B-IncStrDB

Incommensurate Crystallographic-Shear Structure of Ba_xBi_2-2xTi_4-xO_11-4x (x=0.275)

Authors:

Michiue, Yuichi; Yamamoto, Akiji; Onoda, Mitsuko; Sato, Akira; Akashi, Takaya; Yamane, Hisanori; Goto, Takashi

Journal:

Acta Crystallographica, Section B 61 145-153 (2005)

B-IncStrDB ID: 4VTtd9oGhcL Entry date: 2021-12-26 Last revision: 2021-12-26

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Chemical data

Structural Formula Sum: Ba0.0504 Bi0.2661 O1.8165 Ti0.6835 [ Help ]

Formula weight: 124.3 Da [ Help ]

Crystallographic data and experimental details

Crystal system: monoclinic [ Help ]

Superspace group name: I2/m(α1γ) [ Help ]

Symmetry operations of the superspace group: (Show/hide table) [ Help ]

Operation code	Operation in algebraic form
1	x1,x2,x3,x4
2	-x1,x2,-x3,-x4
3	-x1,-x2,-x3,-x4
4	x1,-x2,x3,x4
5	x1+1/2,x2+1/2,x3+1/2,x4+1/2
6	-x1+1/2,x2+1/2,-x3+1/2,-x4+1/2
7	-x1+1/2,-x2+1/2,-x3+1/2,-x4+1/2
8	x1+1/2,-x2+1/2,x3+1/2,x4+1/2

a: 10.6914(3) Å [ Help ]

b: 3.79630(10) Å [ Help ]

c: 3.34570(10) Å [ Help ]

α: 90 ° [ Help ]

β: 92.625(2) ° [ Help ]

γ: 90 ° [ Help ]

Volume: 135.652(7) Å³ [ Help ]

Z: 4 [ Help ]

Cell determination reflection Nb.: 4621 [ Help ]

θ(min) for cell determination: 2.5 ° [ Help ]

θ(max) for cell determination: 45 ° [ Help ]

Cell measurement temperature: 298 K [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: (Show/hide table) [ Help ]

Wave vector id	q_x	q_y	q_z
1	0.00005(8)	0.00000	0.36693(3)

μ: 38.91 mm^-1 [ Help ]

Absorption correction type: empirical [ Help ]

Minimum transmission factor: 0.161 [ Help ]

Maximum transmission factor: 0.274 [ Help ]

Refinement details

Total nb. of reflections: 1059 [ Help ]

Nb. of observed reflections: 925 [ Help ]

Intense reflections threshold: I>2σ(I) [ Help ]

Refinement based on: F [ Help ]

R(obs): 0.0418 [ Help ]

wR(obs): 0.0421 [ Help ]

S(all): 1.85 [ Help ]

Nb. of reflections: 925 [ Help ]

Nb. of parameters: 81 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/σ²(F) [ Help ]

Δ/σ(max): 0.0057 [ Help ]

Δ/σ(mean): 0.0011 [ Help ]

Δρ(max): 3.08 e_Å^-3 [ Help ]

Δρ(min): -2.56 e_Å^-3 [ Help ]

Extinction method: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974) [ Help ]

Extinction coefficient: 0.002725 [ Help ]

Structural Information

Average Structure: (Show/hide table) [ Help ]

Atom site label	x	z	Uiso/equiv	ADP type	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Occupancy	Disordered cluster	Disordered group	Atom symbol
Ba1	0.0822(10)	0.689(3)	0.0089(15)	Uiso	d	.	0.1592	.	.	Ba
Bi1	0.1029(14)	0.755(4)	0.012(3)	Uani	d	.	0.8408	.	.	Bi
Ti1	0.358(2)	0.711(7)	0.0059(3)	Uani	d	.	1	.	.	Ti
O1	0.2102(4)	0.8802(14)	0.0092(13)	Uani	d	.	1	.	.	O
O2	0.5	0.5	0.012(4)	Uani	d	.	1	.	.	O
O3	0.589(6)	0.760(13)	0.0084(16)	Uani	d	.	1	.	.	O

ADP components: (Show/hide table) [ Help ]

Atom site label	U11	U22	U33	U13	Atom site symbol
Bi1	0.051(6)	-0.037(7)	0.023(4)	0.015(3)	Bi
Ti1	0.0044(5)	0.0075(8)	0.0058(4)	-0.0012(3)	Ti
O1	0.0036(15)	0.015(3)	0.0085(18)	-0.0008(12)	O
O2	0.001(3)	0.018(8)	0.018(6)	0.008(4)	O
O3	0.010(2)	0.012(4)	0.0026(18)	-0.0032(15)	O

Fourier Wave Vectors (explicit: q_x,q_y,q_z or coefficients: q_1,q_2,...): (Show/hide table) [ Help ]

Wave vector code	q_x	q_z
1	0.00005	0.36693
2	0.00010	0.73386
3	0.00015	1.10079

Occupation crenel coefficients: (Show/hide table) [ Help ]

Atom site label	Center (x0)	Width
Bi1	0.2517(13)	0.316535

Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Displacement axis	Wave vector code
Bix1	Bi1	x	1
Biz1	Bi1	z	1
Ti1x1	Ti1	x	1
Ti1z1	Ti1	z	1
Ti1x2	Ti1	x	2
Ti1z2	Ti1	z	2
Ti1x3	Ti1	x	3
Ti1z3	Ti1	z	3
O1x1	O1	x	1
O1z1	O1	z	1
O1x2	O1	x	2
O1z2	O1	z	2
O1x3	O1	x	3
O1z3	O1	z	3
O2x1	O2	x	1
O2z1	O2	z	1
O3x1	O3	x	1
O3z1	O3	z	1
O3x2	O3	x	2
O3z2	O3	z	2

Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Bix1	-0.0387(3)	0.0080(16)
Biz1	-0.0236(8)	-0.003(4)
Ti1x1	-0.0134(6)	-0.000(4)
Ti1z1	-0.0483(17)	0.27(11)
Ti1x2	0.001(3)	0.0016(9)
Ti1z2	-0.017(8)	-0.017(3)
Ti1x3	0.0042(9)	-0.0007(14)
Ti1z3	-0.001(3)	-0.015(4)
O1x1	-0.0083(7)	0.0089(5)
O1z1	0.005(2)	0.0226(19)
O1x2	-0.0054(9)	-0.0032(7)
O1z2	-0.012(3)	-0.005(2)
O1x3	0.0017(13)	0.0037(11)
O1z3	-0.007(4)	0.003(3)
O2x1	0	-0.002(2)
O2z1	0	-0.033(9)
O3x1	0.010(8)	0.000(6)
O3z1	0.007(18)	-0.011(13)
O3x2	-0.000(2)	-0.004(5)
O3z2	-0.011(6)	0.009(11)

Displacive sawtooth coefficients: (Show/hide table) [ Help ]

Atom site label	Ax	Az	Center (x0)	Width
Ba1	0.003(2)	-0.021(6)	0.2276(16)	0.316535
Ti1	0.068347	0.136693	0.736(2)	0.683465
O1	0.1	0.2	0.9560(5)	1
O2	0.036693	0.073386	0.5	0.36693
O3	0.063307	0.126614	0.096(5)	0.63307

Definition of the ADP Fourier series: (Show/hide table) [ Help ]

Modulation code	Atom site label	Tensor element	Wave vector code
Bi1U111	Bi1	U11	1
Bi1U221	Bi1	U22	1
Bi1U331	Bi1	U33	1
Bi1U131	Bi1	U13	1

ADP Fourier coefficients: (Show/hide table) [ Help ]

Modulation code	Cosine coefficient	Sine coefficient
Bi1U111	-0.0090(11)	-0.048(6)
Bi1U221	0.0024(19)	0.111(9)
Bi1U331	-0.0047(8)	-0.016(4)
Bi1U131	-0.0037(7)	-0.018(4)

Incommensurate Crystallographic-Shear Structure of BaxBi2-2xTi4-xO11-4x (x=0.275)