-    TAKEDAITE     -    Ca3(BO3)2

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:  167  R-3c 
Lattice parameters (Å):  8.6377  8.6377  11.8490 
Angles (°):  90  90  120 

Symmetry (theoretical): 

Space group:  167  R-3c 
Lattice parameters (Å):  6.3610  6.3610  6.3610 
Angles (°):  85.58  85.58  85.58 

Cell contents: 

Number of atoms:  22 
Number of atom types:  3 
Chemical composition:  0 

Atomic positions (theoretical):

Ca:  0.6088  0.8912  0.2500 
B:  0.1158  0.1158  0.1158 
O:  0.2788  0.9611  0.1009 
Ca:  0.8912  0.2500  0.6088 
O:  0.9611  0.1009  0.2788 
Ca:  0.7500  0.3912  0.1088 
B:  0.6158  0.6158  0.6158 
O:  0.6009  0.4611  0.7788 
Ca:  0.2500  0.6088  0.8912 
O:  0.1009  0.2788  0.9611 
Ca:  0.3912  0.1088  0.7500 
O:  0.4611  0.7788  0.6009 
Ca:  0.1088  0.7500  0.3912 
O:  0.7788  0.6009  0.4611 
B:  0.8842  0.8842  0.8842 
O:  0.7212  0.0389  0.8991 
O:  0.0389  0.8991  0.7212 
B:  0.3842  0.3842  0.3842 
O:  0.3991  0.5389  0.2212 
O:  0.8991  0.7212  0.0389 
O:  0.5389  0.2212  0.3991 
O:  0.2212  0.3991  0.5389 
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
Eg
75
75
75
75
1.464e+39
4.1
2.040e+39
5.8
3.504e+39
9.9
5
Eg
75
75
75
75
1.464e+39
4.1
2.140e+39
6.0
3.604e+39
10.2
6
Eu
131
131
131
131
7
Eu
131
136
136
131
8
Eg
157
157
157
157
1.277e+39
3.6
1.616e+39
4.6
2.893e+39
8.2
9
Eg
157
157
157
157
1.277e+39
3.6
1.986e+39
5.6
3.263e+39
9.2
10
A2u
163
163
163
194
11
A2g
194
194
194
198
12
A1g
198
198
198
204
1.656e+39
4.7
5.209e+37
0.1
1.708e+39
4.8
13
A1u
204
204
204
219
14
Eg
219
219
219
219
1.875e+39
5.3
2.038e+39
5.7
3.913e+39
11.0
15
Eg
219
219
219
223
1.875e+39
5.3
3.119e+39
8.8
4.994e+39
14.1
16
Eu
239
239
239
239
17
Eu
239
239
239
239
18
A2u
250
250
250
255
19
Eg
255
255
255
255
1.529e+39
4.3
1.623e+39
4.6
3.152e+39
8.9
20
Eg
255
255
255
265
1.529e+39
4.3
2.566e+39
7.2
4.095e+39
11.5
21
A2g
265
265
265
268
22
A1g
268
268
268
270
1.257e+38
0.4
4.191e+37
0.1
1.677e+38
0.5
23
Eu
270
270
270
270
24
Eu
270
273
273
282
25
A1u
282
282
282
287
26
Eg
287
287
287
287
7.682e+38
2.2
6.541e+38
1.8
1.422e+39
4.0
27
Eg
287
287
287
289
7.682e+38
2.2
9.783e+38
2.8
1.747e+39
4.9
28
A2g
294
294
294
294
29
Eu
296
296
296
296
30
Eu
296
297
297
296
31
A2u
297
307
307
310
32
A2g
310
310
310
326
33
Eu
326
326
326
326
34
Eu
326
330
330
337
35
Eg
337
337
337
337
1.357e+39
3.8
1.742e+39
4.9
3.098e+39
8.7
36
Eg
337
337
337
338
1.356e+39
3.8
2.003e+39
5.6
3.359e+39
9.5
37
A1u
338
338
338
340
38
A1g
340
340
340
342
5.783e+38
1.6
4.336e+38
1.2
1.012e+39
2.9
39
Eg
344
344
344
344
2.479e+39
7.0
1.998e+39
5.6
4.477e+39
12.6
40
Eg
344
344
344
344
2.479e+39
7.0
2.965e+39
8.4
5.444e+39
15.3
41
Eu
356
356
356
356
42
Eu
356
459
459
356
43
Eg
601
601
601
601
3.364e+37
0.1
4.287e+37
0.1
7.651e+37
0.2
44
Eg
601
601
601
601
3.364e+37
0.1
5.399e+37
0.2
8.763e+37
0.2
45
Eg
606
606
606
606
9.150e+38
2.6
9.463e+38
2.7
1.861e+39
5.2
46
Eg
606
606
606
606
9.150e+38
2.6
8.932e+38
2.5
1.808e+39
5.1
47
Eu
608
608
608
608
48
Eu
608
610
610
608
49
Eu
615
615
615
615
50
Eu
615
617
617
615
51
A2u
681
681
681
714
52
A1u
714
714
714
734
53
A2g
737
737
737
737
54
A1g
756
756
756
756
2.092e+38
0.6
1.295e+35
0.0
2.093e+38
0.6
55
A2u
896
896
896
897
56
A2g
907
907
907
907
57
A1u
917
917
917
917
58
A1g
919
919
919
919
3.533e+40
99.6
1.473e+38
0.4
3.548e+40
100.0
59
Eg
1225
1225
1225
1225
2.326e+38
0.7
3.693e+38
1.0
6.018e+38
1.7
60
Eg
1225
1225
1225
1225
2.326e+38
0.7
2.179e+38
0.6
4.504e+38
1.3
61
Eu
1227
1227
1227
1227
62
Eu
1227
1256
1256
1227
63
Eu
1271
1271
1271
1271
64
Eu
1271
1275
1275
1271
65
Eg
1275
1275
1275
1275
9.776e+38
2.8
1.434e+39
4.0
2.411e+39
6.8
66
Eg
1275
1357
1357
1275
9.776e+38
2.8
1.238e+39
3.5
2.215e+39
6.2
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.