-    KOTOITE     -    Mg3B2O6

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:  58  Pnmn 
Lattice parameters (Å):  5.3980  8.4160  4.4970 
Angles (°):  90  90  90 

Symmetry (theoretical): 

Space group:  58  Pnmn 
Lattice parameters (Å):  5.2741  8.2886  4.4377 
Angles (°):  90  90  90 

Cell contents: 

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

Atomic positions (theoretical):

Mg:  0.0000  0.0000  0.0000 
Mg:  0.0000  0.3134  0.5000 
B:  0.2576  0.0000  0.5477 
O:  0.3236  0.0000  0.2501 
O:  0.2037  0.1400  0.7040 
B:  0.7424  0.0000  0.4523 
O:  0.6764  0.0000  0.7499 
O:  0.7963  0.1400  0.2960 
Mg:  0.5000  0.5000  0.5000 
Mg:  0.5000  0.1866  0.0000 
B:  0.7576  0.5000  0.9523 
O:  0.8236  0.5000  0.2499 
O:  0.7037  0.3600  0.7960 
B:  0.2424  0.5000  0.0477 
O:  0.1764  0.5000  0.7501 
O:  0.2963  0.3600  0.2040 
Mg:  0.0000  0.6866  0.5000 
O:  0.7963  0.8600  0.2960 
O:  0.2037  0.8600  0.7040 
Mg:  0.5000  0.8134  0.0000 
O:  0.2963  0.6400  0.2040 
O:  0.7037  0.6400  0.7960 
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
159
159
159
164
5
B3u
180
182
180
180
6
B3g
196
196
196
196
4.538e+37
0.1
6.240e+37
0.1
1.078e+38
0.2
7
Au
207
207
207
207
8
B1g
220
220
220
220
6.585e+36
0.0
9.054e+36
0.0
1.564e+37
0.0
9
B3g
225
225
225
225
2.627e+37
0.0
3.613e+37
0.1
6.240e+37
0.1
10
Ag
256
256
256
256
7.691e+39
13.4
4.110e+39
7.2
1.180e+40
20.6
11
B1g
271
271
271
271
3.392e+38
0.6
4.664e+38
0.8
8.056e+38
1.4
12
B2u
276
276
283
276
13
B1u
283
283
286
286
14
Au
286
286
287
289
15
B3u
294
294
294
294
16
B2g
295
295
295
295
1.691e+37
0.0
2.325e+37
0.0
4.016e+37
0.1
17
Au
310
310
310
310
18
B3g
312
312
312
312
9.460e+38
1.7
1.301e+39
2.3
2.247e+39
3.9
19
Ag
315
315
315
315
1.548e+38
0.3
9.505e+37
0.2
2.499e+38
0.4
20
B1g
330
330
330
330
9.999e+38
1.7
1.375e+39
2.4
2.375e+39
4.1
21
B1g
342
342
342
342
5.740e+38
1.0
7.892e+38
1.4
1.363e+39
2.4
22
B3g
343
343
343
343
6.648e+38
1.2
9.141e+38
1.6
1.579e+39
2.8
23
B1u
345
345
345
352
24
B2u
352
352
352
353
25
B3u
355
361
355
355
26
Ag
361
363
361
361
1.279e+40
22.3
3.475e+39
6.1
1.626e+40
28.4
27
B2g
363
368
363
363
1.208e+38
0.2
1.661e+38
0.3
2.869e+38
0.5
28
Au
368
376
368
368
29
B2u
379
379
399
379
30
B3u
399
399
399
399
31
B2g
399
417
418
399
1.890e+38
0.3
2.599e+38
0.5
4.490e+38
0.8
32
Ag
418
418
425
418
1.509e+39
2.6
4.496e+38
0.8
1.958e+39
3.4
33
B1u
425
425
428
428
34
B3u
428
428
429
428
35
B2g
429
430
430
429
1.143e+38
0.2
1.571e+38
0.3
2.714e+38
0.5
36
B1g
430
441
441
430
3.361e+37
0.1
4.621e+37
0.1
7.982e+37
0.1
37
B1u
441
445
445
445
38
B3g
445
461
465
470
2.421e+38
0.4
3.329e+38
0.6
5.749e+38
1.0
39
B3u
470
470
470
470
40
Au
470
483
470
496
41
B2u
496
496
509
503
42
B1u
509
509
534
548
43
B1g
548
548
548
575
5.424e+38
0.9
7.459e+38
1.3
1.288e+39
2.3
44
B3g
575
575
575
578
1.462e+39
2.6
2.011e+39
3.5
3.473e+39
6.1
45
Au
578
578
578
578
46
B2u
603
603
606
603
47
B3u
620
621
620
620
48
B1u
621
674
621
624
49
B1u
688
688
688
689
50
Ag
689
689
689
694
1.474e+39
2.6
8.394e+38
1.5
2.314e+39
4.0
51
B3u
694
702
694
697
52
B2g
702
761
702
702
1.752e+38
0.3
2.409e+38
0.4
4.160e+38
0.7
53
Ag
761
761
761
761
2.615e+39
4.6
2.017e+39
3.5
4.633e+39
8.1
54
B2g
761
801
761
761
2.331e+39
4.1
2.113e+39
3.7
4.444e+39
7.8
55
B1u
902
902
902
902
56
B3u
902
904
902
902
57
Ag
918
918
918
918
5.716e+40
99.8
8.863e+37
0.2
5.725e+40
100.0
58
B2g
930
930
930
930
3.164e+37
0.1
4.351e+37
0.1
7.515e+37
0.1
59
B3g
1177
1177
1177
1177
7.575e+38
1.3
1.042e+39
1.8
1.799e+39
3.1
60
B1g
1200
1200
1200
1200
2.173e+38
0.4
2.987e+38
0.5
5.160e+38
0.9
61
B2u
1200
1200
1278
1200
62
Ag
1278
1278
1290
1278
1.338e+39
2.3
4.504e+38
0.8
1.788e+39
3.1
63
B1u
1290
1290
1295
1295
64
B2g
1295
1295
1319
1319
4.492e+37
0.1
6.176e+37
0.1
1.067e+38
0.2
65
B3u
1319
1335
1335
1335
66
Au
1335
1336
1343
1427
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.