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Application of Modulated Structure Analysis to Two-Dimensional Antiphase-Domain Structure of Au(2+x)Cd(1-x)

Authors:

Yamamoto, A.

Journal:

Acta Crystallographica B 39 17-20 (1983)

DOI:

https://doi.org/10.1107/S0108768183001962

B-IncStrDB ID: 3202EEyo32 Entry date: 2010-11-08 Last revision: 2024-01-02

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mod1023715561

Chemical data

Structural Formula Sum: Au0.67 Cd0.33 [ Help ]

Crystallographic data and experimental details

a: 2.919(4) Å [ Help ]

b: 2.919(4) Å [ Help ]

γ: 60 ° [ Help ]

c: 4.808(7) Å [ Help ]

β: 90 ° [ Help ]

α: 90 ° [ Help ]

Modulation dimension: 2 [ Help ]

Crystal system: hexagonal [ Help ]

Superspace group name: P:P63/mmc:p6 1mm [ Help ]

Symmetry operations of the superspace group: [ Help ]

Operation code Operation in algebraic form
1 x1,x2,x3,x4,x5
2 -x2,x1-x2,x3,-x5,x4-x5
3 -x1+x2,-x1,x3,-x4+x5,-x4
4 -x1,-x2,x3+1/2,-x4,-x5
5 x2,-x1+x2,x3+1/2,x5,-x4+x5
6 x1-x2,x1,x3+1/2,x4-x5,x4
7 x2,x1,-x3,x4,x4-x5
8 x1-x2,-x2,-x3,-x5,-x4
9 -x1,-x1+x2,-x3,-x4+x5,x5
10 -x2,-x1,-x3+1/2,-x4,-x4+x5
11 -x1+x2,x2,-x3+1/2,x5,x4
12 x1,x1-x2,-x3+1/2,x4-x5,-x5
13 -x1,-x2,-x3,-x4,-x5
14 x2,-x1+x2,-x3,x5,-x4+x5
15 x1-x2,x1,-x3,x4-x5,x4
16 x1,x2,-x3+1/2,x4,x5
17 -x2,x1-x2,-x3+1/2,-x5,x4-x5
18 -x1+x2,-x1,-x3+1/2,-x4+x5,-x4
19 -x2,-x1,x3,-x4,-x4+x5
20 -x1+x2,x2,x3,x5,x4
21 x1,x1-x2,x3,x4-x5,-x5
22 x2,x1,x3+1/2,x4,x4-x5
23 x1-x2,-x2,x3+1/2,-x5,-x4
24 -x1,-x1+x2,x3+1/2,-x4+x5,x5

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.429 0.429 0
2 -0.429 0.858 0

Refinement details

Nb. of observed reflections: 54 [ Help ]

R(obs): 0.065 [ Help ]

Refinement remarks: structure 7a Warning: Thermal parameters in beta form [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Occupancy Symmetry multiplicity x y z Uiso/equiv ADP type
Au 0.67 ? 0.33 0.66 0.25 0.016(1) Uiso
Cd 0.33 ? 0.33 0.66 0.25 0.016(1) 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 0.429 0.429 0
2 0.429 -0.858 0
3 -0.858 0.429 0

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

Modulation code Atom site label Displacement axis Wave vector code
Aux1 Au x 1
Aux2 Au x 2
Aux3 Au x 3
Auy1 Au y 1
Auy2 Au y 2
Auy3 Au y 3

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
Aux1 -0.0025(11) -0.0005(8)
Aux2 0 0.0010(16)
Aux3 0.0025(11) -0.0005(8)
Auy1 -0.0025(11) 0.0005(8)
Auy2 0.0025(11) 0.0005(8)
Auy3 0 -0.0010(16)

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Auo1 Au 1
Auo2 Au 2
Auo3 Au 3

Occupation Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
Auo1 0 -0.22(4)
Auo2 0 -0.22(4)
Auo3 0 -0.22(4)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
AuU1 Au Uiso 1
AuU2 Au Uiso 2
AuU3 Au Uiso 3

ADP Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
AuU1 0 0.0038(9)
AuU2 0 0.0038(9)
AuU3 0 0.0038(9)