-    VANTHOFFITE     -    Na6Mg(SO4)4

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 AMCSD 

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:  14  P2_1/c 
Lattice parameters (Å):  9.7970  9.2170  8.1990 
Angles (°):  90.0  113.5  90.0 

Symmetry (theoretical): 

Space group:  14  P2_1/c 
Lattice parameters (Å):  9.4940  8.9834  7.9164 
Angles (°):  90.0  113.1  90.0 

Cell contents: 

Number of atoms:  54 
Number of atom types:  4 
Chemical composition:  0 

Atomic positions (theoretical):

Na:  0.3138  0.0151  0.4644 
Na:  0.4453  0.1517  0.0904 
Na:  0.8860  0.1337  0.3169 
Mg:  0.0000  1.0000  0.0000 
S:  0.1425  0.3056  0.2218 
O:  0.0272  0.1847  0.1554 
O:  0.1349  0.3977  0.0649 
O:  0.1027  0.3992  0.3489 
O:  0.2957  0.2407  0.3143 
S:  0.6601  0.3508  0.3457 
O:  0.6667  0.1877  0.3609 
O:  0.6443  0.4170  0.5058 
O:  0.8027  0.4039  0.3283 
O:  0.5321  0.3956  0.1754 
Na:  0.6862  0.5151  0.0356 
Na:  0.5547  0.6517  0.4096 
Na:  0.1140  0.6337  0.1831 
Mg:  0.0000  0.5000  0.5000 
S:  0.8575  0.8056  0.2782 
O:  0.9728  0.6847  0.3446 
O:  0.8651  0.8977  0.4351 
O:  0.8973  0.8992  0.1511 
O:  0.7043  0.7407  0.1857 
S:  0.3399  0.8508  0.1543 
O:  0.3333  0.6877  0.1391 
O:  0.3557  0.9170  0.9942 
O:  0.1973  0.9039  0.1717 
O:  0.4679  0.8956  0.3246 
Na:  0.6862  0.9849  0.5356 
Na:  0.5547  0.8483  0.9096 
Na:  0.1140  0.8663  0.6831 
S:  0.8575  0.6944  0.7782 
O:  0.9728  0.8153  0.8446 
O:  0.8651  0.6023  0.9351 
O:  0.8973  0.6008  0.6511 
O:  0.7043  0.7593  0.6857 
S:  0.3399  0.6492  0.6543 
O:  0.3333  0.8123  0.6391 
O:  0.3557  0.5830  0.4942 
O:  0.1973  0.5961  0.6717 
O:  0.4679  0.6044  0.8246 
Na:  0.3138  0.4849  0.9644 
Na:  0.4453  0.3483  0.5904 
Na:  0.8860  0.3663  0.8169 
S:  0.1425  0.1944  0.7218 
O:  0.0272  0.3153  0.6554 
O:  0.1349  0.1023  0.5649 
O:  0.1027  0.1008  0.8489 
O:  0.2957  0.2593  0.8143 
S:  0.6601  0.1492  0.8457 
O:  0.6667  0.3123  0.8609 
O:  0.6443  0.0830  0.0058 
O:  0.8027  0.0961  0.8283 
O:  0.5321  0.1044  0.6754 
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
ac
0
0
0
0
2
ac
0
0
0
0
3
ac
0
0
0
0
4
Au
41
41
41
41
5
Au
70
70
70
70
6
Bu
73
74
73
75
7
Ag
75
75
75
78
4.104e+38
0.4
5.768e+37
0.1
4.681e+38
0.5
8
Bg
78
78
78
79
6.247e+37
0.1
7.771e+37
0.1
1.402e+38
0.1
9
Ag
80
80
80
80
1.835e+38
0.2
1.634e+38
0.2
3.469e+38
0.3
10
Bg
93
93
93
93
7.000e+37
0.1
1.175e+38
0.1
1.875e+38
0.2
11
Ag
93
93
93
93
4.451e+38
0.4
3.964e+37
0.0
4.847e+38
0.5
12
Bu
96
96
96
96
13
Au
97
97
98
97
14
Bg
98
98
99
98
1.868e+38
0.2
2.006e+38
0.2
3.874e+38
0.4
15
Ag
102
102
102
102
3.042e+38
0.3
5.909e+37
0.1
3.633e+38
0.4
16
Au
103
103
103
103
17
Bu
108
109
108
109
18
Au
109
109
109
110
19
Bu
112
116
112
114
20
Ag
116
116
116
116
2.019e+39
2.0
5.969e+37
0.1
2.079e+39
2.1
21
Bg
117
117
117
117
1.707e+37
0.0
2.347e+37
0.0
4.054e+37
0.0
22
Au
117
117
118
117
23
Bg
118
118
120
118
7.878e+36
0.0
1.083e+37
0.0
1.871e+37
0.0
24
Bu
122
127
122
124
25
Bg
127
127
127
127
1.515e+37
0.0
2.083e+37
0.0
3.597e+37
0.0
26
Au
135
135
135
135
27
Ag
135
135
135
135
7.024e+37
0.1
1.538e+37
0.0
8.561e+37
0.1
28
Bg
138
138
138
138
3.706e+37
0.0
4.311e+37
0.0
8.017e+37
0.1
29
Ag
138
138
138
138
5.435e+38
0.5
5.118e+37
0.1
5.947e+38
0.6
30
Bu
139
142
139
141
31
Au
143
143
143
143
32
Ag
143
143
143
143
3.935e+38
0.4
2.507e+38
0.3
6.442e+38
0.6
33
Au
146
146
147
146
34
Bg
150
150
150
150
3.414e+37
0.0
5.105e+37
0.1
8.519e+37
0.1
35
Bu
150
150
150
150
36
Ag
151
151
151
151
9.828e+37
0.1
4.003e+37
0.0
1.383e+38
0.1
37
Bu
155
155
155
156
38
Bg
156
156
156
158
2.116e+37
0.0
3.411e+37
0.0
5.527e+37
0.1
39
Au
158
158
161
161
40
Ag
161
161
161
161
1.241e+38
0.1
8.216e+37
0.1
2.062e+38
0.2
41
Bg
162
162
162
162
1.621e+38
0.2
2.655e+38
0.3
4.276e+38
0.4
42
Bu
162
164
162
164
43
Au
165
165
166
165
44
Bu
169
169
169
171
45
Ag
171
171
171
171
4.266e+38
0.4
1.101e+38
0.1
5.368e+38
0.5
46
Bg
171
171
171
171
2.923e+36
0.0
4.019e+36
0.0
6.941e+36
0.0
47
Au
179
179
179
179
48
Bu
185
185
185
185
49
Ag
185
185
185
185
5.002e+37
0.0
7.589e+37
0.1
1.259e+38
0.1
50
Bg
185
190
185
189
1.390e+38
0.1
1.363e+38
0.1
2.754e+38
0.3
51
Au
192
192
192
192
52
Bu
193
193
193
194
53
Ag
200
200
200
200
2.174e+38
0.2
8.526e+37
0.1
3.026e+38
0.3
54
Bg
206
206
206
206
3.914e+37
0.0
5.844e+37
0.1
9.758e+37
0.1
55
Ag
207
207
207
207
56
Au
207
207
208
207
2.899e+38
0.3
2.034e+38
0.2
4.932e+38
0.5
57
Au
209
209
209
209
58
Bu
209
210
210
209
59
Bg
210
211
210
210
1.062e+38
0.1
1.321e+38
0.1
2.383e+38
0.2
60
Ag
213
213
213
213
8.188e+38
0.8
1.333e+38
0.1
9.521e+38
1.0
61
Bu
218
218
218
219
62
Au
219
219
220
220
63
Bg
220
220
222
222
6.364e+37
0.1
8.751e+37
0.1
1.512e+38
0.2
64
Ag
222
222
222
223
3.811e+38
0.4
1.830e+38
0.2
5.640e+38
0.6
65
Bg
223
223
223
224
1.584e+37
0.0
2.673e+37
0.0
4.258e+37
0.0
66
Bu
229
230
229
229
67
Bu
234
236
234
236
68
Bg
236
238
236
238
1.387e+38
0.1
2.319e+38
0.2
3.706e+38
0.4
69
Ag
238
239
238
238
4.766e+37
0.0
4.654e+37
0.0
9.419e+37
0.1
70
Bg
239
240
239
239
3.351e+37
0.0
4.179e+37
0.0
7.530e+37
0.1
71
Ag
241
241
241
241
1.666e+39
1.7
1.853e+38
0.2
1.852e+39
1.8
72
Bg
242
242
242
242
2.745e+37
0.0
4.426e+37
0.0
7.170e+37
0.1
73
Au
245
245
245
245
74
Au
248
248
248
248
75
Bu
248
251
251
251
76
Ag
251
254
251
258
2.233e+37
0.0
1.598e+37
0.0
3.831e+37
0.0
77
Au
259
259
268
259
78
Ag
268
268
270
268
2.458e+38
0.2
3.867e+37
0.0
2.845e+38
0.3
79
Bg
270
270
273
270
7.679e+36
0.0
1.292e+37
0.0
2.060e+37
0.0
80
Bu
273
276
277
274
81
Bg
279
279
279
279
1.707e+38
0.2
2.840e+38
0.3
4.547e+38
0.5
82
Au
280
280
283
280
83
Bu
283
287
287
287
84
Ag
287
287
287
290
2.281e+38
0.2
5.603e+37
0.1
2.841e+38
0.3
85
Au
316
316
330
316
86
Bu
332
338
332
339
87
Au
343
343
344
343
88
Bu
350
358
350
358
89
Bu
358
368
358
366
90
Au
368
380
394
368
91
Bg
439
439
439
439
1.327e+38
0.1
1.674e+38
0.2
3.001e+38
0.3
92
Ag
441
441
441
441
3.396e+39
3.4
2.564e+39
2.6
5.959e+39
6.0
93
Bu
442
442
442
442
94
Ag
443
443
443
443
2.982e+38
0.3
2.316e+38
0.2
5.298e+38
0.5
95
Au
444
444
444
444
96
Au
447
447
447
447
97
Bg
448
448
448
448
2.694e+39
2.7
3.119e+39
3.1
5.813e+39
5.8
98
Bu
451
451
451
451
99
Ag
468
468
468
468
2.856e+39
2.9
2.015e+39
2.0
4.872e+39
4.9
100
Ag
473
473
473
473
1.366e+39
1.4
1.178e+39
1.2
2.544e+39
2.5
101
Bu
474
474
474
475
102
Au
475
475
475
475
103
Bg
476
476
476
476
1.836e+39
1.8
2.828e+39
2.8
4.664e+39
4.7
104
Bu
477
478
477
477
105
Bg
478
478
478
478
3.544e+37
0.0
4.262e+37
0.0
7.806e+37
0.1
106
Au
486
486
488
486
107
Ag
586
586
586
586
1.592e+39
1.6
1.599e+39
1.6
3.190e+39
3.2
108
Bu
587
587
587
592
109
Au
592
592
593
592
110
Bg
597
597
597
597
7.692e+38
0.8
1.151e+39
1.2
1.921e+39
1.9
111
Au
604
604
606
604
112
Ag
606
606
606
606
1.778e+39
1.8
1.186e+39
1.2
2.963e+39
3.0
113
Bg
606
606
607
606
7.020e+38
0.7
7.508e+38
0.8
1.453e+39
1.5
114
Bu
607
608
608
608
115
Bg
608
610
610
609
2.958e+38
0.3
3.380e+38
0.3
6.339e+38
0.6
116
Ag
610
611
611
610
2.443e+39
2.4
2.275e+39
2.3
4.718e+39
4.7
117
Au
611
611
612
611
118
Bu
612
612
613
615
119
Ag
616
616
616
616
1.653e+39
1.7
1.775e+39
1.8
3.428e+39
3.4
120
Bg
617
617
617
617
1.272e+39
1.3
1.016e+39
1.0
2.288e+39
2.3
121
Au
624
624
624
624
122
Bu
624
624
624
624
123
Ag
624
625
625
625
2.373e+39
2.4
1.629e+39
1.6
4.002e+39
4.0
124
Ag
625
629
625
629
2.470e+39
2.5
2.202e+39
2.2
4.672e+39
4.7
125
Bu
629
633
629
631
126
Bg
633
633
633
633
2.484e+39
2.5
4.133e+39
4.1
6.617e+39
6.6
127
Bu
635
635
635
637
128
Bg
637
637
637
639
1.193e+38
0.1
2.005e+38
0.2
3.198e+38
0.3
129
Au
639
639
639
640
130
Au
643
643
644
643
131
Bg
990
990
990
990
8.857e+37
0.1
9.908e+37
0.1
1.876e+38
0.2
132
Au
991
991
991
991
133
Ag
991
991
991
991
4.775e+40
47.7
2.188e+38
0.2
4.797e+40
47.9
134
Bu
992
994
992
992
135
Bg
1001
1001
1001
1001
3.955e+37
0.0
4.304e+37
0.0
8.259e+37
0.1
136
Ag
1004
1004
1004
1004
1.000e+41
99.9
7.852e+37
0.1
1.001e+41
100.0
137
Bu
1004
1004
1004
1005
138
Au
1005
1005
1005
1005
139
Ag
1074
1074
1074
1074
1.667e+39
1.7
1.793e+39
1.8
3.461e+39
3.5
140
Bg
1078
1078
1078
1078
1.322e+39
1.3
1.770e+39
1.8
3.093e+39
3.1
141
Bu
1082
1091
1082
1084
142
Au
1091
1099
1092
1091
143
Ag
1099
1105
1099
1099
5.141e+39
5.1
1.320e+39
1.3
6.461e+39
6.5
144
Bu
1107
1107
1107
1107
145
Au
1107
1121
1122
1107
146
Bg
1122
1122
1122
1122
2.240e+39
2.2
2.417e+39
2.4
4.656e+39
4.7
147
Bu
1126
1130
1126
1130
148
Ag
1130
1139
1130
1143
2.119e+39
2.1
1.600e+39
1.6
3.719e+39
3.7
149
Au
1143
1143
1149
1150
150
Ag
1152
1152
1152
1152
2.949e+39
2.9
2.787e+39
2.8
5.737e+39
5.7
151
Au
1157
1157
1158
1157
152
Bu
1158
1159
1159
1159
153
Bg
1159
1161
1162
1162
8.165e+38
0.8
1.369e+39
1.4
2.186e+39
2.2
154
Au
1163
1163
1164
1163
155
Bu
1164
1165
1167
1166
156
Bu
1167
1181
1181
1181
157
Ag
1181
1191
1184
1191
1.681e+39
1.7
1.718e+39
1.7
3.399e+39
3.4
158
Au
1191
1195
1195
1195
159
Bg
1195
1199
1199
1199
1.064e+39
1.1
1.790e+39
1.8
2.854e+39
2.9
160
Ag
1199
1205
1205
1205
2.390e+39
2.4
3.046e+39
3.0
5.435e+39
5.4
161
Bg
1205
1209
1228
1227
1.553e+39
1.6
2.570e+39
2.6
4.123e+39
4.1
162
Bg
1228
1228
1232
1228
4.394e+38
0.4
7.209e+38
0.7
1.160e+39
1.2
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.