Crystal structure of the Al20Mn5.37Ni1.31 phase in the Al–Mn–Ni system

Hu, Q.; Wen, B.; Fan, C.

doi:10.1107/S2414314621009810

inorganic compounds

IUCrDATA

ISSN: 2414-3146

Volume 6| Part 9| September 2021| x210981

https://doi.org/10.1107/S2414314621009810

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Crystal structure of the Al₂₀Mn_5.37Ni_1.31 phase in the Al–Mn–Ni system

Qifa Hu,^a Bin Wen ^a and Changzeng Fan ^a ^*

^aState Key Laboratory of Metastable Materials, Science and Technology, Yanshan University, Qinhuangdao 066004, People's Republic of China
^*Correspondence e-mail: chzfan@ysu.edu.cn

Edited by M. Weil, Vienna University of Technology, Austria (Received 6 August 2021; accepted 21 September 2021; online 24 September 2021)

The intermetallic phase with composition Al₂₀Mn_5.37Ni_1.31 (icosaaluminium pentamanganese nickel) was synthesized by high-temperature sintering of a mixture with initial chemical composition Al₆₀Mn₇Ni₃. Al₂₀Mn_5.37Ni_1.31 adopts the Co₂Al₅ structure type in space-group type P6₃/mmc, replacing the Co atoms with the transition-metal atoms Mn and Ni. Structure analysis revealed that one of the two transition-metal sites is partially occupied by Ni [refined occupancy 0.342 (2)] and the other is co-occupied by Mn and Ni with a ratio of 0.895 (14):0.105 (14). The present refined chemical composition is supported by complementary energy-dispersive X-ray fluorescence (EDX) analysis and is in agreement with the previously determined Al–Mn–Ni phase diagram [Balanetskyy et al. (2011 ). J. Alloys Compd, 509, 3795–3805].

Keywords: crystal structure; high-temperature sintering; φ phase; Al–Mn–Ni system.

CCDC reference: 2110961

Structure description

Phases in the ternary Al–Mn–Ni alloy system are structurally complex, also including quasicrystals (QC). For example, an aperiodic diffraction pattern was observed for the alloy with composition Al₆₀Mn₁₁Ni₄, exhibiting tenfold rotation symmetry and characterized as a quasi-crystalline phase (Tendeloo et al., 1988 ). As a result of their applications in industry, relevant stable and metastable phases in the Al–Mn–Ni system have been investigated thoroughly (Balanetskyy et al., 2011). Three thermodynamically stable ternary intermetallics have been reported, among them the φ phase adopting the Co₂Al₅ structure type [P6₃/mmc, Z = 4, a = 7.6632 (16), c = 7.8296 (15) Å; Balanetskyy et al., 2011]. However, a detailed crystal-structure analysis of the φ phase has not been indicated, although its homogeneity chemical composition regions at 1223, 1123, 1023, 973, 918 and 893 K were determined (see Table S1 of the supporting information). It should be noted that such Co₂Al₅-type phases have also been found in other systems e.g. in the binary Al–Mn system the phase Al₁₀Mn₃ with unit-cell parameters a = 7.543, c = 7.898 Å (Taylor, 1959 ), or the decaaluminium trinickel iron phase Al₁₀Ni₃Fe_0.83 that was recently obtained in our group by high-pressure sintering (HPS) of a stoichiometric mixture with nominal composition Al₇₁Ni₂₄Fe₅ (Wang et al., 2018 ). In the present study, the crystal-structure refinement of a phase with composition Al₂₀Mn_5.37Ni_1.31 based on single-crystal X-ray diffraction data is reported, in accordance with the SEM/EDX results (see Tables S2 and S3 along with Fig. S1 compiled in the supporting information). This phase is located within the diagram region of the φ phase determined previously (see Table S1 of the supporting information).

With respect to the Co₂Al₅ structure type (Newkirk et al., 1961 ), in the crystal structure of the Al₂₀Mn_5.37Ni_1.31 phase the Co atoms are replaced by the transition metals Mn and Ni (Fig. 1). The asymmetric unit of Al₂₀Mn_5.37Ni_1.31 comprises five metal sites, three fully occupied by Al atoms at Wyckoff positions 2 a (Al1), 6 h (Al2) and 12 k (Al3), one partially occupied Ni2 site [occupancy 0.342 (2)] at 2 d and one co-occupied (Mn1/Ni1) site [occupancy ratio 0.895 (14): 0.105 (14)] at 6 h. The environment of the co-occupied (Mn1/Ni1) site is shown in Fig. 2, where twelve vertices include ten Al atoms (Al1, Al2, Al3) and two symmetry-related (Mn1/Ni1) sites. In the crystal structure, the distorted icosahedra centered at Al1 and (Mn1/Ni1) and the polyhedron centered at Al2 are fused with each other, as shown in Fig. 3.

Figure 1
The crystal structure of Al₂₀Mn_5.37Ni_1.31 with two (Mn1/Ni1) sites and two Al1 atoms displayed with their coordination environments as polyhedra.

Figure 2
The environment of the (Mn1/Ni1) site. Displacement ellipsoids are given at the 90% probability level. [Symmetry codes: (i) −x + y, −x + 1, z; (ii) −y + 1, x − y + 1, z; (iii) −x, −y, z + $[{1\over 2}]$ ; (iv) x, y, −z + $[{3\over 2}]$ ; (v) x, y, z − 1; (vi) y, −x + y, z − $[{1\over 2}]$ ; (vii) y, −x + y, −z + 1; (viii) x − y, x, −z + 1; (ix) x − y, x, z − $[{1\over 2}]$ ; (x) −x + y, −x, z; (xi) −y, x − y, z.]

Figure 3
The fusion of five polyhedra centered at one (Mn1/Ni1), two Al1 and two Al2 sites.

Synthesis and crystallization

The high-purity elements Al (indicated purity 99.8%; 2.700 g), Mn (indicated purity 99.96%; 0.6417 g) and Ni (indicated purity 99.9%; 0.2935 g) were mixed in the molar ratio 60:7:3 and ground in an agate mortar. The blended powders were placed into a cemented carbide grinding mound of 9.6 mm diameter and pressed at 4 MPa for about 5 min. The obtained cylindrical block was crushed and a sample with a weight of 50.32 mg was selected and subsequently loaded into a Netzsch STA449C simultaneous thermal analysis apparatus. The sample was heated up to 1373 K for 10 min with a heating rate of 20 K min⁻¹. Finally, the sample was slowly cooled to room temperature by turning off the furnace power. Suitable pieces of single-crystal grains were selected from the products for single-crystal X-ray diffraction experiments.

Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1. For better comparison with the Co₂Al₅ structure type, the labelling scheme and atomic coordinates were adapted from Co₂Al₅ (Newkirk et al., 1961). One of the five metal sites is partially occupied by Ni atoms (Ni2) and one site is co-occupied by Mn and Ni atoms (Mn1/Ni1); all Al atoms show full occupancy. Atoms sharing the same site were constrained to have the same coordinates and anisotropic displacement parameters. The maximum and minimum residual electron densities in the final difference map are located 1.32 Å from the (Mn1/Ni1) site and 0.01 Å from the same site, respectively.

Table 1
Experimental details

Crystal data
Chemical formula	Al₂₀Mn_5.37Ni_1.31
M_r	911.74
Crystal system, space group	Hexagonal, P6₃/mmc
Temperature (K)	296
a, c (Å)	7.6009 (3), 7.8187 (5)
V (Å³)	391.20 (4)
Z	1
Radiation type	Mo Kα
μ (mm⁻¹)	6.85
Crystal size (mm)	0.14 × 0.07 × 0.05

Data collection
Diffractometer	Bruker D8 Venture Photon 100 CMOS
Absorption correction	Multi-scan (SADABS; Krause et al., 2015 )
T_min, T_max	0.588, 0.746
No. of measured, independent and observed [I > 2σ(I)] reflections	14281, 260, 246
R_int	0.048
(sin θ/λ)_max (Å⁻¹)	0.715

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.016, 0.033, 1.20
No. of reflections	260
No. of parameters	21
Δρ_max, Δρ_min (e Å⁻³)	0.35, −0.46
Computer programs: APEX3 and SAINT (Bruker, 2015 ), SHELXT (Sheldrick, 2015a ), SHELXL (Sheldrick, 2015b ), DIAMOND (Brandenburg & Putz, 2017 ) and publCIF (Westrip, 2010 ).

Structural data

CCDC reference: 2110961

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2414314621009810/wm4153sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2414314621009810/wm4153Isup2.hkl

Supporting figures and tables. DOI: https://doi.org/10.1107/S2414314621009810/wm4153sup3.docx

checkCIF report

Computing details top

Data collection: APEX3 (Bruker, 2015); cell refinement: SAINT (Bruker, 2015); data reduction: SAINT (Bruker, 2015); program(s) used to solve structure: SHELXT (Sheldrick, 2015a); program(s) used to refine structure: SHELXL (Sheldrick, 2015b); molecular graphics: DIAMOND (Brandenburg & Putz, 2017); software used to prepare material for publication: publCIF (Westrip, 2010).

Icosaaluminium pentamanganese nickel top

Crystal data top

Al₂₀Mn_5.37Ni_1.31	D_x = 3.870 Mg m⁻³
M_r = 911.74	Mo Kα radiation, λ = 0.71073 Å
Hexagonal, P6₃/mmc	Cell parameters from 5904 reflections
a = 7.6009 (3) Å	θ = 3.1–30.5°
c = 7.8187 (5) Å	µ = 6.85 mm⁻¹
V = 391.20 (4) Å³	T = 296 K
Z = 1	Fragment, metallic
F(000) = 431	0.14 × 0.07 × 0.05 mm

Data collection top

Bruker D8 Venture Photon 100 CMOS diffractometer	246 reflections with I > 2σ(I)
φ and ω scans	R_int = 0.048
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	θ_max = 30.5°, θ_min = 3.1°
T_min = 0.588, T_max = 0.746	h = −10→10
14281 measured reflections	k = −10→10
260 independent reflections	l = −11→11

Refinement top

Refinement on F²	21 parameters
Least-squares matrix: full	0 restraints
R[F² > 2σ(F²)] = 0.016	w = 1/[σ²(F_o²) + (0.0158P)² + 0.1412P] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.033	(Δ/σ)_max < 0.001
S = 1.20	Δρ_max = 0.35 e Å⁻³
260 reflections	Δρ_min = −0.46 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)
Mn1	0.12191 (3)	0.24382 (5)	0.250000	0.00549 (12)	0.895 (14)
Ni1	0.12191 (3)	0.24382 (5)	0.250000	0.00549 (12)	0.105 (14)
Al1	0.000000	0.000000	0.000000	0.0062 (3)
Al2	0.45923 (6)	0.91845 (12)	0.250000	0.00770 (19)
Al3	0.19943 (4)	0.39887 (8)	0.93807 (7)	0.00821 (16)
Ni2	0.666667	0.333333	0.250000	0.0046 (4)	0.342 (2)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Mn1	0.00704 (15)	0.00404 (17)	0.00438 (18)	0.00202 (9)	0.000	0.000
Ni1	0.00704 (15)	0.00404 (17)	0.00438 (18)	0.00202 (9)	0.000	0.000
Al1	0.0067 (3)	0.0067 (3)	0.0053 (5)	0.00333 (17)	0.000	0.000
Al2	0.0056 (3)	0.0091 (4)	0.0095 (3)	0.00454 (19)	0.000	0.000
Al3	0.0079 (2)	0.0095 (3)	0.0077 (3)	0.00477 (13)	0.00001 (10)	0.00003 (19)
Ni2	0.0050 (5)	0.0050 (5)	0.0036 (7)	0.0025 (3)	0.000	0.000

Geometric parameters (Å, º) top

Mn1—Al2ⁱ	2.4251 (3)	Al1—Al3^vi	2.6698 (5)
Mn1—Al2ⁱⁱ	2.4251 (3)	Al2—Ni2^xiv	2.7310 (8)
Mn1—Al1	2.5292 (2)	Al2—Al3^xv	2.8132 (6)
Mn1—Al1ⁱⁱⁱ	2.5292 (2)	Al2—Al3^xvi	2.8132 (6)
Mn1—Al3^iv	2.6438 (6)	Al2—Al3^xvii	2.8132 (6)
Mn1—Al3^v	2.6438 (6)	Al2—Al3^xviii	2.8132 (6)
Mn1—Al3^vi	2.7236 (5)	Al2—Al2ⁱ	2.8707 (14)
Mn1—Al3^vii	2.7236 (5)	Al2—Al2ⁱⁱ	2.8707 (14)
Mn1—Al3^viii	2.7236 (5)	Al2—Al3^xix	2.9801 (5)
Mn1—Al3^ix	2.7236 (5)	Al2—Al3^xx	2.9801 (5)
Mn1—Mn1^x	2.7799 (6)	Al2—Al3^xxi	2.9801 (5)
Mn1—Mn1^xi	2.7799 (6)	Al3—Ni2^xxii	2.2956 (5)
Al1—Al3^ix	2.6698 (5)	Al3—Al3^xxiii	2.7985 (6)
Al1—Al3^xii	2.6698 (5)	Al3—Al3^xxiv	2.7985 (6)
Al1—Al3^v	2.6698 (5)	Al3—Al3^iv	2.9409 (10)
Al1—Al3^xiii	2.6698 (5)

Al2ⁱ—Mn1—Al2ⁱⁱ	72.58 (4)	Al3^xv—Al2—Al2ⁱ	107.340 (16)
Al2ⁱ—Mn1—Al1	120.763 (8)	Al3^xvi—Al2—Al2ⁱ	107.340 (16)
Al2ⁱⁱ—Mn1—Al1	120.763 (8)	Al3^xvii—Al2—Al2ⁱ	147.217 (13)
Al2ⁱ—Mn1—Al1ⁱⁱⁱ	120.763 (9)	Al3^xviii—Al2—Al2ⁱ	147.217 (13)
Al2ⁱⁱ—Mn1—Al1ⁱⁱⁱ	120.763 (8)	Mn1ⁱⁱ—Al2—Al2ⁱⁱ	113.710 (19)
Al1—Mn1—Al1ⁱⁱⁱ	101.222 (13)	Mn1ⁱ—Al2—Al2ⁱⁱ	53.710 (19)
Al2ⁱ—Mn1—Al3^iv	71.871 (12)	Ni2^xiv—Al2—Al2ⁱⁱ	150.0
Al2ⁱⁱ—Mn1—Al3^iv	71.871 (12)	Al3^xv—Al2—Al2ⁱⁱ	147.217 (13)
Al1—Mn1—Al3^iv	163.319 (18)	Al3^xvi—Al2—Al2ⁱⁱ	147.217 (13)
Al1ⁱⁱⁱ—Mn1—Al3^iv	62.097 (12)	Al3^xvii—Al2—Al2ⁱⁱ	107.340 (16)
Al2ⁱ—Mn1—Al3^v	71.871 (12)	Al3^xviii—Al2—Al2ⁱⁱ	107.340 (16)
Al2ⁱⁱ—Mn1—Al3^v	71.871 (12)	Al2ⁱ—Al2—Al2ⁱⁱ	60.0
Al1—Mn1—Al3^v	62.097 (12)	Mn1ⁱⁱ—Al2—Al3^xix	57.471 (11)
Al1ⁱⁱⁱ—Mn1—Al3^v	163.319 (18)	Mn1ⁱ—Al2—Al3^xix	118.729 (14)
Al3^iv—Mn1—Al3^v	134.58 (3)	Ni2^xiv—Al2—Al3^xix	105.093 (16)
Al2ⁱ—Mn1—Al3^vi	65.942 (17)	Al3^xv—Al2—Al3^xix	108.722 (19)
Al2ⁱⁱ—Mn1—Al3^vi	125.493 (18)	Al3^xvi—Al2—Al3^xix	57.684 (15)
Al1—Mn1—Al3^vi	60.965 (11)	Al3^xvii—Al2—Al3^xix	151.28 (3)
Al1ⁱⁱⁱ—Mn1—Al3^vi	110.438 (11)	Al3^xviii—Al2—Al3^xix	91.228 (9)
Al3^iv—Mn1—Al3^vi	122.648 (12)	Al2ⁱ—Al2—Al3^xix	61.207 (14)
Al3^v—Mn1—Al3^vi	62.829 (9)	Al2ⁱⁱ—Al2—Al3^xix	91.756 (15)
Al2ⁱ—Mn1—Al3^vii	65.942 (17)	Mn1ⁱⁱ—Al2—Al3^xx	57.471 (11)
Al2ⁱⁱ—Mn1—Al3^vii	125.493 (18)	Mn1ⁱ—Al2—Al3^xx	118.729 (14)
Al1—Mn1—Al3^vii	110.438 (11)	Ni2^xiv—Al2—Al3^xx	105.093 (16)
Al1ⁱⁱⁱ—Mn1—Al3^vii	60.965 (11)	Al3^xv—Al2—Al3^xx	57.684 (15)
Al3^iv—Mn1—Al3^vii	62.829 (9)	Al3^xvi—Al2—Al3^xx	108.722 (19)
Al3^v—Mn1—Al3^vii	122.648 (12)	Al3^xvii—Al2—Al3^xx	91.228 (9)
Al3^vi—Mn1—Al3^vii	65.35 (2)	Al3^xviii—Al2—Al3^xx	151.28 (3)
Al2ⁱ—Mn1—Al3^viii	125.493 (18)	Al2ⁱ—Al2—Al3^xx	61.207 (14)
Al2ⁱⁱ—Mn1—Al3^viii	65.942 (17)	Al2ⁱⁱ—Al2—Al3^xx	91.756 (15)
Al1—Mn1—Al3^viii	110.438 (11)	Al3^xix—Al2—Al3^xx	109.848 (19)
Al1ⁱⁱⁱ—Mn1—Al3^viii	60.965 (11)	Mn1ⁱⁱ—Al2—Al3^xxi	118.729 (14)
Al3^iv—Mn1—Al3^viii	62.829 (9)	Mn1ⁱ—Al2—Al3^xxi	57.471 (10)
Al3^v—Mn1—Al3^viii	122.648 (12)	Ni2^xiv—Al2—Al3^xxi	105.094 (16)
Al3^vi—Mn1—Al3^viii	167.68 (2)	Al3^xv—Al2—Al3^xxi	91.227 (9)
Al3^vii—Mn1—Al3^viii	113.20 (2)	Al3^xvi—Al2—Al3^xxi	151.28 (3)
Al2ⁱ—Mn1—Al3^ix	125.493 (18)	Al3^xvii—Al2—Al3^xxi	57.684 (15)
Al2ⁱⁱ—Mn1—Al3^ix	65.942 (17)	Al3^xviii—Al2—Al3^xxi	108.722 (19)
Al1—Mn1—Al3^ix	60.965 (11)	Al2ⁱ—Al2—Al3^xxi	91.756 (15)
Al1ⁱⁱⁱ—Mn1—Al3^ix	110.438 (11)	Al2ⁱⁱ—Al2—Al3^xxi	61.207 (14)
Al3^iv—Mn1—Al3^ix	122.647 (12)	Al3^xix—Al2—Al3^xxi	149.81 (3)
Al3^v—Mn1—Al3^ix	62.829 (9)	Al3^xx—Al2—Al3^xxi	61.63 (2)
Al3^vi—Mn1—Al3^ix	113.20 (2)	Ni2^xxii—Al3—Mn1^xxviii	152.54 (3)
Al3^vii—Mn1—Al3^ix	167.68 (2)	Ni2^xxii—Al3—Al1^xxviii	150.62 (2)
Al3^viii—Mn1—Al3^ix	65.35 (2)	Mn1^xxviii—Al3—Al1^xxviii	56.843 (13)
Al2ⁱ—Mn1—Mn1^x	113.710 (19)	Ni2^xxii—Al3—Mn1^vi	99.682 (17)
Al2ⁱⁱ—Mn1—Mn1^x	173.710 (19)	Mn1^xxviii—Al3—Mn1^vi	103.866 (18)
Al1—Mn1—Mn1^x	56.663 (5)	Al1^xxviii—Al3—Mn1^vi	55.920 (12)
Al1ⁱⁱⁱ—Mn1—Mn1^x	56.663 (5)	Ni2^xxii—Al3—Mn1^ix	99.682 (17)
Al3^iv—Mn1—Mn1^x	109.531 (12)	Mn1^xxviii—Al3—Mn1^ix	103.866 (18)
Al3^v—Mn1—Mn1^x	109.531 (12)	Al1^xxviii—Al3—Mn1^ix	55.920 (12)
Al3^vi—Mn1—Mn1^x	59.314 (9)	Mn1^vi—Al3—Mn1^ix	61.373 (18)
Al3^vii—Mn1—Mn1^x	59.314 (9)	Ni2^xxii—Al3—Al3^xxiii	125.585 (12)
Al3^viii—Mn1—Mn1^x	108.937 (11)	Mn1^xxviii—Al3—Al3^xxiii	59.979 (17)
Al3^ix—Mn1—Mn1^x	108.937 (11)	Al1^xxviii—Al3—Al3^xxiii	58.393 (3)
Al2ⁱ—Mn1—Mn1^xi	173.710 (19)	Mn1^vi—Al3—Al3^xxiii	57.191 (12)
Al2ⁱⁱ—Mn1—Mn1^xi	113.710 (19)	Mn1^ix—Al3—Al3^xxiii	106.707 (14)
Al1—Mn1—Mn1^xi	56.663 (5)	Ni2^xxii—Al3—Al3^xxiv	125.584 (12)
Al1ⁱⁱⁱ—Mn1—Mn1^xi	56.663 (5)	Mn1^xxviii—Al3—Al3^xxiv	59.979 (17)
Al3^iv—Mn1—Mn1^xi	109.531 (12)	Al1^xxviii—Al3—Al3^xxiv	58.393 (3)
Al3^v—Mn1—Mn1^xi	109.531 (12)	Mn1^vi—Al3—Al3^xxiv	106.707 (14)
Al3^vi—Mn1—Mn1^xi	108.937 (11)	Mn1^ix—Al3—Al3^xxiv	57.191 (12)
Al3^vii—Mn1—Mn1^xi	108.937 (11)	Al3^xxiii—Al3—Al3^xxiv	108.69 (2)
Al3^viii—Mn1—Mn1^xi	59.314 (9)	Ni2^xxii—Al3—Al2^xxix	63.687 (16)
Al3^ix—Mn1—Mn1^xi	59.314 (9)	Mn1^xxviii—Al3—Al2^xxix	122.461 (14)
Mn1^x—Mn1—Mn1^xi	60.0	Al1^xxviii—Al3—Al2^xxix	103.515 (17)
Mn1—Al1—Mn1^xxv	180.0	Mn1^vi—Al3—Al2^xxix	51.923 (12)
Mn1—Al1—Mn1^xxvi	113.326 (11)	Mn1^ix—Al3—Al2^xxix	103.968 (17)
Mn1^xxv—Al1—Mn1^xxvi	66.674 (10)	Al3^xxiii—Al3—Al2^xxix	64.154 (18)
Mn1—Al1—Mn1^xi	66.674 (10)	Al3^xxiv—Al3—Al2^xxix	158.47 (2)
Mn1^xxv—Al1—Mn1^xi	113.326 (10)	Ni2^xxii—Al3—Al2^xxx	63.685 (16)
Mn1^xxvi—Al1—Mn1^xi	180.0	Mn1^xxviii—Al3—Al2^xxx	122.460 (14)
Mn1—Al1—Mn1^x	66.674 (11)	Al1^xxviii—Al3—Al2^xxx	103.515 (17)
Mn1^xxv—Al1—Mn1^x	113.326 (11)	Mn1^vi—Al3—Al2^xxx	103.968 (17)
Mn1^xxvi—Al1—Mn1^x	113.326 (10)	Mn1^ix—Al3—Al2^xxx	51.923 (12)
Mn1^xi—Al1—Mn1^x	66.674 (10)	Al3^xxiii—Al3—Al2^xxx	158.47 (2)
Mn1—Al1—Mn1^xxvii	113.326 (11)	Al3^xxiv—Al3—Al2^xxx	64.154 (18)
Mn1^xxv—Al1—Mn1^xxvii	66.674 (11)	Al2^xxix—Al3—Al2^xxx	114.43 (3)
Mn1^xxvi—Al1—Mn1^xxvii	66.674 (10)	Ni2^xxii—Al3—Al3^iv	50.167 (13)
Mn1^xi—Al1—Mn1^xxvii	113.326 (10)	Mn1^xxviii—Al3—Al3^iv	157.292 (14)
Mn1^x—Al1—Mn1^xxvii	180.000 (15)	Al1^xxviii—Al3—Al3^iv	100.449 (11)
Mn1—Al1—Al3^ix	63.116 (9)	Mn1^vi—Al3—Al3^iv	57.323 (10)
Mn1^xxv—Al1—Al3^ix	116.885 (9)	Mn1^ix—Al3—Al3^iv	57.323 (10)
Mn1^xxvi—Al1—Al3^ix	116.884 (9)	Al3^xxiii—Al3—Al3^iv	110.25 (2)
Mn1^xi—Al1—Al3^ix	63.116 (9)	Al3^xxiv—Al3—Al3^iv	110.25 (2)
Mn1^x—Al1—Al3^ix	118.940 (13)	Al2^xxix—Al3—Al3^iv	58.486 (11)
Mn1^xxvii—Al1—Al3^ix	61.060 (13)	Al2^xxx—Al3—Al3^iv	58.486 (11)
Mn1—Al1—Al3^xii	116.884 (9)	Ni2^xxii—Al3—Al2^xxxi	106.471 (18)
Mn1^xxv—Al1—Al3^xii	63.115 (9)	Mn1^xxviii—Al3—Al2^xxxi	50.658 (11)
Mn1^xxvi—Al1—Al3^xii	63.116 (9)	Al1^xxviii—Al3—Al2^xxxi	99.196 (16)
Mn1^xi—Al1—Al3^xii	116.884 (9)	Mn1^vi—Al3—Al2^xxxi	153.83 (2)
Mn1^x—Al1—Al3^xii	61.060 (13)	Mn1^ix—Al3—Al2^xxxi	113.945 (17)
Mn1^xxvii—Al1—Al3^xii	118.940 (13)	Al3^xxiii—Al3—Al2^xxxi	104.78 (3)
Al3^ix—Al1—Al3^xii	180.0	Al3^xxiv—Al3—Al2^xxxi	58.16 (2)
Mn1—Al1—Al3^v	61.060 (13)	Al2^xxix—Al3—Al2^xxxi	142.04 (2)
Mn1^xxv—Al1—Al3^v	118.940 (13)	Al2^xxx—Al3—Al2^xxxi	88.772 (9)
Mn1^xxvi—Al1—Al3^v	63.115 (9)	Al3^iv—Al3—Al2^xxxi	144.924 (10)
Mn1^xi—Al1—Al3^v	116.885 (9)	Ni2^xxii—Al3—Al2^xxxii	106.471 (18)
Mn1^x—Al1—Al3^v	116.884 (9)	Mn1^xxviii—Al3—Al2^xxxii	50.658 (11)
Mn1^xxvii—Al1—Al3^v	63.116 (9)	Al1^xxviii—Al3—Al2^xxxii	99.196 (16)
Al3^ix—Al1—Al3^v	63.214 (7)	Mn1^vi—Al3—Al2^xxxii	113.945 (17)
Al3^xii—Al1—Al3^v	116.786 (7)	Mn1^ix—Al3—Al2^xxxii	153.83 (2)
Mn1—Al1—Al3^xiii	118.940 (13)	Al3^xxiii—Al3—Al2^xxxii	58.16 (2)
Mn1^xxv—Al1—Al3^xiii	61.060 (13)	Al3^xxiv—Al3—Al2^xxxii	104.78 (3)
Mn1^xxvi—Al1—Al3^xiii	116.885 (9)	Al2^xxix—Al3—Al2^xxxii	88.772 (9)
Mn1^xi—Al1—Al3^xiii	63.115 (9)	Al2^xxx—Al3—Al2^xxxii	142.04 (2)
Mn1^x—Al1—Al3^xiii	63.116 (9)	Al3^iv—Al3—Al2^xxxii	144.924 (10)
Mn1^xxvii—Al1—Al3^xiii	116.884 (9)	Al2^xxxi—Al3—Al2^xxxii	57.59 (3)
Al3^ix—Al1—Al3^xiii	116.786 (7)	Al3^xxxiii—Ni2—Al3^xxx	79.67 (3)
Al3^xii—Al1—Al3^xiii	63.214 (7)	Al3^xxxiii—Ni2—Al3^ix	134.842 (9)
Al3^v—Al1—Al3^xiii	180.000 (14)	Al3^xxx—Ni2—Al3^ix	83.37 (2)
Mn1—Al1—Al3^vi	63.116 (9)	Al3^xxxiii—Ni2—Al3^xxxiv	83.37 (2)
Mn1^xxv—Al1—Al3^vi	116.884 (9)	Al3^xxx—Ni2—Al3^xxxiv	134.842 (9)
Mn1^xxvi—Al1—Al3^vi	61.060 (13)	Al3^ix—Ni2—Al3^xxxiv	134.842 (9)
Mn1^xi—Al1—Al3^vi	118.940 (13)	Al3^xxxiii—Ni2—Al3^viii	83.37 (2)
Mn1^x—Al1—Al3^vi	63.115 (9)	Al3^xxx—Ni2—Al3^viii	134.842 (9)
Mn1^xxvii—Al1—Al3^vi	116.885 (9)	Al3^ix—Ni2—Al3^viii	79.67 (3)
Al3^ix—Al1—Al3^vi	116.786 (7)	Al3^xxxiv—Ni2—Al3^viii	83.37 (2)
Al3^xii—Al1—Al3^vi	63.214 (7)	Al3^xxxiii—Ni2—Al3^xxii	134.842 (9)
Al3^v—Al1—Al3^vi	63.214 (7)	Al3^xxx—Ni2—Al3^xxii	83.37 (2)
Al3^xiii—Al1—Al3^vi	116.786 (7)	Al3^ix—Ni2—Al3^xxii	83.37 (2)
Mn1ⁱⁱ—Al2—Mn1ⁱ	167.42 (4)	Al3^xxxiv—Ni2—Al3^xxii	79.67 (3)
Mn1ⁱⁱ—Al2—Ni2^xiv	96.289 (19)	Al3^viii—Ni2—Al3^xxii	134.842 (9)
Mn1ⁱ—Al2—Ni2^xiv	96.290 (19)	Al3^xxxiii—Ni2—Al2^xxxv	67.421 (5)
Mn1ⁱⁱ—Al2—Al3^xv	62.135 (13)	Al3^xxx—Ni2—Al2^xxxv	67.421 (5)
Mn1ⁱ—Al2—Al3^xv	127.69 (2)	Al3^ix—Ni2—Al2^xxxv	67.421 (5)
Ni2^xiv—Al2—Al3^xv	48.892 (16)	Al3^xxxiv—Ni2—Al2^xxxv	140.167 (13)
Mn1ⁱⁱ—Al2—Al3^xvi	62.135 (13)	Al3^viii—Ni2—Al2^xxxv	67.421 (5)
Mn1ⁱ—Al2—Al3^xvi	127.69 (2)	Al3^xxii—Ni2—Al2^xxxv	140.167 (13)
Ni2^xiv—Al2—Al3^xvi	48.892 (16)	Al3^xxxiii—Ni2—Al2^xxxvi	67.421 (5)
Al3^xv—Al2—Al3^xvi	63.03 (2)	Al3^xxx—Ni2—Al2^xxxvi	67.421 (5)
Mn1ⁱⁱ—Al2—Al3^xvii	127.69 (2)	Al3^ix—Ni2—Al2^xxxvi	140.167 (13)
Mn1ⁱ—Al2—Al3^xvii	62.135 (13)	Al3^xxxiv—Ni2—Al2^xxxvi	67.421 (5)
Ni2^xiv—Al2—Al3^xvii	48.893 (16)	Al3^viii—Ni2—Al2^xxxvi	140.167 (14)
Al3^xv—Al2—Al3^xvii	65.73 (3)	Al3^xxii—Ni2—Al2^xxxvi	67.421 (5)
Al3^xvi—Al2—Al3^xvii	97.79 (3)	Al2^xxxv—Ni2—Al2^xxxvi	120.0
Mn1ⁱⁱ—Al2—Al3^xviii	127.69 (2)	Al3^xxxiii—Ni2—Al2ⁱⁱ	140.167 (13)
Mn1ⁱ—Al2—Al3^xviii	62.135 (13)	Al3^xxx—Ni2—Al2ⁱⁱ	140.167 (13)
Ni2^xiv—Al2—Al3^xviii	48.893 (16)	Al3^ix—Ni2—Al2ⁱⁱ	67.421 (5)
Al3^xv—Al2—Al3^xviii	97.79 (3)	Al3^xxxiv—Ni2—Al2ⁱⁱ	67.421 (5)
Al3^xvi—Al2—Al3^xviii	65.73 (3)	Al3^viii—Ni2—Al2ⁱⁱ	67.421 (5)
Al3^xvii—Al2—Al3^xviii	63.03 (2)	Al3^xxii—Ni2—Al2ⁱⁱ	67.421 (5)
Mn1ⁱⁱ—Al2—Al2ⁱ	53.710 (19)	Al2^xxxv—Ni2—Al2ⁱⁱ	120.0
Mn1ⁱ—Al2—Al2ⁱ	113.711 (19)	Al2^xxxvi—Ni2—Al2ⁱⁱ	120.0
Ni2^xiv—Al2—Al2ⁱ	150.0

Symmetry codes: (i) −y+1, x−y+1, z; (ii) −x+y, −x+1, z; (iii) −x, −y, z+1/2; (iv) x, y, −z+3/2; (v) x, y, z−1; (vi) x−y, x, −z+1; (vii) x−y, x, z−1/2; (viii) y, −x+y, z−1/2; (ix) y, −x+y, −z+1; (x) −y, x−y, z; (xi) −x+y, −x, z; (xii) −y, x−y, z−1; (xiii) −x, −y, −z+1; (xiv) x, y+1, z; (xv) y, −x+y+1, z−1/2; (xvi) y, −x+y+1, −z+1; (xvii) x−y+1, x+1, z−1/2; (xviii) x−y+1, x+1, −z+1; (xix) −x+y, −x+1, z−1; (xx) −x+y, −x+1, −z+3/2; (xxi) −y+1, x−y+1, −z+3/2; (xxii) −x+1, −y+1, −z+1; (xxiii) x−y, x, −z+2; (xxiv) y, −x+y, −z+2; (xxv) −x, −y, −z; (xxvi) x−y, x, −z; (xxvii) y, −x+y, −z; (xxviii) x, y, z+1; (xxix) y−1, −x+y, −z+1; (xxx) x−y+1, x, −z+1; (xxxi) −x+y, −x+1, z+1; (xxxii) −y+1, x−y+1, z+1; (xxxiii) x−y+1, x, z−1/2; (xxxiv) −x+1, −y+1, z−1/2; (xxxv) x, y−1, z; (xxxvi) −y+2, x−y+1, z.

Acknowledgements

We are indebted to the referee for insightful remarks.

Funding information

Funding for this research was provided by: Research Foundation of Education Bureau of Hebei Province (grant No. ZD2018069); The National Natural Science Foundation of China (grant No. 51771165).

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