-    CRISTOBALITE     -    SiO2

The crystal structure is fully relaxed (both unit cell parameters and atomic positions under symmetry constraints) at 40GPa 

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:  2  Theo P-1 
Lattice parameters (Å):  6.7500  4.0633  6.8344 
Angles (°):  90  90  90 

Symmetry (theoretical): 

Space group:  2  Theo P-1 
Lattice parameters (Å):  6.4418  3.8764  6.6721 
Angles (°):  90.13  98.11  90.09 

Cell contents: 

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

Atomic positions (theoretical):

Si:  0.5000  -0.0000  0.5000 
Si:  0.0000  0.5000  0.0000 
Si:  0.3584  0.9984  0.1180 
Si:  0.1349  0.4995  0.3754 
Si:  0.6416  0.0016  0.8820 
Si:  0.8651  0.5005  0.6246 
Si:  0.2731  0.4952  0.7562 
Si:  0.7269  0.5048  0.2438 
O:  0.3302  0.2266  0.3312 
O:  0.1640  0.7402  0.1667 
O:  0.6698  0.7734  0.6688 
O:  0.8360  0.2598  0.8333 
O:  0.4681  0.2345  0.7108 
O:  0.0464  0.7209  0.7949 
O:  0.5319  0.7655  0.2892 
O:  0.9536  0.2791  0.2051 
O:  0.3000  0.7317  0.5441 
O:  0.2086  0.2554  0.9568 
O:  0.7000  0.2683  0.4559 
O:  0.7914  0.7446  0.0432 
O:  0.4229  0.7615  0.9197 
O:  0.0896  0.2729  0.5838 
O:  0.5771  0.2385  0.0803 
O:  0.9104  0.7271  0.4162 
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: 3.8353 0.0744 -0.0340 
0.3152 3.7995 -0.0207 
0.0355 0.0013 3.9755 
Eig. Value: 4.0139 3.6216 3.9748 
Si: 3.8509 -0.0443 0.0021 
-0.1666 3.0548 0.3405 
-0.0027 0.0703 3.8563 
Eig. Value: 3.8517 2.9930 3.9173 
Si: 3.8518 0.0328 0.0011 
0.0607 3.7708 -0.1332 
-0.0348 -0.0356 3.9443 
Eig. Value: 3.8545 3.7254 3.9870 
Si: 3.8858 -0.0541 -0.0134 
-0.2026 3.1315 -0.0166 
0.0236 -0.0053 3.9332 
Eig. Value: 3.9054 3.1102 3.9350 
Si: 3.8518 0.0328 0.0011 
0.0607 3.7708 -0.1332 
-0.0348 -0.0356 3.9443 
Eig. Value: 3.8545 3.7254 3.9870 
Si: 3.8858 -0.0541 -0.0134 
-0.2026 3.1315 -0.0166 
0.0236 -0.0053 3.9332 
Eig. Value: 3.9054 3.1102 3.9350 
Si: 3.8867 -0.0144 0.0069 
0.0262 3.4039 0.0054 
-0.0289 0.0070 3.9682 
Eig. Value: 3.8853 3.4037 3.9697 
Si: 3.8867 -0.0144 0.0069 
0.0262 3.4039 0.0054 
-0.0289 0.0070 3.9682 
Eig. Value: 3.8853 3.4037 3.9697 
O: -1.9137 0.5172 -0.0236 
0.5716 -1.8788 -0.1177 
-0.0160 -0.1060 -2.0084 
Eig. Value: -2.4503 -1.3383 -2.0123 
O: -1.9184 -0.5725 0.0424 
-0.5547 -1.8220 0.1538 
-0.0343 0.0779 -1.9825 
Eig. Value: -2.4502 -1.2945 -1.9781 
O: -1.9137 0.5172 -0.0236 
0.5716 -1.8788 -0.1177 
-0.0160 -0.1060 -2.0084 
Eig. Value: -2.4503 -1.3383 -2.0123 
O: -1.9184 -0.5725 0.0424 
-0.5547 -1.8220 0.1538 
-0.0343 0.0779 -1.9825 
Eig. Value: -2.4502 -1.2945 -1.9781 
O: -1.9347 0.5046 0.0441 
0.5341 -1.8638 -0.1305 
-0.0294 -0.0634 -1.9976 
Eig. Value: -2.4317 -1.3717 -1.9927 
O: -1.9522 0.0357 -0.0029 
0.0073 -1.3190 -0.0342 
-0.0023 -0.0747 -1.9405 
Eig. Value: -1.9530 -1.3135 -1.9451 
O: -1.9347 0.5046 0.0441 
0.5341 -1.8638 -0.1305 
-0.0294 -0.0634 -1.9976 
Eig. Value: -2.4317 -1.3717 -1.9927 
O: -1.9522 0.0357 -0.0029 
0.0073 -1.3190 -0.0342 
-0.0023 -0.0747 -1.9405 
Eig. Value: -1.9530 -1.3135 -1.9451 
O: -1.9017 -0.5740 -0.0148 
-0.5848 -1.8071 0.0980 
-0.0223 0.1232 -1.9870 
Eig. Value: -2.4441 -1.2609 -1.9908 
O: -1.9441 0.4015 -0.0068 
0.3643 -1.8355 0.4536 
0.0669 0.4186 -1.9510 
Eig. Value: -2.4587 -1.2950 -1.9769 
O: -1.9017 -0.5740 -0.0148 
-0.5848 -1.8071 0.0980 
-0.0223 0.1232 -1.9870 
Eig. Value: -2.4441 -1.2609 -1.9908 
O: -1.9441 0.4015 -0.0068 
0.3643 -1.8355 0.4536 
0.0669 0.4186 -1.9510 
Eig. Value: -2.4587 -1.2950 -1.9769 
O: -1.9507 -0.3611 -0.0108 
-0.3603 -1.8886 -0.4735 
0.0684 -0.3755 -1.9632 
Eig. Value: -2.4666 -1.3516 -1.9843 
O: -1.9519 0.0692 -0.0063 
0.0640 -1.3186 0.0350 
-0.0073 -0.0021 -1.9314 
Eig. Value: -1.9613 -1.3112 -1.9293 
O: -1.9507 -0.3611 -0.0108 
-0.3603 -1.8886 -0.4735 
0.0684 -0.3755 -1.9632 
Eig. Value: -2.4666 -1.3516 -1.9843 
O: -1.9519 0.0692 -0.0063 
0.0640 -1.3186 0.0350 
-0.0073 -0.0021 -1.9314 
Eig. Value: -1.9613 -1.3112 -1.9293 
Atom type  X  Y  Z 

Dielectric tensors: 

 X Y Z 
Ɛ∞: 3.3390 0.0000 0.0000 
0.0000 3.1483 0.0000 
0.0000 0.0000 3.3959 
Eig. Value: 3.3389 3.1482 3.3960 
Refractive index (N): 1.8273 0.0000 0.0000 
0.0000 1.7744 0.0000 
0.0000 0.0000 1.8428 
Eig. Value: 1.8273 1.7743 1.8428 
Ɛ0: 8.9351 0.0663 -0.0277 
0.0663 7.3901 -0.0559 
-0.0277 -0.0559 8.5669 
Eig. Value: 8.9403 7.3848 8.5669