-    SODIUM SULFATE     -    Na2SO4

Theoretical atomic positions and lattice parameters at experimental volum from ICSD database; code 81504 

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:  62  Pbnm 
Lattice parameters (Å):  5.3099  9.4693  7.1436 
Angles (°):  90.0  90.0  90.0 

Symmetry (theoretical): 

Space group:  62  Pbnm 
Lattice parameters (Å):  5.4153  9.4618  7.0101 
Angles (°):  90.0  90.0  90.0 

Cell contents: 

Number of atoms:  28 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Na:  0.0000  0.5000  0.0000 
Na:  0.9321  0.1478  0.2500 
S:  0.0228  0.8235  0.2500 
O:  0.0176  0.6665  0.2500 
O:  0.7654  0.8783  0.2500 
O:  0.1528  0.8739  0.0784 
Na:  0.5000  0.0000  0.0000 
Na:  0.4321  0.3522  0.7500 
S:  0.5228  0.6765  0.7500 
O:  0.5176  0.8335  0.7500 
O:  0.2654  0.6217  0.7500 
O:  0.6528  0.6261  0.9216 
Na:  0.0000  0.5000  0.5000 
Na:  0.0679  0.8522  0.7500 
S:  0.9772  0.1765  0.7500 
O:  0.9824  0.3335  0.7500 
O:  0.2346  0.1217  0.7500 
O:  0.8472  0.1261  0.5784 
Na:  0.5000  0.0000  0.5000 
Na:  0.5679  0.6478  0.2500 
S:  0.4772  0.3235  0.2500 
O:  0.4824  0.1665  0.2500 
O:  0.7346  0.3783  0.2500 
O:  0.3472  0.3739  0.4216 
O:  0.8472  0.1261  0.9216 
O:  0.3472  0.3739  0.0784 
O:  0.1528  0.8739  0.4216 
O:  0.6528  0.6261  0.5784 
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
Ac
0
0
0
0
2
Ac
0
0
0
0
3
Ac
0
0
0
0
4
B3u
34
52
34
34
5
B2u
52
53
53
52
6
B2g
53
55
63
53
5.135e+37
0.0
7.060e+37
0.1
1.220e+38
0.1
7
B3g
67
67
67
67
3.526e+37
0.0
4.848e+37
0.0
8.374e+37
0.1
8
Au
69
69
69
69
9
Au
72
72
72
72
10
B1u
73
73
73
80
11
Ag
80
80
80
88
1.398e+39
1.0
5.660e+37
0.0
1.454e+39
1.1
12
B1g
90
90
90
90
7.434e+37
0.1
1.022e+38
0.1
1.766e+38
0.1
13
B3u
93
95
93
93
14
B2u
95
95
95
95
15
Au
95
99
96
95
16
Ag
101
101
101
101
2.830e+39
2.1
4.556e+38
0.3
3.286e+39
2.4
17
Ag
110
110
110
110
1.278e+38
0.1
9.402e+37
0.1
2.218e+38
0.2
18
B1g
110
110
110
110
1.412e+38
0.1
1.941e+38
0.1
3.353e+38
0.2
19
B2u
118
118
121
118
20
B3u
121
121
121
121
21
B1g
121
123
123
121
1.877e+38
0.1
2.581e+38
0.2
4.458e+38
0.3
22
B1u
123
124
124
124
23
B1u
124
127
127
125
24
Ag
127
129
129
127
5.757e+37
0.0
3.653e+37
0.0
9.411e+37
0.1
25
B3g
129
130
130
129
2.514e+38
0.2
3.456e+38
0.3
5.970e+38
0.4
26
B1g
130
130
130
130
1.117e+38
0.1
1.536e+38
0.1
2.652e+38
0.2
27
Au
130
137
136
130
2.892e+37
0.0
3.977e+37
0.0
6.869e+37
0.0
28
B2u
144
144
149
144
29
B2g
149
149
153
149
5.196e+37
0.0
7.145e+37
0.1
1.234e+38
0.1
30
B2g
153
153
157
153
2.658e+37
0.0
3.655e+37
0.0
6.313e+37
0.0
31
B2u
157
157
158
157
32
B3u
158
163
169
158
33
Au
169
169
170
169
34
Ag
170
170
175
170
1.201e+39
0.9
1.128e+38
0.1
1.314e+39
1.0
35
B3g
175
175
181
175
9.737e+37
0.1
1.339e+38
0.1
2.313e+38
0.2
36
B1u
181
181
182
183
37
B1g
183
183
183
187
6.274e+37
0.0
8.627e+37
0.1
1.490e+38
0.1
38
B3u
187
189
187
188
39
B2g
189
190
189
189
6.931e+37
0.1
9.530e+37
0.1
1.646e+38
0.1
40
B1u
190
197
190
197
41
Au
197
200
197
200
42
B3g
200
200
200
203
6.812e+37
0.0
9.366e+37
0.1
1.618e+38
0.1
43
B3u
203
217
203
217
44
B2u
217
225
221
219
45
B1u
226
226
226
233
46
Au
233
233
233
240
47
B2u
240
240
253
253
48
B3u
253
279
280
258
49
Au
429
429
429
429
50
B1u
432
432
432
432
51
B3g
434
434
434
434
3.857e+39
2.8
5.304e+39
3.9
9.161e+39
6.7
52
Ag
440
440
440
440
1.268e+39
0.9
8.747e+38
0.6
2.143e+39
1.6
53
B2g
441
441
441
441
2.050e+39
1.5
2.818e+39
2.0
4.868e+39
3.5
54
B3u
445
445
445
445
55
B2u
446
446
446
446
56
B1g
449
449
449
449
3.157e+39
2.3
4.341e+39
3.2
7.498e+39
5.5
57
Ag
587
587
587
587
3.517e+39
2.6
2.574e+39
1.9
6.091e+39
4.4
58
B2u
588
588
589
588
59
B3u
589
594
594
589
60
B1g
594
594
594
594
8.721e+38
0.6
1.199e+39
0.9
2.071e+39
1.5
61
B1u
600
600
600
600
62
B2g
600
600
600
603
2.274e+39
1.7
3.126e+39
2.3
5.400e+39
3.9
63
Ag
603
603
603
606
3.452e+39
2.5
2.555e+39
1.9
6.007e+39
4.4
64
B1g
606
606
606
606
2.428e+38
0.2
3.339e+38
0.2
5.767e+38
0.4
65
B2u
606
606
608
608
66
B3u
608
611
610
611
67
Au
611
613
611
613
68
B3g
613
615
613
616
9.423e+38
0.7
1.296e+39
0.9
2.238e+39
1.6
69
B1g
962
962
962
962
1.512e+38
0.1
2.079e+38
0.2
3.590e+38
0.3
70
B3u
963
963
963
963
71
B2u
963
964
963
963
72
Ag
964
965
964
964
1.374e+41
99.9
1.111e+38
0.1
1.376e+41
100.0
73
Ag
1057
1057
1057
1057
5.281e+39
3.8
3.761e+39
2.7
9.043e+39
6.6
74
B2u
1075
1075
1086
1075
75
B3u
1086
1087
1087
1086
76
B1g
1087
1089
1089
1087
1.373e+39
1.0
1.888e+39
1.4
3.260e+39
2.4
77
Ag
1089
1091
1094
1089
7.800e+39
5.7
3.641e+39
2.6
1.144e+40
8.3
78
B3u
1094
1106
1102
1094
79
B1u
1106
1123
1106
1123
80
B2u
1123
1128
1128
1128
81
Au
1128
1132
1132
1132
82
B2g
1132
1162
1162
1162
4.482e+39
3.3
6.163e+39
4.5
1.064e+40
7.7
83
B3g
1162
1168
1172
1172
1.468e+39
1.1
2.018e+39
1.5
3.486e+39
2.5
84
B1g
1172
1172
1176
1190
4.089e+36
0.0
5.623e+36
0.0
9.712e+36
0.0
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.