The structure of the aluminium-abundant γ-brass-type Al8.6Mn4.4

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

doi:10.1107/S2414314621009883

inorganic compounds

IUCrDATA

ISSN: 2414-3146

Volume 6| Part 9| September 2021| x210988

https://doi.org/10.1107/S2414314621009883

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The structure of the aluminium-abundant γ-brass-type Al_8.6Mn_4.4

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 S. Bernès, Benemérita Universidad Autónoma de Puebla, México (Received 30 July 2021; accepted 22 September 2021; online 24 September 2021)

An aluminium-abundant Al₈Mn₅/γ-brass-type intermetallic with formula Al_8.6Mn_4.4, which is isotypic with γ-Al₈Cr₅ and γ-Al₈V₅, was discovered by high-temperature sintering of an Al/Mn mixture with initial composition Al₂Mn. Structure analysis revealed that one special position (Wyckoff site 18h in space group R $[\overline{3}]$ m) is shared by Al and Mn, with refined site occupancy factors of 0.7 and 0.3, respectively. The present low-temperature Al₈Mn₅-type phase crystallizes in the centrosymmetric space group R $[\overline{3}]$ m (No. 166), rather than R3m (No. 160) as previously reported for the same intermetallic characterized by TEM measurements [Zeng et al. (2018 ). Acta Mater. 153, 364–376].

Keywords: crystal structure; Al–Mn; intermetallic; γ-brass phase.

CCDC reference: 2111321

Structure description

The γ-brasses are common phases with rhombohedral symmetry, and have been observed in many systems, including the Al–Cr, Al–Mn, Al–Cu, Ga–Cr, Ga–Mn and Ga–Fe mixtures (Bradley & Lu, 1937 ; Meissner et al., 1965 ; Westman, 1965 ). However, it has long been known that the structure model of the γ-Al₈Mn₅ phase has some conflicts. For example, the Al₈Mn₅ phase was first reported with a hexagonal unit cell (a = 12.713 Å, c = 15.839 Å) and was believed to be associated with Al₈Cr₅ (Schubert et al., 1960 ). Subsequently, this structure was checked with the unit-cell parameters a = 12.630 Å and c = 7.933 Å by powder diffraction patterns (Schonover & Mohanty, 1969 ). In another study, the low-temperature phase Al₈Mn₅ was analysed and considered as a hexagonal structure with unit-cell parameters a = 7.20 Å and c = 22.95 Å. In the meantime, a high-temperature Al₈Mn₅ phase was reported (Koch et al., 1960 ). Further studies were reported on the transformation from the high-temperature Al–Mn phase to the low-temperature Al₈Mn₅ phase, and on the measured metal concentrations, ranging from Mn₄₈Al₅₂ to Mn₃₇Al₆₃, with unit-cell parameters in the range a = 12.598–12.671 Å, and c = 7.911–7.942 Å, by powder diffraction patterns (Ellner, 1990 ). They reached the conclusion that the axial ratio c/a decreases while the molar fraction of aluminium increases. Very recently, the D8₁₀–Al₈Mn₅ phase has been found to nucleate on B2–Al(Mn, Fe) particles in AZ91 magnesium alloys (Zeng et al., 2018). The D8₁₀–Al₈Mn₅ structure model closely resembles that described in the present work; however, its composition includes not only Al and Mn, but also other elements such as Fe and Mg.

Although the Al₈Mn₅ intermetallic phase has been reported many times over many years, the atomic coordinates have not so far been determined accurately by single-crystal X-ray diffraction. In the present work, the crystal structure of the low-temperature γ-Al₈Mn₅-type phase with the refined chemical composition Al_8.6Mn_4.4 was determined by single-crystal X-ray diffraction measurements for the first time. Intermetallic Al_8.6Mn_4.4 is a aluminium-rich phase compared to Mn₃₇Al₆₃, and its axial ratio, c/a = 0.624 is then slightly reduced (Mn₃₇Al₆₃: c/a = 0.626), in agreement with the results reported by Ellner (1990).

Fig. 1 shows the overall atomic distribution of Al_8.6Mn_4.4 in the unit cell. For simplicity, four distorted icosahedra are illustrated here, and the environment of the Mn02 atoms is shown in Fig. 2. The twelve vertices include six Al atoms (Al05) and six co-occupied Al/Mn sites (Al03/Mn03), where the refined site occupancies converged to 0.7 for Al03 and 0.3 for Mn03. In addition, the icosahedron centred at Al04 is shown in Fig. 3; it is constituted of six Mn atoms (Mn01) and six co-occupied Al/Mn sites (Al03/Mn03). In summary, these two icosahedra are packed together and form the main building blocks of Al_8.6Mn_4.4.

Figure 1
The crystal structure of Al_8.6Mn_4.4 with two Mn02 atoms and two Al04 atoms displayed with their coordination environments as polyhedra.

Figure 2
The environment of the Mn02 atom. Displacement ellipsoids are given at the 90% probability level. Symmetry codes: (v) −x + 4/3, −y + $[{2\over 3}]$ , −z + $[{5\over 3}]$ ; (vi) y + $[{1\over 3}]$ , −x + y + $[{2\over 3}]$ , −z + $[{5\over 3}]$ ; (vii) x − y + $[{1\over 3}]$ , x − $[{1\over 3}]$ , −z + $[{5\over 3}]$ ; (viii) −y + 1, x − y, z; (ix) −x + y + 1, −x + 1, z; (x) −x + y + $[{1\over 3}]$ , −x + $[{2\over 3}]$ , z + $[{2\over 3}]$ ; (xi) −y + $[{4\over 3}]$ , x − y + $[{2\over 3}]$ , z + $[{2\over 3}]$ ; (xii) x − y + 1, x, −z + 1; (xiii) y, −x + y, −z + 1; (xiv) −x + 1, −y + 1, −z + 1.

Figure 3
The environment of the Al04 atom. Displacement ellipsoids are given at the 90% probability level. Symmetry codes: (ii) x − y + $[{1\over 3}]$ , x − $[{1\over 3}]$ , −z + $[{2\over 3}]$ ; (iii) y + $[{1\over 3}]$ , −x + y + $[{2\over 3}]$ , −z + $[{2\over 3}]$ ; (viii) −y + 1, x − y, z; (ix) −x + y + 1, −x + 1, z; (xviii) −x + $[{4\over 3}]$ , −y + $[{2\over 3}]$ , −z + $[{2\over 3}]$ .

Synthesis and crystallization

The high-purity elements Al (indicated purity 99.8%; 1.080 g) and Mn (indicated purity 99.96%; 1.100 g) were mixed in the stoichiometric ratio 2:1 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 specimen weighing 50.55 mg was selected and subsequently loaded into the crucible of a Netzsch STA 449 C simultaneous thermal analysis instrument. The sample was heated up to 1250°C for 10 min with a heating rate of 20°C min⁻¹, and then slowly cooled to 700°C with a cooling rate of 10°C min⁻¹. Finally, the sample was cooled down to room temperature by switching off the furnace. Suitable pieces of single-crystal grains were selected from the educts for single-crystal X-ray diffraction experiments. Details of the EDS analysis are given in the supporting information.

Refinement

Table 1 shows the details of data collection and structural refinement. Only one site is co-occupied by Al and Mn atoms (Al03/Mn03). Site occupancies were refined to 0.7 for Al03 and 0.3 for Mn03, and then fixed in the following least-squares cycles. Atoms sharing the same site were constrained to have the same coordinates and displacement parameters. The maximum and minimum residual electron densities in the last difference map are located 0.97 Å from atom Mn01 and 0.85 Å from atom Al05, respectively.

Table 1
Experimental details

Crystal data
Chemical formula	Al_8.6Mn_4.4
M_r	473.76
Crystal system, space group	Trigonal, R $[\overline{3}]$ m:H
Temperature (K)	296
a, c (Å)	12.6751 (13), 7.9137 (9)
V (Å³)	1101.1 (3)
Z	6
Radiation type	Mo Kα
μ (mm⁻¹)	8.32
Crystal size (mm)	0.09 × 0.06 × 0.04

Data collection
Diffractometer	Bruker D8 Venture Photon 100 CMOS
Absorption correction	Multi-scan (SADABS; Bruker, 2015 )
T_min, T_max	0.494, 0.746
No. of measured, independent and observed [I > 2σ(I)] reflections	7162, 323, 298
R_int	0.078
(sin θ/λ)_max (Å⁻¹)	0.649

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.046, 0.125, 1.19
No. of reflections	323
No. of parameters	29
Δρ_max, Δρ_min (e Å⁻³)	0.98, −1.23
Computer programs: APEX3 and SAINT (Bruker, 2015), SHELXT2014/5 (Sheldrick, 2015a ), SHELXL2016/6 (Sheldrick, 2015b ), DIAMOND (Brandenburg & Putz, 2017 ) and publCIF (Westrip, 2010 ).

Structural data

CCDC reference: 2111321

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2414314621009883/bh4065sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2414314621009883/bh4065Isup2.hkl

EDS analysis. DOI: https://doi.org/10.1107/S2414314621009883/bh4065sup3.docx

checkCIF report

Computing details top

Data collection: APEX3 (Bruker, 2015); cell refinement: APEX3 (Bruker, 2015); data reduction: APEX3 and SAINT (Bruker, 2015); program(s) used to solve structure: SHELXT2014/5 (Sheldrick, 2015a); program(s) used to refine structure: SHELXL2016/6 (Sheldrick, 2015b); molecular graphics: DIAMOND (Brandenburg & Putz, 2017); software used to prepare material for publication: publCIF (Westrip, 2010).

Octaluminium pentamanganese top

Crystal data top

Al_8.6Mn_4.4	D_x = 4.287 Mg m⁻³
M_r = 473.76	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3m:H	Cell parameters from 3882 reflections
a = 12.6751 (13) Å	θ = 3.2–30.4°
c = 7.9137 (9) Å	µ = 8.32 mm⁻¹
V = 1101.1 (3) Å³	T = 296 K
Z = 6	Graininess, silver
F(000) = 1331	0.09 × 0.06 × 0.04 mm

Data collection top

Bruker D8 Venture Photon 100 CMOS diffractometer	298 reflections with I > 2σ(I)
φ and ω scans	R_int = 0.078
Absorption correction: multi-scan (SADABS; Bruker, 2015)	θ_max = 27.5°, θ_min = 3.2°
T_min = 0.494, T_max = 0.746	h = −16→16
7162 measured reflections	k = −15→16
323 independent reflections	l = −10→10

Refinement top

Refinement on F²	Primary atom site location: dual
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F² > 2σ(F²)] = 0.046	w = 1/[σ²(F_o²) + (0.0472P)² + 72.2358P] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.125	(Δ/σ)_max < 0.001
S = 1.19	Δρ_max = 0.98 e Å⁻³
323 reflections	Δρ_min = −1.23 e Å⁻³
29 parameters	Extinction correction: SHELXL-2016/6 (Sheldrick, 2015b), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.0015 (3)

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Mn01	0.54960 (7)	0.45040 (7)	0.26408 (19)	0.0082 (5)
Mn02	0.666667	0.333333	0.833333	0.0082 (8)
Al03	0.59276 (11)	0.40724 (11)	0.5828 (3)	0.0082 (6)	0.7
Mn03	0.59276 (11)	0.40724 (11)	0.5828 (3)	0.0082 (6)	0.3
Al04	0.666667	0.333333	0.333333	0.0090 (15)
Al05	0.45078 (13)	0.54922 (13)	0.0926 (4)	0.0101 (7)
Al06	0.333333	0.2900 (3)	0.166667	0.0151 (8)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Mn01	0.0079 (6)	0.0079 (6)	0.0085 (8)	0.0038 (6)	−0.0004 (3)	0.0004 (3)
Mn02	0.0086 (11)	0.0086 (11)	0.0072 (17)	0.0043 (6)	0.000	0.000
Al03	0.0090 (9)	0.0090 (9)	0.0046 (10)	0.0031 (9)	−0.0011 (4)	0.0011 (4)
Mn03	0.0090 (9)	0.0090 (9)	0.0046 (10)	0.0031 (9)	−0.0011 (4)	0.0011 (4)
Al04	0.011 (2)	0.011 (2)	0.006 (3)	0.0053 (11)	0.000	0.000
Al05	0.0127 (12)	0.0127 (12)	0.0096 (14)	0.0098 (13)	0.0005 (5)	−0.0005 (5)
Al06	0.0121 (15)	0.0156 (12)	0.0163 (16)	0.0060 (8)	−0.0051 (12)	−0.0026 (6)

Geometric parameters (Å, º) top

Mn01—Al05	2.559 (3)	Mn02—Al05^xii	2.644 (3)
Mn01—Al06	2.5824 (10)	Mn02—Al05^xiii	2.644 (3)
Mn01—Al06ⁱ	2.5825 (10)	Mn02—Al05^xiv	2.644 (3)
Mn01—Al04	2.6278 (15)	Al03—Al04	2.556 (2)
Mn01—Al03ⁱⁱ	2.6650 (17)	Al03—Al06ⁱⁱⁱ	2.650 (3)
Mn01—Al03ⁱⁱⁱ	2.6650 (17)	Al03—Al06^iv	2.650 (3)
Mn01—Al06ⁱⁱⁱ	2.667 (2)	Al03—Al05^xi	2.655 (3)
Mn01—Al06^iv	2.667 (2)	Al03—Al05^x	2.655 (3)
Mn01—Al03	2.695 (3)	Al03—Al05^xiv	2.741 (4)
Mn01—Mn01ⁱⁱⁱ	2.7941 (18)	Al03—Al03^ix	2.810 (4)
Mn01—Mn01ⁱⁱ	2.7941 (18)	Al03—Al03^viii	2.810 (4)
Mn02—Al03^v	2.562 (2)	Al05—Al05^xv	2.611 (6)
Mn02—Al03^vi	2.562 (2)	Al05—Al05ⁱ	2.832 (4)
Mn02—Al03^vii	2.562 (2)	Al05—Al05^xvi	2.832 (4)
Mn02—Al03^viii	2.562 (2)	Al05—Al06ⁱ	2.909 (3)
Mn02—Al03^ix	2.562 (2)	Al05—Al06	2.909 (3)
Mn02—Al03	2.562 (2)	Al06—Al06^iv	2.804 (2)
Mn02—Al05^x	2.644 (3)	Al06—Al06^xvii	2.804 (2)
Mn02—Al05^xi	2.644 (3)

Al05—Mn01—Al06	68.92 (8)	Mn02—Al03—Al03^viii	56.73 (4)
Al05—Mn01—Al06ⁱ	68.92 (8)	Al06ⁱⁱⁱ—Al03—Al03^viii	163.86 (5)
Al06—Mn01—Al06ⁱ	135.16 (12)	Al06^iv—Al03—Al03^viii	111.76 (7)
Al05—Mn01—Al04	160.01 (9)	Al05^xi—Al03—Al03^viii	108.17 (7)
Al06—Mn01—Al04	107.13 (8)	Al05^x—Al03—Al03^viii	58.04 (6)
Al06ⁱ—Mn01—Al04	107.13 (8)	Mn01ⁱⁱ—Al03—Al03^viii	58.18 (5)
Al05—Mn01—Al03ⁱⁱ	106.00 (8)	Mn01ⁱⁱⁱ—Al03—Al03^viii	107.93 (5)
Al06—Mn01—Al03ⁱⁱ	60.63 (8)	Mn01—Al03—Al03^viii	107.73 (5)
Al06ⁱ—Mn01—Al03ⁱⁱ	118.97 (8)	Al05^xiv—Al03—Al03^viii	107.58 (7)
Al04—Mn01—Al03ⁱⁱ	57.74 (5)	Al03^ix—Al03—Al03^viii	60.0
Al05—Mn01—Al03ⁱⁱⁱ	106.00 (8)	Al03^xviii—Al04—Al03ⁱⁱ	66.71 (8)
Al06—Mn01—Al03ⁱⁱⁱ	118.97 (8)	Al03^xviii—Al04—Al03^ix	113.29 (8)
Al06ⁱ—Mn01—Al03ⁱⁱⁱ	60.63 (8)	Al03ⁱⁱ—Al04—Al03^ix	180.0
Al04—Mn01—Al03ⁱⁱⁱ	57.74 (5)	Al03^xviii—Al04—Al03ⁱⁱⁱ	66.71 (8)
Al03ⁱⁱ—Mn01—Al03ⁱⁱⁱ	63.64 (11)	Al03ⁱⁱ—Al04—Al03ⁱⁱⁱ	66.71 (8)
Al05—Mn01—Al06ⁱⁱⁱ	91.44 (7)	Al03^ix—Al04—Al03ⁱⁱⁱ	113.29 (8)
Al06—Mn01—Al06ⁱⁱⁱ	130.82 (5)	Al03^xviii—Al04—Al03^viii	113.29 (8)
Al06ⁱ—Mn01—Al06ⁱⁱⁱ	64.55 (7)	Al03ⁱⁱ—Al04—Al03^viii	113.29 (8)
Al04—Mn01—Al06ⁱⁱⁱ	104.67 (5)	Al03^ix—Al04—Al03^viii	66.71 (8)
Al03ⁱⁱ—Mn01—Al06ⁱⁱⁱ	162.37 (7)	Al03ⁱⁱⁱ—Al04—Al03^viii	180.00 (10)
Al03ⁱⁱⁱ—Mn01—Al06ⁱⁱⁱ	109.58 (7)	Al03^xviii—Al04—Al03	180.0
Al05—Mn01—Al06^iv	91.43 (7)	Al03ⁱⁱ—Al04—Al03	113.29 (8)
Al06—Mn01—Al06^iv	64.55 (7)	Al03^ix—Al04—Al03	66.71 (8)
Al06ⁱ—Mn01—Al06^iv	130.82 (5)	Al03ⁱⁱⁱ—Al04—Al03	113.29 (8)
Al04—Mn01—Al06^iv	104.67 (5)	Al03^viii—Al04—Al03	66.71 (8)
Al03ⁱⁱ—Mn01—Al06^iv	109.58 (7)	Al03^xviii—Al04—Mn01ⁱⁱⁱ	118.14 (3)
Al03ⁱⁱⁱ—Mn01—Al06^iv	162.37 (7)	Al03ⁱⁱ—Al04—Mn01ⁱⁱⁱ	118.14 (3)
Al06ⁱⁱⁱ—Mn01—Al06^iv	71.75 (12)	Al03^ix—Al04—Mn01ⁱⁱⁱ	61.86 (3)
Al05—Mn01—Al03	142.61 (10)	Al03ⁱⁱⁱ—Al04—Mn01ⁱⁱⁱ	62.63 (6)
Al06—Mn01—Al03	111.28 (5)	Al03^viii—Al04—Mn01ⁱⁱⁱ	117.37 (6)
Al06ⁱ—Mn01—Al03	111.28 (5)	Al03—Al04—Mn01ⁱⁱⁱ	61.86 (3)
Al04—Mn01—Al03	57.37 (6)	Al03^xviii—Al04—Mn01ⁱⁱ	118.14 (3)
Al03ⁱⁱ—Mn01—Al03	105.61 (8)	Al03ⁱⁱ—Al04—Mn01ⁱⁱ	62.63 (6)
Al03ⁱⁱⁱ—Mn01—Al03	105.61 (8)	Al03^ix—Al04—Mn01ⁱⁱ	117.37 (6)
Al06ⁱⁱⁱ—Mn01—Al03	59.22 (5)	Al03ⁱⁱⁱ—Al04—Mn01ⁱⁱ	118.14 (3)
Al06^iv—Mn01—Al03	59.23 (5)	Al03^viii—Al04—Mn01ⁱⁱ	61.86 (3)
Al05—Mn01—Mn01ⁱⁱⁱ	126.73 (2)	Al03—Al04—Mn01ⁱⁱ	61.86 (3)
Al06—Mn01—Mn01ⁱⁱⁱ	164.30 (8)	Mn01ⁱⁱⁱ—Al04—Mn01ⁱⁱ	115.77 (2)
Al06ⁱ—Mn01—Mn01ⁱⁱⁱ	59.33 (7)	Al03^xviii—Al04—Mn01^viii	61.86 (3)
Al04—Mn01—Mn01ⁱⁱⁱ	57.883 (11)	Al03ⁱⁱ—Al04—Mn01^viii	61.86 (3)
Al03ⁱⁱ—Mn01—Mn01ⁱⁱⁱ	109.05 (6)	Al03^ix—Al04—Mn01^viii	118.14 (3)
Al03ⁱⁱⁱ—Mn01—Mn01ⁱⁱⁱ	59.10 (5)	Al03ⁱⁱⁱ—Al04—Mn01^viii	117.37 (6)
Al06ⁱⁱⁱ—Mn01—Mn01ⁱⁱⁱ	56.38 (6)	Al03^viii—Al04—Mn01^viii	62.63 (6)
Al06^iv—Mn01—Mn01ⁱⁱⁱ	112.33 (9)	Al03—Al04—Mn01^viii	118.14 (3)
Al03—Mn01—Mn01ⁱⁱⁱ	58.06 (5)	Mn01ⁱⁱⁱ—Al04—Mn01^viii	180.0
Al05—Mn01—Mn01ⁱⁱ	126.73 (2)	Mn01ⁱⁱ—Al04—Mn01^viii	64.23 (2)
Al06—Mn01—Mn01ⁱⁱ	59.33 (7)	Al03^xviii—Al04—Mn01^ix	61.86 (3)
Al06ⁱ—Mn01—Mn01ⁱⁱ	164.30 (8)	Al03ⁱⁱ—Al04—Mn01^ix	117.37 (6)
Al04—Mn01—Mn01ⁱⁱ	57.883 (11)	Al03^ix—Al04—Mn01^ix	62.63 (6)
Al03ⁱⁱ—Mn01—Mn01ⁱⁱ	59.10 (5)	Al03ⁱⁱⁱ—Al04—Mn01^ix	61.86 (3)
Al03ⁱⁱⁱ—Mn01—Mn01ⁱⁱ	109.05 (6)	Al03^viii—Al04—Mn01^ix	118.14 (3)
Al06ⁱⁱⁱ—Mn01—Mn01ⁱⁱ	112.33 (9)	Al03—Al04—Mn01^ix	118.14 (3)
Al06^iv—Mn01—Mn01ⁱⁱ	56.38 (6)	Mn01ⁱⁱⁱ—Al04—Mn01^ix	64.23 (2)
Al03—Mn01—Mn01ⁱⁱ	58.06 (5)	Mn01ⁱⁱ—Al04—Mn01^ix	180.0
Mn01ⁱⁱⁱ—Mn01—Mn01ⁱⁱ	105.61 (6)	Mn01^viii—Al04—Mn01^ix	115.77 (2)
Al03^v—Mn02—Al03^vi	66.53 (8)	Al03^xviii—Al04—Mn01	117.37 (6)
Al03^v—Mn02—Al03^vii	66.53 (8)	Al03ⁱⁱ—Al04—Mn01	61.86 (3)
Al03^vi—Mn02—Al03^vii	66.53 (8)	Al03^ix—Al04—Mn01	118.14 (3)
Al03^v—Mn02—Al03^viii	113.47 (8)	Al03ⁱⁱⁱ—Al04—Mn01	61.86 (3)
Al03^vi—Mn02—Al03^viii	180.0	Al03^viii—Al04—Mn01	118.14 (3)
Al03^vii—Mn02—Al03^viii	113.47 (9)	Al03—Al04—Mn01	62.63 (6)
Al03^v—Mn02—Al03^ix	113.47 (8)	Mn01ⁱⁱⁱ—Al04—Mn01	64.23 (2)
Al03^vi—Mn02—Al03^ix	113.47 (9)	Mn01ⁱⁱ—Al04—Mn01	64.23 (2)
Al03^vii—Mn02—Al03^ix	180.0	Mn01^viii—Al04—Mn01	115.77 (2)
Al03^viii—Mn02—Al03^ix	66.53 (8)	Mn01^ix—Al04—Mn01	115.77 (2)
Al03^v—Mn02—Al03	180.0	Mn01—Al05—Al05^xv	66.17 (13)
Al03^vi—Mn02—Al03	113.47 (8)	Mn01—Al05—Mn02^xix	135.17 (13)
Al03^vii—Mn02—Al03	113.47 (8)	Al05^xv—Al05—Mn02^xix	158.7 (2)
Al03^viii—Mn02—Al03	66.53 (8)	Mn01—Al05—Al03^xx	147.49 (7)
Al03^ix—Mn02—Al03	66.53 (8)	Al05^xv—Al05—Al03^xx	104.81 (15)
Al03^v—Mn02—Al05^x	118.71 (5)	Mn02^xix—Al05—Al03^xx	57.82 (7)
Al03^vi—Mn02—Al05^x	118.71 (5)	Mn01—Al05—Al03^xxi	147.49 (7)
Al03^vii—Mn02—Al05^x	63.51 (9)	Al05^xv—Al05—Al03^xxi	104.81 (15)
Al03^viii—Mn02—Al05^x	61.29 (5)	Mn02^xix—Al05—Al03^xxi	57.82 (7)
Al03^ix—Mn02—Al05^x	116.49 (9)	Al03^xx—Al05—Al03^xxi	63.92 (12)
Al03—Mn02—Al05^x	61.29 (5)	Mn01—Al05—Al03^xiv	78.39 (10)
Al03^v—Mn02—Al05^xi	118.71 (5)	Al05^xv—Al05—Al03^xiv	144.6 (2)
Al03^vi—Mn02—Al05^xi	63.51 (9)	Mn02^xix—Al05—Al03^xiv	56.78 (8)
Al03^vii—Mn02—Al05^xi	118.71 (5)	Al03^xx—Al05—Al03^xiv	105.11 (11)
Al03^viii—Mn02—Al05^xi	116.49 (9)	Al03^xxi—Al05—Al03^xiv	105.11 (11)
Al03^ix—Mn02—Al05^xi	61.29 (5)	Mn01—Al05—Mn01^xv	122.19 (11)
Al03—Mn02—Al05^xi	61.29 (5)	Al05^xv—Al05—Mn01^xv	56.02 (12)
Al05^x—Mn02—Al05^xi	115.24 (5)	Mn02^xix—Al05—Mn01^xv	102.64 (10)
Al03^v—Mn02—Al05^xii	61.29 (5)	Al03^xx—Al05—Mn01^xv	58.13 (7)
Al03^vi—Mn02—Al05^xii	61.29 (5)	Al03^xxi—Al05—Mn01^xv	58.13 (7)
Al03^vii—Mn02—Al05^xii	116.49 (9)	Al03^xiv—Al05—Mn01^xv	159.42 (13)
Al03^viii—Mn02—Al05^xii	118.71 (5)	Mn01—Al05—Al05ⁱ	99.58 (11)
Al03^ix—Mn02—Al05^xii	63.51 (9)	Al05^xv—Al05—Al05ⁱ	127.52 (4)
Al03—Mn02—Al05^xii	118.71 (5)	Mn02^xix—Al05—Al05ⁱ	57.62 (2)
Al05^x—Mn02—Al05^xii	180.0	Al03^xx—Al05—Al05ⁱ	109.39 (8)
Al05^xi—Mn02—Al05^xii	64.76 (5)	Al03^xxi—Al05—Al05ⁱ	59.82 (8)
Al03^v—Mn02—Al05^xiii	61.29 (5)	Al03^xiv—Al05—Al05ⁱ	56.87 (10)
Al03^vi—Mn02—Al05^xiii	116.49 (9)	Mn01^xv—Al05—Al05ⁱ	114.36 (13)
Al03^vii—Mn02—Al05^xiii	61.29 (5)	Mn01—Al05—Al05^xvi	99.58 (11)
Al03^viii—Mn02—Al05^xiii	63.50 (9)	Al05^xv—Al05—Al05^xvi	127.52 (4)
Al03^ix—Mn02—Al05^xiii	118.71 (5)	Mn02^xix—Al05—Al05^xvi	57.62 (2)
Al03—Mn02—Al05^xiii	118.71 (5)	Al03^xx—Al05—Al05^xvi	59.82 (8)
Al05^x—Mn02—Al05^xiii	64.76 (5)	Al03^xxi—Al05—Al05^xvi	109.39 (8)
Al05^xi—Mn02—Al05^xiii	180.0	Al03^xiv—Al05—Al05^xvi	56.87 (10)
Al05^xii—Mn02—Al05^xiii	115.23 (5)	Mn01^xv—Al05—Al05^xvi	114.36 (13)
Al03^v—Mn02—Al05^xiv	116.49 (9)	Al05ⁱ—Al05—Al05^xvi	104.07 (14)
Al03^vi—Mn02—Al05^xiv	61.29 (5)	Mn01—Al05—Al06ⁱ	55.92 (5)
Al03^vii—Mn02—Al05^xiv	61.29 (5)	Al05^xv—Al05—Al06ⁱ	70.76 (8)
Al03^viii—Mn02—Al05^xiv	118.71 (5)	Mn02^xix—Al05—Al06ⁱ	118.49 (7)
Al03^ix—Mn02—Al05^xiv	118.71 (5)	Al03^xx—Al05—Al06ⁱ	153.69 (11)
Al03—Mn02—Al05^xiv	63.51 (9)	Al03^xxi—Al05—Al06ⁱ	91.59 (6)
Al05^x—Mn02—Al05^xiv	64.77 (5)	Al03^xiv—Al05—Al06ⁱ	89.87 (8)
Al05^xi—Mn02—Al05^xiv	64.77 (5)	Mn01^xv—Al05—Al06ⁱ	101.71 (7)
Al05^xii—Mn02—Al05^xiv	115.23 (5)	Al05ⁱ—Al05—Al06ⁱ	60.87 (6)
Al05^xiii—Mn02—Al05^xiv	115.23 (5)	Al05^xvi—Al05—Al06ⁱ	143.81 (17)
Al04—Al03—Mn02	101.29 (8)	Mn01—Al05—Al06	55.92 (5)
Al04—Al03—Al06ⁱⁱⁱ	107.27 (7)	Al05^xv—Al05—Al06	70.75 (8)
Mn02—Al03—Al06ⁱⁱⁱ	132.71 (7)	Mn02^xix—Al05—Al06	118.49 (7)
Al04—Al03—Al06^iv	107.27 (7)	Al03^xx—Al05—Al06	91.59 (6)
Mn02—Al03—Al06^iv	132.71 (7)	Al03^xxi—Al05—Al06	153.69 (11)
Al06ⁱⁱⁱ—Al03—Al06^iv	72.31 (13)	Al03^xiv—Al05—Al06	89.87 (8)
Al04—Al03—Al05^xi	109.07 (7)	Mn01^xv—Al05—Al06	101.71 (7)
Mn02—Al03—Al05^xi	60.89 (7)	Al05ⁱ—Al05—Al06	143.81 (17)
Al06ⁱⁱⁱ—Al03—Al05^xi	74.36 (8)	Al05^xvi—Al05—Al06	60.87 (6)
Al06^iv—Al03—Al05^xi	136.29 (11)	Al06ⁱ—Al05—Al06	110.28 (11)
Al04—Al03—Al05^x	109.07 (7)	Mn01^xvi—Al06—Mn01	150.27 (16)
Mn02—Al03—Al05^x	60.89 (7)	Mn01^xvi—Al06—Al03^xvii	61.23 (5)
Al06ⁱⁱⁱ—Al03—Al05^x	136.30 (11)	Mn01—Al06—Al03^xvii	141.63 (9)
Al06^iv—Al03—Al05^x	74.36 (8)	Mn01^xvi—Al06—Al03ⁱⁱ	141.63 (9)
Al05^xi—Al03—Al05^x	114.53 (15)	Mn01—Al06—Al03ⁱⁱ	61.23 (5)
Al04—Al03—Mn01ⁱⁱ	60.40 (5)	Al03^xvii—Al06—Al03ⁱⁱ	107.69 (13)
Mn02—Al03—Mn01ⁱⁱ	109.51 (6)	Mn01^xvi—Al06—Mn01^xvii	64.29 (6)
Al06ⁱⁱⁱ—Al03—Mn01ⁱⁱ	117.24 (9)	Mn01—Al06—Mn01^xvii	137.27 (7)
Al06^iv—Al03—Mn01ⁱⁱ	58.15 (5)	Al03^xvii—Al06—Mn01^xvii	60.90 (8)
Al05^xi—Al03—Mn01ⁱⁱ	165.50 (11)	Al03ⁱⁱ—Al06—Mn01^xvii	78.16 (9)
Al05^x—Al03—Mn01ⁱⁱ	64.09 (7)	Mn01^xvi—Al06—Mn01ⁱⁱ	137.27 (7)
Al04—Al03—Mn01ⁱⁱⁱ	60.40 (5)	Mn01—Al06—Mn01ⁱⁱ	64.29 (6)
Mn02—Al03—Mn01ⁱⁱⁱ	109.51 (6)	Al03^xvii—Al06—Mn01ⁱⁱ	78.16 (9)
Al06ⁱⁱⁱ—Al03—Mn01ⁱⁱⁱ	58.14 (5)	Al03ⁱⁱ—Al06—Mn01ⁱⁱ	60.90 (8)
Al06^iv—Al03—Mn01ⁱⁱⁱ	117.23 (9)	Mn01^xvii—Al06—Mn01ⁱⁱ	108.25 (12)
Al05^xi—Al03—Mn01ⁱⁱⁱ	64.09 (7)	Mn01^xvi—Al06—Al06^iv	111.18 (4)
Al05^x—Al03—Mn01ⁱⁱⁱ	165.50 (11)	Mn01—Al06—Al06^iv	59.19 (9)
Mn01ⁱⁱ—Al03—Mn01ⁱⁱⁱ	113.26 (10)	Al03^xvii—Al06—Al06^iv	94.07 (10)
Al04—Al03—Mn01	60.00 (6)	Al03ⁱⁱ—Al06—Al06^iv	106.01 (5)
Mn02—Al03—Mn01	161.29 (11)	Mn01^xvii—Al06—Al06^iv	154.14 (16)
Al06ⁱⁱⁱ—Al03—Mn01	59.88 (6)	Mn01ⁱⁱ—Al06—Al06^iv	56.26 (3)
Al06^iv—Al03—Mn01	59.88 (6)	Mn01^xvi—Al06—Al06^xvii	59.19 (9)
Al05^xi—Al03—Mn01	122.45 (7)	Mn01—Al06—Al06^xvii	111.18 (4)
Al05^x—Al03—Mn01	122.45 (7)	Al03^xvii—Al06—Al06^xvii	106.00 (5)
Mn01ⁱⁱ—Al03—Mn01	62.84 (5)	Al03ⁱⁱ—Al06—Al06^xvii	94.07 (10)
Mn01ⁱⁱⁱ—Al03—Mn01	62.84 (5)	Mn01^xvii—Al06—Al06^xvii	56.25 (3)
Al04—Al03—Al05^xiv	161.01 (12)	Mn01ⁱⁱ—Al06—Al06^xvii	154.14 (16)
Mn02—Al03—Al05^xiv	59.72 (8)	Al06^iv—Al06—Al06^xvii	145.82 (19)
Al06ⁱⁱⁱ—Al03—Al05^xiv	87.92 (8)	Mn01^xvi—Al06—Al05	97.07 (11)
Al06^iv—Al03—Al05^xiv	87.92 (8)	Mn01—Al06—Al05	55.16 (8)
Al05^xi—Al03—Al05^xiv	63.31 (7)	Al03^xvii—Al06—Al05	154.93 (11)
Al05^x—Al03—Al05^xiv	63.31 (7)	Al03ⁱⁱ—Al06—Al05	97.17 (6)
Mn01ⁱⁱ—Al03—Al05^xiv	123.08 (5)	Mn01^xvii—Al06—Al05	123.49 (8)
Mn01ⁱⁱⁱ—Al03—Al05^xiv	123.08 (5)	Mn01ⁱⁱ—Al06—Al05	118.16 (7)
Mn01—Al03—Al05^xiv	139.00 (12)	Al06^iv—Al06—Al05	81.81 (14)
Al04—Al03—Al03^ix	56.65 (4)	Al06^xvii—Al06—Al05	68.22 (8)
Mn02—Al03—Al03^ix	56.73 (4)	Mn01^xvi—Al06—Al05^xvi	55.15 (8)
Al06ⁱⁱⁱ—Al03—Al03^ix	111.75 (7)	Mn01—Al06—Al05^xvi	97.07 (11)
Al06^iv—Al03—Al03^ix	163.86 (5)	Al03^xvii—Al06—Al05^xvi	97.18 (6)
Al05^xi—Al03—Al03^ix	58.04 (6)	Al03ⁱⁱ—Al06—Al05^xvi	154.93 (11)
Al05^x—Al03—Al03^ix	108.17 (7)	Mn01^xvii—Al06—Al05^xvi	118.16 (7)
Mn01ⁱⁱ—Al03—Al03^ix	107.93 (5)	Mn01ⁱⁱ—Al06—Al05^xvi	123.49 (8)
Mn01ⁱⁱⁱ—Al03—Al03^ix	58.18 (5)	Al06^iv—Al06—Al05^xvi	68.22 (8)
Mn01—Al03—Al03^ix	107.73 (5)	Al06^xvii—Al06—Al05^xvi	81.82 (14)
Al05^xiv—Al03—Al03^ix	107.58 (7)	Al05—Al06—Al05^xvi	58.26 (12)
Al04—Al03—Al03^viii	56.65 (4)

Symmetry codes: (i) x−y+2/3, x+1/3, −z+1/3; (ii) x−y+1/3, x−1/3, −z+2/3; (iii) y+1/3, −x+y+2/3, −z+2/3; (iv) −y+2/3, x−y+1/3, z+1/3; (v) −x+4/3, −y+2/3, −z+5/3; (vi) y+1/3, −x+y+2/3, −z+5/3; (vii) x−y+1/3, x−1/3, −z+5/3; (viii) −y+1, x−y, z; (ix) −x+y+1, −x+1, z; (x) −x+y+1/3, −x+2/3, z+2/3; (xi) −y+4/3, x−y+2/3, z+2/3; (xii) x−y+1, x, −z+1; (xiii) y, −x+y, −z+1; (xiv) −x+1, −y+1, −z+1; (xv) −x+1, −y+1, −z; (xvi) y−1/3, −x+y+1/3, −z+1/3; (xvii) −x+y+1/3, −x+2/3, z−1/3; (xviii) −x+4/3, −y+2/3, −z+2/3; (xix) x−1/3, y+1/3, z−2/3; (xx) −y+2/3, x−y+1/3, z−2/3; (xxi) −x+y+2/3, −x+4/3, z−2/3.

Acknowledgements

We acknowledge 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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