-    SODIUM SULFATE     -    Na2SO4

Theoretical atomic positions and lattice parameters at experimental volum 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):  5.7792  5.7792  8.9058 
Angles (°):  90.0  90.0  120.0 

Cell contents: 

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

Atomic positions (theoretical):

Na:  0.0000  1.0000  0.0000 
Na:  0.0000  1.0000  0.5000 
Na:  0.3333  0.6667  0.7072 
S:  0.3333  0.6667  0.3003 
O:  0.3333  0.6667  0.4659 
O:  0.1927  0.8073  0.2459 
O:  0.6146  0.8073  0.2459 
O:  0.1927  0.3854  0.2459 
Na:  0.6667  0.3333  0.2928 
S:  0.6667  0.3333  0.6997 
O:  0.6667  0.3333  0.5341 
O:  0.8073  0.1927  0.7541 
O:  0.3854  0.1927  0.7541 
O:  0.8073  0.6146  0.7541 
Atom type 

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.

Horizontal:
Xmin:
Xmax:
Vertical:
Ymin:
Ymax:
 
Choose the polarization of the lasers.
I ∥ 
I ⊥ 
I Total 

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
A2u
-129
-129
-129
-117
2
A2g
-117
-117
-117
-117
3
A1u
-117
-117
-117
-108
4
Eu
-108
-108
-108
-108
5
Eu
-108
-98
-98
-98
6
Eg
-98
-98
-98
-98
7
Eg
-98
-97
-97
-91
8
Eu
-91
-91
-91
-91
9
Eu
-91
-38
-38
-50
10
Eu
-38
-38
-38
-38
11
Eu
-38
0
0
-38
12
Ac
0
0
0
0
13
Ac
0
0
0
0
14
Ac
0
22
22
0
15
Eg
22
22
22
22
1.068e+39
1.0
1.545e+39
1.4
2.613e+39
2.4
16
Eg
22
24
24
22
1.068e+39
1.0
8.498e+38
0.8
1.918e+39
1.8
17
A2u
24
68
68
43
18
Eg
68
68
68
68
4.115e+38
0.4
4.730e+38
0.4
8.845e+38
0.8
19
Eg
68
71
71
68
4.113e+38
0.4
5.016e+38
0.5
9.129e+38
0.9
20
Eu
82
82
82
82
21
Eu
82
101
101
82
22
A1g
101
160
160
101
3.691e+37
0.0
2.509e+37
0.0
6.200e+37
0.1
23
A1g
222
222
222
222
9.220e+39
8.6
1.138e+39
1.1
1.036e+40
9.6
24
A2u
237
237
237
261
25
Eg
414
414
414
414
3.031e+39
2.8
3.213e+39
3.0
6.244e+39
5.8
26
Eg
414
414
414
414
3.031e+39
2.8
3.221e+39
3.0
6.252e+39
5.8
27
Eu
416
416
416
416
28
Eu
416
416
416
416
29
Eu
579
579
579
579
30
Eu
579
581
581
579
31
Eg
581
581
581
581
1.384e+39
1.3
1.929e+39
1.8
3.313e+39
3.1
32
Eg
581
586
586
581
1.383e+39
1.3
1.472e+39
1.4
2.856e+39
2.7
33
A2u
589
589
589
595
34
A1g
600
600
600
600
8.186e+39
7.6
1.566e+38
0.1
8.342e+39
7.8
35
A2u
941
941
941
943
36
A1g
943
943
943
943
1.060e+41
98.8
1.320e+39
1.2
1.074e+41
100.0
37
Eg
1043
1043
1043
1043
8.507e+39
7.9
8.758e+39
8.2
1.726e+40
16.1
38
Eg
1043
1043
1043
1043
8.507e+39
7.9
1.425e+40
13.3
2.276e+40
21.2
39
Eu
1047
1047
1047
1047
40
Eu
1047
1115
1115
1047
41
A2u
1126
1126
1126
1136
42
A1g
1136
1136
1136
1179
7.745e+39
7.2
5.033e+39
4.7
1.278e+40
11.9
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.