The modulated structure of γ-Na2CO3 in a harmonic approximation
Authors:van Aalst, W.; den Hollander, J.; Peterse, W.J.A.M.; de Wolff, P.M.
Journal:Acta Cryst. B 32 47-58 (1976)
DOI:https://doi.org/10.1107/S056774087600229X
B-IncStrDB ID: 582EqAgoV Entry date: 2010-11-08 Last revision: 2021-12-30
NaCO
Chemical data
Structural Formula Sum: C1 Na2 O3 [ Help ]
Formula weight: 106 Da [ Help ]
Crystallographic data and experimental details
a: 8.904(3) Å [ Help ]
b: 5.239(2) Å [ Help ]
c: 6.042(2) Å [ Help ]
α: 90 ° [ Help ]
β: 101.35 ° [ Help ]
γ: 90 ° [ Help ]
Volume: 276.34(17) Å3 [ Help ]
Z: 4 [ Help ]
Cell measurement temperature: 293 K [ Help ]
Crystal system: monoclinic [ Help ]
Superspace group name (WJJ): P:C 2/m :-1 s [ Help ]
Superspace group name: C2/m(α0γ)0s [ Help ]
Symmetry operations of the superspace group: (Show/hide table) [ Help ]
| Operation code | Operation in algebraic form |
|---|---|
| 1 | x1,x2,x3,x4 |
| 2 | -x1,x2,-x3,1/2-x4 |
| 3 | -x1,-x2,-x3,-x4 |
| 4 | x1,-x2,x3,1/2+x4 |
| 5 | 1/2+x1,1/2+x2,x3,x4 |
| 6 | 1/2-x1,1/2+x2,-x3,1/2-x4 |
| 7 | 1/2-x1,1/2-x2,-x3,-x4 |
| 8 | 1/2+x1,1/2-x2,x3,1/2+x4 |
Space group name (H-M): C 1 2/m 1 [ Help ]
Modulation dimension: 1 [ Help ]
Measured independent wave vectors: (Show/hide table) [ Help ]
| Wave vector id | q_x | q_y | q_z |
|---|---|---|---|
| 1 | 0.182(1) | 0 | 0.318(1) |
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: Bessel functions [ Help ]
Nb. of observed reflections: 1910 [ Help ]
R(obs): 0.108 [ Help ]
wR(all): 0.070 [ Help ]
Structural Information
Average Structure: (Show/hide table) [ Help ]
| Atom site label | Atom symbol | Symmetry multiplicity | Occupancy | x | y | z | Uiso/equiv | ADP type |
|---|---|---|---|---|---|---|---|---|
| Na1 | Na | 2 | 1 | 0 | 0 | 0 | ? | Uani |
| Na2 | Na | 2 | 1 | 0 | 0 | 0.5 | ? | Uani |
| Na3 | Na | 4 | 1 | 0.1706(1) | 0.5 | 0.7478(2) | ? | Uani |
| C | C | 4 | 1 | 0.1641(2) | 0.5 | 0.2496(3) | ? | Uani |
| O2 | O | 4 | 1 | 0.2897(2) | 0.5 | 0.1771(3) | ? | Uani |
| O13 | O | 8 | 1 | 0.1016(2) | 0.2940(3) | 0.2855(2) | ? | 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 | 0.182 | 0 | 0.318 |
Definition of the displacive (translational) Fourier series: (Show/hide table) [ Help ]
| Modulation code | Atom site label | Displacement axis | Wave vector code |
|---|---|---|---|
| Na1y1 | Na1 | y | 1 |
| Na2y1 | Na2 | y | 1 |
| Na3y1 | Na3 | y | 1 |
| Cy1 | C | y | 1 |
| O2y1 | O2 | y | 1 |
| O13x1 | O13 | x | 1 |
| O13y1 | O13 | y | 1 |
| O13z1 | O13 | z | 1 |
Displacive (translational) Fourier coefficients: (Show/hide table) [ Help ]
| Modulation code | Cosine coefficient | Sine coefficient |
|---|---|---|
| Na1y1 | 0 | 0.0567(4) |
| Na2y1 | 0 | 0.0656(4) |
| Na3y1 | -0.0057(4) | 0.0687(3) |
| Cy1 | 0.0009(7) | 0.0589(6) |
| O2y1 | -0.0078(5) | 0.0244(5) |
| O13x1 | -0.0184(3) | -0.0275(2) |
| O13y1 | 0.0070(5) | 0.0770(4) |
| O13z1 | -0.0374(4) | -0.0214(3) |
ADP components: (Show/hide table) [ Help ]
| Atom site label | Atom site symbol | U11 | U22 | U33 | U12 | U13 | U23 |
|---|---|---|---|---|---|---|---|
| Na1 | Na | .0151(4) | .0170(7) | .0140(5) | 0 | .0052(3) | 0 |
| Na2 | Na | .0162(4) | .0103(7) | .0142(5) | 0 | .0060(3) | 0 |
| Na3 | Na | .0193(4) | .0206(6) | .0279(5) | 0 | .0079(3) | 0 |
| C | C | .0097(4) | .0102(8) | .0105(7) | 0 | .0026(5) | 0 |
| O2 | O | .0120(4) | .0264(8) | .0204(5) | 0 | .0092(5) | 0 |
| O13 | O | .0224(8) | .0129(10) | .0240(5) | .0032(9) | .0052(5) | -.0013(6) |