Al10Ni3Fe0.83, an Fe-depleted phase in the Al–Ni–Fe system

Wang, S.; Liu, C.; Fan, C.

doi:10.1107/S2414314618002377

inorganic compounds

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ISSN: 2414-3146

Volume 3| Part 2| February 2018| x180237

https://doi.org/10.1107/S2414314618002377

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Al₁₀Ni₃Fe_0.83, an Fe-depleted phase in the Al–Ni–Fe system

Sai Wang,^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 22 January 2018; accepted 9 February 2018; online 16 February 2018)

Crystals of the phase Al₁₀Ni₃Fe_0.83 (decaaluminium trinickel iron) were obtained by high-pressure sintering (HPS) of a stoichiometric mixture with nominal composition Al₇₁Ni₂₄Fe₅. Al₁₀Ni₃Fe_0.83 adopts the Co₂Al₅ structure type in the space group type P6₃/mmc with the unique Fe site on site 2c partially occupied (occupancy 0.83).

Keywords: crystal structure; high-pressure sintering; Co₂Al₅ structure type; ternary system Al–Ni–Fe; intermetallics.

CCDC reference: 1823108

Structure description

The second natural quasicrystal named decagonite has the composition Al_70.2Ni_24.5Fe_5.3 (Bindi et al., 2015 ), which is very similar to the synthetic phase Al₇₁Ni₂₄Fe₅ (Lemmerz et al., 1994 ). While simulating the growth mechanism of decagonite under high-pressure and high-temperature conditions (HPHT) by the high-pressure sintering (HPS) process, we obtained another phase in the ternary system Al–Ni–Fe (Raghavan, 2010 ) with composition Al₁₀Ni₃Fe_0.83. The occurrence of a phase with composition Al₁₀Ni₃Fe has been reported by Khaidar et al. (1982 ) but it was never observed by other teams afterwards, although the existence of a decagonal phase with composition close to this phase was in argument (Zhang et al., 2008 ). On the other hand, its Fe-rich counterpart Al₁₀Fe₃Ni was frequently observed, and its crystal structure has also been determined (Chumak et al., 2007 ).

The new phase Al₁₀Ni₃Fe_0.83 adopts the Al₅Co₂ structure type (Bradley & Cheng, 1938 ; Newkirk et al., 1961 ) in space group type P6₃/mmc with the two Co sites replaced by Ni and Fe, respectively. This structure type can be derived from a distorted closed-packed arrangement of metal atoms (Wells, 1975 ). The lattice parameters of Al₁₀Ni₃Fe_0.83 (Table 1) are similar to those of Al₁₀Fe₃Ni (Chumak et al., 2007). The asymmetric unit of Al₁₀Ni₃Fe_0.83 comprises of five sites, three fully occupied by Al atoms at Wyckoff sites 2a (Al3), 6h (Al5) and 12k (Al4), one fully occupied by Ni atoms (6h; Ni1) and one partially occupied (occupancy 0.83) by Fe atoms (2c; Fe1). Both the Al3 atom at the 2a position and the Ni1 atom at the 6h position are surrounded by twelve atoms in the form of a distorted icosahedron (Fig. 1). Al3 is bound to six Ni3 and six Al4 atoms (Fig. 2a); Ni1 is bound to two Al3, six Al4, two Al5 and two Ni1 atoms (Fig. 2b). The Fe2 atom is surrounded by nine Al atoms (six Al4 and three Al5), forming an irregular polyhedron as shown in Fig. 3.

Table 1
Experimental details

Crystal data
Chemical formula	Al₁₀Ni₃Fe_0.83
M_r	492.52
Crystal system, space group	Hexagonal, P6₃/mmc
Temperature (K)	293
a, c (Å)	7.6981 (2), 7.6231 (2)
V (Å³)	391.23 (2)
Z	2
Radiation type	Cu Kα
μ (mm⁻¹)	30.59
Crystal size (mm)	0.09 × 0.09 × 0.06

Data collection
Diffractometer	Bruker D8 Venture Photon 100 CMOS
Absorption correction	Multi-scan (SADABS; Bruker, 2015 )
T_min, T_max	0.104, 0.170
No. of measured, independent and observed [I > 2σ(I)] reflections	5095, 178, 177
R_int	0.035
(sin θ/λ)_max (Å⁻¹)	0.624

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.029, 0.090, 1.09
No. of reflections	178
No. of parameters	21
Δρ_max, Δρ_min (e Å⁻³)	0.53, −0.42
Computer programs: APEX3 and SAINT (Bruker, 2015), SHELXT (Sheldrick, 2015a ), SHELXL2014 (Sheldrick, 2015b ), DIAMOND (Brandenburg & Putz, 2017 ) and publCIF (Westrip, 2010 ).

Figure 1
The crystal structure of Al₁₀Ni₃Fe_0.83 with two Al3 atoms on the 2a site and two Ni1 atoms on the 6h site displayed with their coordination environments as polyhedra.

Figure 2
(a) The coordination sphere of the Al3 atom at the 2a site; (b) the coordination sphere of the Ni1 atom at the 6h site. Displacement ellipsoids are drawn at the 99.8% probability level. [Symmetry codes: (i) −y + 1, x − y, z; (ii) x, y, −z + $[{1\over 2}]$ ; (iii) −x, −y, z + $[{1\over 2}]$ ; (iv) y, −x + y, z − $[{1\over 2}]$ ; (v) x − y, x, −z + 1; (vi) y, −x + y, −z + 1; (vii) x − y, x, z − $[{1\over 2}]$ ; (viii) −x + y, −x, z; (ix) −y, x − y, z; (xvi) −x, −y, −z; (xvii) y, −x + y, −z; (xviii) x − y, x, −z; (xix) −x + y, −x, −z + $[{1\over 2}]$ ; (xx) −x, −y, z − $[{1\over 2}]$ ; (xxi) −y, x − y, −z + $[{1\over 2}]$ .]

Figure 3
(a) The coordination polyhedron of the Fe1 atom at the 2c site; (b) the coordination sphere of the Fe1 atom showing all atoms as displacement ellipsoids at 99.8% probability level. [Symmetry codes: (i) −y + 1, x − y, z; (vi) y, −x + y, −z + 1; (x) −y + 1, x − y, −z + $[{3\over 2}]$ ; (xi) −x + y + 1, −x + 1, −z + $[{3\over 2}]$ ; (xii) x, y, −z + $[{3\over 2}]$ ; (xiii) −x + y + 1, −x + 1, z; (xiv) x − y + 1, x, −z + 1; (xv) −x + 1, −y + 1, −z + 1.]

Synthesis and crystallization

Pure aluminium powder (indicated purity 99.8%), nickel powder (indicated purity 99.95%) and iron powder (indicated purity 99.9%) were mixed according to the atomic ratio 71: 24: 5. The detailed description of the employed HPS process can be found elsewhere (Liu & Fan, 2018 ). In the current work, the prepared cylindrical block mixture was pressurized up to 5 GPa and heated to 1473 K for 30 min, cooled to 1073 K, held at that temperature for 1 h, and then was 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. Although iron and nickel atoms have very similar scattering factors and thus cannot be distinguished unambiguously in an X-ray diffraction study, the best model was obtained for the Ni atoms occupying the 6h site and the Fe atoms the 2c site. Free refinement of the occupation factors revealed the Ni site to be fully occupied and the Fe site to have a partial occupancy of 0.834 (11). The refined composition of Al₁₀Ni₃Fe_0.83 is in agreement with the results of energy dispersive X-ray spectroscopy (EDS) analysis (see Supporting information).

Structural data

CCDC reference: 1823108

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2414314618002377/wm4071sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2414314618002377/wm4071Isup2.hkl

Results of energy dispersive X-ray spectroscopy (EDS) analysis. DOI: https://doi.org/10.1107/S2414314618002377/wm4071sup3.pdf

checkCIF report

Computing details top

Data collection: APEX3 and SAINT (Bruker, 2015); cell refinement: APEX3 and SAINT (Bruker, 2015); data reduction: APEX3 and 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).

Decaaluminium trinickel iron top

Crystal data top

Al₁₀Ni₃Fe_0.83	D_x = 4.181 Mg m⁻³
M_r = 492.52	Cu Kα radiation, λ = 1.54178 Å
Hexagonal, P6₃/mmc	Cell parameters from 3731 reflections
a = 7.6981 (2) Å	θ = 5.8–74.2°
c = 7.6231 (2) Å	µ = 30.59 mm⁻¹
V = 391.23 (2) Å³	T = 293 K
Z = 2	Grain, metallic
F(000) = 471	0.09 × 0.09 × 0.06 mm

Data collection top

Bruker APEXII Photon 100 CMOS diffractometer	177 reflections with I > 2σ(I)
Phi and ω scans	R_int = 0.035
Absorption correction: multi-scan (SADABS; Bruker, 2015)	θ_max = 74.2°, θ_min = 6.6°
T_min = 0.104, T_max = 0.170	h = −9→9
5095 measured reflections	k = −9→9
178 independent reflections	l = −9→9

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	w = 1/[σ²(F_o²) + (0.046P)² + 2.8861P] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.029	(Δ/σ)_max < 0.001
wR(F²) = 0.090	Δρ_max = 0.53 e Å⁻³
S = 1.09	Δρ_min = −0.41 e Å⁻³
178 reflections	Extinction correction: SHELXL2014 (Sheldrick, 2015b), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
21 parameters	Extinction coefficient: 0.0025 (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.

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

	x	y	z	U_iso*/U_eq	Occ. (<1)
Ni1	0.25269 (18)	0.12635 (9)	0.250000	0.0105 (5)
Fe2	0.666667	0.333333	0.750000	0.0158 (10)	0.834 (11)
Al3	0.000000	0.000000	0.000000	0.0125 (9)
Al4	0.3919 (3)	0.19597 (13)	0.5598 (2)	0.0155 (6)
Al5	0.53478 (17)	0.46522 (17)	0.250000	0.0160 (7)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ni1	0.0074 (7)	0.0102 (7)	0.0129 (8)	0.0037 (4)	0.000	0.000
Fe2	0.0147 (12)	0.0147 (12)	0.0181 (15)	0.0073 (6)	0.000	0.000
Al3	0.0114 (11)	0.0114 (11)	0.0148 (18)	0.0057 (6)	0.000	0.000
Al4	0.0155 (9)	0.0140 (7)	0.0177 (9)	0.0077 (4)	−0.0016 (6)	−0.0008 (3)
Al5	0.0129 (9)	0.0129 (9)	0.0205 (13)	0.0052 (9)	0.000	0.000

Geometric parameters (Å, º) top

Ni1—Al5	2.4199 (10)	Al3—Al4^xix	2.6525 (17)
Ni1—Al5ⁱ	2.4199 (10)	Al3—Al4^vii	2.6525 (17)
Ni1—Al4	2.5374 (18)	Al3—Al4^xx	2.6525 (17)
Ni1—Al4ⁱⁱ	2.5374 (18)	Al3—Al4ⁱⁱ	2.6525 (17)
Ni1—Al3	2.5436 (8)	Al3—Al4^iv	2.6525 (17)
Ni1—Al3ⁱⁱⁱ	2.5436 (8)	Al3—Al4^xxi	2.6525 (17)
Ni1—Al4^iv	2.7141 (15)	Al4—Al3ⁱⁱⁱ	2.6525 (17)
Ni1—Al4^v	2.7141 (15)	Al4—Ni1^vi	2.7141 (15)
Ni1—Al4^vi	2.7141 (15)	Al4—Ni1^v	2.7141 (15)
Ni1—Al4^vii	2.7141 (15)	Al4—Al4^vi	2.767 (2)
Ni1—Ni1^viii	2.918 (2)	Al4—Al4^v	2.7674 (19)
Ni1—Ni1^ix	2.918 (2)	Al4—Al5^xv	2.7842 (17)
Fe2—Al4^x	2.3360 (17)	Al4—Al5^vi	2.7842 (17)
Fe2—Al4ⁱ	2.3360 (17)	Al4—Al4^xii	2.900 (4)
Fe2—Al4	2.3360 (17)	Al4—Al5ⁱ	2.9669 (16)
Fe2—Al4^xi	2.3360 (17)	Al4—Al5	2.9669 (16)
Fe2—Al4^xii	2.3360 (17)	Al5—Ni1^xiii	2.4199 (10)
Fe2—Al4^xiii	2.3360 (17)	Al5—Fe2^xv	2.686 (2)
Fe2—Al5^vi	2.686 (2)	Al5—Al4^xv	2.7842 (17)
Fe2—Al5^xiv	2.686 (2)	Al5—Al4^vii	2.7842 (17)
Fe2—Al5^xv	2.686 (2)	Al5—Al4^xxii	2.7842 (17)
Al3—Ni1^xvi	2.5436 (8)	Al5—Al4^v	2.7842 (17)
Al3—Ni1^xvii	2.5436 (8)	Al5—Al4^xiii	2.9669 (16)
Al3—Ni1^ix	2.5436 (8)	Al5—Al4ⁱⁱ	2.9669 (16)
Al3—Ni1^xviii	2.5436 (8)	Al5—Al4^xxiii	2.9669 (16)
Al3—Ni1^viii	2.5436 (8)

Al5—Ni1—Al5ⁱ	78.00 (12)	Al4^vii—Al3—Al4ⁱⁱ	62.89 (2)
Al5—Ni1—Al4	73.48 (4)	Al4^xx—Al3—Al4ⁱⁱ	180.00 (9)
Al5ⁱ—Ni1—Al4	73.48 (4)	Ni1^xvi—Al3—Al4^iv	117.06 (3)
Al5—Ni1—Al4ⁱⁱ	73.48 (4)	Ni1—Al3—Al4^iv	62.94 (3)
Al5ⁱ—Ni1—Al4ⁱⁱ	73.48 (4)	Ni1^xvii—Al3—Al4^iv	58.42 (4)
Al4—Ni1—Al4ⁱⁱ	137.08 (9)	Ni1^ix—Al3—Al4^iv	121.58 (4)
Al5—Ni1—Al3	120.98 (3)	Ni1^xviii—Al3—Al4^iv	117.06 (3)
Al5ⁱ—Ni1—Al3	120.98 (3)	Ni1^viii—Al3—Al4^iv	62.94 (3)
Al4—Ni1—Al3	159.99 (6)	Al4^xix—Al3—Al4^iv	62.89 (2)
Al4ⁱⁱ—Ni1—Al3	62.94 (4)	Al4^vii—Al3—Al4^iv	117.11 (2)
Al5—Ni1—Al3ⁱⁱⁱ	120.98 (3)	Al4^xx—Al3—Al4^iv	117.11 (2)
Al5ⁱ—Ni1—Al3ⁱⁱⁱ	120.98 (3)	Al4ⁱⁱ—Al3—Al4^iv	62.89 (2)
Al4—Ni1—Al3ⁱⁱⁱ	62.94 (4)	Ni1^xvi—Al3—Al4^xxi	62.94 (3)
Al4ⁱⁱ—Ni1—Al3ⁱⁱⁱ	159.99 (6)	Ni1—Al3—Al4^xxi	117.06 (3)
Al3—Ni1—Al3ⁱⁱⁱ	97.05 (4)	Ni1^xvii—Al3—Al4^xxi	121.58 (4)
Al5—Ni1—Al4^iv	129.27 (6)	Ni1^ix—Al3—Al4^xxi	58.42 (4)
Al5ⁱ—Ni1—Al4^iv	65.39 (5)	Ni1^xviii—Al3—Al4^xxi	62.94 (3)
Al4—Ni1—Al4^iv	123.24 (4)	Ni1^viii—Al3—Al4^xxi	117.06 (3)
Al4ⁱⁱ—Ni1—Al4^iv	63.50 (3)	Al4^xix—Al3—Al4^xxi	117.11 (2)
Al3—Ni1—Al4^iv	60.49 (4)	Al4^vii—Al3—Al4^xxi	62.89 (2)
Al3ⁱⁱⁱ—Ni1—Al4^iv	107.94 (4)	Al4^xx—Al3—Al4^xxi	62.89 (2)
Al5—Ni1—Al4^v	65.39 (5)	Al4ⁱⁱ—Al3—Al4^xxi	117.11 (2)
Al5ⁱ—Ni1—Al4^v	129.27 (6)	Al4^iv—Al3—Al4^xxi	180.00 (4)
Al4—Ni1—Al4^v	63.50 (3)	Fe2—Al4—Ni1	149.83 (8)
Al4ⁱⁱ—Ni1—Al4^v	123.24 (4)	Fe2—Al4—Al3ⁱⁱⁱ	151.52 (8)
Al3—Ni1—Al4^v	107.94 (4)	Ni1—Al4—Al3ⁱⁱⁱ	58.65 (5)
Al3ⁱⁱⁱ—Ni1—Al4^v	60.49 (4)	Fe2—Al4—Ni1^vi	100.36 (6)
Al4^iv—Ni1—Al4^v	163.98 (7)	Ni1—Al4—Ni1^vi	104.98 (6)
Al5—Ni1—Al4^vi	129.27 (6)	Al3ⁱⁱⁱ—Al4—Ni1^vi	56.57 (4)
Al5ⁱ—Ni1—Al4^vi	65.39 (5)	Fe2—Al4—Ni1^v	100.36 (6)
Al4—Ni1—Al4^vi	63.50 (3)	Ni1—Al4—Ni1^v	104.98 (6)
Al4ⁱⁱ—Ni1—Al4^vi	123.24 (4)	Al3ⁱⁱⁱ—Al4—Ni1^v	56.57 (4)
Al3—Ni1—Al4^vi	107.94 (4)	Ni1^vi—Al4—Ni1^v	65.03 (6)
Al3ⁱⁱⁱ—Ni1—Al4^vi	60.49 (4)	Fe2—Al4—Al4^vi	125.07 (4)
Al4^iv—Ni1—Al4^vi	64.59 (7)	Ni1—Al4—Al4^vi	61.36 (6)
Al4^v—Ni1—Al4^vi	112.97 (7)	Al3ⁱⁱⁱ—Al4—Al4^vi	58.556 (11)
Al5—Ni1—Al4^vii	65.39 (5)	Ni1^vi—Al4—Al4^vi	55.14 (4)
Al5ⁱ—Ni1—Al4^vii	129.27 (6)	Ni1^v—Al4—Al4^vi	107.91 (5)
Al4—Ni1—Al4^vii	123.24 (4)	Fe2—Al4—Al4^v	125.07 (4)
Al4ⁱⁱ—Ni1—Al4^vii	63.50 (3)	Ni1—Al4—Al4^v	61.36 (6)
Al3—Ni1—Al4^vii	60.49 (4)	Al3ⁱⁱⁱ—Al4—Al4^v	58.556 (11)
Al3ⁱⁱⁱ—Ni1—Al4^vii	107.94 (4)	Ni1^vi—Al4—Al4^v	107.91 (5)
Al4^iv—Ni1—Al4^vii	112.97 (7)	Ni1^v—Al4—Al4^v	55.14 (4)
Al4^v—Ni1—Al4^vii	64.59 (7)	Al4^vi—Al4—Al4^v	109.71 (7)
Al4^vi—Ni1—Al4^vii	163.98 (7)	Fe2—Al4—Al5^xv	62.56 (5)
Al5—Ni1—Ni1^viii	171.00 (6)	Ni1—Al4—Al5^xv	123.29 (4)
Al5ⁱ—Ni1—Ni1^viii	111.00 (6)	Al3ⁱⁱⁱ—Al4—Al5^xv	105.21 (5)
Al4—Ni1—Ni1^viii	108.47 (4)	Ni1^vi—Al4—Al5^xv	106.58 (6)
Al4ⁱⁱ—Ni1—Ni1^viii	108.47 (4)	Ni1^v—Al4—Al5^xv	52.20 (4)
Al3—Ni1—Ni1^viii	55.001 (16)	Al4^vi—Al4—Al5^xv	159.64 (7)
Al3ⁱⁱⁱ—Ni1—Ni1^viii	55.001 (16)	Al4^v—Al4—Al5^xv	64.61 (6)
Al4^iv—Ni1—Ni1^viii	57.48 (3)	Fe2—Al4—Al5^vi	62.56 (5)
Al4^v—Ni1—Ni1^viii	107.23 (4)	Ni1—Al4—Al5^vi	123.29 (4)
Al4^vi—Ni1—Ni1^viii	57.48 (3)	Al3ⁱⁱⁱ—Al4—Al5^vi	105.21 (5)
Al4^vii—Ni1—Ni1^viii	107.23 (4)	Ni1^vi—Al4—Al5^vi	52.20 (4)
Al5—Ni1—Ni1^ix	111.00 (6)	Ni1^v—Al4—Al5^vi	106.58 (6)
Al5ⁱ—Ni1—Ni1^ix	171.00 (6)	Al4^vi—Al4—Al5^vi	64.61 (6)
Al4—Ni1—Ni1^ix	108.47 (4)	Al4^v—Al4—Al5^vi	159.64 (7)
Al4ⁱⁱ—Ni1—Ni1^ix	108.47 (4)	Al5^xv—Al4—Al5^vi	113.32 (8)
Al3—Ni1—Ni1^ix	55.001 (16)	Fe2—Al4—Al4^xii	51.63 (4)
Al3ⁱⁱⁱ—Ni1—Ni1^ix	55.001 (16)	Ni1—Al4—Al4^xii	158.54 (5)
Al4^iv—Ni1—Ni1^ix	107.23 (4)	Al3ⁱⁱⁱ—Al4—Al4^xii	99.89 (4)
Al4^v—Ni1—Ni1^ix	57.48 (3)	Ni1^vi—Al4—Al4^xii	57.71 (3)
Al4^vi—Ni1—Ni1^ix	107.23 (4)	Ni1^v—Al4—Al4^xii	57.71 (3)
Al4^vii—Ni1—Ni1^ix	57.48 (3)	Al4^vi—Al4—Al4^xii	109.23 (7)
Ni1^viii—Ni1—Ni1^ix	60.0	Al4^v—Al4—Al4^xii	109.23 (7)
Al4^x—Fe2—Al4ⁱ	76.74 (9)	Al5^xv—Al4—Al4^xii	58.61 (4)
Al4^x—Fe2—Al4	133.84 (3)	Al5^vi—Al4—Al4^xii	58.61 (4)
Al4ⁱ—Fe2—Al4	85.53 (6)	Fe2—Al4—Al5ⁱ	104.03 (5)
Al4^x—Fe2—Al4^xi	85.53 (6)	Ni1—Al4—Al5ⁱ	51.44 (4)
Al4ⁱ—Fe2—Al4^xi	133.84 (3)	Al3ⁱⁱⁱ—Al4—Al5ⁱ	100.34 (5)
Al4—Fe2—Al4^xi	133.84 (3)	Ni1^vi—Al4—Al5ⁱ	111.02 (5)
Al4^x—Fe2—Al4^xii	85.53 (6)	Ni1^v—Al4—Al5ⁱ	155.58 (7)
Al4ⁱ—Fe2—Al4^xii	133.84 (3)	Al4^vi—Al4—Al5ⁱ	57.97 (7)
Al4—Fe2—Al4^xii	76.74 (9)	Al4^v—Al4—Al5ⁱ	108.01 (9)
Al4^xi—Fe2—Al4^xii	85.53 (6)	Al5^xv—Al4—Al5ⁱ	141.91 (7)
Al4^x—Fe2—Al4^xiii	133.84 (3)	Al5^vi—Al4—Al5ⁱ	85.95 (3)
Al4ⁱ—Fe2—Al4^xiii	85.53 (6)	Al4^xii—Al4—Al5ⁱ	142.74 (3)
Al4—Fe2—Al4^xiii	85.53 (6)	Fe2—Al4—Al5	104.03 (5)
Al4^xi—Fe2—Al4^xiii	76.74 (9)	Ni1—Al4—Al5	51.44 (4)
Al4^xii—Fe2—Al4^xiii	133.84 (3)	Al3ⁱⁱⁱ—Al4—Al5	100.34 (5)
Al4^x—Fe2—Al5^vi	66.920 (15)	Ni1^vi—Al4—Al5	155.58 (7)
Al4ⁱ—Fe2—Al5^vi	66.920 (15)	Ni1^v—Al4—Al5	111.02 (5)
Al4—Fe2—Al5^vi	66.920 (15)	Al4^vi—Al4—Al5	108.01 (9)
Al4^xi—Fe2—Al5^vi	141.63 (4)	Al4^v—Al4—Al5	57.97 (7)
Al4^xii—Fe2—Al5^vi	66.920 (15)	Al5^xv—Al4—Al5	85.95 (3)
Al4^xiii—Fe2—Al5^vi	141.63 (4)	Al5^vi—Al4—Al5	141.91 (7)
Al4^x—Fe2—Al5^xiv	66.920 (15)	Al4^xii—Al4—Al5	142.74 (3)
Al4ⁱ—Fe2—Al5^xiv	66.920 (15)	Al5ⁱ—Al4—Al5	61.77 (8)
Al4—Fe2—Al5^xiv	141.63 (4)	Ni1^xiii—Al5—Ni1	162.00 (12)
Al4^xi—Fe2—Al5^xiv	66.920 (15)	Ni1^xiii—Al5—Fe2^xv	99.00 (6)
Al4^xii—Fe2—Al5^xiv	141.63 (4)	Ni1—Al5—Fe2^xv	99.00 (6)
Al4^xiii—Fe2—Al5^xiv	66.920 (15)	Ni1^xiii—Al5—Al4^xv	62.41 (4)
Al5^vi—Fe2—Al5^xiv	120.0	Ni1—Al5—Al4^xv	131.46 (7)
Al4^x—Fe2—Al5^xv	141.63 (4)	Fe2^xv—Al5—Al4^xv	50.52 (5)
Al4ⁱ—Fe2—Al5^xv	141.63 (4)	Ni1^xiii—Al5—Al4^vii	131.46 (7)
Al4—Fe2—Al5^xv	66.920 (15)	Ni1—Al5—Al4^vii	62.41 (4)
Al4^xi—Fe2—Al5^xv	66.920 (15)	Fe2^xv—Al5—Al4^vii	50.52 (5)
Al4^xii—Fe2—Al5^xv	66.920 (15)	Al4^xv—Al5—Al4^vii	101.04 (10)
Al4^xiii—Fe2—Al5^xv	66.920 (15)	Ni1^xiii—Al5—Al4^xxii	62.41 (4)
Al5^vi—Fe2—Al5^xv	120.0	Ni1—Al5—Al4^xxii	131.46 (7)
Al5^xiv—Fe2—Al5^xv	120.0	Fe2^xv—Al5—Al4^xxii	50.52 (5)
Ni1^xvi—Al3—Ni1	180.0	Al4^xv—Al5—Al4^xxii	62.77 (7)
Ni1^xvi—Al3—Ni1^xvii	70.00 (3)	Al4^vii—Al5—Al4^xxii	69.46 (8)
Ni1—Al3—Ni1^xvii	110.00 (3)	Ni1^xiii—Al5—Al4^v	131.46 (7)
Ni1^xvi—Al3—Ni1^ix	110.00 (3)	Ni1—Al5—Al4^v	62.41 (4)
Ni1—Al3—Ni1^ix	70.00 (3)	Fe2^xv—Al5—Al4^v	50.52 (5)
Ni1^xvii—Al3—Ni1^ix	180.00 (3)	Al4^xv—Al5—Al4^v	69.46 (8)
Ni1^xvi—Al3—Ni1^xviii	70.00 (3)	Al4^vii—Al5—Al4^v	62.77 (7)
Ni1—Al3—Ni1^xviii	110.00 (3)	Al4^xxii—Al5—Al4^v	101.04 (10)
Ni1^xvii—Al3—Ni1^xviii	70.00 (3)	Ni1^xiii—Al5—Al4^xiii	55.08 (3)
Ni1^ix—Al3—Ni1^xviii	110.00 (3)	Ni1—Al5—Al4^xiii	118.92 (5)
Ni1^xvi—Al3—Ni1^viii	110.00 (3)	Fe2^xv—Al5—Al4^xiii	106.50 (5)
Ni1—Al3—Ni1^viii	70.00 (3)	Al4^xv—Al5—Al4^xiii	57.42 (5)
Ni1^xvii—Al3—Ni1^viii	110.00 (3)	Al4^vii—Al5—Al4^xiii	154.12 (8)
Ni1^ix—Al3—Ni1^viii	70.00 (3)	Al4^xxii—Al5—Al4^xiii	106.89 (6)
Ni1^xviii—Al3—Ni1^viii	180.00 (5)	Al4^v—Al5—Al4^xiii	94.05 (3)
Ni1^xvi—Al3—Al4^xix	62.94 (3)	Ni1^xiii—Al5—Al4ⁱⁱ	118.92 (5)
Ni1—Al3—Al4^xix	117.06 (3)	Ni1—Al5—Al4ⁱⁱ	55.08 (3)
Ni1^xvii—Al3—Al4^xix	62.94 (3)	Fe2^xv—Al5—Al4ⁱⁱ	106.50 (5)
Ni1^ix—Al3—Al4^xix	117.06 (3)	Al4^xv—Al5—Al4ⁱⁱ	154.12 (8)
Ni1^xviii—Al3—Al4^xix	121.58 (4)	Al4^vii—Al5—Al4ⁱⁱ	57.42 (5)
Ni1^viii—Al3—Al4^xix	58.42 (4)	Al4^xxii—Al5—Al4ⁱⁱ	94.05 (3)
Ni1^xvi—Al3—Al4^vii	117.06 (3)	Al4^v—Al5—Al4ⁱⁱ	106.89 (6)
Ni1—Al3—Al4^vii	62.94 (3)	Al4^xiii—Al5—Al4ⁱⁱ	146.99 (10)
Ni1^xvii—Al3—Al4^vii	117.06 (3)	Ni1^xiii—Al5—Al4^xxiii	55.08 (3)
Ni1^ix—Al3—Al4^vii	62.94 (3)	Ni1—Al5—Al4^xxiii	118.92 (5)
Ni1^xviii—Al3—Al4^vii	58.42 (4)	Fe2^xv—Al5—Al4^xxiii	106.50 (5)
Ni1^viii—Al3—Al4^vii	121.58 (4)	Al4^xv—Al5—Al4^xxiii	106.89 (6)
Al4^xix—Al3—Al4^vii	180.00 (7)	Al4^vii—Al5—Al4^xxiii	94.05 (3)
Ni1^xvi—Al3—Al4^xx	58.42 (4)	Al4^xxii—Al5—Al4^xxiii	57.42 (5)
Ni1—Al3—Al4^xx	121.58 (4)	Al4^v—Al5—Al4^xxiii	154.12 (8)
Ni1^xvii—Al3—Al4^xx	117.06 (3)	Al4^xiii—Al5—Al4^xxiii	105.49 (6)
Ni1^ix—Al3—Al4^xx	62.94 (3)	Al4ⁱⁱ—Al5—Al4^xxiii	64.63 (6)
Ni1^xviii—Al3—Al4^xx	117.06 (3)	Ni1^xiii—Al5—Al4	118.92 (5)
Ni1^viii—Al3—Al4^xx	62.94 (3)	Ni1—Al5—Al4	55.08 (3)
Al4^xix—Al3—Al4^xx	62.89 (2)	Fe2^xv—Al5—Al4	106.50 (5)
Al4^vii—Al3—Al4^xx	117.11 (2)	Al4^xv—Al5—Al4	94.05 (3)
Ni1^xvi—Al3—Al4ⁱⁱ	121.58 (4)	Al4^vii—Al5—Al4	106.89 (6)
Ni1—Al3—Al4ⁱⁱ	58.42 (4)	Al4^xxii—Al5—Al4	154.12 (8)
Ni1^xvii—Al3—Al4ⁱⁱ	62.94 (3)	Al4^v—Al5—Al4	57.42 (5)
Ni1^ix—Al3—Al4ⁱⁱ	117.06 (3)	Al4^xiii—Al5—Al4	64.63 (6)
Ni1^xviii—Al3—Al4ⁱⁱ	62.94 (3)	Al4ⁱⁱ—Al5—Al4	105.49 (6)
Ni1^viii—Al3—Al4ⁱⁱ	117.06 (3)	Al4^xxiii—Al5—Al4	146.99 (10)
Al4^xix—Al3—Al4ⁱⁱ	117.11 (2)

Symmetry codes: (i) −y+1, x−y, z; (ii) x, y, −z+1/2; (iii) −x, −y, z+1/2; (iv) y, −x+y, z−1/2; (v) x−y, x, −z+1; (vi) y, −x+y, −z+1; (vii) x−y, x, z−1/2; (viii) −x+y, −x, z; (ix) −y, x−y, z; (x) −y+1, x−y, −z+3/2; (xi) −x+y+1, −x+1, −z+3/2; (xii) x, y, −z+3/2; (xiii) −x+y+1, −x+1, z; (xiv) x−y+1, x, −z+1; (xv) −x+1, −y+1, −z+1; (xvi) −x, −y, −z; (xvii) y, −x+y, −z; (xviii) x−y, x, −z; (xix) −x+y, −x, −z+1/2; (xx) −x, −y, z−1/2; (xxi) −y, x−y, −z+1/2; (xxii) −x+1, −y+1, z−1/2; (xxiii) −x+y+1, −x+1, −z+1/2.

Acknowledgements

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

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