-    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:  7  Theo Pc 
Lattice parameters (Å):  6.7500  4.0633  6.8344 
Angles (°):  90  90  90 

Symmetry (theoretical): 

Space group:  7  Theo Pc 
Lattice parameters (Å):  6.4326  3.8884  6.6717 
Angles (°):  90.00  98.05  90.00 

Cell contents: 

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

Atomic positions (theoretical):

Si:  0.4917  0.0021  0.5018 
Si:  0.9917  0.4979  0.0018 
Si:  0.3600  0.9956  0.1183 
Si:  0.1370  0.5021  0.3758 
Si:  0.6370  0.9979  0.8758 
Si:  0.8600  0.5044  0.6183 
Si:  0.2687  0.4956  0.7593 
Si:  0.7687  0.0044  0.2593 
O:  0.3298  0.2314  0.3318 
O:  0.1657  0.7326  0.1674 
O:  0.6657  0.7674  0.6674 
O:  0.8298  0.2686  0.8318 
O:  0.4630  0.2326  0.7102 
O:  0.0432  0.7189  0.7958 
O:  0.5432  0.7811  0.2958 
O:  0.9630  0.2674  0.2102 
O:  0.2989  0.7314  0.5458 
O:  0.2061  0.2511  0.9576 
O:  0.7061  0.2489  0.4576 
O:  0.7989  0.7686  0.0458 
O:  0.4226  0.7511  0.9200 
O:  0.0856  0.2811  0.5818 
O:  0.5856  0.2189  0.0818 
O:  0.9226  0.7489  0.4200 
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: 3.8459 0.0704 -0.0121 
0.2459 3.4398 -0.1814 
0.0213 -0.0379 3.9118 
Eig. Value: 3.8816 3.3651 3.9507 
Si: 3.8459 -0.0704 -0.0121 
-0.2459 3.4398 0.1814 
0.0213 0.0379 3.9118 
Eig. Value: 3.8816 3.3651 3.9507 
Si: 3.8769 0.0314 -0.0048 
0.0054 3.4814 0.0542 
-0.0338 0.0199 3.9674 
Eig. Value: 3.8745 3.4776 3.9735 
Si: 3.8459 -0.0704 -0.0121 
-0.2459 3.4398 0.1814 
0.0213 0.0379 3.9118 
Eig. Value: 3.8816 3.3651 3.9507 
Si: 3.8459 0.0704 -0.0121 
0.2459 3.4398 -0.1814 
0.0213 -0.0379 3.9118 
Eig. Value: 3.8816 3.3651 3.9507 
Si: 3.8769 -0.0314 -0.0048 
-0.0054 3.4814 -0.0542 
-0.0338 -0.0199 3.9674 
Eig. Value: 3.8745 3.4776 3.9735 
Si: 3.8769 -0.0314 -0.0048 
-0.0054 3.4814 -0.0542 
-0.0338 -0.0199 3.9674 
Eig. Value: 3.8745 3.4776 3.9735 
Si: 3.8769 0.0314 -0.0048 
0.0054 3.4814 0.0542 
-0.0338 0.0199 3.9674 
Eig. Value: 3.8745 3.4776 3.9735 
O: -1.8922 0.5805 -0.0232 
0.5664 -1.8358 -0.1412 
-0.0212 -0.1213 -1.9967 
Eig. Value: -2.4507 -1.2729 -2.0011 
O: -1.9308 -0.5127 0.0441 
-0.5642 -1.8631 0.1281 
-0.0327 0.0586 -1.9955 
Eig. Value: -2.4468 -1.3510 -1.9916 
O: -1.9308 0.5127 0.0441 
0.5642 -1.8631 -0.1281 
-0.0327 -0.0586 -1.9955 
Eig. Value: -2.4468 -1.3510 -1.9916 
O: -1.8922 -0.5805 -0.0232 
-0.5664 -1.8358 0.1412 
-0.0212 0.1213 -1.9967 
Eig. Value: -2.4507 -1.2729 -2.0011 
O: -1.9308 0.5127 0.0441 
0.5642 -1.8631 -0.1281 
-0.0327 -0.0586 -1.9955 
Eig. Value: -2.4468 -1.3510 -1.9916 
O: -1.9552 0.0352 -0.0066 
0.0293 -1.3572 -0.0129 
0.0001 -0.0565 -1.9480 
Eig. Value: -1.9572 -1.3535 -1.9498 
O: -1.9552 -0.0352 -0.0066 
-0.0293 -1.3572 0.0129 
0.0001 0.0565 -1.9480 
Eig. Value: -1.9572 -1.3535 -1.9498 
O: -1.9308 -0.5127 0.0441 
-0.5642 -1.8631 0.1281 
-0.0327 0.0586 -1.9955 
Eig. Value: -2.4468 -1.3510 -1.9916 
O: -1.8922 -0.5805 -0.0232 
-0.5664 -1.8358 0.1412 
-0.0212 0.1213 -1.9967 
Eig. Value: -2.4507 -1.2729 -2.0011 
O: -1.9445 0.4054 0.0026 
0.3990 -1.8649 0.4940 
0.0663 0.4201 -1.9390 
Eig. Value: -2.4953 -1.2769 -1.9762 
O: -1.9445 -0.4054 0.0026 
-0.3990 -1.8649 -0.4940 
0.0663 -0.4201 -1.9390 
Eig. Value: -2.4953 -1.2769 -1.9762 
O: -1.8922 0.5805 -0.0232 
0.5664 -1.8358 -0.1412 
-0.0212 -0.1213 -1.9967 
Eig. Value: -2.4507 -1.2729 -2.0011 
O: -1.9445 -0.4054 0.0026 
-0.3990 -1.8649 -0.4940 
0.0663 -0.4201 -1.9390 
Eig. Value: -2.4953 -1.2769 -1.9762 
O: -1.9552 0.0352 -0.0066 
0.0293 -1.3572 -0.0129 
0.0001 -0.0565 -1.9480 
Eig. Value: -1.9572 -1.3535 -1.9498 
O: -1.9552 -0.0352 -0.0066 
-0.0293 -1.3572 0.0129 
0.0001 0.0565 -1.9480 
Eig. Value: -1.9572 -1.3535 -1.9498 
O: -1.9445 0.4054 0.0026 
0.3990 -1.8649 0.4940 
0.0663 0.4201 -1.9390 
Eig. Value: -2.4953 -1.2769 -1.9762 
Atom type  X  Y  Z 

Dielectric tensors: 

 X Y Z 
Ɛ∞: 3.3285 0.0000 0.0000 
0.0000 3.1524 0.0000 
0.0000 0.0000 3.3899 
Eig. Value: 3.3285 3.1524 3.3899 
Refractive index (N): 1.8244 0.0000 0.0000 
0.0000 1.7755 0.0000 
0.0000 0.0000 1.8412 
Eig. Value: 1.8244 1.7755 1.8412 
Ɛ0: 8.8567 -0.0000 -0.0414 
-0.0000 7.3320 -0.0000 
-0.0414 -0.0000 8.5757 
Eig. Value: 8.8626 7.3320 8.5697