-    BENITOITE     -    BaTiSi3O9

Theoretical atomic positions and lattice parameters at experimental volum from 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:  188  P-6c2 
Lattice parameters (Å):  6.6410  6.6410  9.7590 
Angles (°):  90.0  90.0  120.0 

Symmetry (theoretical): 

Space group:  188  P-6c2 
Lattice parameters (Å):  6.6285  6.6285  9.7960 
Angles (°):  90.0  90.0  120.0 

Cell contents: 

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

Atomic positions (theoretical):

Ba:  0.6667  0.3333  0.0000 
Ti:  0.3333  0.6667  0.0000 
Si:  0.0703  0.2896  0.2500 
O:  0.2533  0.1926  0.2500 
O:  0.0880  0.4312  0.1136 
Ba:  0.6667  0.3333  0.5000 
Ti:  0.3333  0.6667  0.5000 
Si:  0.7104  0.7807  0.2500 
O:  0.8074  0.0607  0.2500 
O:  0.5688  0.6568  0.3864 
Si:  0.7104  0.9297  0.7500 
O:  0.8074  0.7467  0.7500 
O:  0.5688  0.9120  0.8864 
Si:  0.2193  0.9297  0.2500 
O:  0.9393  0.7467  0.2500 
O:  0.3432  0.9120  0.1136 
Si:  0.0703  0.7807  0.7500 
O:  0.2533  0.0607  0.7500 
O:  0.0880  0.6568  0.6136 
Si:  0.2193  0.2896  0.7500 
O:  0.9393  0.1926  0.7500 
O:  0.3432  0.4312  0.6136 
O:  0.0880  0.4312  0.3864 
O:  0.3432  0.4312  0.8864 
O:  0.0880  0.6568  0.8864 
O:  0.3432  0.9120  0.3864 
O:  0.5688  0.6568  0.1136 
O:  0.5688  0.9120  0.6136 
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
A''2
63
63
63
66
5
A'2
66
66
66
70
6
E''
70
70
70
70
1.014e+39
1.2
1.269e+39
1.5
2.283e+39
2.7
7
E''
70
70
70
71
1.014e+39
1.2
1.518e+39
1.8
2.532e+39
3.0
8
E'
102
102
102
102
1.697e+39
2.0
2.334e+39
2.7
4.031e+39
4.7
9
E'
102
123
123
102
1.697e+39
2.0
1.273e+39
1.5
2.970e+39
3.5
10
E''
127
127
127
127
1.665e+39
1.9
2.809e+39
3.3
4.473e+39
5.2
11
E''
127
127
127
127
1.665e+39
1.9
1.769e+39
2.1
3.433e+39
4.0
12
E''
154
154
154
154
3.198e+37
0.0
4.397e+37
0.1
7.595e+37
0.1
13
E''
154
154
154
154
3.198e+37
0.0
4.397e+37
0.1
7.595e+37
0.1
14
E'
156
156
156
156
3.541e+39
4.1
4.869e+39
5.7
8.410e+39
9.8
15
E'
156
159
159
156
3.541e+39
4.1
2.656e+39
3.1
6.197e+39
7.2
16
A''2
159
159
159
159
17
A''1
179
179
179
179
18
A'2
193
193
193
193
19
E''
195
195
195
195
3.755e+39
4.4
5.279e+39
6.2
9.033e+39
10.5
20
E''
195
195
195
195
3.755e+39
4.4
5.047e+39
5.9
8.802e+39
10.3
21
E''
213
213
213
213
1.330e+40
15.5
1.500e+40
17.5
2.830e+40
33.0
22
E''
213
213
213
213
1.330e+40
15.5
2.157e+40
25.1
3.487e+40
40.7
23
E''
225
225
225
225
4.092e+39
4.8
4.356e+39
5.1
8.448e+39
9.9
24
E''
225
225
225
225
4.092e+39
4.8
6.896e+39
8.0
1.099e+40
12.8
25
A'1
252
252
252
252
4.763e+40
55.5
1.028e+38
0.1
4.774e+40
55.7
26
E'
256
256
256
256
1.118e+38
0.1
1.537e+38
0.2
2.655e+38
0.3
27
E'
256
257
257
256
1.118e+38
0.1
8.385e+37
0.1
1.957e+38
0.2
28
A''1
273
273
273
273
29
E'
280
280
280
280
2.185e+37
0.0
3.004e+37
0.0
5.189e+37
0.1
30
E'
280
280
280
280
2.185e+37
0.0
1.639e+37
0.0
3.824e+37
0.0
31
A''2
300
300
300
311
32
A'2
311
311
311
335
33
A'1
335
335
335
340
7.649e+39
8.9
1.475e+39
1.7
9.124e+39
10.6
34
E'
340
340
340
340
2.705e+39
3.2
3.720e+39
4.3
6.425e+39
7.5
35
E'
340
341
341
341
2.705e+39
3.2
2.029e+39
2.4
4.734e+39
5.5
36
A'2
341
344
344
355
37
E''
355
355
355
355
1.646e+40
19.2
2.756e+40
32.1
4.401e+40
51.3
38
E''
355
355
355
360
1.646e+40
19.2
1.770e+40
20.6
3.416e+40
39.8
39
E'
361
361
361
361
4.528e+39
5.3
6.226e+39
7.3
1.075e+40
12.5
40
E'
361
362
362
361
4.528e+39
5.3
3.396e+39
4.0
7.925e+39
9.2
41
A''2
362
377
377
377
42
E''
377
377
377
377
4.361e+39
5.1
7.086e+39
8.3
1.145e+40
13.3
43
E''
377
381
381
382
4.361e+39
5.1
4.906e+39
5.7
9.267e+39
10.8
44
E'
382
382
382
382
1.959e+38
0.2
2.693e+38
0.3
4.652e+38
0.5
45
E'
382
391
391
409
1.959e+38
0.2
1.469e+38
0.2
3.428e+38
0.4
46
A''1
409
409
409
414
47
E'
425
425
425
425
2.168e+38
0.3
2.981e+38
0.3
5.149e+38
0.6
48
E'
425
451
451
425
2.168e+38
0.3
1.626e+38
0.2
3.794e+38
0.4
49
E'
466
466
466
466
7.236e+39
8.4
9.950e+39
11.6
1.719e+40
20.0
50
E'
466
475
475
466
7.236e+39
8.4
5.427e+39
6.3
1.266e+40
14.8
51
A'2
475
492
492
475
52
E''
492
492
492
492
2.388e+39
2.8
2.679e+39
3.1
5.068e+39
5.9
53
E''
492
504
504
492
2.388e+39
2.8
3.889e+39
4.5
6.277e+39
7.3
54
A'1
516
516
516
516
3.355e+40
39.1
8.751e+35
0.0
3.355e+40
39.1
55
E''
529
529
529
529
1.439e+38
0.2
1.666e+38
0.2
3.105e+38
0.4
56
E''
529
529
529
529
1.439e+38
0.2
2.292e+38
0.3
3.731e+38
0.4
57
A'1 + A'2
553
553
553
553
2.615e+40
30.5
1.168e+38
0.1
2.627e+40
30.6
58
A'1 + A'2
553
553
553
553
3.268e+40
38.1
1.459e+38
0.2
3.283e+40
38.3
59
A''2
556
556
556
562
60
A''1
581
581
581
581
61
A'1
617
617
617
617
1.775e+39
2.1
1.051e+39
1.2
2.826e+39
3.3
62
A'2
640
640
640
640
63
E'
724
724
724
724
2.650e+38
0.3
3.644e+38
0.4
6.295e+38
0.7
64
E'
724
725
725
724
2.650e+38
0.3
1.988e+38
0.2
4.638e+38
0.5
65
E'
729
729
729
729
1.104e+39
1.3
1.518e+39
1.8
2.622e+39
3.1
66
E'
729
765
765
729
1.104e+39
1.3
8.281e+38
1.0
1.932e+39
2.3
67
E'
891
891
891
891
7.250e+38
0.8
9.969e+38
1.2
1.722e+39
2.0
68
E'
891
892
892
891
7.250e+38
0.8
5.438e+38
0.6
1.269e+39
1.5
69
A''2
892
901
901
902
70
E'
902
902
902
902
5.687e+39
6.6
7.820e+39
9.1
1.351e+40
15.8
71
E'
902
913
913
913
5.687e+39
6.6
4.266e+39
5.0
9.953e+39
11.6
72
E''
913
913
913
913
3.222e+40
37.6
3.507e+40
40.9
6.729e+40
78.5
73
E''
913
923
923
923
3.222e+40
37.6
5.354e+40
62.4
8.576e+40
100.0
74
E''
923
923
923
923
1.196e+40
13.9
1.401e+40
16.3
2.597e+40
30.3
75
E''
923
941
941
941
1.196e+40
13.9
1.887e+40
22.0
3.082e+40
35.9
76
A'2
941
941
941
944
77
A'1
944
944
944
986
2.049e+38
0.2
1.304e+38
0.2
3.353e+38
0.4
78
A'2
986
986
986
995
79
E'
995
995
995
995
1.646e+39
1.9
2.263e+39
2.6
3.908e+39
4.6
80
E'
995
997
997
1000
1.646e+39
1.9
1.234e+39
1.4
2.880e+39
3.4
81
E'
1000
1000
1000
1000
2.854e+38
0.3
3.924e+38
0.5
6.778e+38
0.8
82
E'
1000
1027
1027
1027
2.854e+38
0.3
2.140e+38
0.2
4.994e+38
0.6
83
A'1
1027
1070
1070
1075
1.248e+40
14.6
1.610e+39
1.9
1.409e+40
16.4
84
A''1
1103
1103
1103
1103
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.