-    BROOKITE     -    TiO2

 

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:  61  Pbca 
Lattice parameters (Å):  9.1740  5.4490  5.1380 
Angles (°):  90.0  90.0  90.0 

Symmetry (theoretical): 

Space group:  61  Pbca 
Lattice parameters (Å):  9.1696  5.4410  5.1480 
Angles (°):  90.0  90.0  90.0 

Cell contents: 

Number of atoms:  24 
Number of atom types:  2 
Chemical composition:  0 

Atomic positions (theoretical):

Ti:  0.1289  0.0984  0.8622 
O:  0.0114  0.1473  0.1824 
O:  0.2292  0.1081  0.5343 
Ti:  0.3711  0.9016  0.3622 
O:  0.4886  0.8527  0.6824 
O:  0.2708  0.8919  0.0343 
Ti:  0.8711  0.5984  0.6378 
O:  0.9886  0.6473  0.3176 
O:  0.7708  0.6081  0.9657 
Ti:  0.6289  0.4016  0.1378 
O:  0.5114  0.3527  0.8176 
O:  0.7292  0.3919  0.4657 
Ti:  0.8711  0.9016  0.1378 
O:  0.9886  0.8527  0.8176 
O:  0.7708  0.8919  0.4657 
Ti:  0.6289  0.0984  0.6378 
O:  0.5114  0.1473  0.3176 
O:  0.7292  0.1081  0.9657 
Ti:  0.1289  0.4016  0.3622 
O:  0.0114  0.3527  0.6824 
O:  0.2292  0.3919  0.0343 
Ti:  0.3711  0.5984  0.8622 
O:  0.4886  0.6473  0.1824 
O:  0.2708  0.6081  0.5343 
Atom type  X  Y  Z 

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.
 

Dielectric Properties 


We define:

  • The Born effective charges, also called dynamical charges, are tensors that correspond to the energy derivative with respect to atomic displacements and electric fields or, equivalently, to the change in atomic force due to an electric field: The sum of the Born effective charges of all nuclei in one cell must vanish, element by element, along each of the three directions of the space.
  • The dielectric tensors are the energy derivative with respect to two electric fields. They also relate the induced polarization to the external electric field.

Born effective charges (Z): 

Ti: 6.5798 0.0508 0.0634 
-0.0705 6.0985 -0.8320 
0.2755 -1.0946 6.0703 
Eig. Value: 6.5565 7.0800 5.1121 
O: -3.4148 -1.8442 0.1299 
-1.8387 -3.2643 -0.7586 
0.0408 -0.8384 -2.6076 
Eig. Value: -5.2767 -1.1976 -2.8123 
O: -3.1650 1.4998 1.4831 
1.3848 -2.8343 -0.0456 
1.1887 -0.0262 -3.4627 
Eig. Value: -5.1534 -1.1711 -3.1374 
Ti: 6.5798 0.0508 -0.0634 
-0.0705 6.0985 0.8320 
-0.2755 1.0946 6.0703 
Eig. Value: 6.5565 7.0800 5.1121 
O: -3.4148 -1.8442 -0.1299 
-1.8387 -3.2643 0.7586 
-0.0408 0.8384 -2.6076 
Eig. Value: -5.2767 -1.1976 -2.8123 
O: -3.1650 1.4998 -1.4831 
1.3848 -2.8343 0.0456 
-1.1887 0.0262 -3.4627 
Eig. Value: -5.1534 -1.1711 -3.1374 
Ti: 6.5798 -0.0508 0.0634 
0.0705 6.0985 0.8320 
0.2755 1.0946 6.0703 
Eig. Value: 6.5565 7.0800 5.1121 
O: -3.4148 1.8442 0.1299 
1.8387 -3.2643 0.7586 
0.0408 0.8384 -2.6076 
Eig. Value: -5.2767 -1.1976 -2.8123 
O: -3.1650 -1.4998 1.4831 
-1.3848 -2.8343 0.0456 
1.1887 0.0262 -3.4627 
Eig. Value: -5.1534 -1.1711 -3.1374 
Ti: 6.5798 -0.0508 -0.0634 
0.0705 6.0985 -0.8320 
-0.2755 -1.0946 6.0703 
Eig. Value: 6.5565 7.0800 5.1121 
O: -3.4148 1.8442 -0.1299 
1.8387 -3.2643 -0.7586 
-0.0408 -0.8384 -2.6076 
Eig. Value: -5.2767 -1.1976 -2.8123 
O: -3.1650 -1.4998 -1.4831 
-1.3848 -2.8343 -0.0456 
-1.1887 -0.0262 -3.4627 
Eig. Value: -5.1534 -1.1711 -3.1374 
Ti: 6.5798 0.0508 0.0634 
-0.0705 6.0985 -0.8320 
0.2755 -1.0946 6.0703 
Eig. Value: 6.5565 7.0800 5.1121 
O: -3.4148 -1.8442 0.1299 
-1.8387 -3.2643 -0.7586 
0.0408 -0.8384 -2.6076 
Eig. Value: -5.2767 -1.1976 -2.8123 
O: -3.1650 1.4998 1.4831 
1.3848 -2.8343 -0.0456 
1.1887 -0.0262 -3.4627 
Eig. Value: -5.1534 -1.1711 -3.1374 
Ti: 6.5798 0.0508 -0.0634 
-0.0705 6.0985 0.8320 
-0.2755 1.0946 6.0703 
Eig. Value: 6.5565 7.0800 5.1121 
O: -3.4148 -1.8442 -0.1299 
-1.8387 -3.2643 0.7586 
-0.0408 0.8384 -2.6076 
Eig. Value: -5.2767 -1.1976 -2.8123 
O: -3.1650 1.4998 -1.4831 
1.3848 -2.8343 0.0456 
-1.1887 0.0262 -3.4627 
Eig. Value: -5.1534 -1.1711 -3.1374 
Ti: 6.5798 -0.0508 0.0634 
0.0705 6.0985 0.8320 
0.2755 1.0946 6.0703 
Eig. Value: 6.5565 7.0800 5.1121 
O: -3.4148 1.8442 0.1299 
1.8387 -3.2643 0.7586 
0.0408 0.8384 -2.6076 
Eig. Value: -5.2767 -1.1976 -2.8123 
O: -3.1650 -1.4998 1.4831 
-1.3848 -2.8343 0.0456 
1.1887 0.0262 -3.4627 
Eig. Value: -5.1534 -1.1711 -3.1374 
Ti: 6.5798 -0.0508 -0.0634 
0.0705 6.0985 -0.8320 
-0.2755 -1.0946 6.0703 
Eig. Value: 6.5565 7.0800 5.1121 
O: -3.4148 1.8442 -0.1299 
1.8387 -3.2643 -0.7586 
-0.0408 -0.8384 -2.6076 
Eig. Value: -5.2767 -1.1976 -2.8123 
O: -3.1650 -1.4998 -1.4831 
-1.3848 -2.8343 -0.0456 
-1.1887 -0.0262 -3.4627 
Eig. Value: -5.1534 -1.1711 -3.1374 
Atom type  X  Y  Z 

Dielectric tensors: 

 X Y Z 
Ɛ∞: 7.4592 0.0000 0.0000 
0.0000 6.8930 0.0000 
0.0000 0.0000 6.9041 
Eig. Value: 7.4592 6.8930 6.9041 
Refractive index (N): 2.7311 0.0000 0.0000 
0.0000 2.6255 0.0000 
0.0000 0.0000 2.6276 
Eig. Value: 2.7311 2.6255 2.6276 
Ɛ0: 0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 
Eig. Value: 0.0000 0.0000 0.0000