Refinement of incommensurate structures against diffraction data from a twinned crystal
Authors:van Smaalen, Sander; Petricek, Vaclav
Journal:Acta Crystallographica section A 48 610-618 (1992)
DOI:https://doi.org/10.1107/S0108767392001806
B-IncStrDB ID: 2722Eralt6 Entry date: 2010-11-08 Last revision: 2022-01-02
mod1008329837
Chemical data
Structural Formula Sum: (HoS)1.23 Nb S2 [ Help ]
Crystallographic data and experimental details
a: 3.312(1) Å [ Help ]
b: 5.661(1) Å [ Help ]
c: 22.250(14) Å [ Help ]
α: 90 ° [ Help ]
β: 93.01(3) ° [ Help ]
γ: 90 ° [ Help ]
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.614 | 0 | -0.203 |
Number of subsystems: 2 [ Help ]
Subsystem code: 1 [ Help ]
Subsystem description: 1st subsystem: NbS2 [ 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: HoS [ Help ]
W matrix:
| 0.0 | 0.0 | 0.0 | 1.0 |
| 0.0 | 1.0 | 0.0 | 0.0 |
| 0.0 | 0.0 | 1.0 | 0.0 |
| 1.0 | 0.0 | 0.0 | 0.0 |
Crystal system: monoclinic [ Help ]
Superspace group name: P:F2(α O γ)-1 [ Help ]
Symmetry operations of the superspace group: (Show/hide table) [ Help ]
| Operation code | Operation in algebraic form |
|---|---|
| 1 | x1,x2,x3,x4 |
| 2 | -x1,x2,-x3,-x4 |
| 3 | x1+1/2,x2+1/2,x3,x4 |
| 4 | -x1+1/2,x2+1/2,-x3,-x4 |
| 5 | x1+1/2,x2,x3+1/2,x4 |
| 6 | -x1+1/2,x2,-x3+1/2,-x4 |
| 7 | x1,x2+1/2,x3+1/2,x4 |
| 8 | -x1,x2+1/2,-x3+1/2,-x4 |
Refinement details
Nb. of observed reflections: 1250 [ Help ]
R(obs): 0.061 [ Help ]
Structural Information
Average Structure: (Show/hide table) [ Help ]
| Atom site label | Atom symbol | Subsystem | Occupancy | x | y | z | ADP type |
|---|---|---|---|---|---|---|---|
| Nb | Nb | 1 | 1 | 0 | -0.0716(5) | 0 | Uani |
| S1 | S | 1 | 1 | 0.0256(9) | 0.2639(6) | 0.07109(12) | Uani |
| Ho | Ho | 2 | 1 | -0.0030(3) | 0 | 0.17521(3) | Uani |
| S2 | S | 2 | 1 | 0.4993(13) | 0.0081(17) | 0.20114(14) | Uani |
ADP components: (Show/hide table) [ Help ]
| Atom site label | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|
| Nb | 0.0042(5) | -0.0018(4) | 0.0038(5) | 0 | 0.0000(2) | 0 |
| S1 | -0.0086(69) | 0.0011(11) | 0.0046(18) | 0.0032(13) | -0.001(3) | -0.0001(10) |
| Ho | 0.0227(4) | 0.0124(5) | 0.0092(4) | 0.0084(7) | -0.0007(5) | -0.0001(6) |
| S2 | 0.0171(24) | 0.0121(16) | 0.0030(11) | 0.0005(33) | -0.0065(20) | -0.0006(27) |
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 | 0.614 | 0 | -0.203 |
| 2 | 1.228 | 0 | -0.406 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Nbx1 | Nb | x | 1 |
| Nby1 | Nb | y | 1 |
| Nbz1 | Nb | z | 1 |
| Nbx2 | Nb | x | 2 |
| Nby2 | Nb | y | 2 |
| Nbz2 | Nb | z | 2 |
| S1x1 | S1 | x | 1 |
| S1y1 | S1 | y | 1 |
| S1z1 | S1 | z | 1 |
| Hox1 | Ho | x | 1 |
| Hoy1 | Ho | y | 1 |
| Hoz1 | Ho | z | 1 |
| Hox2 | Ho | x | 2 |
| Hoy2 | Ho | y | 2 |
| Hoz2 | Ho | z | 2 |
| S2x1 | S2 | x | 1 |
| S2y1 | S2 | y | 1 |
| S2z1 | S2 | z | 1 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Sine coefficient | Cosine coefficient |
|---|---|---|
| Nbx1 | -0.001(5) | 0 |
| Nby1 | 0 | -0.0061(8) |
| Nbz1 | -0.0001(5) | 0 |
| Nbx2 | -0.0065(21) | 0 |
| Nby2 | 0 | 0.0005(8) |
| Nbz2 | 0.0001(4) | 0 |
| S1x1 | 0.002(21) | 0.051(9) |
| S1y1 | -0.0025(25) | -0.0057(14) |
| S1z1 | 0.0028(8) | 0.0009(11) |
| Hox1 | -0.0035(13) | 0.0003(12) |
| Hoy1 | -0.0088(6) | -0.0201(6) |
| Hoz1 | -0.0006(2) | -0.0013(2) |
| Hox2 | -0.0049(6) | 0.0062(6) |
| Hoy2 | -0.0027(7) | 0.0002(8) |
| Hoz2 | -0.0018(2) | -0.0014(2) |
| S2x1 | 0.009(6) | 0.005(6) |
| S2y1 | 0.0023(30) | 0.009(3) |
| S2z1 | -0.0005(11) | 0.0006(9) |