Importance of true satellite reflections in the analysis of modulated, composite crystal structures. II. The structure of [M'2Cu2O3]7[CuO2]10, M'= Bi0.04Sr0.96
Authors:Jensen, Anette Frost; Petricek, Vaclav; Larsen, Finn Krebs; McCarron (III), Eugene M.
Journal:Acta Crystallographica, Section B 53 125-134 (1997)
DOI:https://doi.org/10.1107/S0108768196011664
B-IncStrDB ID: 2402Eam2pI Entry date: 2010-11-08 Last revision: 2023-05-04
comp1019632429
Chemical data
Structural Formula Sum: Bi0.08 Sr1.92 Cu24 O41 [ Help ]
Crystallographic data and experimental details
Number of subsystems: 2 [ Help ]
Modulation dimension: 1 [ Help ]
Subsystem code: 1 [ Help ]
Subsystem description: subsystem 1 [ 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: subsystem 2 [ 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 |
a: 11.4712(6) Å [ Help ]
b: 13.3765(13) Å [ Help ]
c: 2.7509(10) Å [ Help ]
α: 90 ° [ Help ]
β: 90 ° [ Help ]
γ: 90 ° [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0 | 0 | 0.6997(3) |
Crystal system: orthorhombic [ Help ]
Superspace group name (WJJ): Amma(0 0 1+γ)ss-1 [ Help ]
Symmetry operations of the superspace group: (Show/hide table) [ Help ]
| Operation code | Operation in algebraic form |
|---|---|
| 1 | x1,x2,x3,x4 |
| 2 | 1/2-x1,x2,x3,1/2+x4 |
| 3 | x1,-x2,x3,1/2+x4 |
| 4 | 1/2+x1,x2,-x3,-x4 |
| 5 | -x1,-x2,-x3,-x4 |
| 6 | 1/2+x1,-x2,-x3,1/2-x4 |
| 7 | -x1,x2,-x3,1/2-x4 |
| 8 | 1/2-x1,-x2,x3,x4 |
| 9 | x1,1/2+x2,1/2+x3,1/2+x4 |
| 10 | 1/2-x1,1/2+x2,1/2+x3,x4 |
| 11 | x1,1/2-x2,1/2+x3,x4 |
| 12 | 1/2+x1,1/2+x2,1/2-x3,1/2-x4 |
| 13 | -x1,1/2-x2,1/2-x3,1/2-x4 |
| 14 | 1/2+x1,1/2-x2,1/2-x3,-x4 |
| 15 | -x1,1/2+x2,1/2-x3,-x4 |
| 16 | 1/2-x1,1/2-x2,1/2+x3,1/2+x4 |
Refinement details
Refinement remarks: WARNING: The published displacement parameters have been converted to relative units. The calculated standard uncertainties (s.u.) have been based uniquely on the published ones given the negligible contribution of cell parameters uncertainties. [ Help ]
Structural Information
Average Structure: (Show/hide table) [ Help ]
| Site description | Atom site label | Atom symbol | Subsystem | Symmetry multiplicity | Occupancy | x | y | z | Uiso/equiv | ADP type |
|---|---|---|---|---|---|---|---|---|---|---|
| . | Cu3 | Cu | 1 | 4 | 1 | 0.25 | 0.5 | 0.4118(3) | ? | Uani |
| . | O3 | O | 1 | 8 | 1 | 0.138(2) | 0.5 | 0.9115(11) | ? | Uani |
| . | Cu1 | Cu | 2 | 8 | 1 | 0.3345(13) | 0.25 | 0.751(8) | ? | Uani |
| . | O1 | O | 2 | 8 | 1 | 0.1694(9) | 0.25 | 0.747(6) | ? | Uani |
| . | O2 | O | 2 | 4 | 1 | 0.5 | 0.25 | 0.75 | ? | Uani |
| Sr atom at M site | Sr | Sr | 2 | 8 | 0.956(6) | 0.5 | 0.37938(7) | 0.25 | ? | Uani |
| Bi atom at M site | Bi | Bi | 2 | 8 | 0.044(6) | 0.5 | 0.37938(7) | 0.25 | ? | Uani |
ADP components: (Show/hide table) [ Help ]
| Atom site label | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|
| Cu3 | 0.0034(3) | 0.0147(5) | 0.0379(4) | 0 | 0 | 0 |
| O3 | 0.0055(10) | 0.0230(14) | 0.0403(14) | 0 | 0 | -0.0001(7) |
| Cu1 | 0.0012(7) | 0.0104(8) | 0.0025(9) | 0 | 0.0013(10) | 0 |
| O1 | 0.002(5) | 0.020(6) | 0.0026(0) | 0 | 0.0(0) | 0 |
| O2 | 0.002(4) | 0.015(3) | 0.002(4) | 0 | 0.000(3) | 0 |
| Sr | 0.0049(4) | 0.0058(5) | 0.0072(5) | 0 | 0.0004(3) | 0 |
| Bi | 0.0049(4) | 0.0058(5) | 0.0072(5) | 0 | 0.0004(3) | 0 |
Fourier Wave Vectors (explicit: q_x,q_y,q_z or coefficients: q_1,q_2,...): (Show/hide table) [ Help ]
| Wave vector code | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0 | 0 | 0.6997 |
| 2 | 0 | 0 | 1.3994 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Cu3z2 | Cu3 | z | 2 |
| O3x2 | O3 | x | 2 |
| O3y1 | O3 | y | 1 |
| O3z2 | O3 | z | 2 |
| Cu1x2 | Cu1 | x | 2 |
| Cu1y1 | Cu1 | y | 1 |
| Cu1z2 | Cu1 | z | 2 |
| O1x2 | O1 | x | 2 |
| O1y1 | O1 | y | 1 |
| O1z2 | O1 | z | 2 |
| O2x2 | O2 | x | 2 |
| O2y1 | O2 | y | 1 |
| O2z2 | O2 | z | 2 |
| Srx1 | Sr | x | 1 |
| Srx2 | Sr | x | 2 |
| Sry1 | Sr | y | 1 |
| Sry2 | Sr | y | 2 |
| Srz1 | Sr | z | 1 |
| Srz2 | Sr | z | 2 |
| Bix1 | Bi | x | 1 |
| Bix2 | Bi | x | 2 |
| Biy1 | Bi | y | 1 |
| Biy2 | Bi | y | 2 |
| Biz1 | Bi | z | 1 |
| Biz2 | Bi | z | 2 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Sine coefficient | Cosine coefficient |
|---|---|---|
| Cu3z2 | -0.0050(5) | -0.0013(5) |
| O3x2 | 0.0005(3) | 0.0013(2) |
| O3y1 | -0.0182(3) | 0.0010(2) |
| O3z2 | -0.0098(19) | 0.009(2) |
| Cu1x2 | 0.00086(3) | 0.00055(4) |
| Cu1y1 | -0.00174(4) | -0.00411(5) |
| Cu1z2 | -0.0007(1) | -0.0003(2) |
| O1x2 | 0.0006(3) | 0.0005(3) |
| O1y1 | -0.0025(3) | 0.0024(3) |
| O1z2 | 0.0003(8) | 0.000(1) |
| O2x2 | 0.0006(3) | 0 |
| O2y1 | 0 | -0.0115(5) |
| O2z2 | -0.002(1) | 0 |
| Srx1 | -0.00138(3) | 0 |
| Srx2 | -0.00121(3) | 0 |
| Sry1 | 0 | -0.00236(3) |
| Sry2 | 0 | 0.00037(3) |
| Srz1 | 0.0276(2) | 0 |
| Srz2 | 0.0052(1) | 0 |
| Bix1 | -0.00138(3) | 0 |
| Bix2 | -0.00121(3) | 0 |
| Biy1 | 0 | -0.00236(3) |
| Biy2 | 0 | 0.00037(3) |
| Biz1 | 0.0276(2) | 0 |
| Biz2 | 0.0052(1) | 0 |
Definition of the ADP Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Tensor element | Wave vector code |
|---|---|---|---|
| SrU111 | Sr | U11 | 1 |
| SrU112 | Sr | U11 | 2 |
| SrU221 | Sr | U22 | 1 |
| SrU222 | Sr | U22 | 2 |
| SrU331 | Sr | U33 | 1 |
| SrU332 | Sr | U33 | 2 |
| SrU121 | Sr | U12 | 1 |
| SrU122 | Sr | U12 | 2 |
| SrU131 | Sr | U13 | 1 |
| SrU132 | Sr | U13 | 2 |
| SrU231 | Sr | U23 | 1 |
| SrU232 | Sr | U23 | 2 |
ADP Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Sine coefficient | Cosine coefficient |
|---|---|---|
| SrU111 | 0 | 0.00052(10) |
| SrU112 | 0 | 0.00037(13) |
| SrU221 | 0 | -0.00005(15) |
| SrU222 | 0 | 0.00006(17) |
| SrU331 | 0 | 0.0047(2) |
| SrU332 | 0 | 0.0023(2) |
| SrU121 | 0.00044(9) | 0 |
| SrU122 | 0.00010(13) | 0 |
| SrU131 | 0 | -0.00106(13) |
| SrU132 | 0 | -0.00033(11) |
| SrU231 | 0.0(0) | 0 |
| SrU232 | 0.00028(13) | 0 |