Structural study of three modulated phases in Rb2ZnBr4
Authors:Hogervorst, A.C.R.; Helmholdt, R.B.
Journal:Acta Cryst. B 44 120-128 (1988)
DOI:https://doi.org/10.1107/S0108768187011571
B-IncStrDB ID: 792EKtuGw Entry date: 2010-11-08 Last revision: 2021-12-30
RbZnBr-293
Chemical data
Structural Formula Sum: Br4 Rb2 Zn1 [ Help ]
Formula weight: 555.9 Da [ Help ]
Crystallographic data and experimental details
a: 13.330(3) Å [ Help ]
b: 7.656(2) Å [ Help ]
c: 9.707(2) Å [ Help ]
α: 90 ° [ Help ]
β: 90 ° [ Help ]
γ: 90 ° [ Help ]
Volume: 990.6(4) Å3 [ Help ]
Z: 4 [ Help ]
μ: 28.289 mm-1 [ Help ]
Cell measurement temperature: 293(2) K [ Help ]
Crystal system: orthorhombic [ Help ]
Superspace group name (ITC): P c m n (0 0 γ) s s -1 [ Help ]
Superspace group name: Pcmn(00γ)ss0 [ 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,x2,1/2+x3,1/2+x4 |
| 3 | x1,1/2-x2,x3,1/2+x4 |
| 4 | 1/2-x1,1/2-x2,1/2+x3,x4 |
| 5 | -x1,-x2,-x3,-x4 |
| 6 | 1/2+x1,-x2,1/2-x3,1/2-x4 |
| 7 | -x1,1/2+x2,-x3,1/2-x4 |
| 8 | 1/2+x1,1/2+x2,1/2-x3,-x4 |
Space group name (H-M): P c m n [ Help ]
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0 | 0 | 0.293 |
Refinement details
Modulation functions description: Displacive modulation:Fourier series. 1st-order harmonics. [ Help ]
Total nb. of reflections: 4166 [ Help ]
R(all): 0.08 [ Help ]
wR(all): 0.08 [ Help ]
Structural Information
Average Structure: (Show/hide table) [ Help ]
| Atom site label | Atom symbol | Symmetry multiplicity | Occupancy | x | y | z | Uiso/equiv | ADP type |
|---|---|---|---|---|---|---|---|---|
| Rb(1) | Rb | 4 | 1 | 0.3234(1) | 0.2500 | 0.5153(1) | 0.0438(4) | Uani |
| Rb(2) | Rb | 4 | 1 | 0.5968(1) | 0.2500 | 0.8730(1) | 0.0745(6) | Uani |
| Zn | Zn | 4 | 1 | 0.5777(1) | 0.2500 | 0.2746(1) | 0.0289(4) | Uani |
| Br(1) | Br | 4 | 1 | 0.5831(1) | 0.2500 | 0.5184(1) | 0.0665(7) | Uani |
| Br(2) | Br | 4 | 1 | 0.4126(1) | 0.2500 | 0.1802(1) | 0.0639(8) | Uani |
| Br(3) | Br | 8 | 1 | 0.6593(1) | 0.5012(1) | 0.1839(1) | 0.0664(5) | Uani |
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 | 0.293 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Rb(1)y1 | Rb(1) | y | 1 |
| Rb(2)y1 | Rb(2) | y | 1 |
| Zny1 | Zn | y | 1 |
| Br(1)y1 | Br(1) | y | 1 |
| Br(2)y1 | Br(2) | y | 1 |
| Br(3)x1 | Br(3) | x | 1 |
| Br(3)y1 | Br(3) | y | 1 |
| Br(3)z1 | Br(3) | z | 1 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Amplitude | Phase | Cosine coefficient | Sine coefficient |
|---|---|---|---|---|
| Rb(1)y1 | 0.0147(4) | -0.155(4) | -0.0011(5) | -0.0147(4) |
| Rb(2)y1 | 0.0143(5) | -0.527(5) | 0.0110(5) | 0.0091(5) |
| Zny1 | 0.0098(4) | -0.716(6) | -0.0030(4) | 0.0093(4) |
| Br(1)y1 | 0.0354(5) | -0.694(2) | -0.0060(6) | 0.0349(5) |
| Br(2)y1 | 0.0520(5) | -0.899(2) | -0.0516(5) | 0.0059(7) |
| Br(3)x1 | 0.0252(2) | -0.916(1) | -0.0252(2) | 0.0001(3) |
| Br(3)y1 | 0.0193(3) | -0.468(2) | 0.0183(3) | 0.0062(4) |
| Br(3)z1 | 0.0150(3) | -0.022(3) | -0.118(3) | -0.0092(3) |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| Rb(1) | Rb | 0.0354(6) | 0.0593(9) | 0.0367(6) | 0 | 0.0029(5) | 0 |
| Rb(2) | Rb | 0.1170(14) | 0.0696(11) | 0.0369(8) | 0 | -0.0055(8) | 0 |
| Zn | Zn | 0.0296(7) | 0.0279(7) | 0.0292(7) | 0 | -0.0004(5) | 0 |
| Br(1) | Br | 0.0602(9) | 0.1152(18) | 0.0240(6) | 0 | -0.0074(6) | 0 |
| Br(2) | Br | 0.0338(7) | 0.1165(22) | 0.0414(8) | 0 | -0.0121(6) | 0 |
| Br(3) | Br | 0.0982(11) | 0.0378(7) | 0.0631(8) | -0.0316(8) | 0.0250(9) | -0.0046(6) |