-    LORENZENITE     -    Na2Ti2Si2O9

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:  60  Pbcn 
Lattice parameters (Å):  11.8063  11.8063  11.8063 
Angles (°):  90  90  90 

Symmetry (theoretical): 

Space group:  60  Pbcn 
Lattice parameters (Å):  8.5572  5.1506  14.1978 
Angles (°):  90  90  90 

Cell contents: 

Number of atoms:  60 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Na:  0.0596  0.6411  0.1527 
Ti:  0.1532  0.1311  0.3295 
Si:  0.3426  0.2991  0.5273 
O:  1.0000  0.9978  0.2500 
O:  0.1782  0.4473  0.2744 
O:  0.3330  0.2989  0.4147 
O:  0.0102  0.2455  0.4281 
O:  0.2335  0.0648  0.5690 
Na:  0.4404  0.8589  0.6527 
Ti:  0.3468  0.3689  0.8295 
Si:  0.1574  0.2009  0.0273 
O:  0.5000  0.5022  0.7500 
O:  0.3218  0.0527  0.7744 
O:  0.1670  0.2011  0.9147 
O:  0.4898  0.2545  0.9281 
O:  0.2665  0.4352  0.0690 
Na:  0.9404  0.6411  0.3473 
Ti:  0.8468  0.1311  0.1705 
Si:  0.6574  0.2991  0.9727 
O:  0.8218  0.4473  0.2256 
O:  0.6670  0.2989  0.0853 
O:  0.9898  0.2455  0.0719 
O:  0.7665  0.0648  0.9310 
Na:  0.5596  0.8589  0.8473 
Ti:  0.6532  0.3689  0.6705 
Si:  0.8426  0.2009  0.4727 
O:  0.6782  0.0527  0.7256 
O:  0.8330  0.2011  0.5853 
O:  0.5102  0.2545  0.5719 
O:  0.7335  0.4352  0.4310 
Na:  0.9404  0.3589  0.8473 
Ti:  0.8468  0.8689  0.6705 
Si:  0.6574  0.7009  0.4727 
O:  1.0000  0.0022  0.7500 
O:  0.8218  0.5527  0.7256 
O:  0.6670  0.7011  0.5853 
O:  0.9898  0.7545  0.5719 
O:  0.7665  0.9352  0.4310 
Na:  0.5596  0.1411  0.3473 
Ti:  0.6532  0.6311  0.1705 
Si:  0.8426  0.7991  0.9727 
O:  0.5000  0.4978  0.2500 
O:  0.6782  0.9473  0.2256 
O:  0.8330  0.7989  0.0853 
O:  0.5102  0.7455  0.0719 
O:  0.7335  0.5648  0.9310 
Na:  0.0596  0.3589  0.6527 
Ti:  0.1532  0.8689  0.8295 
Si:  0.3426  0.7009  0.0273 
O:  0.1782  0.5527  0.7744 
O:  0.3330  0.7011  0.9147 
O:  0.0102  0.7545  0.9281 
O:  0.2335  0.9352  0.0690 
Na:  0.4404  0.1411  0.1527 
Ti:  0.3468  0.6311  0.3295 
Si:  0.1574  0.7991  0.5273 
O:  0.3218  0.9473  0.2744 
O:  0.1670  0.7989  0.4147 
O:  0.4898  0.7455  0.4281 
O:  0.2665  0.5648  0.5690 
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
B1u
73
73
73
73
5
Au
89
89
89
89
6
Ag
91
91
91
91
1.958e+39
1.3
1.469e+39
0.9
3.427e+39
2.2
7
Ag
109
109
109
109
1.164e+39
0.7
4.640e+38
0.3
1.628e+39
1.0
8
B3u
111
111
111
111
9
B1g
112
112
112
112
9.117e+38
0.6
1.254e+39
0.8
2.165e+39
1.4
10
B3g
112
112
112
112
1.171e+38
0.1
1.610e+38
0.1
2.781e+38
0.2
11
B3g
127
127
127
127
8.450e+39
5.4
1.162e+40
7.4
2.007e+40
12.9
12
B2u
129
129
130
129
13
B1g
139
139
139
139
1.764e+39
1.1
2.425e+39
1.6
4.189e+39
2.7
14
B2g
140
140
140
140
3.452e+39
2.2
4.747e+39
3.0
8.199e+39
5.3
15
B3g
146
146
146
146
1.733e+39
1.1
2.382e+39
1.5
4.115e+39
2.6
16
B2u
154
154
155
154
17
B1g
155
155
155
155
1.289e+39
0.8
1.773e+39
1.1
3.062e+39
2.0
18
B1u
157
157
157
158
19
Au
164
164
164
164
20
Ag
165
165
165
165
5.640e+38
0.4
3.981e+38
0.3
9.621e+38
0.6
21
B2g
170
170
170
170
1.141e+38
0.1
1.569e+38
0.1
2.711e+38
0.2
22
B1u
170
170
170
171
23
B3u
171
172
171
172
24
B2u
172
172
174
172
25
Ag
174
174
174
174
1.316e+39
0.8
7.033e+38
0.5
2.019e+39
1.3
26
B3g
174
174
174
174
1.772e+38
0.1
2.436e+38
0.2
4.208e+38
0.3
27
B3u
177
177
177
177
28
Au
177
178
177
177
29
B1g
178
180
178
178
2.826e+39
1.8
3.886e+39
2.5
6.712e+39
4.3
30
B3g
180
180
180
180
2.229e+37
0.0
3.064e+37
0.0
5.293e+37
0.0
31
B1u
190
190
190
190
32
B2u
190
190
194
190
33
B3u
198
198
198
198
34
Ag
198
199
198
198
6.392e+39
4.1
1.180e+39
0.8
7.572e+39
4.8
35
B3g
199
201
199
199
1.592e+39
1.0
2.190e+39
1.4
3.782e+39
2.4
36
B1g
201
203
201
201
3.762e+38
0.2
5.173e+38
0.3
8.935e+38
0.6
37
B1u
211
211
211
211
38
B2g
211
211
211
215
1.795e+40
11.5
2.468e+40
15.8
4.262e+40
27.3
39
B2g
215
215
215
216
9.808e+37
0.1
1.349e+38
0.1
2.329e+38
0.1
40
Au
216
216
216
217
41
B2u
217
217
218
217
42
Ag
218
218
222
218
1.185e+40
7.6
3.618e+38
0.2
1.221e+40
7.8
43
B3g
222
222
224
222
2.409e+38
0.2
3.312e+38
0.2
5.721e+38
0.4
44
Au
225
225
225
225
45
B1g
229
229
229
229
1.030e+40
6.6
1.416e+40
9.1
2.445e+40
15.7
46
B3u
230
231
230
230
47
B2g
231
232
231
231
4.938e+37
0.0
6.790e+37
0.0
1.173e+38
0.1
48
B1u
232
234
232
232
49
B3g
234
235
234
234
50
B1u
238
238
238
246
51
B2g
250
250
250
250
7.848e+39
5.0
1.079e+40
6.9
1.864e+40
11.9
52
Au
251
251
251
251
53
Ag
252
252
252
252
1.379e+40
8.8
6.897e+39
4.4
2.069e+40
13.3
54
B1u
258
258
258
259
55
B2u
259
259
262
259
56
B2g
262
262
262
262
1.721e+39
1.1
2.366e+39
1.5
4.086e+39
2.6
57
Au
267
267
267
267
58
B1g
268
268
268
268
2.579e+39
1.7
3.546e+39
2.3
6.125e+39
3.9
59
B3g
268
268
268
268
4.097e+38
0.3
5.634e+38
0.4
9.731e+38
0.6
60
B1g
272
272
272
272
5.253e+38
0.3
7.223e+38
0.5
1.248e+39
0.8
61
B2u
274
274
274
274
62
B3u
275
276
275
275
63
B1u
277
277
277
279
64
B2g
279
279
279
282
1.190e+40
7.6
1.637e+40
10.5
2.827e+40
18.1
65
B3u
282
282
282
282
66
Ag
282
282
282
283
4.026e+40
25.8
3.892e+39
2.5
4.415e+40
28.3
67
Au
283
283
283
286
68
B3g
286
286
286
287
5.356e+39
3.4
7.364e+39
4.7
1.272e+40
8.1
69
B2u
288
288
290
288
70
Ag
292
292
292
292
1.660e+40
10.6
1.157e+40
7.4
2.817e+40
18.0
71
B1u
299
299
299
299
72
Ag
299
299
299
303
1.526e+40
9.8
4.467e+39
2.9
1.973e+40
12.6
73
B3u
303
308
303
308
74
B2u
308
309
316
316
75
B1g
316
316
316
316
2.279e+37
0.0
3.133e+37
0.0
5.412e+37
0.0
76
Au
316
316
317
317
77
B2g
317
317
319
319
1.108e+39
0.7
1.523e+39
1.0
2.631e+39
1.7
78
B3u
319
323
320
323
79
B3g
323
329
323
328
1.455e+40
9.3
2.000e+40
12.8
3.455e+40
22.1
80
Au
329
329
329
329
81
B1g
329
330
329
329
2.678e+40
17.1
3.682e+40
23.6
6.359e+40
40.7
82
B2g
333
333
333
333
1.161e+38
0.1
1.596e+38
0.1
2.757e+38
0.2
83
B3u
335
337
335
335
84
Ag
337
341
337
337
4.030e+40
25.8
6.158e+39
3.9
4.646e+40
29.8
85
B1u
341
341
341
341
7.814e+36
0.0
1.074e+37
0.0
1.856e+37
0.0
86
B3g
341
342
341
342
2.062e+39
1.3
2.836e+39
1.8
4.898e+39
3.1
87
B1g
342
345
342
345
5.461e+39
3.5
7.508e+39
4.8
1.297e+40
8.3
88
Ag
345
346
345
354
1.816e+40
11.6
3.928e+38
0.3
1.855e+40
11.9
89
B2g
354
354
354
354
4.011e+39
2.6
5.515e+39
3.5
9.525e+39
6.1
90
B2u
358
358
358
358
4.548e+36
0.0
6.253e+36
0.0
1.080e+37
0.0
91
B3g
358
358
359
358
2.034e+38
0.1
2.796e+38
0.2
4.830e+38
0.3
92
B1g
360
360
360
360
1.211e+39
0.8
1.665e+39
1.1
2.876e+39
1.8
93
B1g
371
371
371
371
7.951e+39
5.1
1.093e+40
7.0
1.888e+40
12.1
94
B3u
376
377
376
376
95
Au
378
378
378
378
96
B2g
382
382
382
382
1.381e+39
0.9
1.900e+39
1.2
3.281e+39
2.1
97
B2u
386
386
386
386
98
B3u
387
388
387
387
99
B1u
388
389
388
389
100
Ag
389
390
389
389
3.484e+40
22.3
1.956e+39
1.3
3.680e+40
23.6
101
B3g
390
392
390
390
1.008e+39
0.6
1.386e+39
0.9
2.394e+39
1.5
102
Au
392
395
392
392
103
B1u
410
410
410
411
104
B2u
411
411
428
415
105
B2g
429
429
429
429
1.487e+39
1.0
2.045e+39
1.3
3.532e+39
2.3
106
B1u
430
430
430
432
107
B2u
432
432
437
437
108
B1g
437
437
442
440
6.469e+36
0.0
8.895e+36
0.0
1.536e+37
0.0
109
Au
442
442
445
442
110
B3u
445
466
464
445
111
Ag
469
469
469
469
2.899e+39
1.9
1.420e+39
0.9
4.319e+39
2.8
112
B3g
477
477
477
477
1.626e+38
0.1
2.235e+38
0.1
3.861e+38
0.2
113
B2u
487
487
492
487
114
B3u
492
493
493
492
115
Au
493
494
494
493
116
B1u
494
494
495
495
117
Ag
499
499
499
499
5.646e+39
3.6
4.986e+38
0.3
6.145e+39
3.9
118
Au
501
501
501
501
119
B1g
502
502
502
502
1.612e+38
0.1
2.216e+38
0.1
3.827e+38
0.2
120
B3u
503
504
503
503
121
B2g
504
505
504
504
7.737e+35
0.0
1.064e+36
0.0
1.838e+36
0.0
122
B3g
505
509
505
505
3.576e+39
2.3
4.917e+39
3.1
8.493e+39
5.4
123
B2g
509
509
509
509
3.908e+39
2.5
5.373e+39
3.4
9.281e+39
5.9
124
B1g
514
514
514
514
5.908e+40
37.8
8.124e+40
52.0
1.403e+41
89.9
125
Ag
517
517
517
517
3.549e+40
22.7
1.542e+40
9.9
5.092e+40
32.6
126
B2u
518
518
519
518
127
Au
519
519
520
519
128
B3u
520
525
525
520
129
B3g
525
533
533
525
2.246e+39
1.4
3.088e+39
2.0
5.334e+39
3.4
130
Ag
533
533
533
533
9.529e+40
61.0
3.088e+39
2.0
9.837e+40
63.0
131
B1u
533
544
536
536
132
B2u
544
578
578
544
133
B2g
578
584
584
578
7.156e+39
4.6
9.839e+39
6.3
1.699e+40
10.9
134
B1g
584
614
602
584
2.593e+39
1.7
3.565e+39
2.3
6.157e+39
3.9
135
B3u
615
616
615
615
136
B1g
616
633
616
616
1.596e+39
1.0
2.194e+39
1.4
3.790e+39
2.4
137
Au
633
639
633
633
138
B1u
639
639
639
639
8.445e+39
5.4
1.789e+38
0.1
8.624e+39
5.5
139
Ag
639
647
639
647
1.529e+41
97.9
3.239e+39
2.1
1.561e+41
100.0
140
B2u
647
648
648
648
141
B2g
648
655
655
655
2.612e+40
16.7
3.592e+40
23.0
6.204e+40
39.7
142
B3g
655
672
672
659
2.485e+39
1.6
3.417e+39
2.2
5.902e+39
3.8
143
B1u
672
675
675
674
144
B3g
675
678
686
675
7.708e+37
0.0
1.060e+38
0.1
1.831e+38
0.1
145
B2u
693
693
698
693
146
B1u
698
698
701
701
147
Ag
701
701
715
715
1.109e+41
71.1
8.945e+38
0.6
1.118e+41
71.6
148
Au
715
715
716
716
149
B2g
716
716
732
732
1.567e+39
1.0
2.155e+39
1.4
3.722e+39
2.4
150
B3u
732
736
737
737
151
Au
737
737
741
741
152
B1g
741
741
746
751
2.235e+39
1.4
3.074e+39
2.0
5.309e+39
3.4
153
B3u
751
754
751
754
154
B2g
754
759
754
759
6.564e+38
0.4
9.026e+38
0.6
1.559e+39
1.0
155
B1g
759
762
759
804
156
B3g
804
804
804
810
1.799e+38
0.1
2.474e+38
0.2
4.273e+38
0.3
157
Au
894
894
894
894
158
B3u
895
895
895
895
159
B1g
895
896
895
895
4.924e+39
3.2
6.771e+39
4.3
1.170e+40
7.5
160
B2g
896
902
896
896
6.758e+39
4.3
9.293e+39
6.0
1.605e+40
10.3
161
B1u
939
939
939
939
162
B2u
939
939
940
940
163
B1g
940
940
940
940
1.728e+39
1.1
2.298e+39
1.5
4.026e+39
2.6
164
B1g
940
940
962
940
6.983e+38
0.4
5.053e+38
0.3
1.204e+39
0.8
165
Ag
962
962
965
962
1.491e+40
9.5
1.097e+40
7.0
2.589e+40
16.6
166
B3g
965
965
977
965
5.665e+39
3.6
7.790e+39
5.0
1.346e+40
8.6
167
B1u
977
977
983
983
168
B3u
983
986
986
986
169
B1g
986
987
987
987
2.765e+39
1.8
3.802e+39
2.4
6.568e+39
4.2
170
B2g
987
989
987
989
2.677e+40
17.1
3.681e+40
23.6
6.357e+40
40.7
171
Au
989
990
989
990
172
B2u
990
1000
1000
996
173
Ag
1000
1012
1012
1000
3.597e+39
2.3
2.653e+39
1.7
6.250e+39
4.0
174
B3g
1012
1016
1023
1012
2.844e+38
0.2
3.911e+38
0.3
6.755e+38
0.4
175
Au
1023
1023
1023
1023
176
B3u
1023
1038
1028
1023
177
B1g
1038
1041
1038
1038
2.296e+39
1.5
3.156e+39
2.0
5.452e+39
3.5
178
B2g
1041
1068
1041
1041
1.095e+40
7.0
1.506e+40
9.6
2.601e+40
16.7
179
B1u
1068
1092
1068
1123
180
B2u
1123
1123
1123
1129
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.