-    GEIKIELITE     -    MgTiO3

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:  148  R-3 
Lattice parameters (Å):  5.0567  5.0567  13.9034 
Angles (°):  90.0  90.0  120.0 

Symmetry (theoretical): 

Space group:  148  R-3 
Lattice parameters (Å):  5.3784  5.3784  5.3784 
Angles (°):  55.3  55.3  55.3 

Cell contents: 

Number of atoms:  10 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Mg:  0.3547  0.3547  0.3547 
Ti:  0.1446  0.1446  0.1446 
O:  0.5605  0.9522  0.2289 
O:  0.9522  0.2289  0.5605 
O:  0.2289  0.5605  0.9522 
Mg:  0.6453  0.6453  0.6453 
Ti:  0.8554  0.8554  0.8554 
O:  0.4395  0.0478  0.7711 
O:  0.0478  0.7711  0.4395 
O:  0.7711  0.4395  0.0478 
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
Ag
232
232
232
232
1.020e+41
11.8
3.414e+39
0.4
1.054e+41
12.2
5
Eu
279
279
279
279
6
Eu
279
287
287
279
7
Eg
287
287
287
287
4.933e+40
5.7
5.208e+40
6.0
1.014e+41
11.8
8
Eg
287
295
295
287
4.933e+40
5.7
5.426e+40
6.3
1.036e+41
12.0
9
Ag
312
312
312
312
4.790e+40
5.6
6.349e+38
0.1
4.853e+40
5.6
10
Au
314
314
314
330
11
Eg
330
330
330
330
3.349e+40
3.9
5.139e+40
6.0
8.488e+40
9.8
12
Eg
330
330
330
335
3.349e+40
3.9
2.659e+40
3.1
6.008e+40
7.0
13
Eu
335
335
335
335
14
Eu
335
365
365
365
15
Eg
365
365
365
365
6.483e+40
7.5
6.292e+40
7.3
1.277e+41
14.8
16
Eg
365
393
393
380
6.483e+40
7.5
1.075e+41
12.5
1.724e+41
20.0
17
Ag
395
395
395
395
8.886e+40
10.3
2.313e+40
2.7
1.120e+41
13.0
18
Au
415
415
415
445
19
Eu
454
454
454
454
20
Eu
454
491
491
454
21
Eg
491
491
491
491
4.227e+40
4.9
4.039e+40
4.7
8.266e+40
9.6
22
Eg
491
507
507
491
4.227e+40
4.9
4.605e+40
5.3
8.832e+40
10.2
23
Ag
510
510
510
510
6.148e+40
7.1
1.976e+38
0.0
6.168e+40
7.2
24
Au
525
525
525
567
25
Eu
567
567
567
567
26
Eu
567
666
666
634
27
Eg
666
666
666
666
3.238e+40
3.8
4.846e+40
5.6
8.084e+40
9.4
28
Eg
666
717
717
666
3.238e+40
3.8
2.759e+40
3.2
5.996e+40
7.0
29
Au
717
720
720
720
30
Ag
720
817
817
784
8.606e+41
99.8
1.993e+39
0.2
8.626e+41
100.0
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.