- SODIUM SULFATE - Na2SO4
The crystal structure is fully relaxed (both unit cell parameters and atomic positions under symmetry constraints) starting from an experimental structure similar to the one reported in ICSD database; code 31687
Crystal Structure
Because of the translational symmetry all the calculations are performed in the primitive unit cell and not in the conventional unit cell. The following information regarding the structure is given with respect to this primitive unit cell, which sometimes can take an unintuitive shape.
Symmetry (experimental):
| Space group: | 52 | Pbnn | ||||
| Lattice parameters (Å): | 5.6000 | 8.9500 | 6.9900 | |||
| Angles (°): | 90.0 | 90.0 | 90.0 | |||
Symmetry (theoretical):
| Space group: | 52 | Pbnn | ||||
| Lattice parameters (Å): | 5.4664 | 8.6616 | 6.7592 | |||
| Angles (°): | 90.0 | 90.0 | 90.0 | |||
Cell contents:
| Number of atoms: | 28 |
| Number of atom types: | 3 |
| Chemical composition: | 0 |
Atomic positions (theoretical):
| S: | 0.2500 | 0.1004 | 0.2500 |
| Na: | 0.2500 | 0.4387 | 0.2500 |
| Na: | 0.7500 | 0.2500 | 0.0000 |
| O: | 0.0301 | 0.2008 | 0.2500 |
| O: | 0.2500 | 0.0027 | 0.0732 |
| S: | 0.2500 | 0.3996 | 0.7500 |
| Na: | 0.2500 | 0.0613 | 0.7500 |
| O: | 0.0301 | 0.2992 | 0.7500 |
| O: | 0.2500 | 0.4973 | 0.9268 |
| Na: | 0.7500 | 0.2500 | 0.5000 |
| O: | 0.4699 | 0.2992 | 0.7500 |
| O: | 0.2500 | 0.4973 | 0.5732 |
| O: | 0.4699 | 0.2008 | 0.2500 |
| O: | 0.2500 | 0.0027 | 0.4268 |
| S: | 0.7500 | 0.8996 | 0.7500 |
| Na: | 0.7500 | 0.5613 | 0.7500 |
| Na: | 0.2500 | 0.7500 | 0.0000 |
| O: | 0.9699 | 0.7992 | 0.7500 |
| O: | 0.7500 | 0.9973 | 0.9268 |
| S: | 0.7500 | 0.6004 | 0.2500 |
| Na: | 0.7500 | 0.9387 | 0.2500 |
| O: | 0.9699 | 0.7008 | 0.2500 |
| O: | 0.7500 | 0.5027 | 0.0732 |
| Na: | 0.2500 | 0.7500 | 0.5000 |
| O: | 0.5301 | 0.7008 | 0.2500 |
| O: | 0.7500 | 0.5027 | 0.4268 |
| O: | 0.5301 | 0.7992 | 0.7500 |
| O: | 0.7500 | 0.9973 | 0.5732 |
| Atom type | X | Y | Z |
We have listed here the reduced coordinates of all the atoms in the primitive unit cell.
It is enough to know only the position of the atoms from the assymetrical unit cell and then use the symmetry to build the whole crystal structure.
Visualization of the crystal structure:
Please note that the structure is represented using the primitive cell, and not the conventional one.
Parameters of the Calculation
All the calculations have been done using the ABINIT software. This is a list of the most representative parameteres used during the Raman calculation.
| Number of electronic bands: | 64 |
| k-points | |
| grid: | 4 4 4 |
| number of shifts: | 1 |
| shifts: | 0.5 0.5 0.5 |
| Kinetic energy cut-off: | 40 Ha [=1088.464 eV ] |
| eXchange-Correlation functional: | LDA pw90 |
| Pseudopotentials: | |
| O: | oxygen, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local |
| Na: | sodium, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local |
| S: | sulphur, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local |
Powder Raman
Powder Raman spectrum
The intensity of the Raman peaks is computed within the density-functional perturbation theory. The intensity depends on the temperature (for now fixed at 300K), frequency of the input laser (for now fixed at 21834 cm-1, frequency of the phonon mode and the Raman tensor. The Raman tensor represents the derivative of the dielectric tensor during the atomic displacement that corresponds to the phonon vibration. The Raman tensor is related to the polarizability of a specific phonon mode.
Choose the polarization of the lasers.
| Xmin: | |
| Xmax: |
| Ymin: | |
| Ymax: |
Data about the phonon modes
Frequency of the transverse (TO) and longitudinal (LO) phonon modes in the zone-center. The longitudinal modes are computed along the three cartesian directions. You can visualize the atomic displacement pattern corresponding to each phonon by clicking on the appropriate cell in the table below.
| 1 | ||||||||
| 2 | ||||||||
| 3 | ||||||||
| 4 | ||||||||
| 5 | ||||||||
| 6 | ||||||||
| 7 |
3.944e+37
0.0
|
5.423e+37
0.0
|
9.366e+37
0.1
|
|||||
| 8 |
1.595e+38
0.1
|
2.193e+38
0.2
|
3.787e+38
0.3
|
|||||
| 9 | ||||||||
| 10 | ||||||||
| 11 | ||||||||
| 12 | ||||||||
| 13 | ||||||||
| 14 | ||||||||
| 15 | ||||||||
| 16 | ||||||||
| 17 | ||||||||
| 18 | ||||||||
| 19 | ||||||||
| 20 |
4.011e+38
0.3
|
2.828e+38
0.2
|
6.840e+38
0.5
|
|||||
| 21 |
5.635e+38
0.4
|
7.748e+38
0.6
|
1.338e+39
1.0
|
|||||
| 22 | ||||||||
| 23 | ||||||||
| 24 |
1.761e+38
0.1
|
2.422e+38
0.2
|
4.183e+38
0.3
|
|||||
| 25 | ||||||||
| 26 | ||||||||
| 27 |
4.498e+38
0.3
|
6.185e+38
0.5
|
1.068e+39
0.8
|
|||||
| 28 |
1.308e+36
0.0
|
9.797e+35
0.0
|
2.288e+36
0.0
|
|||||
| 29 |
2.986e+38
0.2
|
2.174e+38
0.2
|
5.159e+38
0.4
|
|||||
| 30 | ||||||||
| 31 | ||||||||
| 32 |
1.840e+36
0.0
|
2.529e+36
0.0
|
4.369e+36
0.0
|
|||||
| 33 | ||||||||
| 34 | ||||||||
| 35 | ||||||||
| 36 | ||||||||
| 37 | ||||||||
| 38 | ||||||||
| 39 | ||||||||
| 40 | ||||||||
| 41 | ||||||||
| 42 | ||||||||
| 43 | ||||||||
| 44 | ||||||||
| 45 | ||||||||
| 46 | ||||||||
| 47 | ||||||||
| 48 |
1.105e+38
0.1
|
1.519e+38
0.1
|
2.623e+38
0.2
|
|||||
| 49 | ||||||||
| 50 | ||||||||
| 51 |
6.752e+39
5.0
|
9.284e+39
6.8
|
1.604e+40
11.8
|
|||||
| 52 | ||||||||
| 53 |
4.838e+39
3.5
|
3.508e+39
2.6
|
8.346e+39
6.1
|
|||||
| 54 | ||||||||
| 55 | ||||||||
| 56 | ||||||||
| 57 | ||||||||
| 58 | ||||||||
| 59 |
6.201e+39
4.5
|
8.526e+39
6.3
|
1.473e+40
10.8
|
|||||
| 60 | ||||||||
| 61 | ||||||||
| 62 | ||||||||
| 63 | ||||||||
| 64 | ||||||||
| 65 |
2.477e+39
1.8
|
1.832e+39
1.3
|
4.309e+39
3.2
|
|||||
| 66 |
1.862e+39
1.4
|
1.377e+39
1.0
|
3.239e+39
2.4
|
|||||
| 67 |
3.666e+39
2.7
|
5.040e+39
3.7
|
8.706e+39
6.4
|
|||||
| 68 | ||||||||
| 69 | ||||||||
| 70 |
1.360e+41
99.8
|
3.260e+38
0.2
|
1.363e+41
100.0
|
|||||
| 71 | ||||||||
| 72 | ||||||||
| 73 |
5.582e+39
4.1
|
7.675e+39
5.6
|
1.326e+40
9.7
|
|||||
| 74 | ||||||||
| 75 | ||||||||
| 76 | ||||||||
| 77 |
9.512e+39
7.0
|
3.445e+39
2.5
|
1.296e+40
9.5
|
|||||
| 78 | ||||||||
| 79 | ||||||||
| 80 | ||||||||
| 81 | ||||||||
| 82 | ||||||||
| 83 | ||||||||
| 84 |
6.515e+39
4.8
|
8.959e+39
6.6
|
1.547e+40
11.4
|
| No. | Char. | ω TO | ω LOx | ω LOy | ω LOz | I ∥ | I ⊥ | I Total |
You can define the size of the supercell for the visualization of the vibration.