-    CRISTOBALITE     -    SiO2

 

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:  92  P4_12_12 
Lattice parameters (Å):  4.9717  4.9717  6.9223 
Angles (°):  90  90  90 

Symmetry (theoretical): 

Space group:  92  P4_12_12 
Lattice parameters (Å):  4.9507  4.9507  6.8964 
Angles (°):  90  90  90 

Cell contents: 

Number of atoms:  12 
Number of atom types:  2 
Chemical composition:  0 

Atomic positions (theoretical):

Si:  0.3000  0.3000  0.0000 
O:  0.2392  0.1041  0.1787 
Si:  0.2000  0.8000  0.2500 
O:  0.3959  0.7392  0.4287 
O:  0.2608  0.6041  0.0713 
Si:  0.7000  0.7000  0.5000 
O:  0.7608  0.8959  0.6787 
O:  0.8959  0.7608  0.3213 
O:  0.1041  0.2392  0.8213 
Si:  0.8000  0.2000  0.7500 
O:  0.6041  0.2608  0.9287 
O:  0.7392  0.3959  0.5713 
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): 

Si: 3.3534 0.0211 0.1738 
0.0211 3.3534 -0.1738 
-0.3288 0.3288 3.3065 
Eig. Value: 3.4298 3.3746 3.2091 
O: -1.0494 -0.1566 0.0694 
-0.2145 -2.3040 0.8061 
0.2046 0.8050 -1.6533 
Eig. Value: -1.0193 -2.8765 -1.1109 
Si: 3.3534 -0.0211 0.1738 
-0.0211 3.3534 0.1738 
-0.3288 -0.3288 3.3065 
Eig. Value: 3.4298 3.3746 3.2091 
O: -2.3040 0.2145 -0.8062 
0.1566 -1.0494 0.0694 
-0.8050 0.2046 -1.6533 
Eig. Value: -2.8765 -1.0193 -1.1109 
O: -1.0494 0.1566 0.0694 
0.2145 -2.3040 -0.8062 
0.2046 -0.8050 -1.6533 
Eig. Value: -1.0193 -2.8765 -1.1109 
Si: 3.3534 0.0211 -0.1738 
0.0211 3.3534 0.1738 
0.3288 -0.3288 3.3065 
Eig. Value: 3.4298 3.3746 3.2091 
O: -1.0494 -0.1566 -0.0694 
-0.2145 -2.3040 -0.8061 
-0.2046 -0.8050 -1.6533 
Eig. Value: -1.0193 -2.8765 -1.1109 
O: -2.3040 -0.2145 0.8061 
-0.1566 -1.0494 0.0694 
0.8050 0.2046 -1.6533 
Eig. Value: -2.8765 -1.0193 -1.1109 
O: -2.3040 -0.2145 -0.8061 
-0.1566 -1.0494 -0.0694 
-0.8050 -0.2046 -1.6533 
Eig. Value: -2.8765 -1.0193 -1.1109 
Si: 3.3534 -0.0211 -0.1738 
-0.0211 3.3534 -0.1738 
0.3288 0.3288 3.3065 
Eig. Value: 3.4298 3.3746 3.2091 
O: -2.3040 0.2145 0.8062 
0.1566 -1.0494 -0.0694 
0.8050 -0.2046 -1.6533 
Eig. Value: -2.8765 -1.0193 -1.1109 
O: -1.0494 0.1566 -0.0694 
0.2145 -2.3040 0.8062 
-0.2046 0.8050 -1.6533 
Eig. Value: -1.0193 -2.8765 -1.1109 
Atom type  X  Y  Z 

Dielectric tensors: 

 X Y Z 
Ɛ∞: 2.2676 0.0000 0.0000 
0.0000 2.2676 0.0000 
0.0000 0.0000 2.2567 
Eig. Value: 2.2676 2.2676 2.2567 
Refractive index (N): 1.5059 0.0000 0.0000 
0.0000 1.5059 0.0000 
0.0000 0.0000 1.5022 
Eig. Value: 1.5059 1.5059 1.5022 
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