Incommensurate structure of a lillianite-type samarium chromium sulfide Sm2/3Cr2S4
Authors:Lafond, A.; Cario, L.; van der Lee, A.; Meerschaut, A.
Journal:Journal of solid state chemistry 127 295-301 (1996)
DOI:https://doi.org/10.1006/jssc.1996.0386
B-IncStrDB ID: 2892EPuYxe Entry date: 2010-11-08 Last revision: 2022-01-02
mod1013017260
Chemical data
Structural Formula Sum: Sm2/3 Cr2 S4 [ Help ]
Crystallographic data and experimental details
a: 3.503(3) Å [ Help ]
Z: 4 [ Help ]
b: 10.9199(8) Å [ Help ]
c: 12.7987(8) Å [ Help ]
γ: 90 ° [ Help ]
β: 90 ° [ Help ]
α: 90 ° [ Help ]
Modulation dimension: 2 [ Help ]
Crystal system: orthorhombic [ Help ]
Superspace group name (ITC): Pmnb(αβ0)gmg [ Help ]
Symmetry operations of the superspace group: (Show/hide table) [ Help ]
| Operation code | Operation in algebraic form |
|---|---|
| 1 | x1,x2,x3,x4,x5 |
| 2 | -x1,-x2,-x3,-x4,-x5 |
| 3 | x1+1/2,-x2,-x3,-x5+1/2,-x4+1/2 |
| 4 | -x1+1/2,x2+1/2,-x3+1/2,x5,x4 |
| 5 | -x1,-x2+1/2,x3+1/2,-x4+1/2,-x5+1/2 |
| 6 | -x1+1/2,x2,x3,x5+1/2,x4+1/2 |
| 7 | x1+1/2,-x2+1/2,x3+1/2,-x5,-x4 |
| 8 | x1,x2+1/2,-x3+1/2,x4+1/2,x5+1/2 |
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.3333(3) | 0.3217(10) | 0 |
| 2 | -0.3333(3) | 0.3217(10) | 0 |
Refinement details
Total nb. of reflections: 1706 [ Help ]
R(all): 0.063 [ Help ]
wR(all): 0.083 [ Help ]
Nb. of observed reflections: 916 [ Help ]
R(obs): 0.046 [ Help ]
wR(obs): 0.049 [ Help ]
Structural Information
Average Structure: (Show/hide table) [ Help ]
| Atom site label | Occupancy | Symmetry multiplicity | x | y | z | Uiso/equiv | ADP type |
|---|---|---|---|---|---|---|---|
| Sm | 0.33333 | ? | 0.3111(4) | 0.2357(6) | 0.32922(6) | 0.27(4) | Uiso |
| Cr1 | 1 | ? | 0.25 | 0.0544(2) | 0.11253(15) | 0.3(3) | Uiso |
| Cr2 | 1 | ? | 0.25 | 0.0849(2) | 0.59624(14) | 0.34(3) | Uiso |
| S1 | 1 | ? | 0.25 | 0.2996(3) | 0.6557(2) | 0.44(5) | Uiso |
| S2 | 1 | ? | 0.25 | 0.3815(3) | -0.0292(2) | 0.42(5) | Uiso |
| S3 | 1 | ? | 0.25 | 0.0892(3) | -0.0713(2) | 0.38(5) | Uiso |
| S4 | 1 | ? | 0.25 | -0.0329(3) | 0.2858(2) | 0.46(6) | Uiso |
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 | 0.3333 | 0.3217 | 0 |
| 2 | -0.3333 | 0.3217 | 0 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Smx1 | Sm | x | 1 |
| Smx2 | Sm | x | 2 |
| Smy1 | Sm | y | 1 |
| Smy2 | Sm | y | 2 |
| Smz1 | Sm | z | 1 |
| Smz2 | Sm | z | 2 |
| Cr1x1 | Cr1 | x | 1 |
| Cr1x2 | Cr1 | x | 2 |
| Cr1y1 | Cr1 | y | 1 |
| Cr1y2 | Cr1 | y | 2 |
| Cr1z1 | Cr1 | z | 1 |
| Cr1z2 | Cr1 | z | 2 |
| Cr2x1 | Cr2 | x | 1 |
| Cr2x2 | Cr2 | x | 2 |
| Cr2y1 | Cr2 | y | 1 |
| Cr2y2 | Cr2 | y | 2 |
| Cr2z1 | Cr2 | z | 1 |
| Cr2z2 | Cr2 | z | 2 |
| S1x1 | S1 | x | 1 |
| S1x2 | S1 | x | 2 |
| S1y1 | S1 | y | 1 |
| S1y2 | S1 | y | 2 |
| S1z1 | S1 | z | 1 |
| S1z2 | S1 | z | 2 |
| S2x1 | S2 | x | 1 |
| S2x2 | S2 | x | 2 |
| S2y1 | S2 | y | 1 |
| S2y2 | S2 | y | 2 |
| S2z1 | S2 | z | 1 |
| S2z2 | S2 | z | 2 |
| S3x1 | S3 | x | 1 |
| S3x2 | S3 | x | 2 |
| S3y1 | S3 | y | 1 |
| S3y2 | S3 | y | 2 |
| S3z1 | S3 | z | 1 |
| S3z2 | S3 | z | 2 |
| S4x1 | S4 | x | 1 |
| S4x2 | S4 | x | 2 |
| S4y1 | S4 | y | 1 |
| S4y2 | S4 | y | 2 |
| S4z1 | S4 | z | 1 |
| S4z2 | S4 | z | 2 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Sine coefficient | Cosine coefficient |
|---|---|---|
| Smx1 | -0.004(3) | -0.001(4) |
| Smx2 | -0.06(3) | -0.012(4) |
| Smy1 | -0.0004(5) | -0.0007(5) |
| Smy2 | 0.0009(5) | 0.0006(4) |
| Smz1 | 0.0034(6) | 0.0023(7) |
| Smz2 | -0.0022(6) | -0.0018(6) |
| Cr1x1 | 0.0011(9) | 0.0013(8) |
| Cr1x2 | 0.0011(9) | -0.0013(8) |
| Cr1y1 | -0.0005(3) | -0.0024(3) |
| Cr1y2 | 0.0005(3) | -0.0024(3) |
| Cr1z1 | 0.002(3) | -0.0012(3) |
| Cr1z2 | -0.002(3) | -0.0012(3) |
| Cr2x1 | -0.0014(9) | -0.0043(9) |
| Cr2x2 | -0.0014(9) | 0.0043(9) |
| Cr2y1 | 0.0006(3) | -0.0002(3) |
| Cr2y2 | -0.0006(3) | -0.0002(3) |
| Cr2z1 | 0.0006(3) | -0.0003(3) |
| Cr2z2 | -0.0006(3) | -0.0003(3) |
| S1x1 | 0.0002(12) | 0(1) |
| S1x2 | 0.0002(12) | 0(1) |
| S1y1 | -0.00007(4) | 0.0003(4) |
| S1y2 | 0.00007(4) | 0.0003(4) |
| S1z1 | -0.00008(4) | -0.0039(4) |
| S1z2 | 0.00008(4) | -0.0039(4) |
| S2x1 | -0.006(14) | 0.0015(14) |
| S2x2 | -0.006(14) | -0.0015(14) |
| S2y1 | 0.0001(4) | 0.00082(4) |
| S2y2 | -0.0001(4) | 0.00082(4) |
| S2z1 | 0.0019(4) | 0.0021(4) |
| S2z2 | -0.0019(4) | 0.0021(4) |
| S3x1 | 0.0018(13) | -0.0026(14) |
| S3x2 | 0.0018(13) | 0.0026(14) |
| S3y1 | -0.001(4) | 0.0015(4) |
| S3y2 | 0.001(4) | 0.0015(4) |
| S3z1 | -0.0006(4) | -0.0005(4) |
| S3z2 | 0.0006(4) | -0.0005(4) |
| S4x1 | 0.0011(14) | 0.0043(14) |
| S4x2 | 0.0011(14) | -0.0043(14) |
| S4y1 | 0.0001(4) | -0.0061(4) |
| S4y2 | -0.0001(4) | -0.0061(4) |
| S4z1 | -0.0003(4) | 0.00083(4) |
| S4z2 | 0.0003(4) | -0.00083(4) |
Definition of the occupation Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Wave vector code |
|---|---|---|
| Smo1 | Sm | 1 |
| Smo2 | Sm | 2 |
Occupation Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Sine coefficient | Cosine coefficient |
|---|---|---|
| Smo1 | 0.368(8) | 0.12(2) |
| Smo2 | 0.376(7) | -0.14(2) |