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Crystal Structure of a Modulated Composite Structure with Two Subsystems: Ba1.1064CoO3

Authors:

El Abed, A.; Elqebbaj, S.E.; Zakhour, M.; Champeaux, M.; Perez-Mato, J.M.; Darriet, J.

Journal:

Journal of Solid State Chemistry 161 300-306 (2001)

DOI:

https://doi.org/10.1006/jssc.2001.9314

B-IncStrDB ID: 1282EkSTgq Entry date: 2010-11-08 Last revision: 2022-01-04

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comp1012841408

Chemical data

Structural Formula Sum: Ba1.1064 Co O3 [ Help ]

Crystallographic data and experimental details

Number of subsystems: 2 [ Help ]

Modulation dimension: 1 [ Help ]

a: 9.8842(20) Å [ Help ]

b: 9.8842(20) Å [ Help ]

c: 2.4785(12) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 120 ° [ Help ]

Volume: 209.7(1) Å3 [ Help ]

Z: 3 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0 0 0.5532(2)

Crystal system: trigonal [ Help ]

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

Symmetry operations of the superspace group: [ 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,x1,-x3,-x4+1/2
5 x1-x2,-x2,-x3,-x4+1/2
6 -x1,-x1+x2,-x3,-x4+1/2
7 -x1,-x2,-x3,-x4
8 x2,-x1+x2,-x3,-x4
9 x1-x2,x1,-x3,-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+2/3,x1+1/3,-x3+1/3,-x4+1/2
17 x1+2/3-x2,-x2+1/3,-x3+1/3,-x4+1/2
18 -x1+2/3,-x1+x2+1/3,-x3+1/3,-x4+1/2
19 -x1+2/3,-x2+1/3,-x3+1/3,-x4
20 x2+2/3,-x1+x2+1/3,-x3+1/3,-x4
21 x1-x2+2/3,x1+1/3,-x3+1/3,-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+1/3,x1+2/3,-x3+2/3,-x4+1/2
29 x1+1/3-x2,-x2+2/3,-x3+2/3,-x4+1/2
30 -x1+1/3,-x1+x2+2/3,-x3+2/3,-x4+1/2
31 -x1+1/3,-x2+2/3,-x3+2/3,-x4
32 x2+1/3,-x1+x2+2/3,-x3+2/3,-x4
33 x1-x2+1/3,x1+2/3,-x3+2/3,-x4
34 -x2+1/3,-x1+2/3,x3+2/3,x4+1/2
36 -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

Subsystem code: 1 [ Help ]

Subsystem description: CoO3 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: Ba 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

Refinement details

Nb. of reflections: 1306 [ Help ]

R(obs): 0.0406 [ Help ]

wR(obs): 0.042 [ Help ]

Refinement remarks: Orthogonalized functions have been expanded to calculate the atomic Fourier amplitudes. The homogeneus terms correct the average coordinates and ADP,s [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol Subsystem Occupancy x y z Uiso/equiv ADP type
Co1 Co 1 0.1666 0 0 0 0.0092(1) Uani
Co2 Co 1 0.1666 0 0 0 0.034(10) Uani
O O 1 0.5 0.1453(3) 0.1453(3) 0.5 0.0147(4) Uani
Ba1 Ba 2 0.2372 0.3019(4) 0 0.25 0.0131(5) Uani
Ba2 Ba 2 0.0962 0.3488(5) 0 0.25 0.0054(4) Uani

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23
Co1 0.0154(4) 0.0154(1) 0.0237(10) 0.0078(3) 0 0
Co2 0.0067(6) 0.0067(6) 0.090(3) 0.0034(3) 0 0
O 0.0211(11) 0.0211(11) 0.041(3) 0.004(1) 0.001(1) -0.001(1)
Ba1 0.005(1) 0.024(2) 0.012(1) 0.012(1) 0.0052(1) 0.0103(8)
Ba2 0.0039(5) 0.0017(6) 0.0099(6) 0.0009(3) 0.0002(2) 0.0004(4)

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

Wave vector code q_x q_y q_z
1 0 0 0.5532
2 0 0 1.1064

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
Ba1 0.5 0.237166
Ba2 0 0.096168

Displacive sawtooth coefficients: [ Help ]

Atom site label Az Center (x0) Width
Co1 -0.09949 0 0.4468
Co2 -0.01185 0.25 0.0532
O -0.11134 0.25 0.5

Displacive (translational) ortho-harmonics coefficients: [ Help ]

Atom site label Displacement axis Ortho set id Ortho set order Ortho set coefficient
Co1 z Co1zorth1 1 -0.0235(2)
O x Oxorth1 1 0.0016(1)
O y Oyorth1 1 0.0016(1)
O x Oxorth2 2 -0.00075(8)
O y Oyorth2 2 0.00075(8)
O z Ozorth2 2 0.0338(7)
Ba1 x Ba1xorth1 1 -0.0031(2)
Ba1 y Ba1yorth1 1 -0.0061(3)
Ba1 z Ba1zorth1 1 0.0015(3)
Ba1 x Ba1xorth2 2 0.0096(7)

Definition of the displacive (translational) Fourier series: [ Help ]

Modulation code Atom site label Displacement axis Wave vector code
Co1z1 Co1 z 1
Ox1 O x 1
Oy1 O y 1
Ox2 O x 2
Oy2 O y 2
Oz2 O z 2
Ba1x1 Ba1 x 1
Ba1y1 Ba1 y 1
Ba1z1 Ba1 z 1
Ba1x2 Ba1 x 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
Co1z1 -0.0354(3) 0
Ox1 0.0052(3) 0
Oy1 0.0052(3) 0
Ox2 0 -0.0011(1)
Oy2 0 0.0011(1)
Oz2 0 0.0478(10)
Ba1x1 0.0075(4) 0
Ba1y1 -0.0150(7) 0
Ba1z1 0.0037(7) 0
Ba1x2 0 0.034(2)

ADP ortho-harmonics coefficients: [ Help ]

Atom site label Tensor element Ortho set id Ortho set order Ortho set coefficient
Co1 U11 Co1U11orth2 2 -0.0031(1)
Co1 U22 Co1U22orth2 2 -0.0031(1)
Co1 U33 Co1U33orth2 2 -0.0036(3)
Co1 U12 Co1U12orth2 2 -0.00155(5)
O U11 OU11orth1 1 -0.0054(4)
O U22 OU22orth1 1 -0.0054(4)
O U33 OU33orth1 1 -0.0095(9)
O U12 OU12orth1 1 -0.0011(5)
O U13 OU13orth1 1 -0.0004(4)
O U23 OU23orth1 1 0.0004(4)
O U11 OU11orth2 2 -0.00003(40)
O U22 OU22orth2 2 0.00003(40)
O U13 OU13orth2 2 -0.0020(4)
O U23 OU23orth2 2 0.0020(4)
Ba1 U11 Ba1U11orth1 1 0.0004(4)
Ba1 U12 Ba1U12orth1 1 0.0004(4)
Ba1 U13 Ba1U13orth1 1 -0.0008(3)
Ba1 U11 Ba1U11orth2 2 0.0005(5)
Ba1 U22 Ba1U22orth2 2 -0.0015(7)
Ba1 U33 Ba1U33orth2 2 0.0031(5)
Ba1 U12 Ba1U12orth2 2 -0.0008(4)
Ba1 U13 Ba1U13orth2 2 -0.0000(2)
Ba1 U23 Ba1U23orth2 2 -0.0001(3)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Co1U112 Co1 U11 2
Co1U222 Co1 U22 2
Co1U332 Co1 U33 2
Co1U122 Co1 U12 2
OU111 O U11 1
OU221 O U22 1
OU331 O U33 1
OU121 O U12 1
OU131 O U13 1
OU231 O U23 1
OU112 O U11 2
OU222 O U22 2
OU132 O U13 2
OU232 O U23 2
Ba1U111 Ba1 U11 1
Ba1U121 Ba1 U12 1
Ba1U131 Ba1 U13 1
Ba1U112 Ba1 U11 2
Ba1U222 Ba1 U22 2
Ba1U332 Ba1 U33 2
Ba1U122 Ba1 U12 2
Ba1U132 Ba1 U13 2
Ba1U232 Ba1 U23 2

ADP Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
Co1U112 0 -0.0122(4)
Co1U222 0 -0.0122(4)
Co1U332 0 -0.0141(12)
Co1U122 0 -0.0061(2)
OU111 -0.018(1) 0
OU221 -0.018(1) 0
OU331 -0.031(3) 0
OU121 -0.004(2) 0
OU131 -0.001(1) 0
OU231 0.001(1) 0
OU112 0 -0.0000(6)
OU222 0 0.0000(6)
OU132 0 0.0028(6)
OU232 0 0.0028(6)
Ba1U111 0.001(1) 0
Ba1U121 0.001(1) 0
Ba1U131 -0.0020(7) 0
Ba1U112 0 0.002(2)
Ba1U222 0 -0.005(2)
Ba1U332 0 0.011(2)
Ba1U122 0 -0.005(2)
Ba1U132 0 -0.0002(5)
Ba1U232 0 -0.000(1)