Incommensurate crystallographic shear structure of Ba_xBi_2 − 2xTi_4 − xO_{11 − 4x} (x = 0.275)

The title compound generates diffraction patterns which are indexable within the framework of the higher-dimensional description of incommensurate structures. However, it is difficult to discriminate the main reflections from the satellite ones. This paper has clarified that the structure can be treated as a strongly modulated structure with sawtooth-like modulation functions and is classified as an incommensurate crystallographic shear (CS) structure. The structure consists of domains isostructural to β-Bi₂Ti₄O₁₁ and domain boundaries composed of TiO₆ octahedra. Ba and Bi ions are accommodated in the cavities between TiO₆ octahedra in the domain. Domain boundaries are aperiodically inserted, in contrast to the usual CS structures, forming an incommensurate structure.

Computing details

Program(s) used to refine structure: (Jana2000; Petricek and Dusek, 2000); software used to prepare material for publication: (Jana2000; Petricek and Dusek, 2000).

Figures

(I)

Crystal data

Ba0.0504Bi0.2661O1.8165Ti0.6835	F(000) = 218
Mr = 124.3	Dx = 6.085 (1) Mg m^−3
Monoclinic, I2/m(α1γ)00†	Nb Kα radiation, λ = 0.7476 Å
q = 0.36693c*	Cell parameters from 4621 reflections
a = 10.6914 (3) Å	θ = 2.5–45°
b = 3.7963 (1) Å	µ = 38.91 mm^−1
c = 3.3457 (1) Å	T = 298 K
β = 92.625 (2)°	Prism, pale yellow
V = 135.65 (1) Å^3	0.10 × 0.05 × 0.04 mm
Z = 4

† Symmetry operations: (1) x₁, x₂, x₃, x₄; (2) −x₁, x₂, −x₃, −x₄; (3) −x₁, −x₂, −x₃, −x₄; (4) x₁, −x₂, x₃, x₄; (5) 1/2+x₁, 1/2+x₂, 1/2+x₃, 1/2+x₄; (6) 1/2−x₁, 1/2+x₂, 1/2−x₃, 1/2−x₄; (7) 1/2−x₁, 1/2−x₂, 1/2−x₃, 1/2−x₄; (8) 1/2+x₁, 1/2−x₂, 1/2+x₃, 1/2+x₄.

Data collection

Mac Science DIP320 diffractometer	925 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.033
ω scans	θmax = 45°, θmin = 2.5°
Absorption correction: empirical (using intensity measurements) ?	h = −15→15
Tmin = 0.161, Tmax = 0.274	k = −4→3
2389 measured reflections	l = −7→3
1059 independent reflections

Refinement

Refinement on F	(Δ/σ)max = 0.006
R[F^2 > 2σ(F^2)] = 0.042	Δρmax = 3.08 e Å^−3
S = 1.85	Δρmin = −2.56 e Å^−3
925 reflections	Extinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
81 parameters	Extinction coefficient: 0.002725
Weighting scheme based on measured s.u.'s w = 1/σ^2(F)

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Ba1	0.0822 (10)	0	0.689 (3)	0.0089 (15)*	0.1592
Bi1	0.1029 (14)	0	0.755 (4)	0.012 (3)	0.8408
Ti1	0.358 (2)	0	0.711 (7)	0.0059 (3)
O1	0.2102 (4)	0	0.8802 (14)	0.0092 (13)
O2	0.5	0	0.5	0.012 (4)
O3	0.589 (6)	0	0.760 (13)	0.0084 (16)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Bi1	0.051 (6)	−0.037 (7)	0.023 (4)	0	0.015 (3)	0
Ti1	0.0044 (5)	0.0075 (8)	0.0058 (4)	0	−0.0012 (3)	0
O1	0.0036 (15)	0.015 (3)	0.0085 (18)	0	−0.0008 (12)	0
O2	0.001 (3)	0.018 (8)	0.018 (6)	0	0.008 (4)	0
O3	0.010 (2)	0.012 (4)	0.0026 (18)	0	−0.0032 (15)	0

Bond lengths (Å)

	Average	Minimum	Maximum
Ba1—O1^i	3.07 (3)	2.96 (4)	3.23 (4)
Ba1—O1	2.47 (3)	1.98 (4)	2.80 (4)
Ba1—O1^ii	3.58 (3)	3.29 (4)	3.95 (4)
Ba1—O1^iii	3.55 (3)	3.19 (4)	4.08 (4)
Ba1—O1^iv	3.16 (3)	3.11 (3)	3.22 (3)
Ba1—O1^v	2.49 (2)	2.396 (19)	2.67 (3)
Ba1—O1^vi	2.49 (2)	2.396 (19)	2.67 (3)
Ba1—O2^vii	3.136 (12)	2.79 (2)	3.50 (3)
Ba1—O2^viii	3.136 (12)	2.79 (2)	3.50 (3)
Ba1—O3^ix	2.57 (6)	2.48 (6)	2.75 (7)
Ba1—O3^x	2.57 (6)	2.48 (6)	2.75 (7)
Ba1—O3^v	2.89 (9)	2.72 (10)	3.08 (11)
Ba1—O3^vi	2.89 (9)	2.72 (10)	3.08 (11)
Bi1—O1^i	3.15 (3)	2.99 (3)	3.32 (3)
Bi1—O1	2.12 (3)	1.98 (3)	2.17 (3)
Bi1—O1^ii	3.33 (3)	3.21 (3)	3.53 (3)
Bi1—O1^iv	3.27 (3)	3.13 (3)	3.39 (3)
Bi1—O1^v	2.40 (2)	2.38 (2)	2.47 (2)
Bi1—O1^vi	2.40 (2)	2.38 (2)	2.47 (2)
Bi1—O2^vii	3.379 (17)	3.196 (17)	3.55 (2)
Bi1—O2^viii	3.379 (17)	3.196 (17)	3.55 (2)
Bi1—O3^ix	2.48 (6)	2.43 (5)	2.57 (7)
Bi1—O3^x	2.48 (6)	2.43 (5)	2.57 (7)
Bi1—O3^v	3.12 (10)	3.05 (11)	3.16 (11)
Bi1—O3^vi	3.12 (10)	3.05 (11)	3.16 (11)
Ti1—O1^i	3.12 (6)	2.07 (9)	4.27 (5)
Ti1—O1	2.03 (6)	1.96 (6)	2.12 (6)
Ti1—O1^xi	4.73 (6)	3.70 (6)	5.97 (7)
Ti1—O1^xii	4.73 (6)	3.70 (6)	5.97 (7)
Ti1—O1^xiii	4.38 (5)	3.44 (5)	4.69 (5)
Ti1—O1^v	1.934 (12)	1.913 (7)	1.986 (16)
Ti1—O1^xiv	3.89 (5)	3.58 (5)	4.25 (7)
Ti1—O1^xv	4.38 (5)	3.44 (5)	4.69 (5)
Ti1—O1^vi	1.934 (12)	1.913 (7)	1.986 (16)
Ti1—O1^xvi	3.89 (5)	3.58 (5)	4.25 (7)
Ti1—O2	1.87 (6)	1.80 (5)	1.96 (9)
Ti1—O2^ii	2.21 (5)	2.20 (5)	2.21 (5)
Ti1—O3	1.96 (14)	1.86 (14)	2.03 (15)
Ti1—O3^vii	3.70 (11)	3.59 (11)	3.83 (10)
Ti1—O3^ix	3.74 (11)	3.67 (12)	3.79 (12)
Ti1—O3^viii	3.70 (11)	3.59 (11)	3.83 (10)
Ti1—O3^x	3.74 (11)	3.67 (12)	3.79 (12)
Ti1—O3^xvii	1.87 (10)	1.81 (11)	1.92 (9)
Ti1—O3^xviii	1.89 (11)	1.76 (9)	2.06 (9)

Symmetry codes: (i) x₁, x₂, x₃−1, x₄; (ii) x₁, x₂, x₃+1, x₄; (iii) −x₁, −x₂, −x₃+1, −x₄; (iv) −x₁, −x₂, −x₃+2, −x₄; (v) −x₁+1/2, −x₂−1/2, −x₃+3/2, −x₁/2; (vi) −x₁+1/2, −x₂+1/2, −x₃+3/2, −x₁/2; (vii) x₁−1/2, x₂−1/2, x₃−1/2, x₁/2; (viii) x₁−1/2, x₂+1/2, x₃−1/2, x₁/2; (ix) x₁−1/2, x₂−1/2, x₃+1/2, x₁/2; (x) x₁−1/2, x₂+1/2, x₃+1/2, x₁/2; (xi) x₁+1/2, x₂−1/2, x₃+1/2, x₁/2; (xii) x₁+1/2, x₂+1/2, x₃+1/2, x₁/2; (xiii) −x₁+1/2, −x₂−1/2, −x₃+1/2, −x₁/2; (xiv) −x₁+1/2, −x₂−1/2, −x₃+5/2, −x₁/2; (xv) −x₁+1/2, −x₂+1/2, −x₃+1/2, −x₁/2; (xvi) −x₁+1/2, −x₂+1/2, −x₃+5/2, −x₁/2; (xvii) −x₁+1, −x₂, −x₃+1, −x₄; (xviii) −x₁+1, −x₂, −x₃+2, −x₄.