-    GAHNITE     -    ZnOAl2O3

 

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:  227  Fd-3m 
Lattice parameters (Å):  8.0897  8.0897  8.0897 
Angles (°):  90  90  90 

Symmetry (theoretical): 

Space group:  227  Fd-3m 
Lattice parameters (Å):  5.7937  5.7937  5.7937 
Angles (°):  60  60  60 

Cell contents: 

Number of atoms:  14 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Al:  0.1250  0.1250  0.1250 
Al:  0.8750  0.8750  0.8750 
Zn:  0.5000  0.5000  0.5000 
Zn:  0.5000  0.5000  0.0000 
Zn:  0.5000  0.0000  0.5000 
Zn:  0.0000  0.5000  0.5000 
O:  0.2496  0.2496  0.2496 
O:  0.2496  0.2496  0.7511 
O:  0.2496  0.7511  0.2496 
O:  0.7511  0.2496  0.2496 
O:  0.7504  0.7504  0.2489 
O:  0.7504  0.7504  0.7504 
O:  0.7504  0.2489  0.7504 
O:  0.2489  0.7504  0.7504 
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): 

Al: 3.9640 1.9463 2.2702 
-3.0294 0.2215 1.8103 
-0.3343 2.8416 -11.7918 
Eig. Value: 4.0686 0.6195 -12.2944 
Al: 4.7157 -3.4403 -2.2079 
3.8865 7.7582 -1.2705 
0.5913 -1.9440 17.9739 
Eig. Value: 4.6612 7.5146 18.2720 
Zn: -4.2392 -4.8113 -9.7274 
-4.0103 1.7020 -3.5702 
-4.4165 -0.3468 3.4056 
Eig. Value: -10.3617 3.5353 7.6948 
Zn: 0.7170 10.3662 -8.3860 
0.7475 3.9704 -5.5796 
6.8216 -0.8263 -0.7251 
Eig. Value: -4.0882 9.0841 -1.0336 
Zn: 8.4086 -7.3423 12.2794 
6.2406 -2.1629 3.6563 
4.7553 -1.8503 1.8680 
Eig. Value: 14.2621 -1.6794 -4.4690 
Zn: -0.9977 9.3679 4.3557 
-6.3998 6.0624 2.9289 
-8.6170 0.0331 5.2837 
Eig. Value: -2.0804 7.2071 5.2218 
O: 1.8080 9.7315 -0.7470 
9.4941 -4.6518 -4.1504 
8.6215 4.0987 -0.7415 
Eig. Value: 9.7115 -12.0595 -1.2374 
O: -3.6423 -5.8347 13.3871 
4.3394 -3.9506 5.7340 
-10.1563 -4.3909 -0.9182 
Eig. Value: -3.2030 -5.1649 -0.1432 
O: -2.7946 2.4063 -14.1013 
-3.1686 -1.0775 3.7689 
-4.4718 -0.9282 -0.6490 
Eig. Value: -11.1139 -1.2282 7.8210 
O: -0.1717 -13.9459 -1.1681 
-1.9365 -2.6587 -2.7681 
5.8192 0.9757 -1.6735 
Eig. Value: 7.2447 -9.5449 -2.2038 
O: -5.6188 -11.8547 4.1344 
-8.6067 -1.3303 -2.1635 
-5.4714 2.5282 -1.9863 
Eig. Value: -13.9412 7.0137 -2.0078 
O: 1.4937 3.8099 13.2081 
-3.2417 -0.7756 1.3858 
7.2703 -2.2294 -2.0135 
Eig. Value: 10.1287 -0.7500 -10.6740 
O: -5.4670 10.4196 -2.0525 
0.7126 -4.8670 -0.8719 
-10.5503 3.5523 -5.1077 
Eig. Value: -14.3185 -3.6426 2.5193 
O: 1.8244 -0.8186 -11.2449 
4.9722 1.7598 1.0902 
10.1386 -1.5136 -2.9245 
Eig. Value: 3.9123 -0.2644 -2.9883 
Atom type 

Dielectric tensors: 

 
Ɛ3437.2008 126.6266 6.3682 
139.6111 1615.6161 45.3834 
17.8303 48.3128 2076.6492 
Eig. Value: 3447.0522 1601.5142 2080.8998 
Refractive index (N): 58.6276 11.2528 2.5235 
11.8157 40.1947 6.7367 
4.2226 6.9507 45.5703 
Eig. Value: 58.7116 40.0189 45.6169 
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