Crystal structure of the Al8Cr5-type inter­metallic Al7.85Cr5.16

Geng, X.; Wen, B.; Fan, C.

doi:10.1107/S2414314620004228

inorganic compounds

IUCrDATA

ISSN: 2414-3146

Volume 5| Part 4| April 2020| x200422

https://doi.org/10.1107/S2414314620004228

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Crystal structure of the Al₈Cr₅-type intermetallic Al_7.85Cr_5.16

Xu Geng,^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 24 December 2019; accepted 27 March 2020; online 9 April 2020)

An aluminium-deficient Al₈Cr₅-type intermetallic with formula Al_7.85Cr_5.16 (octaaluminium pentachromium) was uncovered when high-pressure sintering of a mixture with composition Al₁₁Cr₄ was carried out. Structure analysis reveals that there are three co-occupied positions with refined occupancy factors for Al atoms being 0.958, 0.772 and 1/2. The present phase is confirmed to be isotypic with the previously reported rhombohedral Al₈Cr₅ ordered phase [Bradley & Lu (1937). Z. Kristallogr. 96, 20–37] and structurally closely related to the disordered phases of rhombohedral Al₁₆Cr_9.5 and cubic Al₈Cr₅.

Keywords: crystal structure; high-pressure sintering; intermetallic; γ-brass phase.

CCDC reference: 1993113

Structure description

The γ₂-Al₈Cr₅ phase (hereafter named as the γ₂ phase) was determined to have a γ-brass-like structure by powder diffraction photographs. This phase was found in slowly cooled chromium–aluminium alloys (Bradley & Lu, 1937 ). Although the same clusters of 26 atoms are found in the γ₂ phase, the atomic arrangement in the γ₂ phase is much more complex than that of the γ-brass, and results in a rhombohedral rather than cubic symmetry (Bradley & Lu, 1937). A high-temperature γ₁ phase was also reported to be stable between 1350 and 980°C at the same composition (Bradley & Lu, 1937) and its structure has been redetermined by single-crystal methods for a sample sintered at 1000°C for 6 h and re-annealed at 1215°C for 287 h (Brandon et al., 1977 ). As a result of the close agreement of Brandon's analysis with that of Bradley & Lu, it was suggested that either the structure of γ₁ and γ₂ are very similar, or that in the former case the crystals decomposed to γ₂ on quenching. In another work, the high-temperature γ₁ phase prepared by splat cooling was reported to be of the same type as Cu₅Zn₈, by using power diffraction data combined with electron diffraction patterns (Braun et al., 1992 ). When comparing the three aforementioned models (see Table S1 of the supporting information), it was found that there are one vacancy position and three co-occupied positions in the Brandon model, while all atomic sites are fully occupied in Bradley & Lu's model. For the convenience of comparison, the cubic Braun model was transformed to the rhombohedral description, and it was found that there are two co-occupied positions. In the study reported herein, the crystal structure of a third type of Al₈Cr₅ phase, with the refined chemical composition Al_7.85Cr_5.16 and hereafter named as γ₂′-Al₈Cr₅ phase, was determined by single-crystal X-ray diffraction measurements.

Fig. 1 shows the crystal structure of γ₂′-Al₈Cr₅ based on the standardized crystal data in the primitive trigonal setting (see Tables S2 and S3 of the supporting information). There are 78 atoms in the unit cell (a = b = 12.8717 Å, c = 7.8408 Å, α = β = 90°, γ = 120°), whose volume is three times that of the refined model (trigonal cell, rhombohedral axes, see Table 1). For simplicity, only two distorted icosahedra centred at Wyckoff sites 3a (Cr4, with coordinates 0, 0, z) are illustrated in Fig. 1, and the environment of the Cr4 atoms is shown in Fig. 2. The twelve vertices include three Al atoms (Al5), three Cr atoms (Cr6) along with six co-occupied Al/Cr sites (Al1/Cr1 and Al3/Cr3), for which the refined site occupancies converged to 0.772 (4) and 0.958 (4) for Al atoms Al1 and Al3.

Table 1
Experimental details

Crystal data
Chemical formula	Al_7.85Cr_5.16
M_r	479.72
Crystal system, space group	Trigonal, R3m:R
Temperature (K)	296
a (Å)	7.8777 (5), 7.8777 (5)
α (°)	109.566 (2)
V (Å³)	375.01 (7)
Z	2
Radiation type	Mo Kα
μ (mm⁻¹)	8.05
Crystal size (mm)	0.13 × 0.06 × 0.05

Data collection
Diffractometer	Bruker D8 Venture Photon 100 CMOS
Absorption correction	Multi-scan (SADABS; Bruker, 2015 )
T_min, T_max	0.496, 0.523
No. of measured, independent and observed [I > 2σ(I)] reflections	7330, 576, 547
R_int	0.090
(sin θ/λ)_max (Å⁻¹)	0.634

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.068, 0.178, 1.16
No. of reflections	576
No. of parameters	53
No. of restraints	37
Δρ_max, Δρ_min (e Å⁻³)	1.02, −1.27
Absolute structure	Refined as an inversion twin.
Absolute structure parameter	0.3 (2)
Computer programs: APEX3 and SAINT (Bruker, 2015), SHELXT2014/5 (Sheldrick, 2015a ), SHELXL2017/1 (Sheldrick, 2015b), DIAMOND (Brandenburg & Putz, 2017 ) and publCIF (Westrip, 2010 ).

Figure 1
The crystal structure of Al_7.85Cr_5.16. The icosahedra centred on Cr4 are emphasized.

Figure 2
The environment of the Cr4 atom. Displacement ellipsoids are given at the 99% probability level. [Symmetry codes: (i) y, z, x; (v) y, z, x.]

The principle building blocks in the structure can also be represented by four interpenetrating distorted icosahedra centred at one Cr4 and three Al3/Cr3 atomic sites, as shown in Fig. 3, similarly to the building blocks of the I-cell (space group I $[\overline{4}]$ 3m) of the γ-brass phase (Pankova et al., 2013 ). According to the topological analysis of the structure model with the `nanocluster' method available in the ToposPro package (Akhmetshina & Blatov, 2017 ), these one Cr4 and three Al3/Cr3 sites form an inner tetrahedron (IT), followed by an outer tetrahedron (OT), an octahedron (OH), whose vertices are projected onto the edges of the outer tetrahedron, and finally a distorted cuboctahedron (CO) with vertices located above the edges of the octahedron, as illustrated in Fig. 4.

Figure 3
26-atom γ-brass-type cluster represented as four interpenetrating distorted icosahedra centred at one Cr4 and three Al3/Cr3 sites.

Figure 4
26-atom γ-brass-type cluster represented as a sequence of polyhedral shells.

The present rhombohedral γ₂′-Al₈Cr₅ phase is thus confirmed to be isotypic to the previously reported ordered Al₈Cr₅ phase (Bradley & Lu, 1937), and closely related to the the disordered rhombohedral Al₁₆Cr_9.5 phase (Brandon et al., 1977) and the disordered cubic Al₈Cr₅ phase (Braun et al., 1992).

Synthesis and crystallization

The high-purity elements Al (indicated purity 99.8%, 0.588 g) and Cr (indicated purity 99.95%, 0.539 g) were mixed uniformly in the stoichiometric ratio 11:4 and thoroughly ground in an agate mortar. The blended powders were then placed in a cemented carbide grinding mould of 5 mm diameter, and pressed into a tablet at about 4 MPa for 5 min. A cylindrical block (5 mm in diameter and 3 mm in height) was obtained without deformations or cracks. Details of the high-pressure sintering experiment using a six-anvil high-temperature high-pressure apparatus can be found elsewhere (Liu & Fan, 2018 ). The samples were pressurized up to 5 GPa and heated to 1400°C for 30 minutes, slowly cooled to 660°C and held at this temperature for 2 h, and then rapidly cooled to room temperature by turning off the furnace power. Subsequently, a small amount of powder sample was uniformly placed on the inner wall of a quartz tube, annealed in a vacuum environment, heated to 300°C for 24 h, and then cooled within the furnace. A piece of a single crystal (0.13 × 0.06 × 0.05 mm³) was selected and mounted on a glass fibre for single-crystal X-ray diffraction measurements.

Refinement

Table 1 shows the details of data collection and structural refinement. Three sites are co-occupied by Al and Cr atoms (Al1/Cr1, Al2/Cr2, Al3/Cr3). Site occupancies were refined, and then fixed to their as-found values, 0.772, 0.5 and 0.958 for Al1, Al2 and Al3, respectively, assuming full occupancy for each site. Atoms sharing the same site were constrained to have the same coordinates and displacement parameters. Moreover, disordered atoms were restrained to be isotropic, with standard deviations of 0.01 Å² (Sheldrick, 2015b ). The maximum and minimum residual electron densities in the last difference map are located 1.68 Å from atom Cr3 and 0.36 Å from atom Cr4, respectively. The crystal was considered as a sample twinned by inversion (Parsons et al., 2013 ), and the batch scale factor converged to x = 0.3 (2).

Structural data

CCDC reference: 1993113

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2414314620004228/bh4049sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2414314620004228/bh4049Isup2.hkl

supporting information. DOI: https://doi.org/10.1107/S2414314620004228/bh4049sup3.pdf

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: SHELXL2017/1 (Sheldrick, 2015b); molecular graphics: DIAMOND (Brandenburg & Putz, 2017); software used to prepare material for publication: publCIF (Westrip, 2010).

Octaaluminium pentachromium top

Crystal data top

Al_7.85Cr_5.16	D_x = 4.248 Mg m⁻³
M_r = 479.72	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3m:R	Cell parameters from 2208 reflections
a = 7.8777 (5) Å	θ = 3.2–26.3°
α = 109.566 (2)°	µ = 8.05 mm⁻¹
V = 375.01 (7) Å³	T = 296 K
Z = 2	Graininess, metallic silver
F(000) = 451	0.13 × 0.06 × 0.05 mm

Data collection top

Bruker D8 Venture Photon 100 CMOS diffractometer	547 reflections with I > 2σ(I)
φ and ω scans	R_int = 0.090
Absorption correction: multi-scan (SADABS; Bruker, 2015)	θ_max = 26.8°, θ_min = 3.2°
T_min = 0.496, T_max = 0.523	h = −9→9
7330 measured reflections	k = −9→9
576 independent reflections	l = −9→9

Refinement top

Refinement on F²	37 restraints
Least-squares matrix: full	w = 1/[σ²(F_o²) + (0.0652P)² + 19.1482P] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.068	(Δ/σ)_max < 0.001
wR(F²) = 0.178	Δρ_max = 1.02 e Å⁻³
S = 1.16	Δρ_min = −1.27 e Å⁻³
576 reflections	Absolute structure: Refined as an inversion twin.
53 parameters	Absolute structure parameter: 0.3 (2)

Special details top

Refinement. Refined as a two-component inversion twin

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Al1	0.2998 (14)	0.2998 (14)	0.0928 (15)	0.0108 (19)	0.772
Cr1	0.2998 (14)	0.2998 (14)	0.0928 (15)	0.0108 (19)	0.228
Al2	1.3096 (13)	0.6646 (11)	0.6646 (11)	0.0117 (19)	0.5
Cr2	1.3096 (13)	0.6646 (11)	0.6646 (11)	0.0117 (19)	0.5
Al3	0.9238 (18)	0.6488 (14)	0.6488 (14)	0.012 (2)	0.958
Cr3	0.9238 (18)	0.6488 (14)	0.6488 (14)	0.012 (2)	0.042
Cr4	−0.0434 (12)	−0.0434 (12)	−0.0434 (12)	0.006 (2)
Cr5	0.6391 (8)	0.3060 (8)	0.3060 (8)	0.0028 (10)
Cr6	1.3001 (10)	0.9464 (8)	0.9464 (8)	0.0108 (14)
Cr7	0.5198 (13)	0.5198 (13)	0.5198 (13)	0.008 (2)
Al4	0.5500 (17)	−0.0607 (15)	0.2804 (16)	0.018 (2)
Al5	0.0366 (18)	0.0366 (18)	−0.313 (2)	0.015 (3)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Al1	0.007 (3)	0.007 (3)	0.019 (5)	0.005 (3)	0.006 (3)	0.006 (3)
Cr1	0.007 (3)	0.007 (3)	0.019 (5)	0.005 (3)	0.006 (3)	0.006 (3)
Al2	0.008 (4)	0.008 (3)	0.008 (3)	0.000 (3)	0.000 (3)	0.001 (3)
Cr2	0.008 (4)	0.008 (3)	0.008 (3)	0.000 (3)	0.000 (3)	0.001 (3)
Al3	0.013 (5)	0.010 (3)	0.010 (3)	0.007 (3)	0.007 (3)	−0.001 (3)
Cr3	0.013 (5)	0.010 (3)	0.010 (3)	0.007 (3)	0.007 (3)	−0.001 (3)
Cr4	0.007 (4)	0.007 (4)	0.007 (4)	0.005 (4)	0.005 (4)	0.005 (4)
Cr5	0.001 (2)	0.0034 (18)	0.0034 (18)	0.0001 (17)	0.0001 (17)	0.002 (2)
Cr6	0.016 (3)	0.008 (3)	0.008 (3)	0.006 (3)	0.006 (3)	0.003 (3)
Cr7	0.006 (3)	0.006 (3)	0.006 (3)	0.000 (4)	0.000 (4)	0.000 (4)
Al4	0.024 (5)	0.021 (4)	0.031 (5)	0.016 (3)	0.021 (4)	0.021 (4)
Al5	0.015 (4)	0.015 (4)	0.017 (5)	0.004 (5)	0.011 (4)	0.011 (4)

Geometric parameters (Å, º) top

Al1—Cr5	2.611 (7)	Cr2—Al5^xi	2.930 (16)
Al1—Cr5ⁱ	2.611 (7)	Al3—Cr5	2.572 (12)
Al1—Cr6ⁱⁱ	2.634 (7)	Al3—Cr6	2.606 (11)
Al1—Cr6ⁱⁱⁱ	2.634 (7)	Al3—Cr4^xiii	2.655 (12)
Al1—Cr4	2.644 (11)	Al3—Cr7	2.678 (13)
Al1—Al4ⁱ	2.654 (11)	Al3—Al5^xiii	2.758 (11)
Al1—Al4^iv	2.654 (11)	Al3—Al5^xiv	2.758 (11)
Al1—Al5	2.659 (17)	Al3—Al4^xii	2.798 (12)
Al1—Al1ⁱ	2.665 (16)	Al3—Al4^ix	2.798 (12)
Al1—Al1^v	2.665 (16)	Cr3—Cr5	2.572 (12)
Al1—Cr7	2.739 (11)	Cr3—Cr6	2.606 (11)
Cr1—Cr5	2.611 (7)	Cr3—Cr4^xiii	2.655 (12)
Cr1—Cr5ⁱ	2.611 (7)	Cr3—Cr7	2.678 (13)
Cr1—Cr6ⁱⁱ	2.634 (7)	Cr3—Al5^xiii	2.758 (11)
Cr1—Cr6ⁱⁱⁱ	2.634 (7)	Cr3—Al5^xiv	2.758 (11)
Cr1—Cr4	2.644 (11)	Cr3—Al4^xii	2.798 (12)
Cr1—Al4ⁱ	2.654 (11)	Cr3—Al4^ix	2.798 (12)
Cr1—Al4^iv	2.654 (11)	Cr4—Al5	2.616 (10)
Cr1—Al5	2.659 (17)	Cr4—Al5^v	2.616 (10)
Cr1—Cr7	2.739 (11)	Cr4—Al5ⁱ	2.616 (10)
Al2—Cr6	2.604 (9)	Cr4—Cr6ⁱⁱⁱ	2.761 (7)
Al2—Cr7^vi	2.647 (9)	Cr4—Cr6ⁱⁱ	2.761 (7)
Al2—Al4^vii	2.656 (9)	Cr5—Cr7	2.603 (7)
Al2—Al4^viii	2.656 (9)	Cr5—Al4^xii	2.620 (10)
Al2—Cr5^ix	2.754 (6)	Cr5—Al4^ix	2.620 (10)
Al2—Cr5^x	2.754 (6)	Cr5—Al4^iv	2.652 (9)
Al2—Al5^xi	2.930 (16)	Cr5—Al4	2.652 (9)
Al2—Al4^xii	2.996 (10)	Cr5—Al5^x	2.683 (12)
Al2—Al4^ix	2.996 (10)	Cr6—Al5^xi	2.654 (12)
Cr2—Cr6	2.604 (9)	Cr6—Al4^xv	2.739 (11)
Cr2—Cr7^vi	2.647 (9)	Cr6—Al4^xiii	2.739 (11)
Cr2—Al4^vii	2.656 (9)	Cr6—Al5^xiv	2.849 (8)
Cr2—Al4^viii	2.656 (9)	Al4—Al5^x	2.693 (12)
Cr2—Cr5^ix	2.754 (6)	Al4—Al4^ix	2.726 (5)
Cr2—Cr5^x	2.754 (6)	Al4—Al4^xvi	2.726 (5)

Cr5—Al1—Cr5ⁱ	110.4 (5)	Cr3—Cr5—Cr7	62.3 (4)
Cr5—Al1—Cr6ⁱⁱ	63.75 (14)	Al3—Cr5—Cr7	62.3 (4)
Cr5ⁱ—Al1—Cr6ⁱⁱ	167.7 (4)	Cr3—Cr5—Al1^v	116.2 (4)
Cr5—Al1—Cr6ⁱⁱⁱ	167.7 (4)	Al3—Cr5—Al1^v	116.2 (4)
Cr5ⁱ—Al1—Cr6ⁱⁱⁱ	63.75 (14)	Cr7—Cr5—Al1^v	63.4 (3)
Cr6ⁱⁱ—Al1—Cr6ⁱⁱⁱ	119.6 (5)	Cr7—Cr5—Al1	63.4 (3)
Cr5—Al1—Cr4	112.8 (3)	Al1^v—Cr5—Al1	61.4 (4)
Cr5ⁱ—Al1—Cr4	112.8 (3)	Cr7—Cr5—Cr1	63.4 (3)
Cr6ⁱⁱ—Al1—Cr4	63.1 (2)	Cr3—Cr5—Al4^xii	65.2 (3)
Cr6ⁱⁱⁱ—Al1—Cr4	63.1 (2)	Al3—Cr5—Al4^xii	65.2 (3)
Cr5—Al1—Al4ⁱ	125.5 (4)	Cr7—Cr5—Al4^xii	110.8 (3)
Cr5ⁱ—Al1—Al4ⁱ	60.5 (2)	Al1^v—Cr5—Al4^xii	168.9 (3)
Cr6ⁱⁱ—Al1—Al4ⁱ	131.8 (4)	Al1—Cr5—Al4^xii	107.8 (3)
Cr6ⁱⁱⁱ—Al1—Al4ⁱ	62.4 (2)	Cr1—Cr5—Al4^xii	107.8 (3)
Cr4—Al1—Al4ⁱ	120.0 (3)	Cr3—Cr5—Al4^ix	65.2 (3)
Cr5—Al1—Al4^iv	60.5 (2)	Al3—Cr5—Al4^ix	65.2 (3)
Cr5ⁱ—Al1—Al4^iv	125.5 (4)	Cr7—Cr5—Al4^ix	110.8 (3)
Cr6ⁱⁱ—Al1—Al4^iv	62.4 (2)	Al1^v—Cr5—Al4^ix	107.8 (3)
Cr6ⁱⁱⁱ—Al1—Al4^iv	131.8 (4)	Al1—Cr5—Al4^ix	168.9 (3)
Cr4—Al1—Al4^iv	120.0 (3)	Cr1—Cr5—Al4^ix	168.9 (3)
Al4ⁱ—Al1—Al4^iv	81.7 (5)	Al4^xii—Cr5—Al4^ix	83.0 (5)
Cr5—Al1—Al5	124.0 (2)	Cr3—Cr5—Al4^iv	121.2 (3)
Cr5ⁱ—Al1—Al5	124.0 (2)	Al3—Cr5—Al4^iv	121.2 (3)
Cr6ⁱⁱ—Al1—Al5	65.1 (3)	Cr7—Cr5—Al4^iv	115.6 (3)
Cr6ⁱⁱⁱ—Al1—Al5	65.1 (3)	Al1^v—Cr5—Al4^iv	110.7 (4)
Cr4—Al1—Al5	59.1 (3)	Al1—Cr5—Al4^iv	60.5 (3)
Al4ⁱ—Al1—Al5	76.7 (3)	Cr1—Cr5—Al4^iv	60.5 (3)
Al4^iv—Al1—Al5	76.7 (3)	Al4^xii—Cr5—Al4^iv	62.3 (2)
Cr5—Al1—Al1ⁱ	108.1 (2)	Al4^ix—Cr5—Al4^iv	129.1 (2)
Cr5ⁱ—Al1—Al1ⁱ	59.3 (2)	Cr3—Cr5—Al4	121.2 (3)
Cr6ⁱⁱ—Al1—Al1ⁱ	111.0 (2)	Al3—Cr5—Al4	121.2 (3)
Cr6ⁱⁱⁱ—Al1—Al1ⁱ	59.6 (2)	Cr7—Cr5—Al4	115.6 (3)
Cr4—Al1—Al1ⁱ	59.73 (18)	Al1^v—Cr5—Al4	60.5 (3)
Al4ⁱ—Al1—Al1ⁱ	109.0 (2)	Al1—Cr5—Al4	110.7 (4)
Al4^iv—Al1—Al1ⁱ	168.2 (3)	Cr1—Cr5—Al4	110.7 (4)
Al5—Al1—Al1ⁱ	110.2 (3)	Al4^xii—Cr5—Al4	129.1 (2)
Cr5—Al1—Al1^v	59.3 (2)	Al4^ix—Cr5—Al4	62.3 (2)
Cr5ⁱ—Al1—Al1^v	108.1 (2)	Al4^iv—Cr5—Al4	111.7 (5)
Cr6ⁱⁱ—Al1—Al1^v	59.6 (2)	Cr3—Cr5—Al5^x	128.3 (4)
Cr6ⁱⁱⁱ—Al1—Al1^v	111.0 (2)	Al3—Cr5—Al5^x	128.3 (4)
Cr4—Al1—Al1^v	59.73 (18)	Cr7—Cr5—Al5^x	169.4 (4)
Al4ⁱ—Al1—Al1^v	168.2 (3)	Al1^v—Cr5—Al5^x	107.8 (3)
Al4^iv—Al1—Al1^v	109.0 (2)	Al1—Cr5—Al5^x	107.8 (3)
Al5—Al1—Al1^v	110.2 (3)	Cr1—Cr5—Al5^x	107.8 (3)
Al1ⁱ—Al1—Al1^v	60.000 (1)	Al4^xii—Cr5—Al5^x	76.8 (3)
Cr5—Al1—Cr7	58.2 (2)	Al4^ix—Cr5—Al5^x	76.8 (3)
Cr5ⁱ—Al1—Cr7	58.2 (2)	Al4^iv—Cr5—Al5^x	60.6 (3)
Cr6ⁱⁱ—Al1—Cr7	111.2 (3)	Al4—Cr5—Al5^x	60.6 (3)
Cr6ⁱⁱⁱ—Al1—Cr7	111.2 (3)	Cr3—Cr5—Al2^xvi	64.3 (2)
Cr4—Al1—Cr7	110.2 (4)	Al3—Cr5—Al2^xvi	64.3 (2)
Al4ⁱ—Al1—Cr7	111.1 (3)	Cr7—Cr5—Al2^xvi	59.1 (2)
Al4^iv—Al1—Cr7	111.1 (3)	Al1^v—Cr5—Al2^xvi	60.5 (3)
Al5—Al1—Cr7	169.4 (5)	Al1—Cr5—Al2^xvi	110.8 (3)
Al1ⁱ—Al1—Cr7	60.89 (18)	Cr1—Cr5—Al2^xvi	110.8 (3)
Al1^v—Al1—Cr7	60.89 (18)	Al4^xii—Cr5—Al2^xvi	125.9 (4)
Cr5—Cr1—Cr5ⁱ	110.4 (5)	Al4^ix—Cr5—Al2^xvi	59.2 (3)
Cr5—Cr1—Cr6ⁱⁱ	63.75 (14)	Al4^iv—Cr5—Al2^xvi	170.8 (4)
Cr5ⁱ—Cr1—Cr6ⁱⁱ	167.7 (4)	Al4—Cr5—Al2^xvi	67.3 (2)
Cr5—Cr1—Cr6ⁱⁱⁱ	167.7 (4)	Al5^x—Cr5—Al2^xvi	123.0 (2)
Cr5ⁱ—Cr1—Cr6ⁱⁱⁱ	63.75 (14)	Cr2—Cr6—Al1^xiii	149.6 (2)
Cr6ⁱⁱ—Cr1—Cr6ⁱⁱⁱ	119.6 (5)	Al2—Cr6—Al1^xiii	149.6 (2)
Cr5—Cr1—Cr4	112.8 (3)	Cr3—Cr6—Al1^xiii	108.9 (3)
Cr5ⁱ—Cr1—Cr4	112.8 (3)	Al3—Cr6—Al1^xiii	108.9 (3)
Cr6ⁱⁱ—Cr1—Cr4	63.1 (2)	Al1^xiii—Cr6—Al1^xiv	60.8 (4)
Cr6ⁱⁱⁱ—Cr1—Cr4	63.1 (2)	Cr2—Cr6—Al5^xi	67.7 (4)
Cr5—Cr1—Al4ⁱ	125.5 (4)	Al2—Cr6—Al5^xi	67.7 (4)
Cr5ⁱ—Cr1—Al4ⁱ	60.5 (2)	Cr3—Cr6—Al5^xi	136.9 (4)
Cr6ⁱⁱ—Cr1—Al4ⁱ	131.8 (4)	Al3—Cr6—Al5^xi	136.9 (4)
Cr6ⁱⁱⁱ—Cr1—Al4ⁱ	62.4 (2)	Al1^xiii—Cr6—Al5^xi	108.0 (4)
Cr4—Cr1—Al4ⁱ	120.0 (3)	Al1^xiv—Cr6—Al5^xi	108.0 (4)
Cr5—Cr1—Al4^iv	60.5 (2)	Al1^xiii—Cr6—Al4^xv	59.2 (3)
Cr5ⁱ—Cr1—Al4^iv	125.5 (4)	Al1^xiv—Cr6—Al4^xv	107.4 (4)
Cr6ⁱⁱ—Cr1—Al4^iv	62.4 (2)	Al5^xi—Cr6—Al4^xv	59.9 (3)
Cr6ⁱⁱⁱ—Cr1—Al4^iv	131.8 (4)	Cr2—Cr6—Al4^xiii	96.4 (3)
Cr4—Cr1—Al4^iv	120.0 (3)	Al2—Cr6—Al4^xiii	96.4 (3)
Al4ⁱ—Cr1—Al4^iv	81.7 (5)	Cr3—Cr6—Al4^xiii	126.1 (2)
Cr5—Cr1—Al5	124.0 (2)	Al3—Cr6—Al4^xiii	126.1 (2)
Cr5ⁱ—Cr1—Al5	124.0 (2)	Al1^xiii—Cr6—Al4^xiii	107.4 (4)
Cr6ⁱⁱ—Cr1—Al5	65.1 (3)	Al1^xiv—Cr6—Al4^xiii	59.2 (3)
Cr6ⁱⁱⁱ—Cr1—Al5	65.1 (3)	Al5^xi—Cr6—Al4^xiii	59.9 (3)
Cr4—Cr1—Al5	59.1 (3)	Al4^xv—Cr6—Al4^xiii	106.5 (5)
Al4ⁱ—Cr1—Al5	76.7 (3)	Al1^xiii—Cr6—Cr4^xiii	58.6 (2)
Al4^iv—Cr1—Al5	76.7 (3)	Al1^xiv—Cr6—Cr4^xiii	58.6 (2)
Cr5—Cr1—Cr7	58.2 (2)	Al5^xi—Cr6—Cr4^xiii	163.9 (4)
Cr5ⁱ—Cr1—Cr7	58.2 (2)	Al4^xv—Cr6—Cr4^xiii	113.1 (3)
Cr6ⁱⁱ—Cr1—Cr7	111.2 (3)	Al4^xiii—Cr6—Cr4^xiii	113.1 (3)
Cr6ⁱⁱⁱ—Cr1—Cr7	111.2 (3)	Cr2—Cr6—Cr5^xiii	127.0 (4)
Cr4—Cr1—Cr7	110.2 (4)	Al2—Cr6—Cr5^xiii	127.0 (4)
Al4ⁱ—Cr1—Cr7	111.1 (3)	Cr3—Cr6—Cr5^xiii	163.9 (3)
Al4^iv—Cr1—Cr7	111.1 (3)	Al3—Cr6—Cr5^xiii	163.9 (3)
Al5—Cr1—Cr7	169.4 (5)	Al1^xiii—Cr6—Cr5^xiii	57.7 (2)
Cr6—Al2—Cr7^vi	150.7 (4)	Al1^xiv—Cr6—Cr5^xiii	57.7 (2)
Cr6—Al2—Al4^vii	71.0 (2)	Al5^xi—Cr6—Cr5^xiii	59.2 (3)
Cr7^vi—Al2—Al4^vii	108.3 (2)	Al4^xv—Cr6—Cr5^xiii	57.6 (2)
Cr6—Al2—Al4^viii	71.0 (2)	Al4^xiii—Cr6—Cr5^xiii	57.6 (3)
Cr7^vi—Al2—Al4^viii	108.3 (2)	Cr4^xiii—Cr6—Cr5^xiii	104.7 (3)
Al4^vii—Al2—Al4^viii	141.3 (4)	Cr2—Cr6—Al5^xiv	99.6 (3)
Cr6—Al2—Cr5^ix	128.85 (18)	Al2—Cr6—Al5^xiv	99.6 (3)
Cr7^vi—Al2—Cr5^ix	57.6 (2)	Cr3—Cr6—Al5^xiv	60.5 (3)
Al4^vii—Al2—Cr5^ix	159.6 (4)	Al3—Cr6—Al5^xiv	60.5 (3)
Al4^viii—Al2—Cr5^ix	57.9 (2)	Al1^xiii—Cr6—Al5^xiv	105.5 (3)
Cr6—Al2—Cr5^x	128.85 (18)	Al1^xiv—Cr6—Al5^xiv	57.8 (3)
Cr7^vi—Al2—Cr5^x	57.6 (2)	Al5^xi—Cr6—Al5^xiv	127.5 (2)
Al4^vii—Al2—Cr5^x	57.9 (2)	Al4^xv—Cr6—Al5^xiv	164.0 (4)
Al4^viii—Al2—Cr5^x	159.6 (4)	Al4^xiii—Cr6—Al5^xiv	72.2 (3)
Cr5^ix—Al2—Cr5^x	102.2 (4)	Cr4^xiii—Cr6—Al5^xiv	55.6 (2)
Cr6—Al2—Al5^xi	56.9 (3)	Cr5^xiii—Cr6—Al5^xiv	111.8 (3)
Cr7^vi—Al2—Al5^xi	93.8 (4)	Cr5—Cr7—Cr5^v	110.9 (2)
Al4^vii—Al2—Al5^xi	82.8 (3)	Cr5—Cr7—Cr5ⁱ	110.9 (2)
Al4^viii—Al2—Al5^xi	82.8 (3)	Cr5^v—Cr7—Cr5ⁱ	110.9 (2)
Cr5^ix—Al2—Al5^xi	111.2 (3)	Cr5—Cr7—Al2^xviii	166.5 (5)
Cr5^x—Al2—Al5^xi	111.2 (3)	Cr5^v—Cr7—Al2^xviii	63.27 (8)
Cr6—Al2—Al4^xii	99.9 (3)	Cr5ⁱ—Cr7—Al2^xviii	63.27 (8)
Cr7^vi—Al2—Al4^xii	103.8 (3)	Cr5—Cr7—Al2^xix	63.27 (8)
Al4^vii—Al2—Al4^xii	57.30 (18)	Cr5^v—Cr7—Al2^xix	166.5 (5)
Al4^viii—Al2—Al4^xii	123.5 (4)	Cr5ⁱ—Cr7—Al2^xix	63.27 (8)
Cr5^ix—Al2—Al4^xii	108.9 (3)	Cr5—Cr7—Al2^xvi	63.27 (8)
Cr5^x—Al2—Al4^xii	54.7 (2)	Cr5^v—Cr7—Al2^xvi	63.27 (8)
Al5^xi—Al2—Al4^xii	139.6 (3)	Cr5ⁱ—Cr7—Al2^xvi	166.5 (5)
Cr6—Al2—Al4^ix	99.9 (3)	Al2^xviii—Cr7—Al2^xvi	119.39 (7)
Cr7^vi—Al2—Al4^ix	103.8 (3)	Al2^xix—Cr7—Al2^xvi	119.39 (7)
Al4^vii—Al2—Al4^ix	123.5 (4)	Cr5—Cr7—Al3	58.3 (2)
Al4^viii—Al2—Al4^ix	57.30 (18)	Cr5^v—Cr7—Al3	124.25 (17)
Cr5^ix—Al2—Al4^ix	54.7 (2)	Cr5ⁱ—Cr7—Al3	124.25 (17)
Cr5^x—Al2—Al4^ix	108.9 (3)	Cr5—Cr7—Cr3	58.3 (2)
Al5^xi—Al2—Al4^ix	139.6 (3)	Cr5^v—Cr7—Cr3	124.25 (17)
Al4^xii—Al2—Al4^ix	70.8 (4)	Cr5ⁱ—Cr7—Cr3	124.25 (17)
Cr6—Cr2—Cr7^vi	150.7 (4)	Cr5—Cr7—Al3ⁱ	124.25 (17)
Cr6—Cr2—Al4^vii	71.0 (2)	Cr5^v—Cr7—Al3ⁱ	124.25 (17)
Cr7^vi—Cr2—Al4^vii	108.3 (2)	Cr5ⁱ—Cr7—Al3ⁱ	58.3 (2)
Cr6—Cr2—Al4^viii	71.0 (2)	Al2^xviii—Cr7—Al3ⁱ	64.46 (17)
Cr7^vi—Cr2—Al4^viii	108.3 (2)	Al2^xix—Cr7—Al3ⁱ	64.46 (17)
Al4^vii—Cr2—Al4^viii	141.3 (4)	Al2^xvi—Cr7—Al3ⁱ	135.3 (5)
Cr6—Cr2—Cr5^ix	128.85 (18)	Al3—Cr7—Al3ⁱ	82.8 (4)
Cr7^vi—Cr2—Cr5^ix	57.6 (2)	Cr3—Cr7—Al3ⁱ	82.8 (4)
Al4^vii—Cr2—Cr5^ix	159.6 (4)	Cr5—Cr7—Al3^v	124.25 (17)
Al4^viii—Cr2—Cr5^ix	57.9 (2)	Cr5^v—Cr7—Al3^v	58.3 (2)
Cr6—Cr2—Cr5^x	128.85 (18)	Cr5ⁱ—Cr7—Al3^v	124.25 (17)
Cr7^vi—Cr2—Cr5^x	57.6 (2)	Cr5—Cr7—Al1^v	58.5 (2)
Al4^vii—Cr2—Cr5^x	57.9 (2)	Cr5^v—Cr7—Al1^v	58.5 (2)
Al4^viii—Cr2—Cr5^x	159.6 (4)	Cr5ⁱ—Cr7—Al1^v	106.2 (4)
Cr5^ix—Cr2—Cr5^x	102.2 (4)	Al2^xviii—Cr7—Al1^v	110.2 (3)
Cr6—Cr2—Al5^xi	56.9 (3)	Al2^xix—Cr7—Al1^v	110.2 (3)
Cr7^vi—Cr2—Al5^xi	93.8 (4)	Al2^xvi—Cr7—Al1^v	60.3 (3)
Al4^vii—Cr2—Al5^xi	82.8 (3)	Al3—Cr7—Al1^v	108.7 (3)
Al4^viii—Cr2—Al5^xi	82.8 (3)	Cr3—Cr7—Al1^v	108.7 (3)
Cr5^ix—Cr2—Al5^xi	111.2 (3)	Al3ⁱ—Cr7—Al1^v	164.4 (4)
Cr5^x—Cr2—Al5^xi	111.2 (3)	Al3^v—Cr7—Al1^v	108.7 (3)
Cr5—Al3—Cr6	157.4 (4)	Cr5—Cr7—Al1ⁱ	106.2 (4)
Cr5—Al3—Cr4^xiii	139.3 (5)	Cr5^v—Cr7—Al1ⁱ	58.5 (2)
Cr6—Al3—Cr4^xiii	63.3 (3)	Cr5ⁱ—Cr7—Al1ⁱ	58.5 (2)
Cr5—Al3—Cr7	59.4 (3)	Al2^xviii—Cr7—Al1ⁱ	60.3 (3)
Cr6—Al3—Cr7	143.2 (4)	Al2^xix—Cr7—Al1ⁱ	110.2 (3)
Cr4^xiii—Al3—Cr7	79.9 (4)	Al2^xvi—Cr7—Al1ⁱ	110.2 (3)
Cr5—Al3—Al5^xiii	123.2 (3)	Al3—Cr7—Al1ⁱ	164.4 (4)
Cr6—Al3—Al5^xiii	64.1 (3)	Cr3—Cr7—Al1ⁱ	164.4 (4)
Cr4^xiii—Al3—Al5^xiii	57.8 (3)	Al3ⁱ—Cr7—Al1ⁱ	108.7 (3)
Cr7—Al3—Al5^xiii	97.1 (3)	Al3^v—Cr7—Al1ⁱ	108.7 (3)
Cr5—Al3—Al5^xiv	123.2 (3)	Al1^v—Cr7—Al1ⁱ	58.2 (4)
Cr6—Al3—Al5^xiv	64.1 (3)	Cr5^xvi—Al4—Cr5	144.8 (4)
Cr4^xiii—Al3—Al5^xiv	57.8 (3)	Cr5^xvi—Al4—Al1^v	86.3 (4)
Cr7—Al3—Al5^xiv	97.1 (3)	Cr5—Al4—Al1^v	59.0 (3)
Al5^xiii—Al3—Al5^xiv	109.5 (6)	Cr5^xvi—Al4—Al2^xx	62.9 (2)
Cr5—Al3—Al4^xii	58.2 (3)	Cr5—Al4—Al2^xx	150.4 (5)
Cr6—Al3—Al4^xii	105.2 (4)	Al1^v—Al4—Al2^xx	148.8 (4)
Cr4^xiii—Al3—Al4^xii	141.1 (3)	Cr5^xvi—Al4—Al5^x	145.4 (6)
Cr7—Al3—Al4^xii	103.4 (4)	Cr5—Al4—Al5^x	60.2 (3)
Al5^xiii—Al3—Al4^xii	83.5 (3)	Al1^v—Al4—Al5^x	106.3 (3)
Al5^xiv—Al3—Al4^xii	154.2 (5)	Al2^xx—Al4—Al5^x	102.4 (4)
Cr5—Al3—Al4^ix	58.2 (3)	Cr5^xvi—Al4—Al4^ix	134.5 (5)
Cr6—Al3—Al4^ix	105.2 (4)	Cr5—Al4—Al4^ix	58.3 (4)
Cr4^xiii—Al3—Al4^ix	141.1 (3)	Al1^v—Al4—Al4^ix	103.5 (4)
Cr7—Al3—Al4^ix	103.4 (4)	Al2^xx—Al4—Al4^ix	95.5 (4)
Al5^xiii—Al3—Al4^ix	154.2 (5)	Al5^x—Al4—Al4^ix	74.9 (5)
Al5^xiv—Al3—Al4^ix	83.5 (3)	Cr5^xvi—Al4—Al4^xvi	59.4 (3)
Al4^xii—Al3—Al4^ix	76.6 (5)	Cr5—Al4—Al4^xvi	128.9 (4)
Cr5—Cr3—Cr6	157.4 (4)	Al1^v—Al4—Al4^xvi	102.1 (5)
Cr5—Cr3—Cr4^xiii	139.3 (5)	Al2^xx—Al4—Al4^xvi	67.6 (4)
Cr6—Cr3—Cr4^xiii	63.3 (3)	Al5^x—Al4—Al4^xvi	86.1 (5)
Cr5—Cr3—Cr7	59.4 (3)	Al4^ix—Al4—Al4^xvi	151.5 (6)
Cr6—Cr3—Cr7	143.2 (4)	Cr5^xvi—Al4—Cr6ⁱⁱ	106.6 (5)
Cr4^xiii—Cr3—Cr7	79.9 (4)	Cr5—Al4—Cr6ⁱⁱ	61.8 (2)
Cr5—Cr3—Al5^xiii	123.2 (3)	Al1^v—Al4—Cr6ⁱⁱ	58.4 (3)
Cr6—Cr3—Al5^xiii	64.1 (3)	Al2^xx—Al4—Cr6ⁱⁱ	132.5 (4)
Cr4^xiii—Cr3—Al5^xiii	57.8 (3)	Al5^x—Al4—Cr6ⁱⁱ	58.5 (3)
Cr7—Cr3—Al5^xiii	97.1 (3)	Al4^ix—Al4—Cr6ⁱⁱ	116.5 (5)
Cr5—Cr3—Al5^xiv	123.2 (3)	Al4^xvi—Al4—Cr6ⁱⁱ	68.0 (3)
Cr6—Cr3—Al5^xiv	64.1 (3)	Cr5^xvi—Al4—Al3^xvi	56.6 (3)
Cr4^xiii—Cr3—Al5^xiv	57.8 (3)	Cr5—Al4—Al3^xvi	118.0 (5)
Cr7—Cr3—Al5^xiv	97.1 (3)	Al1^v—Al4—Al3^xvi	97.2 (4)
Al5^xiii—Cr3—Al5^xiv	109.5 (6)	Al2^xx—Al4—Al3^xvi	62.7 (3)
Cr5—Cr3—Al4^xii	58.2 (3)	Al5^x—Al4—Al3^xvi	147.5 (5)
Cr6—Cr3—Al4^xii	105.2 (4)	Al4^ix—Al4—Al3^xvi	78.0 (4)
Cr4^xiii—Cr3—Al4^xii	141.1 (3)	Al4^xvi—Al4—Al3^xvi	110.9 (4)
Cr7—Cr3—Al4^xii	103.4 (4)	Cr6ⁱⁱ—Al4—Al3^xvi	153.0 (5)
Al5^xiii—Cr3—Al4^xii	83.5 (3)	Cr5^xvi—Al4—Al2^xvi	99.8 (4)
Al5^xiv—Cr3—Al4^xii	154.2 (5)	Cr5—Al4—Al2^xvi	58.0 (2)
Cr5—Cr3—Al4^ix	58.2 (3)	Al1^v—Al4—Al2^xvi	56.9 (3)
Cr6—Cr3—Al4^ix	105.2 (4)	Al2^xx—Al4—Al2^xvi	120.5 (4)
Cr4^xiii—Cr3—Al4^ix	141.1 (3)	Al5^x—Al4—Al2^xvi	114.1 (4)
Cr7—Cr3—Al4^ix	103.4 (4)	Al4^ix—Al4—Al2^xvi	55.1 (2)
Al5^xiii—Cr3—Al4^ix	154.2 (5)	Al4^xvi—Al4—Al2^xvi	153.3 (5)
Al5^xiv—Cr3—Al4^ix	83.5 (3)	Cr6ⁱⁱ—Al4—Al2^xvi	106.8 (3)
Al4^xii—Cr3—Al4^ix	76.6 (5)	Al3^xvi—Al4—Al2^xvi	61.3 (4)
Al5—Cr4—Al5^v	118.81 (14)	Cr4—Al5—Cr6^xxi	152.4 (6)
Al5—Cr4—Al5ⁱ	118.81 (14)	Cr4—Al5—Cr1	60.2 (4)
Al5^v—Cr4—Al5ⁱ	118.81 (14)	Cr6^xxi—Al5—Cr1	147.5 (5)
Al5—Cr4—Cr1	60.7 (4)	Cr4—Al5—Al1	60.2 (4)
Al5^v—Cr4—Cr1	112.2 (3)	Cr6^xxi—Al5—Al1	147.5 (5)
Al5ⁱ—Cr4—Cr1	112.2 (3)	Cr4—Al5—Cr5^xix	145.1 (6)
Al5—Cr4—Al1	60.7 (4)	Cr6^xxi—Al5—Cr5^xix	62.5 (3)
Al5^v—Cr4—Al1	112.2 (3)	Cr1—Al5—Cr5^xix	84.9 (5)
Al5ⁱ—Cr4—Al1	112.2 (3)	Al1—Al5—Cr5^xix	84.9 (5)
Al5—Cr4—Al1ⁱ	112.2 (3)	Cr4—Al5—Al4^xxii	125.1 (3)
Al5^v—Cr4—Al1ⁱ	112.2 (3)	Cr6^xxi—Al5—Al4^xxii	61.6 (3)
Al5ⁱ—Cr4—Al1ⁱ	60.7 (4)	Al1—Al5—Al4^xxii	102.9 (4)
Cr1—Cr4—Al1ⁱ	60.5 (4)	Cr5^xix—Al5—Al4^xxii	59.1 (3)
Al1—Cr4—Al1ⁱ	60.5 (4)	Cr4—Al5—Al4^xix	125.1 (3)
Al5—Cr4—Al1^v	112.2 (3)	Cr6^xxi—Al5—Al4^xix	61.6 (3)
Al5^v—Cr4—Al1^v	60.7 (4)	Cr1—Al5—Al4^xix	102.9 (4)
Al5ⁱ—Cr4—Al1^v	112.2 (3)	Al1—Al5—Al4^xix	102.9 (4)
Cr1—Cr4—Al1^v	60.5 (4)	Cr5^xix—Al5—Al4^xix	59.1 (3)
Al1—Cr4—Al1^v	60.5 (4)	Al4^xxii—Al5—Al4^xix	109.2 (5)
Al1ⁱ—Cr4—Al1^v	60.5 (4)	Cr4—Al5—Al3ⁱⁱⁱ	59.1 (3)
Al5—Cr4—Al3ⁱⁱⁱ	63.1 (2)	Cr6^xxi—Al5—Al3ⁱⁱⁱ	101.0 (4)
Al5^v—Cr4—Al3ⁱⁱⁱ	134.0 (6)	Cr1—Al5—Al3ⁱⁱⁱ	103.8 (4)
Al5ⁱ—Cr4—Al3ⁱⁱⁱ	63.1 (2)	Al1—Al5—Al3ⁱⁱⁱ	103.8 (4)
Cr1—Cr4—Al3ⁱⁱⁱ	107.2 (3)	Cr5^xix—Al5—Al3ⁱⁱⁱ	138.3 (3)
Al1—Cr4—Al3ⁱⁱⁱ	107.2 (3)	Al4^xxii—Al5—Al3ⁱⁱⁱ	149.3 (6)
Al1ⁱ—Cr4—Al3ⁱⁱⁱ	107.2 (3)	Al4^xix—Al5—Al3ⁱⁱⁱ	79.2 (3)
Al1^v—Cr4—Al3ⁱⁱⁱ	165.2 (4)	Cr4—Al5—Al3ⁱⁱ	59.1 (3)
Al5—Cr4—Al3^xvii	134.0 (6)	Cr6^xxi—Al5—Al3ⁱⁱ	101.0 (4)
Al5^v—Cr4—Al3^xvii	63.1 (2)	Cr1—Al5—Al3ⁱⁱ	103.8 (4)
Al5ⁱ—Cr4—Al3^xvii	63.1 (2)	Al1—Al5—Al3ⁱⁱ	103.8 (4)
Cr1—Cr4—Al3^xvii	165.2 (4)	Cr5^xix—Al5—Al3ⁱⁱ	138.3 (3)
Al1—Cr4—Al3^xvii	165.2 (4)	Al4^xxii—Al5—Al3ⁱⁱ	79.2 (3)
Al1ⁱ—Cr4—Al3^xvii	107.2 (3)	Al4^xix—Al5—Al3ⁱⁱ	149.3 (6)
Al1^v—Cr4—Al3^xvii	107.2 (3)	Al3ⁱⁱⁱ—Al5—Al3ⁱⁱ	79.9 (6)
Al3ⁱⁱⁱ—Cr4—Al3^xvii	83.6 (4)	Cr4—Al5—Cr6ⁱⁱ	60.5 (3)
Al5—Cr4—Al3ⁱⁱ	63.1 (2)	Cr6^xxi—Al5—Cr6ⁱⁱ	126.6 (2)
Al5^v—Cr4—Al3ⁱⁱ	63.1 (2)	Cr1—Al5—Cr6ⁱⁱ	57.0 (2)
Al5ⁱ—Cr4—Al3ⁱⁱ	134.0 (6)	Al1—Al5—Cr6ⁱⁱ	57.0 (2)
Cr1—Cr4—Al3ⁱⁱ	107.2 (3)	Cr5^xix—Al5—Cr6ⁱⁱ	101.9 (3)
Al1—Cr4—Al3ⁱⁱ	107.2 (3)	Al4^xxii—Al5—Cr6ⁱⁱ	66.8 (2)
Al1ⁱ—Cr4—Al3ⁱⁱ	165.2 (4)	Al4^xix—Al5—Cr6ⁱⁱ	155.4 (6)
Al1^v—Cr4—Al3ⁱⁱ	107.2 (3)	Al3ⁱⁱⁱ—Al5—Cr6ⁱⁱ	117.2 (4)
Al3ⁱⁱⁱ—Cr4—Al3ⁱⁱ	83.6 (4)	Al3ⁱⁱ—Al5—Cr6ⁱⁱ	55.4 (2)
Al3^xvii—Cr4—Al3ⁱⁱ	83.6 (4)	Cr4—Al5—Cr6ⁱⁱⁱ	60.5 (3)
Al5—Cr4—Cr6ⁱⁱⁱ	63.93 (12)	Cr6^xxi—Al5—Cr6ⁱⁱⁱ	126.6 (2)
Al5^v—Cr4—Cr6ⁱⁱⁱ	168.5 (6)	Cr1—Al5—Cr6ⁱⁱⁱ	57.0 (2)
Al5ⁱ—Cr4—Cr6ⁱⁱⁱ	63.93 (12)	Al1—Al5—Cr6ⁱⁱⁱ	57.0 (2)
Cr1—Cr4—Cr6ⁱⁱⁱ	58.27 (18)	Cr5^xix—Al5—Cr6ⁱⁱⁱ	101.9 (3)
Al1—Cr4—Cr6ⁱⁱⁱ	58.27 (18)	Al4^xxii—Al5—Cr6ⁱⁱⁱ	155.4 (6)
Al1ⁱ—Cr4—Cr6ⁱⁱⁱ	58.27 (18)	Al4^xix—Al5—Cr6ⁱⁱⁱ	66.8 (2)
Al1^v—Cr4—Cr6ⁱⁱⁱ	107.8 (4)	Al3ⁱⁱⁱ—Al5—Cr6ⁱⁱⁱ	55.4 (2)
Al3ⁱⁱⁱ—Cr4—Cr6ⁱⁱⁱ	57.5 (3)	Al3ⁱⁱ—Al5—Cr6ⁱⁱⁱ	117.2 (4)
Al3^xvii—Cr4—Cr6ⁱⁱⁱ	124.18 (16)	Cr6ⁱⁱ—Al5—Cr6ⁱⁱⁱ	106.1 (4)
Al3ⁱⁱ—Cr4—Cr6ⁱⁱⁱ	124.18 (16)	Cr4—Al5—Al2^xxi	97.0 (4)
Al5—Cr4—Cr6ⁱⁱ	63.93 (12)	Cr6^xxi—Al5—Al2^xxi	55.3 (3)
Al5^v—Cr4—Cr6ⁱⁱ	63.93 (12)	Cr1—Al5—Al2^xxi	157.2 (5)
Al5ⁱ—Cr4—Cr6ⁱⁱ	168.5 (6)	Al1—Al5—Al2^xxi	157.2 (5)
Cr1—Cr4—Cr6ⁱⁱ	58.27 (18)	Cr5^xix—Al5—Al2^xxi	117.9 (4)
Al1—Cr4—Cr6ⁱⁱ	58.27 (18)	Al4^xxii—Al5—Al2^xxi	90.1 (4)
Al1ⁱ—Cr4—Cr6ⁱⁱ	107.8 (4)	Al4^xix—Al5—Al2^xxi	90.1 (4)
Al1^v—Cr4—Cr6ⁱⁱ	58.27 (18)	Al3ⁱⁱⁱ—Al5—Al2^xxi	59.8 (3)
Al3ⁱⁱⁱ—Cr4—Cr6ⁱⁱ	124.18 (16)	Al3ⁱⁱ—Al5—Al2^xxi	59.8 (3)
Al3^xvii—Cr4—Cr6ⁱⁱ	124.18 (16)	Cr6ⁱⁱ—Al5—Al2^xxi	113.8 (3)
Al3ⁱⁱ—Cr4—Cr6ⁱⁱ	57.5 (3)	Cr6ⁱⁱⁱ—Al5—Al2^xxi	113.8 (3)
Cr6ⁱⁱⁱ—Cr4—Cr6ⁱⁱ	111.1 (2)

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

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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