xv	67.24 (9)
Ga1ⁱⁱ—Ga1—Mg4ⁱⁱ	63.49 (11)	Mg2—Mg1—Mg4^xv	112.76 (9)
Ga1ⁱⁱⁱ—Ga1—Mg4ⁱⁱ	116.77 (11)	Zn3^xvii—Mg1—Mg4^xv	56.50 (6)
Ga1^iv—Ga1—Mg4ⁱⁱ	115.72 (11)	Zn3^xviii—Mg1—Mg4^xv	154.20 (9)
Ga1^v—Ga1—Mg4ⁱⁱ	170.08 (8)	Zn3^ix—Mg1—Mg4^xv	100.92 (8)
Mg4—Ga1—Mg4ⁱⁱ	123.23 (13)	Zn3^xix—Mg1—Mg4^xv	99.14 (8)
Mg3^vi—Ga1—Mg4ⁱⁱ	65.70 (8)	Zn2^xvii—Mg1—Mg4^xv	54.45 (7)
Mg3—Ga1—Mg4ⁱⁱ	124.42 (13)	Zn2^ix—Mg1—Mg4^xv	152.04 (8)
Mg4ⁱⁱⁱ—Ga1—Mg4ⁱⁱ	67.3 (2)	Mg2^xiii—Mg1—Mg4^xv	104.46 (13)
Ga1—Zn2—Zn3^vi	119.07 (6)	Mg2^ix—Mg1—Mg4^xv	53.91 (9)
Ga1—Zn2—Zn3	119.07 (6)	Mg4^xiv—Mg1—Mg4^xv	134.48 (18)
Zn3^vi—Zn2—Zn3	116.69 (11)	Mg2—Zn4—Mg2^xiii	116.01 (11)
Ga1—Zn2—Zn3^vii	115.47 (8)	Mg2—Zn4—Mg2^ix	116.01 (11)
Zn3^vi—Zn2—Zn3^vii	111.88 (9)	Mg2^xiii—Zn4—Mg2^ix	128.0 (2)
Zn3—Zn2—Zn3^vii	60.34 (5)	Zn4—Mg2—Mg4ⁱⁱⁱ	112.31 (17)
Ga1—Zn2—Zn3^viii	115.47 (8)	Mg1—Mg2—Mg4ⁱⁱⁱ	112.31 (17)
Zn3^vi—Zn2—Zn3^viii	60.34 (5)	Zn4—Mg2—Mg4^xvi	112.31 (17)
Zn3—Zn2—Zn3^viii	111.88 (9)	Mg1—Mg2—Mg4^xvi	112.31 (17)
Zn3^vii—Zn2—Zn3^viii	61.28 (8)	Mg4ⁱⁱⁱ—Mg2—Mg4^xvi	135.4 (3)
Ga1—Zn2—Mg1^vii	128.08 (13)	Mg1—Mg2—Zn3^xviii	59.12 (13)
Zn3^vi—Zn2—Mg1^vii	62.88 (6)	Mg4ⁱⁱⁱ—Mg2—Zn3^xviii	150.70 (9)
Zn3—Zn2—Mg1^vii	62.88 (6)	Mg4^xvi—Mg2—Zn3^xviii	61.16 (9)
Zn3^vii—Zn2—Mg1^vii	108.74 (11)	Zn4—Mg2—Zn3^xix	59.12 (13)
Zn3^viii—Zn2—Mg1^vii	108.74 (11)	Mg1—Mg2—Zn3^xix	59.12 (13)
Ga1—Zn2—Mg4ⁱⁱ	64.52 (11)	Mg4ⁱⁱⁱ—Mg2—Zn3^xix	150.70 (9)
Zn3^vi—Zn2—Mg4ⁱⁱ	66.47 (10)	Mg4^xvi—Mg2—Zn3^xix	61.16 (9)
Zn3—Zn2—Mg4ⁱⁱ	122.16 (12)	Zn3^xviii—Mg2—Zn3^xix	53.23 (9)
Zn3^vii—Zn2—Mg4ⁱⁱ	177.34 (11)	Zn4—Mg2—Zn3^xvii	59.12 (13)
Zn3^viii—Zn2—Mg4ⁱⁱ	116.18 (9)	Mg1—Mg2—Zn3^xvii	59.12 (13)
Mg1^vii—Zn2—Mg4ⁱⁱ	72.55 (13)	Mg4ⁱⁱⁱ—Mg2—Zn3^xvii	61.16 (9)
Ga1—Zn2—Mg4ⁱⁱⁱ	64.52 (11)	Mg4^xvi—Mg2—Zn3^xvii	150.70 (9)
Zn3^vi—Zn2—Mg4ⁱⁱⁱ	122.16 (12)	Zn3^xviii—Mg2—Zn3^xvii	118.2 (3)
Zn3—Zn2—Mg4ⁱⁱⁱ	66.47 (10)	Zn3^xix—Mg2—Zn3^xvii	94.12 (17)
Zn3^vii—Zn2—Mg4ⁱⁱⁱ	116.18 (9)	Zn4—Mg2—Zn3^ix	59.12 (13)
Zn3^viii—Zn2—Mg4ⁱⁱⁱ	177.34 (11)	Mg1—Mg2—Zn3^ix	59.12 (13)
Mg1^vii—Zn2—Mg4ⁱⁱⁱ	72.55 (13)	Mg4ⁱⁱⁱ—Mg2—Zn3^ix	61.16 (9)
Mg4ⁱⁱ—Zn2—Mg4ⁱⁱⁱ	66.35 (18)	Mg4^xvi—Mg2—Zn3^ix	150.70 (9)
Ga1—Zn2—Mg3^vi	62.62 (12)	Zn3^xviii—Mg2—Zn3^ix	94.12 (17)
Zn3^vi—Zn2—Mg3^vi	64.36 (10)	Zn3^xix—Mg2—Zn3^ix	118.2 (3)
Zn3—Zn2—Mg3^vi	174.43 (10)	Zn3^xvii—Mg2—Zn3^ix	53.23 (9)
Zn3^vii—Zn2—Mg3^vi	114.09 (8)	Mg1—Mg2—Zn3	100.87 (15)
Zn3^viii—Zn2—Mg3^vi	63.46 (10)	Mg4ⁱⁱⁱ—Mg2—Zn3	61.13 (6)
Mg1^vii—Zn2—Mg3^vi	120.86 (7)	Mg4^xvi—Mg2—Zn3	109.86 (13)
Mg4ⁱⁱ—Zn2—Mg3^vi	63.41 (10)	Zn3^xviii—Mg2—Zn3	91.71 (5)
Mg4ⁱⁱⁱ—Zn2—Mg3^vi	118.05 (16)	Zn3^xix—Mg2—Zn3	144.54 (16)
Ga1—Zn2—Mg3	62.62 (12)	Zn3^xvii—Mg2—Zn3	99.42 (6)
Zn3^vi—Zn2—Mg3	174.42 (10)	Zn3^ix—Mg2—Zn3	51.61 (5)
Zn3—Zn2—Mg3	64.36 (10)	Zn4—Mg2—Al3	100.87 (15)
Zn3^vii—Zn2—Mg3	63.46 (10)	Mg4ⁱⁱⁱ—Mg2—Al3	61.13 (6)
Zn3^viii—Zn2—Mg3	114.09 (8)	Mg4^xvi—Mg2—Al3	109.86 (13)
Mg1^vii—Zn2—Mg3	120.86 (7)	Mg1—Mg2—Zn3^xx	100.87 (15)
Mg4ⁱⁱ—Zn2—Mg3	118.05 (15)	Mg4ⁱⁱⁱ—Mg2—Zn3^xx	61.13 (6)
Mg4ⁱⁱⁱ—Zn2—Mg3	63.41 (10)	Mg4^xvi—Mg2—Zn3^xx	109.86 (13)
Mg3^vi—Zn2—Mg3	114.0 (2)	Zn3^xviii—Mg2—Zn3^xx	144.54 (16)
Ga1—Zn2—Mg4	61.62 (11)	Zn3^xix—Mg2—Zn3^xx	91.71 (5)
Zn3^vi—Zn2—Mg4	113.92 (7)	Zn3^xvii—Mg2—Zn3^xx	51.61 (5)
Zn3—Zn2—Mg4	113.92 (7)	Zn3^ix—Mg2—Zn3^xx	99.42 (6)
Zn3^vii—Zn2—Mg4	63.18 (9)	Zn3—Mg2—Zn3^xx	122.25 (11)
Zn3^viii—Zn2—Mg4	63.18 (9)	Mg1—Mg2—Zn3^x	100.87 (15)
Mg1^vii—Zn2—Mg4	170.30 (16)	Mg4ⁱⁱⁱ—Mg2—Zn3^x	109.86 (13)
Mg4ⁱⁱ—Zn2—Mg4	115.29 (17)	Mg4^xvi—Mg2—Zn3^x	61.13 (6)
Mg4ⁱⁱⁱ—Zn2—Mg4	115.29 (17)	Zn3^xviii—Mg2—Zn3^x	51.61 (5)
Mg3^vi—Zn2—Mg4	61.64 (6)	Zn3^xix—Mg2—Zn3^x	99.42 (6)
Mg3—Zn2—Mg4	61.65 (6)	Zn3^xvii—Mg2—Zn3^x	144.54 (16)
Ga1—Zn2—Mg2^vii	176.67 (15)	Zn3^ix—Mg2—Zn3^x	91.71 (5)
Zn3^vi—Zn2—Mg2^vii	61.74 (6)	Zn3—Mg2—Zn3^x	52.79 (6)
Zn3—Zn2—Mg2^vii	61.74 (6)	Zn3^xx—Mg2—Zn3^x	158.3 (3)
Zn3^vii—Zn2—Mg2^vii	61.80 (11)	Ga1^v—Mg3—Ga1ⁱⁱⁱ	52.48 (12)
Zn3^viii—Zn2—Mg2^vii	61.80 (11)	Ga1^v—Mg3—Ga1	52.48 (12)
Mg1^vii—Zn2—Mg2^vii	55.25 (16)	Ga1ⁱⁱⁱ—Mg3—Ga1	52.48 (12)
Mg4ⁱⁱ—Zn2—Mg2^vii	118.11 (14)	Ga1^v—Mg3—Zn3^ix	144.34 (14)
Mg4ⁱⁱⁱ—Zn2—Mg2^vii	118.11 (14)	Ga1ⁱⁱⁱ—Mg3—Zn3^ix	92.77 (6)
Mg3^vi—Zn2—Mg2^vii	116.25 (13)	Ga1—Mg3—Zn3^ix	115.89 (8)
Mg3—Zn2—Mg2^vii	116.25 (13)	Ga1^v—Mg3—Zn3^xi	92.77 (6)
Mg4—Zn2—Mg2^vii	115.05 (17)	Ga1ⁱⁱⁱ—Mg3—Zn3^xi	115.89 (8)
Ga1—Al2—Al3	119.07 (6)	Ga1—Mg3—Zn3^xi	144.34 (14)
Ga1—Al2—Mg4ⁱⁱ	64.52 (11)	Zn3^ix—Mg3—Zn3^xi	96.92 (14)
Al3—Al2—Mg4ⁱⁱ	122.16 (12)	Ga1^v—Mg3—Zn3^vii	115.89 (8)
Ga1—Al2—Mg4ⁱⁱⁱ	64.52 (11)	Ga1ⁱⁱⁱ—Mg3—Zn3^vii	144.34 (14)
Al3—Al2—Mg4ⁱⁱⁱ	66.47 (10)	Ga1—Mg3—Zn3^vii	92.77 (6)
Mg4ⁱⁱ—Al2—Mg4ⁱⁱⁱ	66.35 (18)	Zn3^ix—Mg3—Zn3^vii	96.92 (14)
Ga1—Al2—Mg3^vi	62.62 (12)	Zn3^xi—Mg3—Zn3^vii	96.92 (14)
Mg4ⁱⁱ—Al2—Mg3^vi	63.41 (10)	Ga1^v—Mg3—Zn3	145.14 (14)
Mg4ⁱⁱⁱ—Al2—Mg3^vi	118.05 (16)	Ga1ⁱⁱⁱ—Mg3—Zn3	115.72 (8)
Ga1—Al2—Mg3	62.62 (12)	Ga1—Mg3—Zn3	93.42 (6)
Al3—Al2—Mg3	64.36 (10)	Zn3^ix—Mg3—Zn3	51.09 (6)
Mg4ⁱⁱ—Al2—Mg3	118.05 (15)	Zn3^xi—Mg3—Zn3	119.2 (2)
Mg4ⁱⁱⁱ—Al2—Mg3	63.41 (10)	Zn3^vii—Mg3—Zn3	51.09 (6)
Mg3^vi—Al2—Mg3	114.0 (2)	Ga1^v—Mg3—Al3	145.14 (14)
Ga1—Al2—Mg4	61.62 (11)	Ga1ⁱⁱⁱ—Mg3—Al3	115.72 (8)
Al3—Al2—Mg4	113.92 (7)	Ga1—Mg3—Al3	93.42 (6)
Mg4ⁱⁱ—Al2—Mg4	115.29 (17)	Ga1^v—Mg3—Zn3ⁱⁱⁱ	115.72 (8)
Mg4ⁱⁱⁱ—Al2—Mg4	115.29 (17)	Ga1ⁱⁱⁱ—Mg3—Zn3ⁱⁱⁱ	93.42 (6)
Mg3^vi—Al2—Mg4	61.64 (6)	Ga1—Mg3—Zn3ⁱⁱⁱ	145.14 (14)
Mg3—Al2—Mg4	61.65 (6)	Zn3^ix—Mg3—Zn3ⁱⁱⁱ	51.09 (6)
Ga1—Al2—Mg2^vii	176.67 (15)	Zn3^xi—Mg3—Zn3ⁱⁱⁱ	51.09 (6)
Al3—Al2—Mg2^vii	61.74 (6)	Zn3^vii—Mg3—Zn3ⁱⁱⁱ	119.2 (2)
Mg4ⁱⁱ—Al2—Mg2^vii	118.11 (14)	Zn3—Mg3—Zn3ⁱⁱⁱ	96.35 (14)
Mg4ⁱⁱⁱ—Al2—Mg2^vii	118.11 (14)	Al3—Mg3—Zn3ⁱⁱⁱ	96.35 (14)
Mg3^vi—Al2—Mg2^vii	116.25 (13)	Ga1^v—Mg3—Zn3^v	93.42 (6)
Mg3—Al2—Mg2^vii	116.25 (13)	Ga1ⁱⁱⁱ—Mg3—Zn3^v	145.14 (14)
Mg4—Al2—Mg2^vii	115.05 (17)	Ga1—Mg3—Zn3^v	115.72 (8)
Zn2—Zn3—Zn3^ix	119.01 (9)	Zn3^ix—Mg3—Zn3^v	119.2 (2)
Zn2—Zn3—Zn3^vii	60.91 (7)	Zn3^xi—Mg3—Zn3^v	51.09 (6)
Zn3^ix—Zn3—Zn3^vii	119.992 (2)	Zn3^vii—Mg3—Zn3^v	51.09 (6)
Zn2—Zn3—Zn2^ix	177.23 (9)	Zn3—Mg3—Zn3^v	96.35 (14)
Zn3^ix—Zn3—Zn2^ix	58.75 (7)	Al3—Mg3—Zn3^v	96.35 (14)
Zn3^vii—Zn3—Zn2^ix	121.36 (9)	Zn3ⁱⁱⁱ—Mg3—Zn3^v	96.35 (14)
Zn2—Zn3—Zn3^x	121.41 (5)	Ga1^v—Mg3—Mg3^xi	149.30 (7)
Zn3^ix—Zn3—Zn3^x	108.96 (5)	Ga1ⁱⁱⁱ—Mg3—Mg3^xi	149.30 (7)
Zn3^vii—Zn3—Zn3^x	119.81 (5)	Ga1—Mg3—Mg3^xi	149.30 (7)
Zn2^ix—Zn3—Zn3^x	59.36 (4)	Zn3^ix—Mg3—Mg3^xi	59.80 (11)
Zn2—Zn3—Mg1^vii	64.33 (6)	Zn3^xi—Mg3—Mg3^xi	59.80 (11)
Zn3^ix—Zn3—Mg1^vii	122.71 (12)	Zn3^vii—Mg3—Mg3^xi	59.80 (11)
Zn3^vii—Zn3—Mg1^vii	110.27 (10)	Zn3—Mg3—Mg3^xi	59.37 (11)
Zn2^ix—Zn3—Mg1^vii	115.13 (6)	Zn3ⁱⁱⁱ—Mg3—Mg3^xi	59.37 (11)
Zn3^x—Zn3—Mg1^vii	62.22 (4)	Zn3^v—Mg3—Mg3^xi	59.37 (11)
Zn2—Zn3—Mg2^vii	69.02 (7)	Ga1^v—Mg3—Zn2^v	48.42 (7)
Zn3^ix—Zn3—Mg2^vii	171.76 (8)	Ga1ⁱⁱⁱ—Mg3—Zn2^v	95.93 (15)
Zn3^vii—Zn3—Mg2^vii	64.65 (11)	Ga1—Mg3—Zn2^v	94.16 (15)
Zn2^ix—Zn3—Mg2^vii	113.17 (7)	Zn3^ix—Mg3—Zn2^v	147.23 (14)
Zn3^x—Zn3—Mg2^vii	63.38 (5)	Zn3^xi—Mg3—Zn2^v	51.05 (5)
Mg1^vii—Zn3—Mg2^vii	57.63 (16)	Zn3^vii—Mg3—Zn2^v	94.19 (6)
Zn2—Zn3—Mg2	109.77 (14)	Zn3—Mg3—Zn2^v	144.78 (13)
Zn3^ix—Zn3—Mg2	63.73 (13)	Al3—Mg3—Zn2^v	144.78 (13)
Zn3^vii—Zn3—Mg2	170.67 (15)	Zn3ⁱⁱⁱ—Mg3—Zn2^v	96.79 (6)
Zn2^ix—Zn3—Mg2	67.97 (13)	Zn3^v—Mg3—Zn2^v	49.75 (5)
Zn3^x—Zn3—Mg2	63.61 (3)	Mg3^xi—Mg3—Zn2^v	100.90 (12)
Mg1^vii—Zn3—Mg2	62.75 (17)	Ga1—Mg4—Ga1^iv	52.54 (10)
Mg2^vii—Zn3—Mg2	112.85 (5)	Ga1—Mg4—Ga1^v	52.54 (10)
Zn2—Zn3—Mg3^xi	115.46 (11)	Ga1^iv—Mg4—Ga1^v	52.13 (11)
Zn3^ix—Zn3—Mg3^xi	64.72 (4)	Ga1—Mg4—Zn2^iv	96.72 (12)
Zn3^vii—Zn3—Mg3^xi	64.72 (4)	Ga1^iv—Mg4—Zn2^iv	49.44 (8)
Zn2^ix—Zn3—Mg3^xi	65.49 (9)	Ga1^v—Mg4—Zn2^iv	94.87 (15)
Zn3^x—Zn3—Mg3^xi	114.21 (11)	Ga1—Mg4—Zn2^v	96.72 (12)
Mg1^vii—Zn3—Mg3^xi	172.14 (13)	Ga1^iv—Mg4—Zn2^v	94.87 (15)
Mg2^vii—Zn3—Mg3^xi	114.62 (14)	Ga1^v—Mg4—Zn2^v	49.44 (8)
Mg2—Zn3—Mg3^xi	122.91 (15)	Zn2^iv—Mg4—Zn2^v	113.55 (18)
Zn2—Zn3—Mg3	65.89 (9)	Ga1—Mg4—Mg2^v	148.4 (2)
Zn3^ix—Zn3—Mg3	64.19 (4)	Ga1^iv—Mg4—Mg2^v	149.83 (13)
Zn3^vii—Zn3—Mg3	64.19 (4)	Ga1^v—Mg4—Mg2^v	149.83 (13)
Zn2^ix—Zn3—Mg3	113.26 (10)	Zn2^iv—Mg4—Mg2^v	100.43 (14)
Zn3^x—Zn3—Mg3	172.53 (7)	Zn2^v—Mg4—Mg2^v	100.43 (14)
Mg1^vii—Zn3—Mg3	123.46 (12)	Ga1—Mg4—Zn3^vii	92.58 (14)
Mg2^vii—Zn3—Mg3	123.26 (7)	Ga1^iv—Mg4—Zn3^vii	144.45 (19)
Mg2—Zn3—Mg3	113.54 (7)	Ga1^v—Mg4—Zn3^vii	115.25 (10)
Mg3^xi—Zn3—Mg3	60.8 (2)	Zn2^iv—Mg4—Zn3^vii	147.47 (14)
Zn2—Zn3—Mg4^ix	116.41 (11)	Zn2^v—Mg4—Zn3^vii	96.10 (6)
Zn3^ix—Zn3—Mg4^ix	115.28 (12)	Mg2^v—Mg4—Zn3^vii	59.44 (16)
Zn3^vii—Zn3—Mg4^ix	64.82 (9)	Ga1—Mg4—Zn3^viii	92.58 (14)
Zn2^ix—Zn3—Mg4^ix	66.36 (11)	Ga1^iv—Mg4—Zn3^viii	115.25 (10)
Zn3^x—Zn3—Mg4^ix	63.87 (5)	Ga1^v—Mg4—Zn3^viii	144.45 (19)
Mg1^vii—Zn3—Mg4^ix	109.51 (12)	Zn2^iv—Mg4—Zn3^viii	96.10 (6)
Mg2^vii—Zn3—Mg4^ix	59.40 (14)	Zn2^v—Mg4—Zn3^viii	147.47 (14)
Mg2—Zn3—Mg4^ix	122.48 (9)	Mg2^v—Mg4—Zn3^viii	59.44 (16)
Mg3^xi—Zn3—Mg4^ix	63.14 (12)	Zn3^vii—Mg4—Zn3^viii	52.26 (10)
Mg3—Zn3—Mg4^ix	115.43 (11)	Ga1—Mg4—Zn3^v	115.52 (10)
Zn2—Zn3—Mg4ⁱⁱⁱ	62.96 (10)	Ga1^iv—Mg4—Zn3^v	144.38 (14)
Zn3^ix—Zn3—Mg4ⁱⁱⁱ	64.39 (12)	Ga1^v—Mg4—Zn3^v	93.05 (6)
Zn3^vii—Zn3—Mg4ⁱⁱⁱ	113.77 (11)	Zn2^iv—Mg4—Zn3^v	144.22 (19)
Zn2^ix—Zn3—Mg4ⁱⁱⁱ	114.27 (11)	Zn2^v—Mg4—Zn3^v	50.57 (5)
Zn3^x—Zn3—Mg4ⁱⁱⁱ	117.84 (9)	Mg2^v—Mg4—Zn3^v	59.83 (9)
Mg1^vii—Zn3—Mg4ⁱⁱⁱ	71.77 (13)	Zn3^vii—Mg4—Zn3^v	50.79 (7)
Mg2^vii—Zn3—Mg4ⁱⁱⁱ	121.14 (15)	Zn3^viii—Mg4—Zn3^v	97.44 (14)
Mg2—Zn3—Mg4ⁱⁱⁱ	59.04 (10)	Ga1—Mg4—Zn3^xxi	115.52 (10)
Mg3^xi—Zn3—Mg4ⁱⁱⁱ	115.51 (14)	Ga1^iv—Mg4—Zn3^xxi	93.05 (6)
Mg3—Zn3—Mg4ⁱⁱⁱ	62.87 (13)	Ga1^v—Mg4—Zn3^xxi	144.38 (14)
Mg4^ix—Zn3—Mg4ⁱⁱⁱ	178.29 (12)	Zn2^iv—Mg4—Zn3^xxi	50.57 (5)
Al2—Al3—Mg2^vii	69.02 (7)	Zn2^v—Mg4—Zn3^xxi	144.22 (19)
Al2—Al3—Mg2	109.77 (14)	Mg2^v—Mg4—Zn3^xxi	59.83 (9)
Mg2^vii—Al3—Mg2	112.85 (5)	Zn3^vii—Mg4—Zn3^xxi	97.44 (14)
Mg2^vii—Al3—Mg3^xi	114.62 (14)	Zn3^viii—Mg4—Zn3^xxi	50.79 (7)
Mg2—Al3—Mg3^xi	122.91 (15)	Zn3^v—Mg4—Zn3^xxi	119.66 (18)
Al2—Al3—Mg3	65.89 (9)	Ga1—Mg4—Zn2	48.03 (9)
Mg2^vii—Al3—Mg3	123.26 (7)	Ga1^iv—Mg4—Zn2	94.86 (14)
Mg2—Al3—Mg3	113.54 (7)	Ga1^v—Mg4—Zn2	94.86 (14)
Mg3^xi—Al3—Mg3	60.8 (2)	Zn2^iv—Mg4—Zn2	118.44 (10)
Al2—Al3—Mg4^ix	116.41 (11)	Zn2^v—Mg4—Zn2	118.44 (10)
Mg2^vii—Al3—Mg4^ix	59.40 (14)	Mg2^v—Mg4—Zn2	100.4 (2)
Mg2—Al3—Mg4^ix	122.48 (9)	Zn3^vii—Mg4—Zn2	50.46 (9)
Mg3^xi—Al3—Mg4^ix	63.14 (12)	Zn3^viii—Mg4—Zn2	50.46 (9)
Mg3—Al3—Mg4^ix	115.43 (11)	Zn3^v—Mg4—Zn2	95.50 (12)
Al2—Al3—Mg4ⁱⁱⁱ	62.96 (10)	Zn3^xxi—Mg4—Zn2	95.50 (12)
Mg2^vii—Al3—Mg4ⁱⁱⁱ	121.14 (15)	Ga1—Mg4—Al2	48.03 (9)
Mg2—Al3—Mg4ⁱⁱⁱ	59.04 (10)	Ga1^iv—Mg4—Al2	94.86 (14)
Mg3^xi—Al3—Mg4ⁱⁱⁱ	115.51 (14)	Ga1^v—Mg4—Al2	94.86 (14)
Mg3—Al3—Mg4ⁱⁱⁱ	62.87 (13)	Mg2^v—Mg4—Al2	100.4 (2)
Mg4^ix—Al3—Mg4ⁱⁱⁱ	178.29 (12)

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

Acknowledgements

We are indebted to Yibo Liu and Huizi Liu for useful discussions.

Funding information

Funding for this research was provided by: The National Natural Science Foundation of China (grant No. 52173231; grant No. U23A20537); The Innovation Ability Promotion Project of Hebei supported by Hebei Key Lab for Optimizing Metal Product Technology and Performance (grant No. 22567609H).

References

Bergman, G., Waugh, J. L. T. & Pauling, L. (1957). Acta Cryst. 10, 254–259. CrossRef ICSD CAS IUCr Journals Web of Science Google Scholar
Brandenburg, K. & Putz, H. (2017). DIAMOND. Crystal Impact GbR, Bonn, Germany. Google Scholar
Bruker (2023). APEX5 and SAINT. Bruker AXS Inc. Madison, Wisconsin, USA, 2008. Google Scholar
Edagawa, K., Naito, N. & Takeuchi, S. (1992). Philos. Mag. B 65, 1011–1023. CrossRef CAS Web of Science Google Scholar
Edagawa, K., Naito, N. & Takeuchi, S. (1993). Phase Transit. 44, 121–129. CrossRef CAS Web of Science Google Scholar
Krause, L., Herbst-Irmer, R., Sheldrick, G. M. & Stalke, D. (2015). J. Appl. Cryst. 48, 3–10. Web of Science CSD CrossRef ICSD CAS IUCr Journals Google Scholar
Liu, C. & Fan, C. (2018). IUCrData 3, x180363. Google Scholar
Montagné, P. & Tillard, M. (2016). J. Alloys Compd. 656, 159–165. 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
Westrip, S. P. (2010). J. Appl. Cryst. 43, 920–925. Web of Science CrossRef CAS IUCr Journals Google Scholar