-    RUTILE     -    TiO2

Theoretical atomic positions. Lattice parameters fixed as 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:  136  P4_2/mnm 
Lattice parameters (Å):  4.5870  4.5870  2.9540 
Angles (°):  90.0  90.0  90.0 

Symmetry (theoretical): 

Space group:  136  P4_2/mnm 
Lattice parameters (Å):  4.5870  4.5870  2.9540 
Angles (°):  90.0  90.0  90.0 

Cell contents: 

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

Atomic positions (theoretical):

Ti:  0.0000  0.0000  0.0000 
Ti:  0.5000  0.5000  0.5000 
O:  0.2984  0.2984  0.0000 
O:  0.7016  0.7016  0.0000 
O:  0.2016  0.7984  0.5000 
O:  0.7984  0.2016  0.5000 
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
134
134
134
134
5
B1g
181
181
181
181
2.543e+39
0.1
1.907e+39
0.1
4.451e+39
0.1
6
A2u
212
212
212
257
7
Eu
257
257
257
257
8
Eu
257
380
380
413
9
B1u
413
413
413
421
10
Eg
421
421
421
421
5.185e+41
16.4
5.509e+41
17.4
1.069e+42
33.8
11
Eg
421
421
421
426
5.185e+41
16.4
8.749e+41
27.7
1.393e+42
44.1
12
Eu
426
426
426
426
13
Eu
426
426
426
426
14
A2g
426
465
465
501
15
Eu
501
501
501
501
16
Eu
501
565
565
565
17
A1g
565
809
809
733
2.227e+42
70.4
9.339e+41
29.6
3.160e+42
100.0
18
B2g
809
826
826
809
2.357e+39
0.1
3.241e+39
0.1
5.598e+39
0.2
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.