Mg20.66Al12.24Zn20.04

Yu, J.; Liu, Y.; Liu, H.; Wen, B.; Zhang, L.; Fan, C.

doi:10.1107/S2414314625003062

inorganic compounds

IUCrDATA

ISSN: 2414-3146

Volume 10| Part 4| April 2025| x250306

https://doi.org/10.1107/S2414314625003062

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Mg_20.66Al_12.24Zn_20.04

Jingchao Yu,^a Yibo Liu,^a Huizi Liu,^a Bin Wen,^a Lifeng Zhang ^b and Changzeng Fan ^a,^c ^*

^aState Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, People's Republic of China, ^bSchool of Mechanical and Materials Engineering, North China University of Technology, Beijing, People's Republic of China, and ^cHebei Key Lab for Optimizing Metal Product Technology and Performance, Yanshan University, Qinhuangdao 066004, People's Republic of China
^*Correspondence e-mail: chzfan@ysu.edu.cn

Edited by W. T. A. Harrison, University of Aberdeen, United Kingdom (Received 18 March 2025; accepted 3 April 2025; online 11 April 2025)

The title single-crystal (icosamagnesium dodecaaluminium icosazinc), was obtained during the synthesis of an Mg–Al–Zn alloy at high pressure and temperature. It crystallizes in space group Im3 (No. 204) with seven distinct metal-atom sites: three are occupied by aluminium and zinc, one by zinc and magnesium and three by magnesium (two partially occupied). One of the Al/Zn sites has icosahedral coordination. There are significant difference between the current model and that of previous studies [Montagné & Tillard (2016 ). J. Alloys Compd. 656, 159–165].

Keywords: crystal structure; high-pressure sintering; intermetallic; Mg–Al–Zn phase.

CCDC reference: 2440948

Structure description

The discovery of quasicrystalline compounds in the Mg–Al–Zn systems has stimulated extensive studies (Berthold et al., 2013 ). The quasicrystalline approximant phase with the composition Mg₃₂Al₁₂Zn₃₇ is characterized by a low Al content (Montagné & Tillard, 2016). In a wider context, Mg–Al–Zn coatings are important materials for the corrosion protection of steel sheets. By the addition of some specific alloying elements including Al and Mg to zinc, the corrosion resistance and wear response of the zinc-based coatings are considerably enhanced (Yao et al., 2016 ). The ratio of zinc to aluminium content is also of significance. Zn and Al are commonly used as alloying elements to enhance the mechanical properties of Mg alloys due to their strong solid solution-strengthening effects (Zhang et al., 2022 ). As a result of proper Zn/Al ratio control, significant reduction, or elimination of the thermally unstable Mg₁₇Al₁₂ from the phase composition, Mg–Al–Zn (ZA) alloys are designed to demonstrate creep resistance and high-temperature mechanical capabilities (Edoziuno et al., 2024 ).

In the present study, a cubic phase with a = 14.2100 (8) Å in space group Im $[\overline{3}]$ with composition Mg_20.66Al_12.24Zn_20.04 has been established based on the refinement process by 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: three are occupied by aluminium and zinc, one by zinc and magnesium and three by magnesium (two partially occupied). The environments of the Zn2/Al2 sites are delineated in Fig. 2. The Zn2/Al2 is located at a position with site symmetry m.. (multiplicity 24, Wyckoff letter g). The central Zn2/Al2 atom is surrounded by four Zn3/Al3 atoms (1, 48 h), two Mg3 atoms (.3., 16 f), one Mg2 atom (mm2.., 12 e), one Zn1/Al1 atom (m.., 24 g), one Mg1/Zn4 atom (m2.., 12 e), and three Mg4 atoms (m.., 24 g), which collectively define a icosahedron.

Figure 1
The crystal structure of Mg_20.66Al_12.24Zn_20.04 (one unit cell), with displacement ellipsoids drawn at the 99% probability level.

Figure 2
(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 24 g site. [Symmetry codes: (iv) −y, z, −x; (v) y, z, x; (vi) −x, y, z; (vii) −y + $[{1\over 2}]$ , −z + $[{1\over 2}]$ , −x + $[{1\over 2}]$ ; (viii) y − $[{1\over 2}]$ , −z + $[{1\over 2}]$ , −x + $[{1\over 2}]$ .]

Synthesis and crystallization

Magnesium (99.5% purity; 0.2241 g), aluminium (99.5% purity; 0.1125 g) and zinc (99.5% purity; 0.06633 g) were mixed in a stoichiometric ratio of 6:5:1 and ground 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 1 min to give a cylindrical block that exhibited no signs of deformation or cracking. Further details regarding the high-pressure sintering experiment utilizing the hexanol high-temperature and high-pressure apparatus can be found in the published literature (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 min. The temperature was then reduced to 873 K and maintained for a further 30 min, before being rapidly cooled to room temperature by the deactivation of the furnace power. A grey single crystal was selected and mounted on glass fibres for SXRD measurement.

Refinement

The crystal data, data collection and structure refinement details are outlined in Table 1. The Zn1 and Al1 atoms occupy a position in which the Zn1 atom occupancy is 0.840 (8) and the Al1 atom occupancy is 0.160 (8). Zn2 and Al2 atoms occupy a position in which the Zn2 atom occupancy is 0.550 (10) and the Al2 atom occupancy is 0.450 (10). The Zn3 and Al3 atoms coexist in a position where the Zn3 atom occupies 0.540 (8) and the Al3 atom occupies 0.460 (8). The Mg1 and Zn4 atoms coexist in a position where the Mg1 atom occupies 0.931 (3) and the Zn4 atom occupies 0.069 (3). The occupancy of the Mg2 atom is determined to be partial, with an occupancy number of 0.970 (3) whereas Mg3 is fully occupied. Finally, The Mg4 atom is also partially occupied, with an occupation number of 0.970 (2).

Table 1
Experimental details

Crystal data
Chemical formula	Mg_20.66Al_12.24Zn_20.04
M_r	2143.54
Crystal system, space group	Cubic, Im $[\overline{3}]$
Temperature (K)	296
a (Å)	14.2100 (8)
V (Å³)	2869.3 (5)
Z	3
Radiation type	Mo Kα
μ (mm⁻¹)	12.91
Crystal size (mm)	0.08 × 0.06 × 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	6786, 481, 309
R_int	0.180
(sin θ/λ)_max (Å⁻¹)	0.595

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.061, 0.129, 1.08
No. of reflections	481
No. of parameters	46
Δρ_max, Δρ_min (e Å⁻³)	1.21, −0.89
Computer programs: APEX3 and SAINT (Bruker, 2015 ), SHELXT2018/2 (Sheldrick, 2015a ), SHELXL2018/3 (Sheldrick, 2015b ), DIAMOND (Brandenburg & Putz, 2017 ) and publCIF (Westrip, 2010 ).

Structural data

CCDC reference: 2440948

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2414314625003062/hb4508sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2414314625003062/hb4508Isup2.hkl

Supporting information file. DOI: https://doi.org/10.1107/S2414314625003062/hb4508sup3.docx

checkCIF report

Computing details top

Icosamagnesium dodecaaluminium icosazinc top

Crystal data top

Mg_20.66Al_12.24Zn_20.04	Mo Kα radiation, λ = 0.71073 Å
M_r = 2143.54	Cell parameters from 2565 reflections
Cubic, Im3	θ = 3.2–27.0°
a = 14.2100 (8) Å	µ = 12.91 mm⁻¹
V = 2869.3 (5) Å³	T = 296 K
Z = 3	Lump, gray
F(000) = 3024	0.08 × 0.06 × 0.06 mm
D_x = 3.719 Mg m⁻³

Data collection top

Bruker D8 Venture Photon 100 CMOS diffractometer	309 reflections with I > 2σ(I)
ω scans	R_int = 0.180
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	θ_max = 25.0°, θ_min = 2.9°
T_min = 0.496, T_max = 0.523	h = −15→16
6786 measured reflections	k = −12→16
481 independent reflections	l = −16→11

Refinement top

Refinement on F²	Primary atom site location: dual
Least-squares matrix: full	w = 1/[σ²(F_o²) + (0.0585P)²] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.061	(Δ/σ)_max < 0.001
wR(F²) = 0.129	Δρ_max = 1.21 e Å⁻³
S = 1.08	Δρ_min = −0.89 e Å⁻³
481 reflections	Extinction correction: SHELXL2018/3 (Sheldrick, 2015b), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
46 parameters	Extinction coefficient: 0.00051 (13)
0 restraints

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)
Zn1	0.000000	0.15105 (13)	0.09251 (13)	0.0126 (8)	0.84 (3)
Al1	0.000000	0.15105 (13)	0.09251 (13)	0.0126 (8)	0.16 (3)
Zn2	0.000000	0.30698 (17)	0.17872 (18)	0.0151 (10)	0.55 (3)
Al2	0.000000	0.30698 (17)	0.17872 (18)	0.0151 (10)	0.45 (3)
Zn3	0.15796 (13)	0.40335 (12)	0.19039 (12)	0.0176 (8)	0.54 (3)
Al3	0.15796 (13)	0.40335 (12)	0.19039 (12)	0.0176 (8)	0.46 (3)
Mg1	0.4025 (5)	0.500000	0.000000	0.022 (3)	0.931 (17)
Zn4	0.4025 (5)	0.500000	0.000000	0.022 (3)	0.069 (17)
Mg2	0.1978 (5)	0.500000	0.000000	0.021 (3)	0.97 (3)
Mg3	0.1861 (3)	0.1861 (3)	0.1861 (3)	0.021 (3)
Mg4	0.000000	0.1164 (4)	0.3006 (4)	0.018 (2)	0.97 (2)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Zn1	0.0111 (12)	0.0147 (14)	0.0120 (13)	0.000	0.000	−0.0005 (9)
Al1	0.0111 (12)	0.0147 (14)	0.0120 (13)	0.000	0.000	−0.0005 (9)
Zn2	0.0154 (16)	0.0134 (16)	0.0166 (17)	0.000	0.000	−0.0035 (12)
Al2	0.0154 (16)	0.0134 (16)	0.0166 (17)	0.000	0.000	−0.0035 (12)
Zn3	0.0158 (13)	0.0166 (12)	0.0203 (12)	−0.0007 (9)	0.0011 (8)	0.0023 (8)
Al3	0.0158 (13)	0.0166 (12)	0.0203 (12)	−0.0007 (9)	0.0011 (8)	0.0023 (8)
Mg1	0.019 (5)	0.020 (5)	0.028 (5)	0.000	0.000	0.000
Zn4	0.019 (5)	0.020 (5)	0.028 (5)	0.000	0.000	0.000
Mg2	0.016 (5)	0.027 (6)	0.019 (6)	0.000	0.000	0.000
Mg3	0.021 (3)	0.021 (3)	0.021 (3)	0.0024 (18)	0.0024 (18)	0.0024 (18)
Mg4	0.014 (4)	0.021 (4)	0.019 (4)	0.000	0.000	0.004 (3)

Geometric parameters (Å, º) top

Zn1—Zn2	2.532 (3)	Al2—Mg3^vi	3.1553 (19)
Zn1—Zn1ⁱ	2.629 (4)	Al2—Mg4	3.214 (6)
Zn1—Zn1ⁱⁱ	2.651 (2)	Al2—Mg2^vii	3.256 (5)
Zn1—Zn1ⁱⁱⁱ	2.651 (2)	Zn3—Zn3^vii	2.6790 (18)
Zn1—Zn1^iv	2.651 (2)	Zn3—Zn3^ix	2.6791 (18)
Zn1—Zn1^v	2.651 (2)	Zn3—Zn3^x	2.747 (3)
Zn1—Mg4^v	2.997 (5)	Zn3—Mg1^vii	2.944 (3)
Zn1—Mg4^iv	2.997 (5)	Zn3—Mg2^vii	3.074 (4)
Zn1—Mg4	2.998 (6)	Zn3—Mg2	3.087 (2)
Zn1—Mg3	3.002 (6)	Zn3—Mg3^xi	3.099 (4)
Zn1—Mg3^vi	3.002 (6)	Zn3—Mg3	3.113 (4)
Al1—Al2	2.532 (3)	Zn3—Mg4^ix	3.125 (5)
Al1—Mg4^v	2.997 (5)	Zn3—Mg4^v	3.130 (3)
Al1—Mg4^iv	2.997 (5)	Al3—Mg2^vii	3.074 (4)
Al1—Mg4	2.998 (6)	Al3—Mg2	3.087 (2)
Al1—Mg3	3.002 (6)	Al3—Mg3^xi	3.099 (4)
Al1—Mg3^vi	3.002 (6)	Al3—Mg3	3.113 (4)
Zn2—Zn3	2.635 (2)	Al3—Mg4^ix	3.125 (5)
Zn2—Zn3^vi	2.635 (2)	Al3—Mg4^v	3.130 (3)
Zn2—Zn3^vii	2.697 (3)	Mg1—Mg1^xii	2.771 (13)
Zn2—Zn3^viii	2.697 (3)	Mg1—Mg2	2.909 (10)
Zn2—Mg1^vii	2.976 (4)	Mg1—Mg2^xiii	3.134 (7)
Zn2—Mg4^iv	3.032 (4)	Mg1—Mg2^ix	3.134 (7)
Zn2—Mg4^v	3.032 (4)	Mg1—Mg4^xiv	3.562 (5)
Zn2—Mg3	3.1553 (19)	Mg1—Mg4^xv	3.562 (5)
Zn2—Mg3^vi	3.1553 (19)	Zn4—Mg2	2.909 (10)
Zn2—Mg4	3.214 (6)	Zn4—Mg2^xiii	3.134 (7)
Zn2—Mg2^vii	3.256 (5)	Zn4—Mg2^ix	3.134 (7)
Al2—Al3	2.635 (2)	Mg2—Mg4^v	3.060 (6)
Al2—Mg4^iv	3.032 (4)	Mg2—Mg4^xvi	3.060 (6)
Al2—Mg4^v	3.032 (4)	Mg3—Mg3^xi	3.144 (13)
Al2—Mg3	3.1553 (19)

Zn2—Zn1—Zn1ⁱ	118.94 (7)	Mg1^xii—Mg1—Mg2	180.0
Zn2—Zn1—Zn1ⁱⁱ	123.83 (7)	Mg1^xii—Mg1—Zn3^xvii	116.64 (12)
Zn1ⁱ—Zn1—Zn1ⁱⁱ	108.29 (5)	Mg2—Mg1—Zn3^xvii	63.36 (12)
Zn2—Zn1—Zn1ⁱⁱⁱ	123.83 (7)	Mg1^xii—Mg1—Zn3^xviii	116.64 (12)
Zn1ⁱ—Zn1—Zn1ⁱⁱⁱ	108.29 (5)	Mg2—Mg1—Zn3^xviii	63.36 (12)
Zn1ⁱⁱ—Zn1—Zn1ⁱⁱⁱ	59.45 (10)	Zn3^xvii—Mg1—Zn3^xviii	126.7 (2)
Zn2—Zn1—Zn1^iv	120.97 (4)	Mg1^xii—Mg1—Zn3^ix	116.64 (12)
Zn1ⁱ—Zn1—Zn1^iv	60.27 (5)	Mg2—Mg1—Zn3^ix	63.36 (12)
Zn1ⁱⁱ—Zn1—Zn1^iv	60.0	Zn3^xvii—Mg1—Zn3^ix	55.62 (9)
Zn1ⁱⁱⁱ—Zn1—Zn1^iv	107.64 (6)	Zn3^xviii—Mg1—Zn3^ix	99.36 (15)
Zn2—Zn1—Zn1^v	120.97 (4)	Mg1^xii—Mg1—Zn3^xix	116.64 (12)
Zn1ⁱ—Zn1—Zn1^v	60.27 (5)	Mg2—Mg1—Zn3^xix	63.36 (12)
Zn1ⁱⁱ—Zn1—Zn1^v	107.64 (6)	Zn3^xvii—Mg1—Zn3^xix	99.36 (15)
Zn1ⁱⁱⁱ—Zn1—Zn1^v	60.0	Zn3^xviii—Mg1—Zn3^xix	55.62 (9)
Zn1^iv—Zn1—Zn1^v	108.13 (2)	Zn3^ix—Mg1—Zn3^xix	126.7 (2)
Zn2—Zn1—Mg4^v	65.90 (10)	Mg1^xii—Mg1—Zn2^xix	112.82 (13)
Zn1ⁱ—Zn1—Mg4^v	63.98 (6)	Mg2—Mg1—Zn2^xix	67.18 (13)
Zn1ⁱⁱ—Zn1—Mg4^v	170.25 (9)	Zn3^xvii—Mg1—Zn2^xix	52.85 (6)
Zn1ⁱⁱⁱ—Zn1—Mg4^v	115.98 (11)	Zn3^xviii—Mg1—Zn2^xix	104.84 (14)
Zn1^iv—Zn1—Mg4^v	116.87 (11)	Zn3^ix—Mg1—Zn2^xix	104.84 (14)
Zn1^v—Zn1—Mg4^v	63.77 (12)	Zn3^xix—Mg1—Zn2^xix	52.85 (6)
Zn2—Zn1—Mg4^iv	65.90 (10)	Mg1^xii—Mg1—Zn2^ix	112.82 (13)
Zn1ⁱ—Zn1—Mg4^iv	63.98 (6)	Mg2—Mg1—Zn2^ix	67.18 (13)
Zn1ⁱⁱ—Zn1—Mg4^iv	115.98 (11)	Zn3^xvii—Mg1—Zn2^ix	104.84 (14)
Zn1ⁱⁱⁱ—Zn1—Mg4^iv	170.25 (9)	Zn3^xviii—Mg1—Zn2^ix	52.85 (6)
Zn1^iv—Zn1—Mg4^iv	63.77 (12)	Zn3^ix—Mg1—Zn2^ix	52.85 (6)
Zn1^v—Zn1—Mg4^iv	116.87 (11)	Zn3^xix—Mg1—Zn2^ix	104.84 (14)
Mg4^v—Zn1—Mg4^iv	67.0 (2)	Zn2^xix—Mg1—Zn2^ix	134.4 (3)
Zn2—Zn1—Mg4	70.51 (12)	Mg1^xii—Mg1—Mg2^xiii	63.76 (12)
Zn1ⁱ—Zn1—Mg4	170.56 (11)	Mg2—Mg1—Mg2^xiii	116.24 (12)
Zn1ⁱⁱ—Zn1—Mg4	63.74 (12)	Zn3^xvii—Mg1—Mg2^xiii	151.90 (3)
Zn1ⁱⁱⁱ—Zn1—Mg4	63.74 (11)	Zn3^xviii—Mg1—Mg2^xiii	60.94 (6)
Zn1^iv—Zn1—Mg4	115.95 (8)	Zn3^ix—Mg1—Mg2^xiii	151.90 (3)
Zn1^v—Zn1—Mg4	115.95 (8)	Zn3^xix—Mg1—Mg2^xiii	60.94 (6)
Mg4^v—Zn1—Mg4	123.30 (13)	Zn2^xix—Mg1—Mg2^xiii	99.87 (3)
Mg4^iv—Zn1—Mg4	123.30 (13)	Zn2^ix—Mg1—Mg2^xiii	99.87 (3)
Zn2—Zn1—Mg3	68.92 (7)	Mg1^xii—Mg1—Mg2^ix	63.76 (12)
Zn1ⁱ—Zn1—Mg3	116.30 (4)	Mg2—Mg1—Mg2^ix	116.24 (12)
Zn1ⁱⁱ—Zn1—Mg3	115.61 (10)	Zn3^xvii—Mg1—Mg2^ix	60.94 (6)
Zn1ⁱⁱⁱ—Zn1—Mg3	63.80 (6)	Zn3^xviii—Mg1—Mg2^ix	151.90 (3)
Zn1^iv—Zn1—Mg3	170.11 (8)	Zn3^ix—Mg1—Mg2^ix	60.94 (6)
Zn1^v—Zn1—Mg3	63.80 (6)	Zn3^xix—Mg1—Mg2^ix	151.90 (3)
Mg4^v—Zn1—Mg3	65.81 (8)	Zn2^xix—Mg1—Mg2^ix	99.87 (3)
Mg4^iv—Zn1—Mg3	124.26 (13)	Zn2^ix—Mg1—Mg2^ix	99.87 (3)
Mg4—Zn1—Mg3	65.80 (4)	Mg2^xiii—Mg1—Mg2^ix	127.5 (2)
Zn2—Zn1—Mg3^vi	68.92 (7)	Mg1^xii—Mg1—Mg4^xiv	67.11 (11)
Zn1ⁱ—Zn1—Mg3^vi	116.30 (4)	Mg2—Mg1—Mg4^xiv	112.89 (11)
Zn1ⁱⁱ—Zn1—Mg3^vi	63.80 (6)	Zn3^xvii—Mg1—Mg4^xiv	154.12 (10)
Zn1ⁱⁱⁱ—Zn1—Mg3^vi	115.61 (10)	Zn3^xviii—Mg1—Mg4^xiv	56.57 (6)
Zn1^iv—Zn1—Mg3^vi	63.80 (6)	Zn3^ix—Mg1—Mg4^xiv	99.06 (9)
Zn1^v—Zn1—Mg3^vi	170.11 (8)	Zn3^xix—Mg1—Mg4^xiv	101.03 (9)
Mg4^v—Zn1—Mg3^vi	124.26 (13)	Zn2^xix—Mg1—Mg4^xiv	152.15 (9)
Mg4^iv—Zn1—Mg3^vi	65.81 (8)	Zn2^ix—Mg1—Mg4^xiv	54.38 (7)
Mg4—Zn1—Mg3^vi	65.80 (4)	Mg2^xiii—Mg1—Mg4^xiv	53.94 (10)
Mg3—Zn1—Mg3^vi	123.52 (12)	Mg2^ix—Mg1—Mg4^xiv	104.16 (15)
Al2—Al1—Mg4^v	65.90 (10)	Mg1^xii—Mg1—Mg4^xv	67.11 (11)
Al2—Al1—Mg4^iv	65.90 (10)	Mg2—Mg1—Mg4^xv	112.89 (11)
Mg4^v—Al1—Mg4^iv	67.0 (2)	Zn3^xvii—Mg1—Mg4^xv	56.57 (6)
Al2—Al1—Mg4	70.51 (12)	Zn3^xviii—Mg1—Mg4^xv	154.12 (10)
Mg4^v—Al1—Mg4	123.30 (13)	Zn3^ix—Mg1—Mg4^xv	101.03 (9)
Mg4^iv—Al1—Mg4	123.30 (13)	Zn3^xix—Mg1—Mg4^xv	99.06 (9)
Al2—Al1—Mg3	68.92 (7)	Zn2^xix—Mg1—Mg4^xv	54.38 (7)
Mg4^v—Al1—Mg3	65.81 (8)	Zn2^ix—Mg1—Mg4^xv	152.15 (9)
Mg4^iv—Al1—Mg3	124.26 (13)	Mg2^xiii—Mg1—Mg4^xv	104.16 (15)
Mg4—Al1—Mg3	65.80 (4)	Mg2^ix—Mg1—Mg4^xv	53.94 (10)
Mg4^v—Al1—Mg3^vi	124.26 (13)	Mg4^xiv—Mg1—Mg4^xv	134.2 (2)
Mg4^iv—Al1—Mg3^vi	65.81 (8)	Mg2—Zn4—Mg2^xiii	116.24 (12)
Mg4—Al1—Mg3^vi	65.80 (4)	Mg2—Zn4—Mg2^ix	116.24 (12)
Mg3—Al1—Mg3^vi	123.52 (12)	Mg2^xiii—Zn4—Mg2^ix	127.5 (2)
Zn1—Zn2—Zn3	119.04 (7)	Zn4—Mg2—Mg4^v	112.20 (17)
Zn1—Zn2—Zn3^vi	119.04 (7)	Mg1—Mg2—Mg4^v	112.20 (17)
Zn3—Zn2—Zn3^vi	116.85 (12)	Zn4—Mg2—Mg4^xvi	112.20 (17)
Zn1—Zn2—Zn3^vii	115.37 (9)	Mg1—Mg2—Mg4^xvi	112.20 (17)
Zn3—Zn2—Zn3^vii	60.31 (5)	Mg4^v—Mg2—Mg4^xvi	135.6 (3)
Zn3^vi—Zn2—Zn3^vii	111.87 (10)	Zn4—Mg2—Zn3^xviii	58.88 (12)
Zn1—Zn2—Zn3^viii	115.37 (9)	Mg1—Mg2—Zn3^xviii	58.88 (12)
Zn3—Zn2—Zn3^viii	111.87 (10)	Mg4^v—Mg2—Zn3^xviii	150.62 (9)
Zn3^vi—Zn2—Zn3^viii	60.32 (5)	Mg4^xvi—Mg2—Zn3^xviii	61.26 (10)
Zn3^vii—Zn2—Zn3^viii	61.22 (10)	Zn4—Mg2—Zn3^xix	58.88 (12)
Zn1—Zn2—Mg1^vii	128.24 (15)	Mg1—Mg2—Zn3^xix	58.88 (12)
Zn3—Zn2—Mg1^vii	62.96 (7)	Mg4^v—Mg2—Zn3^xix	150.62 (9)
Zn3^vi—Zn2—Mg1^vii	62.96 (7)	Mg4^xvi—Mg2—Zn3^xix	61.26 (10)
Zn3^vii—Zn2—Mg1^vii	108.72 (12)	Zn3^xviii—Mg2—Zn3^xix	53.08 (9)
Zn3^viii—Zn2—Mg1^vii	108.72 (12)	Zn4—Mg2—Zn3^xvii	58.88 (12)
Zn1—Zn2—Mg4^iv	64.44 (12)	Mg1—Mg2—Zn3^xvii	58.88 (12)
Zn3—Zn2—Mg4^iv	122.22 (13)	Mg4^v—Mg2—Zn3^xvii	61.26 (10)
Zn3^vi—Zn2—Mg4^iv	66.64 (10)	Mg4^xvi—Mg2—Zn3^xvii	150.62 (9)
Zn3^vii—Zn2—Mg4^iv	177.37 (12)	Zn3^xviii—Mg2—Zn3^xvii	117.8 (2)
Zn3^viii—Zn2—Mg4^iv	116.31 (9)	Zn3^xix—Mg2—Zn3^xvii	93.81 (17)
Mg1^vii—Zn2—Mg4^iv	72.71 (14)	Zn4—Mg2—Zn3^ix	58.88 (12)
Zn1—Zn2—Mg4^v	64.44 (12)	Mg1—Mg2—Zn3^ix	58.88 (12)
Zn3—Zn2—Mg4^v	66.64 (10)	Mg4^v—Mg2—Zn3^ix	61.26 (10)
Zn3^vi—Zn2—Mg4^v	122.22 (13)	Mg4^xvi—Mg2—Zn3^ix	150.62 (9)
Zn3^vii—Zn2—Mg4^v	116.31 (9)	Zn3^xviii—Mg2—Zn3^ix	93.81 (17)
Zn3^viii—Zn2—Mg4^v	177.37 (12)	Zn3^xix—Mg2—Zn3^ix	117.8 (2)
Mg1^vii—Zn2—Mg4^v	72.71 (14)	Zn3^xvii—Mg2—Zn3^ix	53.08 (9)
Mg4^iv—Zn2—Mg4^v	66.13 (18)	Mg1—Mg2—Zn3ⁱ	100.57 (14)
Zn1—Zn2—Mg3	62.60 (13)	Mg4^v—Mg2—Zn3ⁱ	61.23 (6)
Zn3—Zn2—Mg3	64.32 (11)	Mg4^xvi—Mg2—Zn3ⁱ	110.04 (12)
Zn3^vi—Zn2—Mg3	174.25 (12)	Zn3^xviii—Mg2—Zn3ⁱ	144.24 (15)
Zn3^vii—Zn2—Mg3	63.38 (11)	Zn3^xix—Mg2—Zn3ⁱ	91.61 (5)
Zn3^viii—Zn2—Mg3	113.93 (10)	Zn3^xvii—Mg2—Zn3ⁱ	51.56 (6)
Mg1^vii—Zn2—Mg3	120.97 (7)	Zn3^ix—Mg2—Zn3ⁱ	99.30 (6)
Mg4^iv—Zn2—Mg3	117.97 (16)	Mg1—Mg2—Zn3^x	100.57 (14)
Mg4^v—Zn2—Mg3	63.53 (10)	Mg4^v—Mg2—Zn3^x	110.04 (12)
Zn1—Zn2—Mg3^vi	62.60 (13)	Mg4^xvi—Mg2—Zn3^x	61.23 (6)
Zn3—Zn2—Mg3^vi	174.25 (12)	Zn3^xviii—Mg2—Zn3^x	51.56 (6)
Zn3^vi—Zn2—Mg3^vi	64.32 (11)	Zn3^xix—Mg2—Zn3^x	99.30 (6)
Zn3^vii—Zn2—Mg3^vi	113.93 (10)	Zn3^xvii—Mg2—Zn3^x	144.24 (15)
Zn3^viii—Zn2—Mg3^vi	63.38 (11)	Zn3^ix—Mg2—Zn3^x	91.61 (5)
Mg1^vii—Zn2—Mg3^vi	120.97 (7)	Zn3ⁱ—Mg2—Zn3^x	158.9 (3)
Mg4^iv—Zn2—Mg3^vi	63.53 (10)	Mg1—Mg2—Zn3^xx	100.57 (14)
Mg4^v—Zn2—Mg3^vi	117.97 (16)	Mg4^v—Mg2—Zn3^xx	110.04 (12)
Mg3—Zn2—Mg3^vi	113.9 (2)	Mg4^xvi—Mg2—Zn3^xx	61.23 (6)
Zn1—Zn2—Mg4	61.54 (11)	Zn3^xviii—Mg2—Zn3^xx	99.30 (6)
Zn3—Zn2—Mg4	113.83 (8)	Zn3^xix—Mg2—Zn3^xx	51.56 (6)
Zn3^vi—Zn2—Mg4	113.82 (8)	Zn3^xvii—Mg2—Zn3^xx	91.61 (5)
Zn3^vii—Zn2—Mg4	63.13 (10)	Zn3^ix—Mg2—Zn3^xx	144.24 (15)
Zn3^viii—Zn2—Mg4	63.13 (10)	Zn3ⁱ—Mg2—Zn3^xx	52.84 (7)
Mg1^vii—Zn2—Mg4	170.22 (18)	Zn3^x—Mg2—Zn3^xx	122.46 (11)
Mg4^iv—Zn2—Mg4	115.22 (17)	Mg1—Mg2—Zn3	100.57 (14)
Mg4^v—Zn2—Mg4	115.22 (17)	Mg4^v—Mg2—Zn3	61.23 (6)
Mg3—Zn2—Mg4	61.54 (6)	Mg4^xvi—Mg2—Zn3	110.04 (12)
Mg3^vi—Zn2—Mg4	61.55 (6)	Zn3^xviii—Mg2—Zn3	91.61 (5)
Zn1—Zn2—Mg2^vii	176.33 (15)	Zn3^xix—Mg2—Zn3	144.23 (15)
Zn3—Zn2—Mg2^vii	61.85 (7)	Zn3^xvii—Mg2—Zn3	99.30 (6)
Zn3^vi—Zn2—Mg2^vii	61.85 (7)	Zn3^ix—Mg2—Zn3	51.56 (6)
Zn3^vii—Zn2—Mg2^vii	61.62 (11)	Zn3ⁱ—Mg2—Zn3	122.46 (11)
Zn3^viii—Zn2—Mg2^vii	61.62 (11)	Zn3^x—Mg2—Zn3	52.84 (7)
Mg1^vii—Zn2—Mg2^vii	55.43 (17)	Zn3^xx—Mg2—Zn3	158.9 (3)
Mg4^iv—Zn2—Mg2^vii	118.46 (14)	Al1—Mg3—Zn1^v	52.40 (12)
Mg4^v—Zn2—Mg2^vii	118.46 (14)	Zn1—Mg3—Zn1^v	52.40 (12)
Mg3—Zn2—Mg2^vii	116.13 (13)	Al1—Mg3—Zn1ⁱⁱⁱ	52.40 (12)
Mg3^vi—Zn2—Mg2^vii	116.13 (13)	Zn1—Mg3—Zn1ⁱⁱⁱ	52.40 (12)
Mg4—Zn2—Mg2^vii	114.79 (17)	Zn1^v—Mg3—Zn1ⁱⁱⁱ	52.40 (12)
Al1—Al2—Al3	119.04 (7)	Al1—Mg3—Zn3^vii	92.83 (7)
Al1—Al2—Mg4^iv	64.44 (12)	Zn1—Mg3—Zn3^vii	92.83 (7)
Al3—Al2—Mg4^iv	122.22 (13)	Zn1^v—Mg3—Zn3^vii	144.35 (15)
Al1—Al2—Mg4^v	64.44 (12)	Zn1ⁱⁱⁱ—Mg3—Zn3^vii	115.83 (9)
Al3—Al2—Mg4^v	66.64 (10)	Al1—Mg3—Zn3^ix	115.83 (9)
Mg4^iv—Al2—Mg4^v	66.13 (18)	Zn1—Mg3—Zn3^ix	115.83 (9)
Al1—Al2—Mg3	62.60 (13)	Zn1^v—Mg3—Zn3^ix	92.83 (7)
Al3—Al2—Mg3	64.32 (11)	Zn1ⁱⁱⁱ—Mg3—Zn3^ix	144.35 (15)
Mg4^iv—Al2—Mg3	117.97 (16)	Zn3^vii—Mg3—Zn3^ix	96.94 (15)
Mg4^v—Al2—Mg3	63.53 (10)	Zn1—Mg3—Zn3^xi	144.35 (15)
Mg4^iv—Al2—Mg3^vi	63.53 (10)	Zn1^v—Mg3—Zn3^xi	115.83 (9)
Mg4^v—Al2—Mg3^vi	117.97 (16)	Zn1ⁱⁱⁱ—Mg3—Zn3^xi	92.83 (7)
Mg3—Al2—Mg3^vi	113.9 (2)	Zn3^vii—Mg3—Zn3^xi	96.94 (15)
Al1—Al2—Mg4	61.54 (11)	Zn3^ix—Mg3—Zn3^xi	96.94 (15)
Al3—Al2—Mg4	113.83 (8)	Al1—Mg3—Zn3^v	145.06 (15)
Mg4^iv—Al2—Mg4	115.22 (17)	Zn1—Mg3—Zn3^v	145.06 (15)
Mg4^v—Al2—Mg4	115.22 (17)	Zn1^v—Mg3—Zn3^v	93.44 (7)
Mg3—Al2—Mg4	61.54 (6)	Zn1ⁱⁱⁱ—Mg3—Zn3^v	115.79 (8)
Mg3^vi—Al2—Mg4	61.55 (6)	Zn3^vii—Mg3—Zn3^v	119.2 (2)
Mg4^iv—Al2—Mg2^vii	118.46 (14)	Zn3^ix—Mg3—Zn3^v	51.09 (6)
Mg4^v—Al2—Mg2^vii	118.46 (14)	Zn3^xi—Mg3—Zn3^v	51.09 (6)
Mg3—Al2—Mg2^vii	116.13 (13)	Al1—Mg3—Zn3ⁱⁱⁱ	115.79 (8)
Mg3^vi—Al2—Mg2^vii	116.13 (13)	Zn1—Mg3—Zn3ⁱⁱⁱ	115.79 (8)
Mg4—Al2—Mg2^vii	114.79 (17)	Zn1^v—Mg3—Zn3ⁱⁱⁱ	145.06 (15)
Zn2—Zn3—Zn3^vii	61.00 (9)	Zn1ⁱⁱⁱ—Mg3—Zn3ⁱⁱⁱ	93.44 (7)
Zn2—Zn3—Zn3^ix	119.01 (11)	Zn3^vii—Mg3—Zn3ⁱⁱⁱ	51.09 (6)
Zn3^vii—Zn3—Zn3^ix	119.988 (3)	Zn3^ix—Mg3—Zn3ⁱⁱⁱ	119.2 (2)
Zn2—Zn3—Zn2^ix	177.08 (10)	Zn3^xi—Mg3—Zn3ⁱⁱⁱ	51.09 (6)
Zn3^vii—Zn3—Zn2^ix	121.46 (10)	Zn3^v—Mg3—Zn3ⁱⁱⁱ	96.36 (15)
Zn3^ix—Zn3—Zn2^ix	58.69 (8)	Zn1—Mg3—Zn3	93.44 (7)
Zn2—Zn3—Zn3^x	121.32 (6)	Zn1^v—Mg3—Zn3	115.79 (8)
Zn3^vii—Zn3—Zn3^x	119.82 (6)	Zn1ⁱⁱⁱ—Mg3—Zn3	145.06 (15)
Zn3^ix—Zn3—Zn3^x	108.98 (5)	Zn3^vii—Mg3—Zn3	51.09 (6)
Zn2^ix—Zn3—Zn3^x	59.39 (5)	Zn3^ix—Mg3—Zn3	51.10 (6)
Zn2—Zn3—Mg1^vii	64.19 (7)	Zn3^xi—Mg3—Zn3	119.2 (2)
Zn3^vii—Zn3—Mg1^vii	110.16 (12)	Zn3^v—Mg3—Zn3	96.36 (15)
Zn3^ix—Zn3—Mg1^vii	122.82 (14)	Zn3ⁱⁱⁱ—Mg3—Zn3	96.36 (15)
Zn2^ix—Zn3—Mg1^vii	115.14 (7)	Al1—Mg3—Al3	93.44 (7)
Zn3^x—Zn3—Mg1^vii	62.19 (4)	Zn1—Mg3—Mg3^xi	149.35 (7)
Zn2—Zn3—Mg2^vii	69.06 (8)	Zn1^v—Mg3—Mg3^xi	149.35 (7)
Zn3^vii—Zn3—Mg2^vii	64.47 (11)	Zn1ⁱⁱⁱ—Mg3—Mg3^xi	149.35 (7)
Zn3^ix—Zn3—Mg2^vii	171.76 (10)	Zn3^vii—Mg3—Mg3^xi	59.82 (11)
Zn2^ix—Zn3—Mg2^vii	113.19 (8)	Zn3^ix—Mg3—Mg3^xi	59.82 (11)
Zn3^x—Zn3—Mg2^vii	63.46 (5)	Zn3^xi—Mg3—Mg3^xi	59.82 (11)
Mg1^vii—Zn3—Mg2^vii	57.76 (17)	Zn3^v—Mg3—Mg3^xi	59.37 (11)
Zn2—Zn3—Mg2	109.42 (14)	Zn3ⁱⁱⁱ—Mg3—Mg3^xi	59.37 (11)
Zn3^vii—Zn3—Mg2	170.40 (16)	Zn3—Mg3—Mg3^xi	59.37 (11)
Zn3^ix—Zn3—Mg2	63.98 (13)	Zn1ⁱⁱ—Mg4—Zn1ⁱⁱⁱ	52.03 (11)
Zn2^ix—Zn3—Mg2	68.14 (13)	Zn1ⁱⁱ—Mg4—Zn1	52.49 (11)
Zn3^x—Zn3—Mg2	63.58 (4)	Zn1ⁱⁱⁱ—Mg4—Zn1	52.49 (11)
Mg1^vii—Zn3—Mg2	62.57 (17)	Zn1ⁱⁱ—Mg4—Zn2ⁱⁱ	49.65 (9)
Mg2^vii—Zn3—Mg2	112.84 (5)	Zn1ⁱⁱⁱ—Mg4—Zn2ⁱⁱ	95.01 (15)
Zn2—Zn3—Mg3^xi	115.56 (11)	Zn1—Mg4—Zn2ⁱⁱ	96.84 (13)
Zn3^vii—Zn3—Mg3^xi	64.72 (5)	Al1—Mg4—Zn2ⁱⁱ	96.84 (13)
Zn3^ix—Zn3—Mg3^xi	64.72 (5)	Zn1ⁱⁱ—Mg4—Zn2ⁱⁱⁱ	95.01 (15)
Zn2^ix—Zn3—Mg3^xi	65.54 (10)	Zn1ⁱⁱⁱ—Mg4—Zn2ⁱⁱⁱ	49.65 (9)
Zn3^x—Zn3—Mg3^xi	114.23 (11)	Zn1—Mg4—Zn2ⁱⁱⁱ	96.84 (13)
Mg1^vii—Zn3—Mg3^xi	172.04 (15)	Al1—Mg4—Zn2ⁱⁱⁱ	96.84 (13)
Mg2^vii—Zn3—Mg3^xi	114.38 (14)	Zn2ⁱⁱ—Mg4—Zn2ⁱⁱⁱ	113.75 (18)
Mg2—Zn3—Mg3^xi	123.21 (14)	Zn1ⁱⁱ—Mg4—Mg2ⁱⁱⁱ	149.90 (13)
Zn2—Zn3—Mg3	65.98 (10)	Zn1ⁱⁱⁱ—Mg4—Mg2ⁱⁱⁱ	149.90 (13)
Zn3^vii—Zn3—Mg3	64.18 (5)	Zn1—Mg4—Mg2ⁱⁱⁱ	148.4 (3)
Zn3^ix—Zn3—Mg3	64.18 (5)	Al1—Mg4—Mg2ⁱⁱⁱ	148.4 (3)
Zn2^ix—Zn3—Mg3	113.23 (11)	Zn2ⁱⁱ—Mg4—Mg2ⁱⁱⁱ	100.28 (14)
Zn3^x—Zn3—Mg3	172.53 (8)	Zn2ⁱⁱⁱ—Mg4—Mg2ⁱⁱⁱ	100.28 (14)
Mg1^vii—Zn3—Mg3	123.50 (12)	Zn1ⁱⁱ—Mg4—Zn3^vii	144.22 (19)
Mg2^vii—Zn3—Mg3	123.16 (7)	Zn1ⁱⁱⁱ—Mg4—Zn3^vii	115.20 (10)
Mg2—Zn3—Mg3	113.61 (8)	Zn1—Mg4—Zn3^vii	92.39 (15)
Mg3^xi—Zn3—Mg3	60.8 (2)	Al1—Mg4—Zn3^vii	92.39 (15)
Zn2—Zn3—Mg4^ix	116.38 (12)	Zn2ⁱⁱ—Mg4—Zn3^vii	147.31 (15)
Zn3^vii—Zn3—Mg4^ix	64.74 (10)	Zn2ⁱⁱⁱ—Mg4—Zn3^vii	96.06 (6)
Zn3^ix—Zn3—Mg4^ix	115.34 (13)	Mg2ⁱⁱⁱ—Mg4—Zn3^vii	59.58 (16)
Zn2^ix—Zn3—Mg4^ix	66.54 (11)	Zn1ⁱⁱ—Mg4—Zn3^viii	115.20 (10)
Zn3^x—Zn3—Mg4^ix	63.93 (5)	Zn1ⁱⁱⁱ—Mg4—Zn3^viii	144.22 (19)
Mg1^vii—Zn3—Mg4^ix	109.42 (14)	Zn1—Mg4—Zn3^viii	92.39 (15)
Mg2^vii—Zn3—Mg4^ix	59.16 (14)	Zn2ⁱⁱ—Mg4—Zn3^viii	96.06 (6)
Mg2—Zn3—Mg4^ix	122.67 (9)	Zn2ⁱⁱⁱ—Mg4—Zn3^viii	147.31 (15)
Mg3^xi—Zn3—Mg4^ix	63.15 (12)	Mg2ⁱⁱⁱ—Mg4—Zn3^viii	59.58 (16)
Mg3—Zn3—Mg4^ix	115.37 (12)	Zn3^vii—Mg4—Zn3^viii	52.13 (11)
Zn2—Zn3—Mg4^v	62.78 (11)	Zn1ⁱⁱ—Mg4—Zn3ⁱⁱⁱ	144.48 (15)
Zn3^vii—Zn3—Mg4^v	113.70 (12)	Zn1ⁱⁱⁱ—Mg4—Zn3ⁱⁱⁱ	93.19 (7)
Zn3^ix—Zn3—Mg4^v	64.55 (12)	Zn1—Mg4—Zn3ⁱⁱⁱ	115.41 (10)
Zn2^ix—Zn3—Mg4^v	114.31 (12)	Al1—Mg4—Zn3ⁱⁱⁱ	115.41 (10)
Zn3^x—Zn3—Mg4^v	117.80 (9)	Zn2ⁱⁱ—Mg4—Zn3ⁱⁱⁱ	144.36 (19)
Mg1^vii—Zn3—Mg4^v	71.72 (13)	Zn2ⁱⁱⁱ—Mg4—Zn3ⁱⁱⁱ	50.59 (5)
Mg2^vii—Zn3—Mg4^v	121.16 (16)	Mg2ⁱⁱⁱ—Mg4—Zn3ⁱⁱⁱ	59.80 (9)
Mg2—Zn3—Mg4^v	58.97 (10)	Zn3^vii—Mg4—Zn3ⁱⁱⁱ	50.71 (7)
Mg3^xi—Zn3—Mg4^v	115.64 (14)	Zn3^viii—Mg4—Zn3ⁱⁱⁱ	97.26 (15)
Mg3—Zn3—Mg4^v	62.93 (13)	Zn1ⁱⁱ—Mg4—Zn3ⁱⁱ	93.19 (7)
Mg4^ix—Zn3—Mg4^v	178.26 (11)	Zn1ⁱⁱⁱ—Mg4—Zn3ⁱⁱ	144.48 (15)
Al2—Al3—Mg2	109.42 (14)	Zn1—Mg4—Zn3ⁱⁱ	115.41 (10)
Mg2^vii—Al3—Mg2	112.84 (5)	Al1—Mg4—Zn3ⁱⁱ	115.41 (10)
Mg2^vii—Al3—Mg3^xi	114.38 (14)	Zn2ⁱⁱ—Mg4—Zn3ⁱⁱ	50.59 (5)
Mg2—Al3—Mg3^xi	123.21 (14)	Zn2ⁱⁱⁱ—Mg4—Zn3ⁱⁱ	144.36 (19)
Al2—Al3—Mg3	65.98 (10)	Mg2ⁱⁱⁱ—Mg4—Zn3ⁱⁱ	59.80 (9)
Mg2^vii—Al3—Mg3	123.16 (7)	Zn3^vii—Mg4—Zn3ⁱⁱ	97.26 (15)
Mg2—Al3—Mg3	113.61 (8)	Zn3^viii—Mg4—Zn3ⁱⁱ	50.71 (7)
Mg3^xi—Al3—Mg3	60.8 (2)	Zn3ⁱⁱⁱ—Mg4—Zn3ⁱⁱ	119.59 (18)
Al2—Al3—Mg4^ix	116.38 (12)	Zn1ⁱⁱ—Mg4—Zn2	94.76 (15)
Mg2^vii—Al3—Mg4^ix	59.16 (14)	Zn1ⁱⁱⁱ—Mg4—Zn2	94.76 (15)
Mg2—Al3—Mg4^ix	122.67 (9)	Zn1—Mg4—Zn2	47.95 (10)
Mg3^xi—Al3—Mg4^ix	63.15 (12)	Zn2ⁱⁱ—Mg4—Zn2	118.41 (10)
Mg3—Al3—Mg4^ix	115.37 (12)	Zn2ⁱⁱⁱ—Mg4—Zn2	118.41 (10)
Al2—Al3—Mg4^v	62.78 (11)	Mg2ⁱⁱⁱ—Mg4—Zn2	100.4 (2)
Mg2^vii—Al3—Mg4^v	121.16 (16)	Zn3^vii—Mg4—Zn2	50.33 (10)
Mg2—Al3—Mg4^v	58.97 (10)	Zn3^viii—Mg4—Zn2	50.33 (10)
Mg3^xi—Al3—Mg4^v	115.64 (14)	Zn3ⁱⁱⁱ—Mg4—Zn2	95.31 (12)
Mg3—Al3—Mg4^v	62.93 (13)	Zn3ⁱⁱ—Mg4—Zn2	95.31 (12)
Mg4^ix—Al3—Mg4^v	178.26 (11)

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) −y+1/2, −z+1/2, −x+1/2; (viii) y−1/2, −z+1/2, −x+1/2; (ix) −z+1/2, −x+1/2, −y+1/2; (x) x, −y+1, z; (xi) −x+1/2, −y+1/2, −z+1/2; (xii) −x+1, −y+1, −z; (xiii) z+1/2, x+1/2, y−1/2; (xiv) x+1/2, y+1/2, −z+1/2; (xv) −x+1/2, −y+1/2, z−1/2; (xvi) y, −z+1, x; (xvii) −z+1/2, −x+1/2, y−1/2; (xviii) −z+1/2, x+1/2, −y+1/2; (xix) −z+1/2, x+1/2, y−1/2; (xx) x, −y+1, −z.

Funding information

Funding for this research was provided by: The National Natural Science Foundation of China (grant No. 52173231; grant No. 51925105); Hebei Natural Science Foundation (grant No. E2022203182); The Innovation Ability Promotion Project of Hebei supported by Hebei Key Lab for Optimizing Metal Product Technology and Performance (grant No. 22567609H).

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