-    SODIUM SULFATE     -    Na2SO4

The crystal structure is fully relaxed (both unit cell parameters and atomic positions under symmetry constraints) starting from a structure reported in “First-principles study of high-T phases of K2SeO4”, Caracas R. and Gonze X., Phys. Rev. B, 74, 195111 (2006); Unstable structure.  

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:  164  P-3m1 
Lattice parameters (Å):  6.1190  6.1190  7.9440 
Angles (°):  90.0  90.0  120.0 

Symmetry (theoretical): 

Space group:  164  P-3m1 
Lattice parameters (Å):  5.3173  5.3173  6.5014 
Angles (°):  90.0  90.0  120.0 

Cell contents: 

Number of atoms:  14 
Number of atom types:  3 
Chemical composition:  0 

Atomic positions (theoretical):

Na:  0.0000  0.0000  0.0000 
Na:  0.0000  0.0000  0.5000 
Na:  0.3333  0.6667  0.8428 
S:  0.3333  0.6667  0.2932 
O:  0.3333  0.6667  0.5156 
O:  0.1834  0.8166  0.2112 
O:  0.6331  0.8166  0.2112 
O:  0.1834  0.3669  0.2112 
Na:  0.6667  0.3333  0.1572 
S:  0.6667  0.3333  0.7068 
O:  0.6667  0.3333  0.4844 
O:  0.8166  0.1834  0.7888 
O:  0.3669  0.1834  0.7888 
O:  0.8166  0.6331  0.7888 
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: 

Size:

 Nx:  Ny:  Nz: 
You can define the size of the supercell to be displayed in the jmol panel as integer translations along the three crys­tallo­gra­phic axis.
Please note that the structure is represented using the pri­mi­tive cell, and not the conventional one.
     

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.

I ∥ 
I ⊥ 
I Total 
Horizontal:
Xmin:
Xmax:
Vertical:
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
A2g
-102
-102
-102
-102
2
Eg
-81
-81
-81
-81
3
Eg
-81
-81
-81
-81
4
A1u
-71
-71
-71
-71
5
Eu
-56
-56
-56
-56
6
Eu
-56
-47
-47
-56
7
Ac
0
0
0
0
8
Ac
0
0
0
0
9
Ac
0
0
0
0
10
Eu
66
66
66
66
11
Eu
66
81
81
66
12
Eg
81
81
81
81
1.058e+39
0.7
8.540e+38
0.6
1.912e+39
1.4
13
Eg
81
117
117
81
1.058e+39
0.7
1.296e+39
0.9
2.354e+39
1.7
14
Eu
118
118
118
118
15
Eu
118
152
152
118
16
A2u
152
157
157
157
17
Eg
157
157
157
157
1.270e+39
0.9
1.901e+39
1.3
3.172e+39
2.2
18
Eg
157
168
168
162
1.270e+39
0.9
1.745e+39
1.2
3.015e+39
2.1
19
A1g
169
169
169
169
2.378e+39
1.7
5.651e+37
0.0
2.434e+39
1.7
20
A2u
243
243
243
252
21
A1g
252
252
252
261
1.283e+39
0.9
7.534e+38
0.5
2.037e+39
1.4
22
Eu
275
275
275
275
23
Eu
275
303
303
275
24
A2u
311
311
311
358
25
Eu
430
430
430
430
26
Eu
430
431
431
430
27
Eg
432
432
432
432
6.971e+39
4.9
1.022e+40
7.2
1.719e+40
12.1
28
Eg
432
432
432
432
6.971e+39
4.9
5.406e+39
3.8
1.238e+40
8.7
29
Eu
600
600
600
600
30
Eu
600
603
603
600
31
Eg
603
603
603
603
4.078e+39
2.9
6.208e+39
4.4
1.029e+40
7.3
32
Eg
603
607
607
603
4.078e+39
2.9
4.144e+39
2.9
8.222e+39
5.8
33
A2u
607
613
613
622
34
A1g
630
630
630
630
4.205e+39
3.0
2.771e+39
2.0
6.976e+39
4.9
35
A2u
1012
1012
1012
1016
36
A1g
1016
1016
1016
1016
1.412e+41
99.8
3.265e+38
0.2
1.415e+41
100.0
37
Eg
1089
1089
1089
1089
4.269e+39
3.0
4.245e+39
3.0
8.514e+39
6.0
38
Eg
1089
1089
1089
1089
4.269e+39
3.0
7.084e+39
5.0
1.135e+40
8.0
39
Eu
1105
1105
1105
1105
40
Eu
1105
1193
1193
1105
41
A2u
1237
1237
1237
1241
42
A1g
1241
1241
1241
1310
5.800e+39
4.1
3.277e+39
2.3
9.077e+39
6.4
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.

Nx: 
Ny: 
Nz: 
Normalized
Raw
Options for intensity.