Description of Ba1+xNixRh1-xO3 with x = 0.1170(5) in superspace: modulated composite versus modulated-layer structure

Authors:

Schonleber, Andreas; Zuniga, F. Javier; Perez-Mato, J. Manuel; Darriet, Jacques; zur Loye, Hans-Conrad

Journal:

Acta Crystallographica, Section B 62 197-204 (2006)

DOI:

https://doi.org/10.1107/S0108768105039212

B-IncStrDB ID: JSPb5ze4QFt Entry date: 2022-01-28 Last revision: 2022-01-28

modulated_composite

Chemical data


Structural Formula Sum: Ba1.117 Ni0.117 O3 Rh0.883 [ Help ]

Formula weight: 299.1 Da [ Help ]

Crystallographic data and experimental details


Crystal system: trigonal [ 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 -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 1/3+x1,2/3+x2,2/3+x3,x4
14 1/3-x2,2/3+x1-x2,2/3+x3,x4
15 1/3-x2,2/3-x1,2/3+x3,1/2+x4
16 1/3-x1+x2,2/3-x1,2/3+x3,x4
17 1/3+x1,2/3+x1-x2,2/3+x3,1/2+x4
18 1/3-x1+x2,2/3+x2,2/3+x3,1/2+x4
19 1/3-x1,2/3-x2,2/3-x3,-x4
20 1/3+x2,2/3-x1+x2,2/3-x3,-x4
21 1/3+x2,2/3+x1,2/3-x3,1/2-x4
22 1/3+x1-x2,2/3+x1,2/3-x3,-x4
23 1/3-x1,2/3-x1+x2,2/3-x3,1/2-x4
24 1/3+x1-x2,2/3-x2,2/3-x3,1/2-x4
25 2/3+x1,1/3+x2,1/3+x3,x4
26 2/3-x2,1/3+x1-x2,1/3+x3,x4
27 2/3-x2,1/3-x1,1/3+x3,1/2+x4
28 2/3-x1+x2,1/3-x1,1/3+x3,x4
29 2/3+x1,1/3+x1-x2,1/3+x3,1/2+x4
30 2/3-x1+x2,1/3+x2,1/3+x3,1/2+x4
31 2/3-x1,1/3-x2,1/3-x3,-x4
32 2/3+x2,1/3-x1+x2,1/3-x3,-x4
33 2/3+x2,1/3+x1,1/3-x3,1/2-x4
34 2/3+x1-x2,1/3+x1,1/3-x3,-x4
35 2/3-x1,1/3-x1+x2,1/3-x3,1/2-x4
36 2/3+x1-x2,1/3-x2,1/3-x3,1/2-x4

a: 10.0576(8) Å [ Help ]

b: 10.0576(8) Å [ Help ]

c: 2.5862(8) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 120 ° [ Help ]

Volume: 226.56(7) Å3 [ Help ]

Z: 3 [ Help ]

Modulation dimension: 1 [ Help ]

Number of subsystems: 2 [ Help ]

Subsystem code: 1 [ Help ]

Subsystem description: 1-st 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: 2-nd 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

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.00000 0.00000 0.5585(5)

μ: 19.776 mm-1 [ Help ]

Absorption correction type: none [ Help ]

Minimum transmission factor: 1.000 [ Help ]

Maximum transmission factor: 1.000 [ Help ]

Refinement details


Total nb. of reflections: 1955 [ Help ]

Nb. of observed reflections: 1127 [ Help ]

Intense reflections threshold: I>3σ(I) [ Help ]

Refinement based on: F [ Help ]

R(all): 0.0379 [ Help ]

R(obs): 0.0379 [ Help ]

wR(obs): 0.0481 [ Help ]

wR(all): 0.0481 [ Help ]

S(all): 1.26 [ Help ]

Nb. of reflections: 1127 [ Help ]

Nb. of parameters: 53 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(F)+0.000625F2) [ Help ]

Δ/σ(max): 0.0002 [ Help ]

Δ/σ(mean): 0.0001 [ Help ]

Δρ(max): 2.01 e_Å-3 [ Help ]

Δρ(min): -2.54 e_Å-3 [ Help ]

Extinction method: none [ Help ]

Structural Information


Average Structure: [ Help ]

Atom symbol Atom site label Subsystem x y z Uiso/equiv ADP type Coords from (d)iffraction or (c)alculated Coords restraints or constraints Occupancy Disordered cluster Disordered group
O O 1 0.1513(5) 0 0.5 0.039(3) Uani d . 1 . .
Rh Rh 1 0 0 0 0.0145(4) Uani d . 1 . .
Ni Ni 1 0 0 0 0.034(2) Uani d . 1 . .
Ba Ba1 2 0.6483(4) 0 0.25 0.0104(4) Uani d . 1 . .
Ba Ba2 2 0.6721(2) 0 0.25 0.0169(5) Uani d . 1 . .

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23 Atom site symbol
O 0.037(3) 0.064(6) 0.024(2) 0.032(3) 0.0070(15) 0.014(3) O
Rh 0.0066(2) 0.0066(2) 0.0304(10) 0.00331(12) 0 0 Rh
Ni 0.024(2) 0.024(2) 0.053(5) 0.0122(10) 0 0 Ni
Ba1 0.0072(4) 0.0081(5) 0.0160(9) 0.0041(3) -0.0005(2) -0.0010(4) Ba
Ba2 0.0111(9) 0.0186(5) 0.0236(7) 0.0093(3) 0.00620(14) 0.0124(3) Ba

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 0.55850
2 0.00000 0.00000 1.11700

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

Modulation code Atom site label Displacement axis Wave vector code
Ox1 O x 1
Oy1 O y 1
Oz1 O z 1
Ox2 O x 2
Oy2 O y 2
Oz2 O z 2
Rhx1 Rh x 1
Rhy1 Rh y 1
Rhz1 Rh z 1
Rhx2 Rh x 2
Rhy2 Rh y 2
Rhz2 Rh z 2
Ba2x1 Ba2 x 1
Ba2y1 Ba2 y 1
Ba2z1 Ba2 z 1

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Ox1 -0.0016(4) 0.0092(7)
Oy1 -0.0033(9) 0
Oz1 -0.012(2) 0
Ox2 0.0031(7) 0.0009(4)
Oy2 0 0.0017(8)
Oz2 0 0.0153(17)
Rhx1 0 0
Rhy1 0 0
Rhz1 0 0.0164(7)
Rhx2 0 0
Rhy2 0 0
Rhz2 0 -0.0221(8)
Ba2x1 0.0063(9) -0.00084(19)
Ba2y1 0 -0.0017(4)
Ba2z1 0 0.0005(5)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
OU111 O U11 1
OU221 O U22 1
OU331 O U33 1
OU121 O U12 1
OU131 O U13 1
OU231 O U23 1
OU112 O U11 2
OU222 O U22 2
OU332 O U33 2
OU122 O U12 2
OU132 O U13 2
OU232 O U23 2
RhU111 Rh U11 1
RhU221 Rh U22 1
RhU331 Rh U33 1
RhU121 Rh U12 1
RhU131 Rh U13 1
RhU231 Rh U23 1
RhU112 Rh U11 2
RhU222 Rh U22 2
RhU332 Rh U33 2
RhU122 Rh U12 2
RhU132 Rh U13 2
RhU232 Rh U23 2

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
OU111 0.008(3) -0.039(4)
OU221 0 -0.067(8)
OU331 0 -0.011(4)
OU121 0.008(3) -0.034(4)
OU131 0.013(2) -0.012(2)
OU231 0 -0.023(4)
OU112 -0.023(3) -0.009(3)
OU222 -0.032(5) 0
OU332 0.006(4) 0
OU122 -0.016(2) -0.009(3)
OU132 -0.0081(18) -0.0074(19)
OU232 -0.016(4) 0
RhU111 0.0021(5) 0
RhU221 0.0021(5) 0
RhU331 -0.0258(15) 0
RhU121 0.0010(3) 0
RhU131 0 0
RhU231 0 0
RhU112 -0.0037(7) 0
RhU222 -0.0037(7) 0
RhU332 0.0151(15) 0
RhU122 -0.0018(3) 0
RhU132 0 0
RhU232 0 0

Displacive sawtooth coefficients: [ Help ]

Atom site label Ax Ay Az Center (x0) Width
O 0 0 -0.1449 0.25 0.5
Rh 0 0 -0.1112 0 0.4415
Ni 0 0 -0.0175 0.25 0.0585

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
Ba1 0 0.1047
Ba2 0.5 0.2286

modulated_layer

Chemical data


Structural Formula Sum: Ba1 Ni0.105 O2.686 Rh0.791 [ Help ]

Formula weight: 267.9 Da [ Help ]

Crystallographic data and experimental details


Crystal system: trigonal [ Help ]

Superspace group name: X-3c1(00γ)000 [ 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,-x1,1/2+x3,x4
4 -x1+x2,-x1,x3,x4
5 x1,x1-x2,1/2+x3,x4
6 -x1+x2,x2,1/2+x3,x4
7 -x1,-x2,-x3,-x4
8 x2,-x1+x2,-x3,-x4
9 x2,x1,1/2-x3,-x4
10 x1-x2,x1,-x3,-x4
11 -x1,-x1+x2,1/2-x3,-x4
12 x1-x2,-x2,1/2-x3,-x4
13 1/3+x1,2/3+x2,x3,1/3+x4
14 1/3-x2,2/3+x1-x2,x3,1/3+x4
15 1/3-x2,2/3-x1,1/2+x3,1/3+x4
16 1/3-x1+x2,2/3-x1,x3,1/3+x4
17 1/3+x1,2/3+x1-x2,1/2+x3,1/3+x4
18 1/3-x1+x2,2/3+x2,1/2+x3,1/3+x4
19 1/3-x1,2/3-x2,-x3,1/3-x4
20 1/3+x2,2/3-x1+x2,-x3,1/3-x4
21 1/3+x2,2/3+x1,1/2-x3,1/3-x4
22 1/3+x1-x2,2/3+x1,-x3,1/3-x4
23 1/3-x1,2/3-x1+x2,1/2-x3,1/3-x4
24 1/3+x1-x2,2/3-x2,1/2-x3,1/3-x4
25 2/3+x1,1/3+x2,x3,2/3+x4
26 2/3-x2,1/3+x1-x2,x3,2/3+x4
27 2/3-x2,1/3-x1,1/2+x3,2/3+x4
28 2/3-x1+x2,1/3-x1,x3,2/3+x4
29 2/3+x1,1/3+x1-x2,1/2+x3,2/3+x4
30 2/3-x1+x2,1/3+x2,1/2+x3,2/3+x4
31 2/3-x1,1/3-x2,-x3,2/3-x4
32 2/3+x2,1/3-x1+x2,-x3,2/3-x4
33 2/3+x2,1/3+x1,1/2-x3,2/3-x4
34 2/3+x1-x2,1/3+x1,-x3,2/3-x4
35 2/3-x1,1/3-x1+x2,1/2-x3,2/3-x4
36 2/3+x1-x2,1/3-x2,1/2-x3,2/3-x4

a: 10.0576(8) Å [ Help ]

b: 10.0576(8) Å [ Help ]

c: 4.6306(7) Å [ Help ]

α: 90 ° [ Help ]

β: 90 ° [ Help ]

γ: 120 ° [ Help ]

Volume: 405.65(8) Å3 [ Help ]

Z: 6 [ Help ]

Modulation dimension: 1 [ Help ]

Measured independent wave vectors: [ Help ]

Wave vector id q_x q_y q_z
1 0.00000 0.00000 0.2095(7)

μ: 19.78 mm-1 [ Help ]

Absorption correction type: none [ Help ]

Minimum transmission factor: 1.000 [ Help ]

Maximum transmission factor: 1.000 [ Help ]

Refinement details


Total nb. of reflections: 2495 [ Help ]

Nb. of observed reflections: 1195 [ Help ]

Intense reflections threshold: I>3σ(I) [ Help ]

Refinement based on: F [ Help ]

R(all): 0.0382 [ Help ]

R(obs): 0.0382 [ Help ]

wR(obs): 0.0504 [ Help ]

wR(all): 0.0504 [ Help ]

S(all): 1.31 [ Help ]

Nb. of reflections: 1195 [ Help ]

Nb. of parameters: 53 [ Help ]

Weighting scheme: sigma [ Help ]

Weighting scheme remarks: w=1/(σ2(F)+0.000625F2) [ Help ]

Δ/σ(max): 0.0003 [ Help ]

Δ/σ(mean): 0.0001 [ Help ]

Δρ(max): 1.85 e_Å-3 [ Help ]

Δρ(min): -2.38 e_Å-3 [ Help ]

Extinction method: none [ Help ]

Structural Information


Average Structure: [ Help ]

Atom symbol Atom site label x y z Uiso/equiv ADP type Coords from (d)iffraction or (c)alculated Coords restraints or constraints Occupancy Disordered cluster Disordered group
O O 0.1521(5) 0 0.25 0.037(3) Uani d . 1 . .
Rh Rh 0 0 0 0.0166(4) Uani d . 1 . .
Ni Ni 0 0 0.25 0.032(4) Uani d . 1 . .
Ba Ba1 0.6467(8) 0 0.25 0.0083(6) Uani d . 1 . .
Ba Ba2 0.67341(18) 0 0.25 0.0171(8) Uani d . 1 . .

ADP components: [ Help ]

Atom site label U11 U22 U33 U12 U13 U23 Atom site symbol
O 0.032(2) 0.059(5) 0.028(3) 0.030(2) 0.0056(14) 0.011(3) O
Rh 0.0091(4) 0.0091(4) 0.0317(9) 0.0046(2) 0 0 Rh
Ni 0.002(4) 0.002(4) 0.091(10) 0.0010(18) 0 0 Ni
Ba1 0.0060(8) 0.0068(7) 0.0125(9) 0.0034(4) -0.0017(3) -0.0033(5) Ba
Ba2 0.0124(9) 0.0159(14) 0.0241(7) 0.0079(7) 0.00579(14) 0.0116(3) Ba

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 0.20950
2 0.00000 0.00000 0.41900

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

Modulation code Atom site label Displacement axis Wave vector code
Ox1 O x 1
Oy1 O y 1
Oz1 O z 1
Ox2 O x 2
Oy2 O y 2
Oz2 O z 2
Rhx1 Rh x 1
Rhy1 Rh y 1
Rhz1 Rh z 1
Rhx2 Rh x 2
Rhy2 Rh y 2
Rhz2 Rh z 2
Ba2x1 Ba2 x 1
Ba2y1 Ba2 y 1
Ba2z1 Ba2 z 1

Displacive (translational) Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
Ox1 0.0073(5) 0.0007(3)
Oy1 0 0.0014(5)
Oz1 0 0.0028(10)
Ox2 -0.0028(7) -0.0004(4)
Oy2 0 -0.0009(7)
Oz2 0 -0.0078(15)
Rhx1 0 0
Rhy1 0 0
Rhz1 0 0.0078(3)
Rhx2 0 0
Rhy2 0 0
Rhz2 0 -0.0154(7)
Ba2x1 -0.0031(8) 0.0010(4)
Ba2y1 0 0.0020(8)
Ba2z1 0 -0.0038(14)

Definition of the ADP Fourier series: [ Help ]

Modulation code Atom site label Tensor element Wave vector code
OU111 O U11 1
OU221 O U22 1
OU331 O U33 1
OU121 O U12 1
OU131 O U13 1
OU231 O U23 1
OU112 O U11 2
OU222 O U22 2
OU332 O U33 2
OU122 O U12 2
OU132 O U13 2
OU232 O U23 2
RhU111 Rh U11 1
RhU221 Rh U22 1
RhU331 Rh U33 1
RhU121 Rh U12 1
RhU131 Rh U13 1
RhU231 Rh U23 1
RhU112 Rh U11 2
RhU222 Rh U22 2
RhU332 Rh U33 2
RhU122 Rh U12 2
RhU132 Rh U13 2
RhU232 Rh U23 2

ADP Fourier coefficients: [ Help ]

Modulation code Cosine coefficient Sine coefficient
OU111 -0.027(3) -0.0018(15)
OU221 -0.053(5) 0
OU331 -0.018(4) 0
OU121 -0.027(3) -0.0018(15)
OU131 -0.0078(17) -0.0075(14)
OU231 -0.016(3) 0
OU112 0.018(2) 0.004(2)
OU222 0.031(4) 0
OU332 0.004(4) 0
OU122 0.015(2) 0.004(2)
OU132 0.0072(16) 0.0067(19)
OU232 0.014(3) 0
RhU111 -0.0027(6) 0
RhU221 -0.0027(6) 0
RhU331 -0.0262(12) 0
RhU121 -0.0014(3) 0
RhU131 0 0
RhU231 0 0
RhU112 0.0022(7) 0
RhU222 0.0022(7) 0
RhU332 0.0249(9) 0
RhU122 0.0011(4) 0
RhU132 0 0
RhU232 0 0

Displacive sawtooth coefficients: [ Help ]

Atom site label Ax Ay Az Center (x0) Width
O 0 0 0.1691 0 0.8953
Rh 0 0 0.1557 0 0.7905
Ni 0 0 0.0206 0.5 0.1047

Occupation crenel coefficients: [ Help ]

Atom site label Center (x0) Width
Ba1 0.5 0.1047
Ba2 0 0.2286