(Al13.28Si2.72)(Fe1.19Ni2.81)

Chen, M.; Fan, C.; Wen, B.; Zhang, L.

doi:10.1107/S2414314625010387

inorganic compounds

IUCrDATA

ISSN: 2414-3146

Volume 10| Part 11| November 2025| x251038

https://doi.org/10.1107/S2414314625010387

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(Al_13.28Si_2.72)(Fe_1.19Ni_2.81)

Mei Chen,^a Changzeng Fan,^a,^b ^* Bin Wen ^a and Lifeng Zhang ^a,^c

^aState Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, People's Republic of China, ^bHebei Key Lab for Optimizing Metal Product Technology and Performance, Yanshan University, Qinhuangdao 066004, People's Republic of China, and ^cSchool of Mechanical and Materials Engineering, North China University of Technology, Beijing 100144, People's Republic of China
^*Correspondence e-mail: [email protected]

Edited by M. Weil, Vienna University of Technology, Austria (Received 28 October 2025; accepted 19 November 2025; online 21 November 2025)

The intermetallic phase (Al_13.28Si_2.72)(Fe_1.19Ni_2.81) was obtained by high-pressure sintering (HPS) of a mixture with an elemental atomic ratio corresponding to (Al,Si)₅(Fe,Ni). The space group was determined to be C2/m with Z = 2. The structure model contains three co-occupied sites with occupancy ratios of Si:Al = 0.679:0.321, Ni:Fe = 0.46:0.54 and Ni:Fe = 0.94:0.06, and five sites with full occupancy of Al atoms.

Keywords: crystal structure; high-pressure; intermetallic; Al_13.28Fe_1.19Ni_2.81Si_2.72 phase.

CCDC reference: 2503943

Structure description

In the quaternary Al–Si–Ni–Fe near-eutectic alloy, an (Al,Si)₅(Fe,Ni) phase exists, which adopts the tetragonal (Al_2.7Si_2.3)Fe structure type. The reported composition is based on TEM-EDX point analysis with atomic percentages of 77.1 (Al), 6.5 (Si), 8.6 (Fe) and 7.8 (Ni) (Cai et al., 2023 ). It has been confirmed through first-principles calculations that the Si sites tend to be co-occupied by Al atoms and are adjacent to the Fe atoms; the co-occupied atoms have stable configurations (Cai et al., 2023). The growth mechanism of this intermetallic phase under high-pressure and high-temperature (HPHT) conditions was investigated by the high-pressure sintering (HPS) process, which eventually led to a new phase with composition (Al_13.28Si_2.72)(Fe_1.19Ni_2.81) in the quaternary Al–Si–Ni–Fe system. The title phase and the Al₁₃Fe₄ phase (Grin et al., 1994 ) both crystallize in space group type C2/m, however without close relationship. The decagonal quasicrystal approximant Al₇₆Ni₉Fe₁₅, studied by Nejadsattari et al. (2016 ) in the Al–Ni–Fe ternary system, is isotypic with Al₁₃Fe₄, where Fe and Ni atoms co-occupy 4i and 8j sites.

The asymmetric unit of (Al_13.28Si_2.72)(Fe_1.19Ni_2.81) comprises eight sites: five are fully occupied by Al atoms at Wyckoff sites 8j (Al2), 4g (Al3), and 4i (Al4, Al5, Al6); one site (8j) is partially occupied by Si1 (occupancy 0.679) and Al1 (occupancy 0.321) atoms; one site (4i) is partially occupied by Ni1 (occupancy 0.46) and Fe1 (occupancy 0.54) atoms; one site (4h) is partially occupied by Ni2 (occupancy 0.94) and Fe2 (occupancy 0.06). The Al4 atom at the 4i site and the (Fe,Ni)2 atoms at the co-occupied 4h site are surrounded by twelve and ten atoms, forming distorted 19-face and 16-face polyhedra, respectively (Figs. 1–3 ).

Figure 1
The crystal structure of (Al_13.28Si_2.72)(Fe_1.19Ni_2.81) with two Al4 atoms on the 4i site and two (Fe,Ni)2 atoms on the 4h site displayed with their coordination environments as polyhedra.

Figure 2
(a) The enneadecahedron formed around the Al4 atom at the 4i site; (b) the environment of the Al4 atom with displacement ellipsoids given at the 80% probability level. [Symmetry codes: (i) x, −y + 1, z; (viii) −x + $[{3\over 2}]$ , −y + $[{1\over 2}]$ , −z; (xi) x, y, z − 1; (xii) −x + $[{3\over 2}]$ , y + $[{1\over 2}]$ , −z; (xiii) x, −y + 1, z − 1.]

Figure 3
(a) The hexadecahedron formed around the (Fe,Ni)2 atoms at the 4h site; (b) the environment of the (Fe,Ni)2 atoms with displacement ellipsoids given at the 90% probability level. [Symmetry codes: (ii) x, y, z + 1; (iv) −x + $[{3\over 2}]$ , −y + $[{1\over 2}]$ , −z + 1; (v) −x + 1, y, −z + 1; (vi) x − $[{1\over 2}]$ , y − $[{1\over 2}]$ , z; (vii) −x + 1, −y + 1, −z + 1.]

Synthesis and crystallization

The high purity elements aluminium (indicated purity 99.9%; 0.6739 g), iron (indicated purity 99.9%; 0.1442 g), nickel (indicated purity 99.9%; 0.1566 g), and silicon (indicated purity 99.9%; 0.0826 g) were evenly mixed with a stoichiometric ratio of 77.1: 8.6: 7.8: 6.5 and ground in an agate mortar for 40 min. The mixed powder was then placed in a cemented carbide grinding mold with a diameter of 5 mm and pressed into a block at about 4 MPa for three min. Cylindrical blocks without deformation and cracks were obtained. Details of high-pressure sintering experiments using six-anvil high-temperature and high-pressure equipment are described in detail (Liu & Fan, 2018 ). The sample was pressurized to 6 GPa and heated at 1676 K for 30 min., then cooled to 1131 K and held for 60 min., and finally rapidly cooled to room temperature by turning off the furnace power. A single-crystal was selected and mounted on a glass fiber for SXRD measurement.

Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1. Due to the similar electron densities of Ni/Fe and Si/Al at co-occupied sites, the site-occupancy refinement for these mixed sites is inherently inaccurate. To obtain a reasonable composition, the total proportion of Fe and Ni was maintained at approximately 20% (to preserve structural validity), while the relative occupancies of Al and Si were adjusted to approximate their ratio determined from EDX data (see the supporting information) as closely as possible. Several compositions were evaluated, and the model with the composition Al 66.42%, Si 13.58%, Fe 5.97%, Ni 14.03% was finally selected. This model maintains structural rationality, closely approximates the composition determined by EDX, and yields satisfactory reliability factors. The maximum and minimum residual electron densities in the final difference map are located 1.50 Å from (Al,Si)1 and 0.93 Å from Al4, respectively.

Table 1
Experimental details

Crystal data
Chemical formula	Al_13.28Fe_1.19Ni_2.81Si_2.72
M_r	666.12
Crystal system, space group	Monoclinic, C2/m
Temperature (K)	296
a, b, c (Å)	14.2407 (16), 8.6413 (10), 4.7167 (5)
β (°)	91.359 (4)
V (Å³)	580.27 (11)
Z	2
Radiation type	Mo Kα
μ (mm⁻¹)	7.20
Crystal size (mm)	0.10 × 0.09 × 0.08

Data collection
Diffractometer	Bruker D8 Venture Photon 100 CMOS
Absorption correction	Multi-scan (SADABS; Krause et al., 2015 )
T_min, T_max	0.600, 0.746
No. of measured, independent and observed [I > 2σ(I)] reflections	3712, 707, 586
R_int	0.057
(sin θ/λ)_max (Å⁻¹)	0.650

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.036, 0.059, 1.11
No. of reflections	707
No. of parameters	55
Δρ_max, Δρ_min (e Å⁻³)	0.81, −0.83
Computer programs: APEX5 and SAINT (Bruker, 2023 ), SHELXT (Sheldrick, 2015a ), SHELXT (Sheldrick, 2015b ), DIAMOND (Brandenburg & Putz, 2017 ) and publCIF (Westrip, 2010 ).

Structural data

CCDC reference: 2503943

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2414314625010387/wm4239sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2414314625010387/wm4239Isup2.hkl

supplementary marerials. DOI: https://doi.org/10.1107/S2414314625010387/wm4239sup3.docx

checkCIF report

Computing details top

Aluminium iron nickel silicide top

Crystal data top

Al_13.28Fe_1.19Ni_2.81Si_2.72	F(000) = 641
M_r = 666.12	D_x = 3.812 Mg m⁻³
Monoclinic, C2/m	Mo Kα radiation, λ = 0.71073 Å
a = 14.2407 (16) Å	Cell parameters from 2307 reflections
b = 8.6413 (10) Å	θ = 2.8–27.5°
c = 4.7167 (5) Å	µ = 7.20 mm⁻¹
β = 91.359 (4)°	T = 296 K
V = 580.27 (11) Å³	Lump, gray
Z = 2	0.10 × 0.09 × 0.08 mm

Data collection top

Bruker D8 Venture Photon 100 CMOS diffractometer	586 reflections with I > 2σ(I)
phi and ω scans	R_int = 0.057
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	θ_max = 27.5°, θ_min = 2.8°
T_min = 0.600, T_max = 0.746	h = −18→18
3712 measured reflections	k = −10→11
707 independent reflections	l = −5→6

Refinement top

Refinement on F²	55 parameters
Least-squares matrix: full	0 restraints
R[F² > 2σ(F²)] = 0.036	w = 1/[σ²(F_o²) + (0.0135P)² + 2.4081P] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.059	(Δ/σ)_max < 0.001
S = 1.11	Δρ_max = 0.81 e Å⁻³
707 reflections	Δρ_min = −0.83 e Å⁻³

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	0.73802 (5)	0.500000	0.53636 (18)	0.0060 (3)	0.46 (5)
Fe1	0.73802 (5)	0.500000	0.53636 (18)	0.0060 (3)	0.54 (5)
Ni2	0.500000	0.24889 (9)	0.500000	0.0076 (3)	0.94 (5)
Fe2	0.500000	0.24889 (9)	0.500000	0.0076 (3)	0.06 (5)
Si1	0.62407 (8)	0.35232 (15)	0.7917 (3)	0.0110 (3)	0.679
Al1	0.62407 (8)	0.35232 (15)	0.7917 (3)	0.0110 (3)	0.321
Al2	0.68103 (9)	0.25081 (16)	0.2938 (3)	0.0116 (3)
Al3	0.500000	0.1550 (2)	0.000000	0.0111 (5)
Al4	0.78856 (14)	0.500000	0.0425 (4)	0.0138 (5)
Al5	0.90936 (13)	0.500000	0.4897 (4)	0.0127 (5)
Al6	0.55911 (13)	0.500000	0.2742 (4)	0.0097 (4)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ni1	0.0077 (5)	0.0047 (4)	0.0055 (5)	0.000	0.0007 (3)	0.000
Fe1	0.0077 (5)	0.0047 (4)	0.0055 (5)	0.000	0.0007 (3)	0.000
Ni2	0.0113 (4)	0.0052 (4)	0.0065 (5)	0.000	0.0008 (3)	0.000
Fe2	0.0113 (4)	0.0052 (4)	0.0065 (5)	0.000	0.0008 (3)	0.000
Si1	0.0115 (7)	0.0135 (7)	0.0081 (7)	−0.0040 (5)	−0.0005 (5)	0.0027 (6)
Al1	0.0115 (7)	0.0135 (7)	0.0081 (7)	−0.0040 (5)	−0.0005 (5)	0.0027 (6)
Al2	0.0168 (7)	0.0071 (6)	0.0107 (7)	0.0012 (6)	−0.0046 (5)	−0.0007 (6)
Al3	0.0218 (11)	0.0074 (10)	0.0042 (10)	0.000	0.0015 (8)	0.000
Al4	0.0198 (10)	0.0172 (11)	0.0044 (11)	0.000	−0.0002 (8)	0.000
Al5	0.0080 (9)	0.0075 (10)	0.0225 (12)	0.000	0.0004 (8)	0.000
Al6	0.0138 (9)	0.0075 (10)	0.0079 (10)	0.000	0.0030 (8)	0.000

Geometric parameters (Å, º) top

Ni1—Si1ⁱ	2.4093 (13)	Ni2—Al2^v	2.7768 (13)
Ni1—Si1	2.4094 (13)	Fe2—Si1	2.3872 (13)
Ni1—Al4	2.455 (2)	Fe2—Si1^v	2.3872 (13)
Ni1—Al5	2.455 (2)	Fe2—Al3ⁱⁱ	2.4939 (7)
Ni1—Al4ⁱⁱ	2.477 (2)	Fe2—Al3	2.4939 (7)
Ni1—Al2ⁱ	2.5612 (14)	Fe2—Al5^vi	2.5082 (12)
Ni1—Al2	2.5612 (14)	Fe2—Al5^iv	2.5082 (12)
Ni1—Al2ⁱⁱⁱ	2.5737 (14)	Fe2—Al6	2.5679 (12)
Ni1—Al2^iv	2.5737 (14)	Fe2—Al6^vii	2.5680 (12)
Ni1—Al6	2.806 (2)	Fe2—Al2	2.7768 (13)
Fe1—Si1ⁱ	2.4093 (13)	Fe2—Al2^v	2.7768 (13)
Fe1—Si1	2.4094 (13)	Si1—Si1ⁱ	2.552 (3)
Fe1—Al4	2.455 (2)	Si1—Al2ⁱⁱ	2.6354 (19)
Fe1—Al5	2.455 (2)	Si1—Al2	2.6518 (19)
Fe1—Al4ⁱⁱ	2.477 (2)	Si1—Al3ⁱⁱ	2.6601 (17)
Fe1—Al2ⁱ	2.5612 (14)	Si1—Al6ⁱⁱ	2.786 (2)
Fe1—Al2	2.5612 (14)	Si1—Al6	2.887 (2)
Fe1—Al2ⁱⁱⁱ	2.5737 (14)	Si1—Al4ⁱⁱ	2.895 (2)
Fe1—Al2^iv	2.5737 (14)	Si1—Al6^vii	2.914 (2)
Fe1—Al6	2.806 (2)	Al2—Al4^viii	2.7264 (18)
Ni2—Si1	2.3872 (13)	Al2—Al5^iv	2.7311 (18)
Ni2—Si1^v	2.3872 (13)	Al2—Al2^iv	2.731 (3)
Ni2—Al3ⁱⁱ	2.4939 (7)	Al2—Al6	2.7663 (18)
Ni2—Al3	2.4939 (7)	Al3—Al3^ix	2.679 (4)
Ni2—Al5^vi	2.5082 (12)	Al3—Al5^viii	2.990 (2)
Ni2—Al5^iv	2.5082 (12)	Al3—Al5^vi	2.990 (2)
Ni2—Al6	2.5679 (12)	Al4—Al5	2.690 (3)
Ni2—Al6^vii	2.5680 (12)	Al5—Al5^x	2.581 (4)
Ni2—Al2	2.7768 (13)	Al6—Al6^vii	2.747 (4)

Si1ⁱ—Ni1—Si1	63.97 (7)	Al2—Si1—Al6	59.74 (5)
Si1ⁱ—Ni1—Al4	133.68 (5)	Al3ⁱⁱ—Si1—Al6	113.15 (5)
Si1—Ni1—Al4	133.68 (5)	Al6ⁱⁱ—Si1—Al6	112.47 (6)
Si1ⁱ—Ni1—Al5	136.66 (5)	Ni2—Si1—Al4ⁱⁱ	168.83 (6)
Si1—Ni1—Al5	136.66 (5)	Ni1—Si1—Al4ⁱⁱ	54.75 (5)
Al4—Ni1—Al5	66.45 (7)	Si1ⁱ—Si1—Al4ⁱⁱ	63.85 (3)
Si1ⁱ—Ni1—Al4ⁱⁱ	72.66 (5)	Al2ⁱⁱ—Si1—Al4ⁱⁱ	63.31 (5)
Si1—Ni1—Al4ⁱⁱ	72.66 (5)	Al2—Si1—Al4ⁱⁱ	104.24 (6)
Al4—Ni1—Al4ⁱⁱ	146.06 (9)	Al3ⁱⁱ—Si1—Al4ⁱⁱ	132.04 (6)
Al5—Ni1—Al4ⁱⁱ	79.61 (7)	Al6ⁱⁱ—Si1—Al4ⁱⁱ	75.26 (6)
Si1ⁱ—Ni1—Al2ⁱ	64.40 (5)	Al6—Si1—Al4ⁱⁱ	112.98 (6)
Si1—Ni1—Al2ⁱ	117.29 (5)	Fe2—Si1—Al6^vii	56.91 (4)
Al4—Ni1—Al2ⁱ	70.92 (4)	Ni2—Si1—Al6^vii	56.91 (4)
Al5—Ni1—Al2ⁱ	105.37 (4)	Ni1—Si1—Al6^vii	109.06 (5)
Al4ⁱⁱ—Ni1—Al2ⁱ	120.81 (4)	Fe1—Si1—Al6^vii	109.06 (5)
Si1ⁱ—Ni1—Al2	117.29 (5)	Si1ⁱ—Si1—Al6^vii	64.03 (3)
Si1—Ni1—Al2	64.40 (5)	Al2ⁱⁱ—Si1—Al6^vii	119.82 (6)
Al4—Ni1—Al2	70.92 (4)	Al2—Si1—Al6^vii	110.02 (6)
Al5—Ni1—Al2	105.37 (4)	Al3ⁱⁱ—Si1—Al6^vii	73.70 (5)
Al4ⁱⁱ—Ni1—Al2	120.81 (4)	Al6ⁱⁱ—Si1—Al6^vii	64.71 (7)
Al2ⁱ—Ni1—Al2	114.44 (7)	Al6—Si1—Al6^vii	56.51 (7)
Si1ⁱ—Ni1—Al2ⁱⁱⁱ	72.57 (4)	Al4ⁱⁱ—Si1—Al6^vii	124.34 (5)
Si1—Ni1—Al2ⁱⁱⁱ	126.33 (5)	Ni1—Al2—Ni1^iv	115.73 (5)
Al4—Ni1—Al2ⁱⁱⁱ	98.98 (4)	Ni1—Al2—Si1^xi	102.07 (6)
Al5—Ni1—Al2ⁱⁱⁱ	65.74 (4)	Ni1^iv—Al2—Si1^xi	133.31 (7)
Al4ⁱⁱ—Ni1—Al2ⁱⁱⁱ	65.31 (4)	Fe1—Al2—Si1	55.02 (4)
Al2ⁱ—Ni1—Al2ⁱⁱⁱ	64.27 (5)	Ni1—Al2—Si1	55.02 (4)
Al2—Ni1—Al2ⁱⁱⁱ	169.06 (3)	Ni1^iv—Al2—Si1	98.46 (6)
Si1ⁱ—Ni1—Al2^iv	126.33 (5)	Si1^xi—Al2—Si1	126.27 (7)
Si1—Ni1—Al2^iv	72.57 (4)	Ni1—Al2—Al4^viii	151.06 (7)
Al4—Ni1—Al2^iv	98.98 (4)	Ni1^iv—Al2—Al4^viii	55.63 (5)
Al5—Ni1—Al2^iv	65.74 (4)	Si1^xi—Al2—Al4^viii	77.96 (6)
Al4ⁱⁱ—Ni1—Al2^iv	65.31 (4)	Si1—Al2—Al4^viii	146.54 (7)
Al2ⁱ—Ni1—Al2^iv	169.06 (3)	Ni1—Al2—Al5^iv	130.35 (7)
Al2—Ni1—Al2^iv	64.27 (5)	Ni1^iv—Al2—Al5^iv	55.04 (5)
Al2ⁱⁱⁱ—Ni1—Al2^iv	114.73 (7)	Si1^xi—Al2—Al5^iv	117.54 (7)
Si1ⁱ—Ni1—Al6	66.74 (5)	Si1—Al2—Al5^iv	76.98 (6)
Si1—Ni1—Al6	66.74 (5)	Al4^viii—Al2—Al5^iv	70.69 (6)
Al4—Ni1—Al6	82.26 (6)	Ni1—Al2—Al2^iv	58.09 (5)
Al5—Ni1—Al6	148.71 (7)	Ni1^iv—Al2—Al2^iv	57.64 (5)
Al4ⁱⁱ—Ni1—Al6	131.68 (7)	Si1^xi—Al2—Al2^iv	147.40 (9)
Al2ⁱ—Ni1—Al6	61.86 (4)	Si1—Al2—Al2^iv	66.49 (6)
Al2—Ni1—Al6	61.86 (4)	Al4^viii—Al2—Al2^iv	106.78 (8)
Al2ⁱⁱⁱ—Ni1—Al6	122.18 (3)	Al5^iv—Al2—Al2^iv	93.85 (8)
Al2^iv—Ni1—Al6	122.18 (3)	Fe1—Al2—Al6	63.42 (5)
Si1ⁱ—Fe1—Si1	63.97 (7)	Ni1—Al2—Al6	63.42 (5)
Si1ⁱ—Fe1—Al4	133.68 (5)	Ni1^iv—Al2—Al6	160.41 (7)
Si1—Fe1—Al4	133.68 (5)	Si1^xi—Al2—Al6	62.04 (6)
Si1ⁱ—Fe1—Al5	136.66 (5)	Si1—Al2—Al6	64.36 (6)
Si1—Fe1—Al5	136.66 (5)	Al4^viii—Al2—Al6	135.03 (8)
Al4—Fe1—Al5	66.45 (7)	Al5^iv—Al2—Al6	109.22 (6)
Si1ⁱ—Fe1—Al4ⁱⁱ	72.66 (5)	Al2^iv—Al2—Al6	117.91 (8)
Si1—Fe1—Al4ⁱⁱ	72.66 (5)	Fe1—Al2—Fe2	97.79 (5)
Al4—Fe1—Al4ⁱⁱ	146.06 (9)	Si1^xi—Al2—Fe2	92.76 (5)
Al5—Fe1—Al4ⁱⁱ	79.61 (7)	Si1—Al2—Fe2	52.11 (4)
Si1ⁱ—Fe1—Al2ⁱ	64.40 (5)	Al4^viii—Al2—Fe2	111.13 (6)
Si1—Fe1—Al2ⁱ	117.29 (5)	Al5^iv—Al2—Fe2	54.17 (4)
Al4—Fe1—Al2ⁱ	70.92 (4)	Al2^iv—Al2—Fe2	114.12 (7)
Al5—Fe1—Al2ⁱ	105.37 (4)	Al6—Al2—Fe2	55.20 (4)
Al4ⁱⁱ—Fe1—Al2ⁱ	120.81 (4)	Ni1—Al2—Ni2	97.79 (5)
Si1ⁱ—Fe1—Al2	117.29 (5)	Ni1^iv—Al2—Ni2	107.38 (5)
Si1—Fe1—Al2	64.40 (5)	Si1^xi—Al2—Ni2	92.76 (5)
Al4—Fe1—Al2	70.92 (4)	Si1—Al2—Ni2	52.11 (4)
Al5—Fe1—Al2	105.37 (4)	Al4^viii—Al2—Ni2	111.13 (6)
Al4ⁱⁱ—Fe1—Al2	120.81 (4)	Al5^iv—Al2—Ni2	54.17 (4)
Al2ⁱ—Fe1—Al2	114.44 (7)	Al2^iv—Al2—Ni2	114.12 (7)
Si1ⁱ—Fe1—Al2ⁱⁱⁱ	72.57 (4)	Al6—Al2—Ni2	55.20 (4)
Si1—Fe1—Al2ⁱⁱⁱ	126.33 (5)	Ni2^xi—Al3—Ni2	142.04 (9)
Al4—Fe1—Al2ⁱⁱⁱ	98.98 (4)	Ni2^xi—Al3—Si1^xi	55.07 (4)
Al5—Fe1—Al2ⁱⁱⁱ	65.74 (4)	Ni2—Al3—Si1^xi	98.96 (6)
Al4ⁱⁱ—Fe1—Al2ⁱⁱⁱ	65.31 (4)	Ni2^xi—Al3—Si1^v	98.96 (6)
Al2ⁱ—Fe1—Al2ⁱⁱⁱ	64.27 (5)	Ni2—Al3—Si1^v	55.07 (4)
Al2—Fe1—Al2ⁱⁱⁱ	169.06 (3)	Si1^xi—Al3—Si1^v	100.28 (8)
Si1ⁱ—Fe1—Al2^iv	126.33 (5)	Ni2^xi—Al3—Al3^ix	108.98 (5)
Si1—Fe1—Al2^iv	72.57 (4)	Ni2—Al3—Al3^ix	108.98 (5)
Al4—Fe1—Al2^iv	98.98 (4)	Si1^xi—Al3—Al3^ix	129.86 (4)
Al5—Fe1—Al2^iv	65.74 (4)	Si1^v—Al3—Al3^ix	129.86 (4)
Al4ⁱⁱ—Fe1—Al2^iv	65.31 (4)	Ni2^xi—Al3—Al5^viii	53.52 (3)
Al2ⁱ—Fe1—Al2^iv	169.06 (3)	Ni2—Al3—Al5^viii	152.38 (4)
Al2—Fe1—Al2^iv	64.27 (5)	Si1^xi—Al3—Al5^viii	72.49 (4)
Al2ⁱⁱⁱ—Fe1—Al2^iv	114.73 (7)	Si1^v—Al3—Al5^viii	151.08 (5)
Si1ⁱ—Fe1—Al6	66.74 (5)	Al3^ix—Al3—Al5^viii	63.38 (4)
Si1—Fe1—Al6	66.74 (5)	Ni2^xi—Al3—Al5^vi	152.38 (4)
Al4—Fe1—Al6	82.26 (6)	Ni2—Al3—Al5^vi	53.52 (3)
Al5—Fe1—Al6	148.71 (7)	Si1^xi—Al3—Al5^vi	151.08 (5)
Al4ⁱⁱ—Fe1—Al6	131.68 (7)	Si1^v—Al3—Al5^vi	72.49 (4)
Al2ⁱ—Fe1—Al6	61.86 (4)	Al3^ix—Al3—Al5^vi	63.38 (4)
Al2—Fe1—Al6	61.86 (4)	Al5^viii—Al3—Al5^vi	126.76 (8)
Al2ⁱⁱⁱ—Fe1—Al6	122.18 (3)	Ni1—Al4—Ni1^xi	146.06 (9)
Al2^iv—Fe1—Al6	122.18 (3)	Fe1—Al4—Al5	56.78 (6)
Si1—Ni2—Si1^v	136.03 (7)	Ni1—Al4—Al5	56.78 (6)
Si1—Ni2—Al3ⁱⁱ	66.00 (4)	Ni1^xi—Al4—Al5	157.15 (9)
Si1^v—Ni2—Al3ⁱⁱ	130.56 (3)	Ni1—Al4—Al2^viii	127.33 (4)
Si1—Ni2—Al3	130.56 (3)	Ni1^xi—Al4—Al2^viii	59.06 (5)
Si1^v—Ni2—Al3	66.00 (4)	Al5—Al4—Al2^viii	110.41 (6)
Al3ⁱⁱ—Ni2—Al3	142.04 (9)	Ni1—Al4—Al2^xii	127.33 (4)
Si1—Ni2—Al5^vi	134.89 (6)	Ni1^xi—Al4—Al2^xii	59.06 (5)
Si1^v—Ni2—Al5^vi	86.35 (5)	Al5—Al4—Al2^xii	110.41 (6)
Al3ⁱⁱ—Ni2—Al5^vi	74.21 (6)	Al2^viii—Al4—Al2^xii	105.30 (8)
Al3—Ni2—Al5^vi	73.40 (6)	Ni1—Al4—Si1^xi	97.76 (7)
Si1—Ni2—Al5^iv	86.35 (5)	Ni1^xi—Al4—Si1^xi	52.59 (5)
Si1^v—Ni2—Al5^iv	134.89 (6)	Al5—Al4—Si1^xi	144.72 (6)
Al3ⁱⁱ—Ni2—Al5^iv	73.40 (6)	Al2^viii—Al4—Si1^xi	63.26 (5)
Al3—Ni2—Al5^iv	74.21 (6)	Al2^xii—Al4—Si1^xi	104.53 (7)
Al5^vi—Ni2—Al5^iv	61.93 (8)	Ni1—Al4—Si1^xiii	97.76 (7)
Si1—Ni2—Al6	71.17 (6)	Ni1^xi—Al4—Si1^xiii	52.59 (5)
Si1^v—Ni2—Al6	71.94 (6)	Al5—Al4—Si1^xiii	144.72 (6)
Al3ⁱⁱ—Ni2—Al6	132.41 (6)	Al2^viii—Al4—Si1^xiii	104.53 (7)
Al3—Ni2—Al6	82.83 (6)	Al2^xii—Al4—Si1^xiii	63.26 (5)
Al5^vi—Ni2—Al6	152.89 (7)	Si1^xi—Al4—Si1^xiii	52.31 (6)
Al5^iv—Ni2—Al6	123.99 (5)	Ni1—Al4—Al2ⁱ	56.25 (4)
Si1—Ni2—Al6^vii	71.94 (6)	Ni1^xi—Al4—Al2ⁱ	104.41 (6)
Si1^v—Ni2—Al6^vii	71.17 (6)	Al5—Al4—Al2ⁱ	90.76 (6)
Al3ⁱⁱ—Ni2—Al6^vii	82.83 (6)	Al2^viii—Al4—Al2ⁱ	156.54 (8)
Al3—Ni2—Al6^vii	132.41 (6)	Al2^xii—Al4—Al2ⁱ	75.01 (5)
Al5^vi—Ni2—Al6^vii	123.99 (5)	Si1^xi—Al4—Al2ⁱ	93.68 (7)
Al5^iv—Ni2—Al6^vii	152.89 (7)	Si1^xiii—Al4—Al2ⁱ	53.99 (4)
Al6—Ni2—Al6^vii	64.66 (7)	Fe1—Al4—Al2	56.25 (4)
Si1—Ni2—Al2	61.25 (4)	Ni1—Al4—Al2	56.25 (4)
Si1^v—Ni2—Al2	118.46 (4)	Ni1^xi—Al4—Al2	104.41 (6)
Al3ⁱⁱ—Ni2—Al2	110.73 (3)	Al5—Al4—Al2	90.76 (6)
Al3—Ni2—Al2	69.51 (3)	Al2^viii—Al4—Al2	75.01 (5)
Al5^vi—Ni2—Al2	118.68 (5)	Al2^xii—Al4—Al2	156.54 (8)
Al5^iv—Ni2—Al2	61.98 (5)	Si1^xi—Al4—Al2	53.99 (4)
Al6—Ni2—Al2	62.19 (5)	Si1^xiii—Al4—Al2	93.68 (7)
Al6^vii—Ni2—Al2	117.15 (5)	Al2ⁱ—Al4—Al2	95.41 (8)
Si1—Ni2—Al2^v	118.46 (4)	Ni1—Al5—Ni2^xiv	120.69 (4)
Si1^v—Ni2—Al2^v	61.25 (4)	Ni1—Al5—Ni2^iv	120.69 (4)
Al3ⁱⁱ—Ni2—Al2^v	69.51 (3)	Ni2^xiv—Al5—Ni2^iv	118.07 (8)
Al3—Ni2—Al2^v	110.73 (3)	Ni1—Al5—Al5^x	172.71 (14)
Al5^vi—Ni2—Al2^v	61.98 (5)	Ni2^xiv—Al5—Al5^x	59.03 (4)
Al5^iv—Ni2—Al2^v	118.68 (5)	Ni2^iv—Al5—Al5^x	59.03 (4)
Al6—Ni2—Al2^v	117.15 (5)	Fe1—Al5—Al4	56.76 (6)
Al6^vii—Ni2—Al2^v	62.19 (5)	Ni1—Al5—Al4	56.76 (6)
Al2—Ni2—Al2^v	179.31 (6)	Ni2^xiv—Al5—Al4	109.53 (6)
Si1—Fe2—Si1^v	136.03 (7)	Ni2^iv—Al5—Al4	109.53 (6)
Si1—Fe2—Al3ⁱⁱ	66.00 (4)	Al5^x—Al5—Al4	130.53 (13)
Si1^v—Fe2—Al3ⁱⁱ	130.56 (3)	Ni1—Al5—Al2^iv	59.22 (4)
Si1—Fe2—Al3	130.56 (3)	Ni2^xiv—Al5—Al2^iv	156.95 (9)
Si1^v—Fe2—Al3	66.00 (4)	Ni2^iv—Al5—Al2^iv	63.84 (3)
Al3ⁱⁱ—Fe2—Al3	142.04 (9)	Al5^x—Al5—Al2^iv	117.76 (7)
Si1—Fe2—Al5^vi	134.89 (6)	Al4—Al5—Al2^iv	89.70 (6)
Si1^v—Fe2—Al5^vi	86.35 (5)	Ni1—Al5—Al2ⁱⁱⁱ	59.22 (4)
Al3ⁱⁱ—Fe2—Al5^vi	74.21 (6)	Ni2^xiv—Al5—Al2ⁱⁱⁱ	63.84 (3)
Al3—Fe2—Al5^vi	73.40 (6)	Ni2^iv—Al5—Al2ⁱⁱⁱ	156.95 (9)
Si1—Fe2—Al5^iv	86.35 (5)	Al5^x—Al5—Al2ⁱⁱⁱ	117.76 (7)
Si1^v—Fe2—Al5^iv	134.89 (6)	Al4—Al5—Al2ⁱⁱⁱ	89.70 (6)
Al3ⁱⁱ—Fe2—Al5^iv	73.40 (6)	Al2^iv—Al5—Al2ⁱⁱⁱ	105.04 (8)
Al3—Fe2—Al5^iv	74.21 (6)	Ni1—Al5—Al3^viii	121.16 (7)
Al5^vi—Fe2—Al5^iv	61.93 (8)	Ni2^xiv—Al5—Al3^viii	99.66 (7)
Si1—Fe2—Al6	71.17 (6)	Ni2^iv—Al5—Al3^viii	53.08 (4)
Si1^v—Fe2—Al6	71.94 (6)	Al5^x—Al5—Al3^viii	65.12 (7)
Al3ⁱⁱ—Fe2—Al6	132.41 (6)	Al4—Al5—Al3^viii	70.97 (6)
Al3—Fe2—Al6	82.83 (6)	Al2^iv—Al5—Al3^viii	98.58 (5)
Al5^vi—Fe2—Al6	152.89 (7)	Al2ⁱⁱⁱ—Al5—Al3^viii	149.36 (7)
Al5^iv—Fe2—Al6	123.99 (5)	Ni1—Al5—Al3^xiv	121.16 (7)
Si1—Fe2—Al6^vii	71.94 (6)	Ni2^xiv—Al5—Al3^xiv	53.08 (4)
Si1^v—Fe2—Al6^vii	71.17 (6)	Ni2^iv—Al5—Al3^xiv	99.66 (7)
Al3ⁱⁱ—Fe2—Al6^vii	82.83 (6)	Al5^x—Al5—Al3^xiv	65.12 (7)
Al3—Fe2—Al6^vii	132.41 (6)	Al4—Al5—Al3^xiv	70.97 (6)
Al5^vi—Fe2—Al6^vii	123.99 (5)	Al2^iv—Al5—Al3^xiv	149.36 (7)
Al5^iv—Fe2—Al6^vii	152.89 (7)	Al2ⁱⁱⁱ—Al5—Al3^xiv	98.58 (5)
Al6—Fe2—Al6^vii	64.66 (7)	Al3^viii—Al5—Al3^xiv	53.24 (8)
Si1—Fe2—Al2	61.25 (4)	Ni2—Al6—Ni2^vii	115.34 (7)
Si1^v—Fe2—Al2	118.46 (4)	Fe2—Al6—Al6^vii	57.67 (4)
Al3ⁱⁱ—Fe2—Al2	110.73 (3)	Ni2—Al6—Al6^vii	57.67 (4)
Al3—Fe2—Al2	69.51 (3)	Ni2^vii—Al6—Al6^vii	57.67 (4)
Al5^vi—Fe2—Al2	118.68 (5)	Ni2—Al6—Al2ⁱ	148.81 (9)
Al5^iv—Fe2—Al2	61.98 (5)	Ni2^vii—Al6—Al2ⁱ	62.61 (3)
Al6—Fe2—Al2	62.19 (5)	Al6^vii—Al6—Al2ⁱ	111.70 (7)
Al6^vii—Fe2—Al2	117.15 (5)	Fe2—Al6—Al2	62.61 (3)
Si1—Fe2—Al2^v	118.46 (4)	Ni2—Al6—Al2	62.61 (3)
Si1^v—Fe2—Al2^v	61.25 (4)	Ni2^vii—Al6—Al2	148.81 (9)
Al3ⁱⁱ—Fe2—Al2^v	69.51 (3)	Al6^vii—Al6—Al2	111.70 (7)
Al3—Fe2—Al2^v	110.73 (3)	Al2ⁱ—Al6—Al2	102.23 (8)
Al5^vi—Fe2—Al2^v	61.98 (5)	Ni2—Al6—Si1^xi	94.03 (3)
Al5^iv—Fe2—Al2^v	118.68 (5)	Ni2^vii—Al6—Si1^xi	147.60 (6)
Al6—Fe2—Al2^v	117.15 (5)	Al6^vii—Al6—Si1^xi	148.77 (6)
Al6^vii—Fe2—Al2^v	62.19 (5)	Al2ⁱ—Al6—Si1^xi	99.42 (7)
Al2—Fe2—Al2^v	179.31 (6)	Al2—Al6—Si1^xi	56.67 (5)
Ni2—Si1—Ni1	114.09 (5)	Ni2—Al6—Si1^xiii	147.60 (6)
Fe2—Si1—Fe1	114.09 (5)	Ni2^vii—Al6—Si1^xiii	94.03 (3)
Ni2—Si1—Si1ⁱ	111.99 (4)	Al6^vii—Al6—Si1^xiii	148.77 (6)
Ni1—Si1—Si1ⁱ	58.02 (3)	Al2ⁱ—Al6—Si1^xiii	56.67 (5)
Ni2—Si1—Al2ⁱⁱ	126.96 (6)	Al2—Al6—Si1^xiii	99.42 (7)
Ni1—Si1—Al2ⁱⁱ	115.40 (6)	Si1^xi—Al6—Si1^xiii	54.52 (6)
Si1ⁱ—Si1—Al2ⁱⁱ	109.44 (4)	Ni2—Al6—Ni1	96.91 (5)
Fe2—Si1—Al2	66.64 (4)	Ni2^vii—Al6—Ni1	96.91 (5)
Ni2—Si1—Al2	66.64 (4)	Al6^vii—Al6—Ni1	103.00 (10)
Ni1—Si1—Al2	60.58 (4)	Al2ⁱ—Al6—Ni1	54.73 (4)
Fe1—Si1—Al2	60.58 (4)	Al2—Al6—Ni1	54.73 (4)
Si1ⁱ—Si1—Al2	109.32 (4)	Si1^xi—Al6—Ni1	92.54 (6)
Al2ⁱⁱ—Si1—Al2	126.27 (7)	Si1^xiii—Al6—Ni1	92.54 (6)
Ni2—Si1—Al3ⁱⁱ	58.93 (3)	Fe2—Al6—Fe1	96.91 (5)
Ni1—Si1—Al3ⁱⁱ	170.13 (6)	Al6^vii—Al6—Fe1	103.00 (10)
Si1ⁱ—Si1—Al3ⁱⁱ	129.86 (4)	Al2ⁱ—Al6—Fe1	54.73 (4)
Al2ⁱⁱ—Si1—Al3ⁱⁱ	69.38 (4)	Al2—Al6—Fe1	54.73 (4)
Al2—Si1—Al3ⁱⁱ	109.56 (6)	Si1^xi—Al6—Fe1	92.54 (6)
Ni2—Si1—Al6ⁱⁱ	112.75 (6)	Si1^xiii—Al6—Fe1	92.54 (6)
Ni1—Si1—Al6ⁱⁱ	113.97 (6)	Fe2—Al6—Si1	51.49 (4)
Si1ⁱ—Si1—Al6ⁱⁱ	62.74 (3)	Ni2—Al6—Si1	51.49 (4)
Al2ⁱⁱ—Si1—Al6ⁱⁱ	61.28 (5)	Ni2^vii—Al6—Si1	97.14 (6)
Al2—Si1—Al6ⁱⁱ	171.58 (6)	Al6^vii—Al6—Si1	62.24 (7)
Al3ⁱⁱ—Si1—Al6ⁱⁱ	75.85 (5)	Al2ⁱ—Al6—Si1	97.32 (7)
Fe2—Si1—Al6	57.33 (4)	Al2—Al6—Si1	55.90 (5)
Ni2—Si1—Al6	57.33 (4)	Si1^xi—Al6—Si1	112.47 (6)
Ni1—Si1—Al6	63.21 (5)	Si1^xiii—Al6—Si1	141.91 (9)
Fe1—Si1—Al6	63.21 (5)	Ni1—Al6—Si1	50.05 (4)
Si1ⁱ—Si1—Al6	63.77 (3)	Fe1—Al6—Si1	50.05 (4)
Al2ⁱⁱ—Si1—Al6	172.99 (6)

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

Funding information

Funding for this research was provided by: The National Natural Science Foundation of China (grant Nos. 52173231 and U23A20537); The Innovation Ability Promotion Project of Hebei supported by Hebei Key Lab for Optimizing Metal Product Technology and Performance (grant No. 22567609H).

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