Incommensurately Modulated Structure of K2SeO4
Authors:Yamada, N.; Ikeda, T.
Journal:J. Phys. Soc. Jpn. 53 2555-2564 (1984)
DOI:https://doi.org/10.1143/JPSJ.53.2555
B-IncStrDB ID: 492E3r0gG Entry date: 2010-11-08 Last revision: 2021-12-30
KSE
Chemical data
Structural Formula Sum: K2 O4 Se1 [ Help ]
Formula weight: 221.2 Da [ Help ]
Crystallographic data and experimental details
a: 7.661(4) Å [ Help ]
b: 10.466(8) Å [ Help ]
c: 6.003(3) Å [ Help ]
α: 90 ° [ Help ]
β: 90 ° [ Help ]
γ: 90 ° [ Help ]
Volume: 481.3(5) Å3 [ Help ]
Z: 4 [ Help ]
μ: 9.424 mm-1 [ Help ]
Cell measurement temperature: 113 K [ Help ]
Crystal system: orthorhombic [ Help ]
Superspace group name (WJJ): P:P n a m:-1 s s [ Help ]
Superspace group name: Pnam(α00)0ss [ 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+x1,1/2-x2,x3,1/2+x4 |
| 3 | x1,x2,1/2-x3,1/2+x4 |
| 4 | 1/2+x1,1/2-x2,1/2-x3,x4 |
| 5 | -x1,-x2,-x3,-x4 |
| 6 | 1/2-x1,1/2+x2,-x3,1/2-x4 |
| 7 | -x1,-x2,1/2+x3,1/2-x4 |
| 8 | 1/2-x1,1/2+x2,1/2+x3,-x4 |
Space group name (H-M): P n a m [ Help ]
Modulation dimension: 1 [ Help ]
Experimental remarks: Modulation wave vector not given [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.3 | 0 | 0 |
Refinement details
Refinement remarks: WARNING: The published thermal displacement parameters have been converted to U,s. The calculated standard uncertainties (s.u.) have been based uniquely on the published ones without considering the s.u. of any other quantity involved in such conversion. [ Help ]
Modulation functions description: Displacive modulation:Fourier series. 1st-order harmonics. [ Help ]
Structure factors calc. details: 10 points Gaussian integration [ Help ]
R(obs): 0.082 [ Help ]
Structural Information
Average Structure: (Show/hide table) [ Help ]
| Atom site label | Atom symbol | Symmetry multiplicity | Occupancy | x | y | z | Uiso/equiv | ADP type |
|---|---|---|---|---|---|---|---|---|
| Se | Se | 4 | 1 | 0.2222(6) | 0.4187(6) | 0.25 | ? | Uani |
| K1 | K | 4 | 1 | 0.1670(14) | 0.0809(15) | 0.25 | ? | Uani |
| K2 | K | 4 | 1 | -0.0017(14) | 0.7075(15) | 0.25 | ? | Uani |
| O1 | O | 8 | 1 | 0.2891(40) | 0.3413(38) | 0.0277(36) | ? | Uani |
| O2 | O | 4 | 1 | 0.3121(52) | 0.5617(49) | 0.25 | ? | Uani |
| O3 | O | 4 | 1 | 0.0093(49) | 0.4291(55) | 0.25 | ? | 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 | 0.3 | 0 | 0 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Wave vector code | Displacement axis |
|---|---|---|---|
| Se1z | Se | 1 | z |
| K11z | K1 | 1 | z |
| K21z | K2 | 1 | z |
| O11x | O1 | 1 | x |
| O11y | O1 | 1 | y |
| O11z | O1 | 1 | z |
| O21z | O2 | 1 | z |
| O31z | O3 | 1 | z |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Se1z | 0.0053(3) | 0.0080(3) |
| K11z | 0.0105(7) | -0.0081(7) |
| K21z | -0.0068(8) | -0.0154(6) |
| O11x | 0.0152(21) | -0.0141(19) |
| O11y | 0.0107(16) | -0.0019(18) |
| O11z | 0.0006(17) | 0.0044(17) |
| O21z | 0.0296(23) | -0.0010(27) |
| O31z | 0.0008(32) | 0.0381(22) |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| Se | Se | 0.0051(3) | 0.0067(6) | 0.00365(18) | 0.0004(4) | 0 | 0 |
| K1 | K | 0.0062(6) | 0.0122(6) | 0.0077(7) | 0.0020(12) | 0 | 0 |
| K2 | K | 0.0059(6) | 0.0078(6) | 0.0069(7) | 0.0004(8) | 0 | 0 |
| O1 | O | 0.019(3) | 0.017(2) | 0.0077(16) | 0.009(4) | 0.000(3) | -0.010(3) |
| O2 | O | 0.014(3) | 0.012(3) | 0.015(3) | -0.010(4) | 0 | 0 |
| O3 | O | 0.005(2) | 0.020(3) | 0.020(4) | 0.004(4) | 0 | 0 |