Crystal structure of Ti4Ni2C

Liu, H.; Liang, X.; Liu, Y.; Fan, C.; Wen, B.; Zhang, L.

doi:10.1107/S2414314624000439

inorganic compounds

IUCrDATA

ISSN: 2414-3146

Volume 9| Part 1| January 2024| x240043

https://doi.org/10.1107/S2414314624000439

Open

access

Crystal structure of Ti₄Ni₂C

Huizi Liu,^a Xinyu Liang,^a Yibo Liu,^a Changzeng Fan,^a,^b ^* Bin Wen ^a and Lifeng Zhang ^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: chzfan@ysu.edu.cn

Edited by M. Weil, Vienna University of Technology, Austria (Received 3 January 2024; accepted 11 January 2024; online 19 January 2024)

Single crystals of the intermetallic phase with composition Ti₄Ni₂C were serendipitously obtained by high-pressure sintering of a mixture with initial chemical composition Ti₂Ni. The Ti₄Ni₂C phase crystallizes in the Fd $[\overline{3}]$ m space group and can be considered as a partially filled Ti₂Ni structure with the C atom occupying an octahedral void. Ti₄Ni₂C is isotypic with Ti₄Ni₂O, Nb₄Ni₂C and Ta₄Ni₂C, all of which were studied previously by means of powder diffraction.

Keywords: crystal structure; high-pressure sintering; intermetallic; Ti₄Ni₂C phase.

CCDC reference: 2324933

Structure description

A large number of intermetallic phases can be grouped into classes of compounds based on structural or chemical similarities. For example, Mueller & Knott (1963 ) investigated the related crystal structures of Ti₂Cu, Ti₂Ni, Ti₄Ni₂O and Ti₄Cu₂O by X-ray and neutron powder diffraction. They determined that the Ti₂Ni phase crystallizes in the Fd $[\overline{3}]$ m space group, with cell parameter a = 11.3193 (2) Å and with 96 atoms per unit cell; the Ti₄Ni₂O (Ti₄Cu₂O) phase also crystallizes in the Fd $[\overline{3}]$ m space group, with cell parameter a = 11.3279 (1) Å [a = 11.4353 (2) Å] and with 112 atoms per unit cell. The latter phases can be considered as partially filled Ti₂Ni variants with the additional oxygen atom occupying an octahedral position. Holleck & Thummler (1967 ) studied a series of carbides, nitrides and oxides in ternary systems and reported that Nb₄Ni₂C (a = 11.64 Å) and Ta₄Ni₂C (a = 11.61 Å) crystallize in the same partially filled Ti₂Ni structure. Sadrnezhaad et al. (2009 ) and Shigeo et al. (1993 ) have confirmed the existence of the Ti₄Ni₂C phase. However, no detailed study has been performed so far with respect to the determination of its crystal structure.

In the present study, the crystal structure model of Ti₄Ni₂C has been refined on the basis of single-crystal X-ray diffraction data. The lattice parameter a is similar to those of previously reported isotypic phases (see above), and its chemical composition was refined to be exactly Ti₄Ni₂C in accordance with the EDX results (see Fig. S1 and Table S1 in the supporting information). Carbon present in the crystal structure most likely originated from the graphite crucible used during high pressure sintering (HPS).

Ti₄Ni₂C crystallizes isotypically with other Ti₄Ni₂X compounds (X = C, N, O) with a partially filled Ti₂Ni structure in space group type Fd $[\overline{3}]$ m. Fig. 1 shows the distribution of the atoms in the unit cell of Ti₄Ni₂C. The environments of the Ti1 and C1 sites are shown in Figs. 2 and 3, respectively. The Ti1 atom is situated at a position with site symmetry . $[\overline{3}]$ m (multiplicity 16, Wyckoff letter c). It is surrounded by six Ti2 atoms (2.mm, 48f) and six Ni1 atoms (.3m; 32e), defining the center of an icosahedron. The C1 atom occupies a position with site symmetry . $[\overline{3}]$ m (16d) and centers an octahedron defined by six Ti2 atoms. The shortest Ti1⋯Ti2 separation is 2.9415 (9) Å and the shortest Ti1⋯Ni1 separation is 2.4750 (4) Å; the C1—Ti2 bond length is 2.1127 (4) Å.

Figure 1
The crystal structure of Ti₄Ni₂C (one unit cell), with displacement ellipsoids drawn at the 99% probability level.

Figure 2
(a) The icosahedron formed around the Ti1 atom at the 16 c site; (b) the environment of the Ti1 atom with displacement ellipsoids given at the 99% probability level. [Symmetry codes: (i) x − $[{1\over 4}]$ , −y, z − $[{1\over 4}]$ ; (ii) −x + $[{1\over 4}]$ , y, −z + $[{1\over 4}]$ ; (iii) −x, y − $[{1\over 4}]$ , z − $[{1\over 4}]$ ; (iv) x − $[{1\over 4}]$ , y − $[{1\over 4}]$ , −z; (v) −x + $[{1\over 4}]$ , −y + $[{1\over 4}]$ , z; (vi) x, −y + $[{1\over 4}]$ , −z + $[{1\over 4}]$ ; (vii) −z, x − $[{1\over 4}]$ , y − $[{1\over 4}]$ ; (viii) z, −x + $[{1\over 4}]$ , −y + $[{1\over 4}]$ ; (ix) y − $[{1\over 4}]$ , −z, x − $[{1\over 4}]$ ; (x) −y + $[{1\over 4}]$ , z, −x + $[{1\over 4}]$ .]

Figure 3
(a) The octahedron formed around the C1 atom at the 16 d site; (b) the environment of the C1 atom with displacement ellipsoids given at the 99% probability level. [Symmetry codes:·(xvi) −y + $[{1\over 2}]$ , −z + $[{1\over 2}]$ , −x + 1; (xvii) x, y + $[{1\over 2}]$ , z + $[{1\over 2}]$ ; (xviii) −x + 1, −y + $[{1\over 2}]$ , −z + $[{1\over 2}]$ ; (xix) z + $[{1\over 2}]$ , x, y + $[{1\over 2}]$ ; (xx) −z + $[{1\over 2}]$ , −x + 1, −y + $[{1\over 2}]$ ; (xxi) y + $[{1\over 2}]$ , z + $[{1\over 2}]$ , x.]

Synthesis and crystallization

The high-purity elements Ti (indicated purity 99.5%; 0.6291 g) and Ni (indicated purity 99.9%; 0.3869 g) were mixed uniformly in the stoichiometric ratio 2:1 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 1 min. A cylindrical block 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 6 GPa and heated to 1573 K for 40 min, and then rapidly cooled to room temperature by turning off the furnace power. A piece of a single-crystal (0.06×0.06×0.04 mm³) was selected and mounted on a glass fibre for SXRD measurements.

Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1. For better comparison, the labeling scheme and atomic coordinates of Ti₄Ni₂C were adapted from Nb₄Ni₂C and Ta₄Ni₂C (Holleck & Thuemmler, 1967). The maximum and minimum residual electron densities in the final difference map are located 1.10 Å from site Ni1 and 0.17 Å from Ti2, respectively.

Table 1
Experimental details

Crystal data
Chemical formula	Ti₄Ni₂C
M_r	320.87
Crystal system, space group	Cubic, Fd $[\overline{3}]$ m
Temperature (K)	296
a (Å)	11.3235 (8)
V (Å³)	1451.9 (3)
Z	16
Radiation type	Mo Kα
μ (mm⁻¹)	18.28
Crystal size (mm)	0.06 × 0.06 × 0.04

Data collection
Diffractometer	Bruker D8 Venture Photon 100 CMOS
Absorption correction	Multi-scan (SADABS; Krause et al., 2015 )
T_min, T_max	0.520, 0.746
No. of measured, independent and observed [I > 2σ(I)] reflections	12231, 105, 97
R_int	0.091
(sin θ/λ)_max (Å⁻¹)	0.649

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.024, 0.051, 1.22
No. of reflections	105
No. of parameters	12
Δρ_max, Δρ_min (e Å⁻³)	0.48, −0.70
Computer programs: APEX3 (Bruker, 2015 ), SAINT (Bruker, 2015), SHELXT (Sheldrick, 2015a ), SHELXL (Sheldrick, 2015b ), DIAMOND (Brandenburg & Putz, 2017 ) and publCIF (Westrip, 2010 ).

Structural data

CCDC reference: 2324933

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2414314624000439/wm4205sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2414314624000439/wm4205Isup2.hkl

Supporting information file. DOI: https://doi.org/10.1107/S2414314624000439/wm4205sup3.docx

checkCIF report

Computing details top

Tetratitanium dinickel carbide top

Crystal data top

Ti₄Ni₂C	Mo Kα radiation, λ = 0.71073 Å
M_r = 320.87	Cell parameters from 3145 reflections
Cubic, Fd3m	θ = 3.1–27.5°
a = 11.3235 (8) Å	µ = 18.28 mm⁻¹
V = 1451.9 (3) Å³	T = 296 K
Z = 16	Lump, gray
F(000) = 2400	0.06 × 0.06 × 0.04 mm
D_x = 5.875 Mg m⁻³

Data collection top

Bruker D8 Venture Photon 100 CMOS diffractometer	97 reflections with I > 2σ(I)
phi and ω scans	R_int = 0.091
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	θ_max = 27.5°, θ_min = 3.1°
T_min = 0.520, T_max = 0.746	h = −14→14
12231 measured reflections	k = −14→14
105 independent reflections	l = −14→14

Refinement top

Refinement on F²	12 parameters
Least-squares matrix: full	0 restraints
R[F² > 2σ(F²)] = 0.024	w = 1/[σ²(F_o²) + (0.0226P)² + 31.699P] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.051	(Δ/σ)_max < 0.001
S = 1.22	Δρ_max = 0.48 e Å⁻³
105 reflections	Δρ_min = −0.70 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
Ti1	0.000000	0.000000	0.000000	0.0054 (5)
Ni1	0.21179 (6)	0.21179 (6)	0.21179 (6)	0.0080 (3)
Ti2	0.44034 (11)	0.125000	0.125000	0.0052 (3)
C1	0.500000	0.500000	0.500000	0.010 (3)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Ti1	0.0054 (5)	0.0054 (5)	0.0054 (5)	0.0004 (5)	0.0004 (5)	0.0004 (5)
Ni1	0.0080 (3)	0.0080 (3)	0.0080 (3)	0.0011 (2)	0.0011 (2)	0.0011 (2)
Ti2	0.0063 (6)	0.0046 (4)	0.0046 (4)	0.000	0.000	−0.0005 (4)
C1	0.010 (3)	0.010 (3)	0.010 (3)	−0.003 (3)	−0.003 (3)	−0.003 (3)

Geometric parameters (Å, º) top

Ti1—Ni1ⁱ	2.4750 (4)	Ni1—Ti2^xiii	2.6249 (9)
Ti1—Ni1ⁱⁱ	2.4750 (4)	Ni1—Ni1^v	2.7797 (18)
Ti1—Ni1ⁱⁱⁱ	2.4750 (4)	Ni1—Ni1^vi	2.7797 (18)
Ti1—Ni1^iv	2.4750 (4)	Ni1—Ni1ⁱⁱ	2.7797 (18)
Ti1—Ni1^v	2.4750 (4)	Ni1—Ti2^xiv	2.9376 (11)
Ti1—Ni1^vi	2.4750 (4)	Ni1—Ti2^xv	2.9376 (11)
Ti1—Ti2^vii	2.9415 (9)	Ni1—Ti2	2.9376 (11)
Ti1—Ti2^viii	2.9415 (9)	Ti2—C1^xvi	2.1127 (4)
Ti1—Ti2^ix	2.9415 (9)	Ti2—C1^xvii	2.1127 (4)
Ti1—Ti2^iv	2.9415 (9)	Ti2—Ti2^xviii	2.9571 (17)
Ti1—Ti2^v	2.9415 (9)	Ti2—Ti2^xix	2.9571 (17)
Ti1—Ti2^x	2.9415 (9)	Ti2—Ti2^xx	2.9571 (17)
Ni1—Ti2^xi	2.6249 (9)	Ti2—Ti2^xxi	2.9571 (17)
Ni1—Ti2^xii	2.6249 (9)

Ni1ⁱ—Ti1—Ni1ⁱⁱ	180.00 (4)	Ti2^xiii—Ni1—Ti2^xiv	65.437 (12)
Ni1ⁱ—Ti1—Ni1ⁱⁱⁱ	68.33 (4)	Ni1^v—Ni1—Ti2^xiv	61.76 (2)
Ni1ⁱⁱ—Ti1—Ni1ⁱⁱⁱ	111.67 (4)	Ni1^vi—Ni1—Ti2^xiv	112.73 (2)
Ni1ⁱ—Ti1—Ni1^iv	68.33 (4)	Ni1ⁱⁱ—Ni1—Ti2^xiv	112.73 (2)
Ni1ⁱⁱ—Ti1—Ni1^iv	111.67 (4)	Ti1^vi—Ni1—Ti2^xv	65.185 (5)
Ni1ⁱⁱⁱ—Ti1—Ni1^iv	68.33 (4)	Ti1^v—Ni1—Ti2^xv	65.185 (5)
Ni1ⁱ—Ti1—Ni1^v	111.67 (4)	Ti1ⁱⁱ—Ni1—Ti2^xv	166.08 (5)
Ni1ⁱⁱ—Ti1—Ni1^v	68.33 (4)	Ti2^xi—Ni1—Ti2^xv	65.437 (12)
Ni1ⁱⁱⁱ—Ti1—Ni1^v	111.67 (4)	Ti2^xii—Ni1—Ti2^xv	123.55 (5)
Ni1^iv—Ti1—Ni1^v	180.00 (6)	Ti2^xiii—Ni1—Ti2^xv	65.437 (12)
Ni1ⁱ—Ti1—Ni1^vi	111.67 (4)	Ni1^v—Ni1—Ti2^xv	112.73 (2)
Ni1ⁱⁱ—Ti1—Ni1^vi	68.33 (4)	Ni1^vi—Ni1—Ti2^xv	112.73 (2)
Ni1ⁱⁱⁱ—Ti1—Ni1^vi	180.0	Ni1ⁱⁱ—Ni1—Ti2^xv	61.76 (2)
Ni1^iv—Ti1—Ni1^vi	111.67 (4)	Ti2^xiv—Ni1—Ti2^xv	118.526 (10)
Ni1^v—Ti1—Ni1^vi	68.33 (4)	Ti1^vi—Ni1—Ti2	166.08 (5)
Ni1ⁱ—Ti1—Ti2^vii	122.80 (3)	Ti1^v—Ni1—Ti2	65.185 (5)
Ni1ⁱⁱ—Ti1—Ti2^vii	57.20 (3)	Ti1ⁱⁱ—Ni1—Ti2	65.185 (5)
Ni1ⁱⁱⁱ—Ti1—Ti2^vii	65.020 (15)	Ti2^xi—Ni1—Ti2	65.437 (12)
Ni1^iv—Ti1—Ti2^vii	65.020 (15)	Ti2^xii—Ni1—Ti2	65.437 (12)
Ni1^v—Ti1—Ti2^vii	114.980 (15)	Ti2^xiii—Ni1—Ti2	123.55 (5)
Ni1^vi—Ti1—Ti2^vii	114.980 (15)	Ni1^v—Ni1—Ti2	112.73 (2)
Ni1ⁱ—Ti1—Ti2^viii	57.20 (3)	Ni1^vi—Ni1—Ti2	61.76 (2)
Ni1ⁱⁱ—Ti1—Ti2^viii	122.80 (3)	Ni1ⁱⁱ—Ni1—Ti2	112.73 (2)
Ni1ⁱⁱⁱ—Ti1—Ti2^viii	114.980 (15)	Ti2^xiv—Ni1—Ti2	118.525 (10)
Ni1^iv—Ti1—Ti2^viii	114.980 (15)	Ti2^xv—Ni1—Ti2	118.525 (10)
Ni1^v—Ti1—Ti2^viii	65.020 (15)	C1^xvi—Ti2—C1^xvii	142.70 (6)
Ni1^vi—Ti1—Ti2^viii	65.020 (15)	C1^xvi—Ti2—Ni1^xxii	88.304 (12)
Ti2^vii—Ti1—Ti2^viii	180.00 (3)	C1^xvii—Ti2—Ni1^xxii	88.304 (12)
Ni1ⁱ—Ti1—Ti2^ix	65.020 (15)	C1^xvi—Ti2—Ni1^xxiii	88.304 (12)
Ni1ⁱⁱ—Ti1—Ti2^ix	114.980 (15)	C1^xvii—Ti2—Ni1^xxiii	88.304 (12)
Ni1ⁱⁱⁱ—Ti1—Ti2^ix	65.020 (15)	Ni1^xxii—Ti2—Ni1^xxiii	169.38 (6)
Ni1^iv—Ti1—Ti2^ix	122.80 (3)	C1^xvi—Ti2—Ni1^vi	136.89 (5)
Ni1^v—Ti1—Ti2^ix	57.20 (3)	C1^xvii—Ti2—Ni1^vi	80.41 (3)
Ni1^vi—Ti1—Ti2^ix	114.980 (15)	Ni1^xxii—Ti2—Ni1^vi	94.68 (3)
Ti2^vii—Ti1—Ti2^ix	118.270 (7)	Ni1^xxiii—Ti2—Ni1^vi	94.68 (3)
Ti2^viii—Ti1—Ti2^ix	61.730 (7)	C1^xvi—Ti2—Ni1	80.41 (3)
Ni1ⁱ—Ti1—Ti2^iv	65.020 (15)	C1^xvii—Ti2—Ni1	136.89 (5)
Ni1ⁱⁱ—Ti1—Ti2^iv	114.980 (15)	Ni1^xxii—Ti2—Ni1	94.68 (3)
Ni1ⁱⁱⁱ—Ti1—Ti2^iv	122.80 (3)	Ni1^xxiii—Ti2—Ni1	94.68 (3)
Ni1^iv—Ti1—Ti2^iv	65.020 (15)	Ni1^vi—Ti2—Ni1	56.48 (5)
Ni1^v—Ti1—Ti2^iv	114.980 (15)	C1^xvi—Ti2—Ti1ⁱⁱ	103.550 (18)
Ni1^vi—Ti1—Ti2^iv	57.20 (3)	C1^xvii—Ti2—Ti1ⁱⁱ	103.550 (18)
Ti2^vii—Ti1—Ti2^iv	118.270 (7)	Ni1^xxii—Ti2—Ti1ⁱⁱ	138.19 (4)
Ti2^viii—Ti1—Ti2^iv	61.730 (7)	Ni1^xxiii—Ti2—Ti1ⁱⁱ	52.426 (19)
Ti2^ix—Ti1—Ti2^iv	118.270 (7)	Ni1^vi—Ti2—Ti1ⁱⁱ	49.79 (2)
Ni1ⁱ—Ti1—Ti2^v	114.980 (15)	Ni1—Ti2—Ti1ⁱⁱ	49.79 (2)
Ni1ⁱⁱ—Ti1—Ti2^v	65.020 (15)	C1^xvi—Ti2—Ti1^v	103.550 (18)
Ni1ⁱⁱⁱ—Ti1—Ti2^v	57.20 (3)	C1^xvii—Ti2—Ti1^v	103.550 (18)
Ni1^iv—Ti1—Ti2^v	114.980 (15)	Ni1^xxii—Ti2—Ti1^v	52.426 (19)
Ni1^v—Ti1—Ti2^v	65.020 (15)	Ni1^xxiii—Ti2—Ti1^v	138.19 (4)
Ni1^vi—Ti1—Ti2^v	122.80 (3)	Ni1^vi—Ti2—Ti1^v	49.79 (2)
Ti2^vii—Ti1—Ti2^v	61.730 (7)	Ni1—Ti2—Ti1^v	49.79 (2)
Ti2^viii—Ti1—Ti2^v	118.270 (7)	Ti1ⁱⁱ—Ti2—Ti1^v	85.77 (3)
Ti2^ix—Ti1—Ti2^v	61.730 (7)	C1^xvi—Ti2—Ti2^xviii	45.58 (2)
Ti2^iv—Ti1—Ti2^v	180.00 (3)	C1^xvii—Ti2—Ti2^xviii	104.34 (3)
Ni1ⁱ—Ti1—Ti2^x	114.980 (15)	Ni1^xxii—Ti2—Ti2^xviii	115.62 (3)
Ni1ⁱⁱ—Ti1—Ti2^x	65.020 (15)	Ni1^xxiii—Ti2—Ti2^xviii	55.72 (2)
Ni1ⁱⁱⁱ—Ti1—Ti2^x	114.980 (15)	Ni1^vi—Ti2—Ti2^xviii	149.263 (5)
Ni1^iv—Ti1—Ti2^x	57.20 (3)	Ni1—Ti2—Ti2^xviii	112.73 (2)
Ni1^v—Ti1—Ti2^x	122.80 (3)	Ti1ⁱⁱ—Ti2—Ti2^xviii	100.245 (14)
Ni1^vi—Ti1—Ti2^x	65.020 (15)	Ti1^v—Ti2—Ti2^xviii	149.135 (4)
Ti2^vii—Ti1—Ti2^x	61.730 (7)	C1^xvi—Ti2—Ti2^xix	45.58 (2)
Ti2^viii—Ti1—Ti2^x	118.270 (7)	C1^xvii—Ti2—Ti2^xix	104.34 (3)
Ti2^ix—Ti1—Ti2^x	180.0	Ni1^xxii—Ti2—Ti2^xix	55.72 (2)
Ti2^iv—Ti1—Ti2^x	61.730 (7)	Ni1^xxiii—Ti2—Ti2^xix	115.62 (3)
Ti2^v—Ti1—Ti2^x	118.270 (7)	Ni1^vi—Ti2—Ti2^xix	149.263 (5)
Ti1^vi—Ni1—Ti1^v	107.95 (2)	Ni1—Ti2—Ti2^xix	112.73 (2)
Ti1^vi—Ni1—Ti1ⁱⁱ	107.95 (2)	Ti1ⁱⁱ—Ti2—Ti2^xix	149.135 (4)
Ti1^v—Ni1—Ti1ⁱⁱ	107.95 (2)	Ti1^v—Ti2—Ti2^xix	100.245 (14)
Ti1^vi—Ni1—Ti2^xi	125.12 (2)	Ti2^xviii—Ti2—Ti2^xix	60.0
Ti1^v—Ni1—Ti2^xi	70.38 (3)	C1^xvi—Ti2—Ti2^xx	104.34 (3)
Ti1ⁱⁱ—Ni1—Ti2^xi	125.12 (2)	C1^xvii—Ti2—Ti2^xx	45.58 (2)
Ti1^vi—Ni1—Ti2^xii	125.12 (2)	Ni1^xxii—Ti2—Ti2^xx	115.62 (3)
Ti1^v—Ni1—Ti2^xii	125.12 (2)	Ni1^xxiii—Ti2—Ti2^xx	55.72 (2)
Ti1ⁱⁱ—Ni1—Ti2^xii	70.38 (3)	Ni1^vi—Ti2—Ti2^xx	112.73 (2)
Ti2^xi—Ni1—Ti2^xii	68.57 (5)	Ni1—Ti2—Ti2^xx	149.262 (5)
Ti1^vi—Ni1—Ti2^xiii	70.38 (3)	Ti1ⁱⁱ—Ti2—Ti2^xx	100.245 (14)
Ti1^v—Ni1—Ti2^xiii	125.12 (2)	Ti1^v—Ti2—Ti2^xx	149.135 (4)
Ti1ⁱⁱ—Ni1—Ti2^xiii	125.12 (2)	Ti2^xviii—Ti2—Ti2^xx	60.0
Ti2^xi—Ni1—Ti2^xiii	68.57 (5)	Ti2^xix—Ti2—Ti2^xx	90.001 (1)
Ti2^xii—Ni1—Ti2^xiii	68.57 (5)	C1^xvi—Ti2—Ti2^xxi	104.34 (3)
Ti1^vi—Ni1—Ni1^v	55.837 (19)	C1^xvii—Ti2—Ti2^xxi	45.58 (2)
Ti1^v—Ni1—Ni1^v	104.31 (2)	Ni1^xxii—Ti2—Ti2^xxi	55.72 (2)
Ti1ⁱⁱ—Ni1—Ni1^v	55.837 (19)	Ni1^xxiii—Ti2—Ti2^xxi	115.62 (3)
Ti2^xi—Ni1—Ni1^v	174.69 (3)	Ni1^vi—Ti2—Ti2^xxi	112.73 (2)
Ti2^xii—Ni1—Ni1^v	115.62 (3)	Ni1—Ti2—Ti2^xxi	149.262 (5)
Ti2^xiii—Ni1—Ni1^v	115.62 (3)	Ti1ⁱⁱ—Ti2—Ti2^xxi	149.135 (3)
Ti1^vi—Ni1—Ni1^vi	104.31 (2)	Ti1^v—Ti2—Ti2^xxi	100.245 (14)
Ti1^v—Ni1—Ni1^vi	55.837 (19)	Ti2^xviii—Ti2—Ti2^xxi	90.0
Ti1ⁱⁱ—Ni1—Ni1^vi	55.837 (19)	Ti2^xix—Ti2—Ti2^xxi	60.0
Ti2^xi—Ni1—Ni1^vi	115.62 (3)	Ti2^xx—Ti2—Ti2^xxi	60.0
Ti2^xii—Ni1—Ni1^vi	115.62 (3)	Ti2^xxiv—C1—Ti2^xxv	91.17 (4)
Ti2^xiii—Ni1—Ni1^vi	174.69 (3)	Ti2^xxiv—C1—Ti2^xxvi	88.83 (4)
Ni1^v—Ni1—Ni1^vi	60.0	Ti2^xxv—C1—Ti2^xxvi	180.0
Ti1^vi—Ni1—Ni1ⁱⁱ	55.837 (19)	Ti2^xxiv—C1—Ti2^xxvii	91.17 (4)
Ti1^v—Ni1—Ni1ⁱⁱ	55.837 (19)	Ti2^xxv—C1—Ti2^xxvii	88.83 (4)
Ti1ⁱⁱ—Ni1—Ni1ⁱⁱ	104.31 (2)	Ti2^xxvi—C1—Ti2^xxvii	91.17 (4)
Ti2^xi—Ni1—Ni1ⁱⁱ	115.62 (3)	Ti2^xxiv—C1—Ti2^xxviii	88.83 (4)
Ti2^xii—Ni1—Ni1ⁱⁱ	174.69 (3)	Ti2^xxv—C1—Ti2^xxviii	91.17 (4)
Ti2^xiii—Ni1—Ni1ⁱⁱ	115.62 (3)	Ti2^xxvi—C1—Ti2^xxviii	88.83 (4)
Ni1^v—Ni1—Ni1ⁱⁱ	60.0	Ti2^xxvii—C1—Ti2^xxviii	180.0
Ni1^vi—Ni1—Ni1ⁱⁱ	60.0	Ti2^xxiv—C1—Ti2^xxix	180.0
Ti1^vi—Ni1—Ti2^xiv	65.185 (5)	Ti2^xxv—C1—Ti2^xxix	88.83 (4)
Ti1^v—Ni1—Ti2^xiv	166.08 (5)	Ti2^xxvi—C1—Ti2^xxix	91.17 (4)
Ti1ⁱⁱ—Ni1—Ti2^xiv	65.185 (5)	Ti2^xxvii—C1—Ti2^xxix	88.83 (4)
Ti2^xi—Ni1—Ti2^xiv	123.55 (5)	Ti2^xxviii—C1—Ti2^xxix	91.17 (4)
Ti2^xii—Ni1—Ti2^xiv	65.437 (12)

Symmetry codes: (i) x−1/4, −y, z−1/4; (ii) −x+1/4, y, −z+1/4; (iii) −x, y−1/4, z−1/4; (iv) x−1/4, y−1/4, −z; (v) −x+1/4, −y+1/4, z; (vi) x, −y+1/4, −z+1/4; (vii) −z, x−1/4, y−1/4; (viii) z, −x+1/4, −y+1/4; (ix) y−1/4, −z, x−1/4; (x) −y+1/4, z, −x+1/4; (xi) y+1/4, −z+1/2, x−1/4; (xii) −z+1/2, x−1/4, y+1/4; (xiii) x−1/4, y+1/4, −z+1/2; (xiv) y, z, x; (xv) z, x, y; (xvi) x, −y+3/4, −z+3/4; (xvii) x, y−1/2, z−1/2; (xviii) −y+3/4, z, −x+3/4; (xix) z+1/2, −x+3/4, −y+1/4; (xx) z+1/2, x−1/2, y; (xxi) y+1/2, z, x−1/2; (xxii) x+1/4, −y+1/2, z−1/4; (xxiii) x+1/4, y−1/4, −z+1/2; (xxiv) −y+1/2, −z+1/2, −x+1; (xxv) x, y+1/2, z+1/2; (xxvi) −x+1, −y+1/2, −z+1/2; (xxvii) z+1/2, x, y+1/2; (xxviii) −z+1/2, −x+1, −y+1/2; (xxix) y+1/2, z+1/2, x.

Acknowledgements

The authors are indebted to Dr Qiang Ren from the High steel center of Yanshan University for assistance in performing the SEM/EDX measurements.

Funding information

Funding for this research was provided by: The National Natural Science Foundation of China (grant No. 52173231; grant No. 51925105); Hebei Natural Science Foundation (grant No. E2022203182); The Innovation Ability Promotion Project of Hebei supported by Hebei Key Lab for Optimizing Metal Product Technology and Performance (grant No. 22567609H).

References

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
Holleck, H. & Thummler, F. (1967). Monatsh. Chem. 98, 133–134. CrossRef ICSD CAS Google Scholar
Krause, L., Herbst-Irmer, R., Sheldrick, G. M. & Stalke, D. (2015). J. Appl. Cryst. 48, 3–10. Web of Science CSD CrossRef ICSD CAS IUCr Journals Google Scholar
Liu, C. & Fan, C. (2018). IUCrData, 3, x180363. Google Scholar
Mueller, M. H. & Knott, H. W. (1963). Trans. Metall. Soc. AIME, 227, 674–677. CAS Google Scholar
Sadrnezhaad, S. K., Ahmadi, E. & Malekzadeh, M. (2009). Mater. Sci. Technol. 25, 699–706. CrossRef CAS 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
Shigeo, K., Yasuyuki, S. & Masafumi, S. (1993). Res. Rep. Fac. Eng. Mie Univ, 18, 7–13. Google Scholar
Westrip, S. P. (2010). J. Appl. Cryst. 43, 920–925. Web of Science CrossRef CAS IUCr Journals Google Scholar