Structural study of the incommensurately and lock-in phases of Rb2ZnCl4
Authors:Hedoux, A.; Grebille, D.; Jaud, J.; Godefroy, G.
Journal:Acta Cryst. B 45 370-378 (1989)
DOI:https://doi.org/10.1107/S0108768189004787
B-IncStrDB ID: 832Ea3uix Entry date: 2010-11-08 Last revision: 2021-12-30
RbZnClL
Chemical data
Structural Formula Sum: Cl4 Rb2 Zn1 [ Help ]
Formula weight: 378.1 Da [ Help ]
Crystallographic data and experimental details
a: 7.230(5) Å [ Help ]
b: 12.608(9) Å [ Help ]
c: 9.199(7) Å [ Help ]
α: 90 ° [ Help ]
β: 90 ° [ Help ]
γ: 90 ° [ Help ]
Volume: 838.5(10) Å3 [ Help ]
Z: 4 [ Help ]
μ: 15.633 mm-1 [ Help ]
Cell measurement temperature: 115 K [ Help ]
Crystal system: orthorhombic [ Help ]
Superspace group name (WJJ): P:P 21 c n:-1 s -1 [ Help ]
Superspace group name: P21cn(00γ)0s0 [ Help ]
Symmetry operations of the superspace group: (Show/hide table) [ Help ]
| Operation code | Operation in algebraic form |
|---|---|
| 1 | x1,x2,x3,x4 |
| 2 | x1,1/2-x2,1/2+x3,1/2+x4 |
| 3 | 1/2+x1,1/2+x2,1/2-x3,-x4 |
| 4 | 1/2+x1,-x2,-x3,1/2-x4 |
Space group name (H-M): P 21 c 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 | 0.333333 |
Refinement details
Refinement remarks: Commensurate structure refined within the superspace formalism. Global phase unknown. [ Help ]
Modulation functions description: Displacive modulation:Fourier series. 1st-order harmonics. [ Help ]
Structure factors calc. details: Gaussian integration [ Help ]
Nb. of observed reflections: 2280 [ Help ]
wR(obs): 0.0587 [ Help ]
Structural Information
Average Structure: (Show/hide table) [ Help ]
| Atom site label | Atom symbol | Symmetry multiplicity | Occupancy | x | y | z | Uiso/equiv | ADP type |
|---|---|---|---|---|---|---|---|---|
| Rb1 | Rb | 4 | 1 | 0.2494 | 0.4059(1) | 0.6289(1) | 0.0289(11) | Uani |
| Rb2 | Rb | 4 | 1 | 0.2424(7) | 0.8191(1) | 0.4876(1) | 0.0153(8) | Uani |
| Zn | Zn | 4 | 1 | 0.2446(8) | 0.4216(1) | 0.2228(1) | 0.0779(9) | Uani |
| Cl1 | Cl | 4 | 1 | 0.2407(12) | 0.4206(2) | -0.0194(2) | 0.0220(21) | Uani |
| Cl2 | Cl | 4 | 1 | 0.2440(9) | 0.5841(2) | 0.3232(2) | 0.0169(20) | Uani |
| Cl3 | Cl | 4 | 1 | -0.0060(9) | 0.3407(5) | 0.3102(6) | 0.0215(23) | Uani |
| Cl4 | Cl | 4 | 1 | 0.4909(9) | 0.3362(4) | 0.3125(6) | 0.0204(23) | 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 | 0.333333 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Rb1x1 | Rb1 | x | 1 |
| Rb1y1 | Rb1 | y | 1 |
| Rb1z1 | Rb1 | z | 1 |
| Rb2x1 | Rb2 | x | 1 |
| Rb2y1 | Rb2 | y | 1 |
| Rb2z1 | Rb2 | z | 1 |
| Znx1 | Zn | x | 1 |
| Zny1 | Zn | y | 1 |
| Znz1 | Zn | z | 1 |
| Cl1x1 | Cl1 | x | 1 |
| Cl1y1 | Cl1 | y | 1 |
| Cl1z1 | Cl1 | z | 1 |
| Cl2x1 | Cl2 | x | 1 |
| Cl2y1 | Cl2 | y | 1 |
| Cl2z1 | Cl2 | z | 1 |
| Cl3x1 | Cl3 | x | 1 |
| Cl3y1 | Cl3 | y | 1 |
| Cl3z1 | Cl3 | z | 1 |
| Cl4x1 | Cl4 | x | 1 |
| Cl4y1 | Cl4 | y | 1 |
| Cl4z1 | Cl4 | z | 1 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Rb1x1 | -0.0116 | 0.0123(3) |
| Rb1y1 | 0.0015(4) | 0.0046(4) |
| Rb1z1 | -0.0017(4) | 0.0014(5) |
| Rb2x1 | -0.0021(3) | 0.0202(2) |
| Rb2y1 | -0.0013(3) | 0.0005(3) |
| Rb2z1 | 0.0012(4) | -0.0012(4) |
| Znx1 | 0.0035(2) | 0.0108(2) |
| Zny1 | 0.0005(4) | -0.0021(3) |
| Znz1 | -0.0003(5) | 0.0014(5) |
| Cl1x1 | 0.0100(10) | 0.0503(8) |
| Cl1y1 | -0.0059(7) | -0.0044(8) |
| Cl1z1 | -0.0013(8) | 0.0057(9) |
| Cl2x1 | 0.0647(6) | 0.0086(10) |
| Cl2y1 | 0.0008(8) | -0.0033(5) |
| Cl2z1 | 0.0004(10) | 0.009(7) |
| Cl3x1 | -0.0249(9) | 0.0069(8) |
| Cl3y1 | 0.0341(7) | -0.0018(5) |
| Cl3z1 | 0.0208(8) | -0.0114(7) |
| Cl4x1 | -0.0244(9) | 0.0044(8) |
| Cl4y1 | -0.0321(7) | -0.0009(5) |
| Cl4z1 | -0.0126(8) | 0.0115(7) |