Crystal structure of ω-Al4Cr

Fan, C.; Liu, C.

doi:10.1107/S241431461800216X

inorganic compounds

IUCrDATA

ISSN: 2414-3146

Volume 3| Part 2| February 2018| x180216

https://doi.org/10.1107/S241431461800216X

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Crystal structure of ω-Al₄Cr

Changzeng Fan ^a ^* and Cong Liu ^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 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.

Keywords: high-pressure sintering; intermetallics; crystal structure; polymorphism.

CCDC reference: 1822152

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 ). 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 ). 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 ). 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) and single-crystal X-ray diffraction (Cao & Kuo, 2008 ). 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 )) and Al₄Mo (Leake, 1964 ). The Al and Cr atoms are arranged in sets of almost close-packed puckered planes arranged perpendicular to [010]. Fig. 1 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). Two (Al1 and Al2) of the seven unique aluminium atoms are also located on a mirror plane.

Figure 1
The crystal structure of ω-Al₄Cr with coordination polyhedra displayed for Cr1 (gold) and Cr2 (pale blue).

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. 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
M_r	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)
V (Å³)	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 )
T_min, T_max	0.757, 0.870
No. of measured, independent and observed [I > 2σ(I)] reflections	4792, 1200, 967
R_int	0.068
(sin θ/λ)_max (Å⁻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
Δρ_max, Δρ_min (e Å⁻³)	0.85, −1.20
Absolute structure	Flack (1983 ); 584 Friedel pairs
Absolute structure parameter	0.16 (7)
Computer programs: APEX3 and SAINT (Bruker, 2015 ), SHELXT2014 (Sheldrick, 2015a ), SHELXL2014 (Sheldrick, 2015b ), DIAMOND (Brandenburg & Putz, 2017 ) and publCIF (Westrip, 2010 ).

Structural data

CCDC reference: 1822152

Crystal structure: contains datablocks global, I. DOI: https://doi.org/10.1107/S241431461800216X/wm4068sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S241431461800216X/wm4068Isup2.hkl

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: 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

Al₄Cr	F(000) = 456
M_r = 159.92	D_x = 3.529 Mg m⁻³
Monoclinic, Cm	Mo Kα radiation, λ = 0.71073 Å
a = 5.1574 (6) Å	Cell parameters from 1199 reflections
b = 17.413 (2) Å	θ = 4.1–27.0°
c = 5.1107 (7) Å	µ = 4.65 mm⁻¹
β = 100.357 (4)°	T = 293 K
V = 451.49 (10) Å³	Fragment, metallic
Z = 6	0.07 × 0.05 × 0.03 mm

Data collection top

Bruker APEXII Photon 100 COMS diffractometer	1200 independent reflections
Graphite monochromator	967 reflections with I > 2σ(I)
Detector resolution: 10.4167 pixels mm^-1	R_int = 0.068
phi and ω scans	θ_max = 28.9°, θ_min = 2.3°
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	h = −6→7
T_min = 0.757, T_max = 0.870	k = −23→21
4792 measured reflections	l = −6→6

Refinement top

Refinement on F²	2 restraints
Least-squares matrix: full	w = 1/[σ²(F_o²) + (0.032P)² + 2.4184P] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.047	(Δ/σ)_max < 0.001
wR(F²) = 0.090	Δρ_max = 0.85 e Å⁻³
S = 1.05	Δρ_min = −1.20 e Å⁻³
1200 reflections	Absolute structure: Flack (1983); 584 Friedel pairs
74 parameters	Absolute 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

	x	y	z	U_iso*/U_eq
Cr1	0.9253 (3)	0.36325 (9)	0.8089 (3)	0.0047 (4)
Al1	0.7655 (11)	0.5	−0.0048 (11)	0.0092 (13)
Cr2	0.2728 (5)	0.5	0.1495 (5)	0.0055 (6)
Al2	0.1177 (11)	0.5	0.6353 (10)	0.0099 (13)
Al4	0.4332 (8)	0.3817 (2)	−0.0771 (7)	0.0098 (9)
Al3	0.0753 (7)	0.3773 (2)	0.3243 (7)	0.0090 (9)
Al5	0.6001 (9)	0.4235 (2)	0.4558 (8)	0.0114 (8)
Al6	0.5715 (7)	0.2664 (2)	0.5621 (8)	0.0126 (9)
Al7	0.7391 (7)	0.2538 (2)	1.0760 (8)	0.0087 (8)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Cr1	0.0051 (10)	0.0072 (8)	0.0011 (8)	−0.0002 (8)	−0.0012 (7)	0.0000 (7)
Al1	0.007 (3)	0.009 (3)	0.013 (3)	0	0.005 (2)	0
Cr2	0.0089 (16)	0.0057 (11)	0.0017 (14)	0	0.0009 (11)	0
Al2	0.016 (4)	0.011 (3)	0.002 (3)	0	−0.001 (2)	0
Al4	0.012 (2)	0.0110 (18)	0.007 (2)	−0.0003 (14)	0.0014 (17)	−0.0007 (15)
Al3	0.012 (2)	0.0102 (18)	0.005 (2)	−0.0015 (14)	0.0033 (17)	−0.0007 (14)
Al5	0.0087 (16)	0.0168 (18)	0.0079 (17)	−0.0003 (15)	−0.0006 (13)	0.0049 (15)
Al6	0.014 (2)	0.0132 (18)	0.011 (2)	−0.0018 (15)	0.0029 (18)	−0.0032 (16)
Al7	0.0030 (19)	0.0126 (17)	0.011 (2)	0.0026 (15)	0.0031 (14)	0.0046 (14)

Geometric parameters (Å, º) top

Cr1—Al5	2.467 (5)	Al2—Al5^xi	2.977 (7)
Cr1—Al4ⁱ	2.599 (5)	Al4—Cr1^xiv	2.599 (5)
Cr1—Al3ⁱ	2.620 (4)	Al4—Cr1^vi	2.723 (5)
Cr1—Al7	2.625 (4)	Al4—Al7^xv	2.731 (5)
Cr1—Al6	2.634 (4)	Al4—Al7^vi	2.759 (6)
Cr1—Al4ⁱⁱ	2.723 (5)	Al4—Al5^vi	2.777 (6)
Cr1—Al3ⁱⁱⁱ	2.735 (4)	Al4—Al5	2.801 (5)
Cr1—Al1ⁱⁱ	2.745 (3)	Al4—Al2^vi	2.862 (6)
Cr1—Al6^iv	2.757 (4)	Al4—Al6^vi	2.900 (5)
Cr1—Al2ⁱⁱⁱ	2.786 (3)	Al4—Al3	2.997 (5)
Cr1—Al7^iv	2.800 (4)	Al3—Cr1^xiv	2.620 (4)
Al1—Cr2ⁱⁱⁱ	2.593 (6)	Al3—Cr1^x	2.735 (4)
Al1—Al4	2.663 (5)	Al3—Al5^x	2.775 (6)
Al1—Al4^v	2.663 (5)	Al3—Al6^xvi	2.783 (5)
Al1—Cr1^vi	2.745 (3)	Al3—Al5	2.788 (6)
Al1—Cr1^vii	2.745 (3)	Al3—Al7^xv	2.814 (5)
Al1—Cr2	2.793 (6)	Al3—Al7^xiv	2.907 (5)
Al1—Al2^viii	2.808 (7)	Al3—Al1^x	2.997 (5)
Al1—Al5^v	2.960 (7)	Al5—Al5^v	2.663 (7)
Al1—Al5	2.960 (7)	Al5—Al3ⁱⁱⁱ	2.775 (6)
Al1—Al3^ix	2.997 (5)	Al5—Al4ⁱⁱ	2.777 (6)
Al1—Al3ⁱⁱⁱ	2.997 (5)	Al5—Al6	2.799 (5)
Cr2—Al5	2.474 (5)	Al5—Al2ⁱⁱⁱ	2.977 (7)
Cr2—Al5^v	2.474 (5)	Al6—Al7	2.622 (5)
Cr2—Al4	2.572 (4)	Al6—Al6^xvi	2.6413 (17)
Cr2—Al4^v	2.572 (4)	Al6—Al6^iv	2.6413 (17)
Cr2—Al1^x	2.593 (6)	Al6—Cr1^xvi	2.757 (4)
Cr2—Al3	2.594 (4)	Al6—Al7^xv	2.776 (5)
Cr2—Al3^v	2.594 (4)	Al6—Al7^vi	2.782 (5)
Cr2—Al2^vi	2.606 (6)	Al6—Al3^iv	2.783 (5)
Cr2—Al2	2.742 (6)	Al6—Al4ⁱⁱ	2.900 (5)
Al2—Cr2ⁱⁱ	2.606 (6)	Al7—Al7^xvi	2.5821 (5)
Al2—Al3	2.648 (4)	Al7—Al7^iv	2.5821 (5)
Al2—Al3^v	2.648 (4)	Al7—Al4^xvii	2.731 (5)
Al2—Cr1^x	2.786 (3)	Al7—Al4ⁱⁱ	2.759 (6)
Al2—Cr1^xi	2.786 (3)	Al7—Al6^xvii	2.776 (5)
Al2—Al1^xii	2.808 (7)	Al7—Al6ⁱⁱ	2.782 (5)
Al2—Al4^xiii	2.862 (6)	Al7—Cr1^xvi	2.800 (4)
Al2—Al4ⁱⁱ	2.862 (6)	Al7—Al3^xvii	2.814 (5)
Al2—Al5^x	2.977 (7)	Al7—Al3ⁱ	2.907 (5)

Al5—Cr1—Al4ⁱ	129.56 (15)	Al1—Al4—Al5	65.55 (16)
Al5—Cr1—Al3ⁱ	137.30 (14)	Cr1^vi—Al4—Al5	95.93 (16)
Al4ⁱ—Cr1—Al3ⁱ	70.10 (12)	Al7^xv—Al4—Al5	90.61 (17)
Al5—Cr1—Al7	115.17 (14)	Al7^vi—Al4—Al5	82.78 (15)
Al4ⁱ—Cr1—Al7	114.91 (13)	Al5^vi—Al4—Al5	132.8 (2)
Al3ⁱ—Cr1—Al7	67.32 (13)	Cr2—Al4—Al2^vi	57.00 (13)
Al5—Cr1—Al6	66.46 (13)	Cr1^xiv—Al4—Al2^vi	61.11 (13)
Al4ⁱ—Cr1—Al6	140.34 (15)	Al1—Al4—Al2^vi	78.84 (17)
Al3ⁱ—Cr1—Al6	126.53 (15)	Cr1^vi—Al4—Al2^vi	116.13 (19)
Al7—Cr1—Al6	59.83 (12)	Al7^xv—Al4—Al2^vi	124.41 (18)
Al5—Cr1—Al4ⁱⁱ	64.48 (14)	Al7^vi—Al4—Al2^vi	165.8 (2)
Al4ⁱ—Cr1—Al4ⁱⁱ	151.41 (17)	Al5^vi—Al4—Al2^vi	66.73 (17)
Al3ⁱ—Cr1—Al4ⁱⁱ	83.80 (14)	Al5—Al4—Al2^vi	111.02 (18)
Al7—Cr1—Al4ⁱⁱ	62.09 (13)	Cr2—Al4—Al6^vi	167.55 (18)
Al6—Cr1—Al4ⁱⁱ	65.53 (13)	Cr1^xiv—Al4—Al6^vi	97.20 (15)
Al5—Cr1—Al3ⁱⁱⁱ	64.23 (13)	Al1—Al4—Al6^vi	113.44 (16)
Al4ⁱ—Cr1—Al3ⁱⁱⁱ	75.77 (13)	Cr1^vi—Al4—Al6^vi	55.75 (10)
Al3ⁱ—Cr1—Al3ⁱⁱⁱ	145.25 (18)	Al7^xv—Al4—Al6^vi	74.30 (14)
Al7—Cr1—Al3ⁱⁱⁱ	136.50 (13)	Al7^vi—Al4—Al6^vi	55.14 (13)
Al6—Cr1—Al3ⁱⁱⁱ	84.71 (13)	Al5^vi—Al4—Al6^vi	59.02 (12)
Al4ⁱⁱ—Cr1—Al3ⁱⁱⁱ	127.55 (13)	Al5—Al4—Al6^vi	136.94 (19)
Al5—Cr1—Al1ⁱⁱ	71.19 (15)	Al2^vi—Al4—Al6^vi	110.72 (16)
Al4ⁱ—Cr1—Al1ⁱⁱ	99.70 (15)	Cr2—Al4—Al3	54.88 (12)
Al3ⁱ—Cr1—Al1ⁱⁱ	67.87 (15)	Cr1^xiv—Al4—Al3	55.28 (12)
Al7—Cr1—Al1ⁱⁱ	106.78 (14)	Al1—Al4—Al3	112.64 (17)
Al6—Cr1—Al1ⁱⁱ	119.74 (17)	Cr1^vi—Al4—Al3	148.85 (17)
Al4ⁱⁱ—Cr1—Al1ⁱⁱ	58.29 (14)	Al7^xv—Al4—Al3	58.63 (13)
Al3ⁱⁱⁱ—Cr1—Al1ⁱⁱ	112.82 (14)	Al7^vi—Al4—Al3	100.16 (16)
Al5—Cr1—Al6^iv	102.70 (13)	Al5^vi—Al4—Al3	156.84 (19)
Al4ⁱ—Cr1—Al6^iv	81.72 (14)	Al5—Al4—Al3	57.35 (14)
Al3ⁱ—Cr1—Al6^iv	118.74 (12)	Al2^vi—Al4—Al3	90.38 (17)
Al7—Cr1—Al6^iv	78.41 (12)	Al6^vi—Al4—Al3	132.06 (19)
Al6—Cr1—Al6^iv	58.63 (6)	Cr2—Al3—Cr1^xiv	78.09 (12)
Al4ⁱⁱ—Cr1—Al6^iv	122.44 (13)	Cr2—Al3—Al2	63.06 (14)
Al3ⁱⁱⁱ—Cr1—Al6^iv	60.90 (13)	Cr1^xiv—Al3—Al2	131.01 (16)
Al1ⁱⁱ—Cr1—Al6^iv	173.15 (16)	Cr2—Al3—Cr1^x	125.32 (15)
Al5—Cr1—Al2ⁱⁱⁱ	68.74 (15)	Cr1^xiv—Al3—Cr1^x	145.25 (18)
Al4ⁱ—Cr1—Al2ⁱⁱⁱ	64.12 (15)	Al2—Al3—Cr1^x	62.30 (11)
Al3ⁱ—Cr1—Al2ⁱⁱⁱ	100.53 (14)	Cr2—Al3—Al5^x	105.24 (15)
Al7—Cr1—Al2ⁱⁱⁱ	166.17 (15)	Cr1^xiv—Al3—Al5^x	99.00 (15)
Al6—Cr1—Al2ⁱⁱⁱ	130.59 (15)	Al2—Al3—Al5^x	66.54 (15)
Al4ⁱⁱ—Cr1—Al2ⁱⁱⁱ	111.51 (15)	Cr1^x—Al3—Al5^x	53.19 (12)
Al3ⁱⁱⁱ—Cr1—Al2ⁱⁱⁱ	57.33 (13)	Cr2—Al3—Al6^xvi	157.66 (18)
Al1ⁱⁱ—Cr1—Al2ⁱⁱⁱ	61.01 (13)	Cr1^xiv—Al3—Al6^xvi	109.33 (15)
Al6^iv—Cr1—Al2ⁱⁱⁱ	114.33 (15)	Al2—Al3—Al6^xvi	118.01 (14)
Al5—Cr1—Al7^iv	157.49 (13)	Cr1^x—Al3—Al6^xvi	59.94 (11)
Al4ⁱ—Cr1—Al7^iv	60.64 (11)	Al5^x—Al3—Al6^xvi	94.56 (15)
Al3ⁱ—Cr1—Al7^iv	62.45 (12)	Cr2—Al3—Al5	54.60 (13)
Al7—Cr1—Al7^iv	56.73 (6)	Cr1^xiv—Al3—Al5	111.56 (17)
Al6—Cr1—Al7^iv	93.29 (13)	Al2—Al3—Al5	69.54 (16)
Al4ⁱⁱ—Cr1—Al7^iv	117.42 (13)	Cr1^x—Al3—Al5	103.18 (15)
Al3ⁱⁱⁱ—Cr1—Al7^iv	105.89 (12)	Al5^x—Al3—Al5	136.00 (19)
Al1ⁱⁱ—Cr1—Al7^iv	130.20 (15)	Al6^xvi—Al3—Al5	103.72 (16)
Al6^iv—Cr1—Al7^iv	56.31 (12)	Cr2—Al3—Al7^xv	110.15 (17)
Al2ⁱⁱⁱ—Cr1—Al7^iv	124.73 (15)	Cr1^xiv—Al3—Al7^xv	61.92 (12)
Cr2ⁱⁱⁱ—Al1—Al4	129.13 (11)	Al2—Al3—Al7^xv	157.80 (19)
Cr2ⁱⁱⁱ—Al1—Al4^v	129.13 (11)	Cr1^x—Al3—Al7^xv	119.51 (15)
Al4—Al1—Al4^v	101.4 (2)	Al5^x—Al3—Al7^xv	133.98 (17)
Cr2ⁱⁱⁱ—Al1—Cr1^vi	75.88 (13)	Al6^xvi—Al3—Al7^xv	59.59 (13)
Al4—Al1—Cr1^vi	60.44 (11)	Al5—Al3—Al7^xv	89.19 (16)
Al4^v—Al1—Cr1^vi	148.1 (2)	Cr2—Al3—Al7^xiv	134.37 (17)
Cr2ⁱⁱⁱ—Al1—Cr1^vii	75.88 (13)	Cr1^xiv—Al3—Al7^xiv	56.42 (11)
Al4—Al1—Cr1^vii	148.1 (2)	Al2—Al3—Al7^xiv	146.85 (17)
Al4^v—Al1—Cr1^vii	60.44 (11)	Cr1^x—Al3—Al7^xiv	94.91 (14)
Cr1^vi—Al1—Cr1^vii	120.3 (2)	Al5^x—Al3—Al7^xiv	80.61 (14)
Cr2ⁱⁱⁱ—Al1—Cr2	146.5 (2)	Al6^xvi—Al3—Al7^xiv	58.34 (12)
Al4—Al1—Cr2	56.19 (11)	Al5—Al3—Al7^xiv	142.75 (18)
Al4^v—Al1—Cr2	56.19 (11)	Al7^xv—Al3—Al7^xiv	53.63 (8)
Cr1^vi—Al1—Cr2	116.29 (13)	Cr2—Al3—Al1^x	54.69 (12)
Cr1^vii—Al1—Cr2	116.29 (13)	Cr1^xiv—Al3—Al1^x	58.06 (12)
Cr2ⁱⁱⁱ—Al1—Al2^viii	57.52 (17)	Al2—Al3—Al1^x	74.92 (14)
Al4—Al1—Al2^viii	112.66 (15)	Cr1^x—Al3—Al1^x	111.29 (16)
Al4^v—Al1—Al2^viii	112.65 (15)	Al5^x—Al3—Al1^x	61.57 (16)
Cr1^vi—Al1—Al2^viii	60.20 (12)	Al6^xvi—Al3—Al1^x	147.27 (18)
Cr1^vii—Al1—Al2^viii	60.20 (12)	Al5—Al3—Al1^x	109.01 (16)
Cr2—Al1—Al2^viii	156.0 (2)	Al7^xv—Al3—Al1^x	119.87 (16)
Cr2ⁱⁱⁱ—Al1—Al5^v	100.2 (2)	Al7^xiv—Al3—Al1^x	93.81 (16)
Al4—Al1—Al5^v	100.83 (18)	Cr2—Al3—Al4	54.20 (12)
Al4^v—Al1—Al5^v	59.47 (12)	Cr1^xiv—Al3—Al4	54.62 (12)
Cr1^vi—Al1—Al5^v	144.40 (18)	Al2—Al3—Al4	113.30 (17)
Cr1^vii—Al1—Al5^v	91.89 (10)	Cr1^x—Al3—Al4	158.64 (17)
Cr2—Al1—Al5^v	50.84 (13)	Al5^x—Al3—Al4	146.91 (18)
Al2^viii—Al1—Al5^v	146.48 (16)	Al6^xvi—Al3—Al4	112.03 (17)
Cr2ⁱⁱⁱ—Al1—Al5	100.2 (2)	Al5—Al3—Al4	57.78 (13)
Al4—Al1—Al5	59.47 (12)	Al7^xv—Al3—Al4	55.96 (13)
Al4^v—Al1—Al5	100.83 (18)	Al7^xiv—Al3—Al4	96.45 (16)
Cr1^vi—Al1—Al5	91.89 (10)	Al1^x—Al3—Al4	85.95 (14)
Cr1^vii—Al1—Al5	144.40 (18)	Cr1—Al5—Cr2	171.39 (18)
Cr2—Al1—Al5	50.84 (13)	Cr1—Al5—Al5^v	115.19 (9)
Al2^viii—Al1—Al5	146.48 (16)	Cr2—Al5—Al5^v	57.45 (9)
Al5^v—Al1—Al5	53.45 (17)	Cr1—Al5—Al3ⁱⁱⁱ	62.58 (13)
Cr2ⁱⁱⁱ—Al1—Al3^ix	54.72 (12)	Cr2—Al5—Al3ⁱⁱⁱ	122.34 (19)
Al4—Al1—Al3^ix	153.4 (2)	Al5^v—Al5—Al3ⁱⁱⁱ	106.88 (10)
Al4^v—Al1—Al3^ix	77.94 (11)	Cr1—Al5—Al4ⁱⁱ	62.24 (13)
Cr1^vi—Al1—Al3^ix	130.5 (2)	Cr2—Al5—Al4ⁱⁱ	113.8 (2)
Cr1^vii—Al1—Al3^ix	54.08 (10)	Al5^v—Al5—Al4ⁱⁱ	105.23 (11)
Cr2—Al1—Al3^ix	105.18 (15)	Al3ⁱⁱⁱ—Al5—Al4ⁱⁱ	123.76 (18)
Al2^viii—Al1—Al3^ix	91.45 (17)	Cr1—Al5—Al3	123.80 (17)
Al5^v—Al1—Al3^ix	55.51 (13)	Cr2—Al5—Al3	58.71 (14)
Al5—Al1—Al3^ix	94.30 (18)	Al5^v—Al5—Al3	106.79 (10)
Cr2ⁱⁱⁱ—Al1—Al3ⁱⁱⁱ	54.72 (12)	Al3ⁱⁱⁱ—Al5—Al3	136.00 (19)
Al4—Al1—Al3ⁱⁱⁱ	77.94 (11)	Al4ⁱⁱ—Al5—Al3	72.16 (16)
Al4^v—Al1—Al3ⁱⁱⁱ	153.4 (2)	Cr1—Al5—Al6	59.63 (11)
Cr1^vi—Al1—Al3ⁱⁱⁱ	54.08 (10)	Cr2—Al5—Al6	126.52 (17)
Cr1^vii—Al1—Al3ⁱⁱⁱ	130.5 (2)	Al5^v—Al5—Al6	167.87 (12)
Cr2—Al1—Al3ⁱⁱⁱ	105.18 (15)	Al3ⁱⁱⁱ—Al5—Al6	80.95 (15)
Al2^viii—Al1—Al3ⁱⁱⁱ	91.45 (17)	Al4ⁱⁱ—Al5—Al6	62.68 (14)
Al5^v—Al1—Al3ⁱⁱⁱ	94.30 (18)	Al3—Al5—Al6	71.44 (14)
Al5—Al1—Al3ⁱⁱⁱ	55.51 (13)	Cr1—Al5—Al4	130.56 (18)
Al3^ix—Al1—Al3ⁱⁱⁱ	91.0 (2)	Cr2—Al5—Al4	57.96 (13)
Al5—Cr2—Al5^v	65.10 (18)	Al5^v—Al5—Al4	105.09 (11)
Al5—Cr2—Al4	67.40 (13)	Al3ⁱⁱⁱ—Al5—Al4	79.60 (16)
Al5^v—Cr2—Al4	118.54 (17)	Al4ⁱⁱ—Al5—Al4	132.8 (2)
Al5—Cr2—Al4^v	118.54 (17)	Al3—Al5—Al4	64.86 (14)
Al5^v—Cr2—Al4^v	67.40 (13)	Al6—Al5—Al4	85.21 (15)
Al4—Cr2—Al4^v	106.5 (2)	Cr1—Al5—Al1	121.2 (2)
Al5—Cr2—Al1^x	136.77 (15)	Cr2—Al5—Al1	61.08 (15)
Al5^v—Cr2—Al1^x	136.77 (15)	Al5^v—Al5—Al1	63.27 (8)
Al4—Cr2—Al1^x	104.58 (13)	Al3ⁱⁱⁱ—Al5—Al1	62.91 (15)
Al4^v—Cr2—Al1^x	104.58 (13)	Al4ⁱⁱ—Al5—Al1	168.50 (18)
Al5—Cr2—Al3	66.69 (13)	Al3—Al5—Al1	110.15 (19)
Al5^v—Cr2—Al3	119.39 (15)	Al6—Al5—Al1	128.82 (17)
Al4—Cr2—Al3	70.93 (11)	Al4—Al5—Al1	54.98 (14)
Al4^v—Cr2—Al3	173.21 (17)	Cr1—Al5—Al2ⁱⁱⁱ	60.70 (12)
Al1^x—Cr2—Al3	70.59 (12)	Cr2—Al5—Al2ⁱⁱⁱ	115.24 (16)
Al5—Cr2—Al3^v	119.39 (15)	Al5^v—Al5—Al2ⁱⁱⁱ	63.43 (9)
Al5^v—Cr2—Al3^v	66.69 (13)	Al3ⁱⁱⁱ—Al5—Al2ⁱⁱⁱ	54.70 (14)
Al4—Cr2—Al3^v	173.21 (17)	Al4ⁱⁱ—Al5—Al2ⁱⁱⁱ	104.59 (18)
Al4^v—Cr2—Al3^v	70.92 (11)	Al3—Al5—Al2ⁱⁱⁱ	168.98 (19)
Al1^x—Cr2—Al3^v	70.59 (12)	Al6—Al5—Al2ⁱⁱⁱ	116.93 (16)
Al3—Cr2—Al3^v	110.9 (2)	Al4—Al5—Al2ⁱⁱⁱ	121.2 (2)
Al5—Cr2—Al2^vi	133.53 (15)	Al1—Al5—Al2ⁱⁱⁱ	70.93 (17)
Al5^v—Cr2—Al2^vi	133.53 (15)	Al7—Al6—Cr1	59.92 (12)
Al4—Cr2—Al2^vi	67.12 (12)	Al7—Al6—Al6^xvi	97.34 (13)
Al4^v—Cr2—Al2^vi	67.12 (12)	Cr1—Al6—Al6^xvi	136.96 (18)
Al1^x—Cr2—Al2^vi	65.38 (17)	Al7—Al6—Al6^iv	80.56 (13)
Al3—Cr2—Al2^vi	106.21 (13)	Cr1—Al6—Al6^iv	63.02 (12)
Al3^v—Cr2—Al2^vi	106.21 (12)	Al6^xvi—Al6—Al6^iv	155.0 (3)
Al5—Cr2—Al2	72.78 (16)	Al7—Al6—Cr1^xvi	62.68 (13)
Al5^v—Cr2—Al2	72.78 (16)	Cr1—Al6—Cr1^xvi	121.88 (17)
Al4—Cr2—Al2	125.27 (10)	Al6^xvi—Al6—Cr1^xvi	58.35 (14)
Al4^v—Cr2—Al2	125.27 (10)	Al6^iv—Al6—Cr1^xvi	99.80 (19)
Al1^x—Cr2—Al2	80.38 (19)	Al7—Al6—Al7^xv	157.7 (2)
Al3—Cr2—Al2	59.44 (11)	Cr1—Al6—Al7^xv	140.64 (18)
Al3^v—Cr2—Al2	59.44 (11)	Al6^xvi—Al6—Al7^xv	61.74 (11)
Al2^vi—Cr2—Al2	145.8 (3)	Al6^iv—Al6—Al7^xv	114.75 (13)
Al5—Cr2—Al1	68.08 (16)	Cr1^xvi—Al6—Al7^xv	97.46 (15)
Al5^v—Cr2—Al1	68.08 (16)	Al7—Al6—Al7^vi	142.0 (2)
Al4—Cr2—Al1	59.35 (11)	Cr1—Al6—Al7^vi	100.29 (16)
Al4^v—Cr2—Al1	59.35 (11)	Al6^xvi—Al6—Al7^vi	116.29 (12)
Al1^x—Cr2—Al1	146.5 (2)	Al6^iv—Al6—Al7^vi	61.50 (12)
Al3—Cr2—Al1	122.06 (10)	Cr1^xvi—Al6—Al7^vi	119.89 (15)
Al3^v—Cr2—Al1	122.06 (10)	Al7^xv—Al6—Al7^vi	55.37 (10)
Al2^vi—Cr2—Al1	81.1 (2)	Al7—Al6—Al3^iv	109.57 (18)
Al2—Cr2—Al1	133.15 (19)	Cr1—Al6—Al3^iv	136.57 (17)
Cr2ⁱⁱ—Al2—Al3	125.62 (10)	Al6^xvi—Al6—Al3^iv	83.61 (18)
Cr2ⁱⁱ—Al2—Al3^v	125.62 (10)	Al6^iv—Al6—Al3^iv	73.86 (18)
Al3—Al2—Al3^v	107.6 (2)	Cr1^xvi—Al6—Al3^iv	59.16 (13)
Cr2ⁱⁱ—Al2—Cr2	145.8 (3)	Al7^xv—Al6—Al3^iv	63.06 (13)
Al3—Al2—Cr2	57.50 (10)	Al7^vi—Al6—Al3^iv	60.76 (12)
Al3^v—Al2—Cr2	57.50 (10)	Al7—Al6—Al5	104.89 (15)
Cr2ⁱⁱ—Al2—Cr1^x	74.99 (13)	Cr1—Al6—Al5	53.91 (11)
Al3—Al2—Cr1^x	60.38 (9)	Al6^xvi—Al6—Al5	107.3 (2)
Al3^v—Al2—Cr1^x	152.3 (2)	Al6^iv—Al6—Al5	97.3 (2)
Cr2—Al2—Cr1^x	117.84 (11)	Cr1^xvi—Al6—Al5	156.61 (19)
Cr2ⁱⁱ—Al2—Cr1^xi	74.99 (13)	Al7^xv—Al6—Al5	89.76 (16)
Al3—Al2—Cr1^xi	152.3 (2)	Al7^vi—Al6—Al5	82.42 (16)
Al3^v—Al2—Cr1^xi	60.38 (9)	Al3^iv—Al6—Al5	142.13 (18)
Cr2—Al2—Cr1^xi	117.84 (11)	Al7—Al6—Al4ⁱⁱ	59.71 (13)
Cr1^x—Al2—Cr1^xi	117.5 (2)	Cr1—Al6—Al4ⁱⁱ	58.72 (13)
Cr2ⁱⁱ—Al2—Al1^xii	57.10 (17)	Al6^xvi—Al6—Al4ⁱⁱ	78.34 (14)
Al3—Al2—Al1^xii	113.55 (14)	Al6^iv—Al6—Al4ⁱⁱ	120.11 (16)
Al3^v—Al2—Al1^xii	113.55 (14)	Cr1^xvi—Al6—Al4ⁱⁱ	99.03 (15)
Cr2—Al2—Al1^xii	157.1 (3)	Al7^xv—Al6—Al4ⁱⁱ	118.28 (17)
Cr1^x—Al2—Al1^xii	58.79 (11)	Al7^vi—Al6—Al4ⁱⁱ	140.71 (17)
Cr1^xi—Al2—Al1^xii	58.79 (11)	Al3^iv—Al6—Al4ⁱⁱ	157.15 (18)
Cr2ⁱⁱ—Al2—Al4^xiii	55.88 (12)	Al5—Al6—Al4ⁱⁱ	58.30 (13)
Al3—Al2—Al4^xiii	150.1 (2)	Al7^xvi—Al7—Al7^iv	174.1 (3)
Al3^v—Al2—Al4^xiii	72.86 (11)	Al7^xvi—Al7—Al6	81.67 (12)
Cr2—Al2—Al4^xiii	103.51 (17)	Al7^iv—Al7—Al6	98.83 (12)
Cr1^x—Al2—Al4^xiii	130.8 (2)	Al7^xvi—Al7—Cr1	119.74 (17)
Cr1^xi—Al2—Al4^xiii	54.77 (10)	Al7^iv—Al7—Cr1	65.06 (13)
Al1^xii—Al2—Al4^xiii	92.21 (16)	Al6—Al7—Cr1	60.25 (12)
Cr2ⁱⁱ—Al2—Al4ⁱⁱ	55.88 (12)	Al7^xvi—Al7—Al4^xvii	111.92 (19)
Al3—Al2—Al4ⁱⁱ	72.86 (11)	Al7^iv—Al7—Al4^xvii	62.50 (16)
Al3^v—Al2—Al4ⁱⁱ	150.1 (2)	Al6—Al7—Al4^xvii	81.79 (16)
Cr2—Al2—Al4ⁱⁱ	103.51 (17)	Cr1—Al7—Al4^xvii	106.91 (15)
Cr1^x—Al2—Al4ⁱⁱ	54.77 (10)	Al7^xvi—Al7—Al4ⁱⁱ	61.40 (14)
Cr1^xi—Al2—Al4ⁱⁱ	130.8 (2)	Al7^iv—Al7—Al4ⁱⁱ	124.2 (2)
Al1^xii—Al2—Al4ⁱⁱ	92.21 (16)	Al6—Al7—Al4ⁱⁱ	65.15 (14)
Al4^xiii—Al2—Al4ⁱⁱ	92.1 (2)	Cr1—Al7—Al4ⁱⁱ	60.70 (13)
Cr2ⁱⁱ—Al2—Al5^x	114.0 (2)	Al4^xvii—Al7—Al4ⁱⁱ	146.7 (2)
Al3—Al2—Al5^x	58.76 (12)	Al7^xvi—Al7—Al6^xvii	116.73 (12)
Al3^v—Al2—Al5^x	101.71 (18)	Al7^iv—Al7—Al6^xvii	62.43 (12)
Cr2—Al2—Al5^x	96.44 (18)	Al6—Al7—Al6^xvii	161.1 (2)
Cr1^x—Al2—Al5^x	50.56 (11)	Cr1—Al7—Al6^xvii	109.43 (16)
Cr1^xi—Al2—Al5^x	97.43 (19)	Al4^xvii—Al7—Al6^xvii	87.00 (15)
Al1^xii—Al2—Al5^x	63.38 (18)	Al4ⁱⁱ—Al7—Al6^xvii	125.86 (18)
Al4^xiii—Al2—Al5^x	151.1 (2)	Al7^xvi—Al7—Al6ⁱⁱ	62.19 (12)
Al4ⁱⁱ—Al2—Al5^x	103.40 (12)	Al7^iv—Al7—Al6ⁱⁱ	118.33 (12)
Cr2ⁱⁱ—Al2—Al5^xi	114.0 (2)	Al6—Al7—Al6ⁱⁱ	142.0 (2)
Al3—Al2—Al5^xi	101.71 (18)	Cr1—Al7—Al6ⁱⁱ	127.48 (16)
Al3^v—Al2—Al5^xi	58.76 (12)	Al4^xvii—Al7—Al6ⁱⁱ	120.85 (16)
Cr2—Al2—Al5^xi	96.44 (18)	Al4ⁱⁱ—Al7—Al6ⁱⁱ	86.33 (16)
Cr1^x—Al2—Al5^xi	97.43 (19)	Al6^xvii—Al7—Al6ⁱⁱ	56.76 (11)
Cr1^xi—Al2—Al5^xi	50.56 (11)	Al7^xvi—Al7—Cr1^xvi	58.21 (12)
Al1^xii—Al2—Al5^xi	63.38 (18)	Al7^iv—Al7—Cr1^xvi	116.89 (18)
Al4^xiii—Al2—Al5^xi	103.40 (12)	Al6—Al7—Cr1^xvi	61.01 (13)
Al4ⁱⁱ—Al2—Al5^xi	151.1 (2)	Cr1—Al7—Cr1^xvi	120.55 (16)
Al5^x—Al2—Al5^xi	53.13 (18)	Al4^xvii—Al7—Cr1^xvi	56.03 (11)
Cr2—Al4—Cr1^xiv	78.87 (14)	Al4ⁱⁱ—Al7—Cr1^xvi	101.43 (14)
Cr2—Al4—Al1	64.46 (15)	Al6^xvii—Al7—Cr1^xvi	123.63 (16)
Cr1^xiv—Al4—Al1	136.39 (17)	Al6ⁱⁱ—Al7—Cr1^xvi	104.35 (14)
Cr2—Al4—Cr1^vi	125.33 (17)	Al7^xvi—Al7—Al3^xvii	65.02 (15)
Cr1^xiv—Al4—Cr1^vi	151.41 (17)	Al7^iv—Al7—Al3^xvii	109.8 (2)
Al1—Al4—Cr1^vi	61.28 (11)	Al6—Al7—Al3^xvii	116.62 (18)
Cr2—Al4—Al7^xv	113.50 (17)	Cr1—Al7—Al3^xvii	172.32 (17)
Cr1^xiv—Al4—Al7^xv	63.33 (12)	Al4^xvii—Al7—Al3^xvii	65.41 (12)
Al1—Al4—Al7^xv	152.67 (18)	Al4ⁱⁱ—Al7—Al3^xvii	125.43 (18)
Cr1^vi—Al4—Al7^xv	111.30 (15)	Al6^xvii—Al7—Al3^xvii	71.38 (15)
Cr2—Al4—Al7^vi	137.10 (18)	Al6ⁱⁱ—Al7—Al3^xvii	59.65 (13)
Cr1^xiv—Al4—Al7^vi	117.76 (18)	Cr1^xvi—Al7—Al3^xvii	55.63 (11)
Al1—Al4—Al7^vi	105.31 (14)	Al7^xvi—Al7—Al3ⁱ	123.73 (19)
Cr1^vi—Al4—Al7^vi	57.20 (10)	Al7^iv—Al7—Al3ⁱ	61.35 (15)
Al7^xv—Al4—Al7^vi	56.10 (9)	Al6—Al7—Al3ⁱ	116.01 (16)
Cr2—Al4—Al5^vi	110.56 (17)	Cr1—Al7—Al3ⁱ	56.26 (11)
Cr1^xiv—Al4—Al5^vi	107.18 (16)	Al4^xvii—Al7—Al3ⁱ	122.91 (17)
Al1—Al4—Al5^vi	67.96 (17)	Al4ⁱⁱ—Al7—Al3ⁱ	78.04 (15)
Cr1^vi—Al4—Al5^vi	53.28 (13)	Al6^xvii—Al7—Al3ⁱ	58.60 (13)
Al7^xv—Al4—Al5^vi	131.25 (17)	Al6ⁱⁱ—Al7—Al3ⁱ	78.95 (15)
Al7^vi—Al4—Al5^vi	101.88 (17)	Cr1^xvi—Al7—Al3ⁱ	176.65 (17)
Cr2—Al4—Al5	54.64 (13)	Al3^xvii—Al7—Al3ⁱ	127.4 (2)
Cr1^xiv—Al4—Al5	111.79 (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, z−1; (vii) x, −y+1, z−1; (viii) x+1, y, z−1; (ix) x+1, −y+1, z; (x) x−1, y, z; (xi) x−1, −y+1, z; (xii) x−1, y, z+1; (xiii) x, −y+1, z+1; (xiv) x−1, y, z−1; (xv) x−1/2, −y+1/2, z−1; (xvi) x−1/2, −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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