-    ANATASE     -    TiO2

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:  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):  5.4539  5.4539  5.4539 
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:  0.2064  0.2064  0.0000 
Ti:  0.7500  0.2500  0.5000 
O:  0.9564  0.4564  0.5000 
O:  0.5436  0.0436  0.5000 
O:  0.7936  0.7936  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
176
176
176
176
7.629e+41
41.8
1.053e+42
57.7
1.816e+42
99.5
5
Eg
176
176
176
176
7.706e+41
42.2
1.054e+42
57.8
1.825e+42
100.0
6
Eg
213
213
213
213
2.212e+41
12.1
3.052e+41
16.7
5.264e+41
28.8
7
Eg
213
213
213
213
2.237e+41
12.3
3.067e+41
16.8
5.304e+41
29.1
8
Eu
298
298
298
298
1.634e+38
0.0
1.712e+38
0.0
3.346e+38
0.0
9
Eu
298
366
366
298
1.544e+38
0.0
1.513e+38
0.0
3.058e+38
0.0
10
B1g
400
400
400
400
5.639e+41
30.9
4.229e+41
23.2
9.868e+41
54.1
11
A2u
410
410
410
477
5.813e+37
0.0
2.525e+37
0.0
8.337e+37
0.0
12
Eu
477
477
477
477
1.396e+38
0.0
1.732e+38
0.0
3.127e+38
0.0
13
Eu
477
530
530
530
2.304e+37
0.0
2.257e+37
0.0
4.561e+37
0.0
14
B1g
530
535
535
535
1.499e+41
8.2
1.125e+41
6.2
2.624e+41
14.4
15
A1g
535
561
561
561
8.723e+41
47.8
1.249e+41
6.8
9.971e+41
54.6
16
B2u
561
673
673
673
17
Eg
673
673
673
673
6.749e+41
37.0
9.282e+41
50.9
1.603e+42
87.8
18
Eg
673
862
862
755
6.754e+41
37.0
9.286e+41
50.9
1.604e+42
87.9
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.