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Structure Determination of Two New Incommensurate Compounds, Ba1+x[(CuxRh1-x)O3] with x=0.1605 and x=0.1695, Using a General Method Based on the Superspace Group Approach

Authors:

Zakhour-Nakhl, Mirvat; Claridge, John B.; Darriet, J.; Weill, Francois; zur Loye, Hans-Conrad; Perez-Mato, Juan Manuel

Journal:

Journal of the American Chemical Society 122 1618-1623 (2000)

DOI:

https://doi.org/10.1021/ja993532s

B-IncStrDB ID: T5EtoleW2oq Entry date: 2021-12-10 Last revision: 2022-01-06

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Ba1_1605Cu0_1605Rh0_8395O3_Crystal_1

Chemical data

Structural Formula Sum: Ba1.1605 Cu0.1605 Rh0.8398 O3 [ Help ]

Formula weight: 303.97 Da [ Help ]

Crystallographic data and experimental details

a: 10.081 Å [ Help ]

b: 10.081 Å [ Help ]

c: 2.6206 Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 120 ° [ Help ]

Volume: 230.642 Å3 [ Help ]

Radiation used for cell measurement: Mo kα [ Help ]

Cell determination reflection Nb.: 25 [ Help ]

Cell measurement temperature: 293 K [ Help ]

θ(max) for cell determination: 15 ° [ Help ]

θ(min) for cell determination: 30 ° [ Help ]

λ for cell measurement: 0.71073 Å [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.00000 0.00000 0.58027

Number of subsystems: 2 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1st 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: 2nd 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

Z: 3 [ Help ]

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 -x2,-x1,x3,1/2+x4
4 -x1+x2,-x1,x3,x4
5 x1,x1-x2,x3,1/2+x4
6 -x1+x2,x2,x3,1/2+x4
7 -x1,-x2,-x3,-x4
8 x2,-x1+x2,-x3,-x4
9 x2,x1,-x3,1/2-x4
10 x1-x2,x1,-x3,-x4
11 -x1,-x1+x2,-x3,1/2-x4
12 x1-x2,-x2,-x3,1/2-x4
13 2/3+x1,1/3+x2,1/3+x3,x4
14 2/3-x2,1/3+x1-x2,1/3+x3,x4
15 2/3-x2,1/3-x1,1/3+x3,1/2+x4
16 2/3-x1+x2,1/3-x1,1/3+x3,x4
17 2/3+x1,1/3+x1-x2,1/3+x3,1/2+x4
18 2/3-x1+x2,1/3+x2,1/3+x3,1/2+x4
19 2/3-x1,1/3-x2,1/3-x3,-x4
20 2/3+x2,1/3-x1+x2,1/3-x3,-x4
21 2/3+x2,1/3+x1,1/3-x3,1/2-x4
22 2/3+x1-x2,1/3+x1,1/3-x3,-x4
23 2/3-x1,1/3-x1+x2,1/3-x3,1/2-x4
24 2/3+x1-x2,1/3-x2,1/3-x3,1/2-x4
25 1/3+x1,2/3+x2,2/3+x3,x4
26 1/3-x2,2/3+x1-x2,2/3+x3,x4
27 1/3-x2,2/3-x1,2/3+x3,1/2+x4
28 1/3-x1+x2,2/3-x1,2/3+x3,x4
29 1/3+x1,2/3+x1-x2,2/3+x3,1/2+x4
30 1/3-x1+x2,2/3+x2,2/3+x3,1/2+x4
31 1/3-x1,2/3-x2,2/3-x3,-x4
32 1/3+x2,2/3-x1+x2,2/3-x3,-x4
33 1/3+x2,2/3+x1,2/3-x3,1/2-x4
34 1/3+x1-x2,2/3+x1,2/3-x3,-x4
35 1/3-x1,2/3-x1+x2,2/3-x3,1/2-x4
36 1/3+x1-x2,2/3-x2,2/3-x3,1/2-x4

Absorption correction type: analytical [ Help ]

Minimum transmission factor: 0.64 [ Help ]

Maximum transmission factor: 0.87 [ Help ]

μ: 20.144 mm-1 [ Help ]

Refinement details

h(min): -13 [ Help ]

h(max): 10 [ Help ]

k(min): -12 [ Help ]

k(max): 16 [ Help ]

l(min): 0 [ Help ]

l(max): 4 [ Help ]

m1(min): -6 [ Help ]

m1(max): 7 [ Help ]

Intense reflections threshold: 3σ [ Help ]

Total nb. of reflections: 864 [ Help ]

Nb. of observed reflections: 864 [ Help ]

Refinement based on: F [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]

R(obs): 0.0370 [ Help ]

wR(obs): 0.0487 [ Help ]

R(all): 0.0370 [ Help ]

wR(all): 0.0487 [ Help ]

Nb. of reflections: 864 [ Help ]

Nb. of parameters: 39 [ Help ]

S(all): 2.91 [ Help ]

S(obs): 2.91 [ Help ]

Δ/σ(max): 0.0052 [ Help ]

Δ/σ(mean): 0.0008 [ Help ]

Δρ(max): 4.31 e_Å-3 [ Help ]

Δρ(min): -3.53 e_Å-3 [ Help ]

Extinction method: B-C type 1 Gaussian isotropic [ Help ]

Extinction coefficient: 0.037(2) [ Help ]

Refinement remarks: WARNING: Dubious CIF. Check the structural parameters against the publication. Atomic occupancies are unrealiable. [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol Subsystem Symmetry multiplicity Occupancy x y z Uiso/equiv
Rh1 Rh 1 6 1 0 0 0 0.0092(1)
Cu1 Cu 1 6 1 0 0 0 0.040(2)
O O 1 18 1 0.1517(3) 0.1517(3) 0.5 0.025(1)
Ba1 Ba 2 18 1 0.32667(7) 0 0.25 0.0180(2)
Ba2 Ba 2 18 1 0.35205(9) 0 0.25 0.0067(2)

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23
Rh1 0.0074(1) 0.0074(1) 0.0126(2) 0.00371(6) 0 0
Cu1 0.033(1) 0.033(1) 0.054(4) 0.0163(7) 0 0
O 0.021(1) 0.021(1) 0.022(2) 0.002(1) -0.0017(8) 0.0017(8)
Ba1 0.0153(3) 0.0239(4) 0.0176(2) 0.0120(2) 0.0052(1) 0.0105(2)
Ba2 0.0082(2) 0.0071(3) 0.0044(2) 0.0036(2) -0.0014(1) -0.0028(2)

Displacive sawtooth coefficients: [ Help ]

Atom site label Ax Ay Az Center (x0) Width
Rh1 0 0 -0.0910 0 0.4197
Cu1 0 0 -0.0968 0.25 0.0802
O 0 0 -0.1497 0.25 0.5
Ba1 0 0 -0.0301 0.5 0.1950
Ba2 0 0 -0.0367 0 0.1383

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 0.00000 0.00000 0.58027
2 0.00000 0.00000 1.16054

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

Modulation code Atom site label Displacement axis Wave vector code
Rh1x1 Rh1 x 1
Rh1y1 Rh1 y 1
Rh1z1 Rh1 z 1
Rh1x2 Rh1 x 2
Rh1y2 Rh1 y 2
Rh1z2 Rh1 z 2
Ox1 O x 1
Oy1 O y 1
Oz1 O z 1
Ox2 O x 2
Oy2 O y 2
Oz2 O z 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Rh1x1 0 0
Rh1y1 0 0
Rh1z1 0 -0.0061(3)
Rh1x2 0 0
Rh1y2 0 0
Rh1z2 0 0.0160(4)
Ox1 0.0000(2) -0.0089(4)
Oy1 0.0000(2) -0.0089(4)
Oz1 -0.023(2) 0
Ox2 0.0047(6) 0.0015(3)
Oy2 0.0047(6) -0.0015(3)
Oz2 0 -0.013(2)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Rh1U11 Rh1 U11 1
Rh1U22 Rh1 U22 1
Rh1U33 Rh1 U33 1
Rh1U12 Rh1 U12 1
Rh1U13 Rh1 U13 1
Rh1U23 Rh1 U23 1
OU11 O U11 1
OU22 O U22 1
OU33 O U33 1
OU12 O U12 1
OU13 O U13 1
OU23 O U23 1

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Rh1U11 -0.0001(2) 0
Rh1U22 -0.0001(2) 0
Rh1U33 -0.0060(3) 0
Rh1U12 -0.00003(9) 0
Rh1U13 0 0
Rh1U23 0 0
OU11 -0.003(1) 0.013(1)
OU22 0.003(1) 0.013(1)
OU33 0 0.015(2)
OU12 0 0.002(2)
OU13 0.009(1) -0.002(1)
OU23 0.009(1) 0.002(1)

Ba1_1695CU0_1695RH0_8305O3_crystal_2

Chemical data

Structural Formula Sum: Ba1.169 Cu0.169 Rh0.831 O3 [ Help ]

Formula weight: 304.8 Da [ Help ]

Crystallographic data and experimental details

a: 10.081 Å [ Help ]

b: 10.081 Å [ Help ]

c: 2.6245 Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 120 ° [ Help ]

Volume: 230.985 Å3 [ Help ]

Radiation used for cell measurement: Mo kα [ Help ]

Cell determination reflection Nb.: 25 [ Help ]

Cell measurement temperature: 293 K [ Help ]

θ(max) for cell determination: 30 ° [ Help ]

θ(min) for cell determination: 15 ° [ Help ]

λ for cell measurement: 0.71073 Å [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.00000 0.00000 0.58476

Number of subsystems: 2 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1st 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: 2nd 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

Z: 3 [ Help ]

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 -x2,-x1,x3,1/2+x4
4 -x1+x2,-x1,x3,x4
5 x1,x1-x2,x3,1/2+x4
6 -x1+x2,x2,x3,1/2+x4
7 -x1,-x2,-x3,-x4
8 x2,-x1+x2,-x3,-x4
9 x2,x1,-x3,1/2-x4
10 x1-x2,x1,-x3,-x4
11 -x1,-x1+x2,-x3,1/2-x4
12 x1-x2,-x2,-x3,1/2-x4
13 2/3+x1,1/3+x2,1/3+x3,x4
14 2/3-x2,1/3+x1-x2,1/3+x3,x4
15 2/3-x2,1/3-x1,1/3+x3,1/2+x4
16 2/3-x1+x2,1/3-x1,1/3+x3,x4
17 2/3+x1,1/3+x1-x2,1/3+x3,1/2+x4
18 2/3-x1+x2,1/3+x2,1/3+x3,1/2+x4
19 2/3-x1,1/3-x2,1/3-x3,-x4
20 2/3+x2,1/3-x1+x2,1/3-x3,-x4
21 2/3+x2,1/3+x1,1/3-x3,1/2-x4
22 2/3+x1-x2,1/3+x1,1/3-x3,-x4
23 2/3-x1,1/3-x1+x2,1/3-x3,1/2-x4
24 2/3+x1-x2,1/3-x2,1/3-x3,1/2-x4
25 1/3+x1,2/3+x2,2/3+x3,x4
26 1/3-x2,2/3+x1-x2,2/3+x3,x4
27 1/3-x2,2/3-x1,2/3+x3,1/2+x4
28 1/3-x1+x2,2/3-x1,2/3+x3,x4
29 1/3+x1,2/3+x1-x2,2/3+x3,1/2+x4
30 1/3-x1+x2,2/3+x2,2/3+x3,1/2+x4
31 1/3-x1,2/3-x2,2/3-x3,-x4
32 1/3+x2,2/3-x1+x2,2/3-x3,-x4
33 1/3+x2,2/3+x1,2/3-x3,1/2-x4
34 1/3+x1-x2,2/3+x1,2/3-x3,-x4
35 1/3-x1,2/3-x1+x2,2/3-x3,1/2-x4
36 1/3+x1-x2,2/3-x2,2/3-x3,1/2-x4

Absorption correction type: psi-scan [ Help ]

Minimum transmission factor: 1.000 [ Help ]

Maximum transmission factor: 1.000 [ Help ]

μ: 20.221 mm-1 [ Help ]

Refinement details

h(min): -15 [ Help ]

h(max): 7 [ Help ]

k(min): -9 [ Help ]

k(max): 18 [ Help ]

l(min): 0 [ Help ]

l(max): 4 [ Help ]

m1(min): -7 [ Help ]

m1(max): 8 [ Help ]

Intense reflections threshold: 5 [ Help ]

Total nb. of reflections: 1176 [ Help ]

Nb. of observed reflections: 1176 [ Help ]

Refinement based on: F [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(F)+0.0001F2) [ Help ]

R(obs): 0.0330 [ Help ]

wR(obs): 0.0502 [ Help ]

R(all): 0.0330 [ Help ]

wR(all): 0.0502 [ Help ]

Nb. of reflections: 1176 [ Help ]

Nb. of parameters: 39 [ Help ]

S(all): 2.67 [ Help ]

S(obs): 2.67 [ Help ]

Δ/σ(max): 0.0217 [ Help ]

Δ/σ(mean): 0.0057 [ Help ]

Δρ(max): 6.24 e_Å-3 [ Help ]

Δρ(min): -6.39 e_Å-3 [ Help ]

Extinction method: B-C type 1 Gaussian isotropic [ Help ]

Extinction coefficient: 0.025(2) [ Help ]

Refinement remarks: WARNING: Dubious CIF. Check the structural parameters against the publication. Atomic occupancies are unrealiable. [ Help ]

Structural Information

Average Structure: [ Help ]

Atom site label Atom symbol Subsystem Symmetry multiplicity Occupancy x y z Uiso/equiv
Rh1 Rh 1 6 1 0 0 0 0.00787(8)
Cu1 Cu 1 6 1 0 0 0 0.0150(8)
Cu2 Cu 1 6 1 0.0490(6) 0.0490(6) 0 0.0150(8)
O O 1 18 1 0.1534(2) 0.1534(2) 0.5 0.0262(8)
Ba1 Ba 2 18 1 0.32717(5) 0 0.25 0.0175(1)
Ba2 Ba 2 18 1 0.35305(6) 0 0.25 0.0080(1)

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23
Rh1 0.00584(9) 0.00584(9) 0.0119(1) 0.00292(4) 0 0
Cu1 0.0023(7) 0.0023(7) 0.040(2) 0.0011(4) 0 0
Cu2 0.0023(7) 0.0023(7) 0.040(2) 0.0011(4) 0 0
O 0.0216(8) 0.0216(8) 0.027(1) 0.004(1) -0.0027(7) 0.0027(7)
Ba1 0.0132(2) 0.0198(2) 0.0218(2) 0.0099(1) 0.00632(9) 0.0126(2)
Ba2 0.0067(1) 0.0051(2) 0.0117(2) 0.00256(9) -0.00146(8) -0.0029(2)

Displacive sawtooth coefficients: [ Help ]

Atom site label Ax Ay Az Center (x0) Width
Rh1 0 0 -0.0910 0 0.4152
Cu1 0 0 -0.0681 0.25 0.0847
Cu2 0 0 -0.0681 0.25 0.0847
O 0 0 -0.1346 0.25 0.5
Ba1 0 0 -0.0260 0.5 0.1883
Ba2 0 0 -0.0206 0 0.1449

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 0.00000 0.00000 0.58476
2 0.00000 0.00000 1.16952

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

Modulation code Atom site label Displacement axis Wave vector code
Rh1x1 Rh1 x 1
Rh1y1 Rh1 y 1
Rh1z1 Rh1 z 1
Rh1x2 Rh1 x 2
Rh1y2 Rh1 y 2
Rh1z2 Rh1 z 2
Ox1 O x 1
Oy1 O y 1
Oz1 O z 1
Ox2 O x 2
Oy2 O y 2
Oz2 O z 2

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Rh1x1 0 0
Rh1y1 0 0
Rh1z1 0 -0.0059(2)
Rh1x2 0 0
Rh1y2 0 0
Rh1z2 0 0.0170(3)
Ox1 -0.0009(2) -0.0051(5)
Oy1 0.0009(2) -0.0051(5)
Oz1 -0.010(2) 0
Ox2 0.0011(5) 0.0009(2)
Oy2 0.0011(5) -0.0009(2)
Oz2 0 -0.010(1)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
Rh1U11 Rh1 U11 1
Rh1U22 Rh1 U22 1
Rh1U33 Rh1 U33 1
Rh1U12 Rh1 U12 1
Rh1U13 Rh1 U13 1
Rh1U23 Rh1 U23 1
OU11 O U11 1
OU22 O U22 1
OU33 O U33 1
OU12 O U12 1
OU13 O U13 1
OU23 O U23 1

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Rh1U11 -0.0011(1) 0
Rh1U22 -0.0011(1) 0
Rh1U33 -0.0032(2) 0
Rh1U12 -0.00056(5) 0
Rh1U13 0 0
Rh1U23 0 0
OU11 -0.0023(9) 0.015(1)
OU22 0.0023(9) 0.015(1)
OU33 0 0.017(2)
OU12 0 0.004(1)
OU13 0.0092(8) -0.0025(9)
OU23 0.0092(8) 0.0025(9)