-    CRISTOBALITE X-I     -    SiO2

2x1x1 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):  12.8731  3.8829  6.6716 
Angles (°): 

Cell contents: 

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

Atomic positions (theoretical):

Si:  0.2508  0.0002  0.5013 
Si:  0.9959  0.4984  0.0008 
Si:  0.1787  0.9983  0.1178 
Si:  0.0697  0.5021  0.3759 
Si:  0.3209  0.0021  0.8831 
Si:  0.4325  0.5006  0.6255 
Si:  0.1358  0.4969  0.7584 
Si:  0.3632  0.5050  0.2441 
O:  0.1660  0.2247  0.3323 
O:  0.0822  0.7325  0.1664 
O:  0.3355  0.7743  0.6703 
O:  0.4183  0.2599  0.8346 
O:  0.2336  0.2345  0.7120 
O:  0.0223  0.7200  0.7949 
O:  0.2660  0.7656  0.2897 
O:  0.4767  0.2794  0.2056 
O:  0.1517  0.7314  0.5458 
O:  0.1027  0.2538  0.9567 
O:  0.3501  0.2688  0.4569 
O:  0.3961  0.7446  0.0439 
O:  0.2114  0.7614  0.9210 
O:  0.0439  0.2813  0.5813 
O:  0.2882  0.2385  0.0808 
O:  0.4549  0.7269  0.4164 
Si:  0.7458  0.0019  0.5004 
Si:  0.5008  0.4992  0.0012 
Si:  0.6812  0.9959  0.1184 
Si:  0.5670  0.4996  0.3753 
Si:  0.8192  0.9974  0.8748 
Si:  0.9308  0.5047  0.6174 
Si:  0.6359  0.4938  0.7570 
Si:  0.8852  0.0043  0.2589 
O:  0.6647  0.2332  0.3306 
O:  0.5834  0.7400  0.1675 
O:  0.8331  0.7666  0.6659 
O:  0.9155  0.2682  0.8306 
O:  0.7328  0.2327  0.7090 
O:  0.5233  0.7198  0.7959 
O:  0.7721  0.7810  0.2951 
O:  0.9824  0.2669  0.2099 
O:  0.6485  0.7319  0.5441 
O:  0.6054  0.2527  0.9577 
O:  0.8536  0.2489  0.4567 
O:  0.8997  0.7679  0.0450 
O:  0.7121  0.7514  0.9187 
O:  0.5444  0.2728  0.5844 
O:  0.7939  0.2191  0.0814 
O:  0.9623  0.7491  0.4196 
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: 3.8189 0.0809 -0.0248 
0.3060 3.7796 -0.0221 
0.0465 0.0006 3.9743 
Eig. Value: 3.9937 3.6042 3.9749 
Si: 3.8381 -0.0656 -0.0081 
-0.2236 3.4081 0.1775 
0.0241 0.0393 3.9075 
Eig. Value: 3.8722 3.3440 3.9375 
Si: 3.8677 0.0498 0.0016 
0.0624 3.7551 -0.1487 
-0.0293 -0.0435 3.9464 
Eig. Value: 3.8713 3.7018 3.9961 
Si: 3.8773 -0.0826 -0.0142 
-0.2519 3.4196 0.2078 
0.0232 0.0501 3.9131 
Eig. Value: 3.9007 3.3382 3.9711 
Si: 3.8500 0.0314 0.0049 
0.0467 3.7662 -0.1363 
-0.0288 -0.0364 3.9444 
Eig. Value: 3.8530 3.7231 3.9845 
Si: 3.8785 -0.0566 -0.0109 
-0.2100 3.1425 -0.0002 
0.0294 0.0001 3.9329 
Eig. Value: 3.8994 3.1191 3.9354 
Si: 3.8899 -0.0208 0.0224 
0.0117 3.4418 -0.0215 
-0.0223 -0.0005 3.9863 
Eig. Value: 3.8899 3.4415 3.9865 
Si: 3.8806 -0.0118 0.0144 
0.0348 3.4098 0.0026 
-0.0212 0.0108 3.9695 
Eig. Value: 3.8807 3.4094 3.9697 
O: -1.9106 0.5024 -0.0326 
0.5065 -1.8743 -0.1757 
-0.0350 -0.1464 -2.0011 
Eig. Value: -2.4165 -1.3572 -2.0123 
O: -1.9305 -0.4992 0.0376 
-0.4933 -1.8488 0.1861 
-0.0464 0.1010 -1.9902 
Eig. Value: -2.4093 -1.3724 -1.9878 
O: -1.9099 0.5122 -0.0308 
0.5704 -1.8871 -0.1615 
-0.0213 -0.1456 -2.0063 
Eig. Value: -2.4580 -1.3325 -2.0128 
O: -1.9190 -0.5651 0.0388 
-0.5375 -1.8179 0.1915 
-0.0412 0.1175 -1.9820 
Eig. Value: -2.4457 -1.2953 -1.9779 
O: -1.9289 0.5003 0.0460 
0.5262 -1.8624 -0.1671 
-0.0265 -0.0996 -2.0013 
Eig. Value: -2.4328 -1.3682 -1.9917 
O: -1.9577 0.0286 -0.0046 
0.0323 -1.3532 -0.0183 
0.0031 -0.0595 -1.9500 
Eig. Value: -1.9594 -1.3492 -1.9523 
O: -1.9307 0.4933 0.0420 
0.5211 -1.8623 -0.1669 
-0.0365 -0.1002 -1.9976 
Eig. Value: -2.4255 -1.3733 -1.9917 
O: -1.9512 0.0265 -0.0056 
0.0075 -1.3214 -0.0344 
-0.0024 -0.0802 -1.9391 
Eig. Value: -1.9524 -1.3157 -1.9437 
O: -1.9081 -0.5586 -0.0215 
-0.5262 -1.8011 0.1489 
-0.0217 0.1575 -1.9886 
Eig. Value: -2.4178 -1.2861 -1.9939 
O: -1.9440 0.4245 -0.0010 
0.3692 -1.8396 0.4556 
0.0738 0.3906 -1.9443 
Eig. Value: -2.4548 -1.2926 -1.9804 
O: -1.9005 -0.5650 -0.0211 
-0.5780 -1.8110 0.1398 
-0.0280 0.1649 -1.9870 
Eig. Value: -2.4454 -1.2596 -1.9935 
O: -1.9392 0.4314 -0.0076 
0.3940 -1.8359 0.4236 
0.0669 0.3889 -1.9516 
Eig. Value: -2.4563 -1.2953 -1.9752 
O: -1.9504 -0.3871 -0.0155 
-0.3896 -1.8933 -0.4421 
0.0622 -0.3488 -1.9606 
Eig. Value: -2.4674 -1.3582 -1.9788 
O: -1.9567 0.0267 -0.0095 
0.0181 -1.3502 -0.0165 
-0.0023 -0.0597 -1.9432 
Eig. Value: -1.9590 -1.3469 -1.9442 
O: -1.9489 -0.3871 -0.0143 
-0.3961 -1.8907 -0.4458 
0.0661 -0.3507 -1.9638 
Eig. Value: -2.4696 -1.3517 -1.9821 
O: -1.9502 0.0707 -0.0026 
0.0649 -1.3214 0.0309 
-0.0066 -0.0081 -1.9318 
Eig. Value: -1.9587 -1.3140 -1.9308 
Si: 3.8661 0.0608 -0.0066 
0.2387 3.4656 -0.2181 
0.0260 -0.0468 3.9115 
Eig. Value: 3.8951 3.3843 3.9639 
Si: 3.8615 -0.0417 0.0042 
-0.1536 3.0877 0.3736 
0.0004 0.0775 3.8574 
Eig. Value: 3.8626 3.0158 3.9282 
Si: 3.8586 0.0131 0.0076 
-0.0029 3.4991 0.0654 
-0.0269 0.0232 3.9682 
Eig. Value: 3.8580 3.4948 3.9731 
Si: 3.8590 -0.0394 -0.0034 
-0.1837 3.1503 -0.0098 
0.0289 -0.0069 3.9291 
Eig. Value: 3.8727 3.1331 3.9325 
Si: 3.8453 0.0649 -0.0053 
0.2359 3.4465 -0.1986 
0.0251 -0.0442 3.9115 
Eig. Value: 3.8813 3.3702 3.9518 
Si: 3.8821 -0.0316 0.0020 
-0.0034 3.4693 -0.0540 
-0.0299 -0.0184 3.9684 
Eig. Value: 3.8811 3.4659 3.9728 
Si: 3.8706 -0.0260 -0.0072 
0.0042 3.4431 -0.0285 
-0.0266 -0.0083 3.9515 
Eig. Value: 3.8677 3.4422 3.9554 
Si: 3.8783 0.0296 0.0022 
0.0019 3.4821 0.0541 
-0.0283 0.0167 3.9690 
Eig. Value: 3.8775 3.4788 3.9731 
O: -1.9026 0.5747 -0.0290 
0.6121 -1.8457 -0.1625 
-0.0166 -0.1583 -1.9972 
Eig. Value: -2.4869 -1.2564 -2.0022 
O: -1.9206 -0.5721 0.0395 
-0.6037 -1.8371 0.1729 
-0.0288 0.1115 -1.9890 
Eig. Value: -2.4889 -1.2752 -1.9826 
O: -1.9370 0.5031 0.0390 
0.5453 -1.8569 -0.1643 
-0.0394 -0.0926 -1.9936 
Eig. Value: -2.4400 -1.3571 -1.9905 
O: -1.8959 -0.5705 -0.0297 
-0.5592 -1.8390 0.1821 
-0.0255 0.1643 -1.9938 
Eig. Value: -2.4553 -1.2725 -2.0009 
O: -1.9349 0.5061 0.0320 
0.5509 -1.8661 -0.1692 
-0.0457 -0.0951 -1.9923 
Eig. Value: -2.4465 -1.3547 -1.9921 
O: -1.9506 0.0333 -0.0035 
0.0016 -1.3228 -0.0317 
-0.0040 -0.0767 -1.9378 
Eig. Value: -1.9516 -1.3175 -1.9420 
O: -1.9568 -0.0264 -0.0090 
-0.0299 -1.3599 0.0135 
0.0027 0.0592 -1.9473 
Eig. Value: -1.9584 -1.3563 -1.9493 
O: -1.9314 -0.4997 0.0414 
-0.5516 -1.8575 0.1658 
-0.0371 0.0969 -1.9952 
Eig. Value: -2.4404 -1.3534 -1.9904 
O: -1.8930 -0.5751 -0.0277 
-0.6052 -1.8408 0.1709 
-0.0341 0.1686 -1.9884 
Eig. Value: -2.4768 -1.2479 -1.9975 
O: -1.9344 0.4402 -0.0034 
0.4605 -1.8612 0.4354 
0.0581 0.3884 -1.9556 
Eig. Value: -2.5000 -1.2780 -1.9732 
O: -1.9451 -0.4328 0.0024 
-0.4305 -1.8617 -0.4614 
0.0671 -0.3877 -1.9408 
Eig. Value: -2.4909 -1.2791 -1.9776 
O: -1.8964 0.5683 -0.0311 
0.5548 -1.8365 -0.1815 
-0.0281 -0.1637 -1.9947 
Eig. Value: -2.4504 -1.2743 -2.0028 
O: -1.9372 -0.4339 0.0054 
-0.4362 -1.8614 -0.4684 
0.0707 -0.3901 -1.9502 
Eig. Value: -2.4951 -1.2719 -1.9818 
O: -1.9519 0.0748 -0.0012 
0.0777 -1.3253 0.0312 
-0.0027 -0.0066 -1.9347 
Eig. Value: -1.9615 -1.3159 -1.9345 
O: -1.9547 -0.0326 -0.0024 
-0.0274 -1.3605 0.0130 
0.0025 0.0582 -1.9488 
Eig. Value: -1.9568 -1.3569 -1.9504 
O: -1.9434 0.4340 0.0009 
0.4379 -1.8630 0.4628 
0.0664 0.3890 -1.9428 
Eig. Value: -2.4961 -1.2763 -1.9767 
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