-    Magnesium Sulfate-beta     -    MgSO4

 

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):  4.7343  8.5817  6.6726 
Angles (°):  90  90  90 

Symmetry (theoretical): 

Space group:  62  Pbnm 
Lattice parameters (Å):  4.6788  8.4992  6.5056 
Angles (°):  90  90  90 

Cell contents: 

Number of atoms:  24 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Mg:  0.0000  0.0000  0.0000 
S:  0.4783  0.1788  0.2500 
O:  0.7792  0.1246  0.2500 
O:  0.4609  0.3541  0.2500 
O:  0.3386  0.1242  0.0638 
Mg:  0.5000  0.5000  0.0000 
S:  0.9783  0.3212  0.7500 
O:  0.2792  0.3754  0.7500 
O:  0.9609  0.1459  0.7500 
O:  0.8386  0.3758  0.9362 
Mg:  0.0000  0.0000  0.5000 
S:  0.5217  0.8212  0.7500 
O:  0.2208  0.8754  0.7500 
O:  0.5391  0.6459  0.7500 
O:  0.6614  0.8758  0.5638 
Mg:  0.5000  0.5000  0.5000 
S:  0.0217  0.6788  0.2500 
O:  0.7208  0.6246  0.2500 
O:  0.0391  0.8541  0.2500 
O:  0.1614  0.6242  0.4362 
O:  0.6614  0.8758  0.9362 
O:  0.1614  0.6242  0.0638 
O:  0.3386  0.1242  0.4362 
O:  0.8386  0.3758  0.5638 
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
B2u
86
86
86
86
5
Au
115
115
115
115
6
B2g
119
119
119
119
7.975e+36
0.0
1.097e+37
0.0
1.894e+37
0.0
7
B1u
127
127
127
143
8
Au
143
143
143
147
9
B3u
147
148
147
149
10
B3g
154
154
154
154
3.471e+38
0.3
4.772e+38
0.4
8.243e+38
0.6
11
Au
160
160
160
160
12
A1g
165
165
165
165
7.257e+37
0.1
2.419e+37
0.0
9.676e+37
0.1
13
Au
176
176
176
176
14
B1u
178
178
178
178
15
B1g
178
178
178
191
2.163e+36
0.0
2.973e+36
0.0
5.136e+36
0.0
16
B2u
199
199
204
199
17
B1u
204
204
209
209
18
B1g
209
209
216
214
3.176e+38
0.2
4.366e+38
0.3
7.542e+38
0.6
19
B3u
216
216
218
216
20
A1g
218
218
233
218
6.309e+39
4.7
6.228e+38
0.5
6.932e+39
5.1
21
B3g
241
241
241
241
8.312e+38
0.6
1.143e+39
0.8
1.974e+39
1.5
22
A1g
243
243
243
243
2.938e+38
0.2
4.821e+37
0.0
3.420e+38
0.3
23
B2u
250
250
254
250
24
B3u
254
259
259
254
25
B1g
259
260
260
259
2.261e+38
0.2
3.109e+38
0.2
5.370e+38
0.4
26
B2g
260
269
269
260
4.524e+38
0.3
6.221e+38
0.5
1.075e+39
0.8
27
B2g
269
297
270
269
4.464e+37
0.0
6.138e+37
0.0
1.060e+38
0.1
28
Au
297
304
297
297
29
B1u
304
307
304
307
30
B3g
307
325
307
321
8.199e+38
0.6
1.127e+39
0.8
1.947e+39
1.4
31
B3u
341
342
341
341
32
B2u
371
371
404
371
33
B2u
404
404
417
404
34
Au
417
417
420
417
35
B3u
420
428
424
420
36
B1u
429
429
429
437
37
A1g
437
437
437
458
1.477e+40
11.0
1.396e+39
1.0
1.616e+40
12.0
38
B1g
461
461
461
461
6.470e+39
4.8
8.896e+39
6.6
1.537e+40
11.4
39
B3g
493
493
493
493
4.135e+39
3.1
5.686e+39
4.2
9.820e+39
7.3
40
B1u
495
495
495
503
41
B2g
503
503
503
503
4.677e+39
3.5
6.431e+39
4.8
1.111e+40
8.2
42
B2u
504
504
506
504
43
Au
506
506
506
506
44
B3u
506
524
527
506
45
B1g
582
582
582
582
1.113e+39
0.8
1.531e+39
1.1
2.644e+39
2.0
46
A1g
586
586
586
586
1.100e+40
8.2
5.921e+39
4.4
1.692e+40
12.6
47
B3u
589
591
589
589
48
B2u
591
598
594
591
49
A1g
598
609
598
598
9.894e+39
7.3
5.948e+39
4.4
1.584e+40
11.8
50
B2u
609
611
611
609
51
B1g
611
612
612
611
8.921e+38
0.7
1.227e+39
0.9
2.119e+39
1.6
52
B3u
624
624
624
624
53
B2g
668
668
668
668
1.749e+39
1.3
2.405e+39
1.8
4.155e+39
3.1
54
B1u
686
686
686
688
55
B3g
688
688
688
707
1.226e+39
0.9
1.686e+39
1.3
2.912e+39
2.2
56
Au
707
707
707
718
57
B1g
995
995
995
995
1.192e+39
0.9
1.639e+39
1.2
2.831e+39
2.1
58
B3u
998
1006
998
998
59
A1g
1006
1006
1006
1006
1.333e+41
98.9
1.472e+39
1.1
1.348e+41
100.0
60
B2u
1008
1008
1013
1008
61
A1g
1036
1036
1036
1036
1.649e+40
12.2
4.831e+39
3.6
2.133e+40
15.8
62
B2u
1058
1058
1098
1058
63
B3u
1098
1107
1116
1098
64
B1g
1116
1116
1123
1116
1.622e+39
1.2
2.230e+39
1.7
3.852e+39
2.9
65
A1g
1128
1128
1128
1128
3.703e+40
27.5
2.809e+39
2.1
3.984e+40
29.6
66
B3u
1138
1168
1138
1138
67
B2u
1168
1196
1196
1168
68
B1u
1196
1213
1213
1213
69
B1g
1213
1223
1223
1223
1.286e+37
0.0
1.768e+37
0.0
3.054e+37
0.0
70
Au
1223
1225
1223
1225
71
B2g
1225
1243
1225
1260
5.865e+39
4.4
8.065e+39
6.0
1.393e+40
10.3
72
B3g
1260
1260
1260
1293
1.397e+39
1.0
1.921e+39
1.4
3.317e+39
2.5
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.