-    CRISTOBALITE     -    SiO2

1x2x1 super structure. The crystal structure is fully relaxed (both unit cell parameters and atomic positions under symmetry constraints) at 10GPa. 

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:  Theo 14  Theo P2_1/n 
Lattice parameters (Å):  6.7500  4.0633  6.8344 
Angles (°):  90  90  90 

Symmetry (theoretical): 

Space group:  Theo 14  Theo P2_1/n 
Lattice parameters (Å):  6.4543  7.7910  6.6941 
Angles (°):  89.98  98.05  89.39 

Cell contents: 

Number of atoms:  48 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Si:  0.4998  0.9890  0.4942 
Si:  0.0067  0.2431  0.0002 
Si:  0.3510  0.5045  0.1118 
Si:  0.1433  0.2469  0.3749 
Si:  0.6423  0.9904  0.8806 
Si:  0.8625  0.2501  0.6313 
Si:  0.2769  0.2427  0.7591 
Si:  0.7217  0.2155  0.2429 
O:  0.3328  0.1166  0.3311 
O:  0.1686  0.3664  0.1664 
O:  0.6656  0.3851  0.6695 
O:  0.8309  0.1361  0.8371 
O:  0.4677  0.1125  0.7083 
O:  0.0457  0.3588  0.7974 
O:  0.5510  0.3862  0.2900 
O:  0.9580  0.1382  0.2080 
O:  0.2994  0.3646  0.5438 
O:  0.2116  0.1224  0.9577 
O:  0.7036  0.1333  0.4631 
O:  0.7933  0.3770  0.0558 
O:  0.4222  0.3800  0.9182 
O:  0.0854  0.1439  0.5811 
O:  0.5706  0.1172  0.0729 
O:  0.9059  0.3695  0.4077 
Si:  0.4878  0.5037  0.5058 
Si:  0.9837  0.7600  0.0002 
Si:  0.3657  0.9831  0.1249 
Si:  0.1288  0.7622  0.3789 
Si:  0.6378  0.5047  0.8737 
Si:  0.8669  0.7588  0.6136 
Si:  0.2658  0.7509  0.7577 
Si:  0.7701  0.5356  0.2614 
O:  0.3300  0.6112  0.3302 
O:  0.1602  0.8686  0.1663 
O:  0.6694  0.8838  0.6658 
O:  0.8348  0.6291  0.8315 
O:  0.4633  0.6183  0.7112 
O:  0.0446  0.8615  0.7944 
O:  0.5298  0.8833  0.2936 
O:  0.9699  0.6331  0.2066 
O:  0.3006  0.8654  0.5485 
O:  0.2037  0.6301  0.9562 
O:  0.7013  0.6245  0.4620 
O:  0.7937  0.8800  0.0363 
O:  0.4222  0.8751  0.9187 
O:  0.0909  0.6345  0.5835 
O:  0.5829  0.6116  0.0811 
O:  0.9241  0.8703  0.4260 
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.
   

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: 3.8138 0.1808 0.1530 
0.3902 3.7838 -0.1998 
0.0382 -0.0628 3.9231 
Eig. Value: 4.0883 3.4572 3.9752 
Si: 3.8488 -0.0506 -0.0281 
-0.1932 3.0772 0.4060 
-0.0877 0.1571 3.8814 
Eig. Value: 3.8085 2.9771 4.0218 
Si: 3.9859 0.0002 0.0562 
-0.1243 3.5291 -0.0366 
-0.0337 0.0128 3.9307 
Eig. Value: 3.9967 3.5206 3.9285 
Si: 3.9768 -0.0631 0.0170 
-0.3185 3.1715 0.0230 
0.0976 -0.0333 3.9061 
Eig. Value: 4.0434 3.1285 3.8824 
Si: 3.9550 0.0084 0.0671 
0.0420 3.8202 -0.0817 
-0.1377 0.1214 3.8289 
Eig. Value: 3.9668 3.7933 3.8440 
Si: 3.8667 -0.0841 0.0753 
-0.1724 3.1602 -0.1390 
0.0151 -0.0364 4.0891 
Eig. Value: 3.8733 3.1312 4.1115 
Si: 3.9141 -0.0017 -0.0033 
-0.0236 3.3807 -0.0391 
-0.0151 -0.0049 4.0063 
Eig. Value: 3.9136 3.3796 4.0079 
Si: 3.7682 0.0756 -0.0230 
0.2405 3.6933 0.0750 
-0.0340 0.0288 3.7685 
Eig. Value: 3.8940 3.5525 3.7834 
O: -1.9074 0.5201 -0.0078 
0.5756 -1.9616 -0.1593 
-0.0173 -0.1485 -1.9524 
Eig. Value: -1.3631 -2.5026 -1.9556 
O: -1.9524 -0.5646 0.0508 
-0.5007 -1.8233 0.1744 
-0.0033 0.1011 -1.9855 
Eig. Value: -2.4504 -1.3393 -1.9715 
O: -1.9268 0.4858 0.0199 
0.5409 -1.8200 -0.1642 
-0.0479 -0.1274 -2.0393 
Eig. Value: -2.4108 -1.3373 -2.0380 
O: -1.9144 -0.5549 -0.0202 
-0.5441 -1.8207 0.1798 
-0.0486 0.1083 -1.9641 
Eig. Value: -2.4306 -1.2910 -1.9776 
O: -1.9152 0.4886 0.0288 
0.5193 -1.9010 -0.1784 
-0.0302 -0.1079 -2.0042 
Eig. Value: -2.4358 -1.3868 -1.9977 
O: -1.9725 0.0395 -0.0334 
0.0218 -1.3014 -0.0082 
-0.0017 -0.0493 -1.9505 
Eig. Value: -1.9825 -1.2986 -1.9433 
O: -2.1367 0.3290 0.1027 
0.3290 -1.9372 -0.1562 
0.0705 -0.0576 -1.9563 
Eig. Value: -2.4192 -1.6883 -1.9227 
O: -2.0156 -0.0378 0.0142 
0.0192 -1.2656 -0.0375 
0.0077 -0.0550 -1.8916 
Eig. Value: -2.0166 -1.2620 -1.8942 
O: -1.9012 -0.5820 -0.0314 
-0.5414 -1.8292 0.1442 
-0.0674 0.1613 -2.0087 
Eig. Value: -2.4394 -1.2735 -2.0262 
O: -1.9224 0.4242 -0.0004 
0.3826 -1.8227 0.4089 
0.0665 0.3863 -1.9468 
Eig. Value: -2.4300 -1.2942 -1.9677 
O: -1.9035 -0.5811 -0.0890 
-0.6040 -1.7838 0.1106 
-0.0412 0.1034 -2.0044 
Eig. Value: -2.4405 -1.2286 -2.0226 
O: -1.8797 0.4690 0.0528 
0.3747 -2.0517 0.1144 
0.1028 0.1228 -2.1751 
Eig. Value: -1.5076 -2.4049 -2.1940 
O: -1.9538 -0.4245 -0.0179 
-0.3773 -1.8469 -0.4236 
0.0588 -0.3749 -1.9576 
Eig. Value: -2.4586 -1.3236 -1.9762 
O: -1.9855 0.0614 0.0094 
0.0592 -1.2394 0.0162 
0.0058 -0.0112 -1.9846 
Eig. Value: -1.9954 -1.2345 -1.9796 
O: -1.9445 -0.4177 0.0322 
-0.4077 -1.8817 -0.4337 
0.0753 -0.3532 -2.0254 
Eig. Value: -2.4779 -1.3339 -2.0398 
O: -2.0167 0.2988 -0.1167 
0.2700 -1.8963 0.3190 
-0.0845 0.2524 -2.0383 
Eig. Value: -2.4318 -1.5926 -1.9269 
Si: 3.9140 0.0249 -0.1236 
0.1502 3.4854 -0.0296 
-0.0060 -0.0015 3.9768 
Eig. Value: 3.8837 3.4682 4.0244 
Si: 3.8813 -0.0330 -0.0014 
-0.2419 3.4798 0.1951 
0.2109 -0.1210 3.8886 
Eig. Value: 4.0003 3.4274 3.8220 
Si: 3.7286 0.1407 -0.1112 
0.2253 3.7712 -0.0221 
0.0129 -0.0311 4.0213 
Eig. Value: 3.5649 3.9097 4.0466 
Si: 3.7736 0.0043 -0.0117 
-0.0683 3.4050 0.1602 
-0.1163 0.1183 3.9804 
Eig. Value: 3.7556 3.3724 4.0312 
Si: 3.8023 0.1053 -0.0193 
0.2357 3.4464 -0.2939 
0.0631 -0.1273 4.0036 
Eig. Value: 3.8563 3.3170 4.0790 
Si: 3.9232 0.0586 -0.1246 
-0.0509 3.4310 0.0564 
0.0272 0.0656 3.8466 
Eig. Value: 3.9480 3.4220 3.8309 
Si: 3.8561 -0.0248 0.0461 
0.0780 3.5116 -0.0035 
-0.0099 0.0004 3.9738 
Eig. Value: 3.8554 3.5096 3.9766 
Si: 3.6841 0.0837 0.0458 
0.1962 3.7023 0.0980 
-0.0062 0.0342 3.7735 
Eig. Value: 3.5485 3.8729 3.7384 
O: -1.9096 0.5668 -0.0211 
0.5328 -1.8227 -0.1811 
-0.0095 -0.1723 -2.0276 
Eig. Value: -2.4471 -1.2877 -2.0252 
O: -1.9227 -0.4815 -0.0118 
-0.6236 -1.8389 0.1861 
-0.1015 0.0923 -2.0461 
Eig. Value: -2.4424 -1.3001 -2.0653 
O: -1.9630 0.5094 -0.0469 
0.5786 -1.8716 -0.1527 
-0.0536 -0.1113 -1.9918 
Eig. Value: -2.4691 -1.3447 -2.0126 
O: -1.8936 -0.6020 0.0422 
-0.5720 -1.9345 0.1786 
0.0061 0.1786 -1.9883 
Eig. Value: -1.3094 -2.5403 -1.9666 
O: -1.9374 0.5097 0.0305 
0.5481 -1.8264 -0.1670 
-0.0660 -0.0982 -1.9766 
Eig. Value: -2.4267 -1.3310 -1.9827 
O: -1.9608 0.0258 0.0393 
0.0074 -1.3734 -0.0572 
0.0163 -0.0798 -1.9704 
Eig. Value: -1.9390 -1.3653 -2.0003 
O: -1.4689 0.0252 -0.1349 
0.0224 -1.5407 0.0004 
-0.1700 0.0132 -1.9737 
Eig. Value: -1.4227 -1.5441 -2.0165 
O: -1.9307 -0.5273 0.0283 
-0.5565 -1.8482 0.1516 
-0.0388 0.0865 -2.0698 
Eig. Value: -2.4489 -1.3347 -2.0651 
O: -1.9437 -0.5539 0.0005 
-0.6297 -1.8202 0.1858 
0.0289 0.1743 -1.9940 
Eig. Value: -2.5112 -1.2654 -1.9813 
O: -1.9253 0.4377 -0.0059 
0.4161 -1.8824 0.4754 
0.0694 0.4046 -1.9513 
Eig. Value: -2.5081 -1.2813 -1.9697 
O: -1.9923 -0.4695 0.0237 
-0.4679 -1.8040 -0.4589 
0.0639 -0.3517 -1.9414 
Eig. Value: -2.4894 -1.2423 -2.0060 
O: -1.9567 0.4960 -0.1657 
0.5908 -1.8906 0.1282 
-0.1397 0.1001 -1.4620 
Eig. Value: -2.5025 -1.3712 -1.4355 
O: -1.9575 -0.3976 0.0375 
-0.4625 -1.9068 -0.4885 
0.0972 -0.3363 -1.9636 
Eig. Value: -2.4958 -1.3042 -2.0279 
O: -1.9485 0.0417 -0.0444 
0.0598 -1.4942 0.0106 
-0.0388 -0.0483 -1.9237 
Eig. Value: -1.9814 -1.4873 -1.8977 
O: -1.9967 -0.0652 -0.0483 
-0.0264 -1.3132 0.0210 
-0.0223 0.0085 -1.9418 
Eig. Value: -2.0157 -1.3097 -1.9263 
O: -1.7369 0.1055 0.2690 
0.1003 -1.4985 0.0929 
0.2948 0.0691 -1.6917 
Eig. Value: -1.9980 -1.5979 -1.3311 
Atom type 

Dielectric tensors: 

 
Ɛ0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 
Eig. Value: 0.0000 0.0000 0.0000 
Refractive index (N): 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 
Ɛ00.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 
Eig. Value: 0.0000 0.0000 0.0000