-    EUCRYPTITE     -    LiAlSiO4

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:  146  R3 
Lattice parameters (Å):  13.5320  13.5320  9.0440 
Angles (°):  90  90  120 

Symmetry (theoretical): 

Space group:  146  R3 
Lattice parameters (Å):  8.1867  8.1867  8.1867 
Angles (°):  107.84  107.84  107.84 

Cell contents: 

Number of atoms:  42 
Number of atom types:  4 
Chemical composition:  0 

Atomic positions (theoretical):

Li:  0.2317  0.4559  0.0613 
Li:  0.7727  0.5423  0.9407 
Si:  0.2802  0.0994  0.8698 
Al:  0.7208  0.9004  0.1331 
Si:  0.7938  0.3857  0.5701 
Al:  0.2077  0.6145  0.4317 
O:  0.3525  0.6511  0.3187 
O:  0.6667  0.3522  0.6844 
O:  0.6718  0.9448  0.6095 
O:  0.3131  0.0416  0.3765 
O:  0.9640  0.2821  0.9532 
O:  0.0381  0.7279  0.0625 
O:  0.5848  0.9084  0.2580 
O:  0.4063  0.0891  0.7529 
Li:  0.4559  0.0613  0.2317 
Li:  0.5423  0.9407  0.7727 
Si:  0.0994  0.8698  0.2802 
Al:  0.9004  0.1331  0.7208 
Si:  0.3857  0.5701  0.7938 
Al:  0.6145  0.4317  0.2077 
O:  0.6511  0.3187  0.3525 
O:  0.3522  0.6844  0.6667 
O:  0.9448  0.6095  0.6718 
O:  0.0416  0.3765  0.3131 
O:  0.2821  0.9532  0.9640 
O:  0.7279  0.0625  0.0381 
O:  0.9084  0.2580  0.5848 
O:  0.0891  0.7529  0.4063 
Li:  0.0613  0.2317  0.4559 
Li:  0.9407  0.7727  0.5423 
Si:  0.8698  0.2802  0.0994 
Al:  0.1331  0.7208  0.9004 
Si:  0.5701  0.7938  0.3857 
Al:  0.4317  0.2077  0.6145 
O:  0.3187  0.3525  0.6511 
O:  0.6844  0.6667  0.3522 
O:  0.6095  0.6718  0.9448 
O:  0.3765  0.3131  0.0416 
O:  0.9532  0.9640  0.2821 
O:  0.0625  0.0381  0.7279 
O:  0.2580  0.5848  0.9084 
O:  0.7529  0.4063  0.0891 
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
E
109
109
109
109
1.096e+38
0.6
8.414e+37
0.5
1.938e+38
1.1
5
E
109
109
109
109
1.096e+38
0.6
1.593e+38
0.9
2.689e+38
1.5
6
A
125
125
125
125
1.178e+38
0.7
8.329e+37
0.5
2.011e+38
1.2
7
A
144
144
144
144
2.957e+39
16.9
4.562e+37
0.3
3.002e+39
17.2
8
E
151
151
151
151
1.702e+38
1.0
2.006e+38
1.1
3.709e+38
2.1
9
E
151
151
151
151
1.702e+38
1.0
2.755e+38
1.6
4.457e+38
2.6
10
A
164
164
164
164
1.176e+38
0.7
1.942e+37
0.1
1.370e+38
0.8
11
E
166
166
166
166
3.052e+37
0.2
3.122e+37
0.2
6.174e+37
0.4
12
E
166
166
166
166
3.052e+37
0.2
3.880e+37
0.2
6.933e+37
0.4
13
E
172
172
172
172
1.747e+38
1.0
2.083e+38
1.2
3.830e+38
2.2
14
E
172
172
172
172
1.747e+38
1.0
1.519e+38
0.9
3.266e+38
1.9
15
A
172
172
172
172
1.657e+38
0.9
1.099e+37
0.1
1.767e+38
1.0
16
A
189
189
189
189
7.536e+37
0.4
6.000e+35
0.0
7.596e+37
0.4
17
E
196
196
196
196
7.019e+36
0.0
9.651e+36
0.1
1.667e+37
0.1
18
E
196
196
196
196
7.019e+36
0.0
9.651e+36
0.1
1.667e+37
0.1
19
A
199
199
199
199
6.718e+36
0.0
2.239e+36
0.0
8.957e+36
0.1
20
E
210
210
210
210
5.777e+37
0.3
4.426e+37
0.3
1.020e+38
0.6
21
E
210
210
210
210
5.777e+37
0.3
8.287e+37
0.5
1.406e+38
0.8
22
A
216
216
216
218
1.456e+38
0.8
2.040e+35
0.0
1.458e+38
0.8
23
E
232
232
232
232
1.008e+38
0.6
8.362e+37
0.5
1.844e+38
1.1
24
E
232
232
232
232
1.008e+38
0.6
1.486e+38
0.9
2.494e+38
1.4
25
A
239
239
239
239
2.207e+38
1.3
1.348e+37
0.1
2.342e+38
1.3
26
A
242
242
242
243
3.099e+38
1.8
4.236e+37
0.2
3.523e+38
2.0
27
E
250
250
250
250
1.149e+38
0.7
1.878e+38
1.1
3.027e+38
1.7
28
E
250
251
251
250
1.149e+38
0.7
1.324e+38
0.8
2.474e+38
1.4
29
E
266
266
266
266
1.198e+38
0.7
1.704e+38
1.0
2.902e+38
1.7
30
E
266
266
266
266
1.198e+38
0.7
1.788e+38
1.0
2.986e+38
1.7
31
A
281
281
281
282
1.707e+39
9.8
9.187e+36
0.1
1.717e+39
9.8
32
E
282
282
282
282
4.214e+38
2.4
4.759e+38
2.7
8.973e+38
5.1
33
E
282
284
284
285
4.214e+38
2.4
3.632e+38
2.1
7.846e+38
4.5
34
A
293
293
293
298
3.569e+38
2.0
2.749e+35
0.0
3.572e+38
2.0
35
E
298
298
298
298
2.335e+38
1.3
2.685e+38
1.5
5.020e+38
2.9
36
E
298
298
298
303
2.335e+38
1.3
2.370e+38
1.4
4.705e+38
2.7
37
A
320
320
320
321
2.874e+38
1.6
8.007e+36
0.0
2.954e+38
1.7
38
E
337
337
337
337
1.780e+38
1.0
2.812e+38
1.6
4.592e+38
2.6
39
E
337
338
338
337
1.780e+38
1.0
1.842e+38
1.1
3.622e+38
2.1
40
E
348
348
348
348
1.823e+38
1.0
3.034e+38
1.7
4.857e+38
2.8
41
E
348
348
348
348
1.823e+38
1.0
2.196e+38
1.3
4.018e+38
2.3
42
A
348
354
354
350
1.186e+38
0.7
9.930e+36
0.1
1.285e+38
0.7
43
A
359
359
359
361
6.150e+38
3.5
1.371e+37
0.1
6.287e+38
3.6
44
E
363
363
363
363
2.725e+37
0.2
4.287e+37
0.2
7.013e+37
0.4
45
E
363
369
369
363
2.725e+37
0.2
2.975e+37
0.2
5.701e+37
0.3
46
A
369
372
372
369
1.620e+38
0.9
5.505e+36
0.0
1.675e+38
1.0
47
A
375
375
375
375
1.850e+38
1.1
8.462e+37
0.5
2.696e+38
1.5
48
E
377
377
377
377
3.017e+37
0.2
3.338e+37
0.2
6.355e+37
0.4
49
E
377
378
378
377
3.017e+37
0.2
3.265e+37
0.2
6.282e+37
0.4
50
E
401
401
401
401
2.775e+38
1.6
3.571e+38
2.0
6.346e+38
3.6
51
E
401
403
403
401
2.775e+38
1.6
4.078e+38
2.3
6.852e+38
3.9
52
E
408
408
408
408
2.281e+38
1.3
1.895e+38
1.1
4.177e+38
2.4
53
E
408
409
409
408
2.281e+38
1.3
2.518e+38
1.4
4.799e+38
2.7
54
A
409
413
413
409
1.050e+39
6.0
6.852e+37
0.4
1.118e+39
6.4
55
E
428
428
428
428
2.320e+37
0.1
3.385e+37
0.2
5.705e+37
0.3
56
E
428
428
428
428
2.319e+37
0.1
1.815e+37
0.1
4.135e+37
0.2
57
A
443
443
443
443
5.393e+38
3.1
3.320e+38
1.9
8.713e+38
5.0
58
E
451
451
451
451
1.110e+38
0.6
1.315e+38
0.8
2.424e+38
1.4
59
E
451
452
452
451
1.110e+38
0.6
1.851e+38
1.1
2.961e+38
1.7
60
A
455
455
455
457
1.147e+39
6.6
1.080e+38
0.6
1.255e+39
7.2
61
E
460
460
460
460
8.817e+37
0.5
9.677e+37
0.6
1.849e+38
1.1
62
E
460
462
462
460
8.817e+37
0.5
9.692e+37
0.6
1.851e+38
1.1
63
A
462
465
465
462
4.171e+39
23.9
1.676e+37
0.1
4.188e+39
24.0
64
A
469
469
469
470
4.641e+39
26.6
3.730e+37
0.2
4.678e+39
26.8
65
E
472
472
472
472
9.424e+37
0.5
1.146e+38
0.7
2.089e+38
1.2
66
E
472
474
474
472
9.424e+37
0.5
9.580e+37
0.5
1.900e+38
1.1
67
A
474
485
485
476
1.300e+40
74.5
6.333e+36
0.0
1.300e+40
74.5
68
E
492
492
492
492
1.149e+38
0.7
1.317e+38
0.8
2.467e+38
1.4
69
E
492
495
495
492
1.149e+38
0.7
1.669e+38
1.0
2.818e+38
1.6
70
E
498
498
498
498
4.830e+37
0.3
5.118e+37
0.3
9.948e+37
0.6
71
E
498
500
500
498
4.830e+37
0.3
7.055e+37
0.4
1.189e+38
0.7
72
A
500
501
501
500
1.241e+40
71.1
2.209e+37
0.1
1.243e+40
71.2
73
A
501
504
504
505
9.393e+37
0.5
4.624e+37
0.3
1.402e+38
0.8
74
E
505
505
505
505
7.407e+37
0.4
1.041e+38
0.6
1.781e+38
1.0
75
E
505
513
513
518
7.407e+37
0.4
6.517e+37
0.4
1.392e+38
0.8
76
A
521
521
521
524
2.007e+38
1.2
3.891e+37
0.2
2.396e+38
1.4
77
E
524
524
524
524
1.516e+38
0.9
2.540e+38
1.5
4.056e+38
2.3
78
E
524
526
526
549
1.516e+38
0.9
1.732e+38
1.0
3.248e+38
1.9
79
A
551
551
551
555
1.464e+39
8.4
3.214e+36
0.0
1.467e+39
8.4
80
A
562
562
562
562
1.745e+40
100.0
7.520e+36
0.0
1.745e+40
100.0
81
E
568
568
568
568
2.404e+37
0.1
2.660e+37
0.2
5.065e+37
0.3
82
E
568
574
574
568
2.404e+37
0.1
3.952e+37
0.2
6.356e+37
0.4
83
E
593
593
593
593
3.376e+37
0.2
4.054e+37
0.2
7.430e+37
0.4
84
E
593
593
593
593
3.376e+37
0.2
3.379e+37
0.2
6.755e+37
0.4
85
E
612
612
612
612
1.475e+37
0.1
1.450e+37
0.1
2.925e+37
0.2
86
E
612
613
613
612
1.475e+37
0.1
1.783e+37
0.1
3.258e+37
0.2
87
A
617
617
617
624
2.681e+37
0.2
1.993e+37
0.1
4.674e+37
0.3
88
E
657
657
657
657
5.576e+37
0.3
6.847e+37
0.4
1.242e+38
0.7
89
E
657
657
657
657
5.576e+37
0.3
5.603e+37
0.3
1.118e+38
0.6
90
E
687
687
687
687
8.390e+37
0.5
7.459e+37
0.4
1.585e+38
0.9
91
E
687
687
687
687
8.390e+37
0.5
1.337e+38
0.8
2.176e+38
1.2
92
A
687
692
692
687
7.838e+38
4.5
1.368e+38
0.8
9.205e+38
5.3
93
A
692
693
693
692
4.671e+37
0.3
2.592e+37
0.1
7.263e+37
0.4
94
A
701
701
701
702
4.494e+37
0.3
4.560e+36
0.0
4.950e+37
0.3
95
E
702
702
702
702
1.256e+38
0.7
1.273e+38
0.7
2.528e+38
1.4
96
E
702
717
717
719
1.256e+38
0.7
2.014e+38
1.2
3.270e+38
1.9
97
E
719
719
719
719
6.446e+37
0.4
8.450e+37
0.5
1.490e+38
0.9
98
E
719
735
735
728
6.446e+37
0.4
9.291e+37
0.5
1.574e+38
0.9
99
A
738
738
738
738
8.202e+38
4.7
1.214e+38
0.7
9.417e+38
5.4
100
E
768
768
768
768
8.821e+37
0.5
1.063e+38
0.6
1.945e+38
1.1
101
E
768
769
769
768
8.821e+37
0.5
6.901e+37
0.4
1.572e+38
0.9
102
A
770
770
770
771
7.090e+37
0.4
6.649e+31
0.0
7.090e+37
0.4
103
A
902
902
902
912
8.059e+39
46.2
1.863e+38
1.1
8.245e+39
47.2
104
E
912
912
912
912
5.564e+38
3.2
6.348e+38
3.6
1.191e+39
6.8
105
E
912
916
916
920
5.564e+38
3.2
9.203e+38
5.3
1.477e+39
8.5
106
E
929
929
929
929
3.480e+38
2.0
4.803e+38
2.8
8.283e+38
4.7
107
E
929
930
930
929
3.480e+38
2.0
4.115e+38
2.4
7.596e+38
4.4
108
A
932
932
932
933
7.724e+38
4.4
1.433e+36
0.0
7.738e+38
4.4
109
E
933
933
933
933
3.591e+38
2.1
3.028e+38
1.7
6.619e+38
3.8
110
E
933
936
936
933
3.591e+38
2.1
4.754e+38
2.7
8.345e+38
4.8
111
A
936
945
945
939
6.906e+38
4.0
1.823e+37
0.1
7.088e+38
4.1
112
A
952
952
952
953
3.137e+39
18.0
1.462e+37
0.1
3.152e+39
18.1
113
E
953
953
953
953
2.339e+38
1.3
2.509e+38
1.4
4.848e+38
2.8
114
E
953
957
957
957
2.339e+38
1.3
2.009e+38
1.2
4.348e+38
2.5
115
A
957
967
967
965
1.349e+39
7.7
6.708e+38
3.8
2.020e+39
11.6
116
A
967
967
967
971
1.242e+38
0.7
1.177e+37
0.1
1.360e+38
0.8
117
E
971
971
971
971
3.536e+38
2.0
5.877e+38
3.4
9.414e+38
5.4
118
E
971
977
977
972
3.536e+38
2.0
4.007e+38
2.3
7.544e+38
4.3
119
A
977
980
980
981
3.355e+38
1.9
1.467e+38
0.8
4.822e+38
2.8
120
E
981
981
981
981
1.850e+38
1.1
1.409e+38
0.8
3.259e+38
1.9
121
E
981
998
998
1007
1.850e+38
1.1
2.410e+38
1.4
4.260e+38
2.4
122
E
1007
1007
1007
1007
2.215e+38
1.3
3.084e+38
1.8
5.298e+38
3.0
123
E
1007
1040
1040
1043
2.215e+38
1.3
3.478e+38
2.0
5.693e+38
3.3
124
E
1043
1043
1043
1043
5.511e+37
0.3
5.881e+37
0.3
1.139e+38
0.7
125
E
1043
1047
1047
1047
5.511e+37
0.3
7.627e+37
0.4
1.314e+38
0.8
126
A
1047
1086
1086
1075
1.731e+37
0.1
8.166e+36
0.0
2.548e+37
0.1
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.