-    RUTILE     -    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:  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):  4.5230  4.5230  2.9060 
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 
O:  0.3042  0.3042  0.0000 
Ti:  0.5000  0.5000  0.5000 
O:  0.1958  0.8042  0.5000 
O:  0.6958  0.6958  0.0000 
O:  0.8042  0.1958  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
B1g
137
137
137
137
9.568e+39
0.4
7.176e+39
0.3
1.674e+40
0.7
5
B1u
186
186
186
186
6
Eu
268
268
268
268
7
Eu
268
364
364
268
8
A2u
364
378
378
424
9
A2g
424
424
424
425
10
Eu
425
425
425
425
11
Eu
425
476
476
501
12
B1u
501
501
501
503
13
Eg
503
503
503
503
3.776e+41
16.7
5.580e+41
24.7
9.356e+41
41.5
14
Eg
503
503
503
573
3.776e+41
16.7
4.805e+41
21.3
8.582e+41
38.1
15
Eu
573
573
573
573
16
Eu
573
656
656
656
17
A1g
656
858
858
836
1.714e+42
76.0
5.410e+41
24.0
2.255e+42
100.0
18
B2g
858
868
868
858
1.028e+39
0.0
1.413e+39
0.1
2.441e+39
0.1
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.