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Lattice modulation of the ε-phase in a Cu-Sb alloy

Authors:

Motai, Kumi; Watanabe, Yousuke; Hashimoto, Shinya

Journal:

Acta Crystallographica Section B 49 655-661 (1993)

DOI:

https://doi.org/10.1107/S0108768193003192

B-IncStrDB ID: 3092EAOGpq Entry date: 2010-11-08 Last revision: 2024-01-02

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mod1014887632

Chemical data

Structural Formula Sum: Cu0.805 Sb0.195 [ Help ]

Crystallographic data and experimental details

a: 2.737(4) Å [ Help ]

b: 2.737(4) Å [ Help ]

c: 4.320(2) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 120 ° [ Help ]

Volume: 28.03(6) Å3 [ Help ]

Z: 2 [ 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 0.430(1) 0.430(1) 0
2 -0.430(1) 0.860(2) 0

Refinement details

Structural Information

Average Structure: [ Help ]

Atom site label Occupancy Symmetry multiplicity x y z Uiso/equiv ADP type
Cu 0.805 2 0.33333 0.66667 0.25 0.072(2) Uiso
Sb 0.195 2 0.33333 0.66667 0.25 0.072(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 0.430 0.430 0
2 -0.430 0.860 0
3 0.860 -0.430 0
4 0 1.290 0
5 1.290 0 0
6 -1.290 1.290 0

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

Modulation code Atom site label Displacement axis Wave vector code
Cux1 Cu x 1
Cux2 Cu x 2
Cux3 Cu x 3
Cux4 Cu x 4
Cux5 Cu x 5
Cux6 Cu x 6
Cuy1 Cu y 1
Cuy2 Cu y 2
Cuy3 Cu y 3
Cuy4 Cu y 4
Cuy5 Cu y 5
Cuy6 Cu y 6
Sbx1 Sb x 1
Sbx2 Sb x 2
Sbx3 Sb x 3
Sbx4 Sb x 4
Sbx5 Sb x 5
Sbx6 Sb x 6
Sby1 Sb y 1
Sby2 Sb y 2
Sby3 Sb y 3
Sby4 Sb y 4
Sby5 Sb y 5
Sby6 Sb y 6

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
Cux1 0.0036(9) 0.0062(5)
Cux2 0 -0.0124(10)
Cux3 0.0036(9) 0.0062(5)
Cux4 -0.0023(1) -0.0030(1)
Cux5 -0.0046(2) 0.0060(2)
Cux6 0.0023(1) -0.0030(1)
Cuy1 0.0036(9) -0.0062(3)
Cuy2 0.0036(9) -0.0062(3)
Cuy3 0 0.0124(10)
Cuy4 -0.0046(1) -0.0060(2)
Cuy5 -0.0023(1) 0.0030(1)
Cuy6 -0.0023(1) 0.0030(1)
Sbx1 0.0036(9) 0.0062(5)
Sbx2 0 -0.0124(10)
Sbx3 0.0036(9) 0.0062(5)
Sbx4 -0.0023(1) -0.0030(1)
Sbx5 -0.0046(2) 0.0060(2)
Sbx6 0.0023(1) -0.0030(1)
Sby1 0.0036(9) -0.0062(3)
Sby2 0.0036(9) -0.0062(3)
Sby3 0 0.0124(10)
Sby4 -0.0046(1) -0.0060(2)
Sby5 -0.0023(1) 0.0030(1)
Sby6 -0.0023(1) 0.0030(1)

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
Cuo6 Cu 6
Sbo1 Sb 1
Sbo2 Sb 2
Sbo3 Sb 3
Sbo4 Sb 4
Sbo5 Sb 5
Sbo6 Sb 6

Occupation Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
Cuo1 0 0.115(6)
Cuo2 0 0.115(6)
Cuo3 0 0.115(6)
Cuo4 0.013(2) -0.062(3)
Cuo5 -0.013(2) -0.062(3)
Cuo6 -0.013(2) -0.062(3)
Sbo1 0 -0.115(6)
Sbo2 0 -0.115(6)
Sbo3 0 -0.115(6)
Sbo4 -0.013(2) 0.062(3)
Sbo5 0.013(2) 0.062(3)
Sbo6 0.013(2) 0.062(3)

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
CuU6 Cu Uiso 6
SbU1 Sb Uiso 1
SbU2 Sb Uiso 2
SbU3 Sb Uiso 3
SbU4 Sb Uiso 4
SbU5 Sb Uiso 5
SbU6 Sb Uiso 6

ADP Fourier coefficients: [ Help ]

Modulation code Sine coefficient Cosine coefficient
CuU1 0 0.041(3)
CuU2 0 0.041(3)
CuU3 0 0.041(3)
CuU4 -0.009(2) 0.038(2)
CuU5 0.009(2) 0.038(2)
CuU6 0.009(2) 0.038(2)
SbU1 0 0.041(3)
SbU2 0 0.041(3)
SbU3 0 0.041(3)
SbU4 -0.009(2) 0.038(2)
SbU5 0.009(2) 0.038(2)
SbU6 0.009(2) 0.038(2)