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Structure refinement of the incommensurate composite crystal Sr1.145TiS3 through the Rietveld analysis process

Authors:

Onoda, Mitsuko; Saeki, Masanobu; Yamamoto, Akiji; Kato, Katsuo

Journal:

Acta Crystallographica Section B 49 929-936 (1993)

DOI:

https://doi.org/10.1107/S0108768193005324

B-IncStrDB ID: 1982Ea7jfc Entry date: 2021-12-19 Last revision: 2021-12-19

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comp1015862270

Chemical data

Structural Formula Sum: Sr1.145 Ti S3 [ Help ]

Formula weight: 244.42 Da [ Help ]

Crystallographic data and experimental details

a: 11.5108(2) Å [ Help ]

b: 11.5108(2) Å [ Help ]

c: 2.99094(5) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 120 ° [ Help ]

Volume: 343.19 Å3 [ Help ]

Z: 3 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0 0 0.57227(2)

Number of subsystems: 2 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: TiS3 [ 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: Sr [ 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

Crystal system: hexagonal [ Help ]

Superspace group name: 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,x3,4+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-x2+2/3,-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-x2+1/3,-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
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

Refinement details

Refinement remarks: WARNING: The published isotropic thermal displacement parameters have been converted to U,s. [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol Subsystem Occupancy Symmetry multiplicity x y z Uiso/equiv ADP type
Ti Ti 1 1 3 0.0 0.0 0.0 0.017(2) Uiso
S S 1 1 18 0.1611(13) 0.080(7) 0.527(10) 0.018(3) Uiso
Sr Sr 2 1 36 0.33333 0.0 -0.018(8) 0.031(2) Uiso

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 0.57227
2 0 0 1.14454
3 0 0 1.71681
4 0 0 2.28908
5 0 0 2.86135
6 0 0 3.43362

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

Modulation code Atom site label Displacement axis Wave vector code
Tiz2 Ti z 2
Tiz4 Ti z 4
Tyz6 Ti z 6
Sy1 S y 1
Sx2 S x 2
Sy2 S y 2
Sz2 S z 2
Sy3 S y 3
Sx4 S x 4
Sy4 S y 4
Sz4 S z 4
Sy5 S y 5
Sx6 S x 6
Sy6 S y 6
Syz6 S z 6
Srx1 Sr x 1
Sry1 Sr y 1
Srx2 Sr x 2
Sry2 Sr y 2
Srz3 Sr z 3
Srx4 Sr x 4
Sry4 Sr y 4
Srx5 Sr x 5
Sry5 Sr y 5
Srz6 Sr z 6

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
Tiz2 0.058(6) 0.042(12)
Tiz4 -0.016(10) 0.013(10)
Tyz6 -0.018(11) 0.009(10)
Sy1 -0.066(4) 0.100(4)
Sx2 0.008(3) 0.0197(19)
Sy2 0.0041(15) 0.0099(9)
Sz2 -0.047(6) -0.037(9)
Sy3 0.040(2) -0.009(5)
Sx4 -0.004(3) -0.015(2)
Sy4 -0.0021(17) -0.0074(11)
Sz4 -0.002(8) 0.000(5)
Sy5 -0.026(4) -0.017(6)
Sx6 0.003(3) 0.015(2)
Sy6 0.001(2) 0.0073(12)
Syz6 0.027(8) 0.002(10)
Srx1 -0.007(2) 0.0241(6)
Sry1 -0.0243(12) 0.062(19)
Srx2 0.0128(6) -0.000(2)
Sry2 0.006(2) -0.0113(12)
Srz3 -0.008(6) 0.018(3)
Srx4 -0.008(3) -0.007(2)
Sry4 0.002(2) -0.010(2)
Srx5 -0.0077(12) 0.001(3)
Sry5 -0.003(3) 0.007(2)
Srz6 0.0 -0.015(2)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
SU2 S Uiso 2
SU4 S Uiso 4
SrU3 Sr Uiso 3

ADP Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
SU2 -0.005(9) -0.020(5)
SU4 -0.010(8) 0.011(8)
SrU3 -0.011(5) 0.016(5)