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Determination of the modulated structure of Sr_14/11CoO₃ through a (3 + 1)-dimensional space description and using non-harmonic ADPs

Authors:

Gourdon, O.; Petricek, V.; Dusek, M.; Bezdicka, P.; Durovic, S.; Gyepesova, D.; Evain, M.

Journal:

Acta Crystallographica Section B 55 841-848 (1999)

DOI:

https://doi.org/10.1107/S0108768199006485

B-IncStrDB ID: 5392EqE0Xp Entry date: 2011-11-24 Last revision: 2022-01-02

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Chemical data

Structural Formula Sum: Co1 O3 Sr1 [ Help ]

Formula weight: 194.6 Da [ Help ]

Crystallographic data and experimental details

Crystal system: trigonal [ Help ]

Superspace group name: R-3m(00γ)0s [ Help ]

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

Operation code	Operation in algebraic form
1	x1,x2,x3,x4
2	-x2,x1-x2,x3,x4
3	-x1+x2,-x1,x3,x4
4	x2+2/3,x1+1/3,-x3+1/3,-x4+1/2
5	x1-x2+2/3,-x2+1/3,-x3+1/3,-x4+1/2
6	-x1+2/3,-x1+x2+1/3,-x3+1/3,-x4+1/2
7	-x1+2/3,-x2+1/3,-x3+1/3,-x4
8	x2+2/3,-x1+x2+1/3,-x3+1/3,-x4
9	x1-x2+2/3,x1+1/3,-x3+1/3,-x4
10	-x2,-x1,x3,x4+1/2
11	-x1+x2,x2,x3,x4+1/2
12	x1,x1-x2,x3,x4+1/2
13	x1+2/3,x2+1/3,x3+1/3,x4
14	-x2+2/3,x1-x2+1/3,x3+1/3,x4
15	-x1+x2+2/3,-x1+1/3,x3+1/3,x4
16	x2+1/3,x1+2/3,-x3+2/3,-x4+1/2
17	x1-x2+1/3,-x2+2/3,-x3+2/3,-x4+1/2
18	-x1+1/3,-x1+x2+2/3,-x3+2/3,-x4+1/2
19	-x1+1/3,-x2+2/3,-x3+2/3,-x4
20	x2+1/3,-x1+x2+2/3,-x3+2/3,-x4
21	x1-x2+1/3,x1+2/3,-x3+2/3,-x4
22	-x2+2/3,-x1+1/3,x3+1/3,x4+1/2
23	-x1+x2+2/3,x2+1/3,x3+1/3,x4+1/2
24	x1+2/3,x1-x2+1/3,x3+1/3,x4+1/2
25	x1+1/3,x2+2/3,x3+2/3,x4
26	-x2+1/3,x1-x2+2/3,x3+2/3,x4
27	-x1+x2+1/3,-x1+2/3,x3+2/3,x4
28	x2,x1,-x3,-x4+1/2
29	x1-x2,-x2,-x3,-x4+1/2
30	-x1,-x1+x2,-x3,-x4+1/2
31	-x1,-x2,-x3,-x4
32	x2,-x1+x2,-x3,-x4
33	x1-x2,x1,-x3,-x4
34	-x2+1/3,-x1+2/3,x3+2/3,x4+1/2
35	-x1+x2+1/3,x2+2/3,x3+2/3,x4+1/2
36	x1+1/3,x1-x2+2/3,x3+2/3,x4+1/2

a: 9.505(6) Å [ Help ]

b: 9.505(6) Å [ Help ]

c: 2.53(3) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 120 ° [ Help ]

Volume: 197.9(3) Å³ [ Help ]

Modulation dimension: 1 [ Help ]

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

Wave vector id	q_x	q_y	q_z
1	0	0	0.6341

Number of subsystems: 2 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1st subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	0.0
0.0	0.0	1.0	0.0
0.0	0.0	0.0	1.0

Subsystem code: 2 [ Help ]

Subsystem description: 2nd subsystem [ Help ]

W matrix:

1.0	0.0	0.0	0.0
0.0	1.0	0.0	0.0
0.0	0.0	0.0	1.0
0.0	0.0	1.0	0.0

Z: 36 [ Help ]

Cell measurement temperature: 297.6 K [ Help ]

μ: 314.761 mm^-1 [ Help ]

Refinement details

Refinement remarks: The structure is an obverse-reverse twin [ Help ]

Total nb. of reflections: 1163 [ Help ]

Nb. of observed reflections: 685 [ Help ]

Intense reflections threshold: I>3σ(I) [ Help ]

Refinement based on: F [ Help ]

R(obs): 0.037 [ Help ]

wR(obs): 0.0474 [ Help ]

R(all): 0.0733 [ Help ]

wR(all): 0.0567 [ Help ]

S(all): 1.94 [ Help ]

S(obs): 2.16 [ Help ]

Nb. of reflections: 1163 [ Help ]

Nb. of parameters: 71 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ²(F)+0.0001F²) [ Help ]

Δ/σ(max): 0.0206 [ Help ]

Δ/σ(mean): 0.0039 [ Help ]

Extinction method: none [ Help ]

Structural Information

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

Atom site label	Atom symbol	y	z	ADP type	Uiso/equiv	Symmetry multiplicity	Occupancy	Coords from (d)iffraction or (c)alculated	Coords restraints or constraints	Disordered cluster	Disordered group	Subsystem
Co1	Co	0	0	Uani	0.0123(3)	3	1	d	?	?	?	1
O1	O	-0.1484(4)	0.5	Uani	0.0168(19)	18	0.5	d	?	?	?	1
Sr1	Sr	-0.6562(14)	-0.25	Uani	0.0089(14)	18	0.3333	d	?	?	?	2

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

Atom site label	Atom site symbol	U11	U22	U33	U12	U13	U23
Co1	Co	0.0111(3)	0.0111(3)	0.0147(5)	0.00553(17)	0	0
O1	O	0.024(3)	0.0149(17)	0.014(2)	0.0121(16)	0.003(2)	0.0017(10)
Sr1	Sr	0.0123(18)	0.0058(19)	0.011(2)	0.0061(9)	0.0059(15)	0.0029(7)

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

Wave vector code	q_1
1	1
2	2
3	3
4	4

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

Atom site label	Center (x0)	Width
O1	0.75	0.5
Sr1	0	1

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

Modulation code	Atom site label	Displacement axis	Wave vector code
Co1x1	Co1	x	1
Co1y1	Co1	y	1
Co1z1	Co1	z	1
Co1x2	Co1	x	2
Co1y2	Co1	y	2
Co1z2	Co1	z	2
Co1x3	Co1	x	3
Co1y3	Co1	y	3
Co1z3	Co1	z	3
Co1x4	Co1	x	4
Co1y4	Co1	y	4
Co1z4	Co1	z	4

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

Modulation code	Cosine coefficient	Sine coefficient
Co1x1	0	0
Co1y1	0	0
Co1z1	0	0
Co1x2	0	0
Co1y2	0	0
Co1z2	0	-0.0281(4)
Co1x3	0	0
Co1y3	0	0
Co1z3	0	0
Co1x4	0	0
Co1y4	0	0
Co1z4	0	0.0031(4)

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

Atom site label	Displacement axis	Polynomial order	Polynomial coeff.
O1	x	1	0.0335(15)
O1	y	1	0.0167(7)
O1	z	1	-0.035(3)
O1	x	2	0
O1	y	2	0.0321(14)
O1	z	2	0
O1	x	3	0.084(3)
O1	y	3	0.0419(13)
O1	z	3	0.114(7)
O1	x	4	0
O1	y	4	0.04(2)
O1	z	4	0
O1	x	5	0.059(3)
O1	y	5	0.0297(14)
O1	z	5	0.11(7)
O1	x	6	0
O1	y	6	0.03(2)
O1	z	6	0
O1	x	7	0.052(3)
O1	y	7	0.0262(14)
O1	z	7	0.052(5)
O1	x	8	0
O1	y	8	0.013(3)
O1	z	8	0
Sr1	x	1	0.0272(16)
Sr1	y	1	0.0136(8)
Sr1	z	1	-0.028(4)
Sr1	x	2	0
Sr1	y	2	-0.0296(17)
Sr1	z	2	0
Sr1	x	3	-0.0083(16)
Sr1	y	3	-0.0041(8)
Sr1	z	3	0.021(5)
Sr1	x	4	0
Sr1	y	4	0.0187(16)
Sr1	z	4	0
Sr1	x	5	-0.019(2)
Sr1	y	5	-0.0095(12)
Sr1	z	5	-0.028(6)
Sr1	x	6	0
Sr1	y	6	-0.008(2)
Sr1	z	6	0

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

Modulation code	Atom site label	Tensor element	Wave vector code
Co1U111	Co1	U11	1
Co1U221	Co1	U22	1
Co1U331	Co1	U33	1
Co1U121	Co1	U12	1
Co1U131	Co1	U13	1
Co1U231	Co1	U23	1
Co1U112	Co1	U11	2
Co1U222	Co1	U22	2
Co1U332	Co1	U33	2
Co1U122	Co1	U12	2
Co1U132	Co1	U13	2
Co1U232	Co1	U23	2
Co1U113	Co1	U11	3
Co1U223	Co1	U22	3
Co1U333	Co1	U33	3
Co1U123	Co1	U12	3
Co1U133	Co1	U13	3
Co1U233	Co1	U23	3
Co1U114	Co1	U11	4
Co1U224	Co1	U22	4
Co1U334	Co1	U33	4
Co1U124	Co1	U12	4
Co1U134	Co1	U13	4
Co1U234	Co1	U23	4

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

Modulation code	Cosine coefficient	Sine coefficient
Co1U111	0	0
Co1U221	0	0
Co1U331	0	0
Co1U121	0	0
Co1U131	0	0
Co1U231	0	0
Co1U112	-0.0095(3)	0
Co1U222	-0.0095(3)	0
Co1U332	-0.009(5)	0
Co1U122	-0.00474(17)	0
Co1U132	0	0
Co1U232	0	0
Co1U113	0	0
Co1U223	0	0
Co1U333	0	0
Co1U123	0	0
Co1U133	0	0
Co1U233	0	0
Co1U114	0.0039(4)	0
Co1U224	0.0039(4)	0
Co1U334	0.0039(6)	0
Co1U124	0.00197(18)	0
Co1U134	0	0
Co1U234	0	0

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

Atom site label	Tensor element	Polynomial order	Polynomial coeff.
O1	U11	1	0
O1	U22	1	0.011(4)
O1	U33	1	0
O1	U12	1	0.011(4)
O1	U13	1	0
O1	U23	1	0.013(3)
O1	U11	2	0.023(11)
O1	U22	2	0.02(5)
O1	U33	2	0.011(7)
O1	U12	2	0.012(6)
O1	U13	2	0.013(8)
O1	U23	2	0.006(4)
O1	U11	3	0
O1	U22	3	0.013(5)
O1	U33	3	0
O1	U12	3	0.013(5)
O1	U13	3	0
O1	U23	3	0.008(4)
O1	U11	4	-0.006(11)
O1	U22	4	-0.005(5)
O1	U33	4	-0.004(7)
O1	U12	4	-0.003(5)
O1	U13	4	0.008(7)
O1	U23	4	0.004(4)
Sr1	U11	1	0
Sr1	U22	1	-0.017(3)
Sr1	U33	1	0
Sr1	U12	1	-0.017(3)
Sr1	U13	1	0
Sr1	U23	1	0.0022(15)
Sr1	U11	2	-0.016(6)
Sr1	U22	2	-0.001(3)
Sr1	U33	2	-0.003(2)
Sr1	U12	2	-0.008(3)
Sr1	U13	2	-0.005(17)
Sr1	U23	2	-0.0025(9)
Sr1	U11	3	0
Sr1	U22	3	-0.001(3)
Sr1	U33	3	0
Sr1	U12	3	-0.001(3)
Sr1	U13	3	0
Sr1	U23	3	0.0041(16)
Sr1	U11	4	0.015(7)
Sr1	U22	4	0.004(5)
Sr1	U33	4	-0.01(2)
Sr1	U12	4	0.008(4)
Sr1	U13	4	-0.003(2)
Sr1	U23	4	-0.0013(10)
Sr1	U11	5	0
Sr1	U22	5	-0.012(4)
Sr1	U33	5	0
Sr1	U12	5	-0.012(4)
Sr1	U13	5	0
Sr1	U23	5	-0.002(2)
Sr1	U11	6	0.021(7)
Sr1	U22	6	0.009(4)
Sr1	U33	6	0.003(3)
Sr1	U12	6	0.011(3)
Sr1	U13	6	0(3)
Sr1	U23	6	-0.0001(16)

Determination of the modulated structure of Sr14/11CoO3 through a (3 + 1)-dimensional space description and using non-harmonic ADPs