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: |
15 |
C2/c |
| Lattice parameters (Å): |
28.5830 |
8.6000 |
5.2100 |
| Angles (°): |
90 |
91.03 |
90 |
Symmetry (theoretical):
| Space group: |
15 |
C2/c |
| Lattice parameters (Å): |
14.5565 |
14.5565 |
5.1125 |
| Angles (°): |
89.25 |
90.74 |
146.35 |
Cell contents:
| Number of atoms: |
60 |
| Number of atom types: |
6 |
| Chemical composition: |
0 |
Atomic positions (theoretical):
| Na: |
0.3530 |
0.0225 |
0.1132 |
| Na: |
0.3680 |
0.3680 |
0.7500 |
| Li: |
0.0062 |
0.0062 |
0.2500 |
| Ti: |
0.5707 |
0.2433 |
0.6246 |
| Si: |
0.6697 |
0.1424 |
0.2916 |
| Si: |
0.1906 |
0.0076 |
0.5388 |
| O: |
0.2292 |
0.7999 |
0.4429 |
| O: |
0.4781 |
0.0506 |
0.7480 |
| O: |
0.3753 |
0.1255 |
0.4810 |
| O: |
0.1653 |
0.0932 |
0.5114 |
| O: |
0.5586 |
0.2906 |
0.9379 |
| O: |
0.1434 |
0.9242 |
0.8251 |
| O: |
0.6213 |
0.2089 |
0.2896 |
| O: |
0.4363 |
0.3478 |
0.1237 |
| H: |
0.3518 |
0.2666 |
0.2589 |
| H: |
0.4800 |
0.3234 |
0.0722 |
| Na: |
0.0225 |
0.3530 |
0.3868 |
| Ti: |
0.2433 |
0.5707 |
0.8754 |
| Si: |
0.1424 |
0.6697 |
0.2084 |
| Si: |
0.0076 |
0.1906 |
0.9612 |
| O: |
0.7999 |
0.2292 |
0.0571 |
| O: |
0.0506 |
0.4781 |
0.7520 |
| O: |
0.1255 |
0.3753 |
0.0190 |
| O: |
0.0932 |
0.1653 |
0.9886 |
| O: |
0.2906 |
0.5586 |
0.5621 |
| O: |
0.9242 |
0.1434 |
0.6749 |
| O: |
0.2089 |
0.6213 |
0.2104 |
| O: |
0.3478 |
0.4363 |
0.3763 |
| H: |
0.2666 |
0.3518 |
0.2411 |
| H: |
0.3234 |
0.4800 |
0.4278 |
| Na: |
0.6470 |
0.9775 |
0.8868 |
| Na: |
0.6320 |
0.6320 |
0.2500 |
| Li: |
0.9938 |
0.9938 |
0.7500 |
| Ti: |
0.4293 |
0.7567 |
0.3754 |
| Si: |
0.3303 |
0.8576 |
0.7084 |
| Si: |
0.8094 |
0.9924 |
0.4612 |
| O: |
0.7708 |
0.2001 |
0.5571 |
| O: |
0.5219 |
0.9494 |
0.2520 |
| O: |
0.6247 |
0.8745 |
0.5190 |
| O: |
0.8347 |
0.9068 |
0.4886 |
| O: |
0.4414 |
0.7094 |
0.0621 |
| O: |
0.8566 |
0.0758 |
0.1749 |
| O: |
0.3787 |
0.7911 |
0.7104 |
| O: |
0.5637 |
0.6522 |
0.8763 |
| H: |
0.6482 |
0.7334 |
0.7411 |
| H: |
0.5200 |
0.6766 |
0.9278 |
| Na: |
0.9775 |
0.6470 |
0.6132 |
| Ti: |
0.7567 |
0.4293 |
0.1246 |
| Si: |
0.8576 |
0.3303 |
0.7916 |
| Si: |
0.9924 |
0.8094 |
0.0388 |
| O: |
0.2001 |
0.7708 |
0.9429 |
| O: |
0.9494 |
0.5219 |
0.2480 |
| O: |
0.8745 |
0.6247 |
0.9810 |
| O: |
0.9068 |
0.8347 |
0.0114 |
| O: |
0.7094 |
0.4414 |
0.4379 |
| O: |
0.0758 |
0.8566 |
0.3251 |
| O: |
0.7911 |
0.3787 |
0.7896 |
| O: |
0.6522 |
0.5637 |
0.6237 |
| H: |
0.7334 |
0.6482 |
0.7589 |
| H: |
0.6766 |
0.5200 |
0.5722 |
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:
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.
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.