inorganic compounds
The structure of the aluminium-abundant γ-brass-type Al8.6Mn4.4
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
An aluminium-abundant Al8Mn5/γ-brass-type intermetallic with formula Al8.6Mn4.4, 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 Rm) 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 Rm (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 (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 of the low-temperature γ-Al8Mn5-type phase with the refined chemical composition Al8.6Mn4.4 was determined by single-crystal X-ray diffraction measurements for the first time. Intermetallic Al8.6Mn4.4 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 Al8.6Mn4.4 in the 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 Al8.6Mn4.4.
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 −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.
instrument. The sample was heated up to 1250°C for 10 min with a heating rate of 20°C minRefinement
Table 1 shows the details of data collection and structural 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.
Structural data
CCDC reference: 2111321
https://doi.org/10.1107/S2414314621009883/bh4065sup1.cif
contains datablock I. DOI: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
Data collection: APEX3 (Bruker, 2015); cell
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).Al8.6Mn4.4 | Dx = 4.287 Mg m−3 |
Mr = 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 |
Bruker D8 Venture Photon 100 CMOS diffractometer | 298 reflections with I > 2σ(I) |
φ and ω scans | Rint = 0.078 |
Absorption correction: multi-scan (SADABS; Bruker, 2015) | θmax = 27.5°, θmin = 3.2° |
Tmin = 0.494, Tmax = 0.746 | h = −16→16 |
7162 measured reflections | k = −15→16 |
323 independent reflections | l = −10→10 |
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(Fo2) + (0.0472P)2 + 72.2358P] where P = (Fo2 + 2Fc2)/3 |
wR(F2) = 0.125 | (Δ/σ)max < 0.001 |
S = 1.19 | Δρmax = 0.98 e Å−3 |
323 reflections | Δρmin = −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) |
x | y | z | Uiso*/Ueq | 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) |
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) |
Mn01—Al05 | 2.559 (3) | Mn02—Al05xii | 2.644 (3) |
Mn01—Al06 | 2.5824 (10) | Mn02—Al05xiii | 2.644 (3) |
Mn01—Al06i | 2.5825 (10) | Mn02—Al05xiv | 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—Al06iv | 2.650 (3) |
Mn01—Al06iii | 2.667 (2) | Al03—Al05xi | 2.655 (3) |
Mn01—Al06iv | 2.667 (2) | Al03—Al05x | 2.655 (3) |
Mn01—Al03 | 2.695 (3) | Al03—Al05xiv | 2.741 (4) |
Mn01—Mn01iii | 2.7941 (18) | Al03—Al03ix | 2.810 (4) |
Mn01—Mn01ii | 2.7941 (18) | Al03—Al03viii | 2.810 (4) |
Mn02—Al03v | 2.562 (2) | Al05—Al05xv | 2.611 (6) |
Mn02—Al03vi | 2.562 (2) | Al05—Al05i | 2.832 (4) |
Mn02—Al03vii | 2.562 (2) | Al05—Al05xvi | 2.832 (4) |
Mn02—Al03viii | 2.562 (2) | Al05—Al06i | 2.909 (3) |
Mn02—Al03ix | 2.562 (2) | Al05—Al06 | 2.909 (3) |
Mn02—Al03 | 2.562 (2) | Al06—Al06iv | 2.804 (2) |
Mn02—Al05x | 2.644 (3) | Al06—Al06xvii | 2.804 (2) |
Mn02—Al05xi | 2.644 (3) | ||
Al05—Mn01—Al06 | 68.92 (8) | Mn02—Al03—Al03viii | 56.73 (4) |
Al05—Mn01—Al06i | 68.92 (8) | Al06iii—Al03—Al03viii | 163.86 (5) |
Al06—Mn01—Al06i | 135.16 (12) | Al06iv—Al03—Al03viii | 111.76 (7) |
Al05—Mn01—Al04 | 160.01 (9) | Al05xi—Al03—Al03viii | 108.17 (7) |
Al06—Mn01—Al04 | 107.13 (8) | Al05x—Al03—Al03viii | 58.04 (6) |
Al06i—Mn01—Al04 | 107.13 (8) | Mn01ii—Al03—Al03viii | 58.18 (5) |
Al05—Mn01—Al03ii | 106.00 (8) | Mn01iii—Al03—Al03viii | 107.93 (5) |
Al06—Mn01—Al03ii | 60.63 (8) | Mn01—Al03—Al03viii | 107.73 (5) |
Al06i—Mn01—Al03ii | 118.97 (8) | Al05xiv—Al03—Al03viii | 107.58 (7) |
Al04—Mn01—Al03ii | 57.74 (5) | Al03ix—Al03—Al03viii | 60.0 |
Al05—Mn01—Al03iii | 106.00 (8) | Al03xviii—Al04—Al03ii | 66.71 (8) |
Al06—Mn01—Al03iii | 118.97 (8) | Al03xviii—Al04—Al03ix | 113.29 (8) |
Al06i—Mn01—Al03iii | 60.63 (8) | Al03ii—Al04—Al03ix | 180.0 |
Al04—Mn01—Al03iii | 57.74 (5) | Al03xviii—Al04—Al03iii | 66.71 (8) |
Al03ii—Mn01—Al03iii | 63.64 (11) | Al03ii—Al04—Al03iii | 66.71 (8) |
Al05—Mn01—Al06iii | 91.44 (7) | Al03ix—Al04—Al03iii | 113.29 (8) |
Al06—Mn01—Al06iii | 130.82 (5) | Al03xviii—Al04—Al03viii | 113.29 (8) |
Al06i—Mn01—Al06iii | 64.55 (7) | Al03ii—Al04—Al03viii | 113.29 (8) |
Al04—Mn01—Al06iii | 104.67 (5) | Al03ix—Al04—Al03viii | 66.71 (8) |
Al03ii—Mn01—Al06iii | 162.37 (7) | Al03iii—Al04—Al03viii | 180.00 (10) |
Al03iii—Mn01—Al06iii | 109.58 (7) | Al03xviii—Al04—Al03 | 180.0 |
Al05—Mn01—Al06iv | 91.43 (7) | Al03ii—Al04—Al03 | 113.29 (8) |
Al06—Mn01—Al06iv | 64.55 (7) | Al03ix—Al04—Al03 | 66.71 (8) |
Al06i—Mn01—Al06iv | 130.82 (5) | Al03iii—Al04—Al03 | 113.29 (8) |
Al04—Mn01—Al06iv | 104.67 (5) | Al03viii—Al04—Al03 | 66.71 (8) |
Al03ii—Mn01—Al06iv | 109.58 (7) | Al03xviii—Al04—Mn01iii | 118.14 (3) |
Al03iii—Mn01—Al06iv | 162.37 (7) | Al03ii—Al04—Mn01iii | 118.14 (3) |
Al06iii—Mn01—Al06iv | 71.75 (12) | Al03ix—Al04—Mn01iii | 61.86 (3) |
Al05—Mn01—Al03 | 142.61 (10) | Al03iii—Al04—Mn01iii | 62.63 (6) |
Al06—Mn01—Al03 | 111.28 (5) | Al03viii—Al04—Mn01iii | 117.37 (6) |
Al06i—Mn01—Al03 | 111.28 (5) | Al03—Al04—Mn01iii | 61.86 (3) |
Al04—Mn01—Al03 | 57.37 (6) | Al03xviii—Al04—Mn01ii | 118.14 (3) |
Al03ii—Mn01—Al03 | 105.61 (8) | Al03ii—Al04—Mn01ii | 62.63 (6) |
Al03iii—Mn01—Al03 | 105.61 (8) | Al03ix—Al04—Mn01ii | 117.37 (6) |
Al06iii—Mn01—Al03 | 59.22 (5) | Al03iii—Al04—Mn01ii | 118.14 (3) |
Al06iv—Mn01—Al03 | 59.23 (5) | Al03viii—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) | Al03xviii—Al04—Mn01viii | 61.86 (3) |
Al04—Mn01—Mn01iii | 57.883 (11) | Al03ii—Al04—Mn01viii | 61.86 (3) |
Al03ii—Mn01—Mn01iii | 109.05 (6) | Al03ix—Al04—Mn01viii | 118.14 (3) |
Al03iii—Mn01—Mn01iii | 59.10 (5) | Al03iii—Al04—Mn01viii | 117.37 (6) |
Al06iii—Mn01—Mn01iii | 56.38 (6) | Al03viii—Al04—Mn01viii | 62.63 (6) |
Al06iv—Mn01—Mn01iii | 112.33 (9) | Al03—Al04—Mn01viii | 118.14 (3) |
Al03—Mn01—Mn01iii | 58.06 (5) | Mn01iii—Al04—Mn01viii | 180.0 |
Al05—Mn01—Mn01ii | 126.73 (2) | Mn01ii—Al04—Mn01viii | 64.23 (2) |
Al06—Mn01—Mn01ii | 59.33 (7) | Al03xviii—Al04—Mn01ix | 61.86 (3) |
Al06i—Mn01—Mn01ii | 164.30 (8) | Al03ii—Al04—Mn01ix | 117.37 (6) |
Al04—Mn01—Mn01ii | 57.883 (11) | Al03ix—Al04—Mn01ix | 62.63 (6) |
Al03ii—Mn01—Mn01ii | 59.10 (5) | Al03iii—Al04—Mn01ix | 61.86 (3) |
Al03iii—Mn01—Mn01ii | 109.05 (6) | Al03viii—Al04—Mn01ix | 118.14 (3) |
Al06iii—Mn01—Mn01ii | 112.33 (9) | Al03—Al04—Mn01ix | 118.14 (3) |
Al06iv—Mn01—Mn01ii | 56.38 (6) | Mn01iii—Al04—Mn01ix | 64.23 (2) |
Al03—Mn01—Mn01ii | 58.06 (5) | Mn01ii—Al04—Mn01ix | 180.0 |
Mn01iii—Mn01—Mn01ii | 105.61 (6) | Mn01viii—Al04—Mn01ix | 115.77 (2) |
Al03v—Mn02—Al03vi | 66.53 (8) | Al03xviii—Al04—Mn01 | 117.37 (6) |
Al03v—Mn02—Al03vii | 66.53 (8) | Al03ii—Al04—Mn01 | 61.86 (3) |
Al03vi—Mn02—Al03vii | 66.53 (8) | Al03ix—Al04—Mn01 | 118.14 (3) |
Al03v—Mn02—Al03viii | 113.47 (8) | Al03iii—Al04—Mn01 | 61.86 (3) |
Al03vi—Mn02—Al03viii | 180.0 | Al03viii—Al04—Mn01 | 118.14 (3) |
Al03vii—Mn02—Al03viii | 113.47 (9) | Al03—Al04—Mn01 | 62.63 (6) |
Al03v—Mn02—Al03ix | 113.47 (8) | Mn01iii—Al04—Mn01 | 64.23 (2) |
Al03vi—Mn02—Al03ix | 113.47 (9) | Mn01ii—Al04—Mn01 | 64.23 (2) |
Al03vii—Mn02—Al03ix | 180.0 | Mn01viii—Al04—Mn01 | 115.77 (2) |
Al03viii—Mn02—Al03ix | 66.53 (8) | Mn01ix—Al04—Mn01 | 115.77 (2) |
Al03v—Mn02—Al03 | 180.0 | Mn01—Al05—Al05xv | 66.17 (13) |
Al03vi—Mn02—Al03 | 113.47 (8) | Mn01—Al05—Mn02xix | 135.17 (13) |
Al03vii—Mn02—Al03 | 113.47 (8) | Al05xv—Al05—Mn02xix | 158.7 (2) |
Al03viii—Mn02—Al03 | 66.53 (8) | Mn01—Al05—Al03xx | 147.49 (7) |
Al03ix—Mn02—Al03 | 66.53 (8) | Al05xv—Al05—Al03xx | 104.81 (15) |
Al03v—Mn02—Al05x | 118.71 (5) | Mn02xix—Al05—Al03xx | 57.82 (7) |
Al03vi—Mn02—Al05x | 118.71 (5) | Mn01—Al05—Al03xxi | 147.49 (7) |
Al03vii—Mn02—Al05x | 63.51 (9) | Al05xv—Al05—Al03xxi | 104.81 (15) |
Al03viii—Mn02—Al05x | 61.29 (5) | Mn02xix—Al05—Al03xxi | 57.82 (7) |
Al03ix—Mn02—Al05x | 116.49 (9) | Al03xx—Al05—Al03xxi | 63.92 (12) |
Al03—Mn02—Al05x | 61.29 (5) | Mn01—Al05—Al03xiv | 78.39 (10) |
Al03v—Mn02—Al05xi | 118.71 (5) | Al05xv—Al05—Al03xiv | 144.6 (2) |
Al03vi—Mn02—Al05xi | 63.51 (9) | Mn02xix—Al05—Al03xiv | 56.78 (8) |
Al03vii—Mn02—Al05xi | 118.71 (5) | Al03xx—Al05—Al03xiv | 105.11 (11) |
Al03viii—Mn02—Al05xi | 116.49 (9) | Al03xxi—Al05—Al03xiv | 105.11 (11) |
Al03ix—Mn02—Al05xi | 61.29 (5) | Mn01—Al05—Mn01xv | 122.19 (11) |
Al03—Mn02—Al05xi | 61.29 (5) | Al05xv—Al05—Mn01xv | 56.02 (12) |
Al05x—Mn02—Al05xi | 115.24 (5) | Mn02xix—Al05—Mn01xv | 102.64 (10) |
Al03v—Mn02—Al05xii | 61.29 (5) | Al03xx—Al05—Mn01xv | 58.13 (7) |
Al03vi—Mn02—Al05xii | 61.29 (5) | Al03xxi—Al05—Mn01xv | 58.13 (7) |
Al03vii—Mn02—Al05xii | 116.49 (9) | Al03xiv—Al05—Mn01xv | 159.42 (13) |
Al03viii—Mn02—Al05xii | 118.71 (5) | Mn01—Al05—Al05i | 99.58 (11) |
Al03ix—Mn02—Al05xii | 63.51 (9) | Al05xv—Al05—Al05i | 127.52 (4) |
Al03—Mn02—Al05xii | 118.71 (5) | Mn02xix—Al05—Al05i | 57.62 (2) |
Al05x—Mn02—Al05xii | 180.0 | Al03xx—Al05—Al05i | 109.39 (8) |
Al05xi—Mn02—Al05xii | 64.76 (5) | Al03xxi—Al05—Al05i | 59.82 (8) |
Al03v—Mn02—Al05xiii | 61.29 (5) | Al03xiv—Al05—Al05i | 56.87 (10) |
Al03vi—Mn02—Al05xiii | 116.49 (9) | Mn01xv—Al05—Al05i | 114.36 (13) |
Al03vii—Mn02—Al05xiii | 61.29 (5) | Mn01—Al05—Al05xvi | 99.58 (11) |
Al03viii—Mn02—Al05xiii | 63.50 (9) | Al05xv—Al05—Al05xvi | 127.52 (4) |
Al03ix—Mn02—Al05xiii | 118.71 (5) | Mn02xix—Al05—Al05xvi | 57.62 (2) |
Al03—Mn02—Al05xiii | 118.71 (5) | Al03xx—Al05—Al05xvi | 59.82 (8) |
Al05x—Mn02—Al05xiii | 64.76 (5) | Al03xxi—Al05—Al05xvi | 109.39 (8) |
Al05xi—Mn02—Al05xiii | 180.0 | Al03xiv—Al05—Al05xvi | 56.87 (10) |
Al05xii—Mn02—Al05xiii | 115.23 (5) | Mn01xv—Al05—Al05xvi | 114.36 (13) |
Al03v—Mn02—Al05xiv | 116.49 (9) | Al05i—Al05—Al05xvi | 104.07 (14) |
Al03vi—Mn02—Al05xiv | 61.29 (5) | Mn01—Al05—Al06i | 55.92 (5) |
Al03vii—Mn02—Al05xiv | 61.29 (5) | Al05xv—Al05—Al06i | 70.76 (8) |
Al03viii—Mn02—Al05xiv | 118.71 (5) | Mn02xix—Al05—Al06i | 118.49 (7) |
Al03ix—Mn02—Al05xiv | 118.71 (5) | Al03xx—Al05—Al06i | 153.69 (11) |
Al03—Mn02—Al05xiv | 63.51 (9) | Al03xxi—Al05—Al06i | 91.59 (6) |
Al05x—Mn02—Al05xiv | 64.77 (5) | Al03xiv—Al05—Al06i | 89.87 (8) |
Al05xi—Mn02—Al05xiv | 64.77 (5) | Mn01xv—Al05—Al06i | 101.71 (7) |
Al05xii—Mn02—Al05xiv | 115.23 (5) | Al05i—Al05—Al06i | 60.87 (6) |
Al05xiii—Mn02—Al05xiv | 115.23 (5) | Al05xvi—Al05—Al06i | 143.81 (17) |
Al04—Al03—Mn02 | 101.29 (8) | Mn01—Al05—Al06 | 55.92 (5) |
Al04—Al03—Al06iii | 107.27 (7) | Al05xv—Al05—Al06 | 70.75 (8) |
Mn02—Al03—Al06iii | 132.71 (7) | Mn02xix—Al05—Al06 | 118.49 (7) |
Al04—Al03—Al06iv | 107.27 (7) | Al03xx—Al05—Al06 | 91.59 (6) |
Mn02—Al03—Al06iv | 132.71 (7) | Al03xxi—Al05—Al06 | 153.69 (11) |
Al06iii—Al03—Al06iv | 72.31 (13) | Al03xiv—Al05—Al06 | 89.87 (8) |
Al04—Al03—Al05xi | 109.07 (7) | Mn01xv—Al05—Al06 | 101.71 (7) |
Mn02—Al03—Al05xi | 60.89 (7) | Al05i—Al05—Al06 | 143.81 (17) |
Al06iii—Al03—Al05xi | 74.36 (8) | Al05xvi—Al05—Al06 | 60.87 (6) |
Al06iv—Al03—Al05xi | 136.29 (11) | Al06i—Al05—Al06 | 110.28 (11) |
Al04—Al03—Al05x | 109.07 (7) | Mn01xvi—Al06—Mn01 | 150.27 (16) |
Mn02—Al03—Al05x | 60.89 (7) | Mn01xvi—Al06—Al03xvii | 61.23 (5) |
Al06iii—Al03—Al05x | 136.30 (11) | Mn01—Al06—Al03xvii | 141.63 (9) |
Al06iv—Al03—Al05x | 74.36 (8) | Mn01xvi—Al06—Al03ii | 141.63 (9) |
Al05xi—Al03—Al05x | 114.53 (15) | Mn01—Al06—Al03ii | 61.23 (5) |
Al04—Al03—Mn01ii | 60.40 (5) | Al03xvii—Al06—Al03ii | 107.69 (13) |
Mn02—Al03—Mn01ii | 109.51 (6) | Mn01xvi—Al06—Mn01xvii | 64.29 (6) |
Al06iii—Al03—Mn01ii | 117.24 (9) | Mn01—Al06—Mn01xvii | 137.27 (7) |
Al06iv—Al03—Mn01ii | 58.15 (5) | Al03xvii—Al06—Mn01xvii | 60.90 (8) |
Al05xi—Al03—Mn01ii | 165.50 (11) | Al03ii—Al06—Mn01xvii | 78.16 (9) |
Al05x—Al03—Mn01ii | 64.09 (7) | Mn01xvi—Al06—Mn01ii | 137.27 (7) |
Al04—Al03—Mn01iii | 60.40 (5) | Mn01—Al06—Mn01ii | 64.29 (6) |
Mn02—Al03—Mn01iii | 109.51 (6) | Al03xvii—Al06—Mn01ii | 78.16 (9) |
Al06iii—Al03—Mn01iii | 58.14 (5) | Al03ii—Al06—Mn01ii | 60.90 (8) |
Al06iv—Al03—Mn01iii | 117.23 (9) | Mn01xvii—Al06—Mn01ii | 108.25 (12) |
Al05xi—Al03—Mn01iii | 64.09 (7) | Mn01xvi—Al06—Al06iv | 111.18 (4) |
Al05x—Al03—Mn01iii | 165.50 (11) | Mn01—Al06—Al06iv | 59.19 (9) |
Mn01ii—Al03—Mn01iii | 113.26 (10) | Al03xvii—Al06—Al06iv | 94.07 (10) |
Al04—Al03—Mn01 | 60.00 (6) | Al03ii—Al06—Al06iv | 106.01 (5) |
Mn02—Al03—Mn01 | 161.29 (11) | Mn01xvii—Al06—Al06iv | 154.14 (16) |
Al06iii—Al03—Mn01 | 59.88 (6) | Mn01ii—Al06—Al06iv | 56.26 (3) |
Al06iv—Al03—Mn01 | 59.88 (6) | Mn01xvi—Al06—Al06xvii | 59.19 (9) |
Al05xi—Al03—Mn01 | 122.45 (7) | Mn01—Al06—Al06xvii | 111.18 (4) |
Al05x—Al03—Mn01 | 122.45 (7) | Al03xvii—Al06—Al06xvii | 106.00 (5) |
Mn01ii—Al03—Mn01 | 62.84 (5) | Al03ii—Al06—Al06xvii | 94.07 (10) |
Mn01iii—Al03—Mn01 | 62.84 (5) | Mn01xvii—Al06—Al06xvii | 56.25 (3) |
Al04—Al03—Al05xiv | 161.01 (12) | Mn01ii—Al06—Al06xvii | 154.14 (16) |
Mn02—Al03—Al05xiv | 59.72 (8) | Al06iv—Al06—Al06xvii | 145.82 (19) |
Al06iii—Al03—Al05xiv | 87.92 (8) | Mn01xvi—Al06—Al05 | 97.07 (11) |
Al06iv—Al03—Al05xiv | 87.92 (8) | Mn01—Al06—Al05 | 55.16 (8) |
Al05xi—Al03—Al05xiv | 63.31 (7) | Al03xvii—Al06—Al05 | 154.93 (11) |
Al05x—Al03—Al05xiv | 63.31 (7) | Al03ii—Al06—Al05 | 97.17 (6) |
Mn01ii—Al03—Al05xiv | 123.08 (5) | Mn01xvii—Al06—Al05 | 123.49 (8) |
Mn01iii—Al03—Al05xiv | 123.08 (5) | Mn01ii—Al06—Al05 | 118.16 (7) |
Mn01—Al03—Al05xiv | 139.00 (12) | Al06iv—Al06—Al05 | 81.81 (14) |
Al04—Al03—Al03ix | 56.65 (4) | Al06xvii—Al06—Al05 | 68.22 (8) |
Mn02—Al03—Al03ix | 56.73 (4) | Mn01xvi—Al06—Al05xvi | 55.15 (8) |
Al06iii—Al03—Al03ix | 111.75 (7) | Mn01—Al06—Al05xvi | 97.07 (11) |
Al06iv—Al03—Al03ix | 163.86 (5) | Al03xvii—Al06—Al05xvi | 97.18 (6) |
Al05xi—Al03—Al03ix | 58.04 (6) | Al03ii—Al06—Al05xvi | 154.93 (11) |
Al05x—Al03—Al03ix | 108.17 (7) | Mn01xvii—Al06—Al05xvi | 118.16 (7) |
Mn01ii—Al03—Al03ix | 107.93 (5) | Mn01ii—Al06—Al05xvi | 123.49 (8) |
Mn01iii—Al03—Al03ix | 58.18 (5) | Al06iv—Al06—Al05xvi | 68.22 (8) |
Mn01—Al03—Al03ix | 107.73 (5) | Al06xvii—Al06—Al05xvi | 81.82 (14) |
Al05xiv—Al03—Al03ix | 107.58 (7) | Al05—Al06—Al05xvi | 58.26 (12) |
Al04—Al03—Al03viii | 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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