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Modulated structure of CuAu II (One-dimensional modulation)

Authors:

Yamamoto, Akiji

Journal:

Acta Crystallographica Section B 38 1446-1451 (1982)

DOI:

https://doi.org/10.1107/S0567740882006128

B-IncStrDB ID: 2942E0h9ZW Entry date: 2010-11-08 Last revision: 2021-12-08

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mod1013079904

Chemical data

Structural Formula Sum: Au0.5 Cu0.5 [ Help ]

Crystallographic data and experimental details

a: 3.956(3) Å [ Help ]

b: 3.972(2) Å [ Help ]

c: 3.976(2) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 90 ° [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0 0.1 0

Crystal system: orthorhombic [ Help ]

Superspace group name (ITC): Fmmm(1β0)000 [ Help ]

Superspace group name (WJJ): L:Fmmm:(1-11) [ Help ]

Symmetry operations of the superspace group: [ Help ]

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

Refinement details

R(obs): 0.096 [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Occupancy Symmetry multiplicity x y z Uiso/equiv ADP type
Cu 0.5 8 0.25 0.25 0 0.062(6) Uiso
Au 0.5 8 0.25 0.25 0 0.062(6) 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 0.1 0
2 0 0.2 0
3 0 0.3 0
4 0 0.4 0
5 0 0.5 0

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

Modulation code Atom site label Displacement axis Wave vector code
Cuy1 Cu y 1
Cuy2 Cu y 2
Cuy3 Cu y 3
Cuy4 Cu y 4
Cuy5 Cu y 5
Auy1 Au y 1
Auy2 Au y 2
Auy3 Au y 3
Auy4 Au y 4
Auy5 Au y 5

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
Cuy1 -0.0088(14) 0
Cuy2 0.0011(17) 0
Cuy3 0.0040(16) 0
Cuy4 0.0027(15) 0
Cuy5 0.0006(12) 0
Auy1 -0.0088(14) 0
Auy2 0.0011(17) 0
Auy3 0.0040(16) 0
Auy4 0.0027(15) 0
Auy5 0.0006(12) 0

Definition of the occupation Fourier series: [ Help ]

Modulation code Atom site label Wave vector code
Cuo1 Cu 1
Cuo2 Cu 2
Cuo3 Cu 3
Cuo4 Cu 4
Cuo5 Cu 5
Auo1 Au 1
Auo2 Au 2
Auo3 Au 3
Auo4 Au 4
Auo5 Au 5

Occupation Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
Cuo1 0 0.62(2)
Cuo2 0 -0.03(1)
Cuo3 0 -0.23(2)
Cuo4 0 0.00(1)
Cuo5 0 0.09(1)
Auo1 0 -0.62(2)
Auo2 0 0.03(1)
Auo3 0 0.23(2)
Auo4 0 -0.00(1)
Auo5 0 -0.09(1)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
CuU1 Cu Uiso 1
CuU2 Cu Uiso 2
CuU3 Cu Uiso 3
CuU4 Cu Uiso 4
CuU5 Cu Uiso 5
AuU1 Au Uiso 1
AuU2 Au Uiso 2
AuU3 Au Uiso 3
AuU4 Au Uiso 4
AuU5 Au Uiso 5

ADP Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
CuU1 0 0.052(11)
CuU2 0 0.033(9)
CuU3 0 0.023(9)
CuU4 0 0.003(8)
CuU5 0 -0.007(5)
AuU1 0 0.052(11)
AuU2 0 0.033(9)
AuU3 0 0.023(9)
AuU4 0 0.003(8)
AuU5 0 -0.007(5)