-    ANATASE     -    TiO2

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:  141  I4_1/amd 
Lattice parameters (Å):  3.7842  3.7842  9.5146 
Angles (°):  90.0  90.0  90.0 

Symmetry (theoretical): 

Space group:  141  I4_1/amd 
Lattice parameters (Å):  5.3148  5.3148  5.3148 
Angles (°):  138.6  138.6  60.0 

Cell contents: 

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

Atomic positions (theoretical):

Ti:  0.0000  0.0000  0.0000 
O:  0.2106  0.2106  0.0000 
Ti:  0.7500  0.2500  0.5000 
O:  0.9606  0.4606  0.5000 
O:  0.5394  0.0394  0.5000 
O:  0.7894  0.7894  0.0000 
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
Eg
191
191
191
191
2.157e+41
14.9
2.955e+41
20.4
5.111e+41
35.3
5
Eg
191
191
191
191
2.139e+41
14.8
2.952e+41
20.4
5.092e+41
35.2
6
Eg
215
215
215
215
4.356e+41
30.1
6.000e+41
41.5
1.036e+42
71.6
7
Eg
215
215
215
215
4.403e+41
30.4
6.044e+41
41.8
1.045e+42
72.2
8
Eu
299
299
299
299
1.721e+38
0.0
2.106e+38
0.0
3.827e+38
0.0
9
Eu
299
368
368
299
1.037e+38
0.0
1.166e+38
0.0
2.203e+38
0.0
10
B1g
417
417
417
417
3.361e+41
23.2
2.521e+41
17.4
5.881e+41
40.7
11
A2u
446
446
446
552
3.697e+37
0.0
1.624e+37
0.0
5.321e+37
0.0
12
Eu
552
552
552
552
1.329e+38
0.0
1.663e+38
0.0
2.992e+38
0.0
13
Eu
552
558
558
558
2.275e+37
0.0
2.559e+37
0.0
4.834e+37
0.0
14
A1g
558
565
565
565
9.543e+41
66.0
1.340e+41
9.3
1.088e+42
75.2
15
B1g
565
586
586
586
2.541e+41
17.6
1.906e+41
13.2
4.447e+41
30.7
16
B2u
586
720
720
720
17
Eg
720
720
720
720
6.087e+41
42.1
8.373e+41
57.9
1.446e+42
100.0
18
Eg
720
927
927
786
6.093e+41
42.1
8.375e+41
57.9
1.447e+42
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.