Al13Fe3

Xia, Z.; Liu, C.; Fan, C.

doi:10.1107/S241431461800593X

inorganic compounds

IUCrDATA

ISSN: 2414-3146

Volume 3| Part 4| April 2018| x180593

https://doi.org/10.1107/S241431461800593X

Open

access

Al₁₃Fe₃

Zheng Xia,^a Cong Liu ^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 M. Weil, Vienna University of Technology, Austria (Received 21 March 2018; accepted 16 April 2018; online 19 April 2018)

A new trigonal phase with composition Al₁₃Fe₃ (tridecaaluminium triiron) was obtained in the binary Fe–Al diagram by high-pressure sintering (HPS) of a stoichiometric Al₃Fe mixture. The refined crystal structure agrees with the descriptions of an unresolved rhombohedral phase reported 30 years ago [Chandrasekaran et al. (1988). Scr. Metall. 22, 797–802]. The structure was refined as an inversion twin with a ratio of 0.506 (18):0.494 (18) for the two twin components.

Keywords: crystal structure; intermetallics; crystal structure; X-ray diffraction.

CCDC reference: 1837556

Structure description

Investigations on the crystal structure of a phase with composition Al₃Fe can be traced back to as early as one century ago (Groth, 1906 ). Similar efforts continued in the following half century (Osawa, 1933 ; Bachmetew, 1934 ; Phragmén, 1950 ). However, an accurate composition and crystal structure analysis of this phase has been generally accepted to result in a compound with formula λ-Al₁₃Fe₄ (Black, 1955a ,b ; Armbrüster et al., 2012 ). A new mineral named hollisterite (Al₃Fe with the λ-Al₁₃Fe₄ structure) was discovered very recently during investigation of one fragment of a recovered Khatyrka CV3 carbonaceous chondrite (Ma et al., 2017 ) while searching for samples to explain the origin of a quasicrystal mineral (Bindi & Steinhardt, 2018 ). In the present work, a trigonal phase with composition Al₁₃Fe₃ was uncovered to be coexistent with the λ-Al₁₃Fe₄ phase in the products while simulating the formation of hollisterite under high-pressure and high-temperature conditions (HPHT) by the HPS approach.

There are 96 atoms (78 aluminium plus 18 iron) in the unit cell of the Al₁₃Fe₃ structure. The projection of the structure along [001] is shown in Fig. 1, using coordination polyhedra around Al4 atoms for visualization. It is found that there are 18 Al atoms in the unit cell, each of which is coordinated in form of a distorted icosahedron that is formed by two, three, four and three atoms of Fe1, Al2, Al3 and Al6, respectively. All the above mentioned atoms occupy the 18b Wyckoff sites while the Al5 atom occupies the 6a Wyckoff site.

Figure 1
Projection of the new Al₁₃Fe₃ phase along the [001] direction showing Al4 atoms with their coordination polyhedra.

Fig. 2 shows the environments of the Fe1 and Al5 atoms. Each Fe1 atom is surrounded by ten aluminium atoms including two Al2, two Al3, two Al4, one Al5 and three Al6 atoms, while each Al5 atom is surrounded by three Fe1 atoms, three Al2 and three Al6 atoms.

Figure 2
Environments of Fe1 (left) and Al5 (right) atoms. Displacement ellipsoids are given at the 99% probability level. [Symmetry codes: (i) $[{1\over 3}]$ − x + y, − $[{1\over 3}]$ + y, $[{1\over 6}]$ + z; (ii) $[{1\over 3}]$ − x + y, $[{2\over 3}]$ − x, − $[{1\over 3}]$ + z; (iii) 1 − y, 1 − x, − $[{1\over 2}]$ + z; (iv) x, x − y, $[{1\over 2}]$ + z; (v) x, x − y, − $[{1\over 2}]$ + z; (vi) 1 − y, x − y, z; (vii) $[{2\over 3}]$ − y, $[{1\over 3}]$ + x − y, $[{1\over 3}]$ + z; (viii) − $[{1\over 3}]$ + x, $[{1\over 3}]$ + x − y, − $[{1\over 6}]$ + z; (ix) 1 − y, 1 − x, $[{1\over 2}]$ + z; (x) 1 − x + y, 1 − x, z; (xi) $[{2\over 3}]$ − x + y, $[{1\over 3}]$ + y, − $[{1\over 6}]$ + z; (xii) $[{1\over 3}]$ + x, $[{2\over 3}]$ + x − y, $[{1\over 6}]$ + z.]

It should be noted that the present Al₁₃Fe₃ phase agrees with the descriptions of an unresolved rhombohedral phase reported 30 years ago (Chandrasekaran et al., 1988 ).

Synthesis and crystallization

Pure aluminium powder (indicated purity 99.8%) and pure iron powder (indicated purity 99.8%) were mixed according to an atomic ratio of 3:1. The detailed description and the assembled crucible sketch map of the employed HPS process can be found elsewhere (Liu & Fan, 2018 ). In the current work, the sample was pressurized up to 5 GPa and heated to 1493 K for 30 min, cooled to 1343 K and held at this temperature for one h, and then cooled down rapidly to room temperature. A brick-shaped fragment with dimensions 0.09 × 0.06 × 0.03 mm³ was selected and mounted on a thin 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 0.506 (18): 0.494 (18) for the two twin components. Although the ADDSYM function in PLATON (Spek, 2009 ) suggested a change from the present space group R3c to centrosymmetric R $[\overline{3}]$ c, the reliability factors were significantly higher for the centrosymmetric case. Hence the non-centrosymmetric space group was used for the present model.

Table 1
Experimental details

Crystal data
Chemical formula	Al13Fe3
M_r	518.29
Crystal system, space group	Trigonal, R3c:H
Temperature (K)	293
a, c (Å)	14.5784 (9), 7.7020 (5)
V (Å³)	1417.6 (2)
Z	6
Radiation type	Mo Kα
μ (mm⁻¹)	5.69
Crystal size (mm)	0.09 × 0.06 × 0.03

Data collection
Diffractometer	Bruker D8 Venture Photon 100 COMS
Absorption correction	Multi-scan (SADABS; Krause et al., 2015 )
T_min, T_max	0.590, 0.746
No. of measured, independent and observed [I > 2σ(I)] reflections	20029, 1017, 954
R_int	0.031
(sin θ/λ)_max (Å⁻¹)	0.735

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.020, 0.039, 1.12
No. of reflections	1017
No. of parameters	50
No. of restraints	1
Δρ_max, Δρ_min (e Å⁻³)	0.45, −0.82
Absolute structure	Refined as an inversion twin.
Absolute structure parameter	0.494 (18)
Computer programs: APEX3 and SAINT (Bruker, 2015 ), SHELXT (Sheldrick, 2015a ), SHELXL2014 (Sheldrick, 2015b ), DIAMOND (Brandenburg & Putz, 2017 ) and publCIF (Westrip, 2010 )..

Structural data

CCDC reference: 1837556

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S241431461800593X/wm4075sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S241431461800593X/wm4075Isup2.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: SHELXT (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)..

Tridecaaluminium triiron top

Crystal data top

Al13Fe3	D_x = 3.642 Mg m⁻³
M_r = 518.29	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3c:H	Cell parameters from 21502 reflections
a = 14.5784 (9) Å	θ = 2.8–31.5°
c = 7.7020 (5) Å	µ = 5.69 mm⁻¹
V = 1417.6 (2) Å³	T = 293 K
Z = 6	Grain, metallic
F(000) = 741	0.09 × 0.06 × 0.03 mm

Data collection top

Bruker D8 Venture Photon 100 COMS diffractometer	954 reflections with I > 2σ(I)
phi and ω scans	R_int = 0.031
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	θ_max = 31.5°, θ_min = 2.8°
T_min = 0.590, T_max = 0.746	h = −21→21
20029 measured reflections	k = −20→21
1017 independent reflections	l = −11→11

Refinement top

Refinement on F²	1 restraint
Least-squares matrix: full	w = 1/[σ²(F_o²) + (0.0208P)² + 1.1916P] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.020	(Δ/σ)_max < 0.001
wR(F²) = 0.039	Δρ_max = 0.45 e Å⁻³
S = 1.12	Δρ_min = −0.81 e Å⁻³
1017 reflections	Absolute structure: Refined as an inversion twin.
50 parameters	Absolute structure parameter: 0.494 (18)

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
Fe01	0.49239 (3)	0.33140 (5)	0.49860 (8)	0.00526 (10)
Al02	0.48081 (7)	0.18100 (8)	0.33067 (12)	0.0153 (2)
Al03	0.35885 (7)	0.36146 (7)	0.65909 (13)	0.00896 (16)
Al04	0.50297 (11)	0.49974 (10)	0.4148 (3)	0.01602 (18)
Al05	0.666667	0.333333	0.4775 (3)	0.0134 (3)
Al06	0.63864 (9)	0.47463 (10)	0.66904 (10)	0.0152 (3)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Fe01	0.00493 (19)	0.00516 (14)	0.00559 (16)	0.00245 (16)	−0.00091 (16)	−0.00119 (11)
Al02	0.0279 (6)	0.0094 (4)	0.0099 (4)	0.0103 (5)	−0.0025 (5)	−0.0030 (4)
Al03	0.0149 (5)	0.0144 (5)	0.0049 (4)	0.0128 (3)	0.0002 (4)	−0.0011 (5)
Al04	0.0114 (3)	0.0066 (3)	0.0311 (5)	0.0053 (3)	0.0047 (3)	0.0037 (3)
Al05	0.0071 (3)	0.0071 (3)	0.0259 (10)	0.00355 (16)	0.000	0.000
Al06	0.0129 (5)	0.0135 (5)	0.0096 (5)	−0.0006 (4)	−0.0016 (4)	−0.0056 (4)

Geometric parameters (Å, º) top

Fe01—Al04	2.4667 (16)	Al02—Al04ⁱⁱ	2.832 (2)
Fe01—Al04ⁱ	2.4697 (15)	Al02—Al04ⁱ	2.8522 (19)
Fe01—Al02	2.4776 (13)	Al03—Al03ⁱⁱ	2.6558 (3)
Fe01—Al06	2.4854 (12)	Al03—Al03^vii	2.6558 (4)
Fe01—Al03ⁱⁱ	2.5115 (12)	Al03—Al04^vii	2.7230 (19)
Fe01—Al03	2.5226 (12)	Al03—Al04ⁱ	2.7254 (18)
Fe01—Al05	2.5319 (4)	Al03—Al06^viii	2.7454 (18)
Fe01—Al06ⁱⁱⁱ	2.5797 (11)	Al03—Al04	2.790 (2)
Fe01—Al02^iv	2.5893 (13)	Al03—Al04^ix	2.821 (2)
Al02—Al06ⁱⁱⁱ	2.6790 (17)	Al04—Al06ⁱⁱⁱ	2.901 (2)
Al02—Al03^v	2.7043 (17)	Al04—Al06	2.933 (2)
Al02—Al06^vi	2.7269 (11)	Al04—Al06^viii	2.9428 (19)
Al02—Al06^v	2.7341 (18)	Al05—Al06^x	2.7253 (16)
Al02—Al05	2.7450 (13)	Al05—Al06^vi	2.7253 (16)
Al02—Al04^vi	2.820 (2)	Al05—Al06	2.7254 (16)

Al04—Fe01—Al04ⁱ	126.125 (12)	Fe01^xi—Al04—Al02^x	108.89 (6)
Al04—Fe01—Al02	133.36 (8)	Al03ⁱⁱ—Al04—Al02^x	112.86 (6)
Al04ⁱ—Fe01—Al02	70.41 (5)	Al03^xi—Al04—Al02^x	67.36 (4)
Al04—Fe01—Al06	72.65 (5)	Al03—Al04—Al02^x	126.10 (6)
Al04ⁱ—Fe01—Al06	133.11 (7)	Fe01—Al04—Al03ⁱⁱⁱ	125.60 (8)
Al02—Fe01—Al06	132.02 (4)	Fe01^xi—Al04—Al03ⁱⁱⁱ	56.20 (4)
Al04—Fe01—Al03ⁱⁱ	66.31 (4)	Al03ⁱⁱ—Al04—Al03ⁱⁱⁱ	120.99 (10)
Al04ⁱ—Fe01—Al03ⁱⁱ	68.99 (6)	Al03^xi—Al04—Al03ⁱⁱⁱ	57.19 (3)
Al02—Fe01—Al03ⁱⁱ	86.95 (4)	Al03—Al04—Al03ⁱⁱⁱ	176.46 (8)
Al06—Fe01—Al03ⁱⁱ	137.21 (4)	Al02^x—Al04—Al03ⁱⁱⁱ	57.29 (4)
Al04—Fe01—Al03	67.99 (5)	Fe01—Al04—Al02^vii	121.54 (9)
Al04ⁱ—Fe01—Al03	66.17 (4)	Fe01^xi—Al04—Al02^vii	57.99 (5)
Al02—Fe01—Al03	133.83 (4)	Al03ⁱⁱ—Al04—Al02^vii	122.36 (7)
Al06—Fe01—Al03	90.44 (4)	Al03^xi—Al04—Al02^vii	58.20 (5)
Al03ⁱⁱ—Fe01—Al03	63.682 (17)	Al03—Al04—Al02^vii	75.26 (6)
Al04—Fe01—Al05	114.14 (4)	Al02^x—Al04—Al02^vii	121.54 (6)
Al04ⁱ—Fe01—Al05	119.65 (4)	Al03ⁱⁱⁱ—Al04—Al02^vii	103.99 (5)
Al02—Fe01—Al05	66.44 (4)	Fe01—Al04—Al02^xi	123.48 (7)
Al06—Fe01—Al05	65.80 (4)	Fe01^xi—Al04—Al02^xi	54.92 (4)
Al03ⁱⁱ—Fe01—Al05	143.61 (5)	Al03ⁱⁱ—Al04—Al02^xi	66.93 (5)
Al03—Fe01—Al05	152.47 (5)	Al03^xi—Al04—Al02^xi	111.09 (6)
Al04—Fe01—Al06ⁱⁱⁱ	70.15 (6)	Al03—Al04—Al02^xi	102.12 (5)
Al04ⁱ—Fe01—Al06ⁱⁱⁱ	115.20 (7)	Al02^x—Al04—Al02^xi	123.32 (8)
Al02—Fe01—Al06ⁱⁱⁱ	63.94 (4)	Al03ⁱⁱⁱ—Al04—Al02^xi	74.46 (6)
Al06—Fe01—Al06ⁱⁱⁱ	111.62 (3)	Al02^vii—Al04—Al02^xi	95.95 (6)
Al03ⁱⁱ—Fe01—Al06ⁱⁱⁱ	65.25 (4)	Fe01—Al04—Al06ⁱⁱⁱ	56.75 (5)
Al03—Fe01—Al06ⁱⁱⁱ	123.20 (4)	Fe01^xi—Al04—Al06ⁱⁱⁱ	123.79 (9)
Al05—Fe01—Al06ⁱⁱⁱ	80.44 (6)	Al03ⁱⁱ—Al04—Al06ⁱⁱⁱ	58.33 (5)
Al04—Fe01—Al02^iv	113.68 (7)	Al03^xi—Al04—Al06ⁱⁱⁱ	121.20 (7)
Al04ⁱ—Fe01—Al02^iv	68.04 (6)	Al03—Al04—Al06ⁱⁱⁱ	104.09 (5)
Al02—Fe01—Al02^iv	112.87 (3)	Al02^x—Al04—Al06ⁱⁱⁱ	57.08 (5)
Al06—Fe01—Al02^iv	65.16 (4)	Al03ⁱⁱⁱ—Al04—Al06ⁱⁱⁱ	76.79 (6)
Al03ⁱⁱ—Fe01—Al02^iv	121.68 (4)	Al02^vii—Al04—Al06ⁱⁱⁱ	177.80 (8)
Al03—Fe01—Al02^iv	63.86 (4)	Al02^xi—Al04—Al06ⁱⁱⁱ	86.24 (6)
Al05—Fe01—Al02^iv	92.36 (6)	Fe01—Al04—Al06	53.97 (5)
Al06ⁱⁱⁱ—Fe01—Al02^iv	172.79 (4)	Fe01^xi—Al04—Al06	127.63 (7)
Fe01—Al02—Fe01^v	129.49 (5)	Al03ⁱⁱ—Al04—Al06	110.62 (6)
Fe01—Al02—Al06ⁱⁱⁱ	59.88 (4)	Al03^xi—Al04—Al06	71.35 (5)
Fe01^v—Al02—Al06ⁱⁱⁱ	69.76 (3)	Al03—Al04—Al06	76.75 (6)
Fe01—Al02—Al03^v	148.34 (5)	Al02^x—Al04—Al06	56.54 (4)
Fe01^v—Al02—Al03^v	56.87 (3)	Al03ⁱⁱⁱ—Al04—Al06	106.71 (5)
Al06ⁱⁱⁱ—Al02—Al03^v	117.46 (5)	Al02^vii—Al04—Al06	86.01 (6)
Fe01—Al02—Al06^vi	70.58 (4)	Al02^xi—Al04—Al06	177.44 (7)
Fe01^v—Al02—Al06^vi	154.40 (4)	Al06ⁱⁱⁱ—Al04—Al06	91.80 (6)
Al06ⁱⁱⁱ—Al02—Al06^vi	125.55 (5)	Fe01—Al04—Al06^viii	110.76 (6)
Al03^v—Al02—Al06^vi	116.47 (6)	Fe01^xi—Al04—Al06^viii	67.01 (4)
Fe01—Al02—Al06^v	129.03 (5)	Al03ⁱⁱ—Al04—Al06^viii	71.23 (5)
Fe01^v—Al02—Al06^v	55.58 (3)	Al03^xi—Al04—Al06^viii	108.48 (6)
Al06ⁱⁱⁱ—Al02—Al06^v	94.31 (6)	Al03—Al04—Al06^viii	57.15 (5)
Al03^v—Al02—Al06^v	81.63 (4)	Al02^x—Al04—Al06^viii	175.59 (6)
Al06^vi—Al02—Al06^v	100.22 (3)	Al03ⁱⁱⁱ—Al04—Al06^viii	119.52 (6)
Fe01—Al02—Al05	57.73 (3)	Al02^vii—Al04—Al06^viii	55.24 (4)
Fe01^v—Al02—Al05	113.86 (6)	Al02^xi—Al04—Al06^viii	56.11 (4)
Al06ⁱⁱⁱ—Al02—Al05	74.96 (5)	Al06ⁱⁱⁱ—Al04—Al06^viii	126.25 (7)
Al03^v—Al02—Al05	153.71 (5)	Al06—Al04—Al06^viii	124.25 (8)
Al06^vi—Al02—Al05	59.74 (5)	Fe01^vi—Al05—Fe01^x	119.592 (12)
Al06^v—Al02—Al05	74.09 (5)	Fe01^vi—Al05—Fe01	119.591 (12)
Fe01—Al02—Al04^vi	134.41 (5)	Fe01^x—Al05—Fe01	119.593 (12)
Fe01^v—Al02—Al04^vi	94.65 (5)	Fe01^vi—Al05—Al06^x	69.84 (4)
Al06ⁱⁱⁱ—Al02—Al04^vi	157.26 (5)	Fe01^x—Al05—Al06^x	56.28 (3)
Al03^v—Al02—Al04^vi	61.38 (5)	Fe01—Al05—Al06^x	142.70 (10)
Al06^vi—Al02—Al04^vi	63.83 (5)	Fe01^vi—Al05—Al06^vi	56.28 (3)
Al06^v—Al02—Al04^vi	62.96 (5)	Fe01^x—Al05—Al06^vi	142.70 (10)
Al05—Al02—Al04^vi	97.86 (5)	Fe01—Al05—Al06^vi	69.84 (4)
Fe01—Al02—Al04ⁱⁱ	98.01 (5)	Al06^x—Al05—Al06^vi	93.47 (6)
Fe01^v—Al02—Al04ⁱⁱ	53.97 (4)	Fe01^vi—Al05—Al06	142.70 (10)
Al06ⁱⁱⁱ—Al02—Al04ⁱⁱ	64.48 (4)	Fe01^x—Al05—Al06	69.84 (4)
Al03^v—Al02—Al04ⁱⁱ	58.92 (4)	Fe01—Al05—Al06	56.28 (3)
Al06^vi—Al02—Al04ⁱⁱ	148.11 (6)	Al06^x—Al05—Al06	93.47 (6)
Al06^v—Al02—Al04ⁱⁱ	109.50 (4)	Al06^vi—Al05—Al06	93.47 (6)
Al05—Al02—Al04ⁱⁱ	139.40 (6)	Fe01^vi—Al05—Al02	73.73 (3)
Al04^vi—Al02—Al04ⁱⁱ	120.25 (6)	Fe01^x—Al05—Al02	157.09 (9)
Fe01—Al02—Al04ⁱ	54.67 (4)	Fe01—Al05—Al02	55.83 (3)
Fe01^v—Al02—Al04ⁱ	138.74 (6)	Al06^x—Al05—Al02	142.93 (3)
Al06ⁱⁱⁱ—Al02—Al04ⁱ	100.82 (5)	Al06^vi—Al05—Al02	59.80 (3)
Al03^v—Al02—Al04ⁱ	99.00 (5)	Al06—Al05—Al02	111.97 (2)
Al06^vi—Al02—Al04ⁱ	63.62 (5)	Fe01^vi—Al05—Al02^vi	55.83 (3)
Al06^v—Al02—Al04ⁱ	162.42 (6)	Fe01^x—Al05—Al02^vi	73.73 (3)
Al05—Al02—Al04ⁱ	101.15 (6)	Fe01—Al05—Al02^vi	157.09 (9)
Al04^vi—Al02—Al04ⁱ	101.74 (6)	Al06^x—Al05—Al02^vi	59.80 (3)
Al04ⁱⁱ—Al02—Al04ⁱ	85.30 (5)	Al06^vi—Al05—Al02^vi	111.97 (2)
Fe01^vii—Al03—Fe01	143.98 (3)	Al06—Al05—Al02^vi	142.93 (3)
Fe01^vii—Al03—Al03ⁱⁱ	133.94 (6)	Al02—Al05—Al02^vi	104.21 (6)
Fe01—Al03—Al03ⁱⁱ	57.96 (4)	Fe01^vi—Al05—Al02^x	157.09 (9)
Fe01^vii—Al03—Al03^vii	58.36 (4)	Fe01^x—Al05—Al02^x	55.83 (3)
Fe01—Al03—Al03^vii	129.21 (6)	Fe01—Al05—Al02^x	73.73 (3)
Al03ⁱⁱ—Al03—Al03^vii	154.39 (4)	Al06^x—Al05—Al02^x	111.97 (2)
Fe01^vii—Al03—Al02^iv	111.32 (4)	Al06^vi—Al05—Al02^x	142.93 (3)
Fe01—Al03—Al02^iv	59.27 (4)	Al06—Al05—Al02^x	59.80 (3)
Al03ⁱⁱ—Al03—Al02^iv	112.41 (7)	Al02—Al05—Al02^x	104.21 (6)
Al03^vii—Al03—Al02^iv	70.04 (4)	Al02^vi—Al05—Al02^x	104.21 (6)
Fe01^vii—Al03—Al04^vii	56.05 (5)	Fe01—Al06—Fe01^ix	132.10 (5)
Fe01—Al03—Al04^vii	158.60 (6)	Fe01—Al06—Al02^ix	140.79 (6)
Al03ⁱⁱ—Al03—Al04^vii	103.57 (8)	Fe01^ix—Al06—Al02^ix	56.18 (3)
Al03^vii—Al03—Al04^vii	62.47 (6)	Fe01—Al06—Al05	57.92 (3)
Al02^iv—Al03—Al04^vii	129.43 (7)	Fe01^ix—Al06—Al05	126.73 (6)
Fe01^vii—Al03—Al04ⁱ	155.79 (6)	Al02^ix—Al06—Al05	86.27 (5)
Fe01—Al03—Al04ⁱ	55.99 (5)	Fe01—Al06—Al02^x	74.77 (3)
Al03ⁱⁱ—Al03—Al04ⁱ	63.22 (7)	Fe01^ix—Al06—Al02^x	153.01 (4)
Al03^vii—Al03—Al04ⁱ	99.06 (7)	Al02^ix—Al06—Al02^x	102.72 (3)
Al02^iv—Al03—Al04ⁱ	62.88 (6)	Al05—Al06—Al02^x	60.46 (5)
Al04^vii—Al03—Al04ⁱ	107.73 (2)	Fe01—Al06—Al02^iv	59.25 (4)
Fe01^vii—Al03—Al06^viii	58.57 (4)	Fe01^ix—Al06—Al02^iv	73.19 (3)
Fe01—Al03—Al06^viii	115.62 (4)	Al02^ix—Al06—Al02^iv	106.32 (5)
Al03ⁱⁱ—Al03—Al06^viii	75.42 (4)	Al05—Al06—Al02^iv	85.20 (6)
Al03^vii—Al03—Al06^viii	112.38 (7)	Al02^x—Al06—Al02^iv	132.89 (4)
Al02^iv—Al03—Al06^viii	157.83 (4)	Fe01—Al06—Al03^xii	140.38 (5)
Al04^vii—Al03—Al06^viii	64.09 (6)	Fe01^ix—Al06—Al03^xii	56.18 (3)
Al04ⁱ—Al03—Al06^viii	134.87 (8)	Al02^ix—Al06—Al03^xii	78.51 (3)
Fe01^vii—Al03—Al04	98.30 (5)	Al05—Al06—Al03^xii	157.46 (5)
Fe01—Al03—Al04	55.06 (4)	Al02^x—Al06—Al03^xii	106.64 (6)
Al03ⁱⁱ—Al03—Al04	59.94 (6)	Al02^iv—Al06—Al03^xii	114.89 (4)
Al03^vii—Al03—Al04	145.67 (7)	Fe01—Al06—Al04^ix	94.96 (5)
Al02^iv—Al03—Al04	100.78 (5)	Fe01^ix—Al06—Al04^ix	53.10 (4)
Al04^vii—Al03—Al04	128.21 (7)	Al02^ix—Al06—Al04^ix	108.84 (4)
Al04ⁱ—Al03—Al04	105.86 (8)	Al05—Al06—Al04^ix	144.45 (6)
Al06^viii—Al03—Al04	64.23 (5)	Al02^x—Al06—Al04^ix	139.57 (6)
Fe01^vii—Al03—Al04^ix	54.81 (4)	Al02^iv—Al06—Al04^ix	59.96 (4)
Fe01—Al03—Al04^ix	96.12 (5)	Al03^xii—Al06—Al04^ix	57.58 (4)
Al03ⁱⁱ—Al03—Al04^ix	145.22 (7)	Fe01—Al06—Al04	53.38 (3)
Al03^vii—Al03—Al04^ix	59.59 (5)	Fe01^ix—Al06—Al04	134.06 (6)
Al02^iv—Al03—Al04^ix	61.33 (5)	Al02^ix—Al06—Al04	157.10 (6)
Al04^vii—Al03—Al04^ix	105.06 (8)	Al05—Al06—Al04	95.64 (6)
Al04ⁱ—Al03—Al04^ix	124.15 (7)	Al02^x—Al06—Al04	59.63 (5)
Al06^viii—Al03—Al04^ix	99.98 (5)	Al02^iv—Al06—Al04	96.58 (4)
Al04—Al03—Al04^ix	86.68 (2)	Al03^xii—Al06—Al04	92.20 (6)
Fe01—Al04—Fe01^xi	177.68 (6)	Al04^ix—Al06—Al04	82.61 (5)
Fe01—Al04—Al03ⁱⁱ	57.63 (4)	Fe01—Al06—Al04^xii	134.86 (5)
Fe01^xi—Al04—Al03ⁱⁱ	120.42 (7)	Fe01^ix—Al06—Al04^xii	93.02 (5)
Fe01—Al04—Al03^xi	124.13 (7)	Al02^ix—Al06—Al04^xii	60.28 (4)
Fe01^xi—Al04—Al03^xi	57.85 (4)	Al05—Al06—Al04^xii	99.36 (5)
Al03ⁱⁱ—Al04—Al03^xi	177.86 (11)	Al02^x—Al06—Al04^xii	60.26 (5)
Fe01—Al04—Al03	56.96 (4)	Al02^iv—Al06—Al04^xii	165.19 (5)
Fe01^xi—Al04—Al03	121.17 (7)	Al03^xii—Al06—Al04^xii	58.62 (5)
Al03ⁱⁱ—Al04—Al03	57.58 (3)	Al04^ix—Al06—Al04^xii	116.13 (6)
Al03^xi—Al04—Al03	124.16 (10)	Al04—Al06—Al04^xii	96.98 (5)
Fe01—Al04—Al02^x	73.36 (4)

Symmetry codes: (i) −x+y+1/3, y−1/3, z+1/6; (ii) −x+y+1/3, −x+2/3, z−1/3; (iii) −y+1, −x+1, z−1/2; (iv) x, x−y, z+1/2; (v) x, x−y, z−1/2; (vi) −y+1, x−y, z; (vii) −y+2/3, x−y+1/3, z+1/3; (viii) x−1/3, x−y+1/3, z−1/6; (ix) −y+1, −x+1, z+1/2; (x) −x+y+1, −x+1, z; (xi) −x+y+2/3, y+1/3, z−1/6; (xii) x+1/3, x−y+2/3, z+1/6.

Acknowledgements

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

References

Armbrüster, M., Kovnir, K., Friedrich, M., Teschner, D., Wowsnick, G., Hahne, M., Gille, P., Szentmiklósi, L., Feuerbacher, M., Heggen, M., Girgsdies, F., Rosenthal, D., Schlögl, R. & Grin, Y. (2012). Nat. Mater. 11, 690–693. Google Scholar
Bachmetew, E. (1934). Z. Kristallogr. 89, 575–586. Google Scholar
Bindi, L. & Steinhardt, P. J. (2018). Rocks Miner. 93, 50–59. Google Scholar
Black, P. J. (1955a). Acta Cryst. 8, 43–48. CrossRef CAS IUCr Journals Web of Science Google Scholar
Black, P. J. (1955b). Acta Cryst. 8, 175–182. CrossRef CAS IUCr Journals Web of Science Google Scholar
Brandenburg, K. & Putz, H. (2017). DIAMOND. Crystal Impact GbR, Bonn, Germany. Google Scholar
Bruker (2015). APEX3 and SAINT. Bruker AXS Inc. Madison, Wisconsin, USA, 2008. Google Scholar
Chandrasekaran, M., Lin, Y. P., Vincent, R. & Staniek, G. (1988). Scr. Metall. 22, 797–802. CAS Google Scholar
Groth, P. (1906). Chemische Krystallographie, Erster Teil, pp. 47–48. Leipzig: Verlag Wilhelm Engelmann. Google Scholar
Krause, L., Herbst-Irmer, R., Sheldrick, G. M. & Stalke, D. (2015). J. Appl. Cryst. 48, 3–10. Web of Science CSD CrossRef CAS IUCr Journals Google Scholar
Liu, C. & Fan, C. (2018). IUCrData, 3, x180363. Google Scholar
Ma, C., Lin, C., Bindi, L. & Steinhardt, P. J. (2017). Am. Mineral. 102, 690–693. Google Scholar
Osawa, A. (1933). Sci. Rep. Tohoku Univ. 22, 803–823. Google Scholar
Phragmén, G. (1950). J. Inst. Met. 77, 489–551. Google Scholar
Sheldrick, G. M. (2015a). Acta Cryst. A71, 3–8. Web of Science CrossRef IUCr Journals Google Scholar
Sheldrick, G. M. (2015b). Acta Cryst. C71, 3–8. Web of Science CrossRef IUCr Journals Google Scholar
Spek, A. L. (2009). Acta Cryst. D65, 148–155. Web of Science CrossRef CAS IUCr Journals Google Scholar
Westrip, S. P. (2010). J. Appl. Cryst. 43, 920–925. Web of Science CrossRef CAS IUCr Journals Google Scholar

This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.