- CRISTOBALITE - SiO2
1x2x1 super structure. The crystal structure is fully relaxed (both unit cell parameters and atomic positions under symmetry constraints) at 10GPa.
Parameters of the Calculation
All the calculations have been done using the ABINIT software. This is a list of the most representative parameteres used during the Raman calculation.
| Number of electronic bands: | 128 |
| k-points | |
| grid: | 4 4 4 |
| number of shifts: | 1 |
| shifts: | 0.5 0.5 0.5 |
| Kinetic energy cut-off: | 40 Ha [=1088.464 eV ] |
| eXchange-Correlation functional: |
| Pseudopotentials: | |
| Si: | silicon, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local |
| O: | oxygen, fhi98PP : Trouiller-Martins-type, LDA Ceperley/Alder Perdew/Wang (1992), l= 2 local |
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 | X | Y | Z |
Dielectric tensors:
| X | Y | Z | |
| Ɛ∞: | 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 |
| 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 |
| 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 |
Powder Raman
Powder Raman spectrum
The intensity of the Raman peaks is computed within the density-functional perturbation theory. The intensity depends on the temperature (for now fixed at 300K), frequency of the input laser (for now fixed at 21834 cm-1, frequency of the phonon mode and the Raman tensor. The Raman tensor represents the derivative of the dielectric tensor during the atomic displacement that corresponds to the phonon vibration. The Raman tensor is related to the polarizability of a specific phonon mode.
Choose the polarization of the lasers.
| Xmin: | |
| Xmax: |
| Ymin: | |
| Ymax: |
Data about the phonon modes
Frequency of the transverse (TO) and longitudinal (LO) phonon modes in the zone-center. The longitudinal modes are computed along the three cartesian directions. You can visualize the atomic displacement pattern corresponding to each phonon by clicking on the appropriate cell in the table below.
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| No. | Char. | ω TO | ω LOx | ω LOy | ω LOz | I ∥ | I ⊥ | I Total |
You can define the size of the supercell for the visualization of the vibration.
Single Crystal Raman spectra
Single crystal Raman spectrum
The intensity of the Raman peaks is computed within the density-functional perturbation theory. The intensity depends on the temperature (for now fixed at 300K), frequency of the input laser (for now fixed at 21834 cm-1, frequency of the phonon mode and the Raman tensor. The Raman tensor represents the derivative of the dielectric tensor during the atomic displacement that corresponds to the phonon vibration. The Raman tensor is related to the polarizability of a specific phonon mode.
The Raman measurements performed on single crystals employ polarized lasers and allow for the selection of specific elements of the individual Raman tensors of the Raman-active modes.
By convention, in the following we assume a measurement as X(XZ)Z, i.e. incident laser polarized along the X axis, emergent light polarized along the Z axis. If the crystal is aligned with the xyz reference frame, we sample the αxz element. As you rotate the crystal you can sample other entries of the Raman tensor or various linear combineations.
| Xmin: | |
| Xmax: |
| Ymin: | |
| Ymax: |
Choose the orientation of the crystal with respect to the reference system:
| Rotation around X axis: | |||
| Rotation around Z axis: | |||
| Rotation around Y axis: |