- WADEITE - K2ZrSi3O9
Theoretical atomic positions and lattice parameters at experimental volum from AMCSD
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: | 176 | P6_3/m | ||||
| Lattice parameters (Å): | 6.6120 | 6.6120 | 9.5100 | |||
| Angles (°): | 90 | 90 | 120 | |||
Symmetry (theoretical):
| Space group: | 176 | P6_3/m | ||||
| Lattice parameters (Å): | 6.4624 | 6.4624 | 9.9554 | |||
| Angles (°): | 90 | 90 | 120 | |||
Cell contents:
| Number of atoms: | 30 |
| Number of atom types: | 4 |
| Chemical composition: | 0 |
Atomic positions (theoretical):
| K: | 0.6667 | 0.3333 | 0.9792 |
| Zr: | 0.0000 | 0.0000 | 0.0000 |
| Si: | 0.3818 | 0.2887 | 0.2500 |
| O: | 0.4582 | 0.0857 | 0.2500 |
| O: | 0.2516 | 0.2743 | 0.1134 |
| K: | 0.3333 | 0.6667 | 0.4792 |
| Zr: | 0.0000 | 0.0000 | 0.5000 |
| Si: | 0.0931 | 0.3818 | 0.7500 |
| O: | 0.3725 | 0.4582 | 0.7500 |
| O: | 0.9773 | 0.2516 | 0.6134 |
| Si: | 0.7113 | 0.0931 | 0.2500 |
| O: | 0.9143 | 0.3725 | 0.2500 |
| O: | 0.7257 | 0.9773 | 0.1134 |
| Si: | 0.6182 | 0.7113 | 0.7500 |
| O: | 0.5418 | 0.9143 | 0.7500 |
| O: | 0.7484 | 0.7257 | 0.6134 |
| Si: | 0.9069 | 0.6182 | 0.2500 |
| O: | 0.6275 | 0.5418 | 0.2500 |
| O: | 0.0227 | 0.7484 | 0.1134 |
| Si: | 0.2887 | 0.9069 | 0.7500 |
| O: | 0.0857 | 0.6275 | 0.7500 |
| O: | 0.2743 | 0.0227 | 0.6134 |
| K: | 0.3333 | 0.6667 | 0.0208 |
| O: | 0.7484 | 0.7257 | 0.8866 |
| K: | 0.6667 | 0.3333 | 0.5208 |
| O: | 0.0227 | 0.7484 | 0.3866 |
| O: | 0.2743 | 0.0227 | 0.8866 |
| O: | 0.2516 | 0.2743 | 0.3866 |
| O: | 0.9773 | 0.2516 | 0.8866 |
| O: | 0.7257 | 0.9773 | 0.3866 |
| 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:
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.
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):
| K: | 1.1017 | -0.0062 | -0.0000 |
| 0.0062 | 1.1017 | 0.0000 | |
| -0.0000 | 0.0000 | 1.0867 | |
| Eig. Value: | 1.1017 | 1.1017 | 1.0867 |
| Zr: | 4.5376 | 0.5446 | -0.0000 |
| -0.5446 | 4.5376 | 0.0000 | |
| 0.0000 | 0.0000 | 5.6225 | |
| Eig. Value: | 4.5376 | 4.5376 | 5.6225 |
| Si: | 3.6003 | 0.1197 | 0.0000 |
| 0.7845 | 2.8955 | -0.0000 | |
| -0.0000 | 0.0000 | 3.4330 | |
| Eig. Value: | 3.8211 | 2.6747 | 3.4330 |
| O: | -2.7942 | 0.5391 | 0.0000 |
| 0.1873 | -1.3357 | 0.0000 | |
| 0.0000 | 0.0000 | -1.1682 | |
| Eig. Value: | -2.8796 | -1.2502 | -1.1682 |
| O: | -1.6727 | -0.5302 | -0.6955 |
| -0.5093 | -1.7573 | -0.5882 | |
| -0.7521 | -0.7922 | -2.4318 | |
| Eig. Value: | -1.1801 | -1.3436 | -3.3380 |
| K: | 1.1017 | -0.0062 | 0.0000 |
| 0.0062 | 1.1017 | -0.0000 | |
| -0.0000 | -0.0000 | 1.0867 | |
| Eig. Value: | 1.1017 | 1.1017 | 1.0867 |
| Zr: | 4.5376 | 0.5446 | 0.0000 |
| -0.5446 | 4.5376 | -0.0000 | |
| -0.0000 | -0.0000 | 5.6225 | |
| Eig. Value: | 4.5376 | 4.5376 | 5.6225 |
| Si: | 2.6802 | -0.2532 | -0.0000 |
| 0.4116 | 3.8156 | -0.0000 | |
| 0.0000 | 0.0000 | 3.4330 | |
| Eig. Value: | 2.6747 | 3.8211 | 3.4330 |
| O: | -2.0148 | -0.6372 | 0.0000 |
| -0.9891 | -2.1150 | -0.0000 | |
| 0.0000 | -0.0000 | -1.1682 | |
| Eig. Value: | -1.2502 | -2.8796 | -1.1682 |
| O: | -1.2860 | 0.2860 | 0.1617 |
| 0.3070 | -2.1440 | -0.8965 | |
| 0.3100 | -1.0474 | -2.4318 | |
| Eig. Value: | -1.1801 | -1.3436 | -3.3380 |
| Si: | 3.4632 | -0.8636 | 0.0000 |
| -0.1988 | 3.0326 | 0.0000 | |
| 0.0000 | -0.0000 | 3.4330 | |
| Eig. Value: | 3.8211 | 2.6747 | 3.4330 |
| O: | -1.3858 | 0.6259 | -0.0000 |
| 0.2740 | -2.7441 | 0.0000 | |
| -0.0000 | 0.0000 | -1.1682 | |
| Eig. Value: | -1.2502 | -2.8796 | -1.1682 |
| O: | -2.1863 | 0.2128 | 0.8572 |
| 0.2337 | -1.2437 | -0.3082 | |
| 1.0621 | -0.2553 | -2.4318 | |
| Eig. Value: | -1.3436 | -1.1801 | -3.3380 |
| Si: | 3.6003 | 0.1197 | 0.0000 |
| 0.7845 | 2.8955 | -0.0000 | |
| -0.0000 | 0.0000 | 3.4330 | |
| Eig. Value: | 3.8211 | 2.6747 | 3.4330 |
| O: | -2.7942 | 0.5391 | 0.0000 |
| 0.1873 | -1.3357 | 0.0000 | |
| 0.0000 | 0.0000 | -1.1682 | |
| Eig. Value: | -2.8796 | -1.2502 | -1.1682 |
| O: | -1.6727 | -0.5302 | 0.6955 |
| -0.5093 | -1.7573 | 0.5882 | |
| 0.7521 | 0.7922 | -2.4318 | |
| Eig. Value: | -1.1801 | -1.3436 | -3.3380 |
| Si: | 2.6802 | -0.2532 | -0.0000 |
| 0.4116 | 3.8156 | -0.0000 | |
| 0.0000 | 0.0000 | 3.4330 | |
| Eig. Value: | 2.6747 | 3.8211 | 3.4330 |
| O: | -2.0148 | -0.6372 | 0.0000 |
| -0.9891 | -2.1150 | -0.0000 | |
| 0.0000 | -0.0000 | -1.1682 | |
| Eig. Value: | -1.2502 | -2.8796 | -1.1682 |
| O: | -1.2860 | 0.2860 | -0.1617 |
| 0.3070 | -2.1440 | 0.8965 | |
| -0.3100 | 1.0474 | -2.4318 | |
| Eig. Value: | -1.1801 | -1.3436 | -3.3380 |
| Si: | 3.4632 | -0.8636 | 0.0000 |
| -0.1988 | 3.0326 | 0.0000 | |
| 0.0000 | -0.0000 | 3.4330 | |
| Eig. Value: | 3.8211 | 2.6747 | 3.4330 |
| O: | -1.3858 | 0.6259 | -0.0000 |
| 0.2740 | -2.7441 | 0.0000 | |
| -0.0000 | 0.0000 | -1.1682 | |
| Eig. Value: | -1.2502 | -2.8796 | -1.1682 |
| O: | -2.1863 | 0.2128 | -0.8572 |
| 0.2337 | -1.2437 | 0.3082 | |
| -1.0621 | 0.2553 | -2.4318 | |
| Eig. Value: | -1.3436 | -1.1801 | -3.3380 |
| K: | 1.1017 | -0.0062 | -0.0000 |
| 0.0062 | 1.1017 | 0.0000 | |
| 0.0000 | -0.0000 | 1.0867 | |
| Eig. Value: | 1.1017 | 1.1017 | 1.0867 |
| O: | -1.6727 | -0.5302 | -0.6955 |
| -0.5093 | -1.7573 | -0.5882 | |
| -0.7521 | -0.7922 | -2.4318 | |
| Eig. Value: | -1.1801 | -1.3436 | -3.3380 |
| K: | 1.1017 | -0.0062 | 0.0000 |
| 0.0062 | 1.1017 | -0.0000 | |
| 0.0000 | -0.0000 | 1.0867 | |
| Eig. Value: | 1.1017 | 1.1017 | 1.0867 |
| O: | -1.2860 | 0.2860 | 0.1617 |
| 0.3070 | -2.1440 | -0.8965 | |
| 0.3100 | -1.0474 | -2.4318 | |
| Eig. Value: | -1.1801 | -1.3436 | -3.3380 |
| O: | -2.1863 | 0.2128 | 0.8572 |
| 0.2337 | -1.2437 | -0.3082 | |
| 1.0621 | -0.2553 | -2.4318 | |
| Eig. Value: | -1.3436 | -1.1801 | -3.3380 |
| O: | -1.6727 | -0.5302 | 0.6955 |
| -0.5093 | -1.7573 | 0.5882 | |
| 0.7521 | 0.7922 | -2.4318 | |
| Eig. Value: | -1.1801 | -1.3436 | -3.3380 |
| O: | -1.2860 | 0.2860 | -0.1617 |
| 0.3070 | -2.1440 | 0.8965 | |
| -0.3100 | 1.0474 | -2.4318 | |
| Eig. Value: | -1.1801 | -1.3436 | -3.3380 |
| O: | -2.1863 | 0.2128 | -0.8572 |
| 0.2337 | -1.2437 | 0.3082 | |
| -1.0621 | 0.2553 | -2.4318 | |
| Eig. Value: | -1.3436 | -1.1801 | -3.3380 |
| Atom type | X | Y | Z |
Dielectric tensors:
| X | Y | Z | |
| Ɛ∞: | 2.7318 | 0.0000 | 0.0000 |
| 0.0000 | 2.7318 | 0.0000 | |
| 0.0000 | 0.0000 | 3.0233 | |
| Eig. Value: | 2.7318 | 2.7318 | 3.0233 |
| Refractive index (N): | 1.6528 | 0.0000 | 0.0000 |
| 0.0000 | 1.6528 | 0.0000 | |
| 0.0000 | 0.0000 | 1.7388 | |
| Eig. Value: | 1.6528 | 1.6528 | 1.7388 |
| 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 |