Crystal structure of TiBi2

Watanabe, K.; Yamane, H.

doi:10.1107/S2056989016012391

research communications

CRYSTALLOGRAPHIC
COMMUNICATIONS

ISSN: 2056-9890

Volume 72| Part 9| September 2016| Pages 1254-1256

https://doi.org/10.1107/S2056989016012391

Open

access

Crystal structure of TiBi₂

Kei Watanabe ^a and Hisanori Yamane ^a ^*

^aInstitute of Multidisciplinary Research for Advanced Materials, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
^*Correspondence e-mail: yamane@tagen.tohoku.ac.jp

Edited by I. D. Brown, McMaster University, Canada (Received 14 July 2016; accepted 1 August 2016; online 5 August 2016)

Black granular single crystals of monotitanium dibismuth, TiBi₂, were synthesized by slow cooling of a mixture of Bi and Ti from 693 K. The title compound is isostructural with CuMg₂ (orthorhombic Fddd symmetry). Ti atoms are located in square antiprisms of Bi atoms. The network of one type of Bi atom spirals along the a-axis direction while honeycomb layers of the other type of Bi atom spreading in the ab plane interlace one another.

Keywords: crystal structure; CuMg₂ structure type; titanium; bismuth.

CCDC reference: 1497032

1. Chemical context

TiBi₂ was first reported in the study of the Ti–Bi binary phase diagram by Vassilev (2006 ). Maruyama et al. (2013 ) confirmed the presence of TiBi₂ in their phase-diagram study and showed that the powder X-ray diffraction (XRD) pattern was consistent with that of a Ti–Bi film prepared by RF sputtering (Simić & Marinković, 1990 ). However, the crystal system, lattice parameters and structure of TiBi₂ were not reported.

In the present study, we prepared single crystals of TiBi₂ to clarify the structure. The pellet of the starting mixture maintained the original shape after heating at 693 K. The powder XRD pattern of the sample showed that a mixture of TiBi₂, Bi, and Ti had been obtained. Single crystals of TiBi₂ approximately 120 µm in size were picked up from the fractured sample. TiBi₂ is unstable and decomposes in air. When the mixture was heated at 703 K, the obtained sample was a mixture of Bi and Ti₈Bi₉. This temperature was above the peritectic temperature of TiBi₂ (698 K) reported in the phase diagram by Maruyama et al. (2013).

2. Structural commentary

TiBi₂ is isotypic with CuMg₂ (Schubert & Anderko, 1951 ; Gingl et al., 1993 ), NbSn₂, VSn₂, CrSn₂ (Wölpl & Jeitschko, 1994 ; Larsson & Lidin, 1995 ), and IrIn₂ (Zumdick et al., 2000 ). TiSnSb is the only reported compound which contains Ti and crystallizes in the CuMg₂-type structure (Malaman & Steinmetz, 1979 ; Dashjav & Kleinke, 2003 ). The crystal structure of TiSb₂ adopts the CuAl₂ type, while that of TiSn₂ is not known. TiBi₂ is the first binary compound that is composed of Ti and a group 15 element and has the CuMg₂-type structure.

Fig. 1 shows the crystal structure of TiBi₂ while the coordination environments of the Ti1, Bi1, and Bi2 atoms are illustrated in Fig. 2. The Ti1 site is located in a square antiprism of Bi atoms. The Bi square antiprisms are aligned alternately along the a + b and a − b directions by sharing the square planes. Bi—Ti bond lengths in the Bi square antiprism and the Ti—Ti distance of the inter-antiprisms are 2.9382 (16)–3.0825 (6) and 2.9546 (2) Å, respectively, which are in the ranges reported for Ti₈Bi₉ [Bi—Ti = 2.818 (4)–3.144 (6) Å and Ti—Ti = 2.934 (6)–3.715 (5) Å; Richter & Jeitschko, 1997 ].

Figure 1
Crystal structure of TiBi₂ illustrated with Ti-centered Bi1–Bi2 square antiprisms and Bi1—Bi1 and Bi2—Bi2 bonds.

Figure 2
The atomic arrangement around Ti and Bi atoms in the structure of TiBi₂. Displacement ellipsoids are drawn at 99% probability. [Symmetry codes: (i) x, −y + $[{1\over 4}]$ , −z + $[{1\over 4}]$ ; (ii) −x, −y, −z; (iii) x + $[{1\over 4}]$ , y + $[{1\over 4}]$ , −z; (iv) x − $[{3\over 4}]$ , y + $[{1\over 4}]$ , −z; (v) −x − $[{1\over 4}]$ , −y + $[{3\over 4}]$ , z; (vi) x, y − 1, z; (vii) −x + $[{3\over 4}]$ , y − $[{1\over 2}]$ , −z + $[{1\over 4}]$ ; (viii) −x + $[{3\over 4}]$ , −y + $[{3\over 4}]$ , z; (ix) −x − $[{1\over 4}]$ , y − $[{1\over 2}]$ , −z + $[{1\over 4}]$ ; (x) −x, −y + 1, −z; (xi) −x, y − $[{1\over 4}]$ , z − $[{1\over 4}]$ ; (xii) x, −y − $[{1\over 4}]$ , −z + $[{3\over 4}]$ ; (xiii) x, y − $[{1\over 2}]$ , z − $[{1\over 2}]$ ; (xiv) x + $[{1\over 4}]$ , y − $[{1\over 4}]$ , − z + $[{1\over 2}]$ ; (xv) − x + $[{3\over 4}]$ , −y + $[{1\over 4}]$ , z − $[{1\over 2}]$ ; (xvi) −x − $[{1\over 4}]$ , −y + $[{1\over 4}]$ , z − $[{1\over 2}]$ ; (xvii) −x, −y + $[{1\over 2}]$ , −z + $[{1\over 2}]$ .]

The Bi1—Bi1 bond lengths in the Bi1 spiral-like network are 3.0730 (8) Å in the c-axis direction and 3.4589 (4) Å in the other direction. The Bi2—Bi2 bond lengths in the Bi2 honeycomb layers in the ab plane are 3.4639 (8) Å in the b-axis direction and 3.3435 (4) Å in the other direction. The Bi—Bi bond lengths in the spiral rings and honeycomb layers in TiBi₂ are in the range of those in Bi metal (3.071 and 3.529 Å; Cucka & Barrett, 1962 ). The interatomic distances between the Bi atoms of the spiral network and the honeycomb layers (Bi1—Bi2) are 3.6974 (3), 3.7309 (4) and 3.7546 (4) Å, which are longer than the Bi—Bi bond lengths in Bi metal.

3. Synthesis and crystallization

Starting powders of Bi (1 mmol, Mitsuwa Chemicals Co., Ltd, 99.999%) and Ti (0.5 mmol, Mitsuwa Chemicals Co., Ltd, 99.99%) were weighed, mixed in an alumina mortar with a pestle and formed into a pellet by uniaxial pressing in an Ar gas-filled glove box (O₂ and H₂O < 1 p.p.m.). The pellet was put in a tantalum boat (Nilaco Corp., 99.95%). The boat was sealed in a stainless-steel (SUS 316) tube. The sample was heated to 693 K in an electric furnace with a heating rate of 3.5 K min⁻¹. This temperature was kept for 10 h, and then lowered to 473 K with a cooling rate of 5 K h⁻¹. After cooling to room temperature by shutting off the electrical power to the furnace, the stainless-steel tube was cut and opened in the glove box. To identify the crystalline phases, powder XRD (Cu Kα, Bruker, D2 phaser) was carried out for a portion of the sample which was ground in the alumina mortar and sealed under an Ar atmosphere in a holder with a kapton film window. The chemical compositions of TiBi₂ single crystals placed on a carbon tape were determined with an electron probe microanalyzer (EPMA, JEOL, JXA-8200). Bi and TiO₂ (Japan Electronics Co., Ltd) were used as standard samples. The analyzed composition ratio of Ti:Bi in the crystals was 1.0 (1):2.0 (1). A single crystal of TiBi₂ was sealed in a glass capillary with Ar gas in the glove box for the single-crystal XRD experiment.

4. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1.

Table 1
Experimental details

Crystal data
Chemical formula	TiBi₂
M_r	465.86
Crystal system, space group	Orthorhombic, Fddd
Temperature (K)	298
a, b, c (Å)	5.7654 (4), 10.3155 (6), 19.4879 (12)
V (Å³)	1159.00 (13)
Z	16
Radiation type	Mo Kα
μ (mm⁻¹)	123.50
Crystal size (mm)	0.14 × 0.09 × 0.06

Data collection
Diffractometer	Bruker D8 goniometer
Absorption correction	Numerical (SADABS; Bruker, 2014 )
T_min, T_max	0.016, 0.102
No. of measured, independent and observed [I > 2σ(I)] reflections	3881, 339, 309
R_int	0.048
(sin θ/λ)_max (Å⁻¹)	0.649

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.024, 0.062, 1.31
No. of reflections	339
No. of parameters	17

Δρ_max, Δρ_min (e Å⁻³)	2.54, −3.80
Computer programs: Instrument Service, APEX2 and SAINT-Plus (Bruker, 2014), SHELXL2014 (Sheldrick, 2015 ) and VESTA (Momma & Izumi, 2011 ).

Supporting information

CCDC reference: 1497032

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2056989016012391/br2262sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2056989016012391/br2262Isup2.hkl

checkCIF report

Computing details top

Data collection: Instrument Service (Bruker, 2014); cell refinement: APEX2 (Bruker, 2014); data reduction: SAINT-Plus (Bruker, 2014); program(s) used to solve structure: APEX2 (Bruker, 2014); program(s) used to refine structure: SHELXL2014 (Sheldrick, 2015); molecular graphics: VESTA (Momma & Izumi, 2011).

Titanium dibismuth top

Crystal data top

TiBi₂	D_x = 10.679 Mg m⁻³
M_r = 465.86	Mo Kα radiation, λ = 0.71073 Å
Orthorhombic, Fddd	Cell parameters from 4528 reflections
a = 5.7654 (4) Å	θ = 4.2–31.4°
b = 10.3155 (6) Å	µ = 123.50 mm⁻¹
c = 19.4879 (12) Å	T = 298 K
V = 1159.00 (13) Å³	Granule, black
Z = 16	0.14 × 0.09 × 0.06 mm
F(000) = 3008

Data collection top

Bruker D8 goniometer diffractometer	339 independent reflections
Radiation source: micro focus sealed tube	309 reflections with I > 2σ(I)
Detector resolution: 10.4167 pixels mm^-1	R_int = 0.048
ω, φ scans	θ_max = 27.5°, θ_min = 4.2°
Absorption correction: numerical (SADABS; Bruker, 2014)	h = −7→7
T_min = 0.016, T_max = 0.102	k = −13→13
3881 measured reflections	l = −25→25

Refinement top

Refinement on F²	Primary atom site location: dual
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F² > 2σ(F²)] = 0.024	w = 1/[σ²(F_o²) + (0.0275P)² + 47.1241P] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.062	(Δ/σ)_max < 0.001
S = 1.31	Δρ_max = 2.54 e Å⁻³
339 reflections	Δρ_min = −3.80 e Å⁻³
17 parameters	Extinction correction: SHELXL2014 (Sheldrick, 2015), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.00038 (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
Bi1	0.1250	0.1250	0.04615 (2)	0.0064 (2)
Bi2	0.1250	0.45710 (4)	0.1250	0.0066 (2)
Ti1	0.1250	0.1250	0.49898 (10)	0.0050 (4)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Bi1	0.0035 (3)	0.0076 (3)	0.0082 (3)	0.00176 (15)	0.000	0.000
Bi2	0.0058 (3)	0.0080 (3)	0.0060 (3)	0.000	−0.00212 (15)	0.000
Ti1	0.0039 (9)	0.0060 (9)	0.0051 (8)	0.0005 (8)	0.000	0.000

Geometric parameters (Å, º) top

Ti1—Bi2ⁱ	2.9382 (16)	Bi1—Bi2^xix	3.7546 (4)
Ti1—Bi2ⁱⁱ	2.9382 (16)	Bi1—Bi2	3.7546 (4)
Ti1—Bi2ⁱⁱⁱ	3.0051 (16)	Bi1—Ti1^xx	3.0257 (6)
Ti1—Bi2^iv	3.0051 (16)	Bi1—Ti1^xxi	3.0257 (6)
Ti1—Bi1^v	3.0257 (6)	Bi1—Ti1^vii	3.0825 (6)
Ti1—Bi1^vi	3.0257 (6)	Bi1—Ti1ⁱ	3.0825 (6)
Ti1—Bi1^vii	3.0825 (6)	Bi1—Ti1^xxii	4.9243 (16)
Ti1—Bi1ⁱ	3.0825 (6)	Bi1—Ti1^xxiii	4.9243 (16)
Ti1—Ti1^viii	2.9546 (2)	Bi1—Ti1^xxiv	4.9348 (16)
Ti1—Ti1^ix	2.9546 (2)	Bi1—Ti1^xxv	4.9348 (16)
Bi1—Bi1^x	3.0730 (8)	Bi1—Ti1^xxvi	5.1110 (4)
Bi1—Bi1^xi	3.4589 (4)	Bi2—Ti1ⁱ	2.9382 (16)
Bi1—Bi1^xii	3.4589 (4)	Bi2—Ti1^xxiv	2.9382 (16)
Bi2—Bi2^xiii	3.3435 (4)	Bi2—Ti1^xxvii	3.0051 (16)
Bi2—Bi2^xiv	3.3435 (4)	Bi2—Ti1^xxviii	3.0051 (16)
Bi2—Bi2^xv	3.4639 (8)	Bi2—Bi1^xxix	3.6974 (3)
Bi1—Bi2^xiv	3.6974 (3)	Bi2—Bi1^xxx	3.6974 (3)
Bi1—Bi2^xvi	3.6974 (3)	Bi2—Bi1^xxxi	3.6974 (3)
Bi1—Bi2^xvii	3.6974 (3)	Bi2—Bi1^xxxii	3.6974 (3)
Bi1—Bi2^xiii	3.6974 (3)	Bi2—Bi1^xii	3.7310 (4)
Bi1—Bi2^xviii	3.7309 (4)	Ti1—Bi1^xxii	4.9242 (16)
Bi1—Bi2^xii	3.7309 (4)	Ti1—Bi1^xxiii	4.9242 (16)

Ti1ⁱ—Bi2—Bi1^xxx	100.12 (2)	Bi2^xiv—Bi1—Ti1^xxiv	36.352 (10)
Bi1^xxix—Bi2—Bi1^xii	100.174 (6)	Bi2—Bi1—Ti1^xxiv	36.426 (10)
Bi2^xvi—Bi1—Bi2^xviii	100.175 (5)	Bi1^v—Ti1—Bi1^xxii	36.48 (2)
Bi1^xii—Bi1—Ti1^xxii	100.237 (12)	Bi1^x—Bi1—Ti1^xxiv	36.775 (14)
Bi1^xii—Bi1—Bi2^xiii	101.056 (6)	Bi2^xiv—Bi1—Ti1^xxii	37.501 (10)
Bi1^xi—Bi1—Bi2^xvii	101.056 (7)	Bi2ⁱⁱⁱ—Ti1—Bi1^xxii	48.51 (2)
Bi2^xvi—Bi1—Bi2^xvii	102.459 (10)	Bi1^xxix—Bi2—Bi1^xxx	49.109 (12)
Bi1^xxix—Bi2—Bi1^xxxii	102.460 (10)	Ti1^vii—Bi1—Bi2^xix	49.72 (3)
Bi1^xxx—Bi2—Bi1^xxxi	102.460 (11)	Ti1^xx—Bi1—Bi2^xviii	50.23 (3)
Bi2^xiii—Bi2—Bi1^xii	102.596 (8)	Ti1^vii—Bi1—Bi2^xvii	50.37 (3)
Bi2^xv—Bi2—Bi1^xii	103.120 (6)	Ti1ⁱ—Bi1—Bi2^xviii	51.27 (3)
Ti1^xxi—Bi1—Bi1^xi	103.83 (2)	Ti1^xxi—Bi1—Bi2^xiv	51.93 (3)
Bi1^xii—Bi1—Bi2^xvii	103.916 (6)	Ti1ⁱ—Bi2—Bi1^xii	52.331 (19)
Bi2^xiv—Bi1—Bi2^xix	104.912 (8)	Ti1^xxvii—Bi2—Bi1^xxix	52.441 (7)
Ti1^ix—Ti1—Bi1^xxii	105.95 (7)	Ti1^xxviii—Bi2—Bi1^xii	53.148 (19)
Ti1^xxiv—Bi2—Bi2^xiii	106.077 (14)	Bi2^xviii—Bi1—Bi2^xii	53.241 (9)
Ti1ⁱ—Bi1—Bi1^xi	106.29 (3)	Bi2^xvi—Bi1—Bi2^xix	53.310 (6)
Bi1^x—Bi1—Ti1^vii	106.58 (4)	Ti1^xxiv—Bi2—Bi1^xxix	53.901 (6)
Ti1ⁱ—Bi2—Bi2^xv	106.753 (12)	Ti1^vii—Bi1—Bi1^xi	54.737 (17)
Ti1^xxvii—Bi2—Bi2^xiii	106.976 (10)	Ti1^xxvii—Bi2—Bi2^xv	54.81 (2)
Ti1^xx—Bi1—Bi1^x	107.69 (4)	Ti1ⁱ—Bi2—Bi2^xiii	55.32 (2)
Bi1^vi—Ti1—Bi1^xxii	108.14 (5)	Bi1^xxx—Bi2—Bi1^xii	55.502 (6)
Ti1^xxvii—Bi2—Ti1^xxviii	109.61 (4)	Bi2^xiv—Bi1—Bi2^xvii	55.865 (12)
Ti1^xx—Bi1—Ti1^vii	111.026 (7)	Ti1^xx—Bi1—Bi1^xi	56.289 (16)
Bi1^xi—Bi1—Bi1^xii	117.32 (2)	Ti1^xxi—Bi1—Ti1^vii	57.847 (3)
Ti1^ix—Ti1—Bi1^v	117.43 (3)	Ti1^viii—Ti1—Bi2ⁱⁱⁱ	59.07 (5)
Ti1^xxiv—Bi2—Bi1^xii	118.70 (2)	Ti1^xxiv—Bi2—Ti1^xxvii	59.609 (4)
Bi2^xiii—Bi2—Bi2^xiv	119.12 (2)	Ti1^ix—Ti1—Bi1^vii	60.113 (19)
Ti1^ix—Ti1—Bi2ⁱⁱⁱ	119.48 (9)	Bi2ⁱⁱ—Ti1—Ti1^viii	61.32 (5)
Bi2^xvii—Bi1—Ti1^xxvi	119.656 (11)	Ti1^xxiii—Bi1—Ti1^xxiv	61.418 (6)
Bi2^xii—Bi1—Ti1^xxii	119.910 (14)	Bi1^xii—Bi1—Bi2^xviii	61.757 (12)
Bi2ⁱ—Ti1—Ti1^viii	120.13 (9)	Ti1^viii—Ti1—Bi1^v	62.04 (2)
Ti1ⁱ—Bi1—Ti1^xxii	120.34 (3)	Bi2^xv—Bi2—Bi1^xxix	62.067 (6)
Bi1ⁱ—Ti1—Bi1^xxii	120.34 (3)	Bi2^xv—Bi2—Bi1^xxx	62.067 (6)
Ti1^viii—Ti1—Bi1^vii	120.39 (3)	Bi1^xi—Bi1—Bi2^xix	62.132 (6)
Bi2ⁱⁱ—Ti1—Bi2ⁱⁱⁱ	120.391 (4)	Bi1^xii—Bi1—Bi2^xiv	62.742 (7)
Bi2^xiii—Bi2—Bi2^xv	120.438 (12)	Bi1^xi—Bi1—Bi2^xviii	62.826 (12)
Bi1^x—Bi1—Bi1^xi	121.338 (11)	Bi2^xiv—Bi2—Bi1^xii	63.380 (4)
Ti1^xx—Bi1—Ti1^xxiv	121.44 (3)	Bi2^xiv—Bi2—Bi1^xxix	64.221 (7)
Ti1^vii—Bi1—Ti1^xxiv	121.95 (3)	Bi2^xiii—Bi2—Bi1^xxxi	64.221 (7)
Bi2—Bi1—Ti1^xxvi	122.061 (9)	Bi1^x—Bi1—Bi2^xiv	65.444 (6)
Bi1^vi—Ti1—Bi1^vii	122.154 (4)	Bi1^x—Bi1—Bi2^xix	65.843 (6)
Bi1^xxix—Bi2—Bi1^xxxi	124.135 (12)	Bi2^xix—Bi1—Ti1^xxvi	67.048 (12)
Bi2^xiv—Bi1—Bi2^xviii	124.499 (6)	Ti1^xxv—Bi1—Ti1^xxvi	68.10 (3)
Bi2^xviii—Bi1—Bi2^xix	124.958 (7)	Bi2^xviii—Bi1—Ti1^xxvi	68.52 (2)
Ti1^xxii—Bi1—Ti1^xxvi	129.41 (3)	Bi1^v—Ti1—Bi1^vii	68.975 (7)
Bi1^xii—Bi1—Ti1^xxvi	129.73 (2)	Ti1^xxiii—Bi1—Ti1^xxvi	69.162 (10)
Ti1^xxiv—Bi1—Ti1^xxvi	130.440 (11)	Bi2ⁱ—Ti1—Bi2ⁱⁱ	69.36 (4)
Bi2^xiv—Bi1—Bi2^xvi	130.889 (12)	Bi2^xiii—Bi1—Ti1^xxvi	69.407 (12)
Bi2^xix—Bi1—Bi2	131.685 (13)	Bi2^xiii—Bi1—Ti1^xxiv	69.516 (7)
Bi1^xi—Bi1—Ti1^xxii	131.728 (9)	Bi2ⁱⁱⁱ—Ti1—Bi2^iv	70.39 (4)
Bi2^xviii—Bi1—Ti1^xxiv	135.259 (12)	Bi2^xix—Bi1—Ti1^xxii	70.622 (7)
Bi2ⁱⁱⁱ—Ti1—Bi1^vii	135.68 (5)	Bi2^xvii—Bi1—Ti1^xxiv	71.591 (8)
Bi2ⁱ—Ti1—Bi1^v	135.83 (5)	Ti1^xxii—Bi1—Ti1^xxiii	71.66 (3)
Bi2^xii—Bi1—Ti1^xxiv	136.209 (11)	Bi1^xxii—Ti1—Bi1^xxiii	71.66 (3)
Ti1^xxi—Bi1—Ti1^xxvi	138.917 (11)	Ti1^xxi—Bi1—Ti1^xxii	71.85 (5)
Bi1^xxxii—Bi2—Bi1^xii	141.173 (9)	Ti1^viii—Ti1—Bi1^xxii	72.76 (6)
Bi2^xvii—Bi1—Bi2^xviii	141.174 (9)	Ti1^xxiv—Bi1—Ti1^xxv	73.55 (3)
Ti1^xx—Bi1—Ti1^xxii	143.52 (2)	Bi2^iv—Ti1—Bi1^vii	75.584 (18)
Bi1^v—Ti1—Bi1^vi	144.62 (7)	Bi2ⁱⁱⁱ—Ti1—Bi1^v	75.62 (3)
Ti1^xx—Bi1—Ti1^xxi	144.63 (7)	Bi2ⁱ—Ti1—Bi1^vii	75.73 (3)
Ti1ⁱ—Bi2—Ti1^xxiv	146.49 (2)	Bi2ⁱⁱ—Ti1—Bi1^vii	77.12 (3)
Ti1^vii—Bi1—Ti1ⁱ	146.84 (7)	Bi2ⁱⁱ—Ti1—Bi1^v	77.437 (16)
Bi1^vii—Ti1—Bi1ⁱ	146.84 (7)	Bi1^xii—Bi1—Ti1^xxiv	84.563 (17)
Ti1ⁱ—Bi2—Ti1^xxvii	146.946 (8)	Ti1^vii—Bi1—Ti1^xxvi	85.661 (13)
Bi2ⁱ—Ti1—Bi2ⁱⁱⁱ	146.946 (8)	Ti1ⁱ—Bi1—Ti1^xxiv	85.87 (4)
Ti1ⁱ—Bi2—Bi1^xxix	149.23 (2)	Ti1^vii—Bi1—Ti1^xxii	87.57 (2)
Ti1^xxvii—Bi2—Bi1^xii	149.475 (16)	Bi1^vii—Ti1—Bi1^xxii	87.57 (2)
Ti1^xx—Bi1—Bi2^xiv	150.350 (13)	Bi2^xiii—Bi1—Bi2^xviii	87.936 (5)
Ti1ⁱ—Bi1—Bi2^xvii	151.051 (14)	Ti1^xxi—Bi1—Ti1^xxiv	88.00 (2)
Ti1ⁱ—Bi1—Bi2^xix	151.659 (13)	Ti1ⁱ—Bi1—Ti1^xxvi	88.706 (13)
Bi1^xi—Bi1—Bi2^xiv	152.907 (6)	Bi1^xxxi—Bi2—Bi1^xii	92.064 (5)
Bi1^xii—Bi1—Bi2^xix	153.267 (4)	Bi2^xii—Bi1—Ti1^xxvi	93.35 (2)
Bi1^x—Bi1—Bi2^xviii	153.380 (4)	Ti1^xxviii—Bi2—Bi1^xxix	93.992 (16)
Bi2^xiii—Bi2—Bi1^xxix	155.439 (6)	Ti1ⁱ—Bi1—Bi2^xiv	95.236 (16)
Bi1^xi—Bi1—Ti1^xxiv	158.113 (19)	Ti1^xxiv—Bi2—Bi1^xxx	95.410 (14)
Bi2^xviii—Bi1—Ti1^xxii	161.981 (11)	Ti1^xxi—Bi1—Bi2^xviii	95.54 (4)
Bi2ⁱ—Ti1—Bi1^xxii	162.533 (7)	Ti1^vii—Bi1—Bi2^xviii	96.63 (4)
Bi2^xiv—Bi1—Ti1^xxvi	165.35 (2)	Bi2^xvi—Bi1—Ti1^xxii	96.863 (15)
Ti1^viii—Ti1—Ti1^ix	178.47 (15)	Ti1^xx—Bi1—Bi2^xix	97.142 (14)
Ti1^xx—Bi1—Ti1^xxvi	30.870 (13)	Bi2^xvi—Bi1—Ti1^xxiv	98.027 (15)
Bi2^xvi—Bi1—Ti1^xxvi	34.47 (2)	Ti1^vii—Bi1—Bi2^xiv	98.391 (15)
Ti1^xxii—Bi1—Ti1^xxiv	34.877 (3)	Bi2^xix—Bi1—Ti1^xxiv	98.570 (15)
Bi1^xi—Bi1—Ti1^xxvi	35.089 (15)	Bi2^xii—Bi1—Bi2^xix	99.134 (9)
Bi1^x—Bi1—Ti1^xxii	35.832 (14)	Bi1^x—Bi1—Ti1^xxvi	99.91 (2)

Symmetry codes: (i) −x, −y+1/2, −z+1/2; (ii) x+1/4, y−1/4, −z+1/2; (iii) −x+1/4, −y+3/4, z+1/2; (iv) x, y−1/2, z+1/2; (v) x+1/2, y, z+1/2; (vi) x−1/2, y, z+1/2; (vii) −x+1/2, −y, −z+1/2; (viii) −x+1/2, −y+1/2, −z+1; (ix) −x, −y, −z+1; (x) −x+1/4, y, −z+1/4; (xi) −x, −y, −z; (xii) −x+1/2, −y+1/2, −z; (xiii) −x−1/4, −y+3/4, z; (xiv) −x+3/4, −y+3/4, z; (xv) −x+1/4, −y+5/4, z; (xvi) x−1/2, y−1/2, z; (xvii) x+1/2, y−1/2, z; (xviii) x−1/4, y−1/4, −z; (xix) −x+1/4, −y+1/4, z; (xx) x−1/2, y, z−1/2; (xxi) x+1/2, y, z−1/2; (xxii) −x+3/4, y, −z+3/4; (xxiii) −x−1/4, y, −z+3/4; (xxiv) x+1/4, −y+1/2, z−1/4; (xxv) x−1/4, −y, z−1/4; (xxvi) −x−1/2, −y, −z+1/2; (xxvii) −x+1/4, y+1/2, −z+3/4; (xxviii) x, y+1/2, z−1/2; (xxix) −x+3/4, y+1/2, −z+1/4; (xxx) x+1/2, y+1/2, z; (xxxi) x−1/2, y+1/2, z; (xxxii) −x−1/4, y+1/2, −z+1/4.

Acknowledgements

This work was supported in part by a Grant-in-Aid for Scientific Research (B) (No. 16H04494) from the Ministry of Education, Culture, Sports and Technology (MEXT), Japan.

References

Bruker (2014). Instrument Service, APEX2, SADABS and SAINT-Plus. Bruker AXS Inc., Madison, Wisconsin, USA. Google Scholar
Cucka, P. & Barrett, C. S. (1962). Acta Cryst. 15, 865–872. CrossRef IUCr Journals Web of Science Google Scholar
Dashjav, E. & Kleinke, H. (2003). J. Solid State Chem. 176, 329–337. Web of Science CrossRef CAS Google Scholar
Gingl, F., Selvam, P. & Yvon, K. (1993). Acta Cryst. B49, 201–203. CrossRef CAS Web of Science IUCr Journals Google Scholar
Larsson, A. K. & Lidin, S. (1995). J. Alloys Compd. 221, 136–142. CrossRef CAS Web of Science Google Scholar
Malaman, B. & Steinmetz, J. (1979). J. Less-Common Met. 65, 285–288. CrossRef CAS Web of Science Google Scholar
Maruyama, S., Kado, Y. & Uda, T. (2013). J. Phase Equilib. Diffus. 34, 289–296. Web of Science CrossRef CAS Google Scholar
Momma, K. & Izumi, F. (2011). J. Appl. Cryst. 44, 1272–1276. Web of Science CrossRef CAS IUCr Journals Google Scholar
Richter, C. G. & Jeitschko, W. (1997). J. Solid State Chem. 134, 26–30. Web of Science CrossRef CAS Google Scholar
Schubert, K. & Anderko, K. (1951). Z. Metallkd. 42, 321–325. Google Scholar
Sheldrick, G. M. (2015). Acta Cryst. C71, 3–8. Web of Science CrossRef IUCr Journals Google Scholar
Simić, V. & Marinković, Z. (1990). Thin Solid Films, 191, 165–171. Google Scholar
Vassilev, G. P. (2006). Cryst. Res. Technol. 41, 349–357. Web of Science CrossRef CAS Google Scholar
Wölpl, T. & Jeitschko, W. (1994). J. Alloys Compd. 210, 185–190. Google Scholar
Zumdick, M. F., Landrum, G. A., Dronskowski, R., Hoffmann, R. D. & Pöttgen, R. (2000). J. Solid State Chem. 150, 19–30. Web of Science CrossRef CAS Google Scholar