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: 772E43YaC Entry date: 2010-11-08 Last revision: 2021-12-30
RbZnBr-140
Chemical data
Structural Formula Sum: Br4 Rb2 Zn1 [ Help ]
Formula weight: 555.9 Da [ Help ]
Crystallographic data and experimental details
a: 13.198(5) Å [ Help ]
b: 7.594(4) Å [ Help ]
c: 9.614(3) Å [ Help ]
α: 90 ° [ Help ]
β: 90 ° [ Help ]
γ: 90 ° [ Help ]
Volume: 963.6(7) Å3 [ Help ]
Z: 4 [ Help ]
μ: 29.084 mm-1 [ Help ]
Cell measurement temperature: 140(3) K [ Help ]
Crystal system: orthorhombic [ Help ]
Superspace group name (ITC): P c 21 n (0 0 γ) s -1 -1 [ Help ]
Superspace group name: Pc21n(00γ)s00 [ 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,-x3,1/3-x4 |
| 4 | 1/2+x1,1/2+x2,1/2-x3,5/6-x4 |
Space group name (H-M): P c 21 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 within the superspace formalism. Global phase unknown. [ Help ]
Modulation functions description: Displacive modulation:Fourier series. 1st-order harmonics. [ Help ]
Total nb. of reflections: 4496 [ Help ]
R(all): 0.12 [ Help ]
wR(all): 0.119 [ 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 | 0.3229(1) | 0.2476(8) | 0.5127(1) | 0.0265(4) | Uani |
| Rb(2) | Rb | 4 | 1 | 0.5970(2) | 0.2530(9) | 0.8759(2) | 0.0427(6) | Uani |
| Zn | Zn | 4 | 1 | 0.5785(1) | 0.2491 | 0.2766(1) | 0.0189(4) | Uani |
| Br(1) | Br | 4 | 1 | 0.5803(1) | 0.2479(8) | 0.5224(1) | 0.0345(6) | Uani |
| Br(2) | Br | 4 | 1 | 0.4146(1) | 0.2603(8) | 0.1756(2) | 0.0346(5) | Uani |
| Br(3) | Br | 4 | 1 | 0.6687(2) | 0.4966(6) | 0.1910(3) | 0.0377(8) | Uani |
| Br(4) | Br | 4 | 1 | 0.6569(2) | -0.0047(6) | 0.1858(3) | 0.0374(8) | 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 |
|---|---|---|---|
| Rb(1)x1 | Rb(1) | x | 1 |
| Rb(1)y1 | Rb(1) | y | 1 |
| Rb(1)z1 | Rb(1) | z | 1 |
| Rb(2)x1 | Rb(2) | x | 1 |
| Rb(2)y1 | Rb(2) | y | 1 |
| Rb(2)z1 | Rb(2) | z | 1 |
| Znx1 | Zn | x | 1 |
| Zny1 | Zn | y | 1 |
| Znz1 | Zn | z | 1 |
| Br(1)x1 | Br(1) | x | 1 |
| Br(1)y1 | Br(1) | y | 1 |
| Br(1)z1 | Br(1) | z | 1 |
| Br(2)x1 | Br(2) | x | 1 |
| Br(2)y1 | Br(2) | y | 1 |
| Br(2)z1 | Br(2) | z | 1 |
| Br(3)x1 | Br(3) | x | 1 |
| Br(3)y1 | Br(3) | y | 1 |
| Br(3)z1 | Br(3) | z | 1 |
| Br(4)x1 | Br(4) | x | 1 |
| Br(4)y1 | Br(4) | y | 1 |
| Br(4)z1 | Br(4) | z | 1 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Amplitude | Phase | Cosine coefficient | Sine coefficient |
|---|---|---|---|---|
| Rb(1)x1 | 0.0033(3) | -0.87(1) | 0.0023(3) | -0.0024(3) |
| Rb(1)y1 | 0.0233(3) | -0.134(2) | 0.0149(3) | 0.0167(3) |
| Rb(1)z1 | 0.0014(5) | -0.75(5) | 0(4) | -0.0014(5) |
| Rb(2)x1 | 0.0056(4) | -0.19(1) | 0.0020(5) | 0.0053(4) |
| Rb(2)y1 | 0.0198(4) | -0.527(3) | -0.0195(4) | -0.0034(4) |
| Rb(2)z1 | 0.0032(5) | -0.84(2) | 0.0016(5) | -0.0028(5) |
| Znx1 | 0.0012(4) | -0.33(5) | -0.0006(3) | 0.0010(4) |
| Zny1 | 0.0138(3) | -0.730(4) | -0.0017(3) | -0.0137(3) |
| Znz1 | 0.0011(5) | -0.76(7) | 0.0001(5) | -0.0011(5) |
| Br(1)x1 | 0.0053(3) | -0.67(1) | -0.0027(3) | -0.0046(3) |
| Br(1)y1 | 0.0535(4) | -0.699(1) | -0.0169(5) | -0.0508(4) |
| Br(1)z1 | 0.0041(4) | -0.03(1) | 0.0040(4) | 0.0007(4) |
| Br(2)x1 | 0.0013(3) | -0.27(4) | -0.0001(3) | 0.0013(3) |
| Br(2)y1 | 0.0699(5) | -0.892(1) | 0.0545(5) | -0.0438(5) |
| Br(2)z1 | 0.0023(4) | -0.77(3) | 0.0004(5) | -0.0023(4) |
| Br(3)x1 | 0.0341(3) | -0.913(1) | 0.0291(3) | -0.0178(3) |
| Br(3)y1 | 0.0251(5) | -0.460(3) | -0.0243(5) | 0.0062(4) |
| Br(3)z1 | 0.0247(4) | -0.038(2) | 0.0240(4) | 0.0058(4) |
| Br(4)x1 | 0.0348(3) | -0.413(1) | -0.0297(3) | 0.0182(3) |
| Br(4)y1 | 0.0291(5) | -0.453(3) | -0.0278(5) | 0.0085(3) |
| Br(4)z1 | 0.0184(4) | -0.508(3) | -0.0184(4) | -0.0009(3) |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| Rb(1) | Rb | 0.0254(6) | 0.0369(8) | 0.0172(6) | -0.0001(13) | 0.0009(5) | -0.0022(18) |
| Rb(2) | Rb | 0.0654(12) | 0.0450(11) | 0.0176(7) | 0.0090(21) | -0.0006(7) | -0.0008(19) |
| Zn | Zn | 0.0217(6) | 0.0210(7) | 0.0140(6) | -0.0002(16) | 0.0000(5) | 0.0004(18) |
| Br(1) | Br | 0.0376(8) | 0.0540(13) | 0.0119(6) | -0.0081(16) | -0.0036(6) | -0.0023(15) |
| Br(2) | Br | 0.0258(7) | 0.0581(12) | 0.0200(7) | 0.0053(15) | -0.0054(6) | -0.0010(17) |
| Br(3) | Br | 0.0604(16) | 0.0237(13) | 0.0291(13) | -0.0165(12) | 0.0133(13) | -0.0025(12) |
| Br(4) | Br | 0.0549(15) | 0.0266(14) | 0.0306(14) | 0.0090(12) | 0.0071(13) | 0.0010(12) |