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ISSN: 2414-3146

Crystal structure of ω-Al4Cr

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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 16 January 2018; accepted 5 February 2018; online 7 February 2018)

The new polymorph of tetra­aluminium chromium, Al4Cr, designated as the ω-phase, was obtained as the product from a high-pressure sinter­ing (HPS) process of a stoichiometric Al4Cr mixture. The crystal structure is isotypic with Al4Mo and Al4W. The unit cell of ω-Al4Cr is much smaller than any of the other reported Al4Cr polymorphs, containing 30 rather than several hundred atoms.

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[Scheme 3D1]

Structure description

Several polymorphs of Al4Cr have been extensively investigated since the discovery of the icosa­hedral quasicrystal in rapidly solidified Al-Mn and Al-Cr alloys (Shechtman et al., 1984[Shechtman, D., Blech, I., Gratias, D. & Cahn, J. W. (1984). Phys. Rev. Lett. 53, 1951-1953.]). The orthorhombic -Al4Cr phase was originally determined by electron diffraction in space group Bbmm with a = 34.6, b = 20.0, c = 12.4 Å and at elevated temperature shows a transformation to another phase (named ) in space group Pbmm with the same lattice parameters (Wen et al., 1992[Wen, K. Y., Chen, Y. L. & Kuo, K. H. (1992). Metall. Trans. A, 23, 2437-2445.]). Later, the crystal structure of the -Al4Cr phase was refined by single-crystal X-ray diffraction with lattice parameters a = 12.521 (1), b = 34.705 (2), c = 20.223 (1) Å in the space group Cmcm (Li et al., 1997[Li, X. Z., Sugiyama, K., Hiraga, K., Sato, A., Yamamoto, A., Sui, H. X. & Kuo, K. H. (1997). Z. Kristallogr. 212, 628-633.]). The hexa­gonal μ-Al4Cr pholymorph, isostructural with μ-Al4Mn, was also reported. It crystallizes in space group P63/mmc with a ≃ 20.0, c ≃ 24.7 Å as determined by electron diffraction (Wen et al., 1992[Wen, K. Y., Chen, Y. L. & Kuo, K. H. (1992). Metall. Trans. A, 23, 2437-2445.]) and single-crystal X-ray diffraction (Cao & Kuo, 2008[Cao, B. B. & Kuo, K. H. (2008). J. Alloys Compd. 458, 238-247.]). Both the -Al4Cr and the μ-Al4Cr phase have rather large unit cells, containing 682 and 566 atoms, respectively.

In contrast to the ortho­rhom­bic - and the hexa­gonal μ-polymorphs, the unit cell of the new ω-Al4Cr phase contains only 30 atoms (24 Al and 6 Cr atoms; Z = 6). The crystal structure is isotypic with Al4W (Bland & Clark, 1958[Bland, J. A. & Clark, D. (1958). Acta Cryst. 11, 231-236.])) and Al4Mo (Leake, 1964[Leake, J. A. (1964). Acta Cryst. 17, 918-924.]). The Al and Cr atoms are arranged in sets of almost close-packed puckered planes arranged perpendicular to [010]. Fig. 1[link] shows the coordination polyhedra around the two distinct chromium atoms, Cr1 and Cr2. The first chromium atom is located on a general site (4b) and connects to eleven aluminium atoms whereas Cr2 atom is located on a site with mirror symmetry (2a) and is connected to ten Al atoms (Fig. 2[link]). Two (Al1 and Al2) of the seven unique aluminium atoms are also located on a mirror plane.

[Figure 1]
Figure 1
The crystal structure of ω-Al4Cr with coordination polyhedra displayed for Cr1 (gold) and Cr2 (pale blue).
[Figure 2]
Figure 2
Details of the coordination polyhedra around Cr1 (left) and Cr2 (right). Displacement ellipsoids are given at the 99.8% probability level. [Symmetry codes: (i) 1 + x, y, 1 + z; (ii) x, y, 1 + z; (iii) 1 + x, y, z; (iv) [{1\over 2}] + x, [{1\over 2}] − y, z; (v) x, 1 − y, z; (vi) x, y, −1 + z; (x) −1 + x, y, z.]

Synthesis and crystallization

The elements Al (purity 99.8%, product No. 00010 from Alfa Aesar) and Cr (purity 99.95%, product No. 13796 from Alfa Aesar) were mixed in the stoichiometric ratio 4:1 and initially ground in an agate mortar. The blended powders were then put into a grinding tool with a diameter of 9.6 mm and pressed into a tablet at 3–4 MPa slowly and continuously for about 5 min. A cylindrical block with 9.6 mm in diameter and 10.0 mm in height was obtained without cracks or deformations defects. The cylindrical block was then inserted into a six-anvil high-pressure apparatus for HPS experiments, pressurized up to 5 GPa and heated to 1299 K for 30 minutes, cooled to 1169 K and held at that temperature for 2 h, and then rapidly cooled down to room temperature. A fragment was selected and mounted on a glass fiber for single-crystal X-ray diffraction measurements.

Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1[link]. The crystal was refined as an inversion twin with a ratio of 0.84 (7):0.16 (7) for the two twin components.

Table 1
Experimental details

Crystal data
Chemical formula Al4Cr
Mr 159.92
Crystal system, space group Monoclinic, Cm
Temperature (K) 293
a, b, c (Å) 5.1574 (6), 17.413 (2), 5.1107 (7)
β (°) 100.357 (4)
V3) 451.49 (10)
Z 6
Radiation type Mo Kα
μ (mm−1) 4.65
Crystal size (mm) 0.07 × 0.05 × 0.03
 
Data collection
Diffractometer Bruker APEXII Photon 100 COMS
Absorption correction Multi-scan (SADABS; Krause et al., 2015[Krause, L., Herbst-Irmer, R., Sheldrick, G. M. & Stalke, D. (2015). J. Appl. Cryst. 48, 3-10.])
Tmin, Tmax 0.757, 0.870
No. of measured, independent and observed [I > 2σ(I)] reflections 4792, 1200, 967
Rint 0.068
(sin θ/λ)max−1) 0.681
 
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.047, 0.090, 1.05
No. of reflections 1200
No. of parameters 74
No. of restraints 2
Δρmax, Δρmin (e Å−3) 0.85, −1.20
Absolute structure Flack (1983[Flack, H. D. (1983). Acta Cryst. A39, 876-881.]); 584 Friedel pairs
Absolute structure parameter 0.16 (7)
Computer programs: APEX3 and SAINT (Bruker, 2015[Bruker (2015). APEX3 and SAINT. Bruker AXS Inc. Madison, Wisconsin, USA, 2008.]), SHELXT2014 (Sheldrick, 2015a[Sheldrick, G. M. (2015a). Acta Cryst. A71, 3-8.]), SHELXL2014 (Sheldrick, 2015b[Sheldrick, G. M. (2015b). Acta Cryst. C71, 3-8.]), DIAMOND (Brandenburg & Putz, 2017[Brandenburg, K. & Putz, H. (2017). DIAMOND. Crystal Impact GbR, Bonn, Germany.]) and publCIF (Westrip, 2010[Westrip, S. P. (2010). J. Appl. Cryst. 43, 920-925.]).

Structural data


Computing details top

Data collection: APEX3 (Bruker, 2015); cell refinement: SAINT (Bruker, 2015); data reduction: SAINT (Bruker, 2015); program(s) used to solve structure: SHELXT2014 (Sheldrick, 2015a); program(s) used to refine structure: SHELXL2014 (Sheldrick, 2015b); molecular graphics: DIAMOND (Brandenburg & Putz, 2017); software used to prepare material for publication: publCIF (Westrip, 2010).

Tetraaluminium chromium top
Crystal data top
Al4CrF(000) = 456
Mr = 159.92Dx = 3.529 Mg m3
Monoclinic, CmMo Kα radiation, λ = 0.71073 Å
a = 5.1574 (6) ÅCell parameters from 1199 reflections
b = 17.413 (2) Åθ = 4.1–27.0°
c = 5.1107 (7) ŵ = 4.65 mm1
β = 100.357 (4)°T = 293 K
V = 451.49 (10) Å3Fragment, metallic
Z = 60.07 × 0.05 × 0.03 mm
Data collection top
Bruker APEXII Photon 100 COMS
diffractometer
1200 independent reflections
Graphite monochromator967 reflections with I > 2σ(I)
Detector resolution: 10.4167 pixels mm-1Rint = 0.068
phi and ω scansθmax = 28.9°, θmin = 2.3°
Absorption correction: multi-scan
(SADABS; Krause et al., 2015)
h = 67
Tmin = 0.757, Tmax = 0.870k = 2321
4792 measured reflectionsl = 66
Refinement top
Refinement on F22 restraints
Least-squares matrix: full w = 1/[σ2(Fo2) + (0.032P)2 + 2.4184P]
where P = (Fo2 + 2Fc2)/3
R[F2 > 2σ(F2)] = 0.047(Δ/σ)max < 0.001
wR(F2) = 0.090Δρmax = 0.85 e Å3
S = 1.05Δρmin = 1.20 e Å3
1200 reflectionsAbsolute structure: Flack (1983); 584 Friedel pairs
74 parametersAbsolute structure parameter: 0.16 (7)
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.

Refinement. Refined as a 2-component inversion twin.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Cr10.9253 (3)0.36325 (9)0.8089 (3)0.0047 (4)
Al10.7655 (11)0.50.0048 (11)0.0092 (13)
Cr20.2728 (5)0.50.1495 (5)0.0055 (6)
Al20.1177 (11)0.50.6353 (10)0.0099 (13)
Al40.4332 (8)0.3817 (2)0.0771 (7)0.0098 (9)
Al30.0753 (7)0.3773 (2)0.3243 (7)0.0090 (9)
Al50.6001 (9)0.4235 (2)0.4558 (8)0.0114 (8)
Al60.5715 (7)0.2664 (2)0.5621 (8)0.0126 (9)
Al70.7391 (7)0.2538 (2)1.0760 (8)0.0087 (8)
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Cr10.0051 (10)0.0072 (8)0.0011 (8)0.0002 (8)0.0012 (7)0.0000 (7)
Al10.007 (3)0.009 (3)0.013 (3)00.005 (2)0
Cr20.0089 (16)0.0057 (11)0.0017 (14)00.0009 (11)0
Al20.016 (4)0.011 (3)0.002 (3)00.001 (2)0
Al40.012 (2)0.0110 (18)0.007 (2)0.0003 (14)0.0014 (17)0.0007 (15)
Al30.012 (2)0.0102 (18)0.005 (2)0.0015 (14)0.0033 (17)0.0007 (14)
Al50.0087 (16)0.0168 (18)0.0079 (17)0.0003 (15)0.0006 (13)0.0049 (15)
Al60.014 (2)0.0132 (18)0.011 (2)0.0018 (15)0.0029 (18)0.0032 (16)
Al70.0030 (19)0.0126 (17)0.011 (2)0.0026 (15)0.0031 (14)0.0046 (14)
Geometric parameters (Å, º) top
Cr1—Al52.467 (5)Al2—Al5xi2.977 (7)
Cr1—Al4i2.599 (5)Al4—Cr1xiv2.599 (5)
Cr1—Al3i2.620 (4)Al4—Cr1vi2.723 (5)
Cr1—Al72.625 (4)Al4—Al7xv2.731 (5)
Cr1—Al62.634 (4)Al4—Al7vi2.759 (6)
Cr1—Al4ii2.723 (5)Al4—Al5vi2.777 (6)
Cr1—Al3iii2.735 (4)Al4—Al52.801 (5)
Cr1—Al1ii2.745 (3)Al4—Al2vi2.862 (6)
Cr1—Al6iv2.757 (4)Al4—Al6vi2.900 (5)
Cr1—Al2iii2.786 (3)Al4—Al32.997 (5)
Cr1—Al7iv2.800 (4)Al3—Cr1xiv2.620 (4)
Al1—Cr2iii2.593 (6)Al3—Cr1x2.735 (4)
Al1—Al42.663 (5)Al3—Al5x2.775 (6)
Al1—Al4v2.663 (5)Al3—Al6xvi2.783 (5)
Al1—Cr1vi2.745 (3)Al3—Al52.788 (6)
Al1—Cr1vii2.745 (3)Al3—Al7xv2.814 (5)
Al1—Cr22.793 (6)Al3—Al7xiv2.907 (5)
Al1—Al2viii2.808 (7)Al3—Al1x2.997 (5)
Al1—Al5v2.960 (7)Al5—Al5v2.663 (7)
Al1—Al52.960 (7)Al5—Al3iii2.775 (6)
Al1—Al3ix2.997 (5)Al5—Al4ii2.777 (6)
Al1—Al3iii2.997 (5)Al5—Al62.799 (5)
Cr2—Al52.474 (5)Al5—Al2iii2.977 (7)
Cr2—Al5v2.474 (5)Al6—Al72.622 (5)
Cr2—Al42.572 (4)Al6—Al6xvi2.6413 (17)
Cr2—Al4v2.572 (4)Al6—Al6iv2.6413 (17)
Cr2—Al1x2.593 (6)Al6—Cr1xvi2.757 (4)
Cr2—Al32.594 (4)Al6—Al7xv2.776 (5)
Cr2—Al3v2.594 (4)Al6—Al7vi2.782 (5)
Cr2—Al2vi2.606 (6)Al6—Al3iv2.783 (5)
Cr2—Al22.742 (6)Al6—Al4ii2.900 (5)
Al2—Cr2ii2.606 (6)Al7—Al7xvi2.5821 (5)
Al2—Al32.648 (4)Al7—Al7iv2.5821 (5)
Al2—Al3v2.648 (4)Al7—Al4xvii2.731 (5)
Al2—Cr1x2.786 (3)Al7—Al4ii2.759 (6)
Al2—Cr1xi2.786 (3)Al7—Al6xvii2.776 (5)
Al2—Al1xii2.808 (7)Al7—Al6ii2.782 (5)
Al2—Al4xiii2.862 (6)Al7—Cr1xvi2.800 (4)
Al2—Al4ii2.862 (6)Al7—Al3xvii2.814 (5)
Al2—Al5x2.977 (7)Al7—Al3i2.907 (5)
Al5—Cr1—Al4i129.56 (15)Al1—Al4—Al565.55 (16)
Al5—Cr1—Al3i137.30 (14)Cr1vi—Al4—Al595.93 (16)
Al4i—Cr1—Al3i70.10 (12)Al7xv—Al4—Al590.61 (17)
Al5—Cr1—Al7115.17 (14)Al7vi—Al4—Al582.78 (15)
Al4i—Cr1—Al7114.91 (13)Al5vi—Al4—Al5132.8 (2)
Al3i—Cr1—Al767.32 (13)Cr2—Al4—Al2vi57.00 (13)
Al5—Cr1—Al666.46 (13)Cr1xiv—Al4—Al2vi61.11 (13)
Al4i—Cr1—Al6140.34 (15)Al1—Al4—Al2vi78.84 (17)
Al3i—Cr1—Al6126.53 (15)Cr1vi—Al4—Al2vi116.13 (19)
Al7—Cr1—Al659.83 (12)Al7xv—Al4—Al2vi124.41 (18)
Al5—Cr1—Al4ii64.48 (14)Al7vi—Al4—Al2vi165.8 (2)
Al4i—Cr1—Al4ii151.41 (17)Al5vi—Al4—Al2vi66.73 (17)
Al3i—Cr1—Al4ii83.80 (14)Al5—Al4—Al2vi111.02 (18)
Al7—Cr1—Al4ii62.09 (13)Cr2—Al4—Al6vi167.55 (18)
Al6—Cr1—Al4ii65.53 (13)Cr1xiv—Al4—Al6vi97.20 (15)
Al5—Cr1—Al3iii64.23 (13)Al1—Al4—Al6vi113.44 (16)
Al4i—Cr1—Al3iii75.77 (13)Cr1vi—Al4—Al6vi55.75 (10)
Al3i—Cr1—Al3iii145.25 (18)Al7xv—Al4—Al6vi74.30 (14)
Al7—Cr1—Al3iii136.50 (13)Al7vi—Al4—Al6vi55.14 (13)
Al6—Cr1—Al3iii84.71 (13)Al5vi—Al4—Al6vi59.02 (12)
Al4ii—Cr1—Al3iii127.55 (13)Al5—Al4—Al6vi136.94 (19)
Al5—Cr1—Al1ii71.19 (15)Al2vi—Al4—Al6vi110.72 (16)
Al4i—Cr1—Al1ii99.70 (15)Cr2—Al4—Al354.88 (12)
Al3i—Cr1—Al1ii67.87 (15)Cr1xiv—Al4—Al355.28 (12)
Al7—Cr1—Al1ii106.78 (14)Al1—Al4—Al3112.64 (17)
Al6—Cr1—Al1ii119.74 (17)Cr1vi—Al4—Al3148.85 (17)
Al4ii—Cr1—Al1ii58.29 (14)Al7xv—Al4—Al358.63 (13)
Al3iii—Cr1—Al1ii112.82 (14)Al7vi—Al4—Al3100.16 (16)
Al5—Cr1—Al6iv102.70 (13)Al5vi—Al4—Al3156.84 (19)
Al4i—Cr1—Al6iv81.72 (14)Al5—Al4—Al357.35 (14)
Al3i—Cr1—Al6iv118.74 (12)Al2vi—Al4—Al390.38 (17)
Al7—Cr1—Al6iv78.41 (12)Al6vi—Al4—Al3132.06 (19)
Al6—Cr1—Al6iv58.63 (6)Cr2—Al3—Cr1xiv78.09 (12)
Al4ii—Cr1—Al6iv122.44 (13)Cr2—Al3—Al263.06 (14)
Al3iii—Cr1—Al6iv60.90 (13)Cr1xiv—Al3—Al2131.01 (16)
Al1ii—Cr1—Al6iv173.15 (16)Cr2—Al3—Cr1x125.32 (15)
Al5—Cr1—Al2iii68.74 (15)Cr1xiv—Al3—Cr1x145.25 (18)
Al4i—Cr1—Al2iii64.12 (15)Al2—Al3—Cr1x62.30 (11)
Al3i—Cr1—Al2iii100.53 (14)Cr2—Al3—Al5x105.24 (15)
Al7—Cr1—Al2iii166.17 (15)Cr1xiv—Al3—Al5x99.00 (15)
Al6—Cr1—Al2iii130.59 (15)Al2—Al3—Al5x66.54 (15)
Al4ii—Cr1—Al2iii111.51 (15)Cr1x—Al3—Al5x53.19 (12)
Al3iii—Cr1—Al2iii57.33 (13)Cr2—Al3—Al6xvi157.66 (18)
Al1ii—Cr1—Al2iii61.01 (13)Cr1xiv—Al3—Al6xvi109.33 (15)
Al6iv—Cr1—Al2iii114.33 (15)Al2—Al3—Al6xvi118.01 (14)
Al5—Cr1—Al7iv157.49 (13)Cr1x—Al3—Al6xvi59.94 (11)
Al4i—Cr1—Al7iv60.64 (11)Al5x—Al3—Al6xvi94.56 (15)
Al3i—Cr1—Al7iv62.45 (12)Cr2—Al3—Al554.60 (13)
Al7—Cr1—Al7iv56.73 (6)Cr1xiv—Al3—Al5111.56 (17)
Al6—Cr1—Al7iv93.29 (13)Al2—Al3—Al569.54 (16)
Al4ii—Cr1—Al7iv117.42 (13)Cr1x—Al3—Al5103.18 (15)
Al3iii—Cr1—Al7iv105.89 (12)Al5x—Al3—Al5136.00 (19)
Al1ii—Cr1—Al7iv130.20 (15)Al6xvi—Al3—Al5103.72 (16)
Al6iv—Cr1—Al7iv56.31 (12)Cr2—Al3—Al7xv110.15 (17)
Al2iii—Cr1—Al7iv124.73 (15)Cr1xiv—Al3—Al7xv61.92 (12)
Cr2iii—Al1—Al4129.13 (11)Al2—Al3—Al7xv157.80 (19)
Cr2iii—Al1—Al4v129.13 (11)Cr1x—Al3—Al7xv119.51 (15)
Al4—Al1—Al4v101.4 (2)Al5x—Al3—Al7xv133.98 (17)
Cr2iii—Al1—Cr1vi75.88 (13)Al6xvi—Al3—Al7xv59.59 (13)
Al4—Al1—Cr1vi60.44 (11)Al5—Al3—Al7xv89.19 (16)
Al4v—Al1—Cr1vi148.1 (2)Cr2—Al3—Al7xiv134.37 (17)
Cr2iii—Al1—Cr1vii75.88 (13)Cr1xiv—Al3—Al7xiv56.42 (11)
Al4—Al1—Cr1vii148.1 (2)Al2—Al3—Al7xiv146.85 (17)
Al4v—Al1—Cr1vii60.44 (11)Cr1x—Al3—Al7xiv94.91 (14)
Cr1vi—Al1—Cr1vii120.3 (2)Al5x—Al3—Al7xiv80.61 (14)
Cr2iii—Al1—Cr2146.5 (2)Al6xvi—Al3—Al7xiv58.34 (12)
Al4—Al1—Cr256.19 (11)Al5—Al3—Al7xiv142.75 (18)
Al4v—Al1—Cr256.19 (11)Al7xv—Al3—Al7xiv53.63 (8)
Cr1vi—Al1—Cr2116.29 (13)Cr2—Al3—Al1x54.69 (12)
Cr1vii—Al1—Cr2116.29 (13)Cr1xiv—Al3—Al1x58.06 (12)
Cr2iii—Al1—Al2viii57.52 (17)Al2—Al3—Al1x74.92 (14)
Al4—Al1—Al2viii112.66 (15)Cr1x—Al3—Al1x111.29 (16)
Al4v—Al1—Al2viii112.65 (15)Al5x—Al3—Al1x61.57 (16)
Cr1vi—Al1—Al2viii60.20 (12)Al6xvi—Al3—Al1x147.27 (18)
Cr1vii—Al1—Al2viii60.20 (12)Al5—Al3—Al1x109.01 (16)
Cr2—Al1—Al2viii156.0 (2)Al7xv—Al3—Al1x119.87 (16)
Cr2iii—Al1—Al5v100.2 (2)Al7xiv—Al3—Al1x93.81 (16)
Al4—Al1—Al5v100.83 (18)Cr2—Al3—Al454.20 (12)
Al4v—Al1—Al5v59.47 (12)Cr1xiv—Al3—Al454.62 (12)
Cr1vi—Al1—Al5v144.40 (18)Al2—Al3—Al4113.30 (17)
Cr1vii—Al1—Al5v91.89 (10)Cr1x—Al3—Al4158.64 (17)
Cr2—Al1—Al5v50.84 (13)Al5x—Al3—Al4146.91 (18)
Al2viii—Al1—Al5v146.48 (16)Al6xvi—Al3—Al4112.03 (17)
Cr2iii—Al1—Al5100.2 (2)Al5—Al3—Al457.78 (13)
Al4—Al1—Al559.47 (12)Al7xv—Al3—Al455.96 (13)
Al4v—Al1—Al5100.83 (18)Al7xiv—Al3—Al496.45 (16)
Cr1vi—Al1—Al591.89 (10)Al1x—Al3—Al485.95 (14)
Cr1vii—Al1—Al5144.40 (18)Cr1—Al5—Cr2171.39 (18)
Cr2—Al1—Al550.84 (13)Cr1—Al5—Al5v115.19 (9)
Al2viii—Al1—Al5146.48 (16)Cr2—Al5—Al5v57.45 (9)
Al5v—Al1—Al553.45 (17)Cr1—Al5—Al3iii62.58 (13)
Cr2iii—Al1—Al3ix54.72 (12)Cr2—Al5—Al3iii122.34 (19)
Al4—Al1—Al3ix153.4 (2)Al5v—Al5—Al3iii106.88 (10)
Al4v—Al1—Al3ix77.94 (11)Cr1—Al5—Al4ii62.24 (13)
Cr1vi—Al1—Al3ix130.5 (2)Cr2—Al5—Al4ii113.8 (2)
Cr1vii—Al1—Al3ix54.08 (10)Al5v—Al5—Al4ii105.23 (11)
Cr2—Al1—Al3ix105.18 (15)Al3iii—Al5—Al4ii123.76 (18)
Al2viii—Al1—Al3ix91.45 (17)Cr1—Al5—Al3123.80 (17)
Al5v—Al1—Al3ix55.51 (13)Cr2—Al5—Al358.71 (14)
Al5—Al1—Al3ix94.30 (18)Al5v—Al5—Al3106.79 (10)
Cr2iii—Al1—Al3iii54.72 (12)Al3iii—Al5—Al3136.00 (19)
Al4—Al1—Al3iii77.94 (11)Al4ii—Al5—Al372.16 (16)
Al4v—Al1—Al3iii153.4 (2)Cr1—Al5—Al659.63 (11)
Cr1vi—Al1—Al3iii54.08 (10)Cr2—Al5—Al6126.52 (17)
Cr1vii—Al1—Al3iii130.5 (2)Al5v—Al5—Al6167.87 (12)
Cr2—Al1—Al3iii105.18 (15)Al3iii—Al5—Al680.95 (15)
Al2viii—Al1—Al3iii91.45 (17)Al4ii—Al5—Al662.68 (14)
Al5v—Al1—Al3iii94.30 (18)Al3—Al5—Al671.44 (14)
Al5—Al1—Al3iii55.51 (13)Cr1—Al5—Al4130.56 (18)
Al3ix—Al1—Al3iii91.0 (2)Cr2—Al5—Al457.96 (13)
Al5—Cr2—Al5v65.10 (18)Al5v—Al5—Al4105.09 (11)
Al5—Cr2—Al467.40 (13)Al3iii—Al5—Al479.60 (16)
Al5v—Cr2—Al4118.54 (17)Al4ii—Al5—Al4132.8 (2)
Al5—Cr2—Al4v118.54 (17)Al3—Al5—Al464.86 (14)
Al5v—Cr2—Al4v67.40 (13)Al6—Al5—Al485.21 (15)
Al4—Cr2—Al4v106.5 (2)Cr1—Al5—Al1121.2 (2)
Al5—Cr2—Al1x136.77 (15)Cr2—Al5—Al161.08 (15)
Al5v—Cr2—Al1x136.77 (15)Al5v—Al5—Al163.27 (8)
Al4—Cr2—Al1x104.58 (13)Al3iii—Al5—Al162.91 (15)
Al4v—Cr2—Al1x104.58 (13)Al4ii—Al5—Al1168.50 (18)
Al5—Cr2—Al366.69 (13)Al3—Al5—Al1110.15 (19)
Al5v—Cr2—Al3119.39 (15)Al6—Al5—Al1128.82 (17)
Al4—Cr2—Al370.93 (11)Al4—Al5—Al154.98 (14)
Al4v—Cr2—Al3173.21 (17)Cr1—Al5—Al2iii60.70 (12)
Al1x—Cr2—Al370.59 (12)Cr2—Al5—Al2iii115.24 (16)
Al5—Cr2—Al3v119.39 (15)Al5v—Al5—Al2iii63.43 (9)
Al5v—Cr2—Al3v66.69 (13)Al3iii—Al5—Al2iii54.70 (14)
Al4—Cr2—Al3v173.21 (17)Al4ii—Al5—Al2iii104.59 (18)
Al4v—Cr2—Al3v70.92 (11)Al3—Al5—Al2iii168.98 (19)
Al1x—Cr2—Al3v70.59 (12)Al6—Al5—Al2iii116.93 (16)
Al3—Cr2—Al3v110.9 (2)Al4—Al5—Al2iii121.2 (2)
Al5—Cr2—Al2vi133.53 (15)Al1—Al5—Al2iii70.93 (17)
Al5v—Cr2—Al2vi133.53 (15)Al7—Al6—Cr159.92 (12)
Al4—Cr2—Al2vi67.12 (12)Al7—Al6—Al6xvi97.34 (13)
Al4v—Cr2—Al2vi67.12 (12)Cr1—Al6—Al6xvi136.96 (18)
Al1x—Cr2—Al2vi65.38 (17)Al7—Al6—Al6iv80.56 (13)
Al3—Cr2—Al2vi106.21 (13)Cr1—Al6—Al6iv63.02 (12)
Al3v—Cr2—Al2vi106.21 (12)Al6xvi—Al6—Al6iv155.0 (3)
Al5—Cr2—Al272.78 (16)Al7—Al6—Cr1xvi62.68 (13)
Al5v—Cr2—Al272.78 (16)Cr1—Al6—Cr1xvi121.88 (17)
Al4—Cr2—Al2125.27 (10)Al6xvi—Al6—Cr1xvi58.35 (14)
Al4v—Cr2—Al2125.27 (10)Al6iv—Al6—Cr1xvi99.80 (19)
Al1x—Cr2—Al280.38 (19)Al7—Al6—Al7xv157.7 (2)
Al3—Cr2—Al259.44 (11)Cr1—Al6—Al7xv140.64 (18)
Al3v—Cr2—Al259.44 (11)Al6xvi—Al6—Al7xv61.74 (11)
Al2vi—Cr2—Al2145.8 (3)Al6iv—Al6—Al7xv114.75 (13)
Al5—Cr2—Al168.08 (16)Cr1xvi—Al6—Al7xv97.46 (15)
Al5v—Cr2—Al168.08 (16)Al7—Al6—Al7vi142.0 (2)
Al4—Cr2—Al159.35 (11)Cr1—Al6—Al7vi100.29 (16)
Al4v—Cr2—Al159.35 (11)Al6xvi—Al6—Al7vi116.29 (12)
Al1x—Cr2—Al1146.5 (2)Al6iv—Al6—Al7vi61.50 (12)
Al3—Cr2—Al1122.06 (10)Cr1xvi—Al6—Al7vi119.89 (15)
Al3v—Cr2—Al1122.06 (10)Al7xv—Al6—Al7vi55.37 (10)
Al2vi—Cr2—Al181.1 (2)Al7—Al6—Al3iv109.57 (18)
Al2—Cr2—Al1133.15 (19)Cr1—Al6—Al3iv136.57 (17)
Cr2ii—Al2—Al3125.62 (10)Al6xvi—Al6—Al3iv83.61 (18)
Cr2ii—Al2—Al3v125.62 (10)Al6iv—Al6—Al3iv73.86 (18)
Al3—Al2—Al3v107.6 (2)Cr1xvi—Al6—Al3iv59.16 (13)
Cr2ii—Al2—Cr2145.8 (3)Al7xv—Al6—Al3iv63.06 (13)
Al3—Al2—Cr257.50 (10)Al7vi—Al6—Al3iv60.76 (12)
Al3v—Al2—Cr257.50 (10)Al7—Al6—Al5104.89 (15)
Cr2ii—Al2—Cr1x74.99 (13)Cr1—Al6—Al553.91 (11)
Al3—Al2—Cr1x60.38 (9)Al6xvi—Al6—Al5107.3 (2)
Al3v—Al2—Cr1x152.3 (2)Al6iv—Al6—Al597.3 (2)
Cr2—Al2—Cr1x117.84 (11)Cr1xvi—Al6—Al5156.61 (19)
Cr2ii—Al2—Cr1xi74.99 (13)Al7xv—Al6—Al589.76 (16)
Al3—Al2—Cr1xi152.3 (2)Al7vi—Al6—Al582.42 (16)
Al3v—Al2—Cr1xi60.38 (9)Al3iv—Al6—Al5142.13 (18)
Cr2—Al2—Cr1xi117.84 (11)Al7—Al6—Al4ii59.71 (13)
Cr1x—Al2—Cr1xi117.5 (2)Cr1—Al6—Al4ii58.72 (13)
Cr2ii—Al2—Al1xii57.10 (17)Al6xvi—Al6—Al4ii78.34 (14)
Al3—Al2—Al1xii113.55 (14)Al6iv—Al6—Al4ii120.11 (16)
Al3v—Al2—Al1xii113.55 (14)Cr1xvi—Al6—Al4ii99.03 (15)
Cr2—Al2—Al1xii157.1 (3)Al7xv—Al6—Al4ii118.28 (17)
Cr1x—Al2—Al1xii58.79 (11)Al7vi—Al6—Al4ii140.71 (17)
Cr1xi—Al2—Al1xii58.79 (11)Al3iv—Al6—Al4ii157.15 (18)
Cr2ii—Al2—Al4xiii55.88 (12)Al5—Al6—Al4ii58.30 (13)
Al3—Al2—Al4xiii150.1 (2)Al7xvi—Al7—Al7iv174.1 (3)
Al3v—Al2—Al4xiii72.86 (11)Al7xvi—Al7—Al681.67 (12)
Cr2—Al2—Al4xiii103.51 (17)Al7iv—Al7—Al698.83 (12)
Cr1x—Al2—Al4xiii130.8 (2)Al7xvi—Al7—Cr1119.74 (17)
Cr1xi—Al2—Al4xiii54.77 (10)Al7iv—Al7—Cr165.06 (13)
Al1xii—Al2—Al4xiii92.21 (16)Al6—Al7—Cr160.25 (12)
Cr2ii—Al2—Al4ii55.88 (12)Al7xvi—Al7—Al4xvii111.92 (19)
Al3—Al2—Al4ii72.86 (11)Al7iv—Al7—Al4xvii62.50 (16)
Al3v—Al2—Al4ii150.1 (2)Al6—Al7—Al4xvii81.79 (16)
Cr2—Al2—Al4ii103.51 (17)Cr1—Al7—Al4xvii106.91 (15)
Cr1x—Al2—Al4ii54.77 (10)Al7xvi—Al7—Al4ii61.40 (14)
Cr1xi—Al2—Al4ii130.8 (2)Al7iv—Al7—Al4ii124.2 (2)
Al1xii—Al2—Al4ii92.21 (16)Al6—Al7—Al4ii65.15 (14)
Al4xiii—Al2—Al4ii92.1 (2)Cr1—Al7—Al4ii60.70 (13)
Cr2ii—Al2—Al5x114.0 (2)Al4xvii—Al7—Al4ii146.7 (2)
Al3—Al2—Al5x58.76 (12)Al7xvi—Al7—Al6xvii116.73 (12)
Al3v—Al2—Al5x101.71 (18)Al7iv—Al7—Al6xvii62.43 (12)
Cr2—Al2—Al5x96.44 (18)Al6—Al7—Al6xvii161.1 (2)
Cr1x—Al2—Al5x50.56 (11)Cr1—Al7—Al6xvii109.43 (16)
Cr1xi—Al2—Al5x97.43 (19)Al4xvii—Al7—Al6xvii87.00 (15)
Al1xii—Al2—Al5x63.38 (18)Al4ii—Al7—Al6xvii125.86 (18)
Al4xiii—Al2—Al5x151.1 (2)Al7xvi—Al7—Al6ii62.19 (12)
Al4ii—Al2—Al5x103.40 (12)Al7iv—Al7—Al6ii118.33 (12)
Cr2ii—Al2—Al5xi114.0 (2)Al6—Al7—Al6ii142.0 (2)
Al3—Al2—Al5xi101.71 (18)Cr1—Al7—Al6ii127.48 (16)
Al3v—Al2—Al5xi58.76 (12)Al4xvii—Al7—Al6ii120.85 (16)
Cr2—Al2—Al5xi96.44 (18)Al4ii—Al7—Al6ii86.33 (16)
Cr1x—Al2—Al5xi97.43 (19)Al6xvii—Al7—Al6ii56.76 (11)
Cr1xi—Al2—Al5xi50.56 (11)Al7xvi—Al7—Cr1xvi58.21 (12)
Al1xii—Al2—Al5xi63.38 (18)Al7iv—Al7—Cr1xvi116.89 (18)
Al4xiii—Al2—Al5xi103.40 (12)Al6—Al7—Cr1xvi61.01 (13)
Al4ii—Al2—Al5xi151.1 (2)Cr1—Al7—Cr1xvi120.55 (16)
Al5x—Al2—Al5xi53.13 (18)Al4xvii—Al7—Cr1xvi56.03 (11)
Cr2—Al4—Cr1xiv78.87 (14)Al4ii—Al7—Cr1xvi101.43 (14)
Cr2—Al4—Al164.46 (15)Al6xvii—Al7—Cr1xvi123.63 (16)
Cr1xiv—Al4—Al1136.39 (17)Al6ii—Al7—Cr1xvi104.35 (14)
Cr2—Al4—Cr1vi125.33 (17)Al7xvi—Al7—Al3xvii65.02 (15)
Cr1xiv—Al4—Cr1vi151.41 (17)Al7iv—Al7—Al3xvii109.8 (2)
Al1—Al4—Cr1vi61.28 (11)Al6—Al7—Al3xvii116.62 (18)
Cr2—Al4—Al7xv113.50 (17)Cr1—Al7—Al3xvii172.32 (17)
Cr1xiv—Al4—Al7xv63.33 (12)Al4xvii—Al7—Al3xvii65.41 (12)
Al1—Al4—Al7xv152.67 (18)Al4ii—Al7—Al3xvii125.43 (18)
Cr1vi—Al4—Al7xv111.30 (15)Al6xvii—Al7—Al3xvii71.38 (15)
Cr2—Al4—Al7vi137.10 (18)Al6ii—Al7—Al3xvii59.65 (13)
Cr1xiv—Al4—Al7vi117.76 (18)Cr1xvi—Al7—Al3xvii55.63 (11)
Al1—Al4—Al7vi105.31 (14)Al7xvi—Al7—Al3i123.73 (19)
Cr1vi—Al4—Al7vi57.20 (10)Al7iv—Al7—Al3i61.35 (15)
Al7xv—Al4—Al7vi56.10 (9)Al6—Al7—Al3i116.01 (16)
Cr2—Al4—Al5vi110.56 (17)Cr1—Al7—Al3i56.26 (11)
Cr1xiv—Al4—Al5vi107.18 (16)Al4xvii—Al7—Al3i122.91 (17)
Al1—Al4—Al5vi67.96 (17)Al4ii—Al7—Al3i78.04 (15)
Cr1vi—Al4—Al5vi53.28 (13)Al6xvii—Al7—Al3i58.60 (13)
Al7xv—Al4—Al5vi131.25 (17)Al6ii—Al7—Al3i78.95 (15)
Al7vi—Al4—Al5vi101.88 (17)Cr1xvi—Al7—Al3i176.65 (17)
Cr2—Al4—Al554.64 (13)Al3xvii—Al7—Al3i127.4 (2)
Cr1xiv—Al4—Al5111.79 (18)
Symmetry codes: (i) x+1, y, z+1; (ii) x, y, z+1; (iii) x+1, y, z; (iv) x+1/2, y+1/2, z; (v) x, y+1, z; (vi) x, y, z1; (vii) x, y+1, z1; (viii) x+1, y, z1; (ix) x+1, y+1, z; (x) x1, y, z; (xi) x1, y+1, z; (xii) x1, y, z+1; (xiii) x, y+1, z+1; (xiv) x1, y, z1; (xv) x1/2, y+1/2, z1; (xvi) x1/2, y+1/2, z; (xvii) x+1/2, y+1/2, z+1.
 

Acknowledgements

We greatly acknowledge financial support from the Hebei Province Youth Top-notch Talent Program (2013–2018).

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