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: 812ExYP9f Entry date: 2010-11-08 Last revision: 2021-12-30
RbZnBr-95
Chemical data
Structural Formula Sum: Br4 Rb2 Zn1 [ Help ]
Formula weight: 555.9 Da [ Help ]
Crystallographic data and experimental details
a: 13.184(4) Å [ Help ]
b: 7.599(2) Å [ Help ]
c: 9.623(5) Å [ Help ]
α: 90 ° [ Help ]
β: 90 ° [ Help ]
γ: 90 ° [ Help ]
Volume: 964.1(6) Å3 [ Help ]
Z: 4 [ Help ]
Cell measurement temperature: 95(1) 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: 1482 [ Help ]
R(all): 0.05 [ Help ]
wR(all): 0.050 [ 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 | 0.3223(1) | 0.2489(10) | 0.5120(2) | 0.0157(6) | Uani |
| Rb(2) | Rb | 4 | 1 | 0.5970(2) | 0.2519(12) | 0.8765(2) | 0.0317(7) | Uani |
| Zn | Zn | 4 | 1 | 0.5789(1) | 0.2497 | 0.2772(2) | 0.0085(6) | Uani |
| Br(1) | Br | 4 | 1 | 0.5792(1) | 0.2497(10) | 0.5234(2) | 0.0196(7) | Uani |
| Br(2) | Br | 4 | 1 | 0.4157(1) | 0.2619(9) | 0.1740(2) | 0.0235(8) | Uani |
| Br(3) | Br | 4 | 1 | 0.6704(3) | 0.4941(8) | 0.1922(3) | 0.0217(11) | Uani |
| Br(4) | Br | 4 | 1 | 0.6580(3) | -0.0064(8) | 0.1888(3) | 0.0217(11) | 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 | 0.0015(4) | -0.78(5) | 0.0003(5) | -0.0015(4) |
| Rb(1)y1 | 0.0268(4) | -0.138(3) | 0.0174(4) | 0.0204(4) |
| Rb(1)z1 | 0.0023(6) | -0.98(4) | 0.0023(6) | -0.0003(6) |
| Rb(2)x1 | 0.0057(6) | -0.17(2) | 0.0027(6) | 0.0050(6) |
| Rb(2)y1 | 0.0225(5) | -0.520(3) | -0.0223(5) | -0.0028(5) |
| Rb(2)z1 | 0.0026(6) | -0.79(4) | 0.0006(7) | -0.0025(6) |
| Znx1 | 0.0011(6) | -0.63(9) | -0.0007(6) | -0.0008(6) |
| Zny1 | 0.0133(4) | -0.731(5) | -0.0016(4) | -0.0132(4) |
| Znz1 | 0.0041(7) | -0.93(3) | 0.0037(7) | -0.0018(6) |
| Br(1)x1 | 0.0059(5) | -0.67(1) | -0.0027(5) | -0.0052(5) |
| Br(1)y1 | 0.0585(5) | -0.702(1) | -0.0172(6) | -0.0560(5) |
| Br(1)z1 | 0.0026(5) | -0.89(3) | 0.0020(5) | -0.0016(6) |
| Br(2)x1 | 0.0007(4) | -0.3(1) | -0.0003(5) | 0.0006(4) |
| Br(2)y1 | 0.0769(7) | -0.890(1) | 0.0593(6) | -0.0490(7) |
| Br(2)z1 | 0.0033(6) | -0.74(3) | -0.0002(6) | -0.0033(6) |
| Br(3)x1 | 0.0383(4) | -0.904(2) | 0.0316(4) | -0.0218(4) |
| Br(3)y1 | 0.0265(7) | -0.434(4) | -0.0243(7) | 0.0107(6) |
| Br(3)z1 | 0.0286(4) | -0.026(2) | 0.0283(4) | 0.0046(4) |
| Br(4)x1 | 0.0373(4) | -0.410(2) | -0.0315(4) | 0.0200(4) |
| Br(4)y1 | 0.0295(6) | -0.442(3) | -0.0276(6) | 0.0105(6) |
| Br(4)z1 | 0.0208(4) | -0.535(3) | -0.0203(4) | -0.0046(4) |
ADP components: (Show/hide table) [ Help ]
| Atom site label | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|
| Rb(1) | 0.0118(9) | 0.0232(11) | 0.0120(9) | -0.0022(21) | 0.0002(8) | 0.0022(29) |
| Rb(2) | 0.0444(13) | 0.0396(13) | 0.0112(10) | -0.0008(32) | 0.0000(9) | 0.0060(28) |
| Zn | 0.0090(11) | 0.0104(11) | 0.0060(11) | -0.0027(33) | 0.0001(9) | 0.0023(27) |
| Br(1) | 0.0178(12) | 0.0345(17) | 0.0065(9) | -0.0079(25) | -0.0023(9) | 0(24) |
| Br(2) | 0.0137(10) | 0.0441(17) | 0.0126(11) | 0.0069(24) | -0.0060(9) | 0.0030(23) |
| Br(3) | 0.0340(18) | 0.0146(21) | 0.0164(17) | -0.0126(18) | 0.0078(17) | -0.0037(17) |
| Br(4) | 0.0382(19) | 0.0073(20) | 0.0195(19) | 0.0054(17) | 0.0118(17) | -0.0008(19) |