-    TOPAZ     -    Al2SiO4F2

The crystal structure is fully relaxed (both unit cell parameters and atomic positions under symmetry constraints) starting from an experimental structure similar to the one reported in 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:  62  Pbnm 
Lattice parameters (Å):  4.6499  8.7968  8.3909 
Angles (°):  90.0  90.0  90.0 

Symmetry (theoretical): 

Space group:  62  Pbnm 
Lattice parameters (Å):  4.5849  8.6722  8.2651 
Angles (°):  90.0  90.0  90.0 

Cell contents: 

Number of atoms:  36 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Al:  0.9039  0.1309  0.0826 
Si:  0.3983  0.9404  0.2500 
O:  0.7939  0.5320  0.2500 
O:  0.4572  0.7551  0.2500 
O:  0.7892  0.0105  0.9087 
F:  0.9022  0.7522  0.0571 
Al:  0.4039  0.3691  0.9174 
Si:  0.8983  0.5596  0.7500 
O:  0.2939  0.9680  0.7500 
O:  0.9572  0.7449  0.7500 
O:  0.2892  0.4895  0.0913 
F:  0.4022  0.7478  0.9429 
Al:  0.0961  0.8691  0.5826 
Si:  0.6017  0.0596  0.7500 
O:  0.2061  0.4680  0.7500 
O:  0.5428  0.2449  0.7500 
O:  0.2108  0.9895  0.4087 
F:  0.0978  0.2478  0.5571 
Al:  0.5961  0.6309  0.4174 
Si:  0.1017  0.4404  0.2500 
O:  0.7061  0.0320  0.2500 
O:  0.0428  0.2551  0.2500 
O:  0.7108  0.5105  0.5913 
F:  0.5978  0.2522  0.4429 
Al:  0.0961  0.8691  0.9174 
O:  0.2108  0.9895  0.0913 
F:  0.0978  0.2478  0.9429 
Al:  0.5961  0.6309  0.0826 
O:  0.7108  0.5105  0.9087 
F:  0.5978  0.2522  0.0571 
Al:  0.9039  0.1309  0.4174 
O:  0.7892  0.0105  0.5913 
F:  0.9022  0.7522  0.4429 
Al:  0.4039  0.3691  0.5826 
O:  0.2892  0.4895  0.4087 
F:  0.4022  0.7478  0.5571 
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: 2.9354 0.0564 -0.0972 
-0.0028 3.0015 0.0752 
0.1596 0.0372 3.0832 
Eig. Value: 2.9249 2.9748 3.1205 
Si: 3.3310 -0.0689 0.0000 
0.0007 3.3215 -0.0000 
-0.0000 -0.0000 3.1967 
Eig. Value: 3.3607 3.2918 3.1967 
O: -2.1329 0.6230 0.0000 
0.6033 -1.5687 -0.0000 
-0.0000 -0.0000 -1.6864 
Eig. Value: -2.5258 -1.1759 -1.6864 
O: -1.2703 0.3527 0.0000 
0.3563 -2.4129 0.0000 
-0.0000 -0.0000 -1.5892 
Eig. Value: -1.1693 -2.5139 -1.5892 
O: -1.7635 0.2935 -0.4335 
0.2846 -1.5232 -0.0471 
-0.4664 -0.0250 -2.0309 
Eig. Value: -1.7148 -1.2103 -2.3924 
F: -1.1359 -0.3162 0.1760 
-0.3221 -1.1483 0.1530 
0.1873 0.1536 -1.0128 
Eig. Value: -0.8183 -1.5631 -0.9156 
Al: 2.9354 -0.0564 0.0972 
0.0028 3.0015 0.0752 
-0.1596 0.0372 3.0832 
Eig. Value: 2.9249 2.9748 3.1205 
Si: 3.3310 0.0689 0.0000 
-0.0007 3.3215 0.0000 
-0.0000 0.0000 3.1967 
Eig. Value: 3.3607 3.2918 3.1967 
O: -2.1329 -0.6230 0.0000 
-0.6033 -1.5687 0.0000 
-0.0000 0.0000 -1.6864 
Eig. Value: -2.5258 -1.1759 -1.6864 
O: -1.2703 -0.3527 0.0000 
-0.3563 -2.4129 -0.0000 
-0.0000 0.0000 -1.5892 
Eig. Value: -1.1693 -2.5139 -1.5892 
O: -1.7635 -0.2935 0.4335 
-0.2846 -1.5232 -0.0471 
0.4664 -0.0250 -2.0309 
Eig. Value: -1.7148 -1.2103 -2.3924 
F: -1.1359 0.3162 -0.1760 
0.3221 -1.1483 0.1530 
-0.1873 0.1536 -1.0128 
Eig. Value: -0.8183 -1.5631 -0.9156 
Al: 2.9354 0.0564 0.0972 
-0.0028 3.0015 -0.0752 
-0.1596 -0.0372 3.0832 
Eig. Value: 2.9249 2.9748 3.1205 
Si: 3.3310 -0.0689 -0.0000 
0.0007 3.3215 0.0000 
0.0000 0.0000 3.1967 
Eig. Value: 3.3607 3.2918 3.1967 
O: -2.1329 0.6230 -0.0000 
0.6033 -1.5687 0.0000 
0.0000 0.0000 -1.6864 
Eig. Value: -2.5258 -1.1759 -1.6864 
O: -1.2703 0.3527 -0.0000 
0.3563 -2.4129 -0.0000 
0.0000 0.0000 -1.5892 
Eig. Value: -1.1693 -2.5139 -1.5892 
O: -1.7635 0.2935 0.4335 
0.2846 -1.5232 0.0471 
0.4664 0.0250 -2.0309 
Eig. Value: -1.7148 -1.2103 -2.3924 
F: -1.1359 -0.3162 -0.1760 
-0.3221 -1.1483 -0.1530 
-0.1873 -0.1536 -1.0128 
Eig. Value: -0.8183 -1.5631 -0.9156 
Al: 2.9354 -0.0564 -0.0972 
0.0028 3.0015 -0.0752 
0.1596 -0.0372 3.0832 
Eig. Value: 2.9249 2.9748 3.1205 
Si: 3.3310 0.0689 -0.0000 
-0.0007 3.3215 -0.0000 
0.0000 -0.0000 3.1967 
Eig. Value: 3.3607 3.2918 3.1967 
O: -2.1329 -0.6230 -0.0000 
-0.6033 -1.5687 -0.0000 
0.0000 -0.0000 -1.6864 
Eig. Value: -2.5258 -1.1759 -1.6864 
O: -1.2703 -0.3527 -0.0000 
-0.3563 -2.4129 0.0000 
0.0000 -0.0000 -1.5892 
Eig. Value: -1.1693 -2.5139 -1.5892 
O: -1.7635 -0.2935 -0.4335 
-0.2846 -1.5232 0.0471 
-0.4664 0.0250 -2.0309 
Eig. Value: -1.7148 -1.2103 -2.3924 
F: -1.1359 0.3162 0.1760 
0.3221 -1.1483 -0.1530 
0.1873 -0.1536 -1.0128 
Eig. Value: -0.8183 -1.5631 -0.9156 
Al: 2.9354 0.0564 -0.0972 
-0.0028 3.0015 0.0752 
0.1596 0.0372 3.0832 
Eig. Value: 2.9249 2.9748 3.1205 
O: -1.7635 0.2935 -0.4335 
0.2846 -1.5232 -0.0471 
-0.4664 -0.0250 -2.0309 
Eig. Value: -1.7148 -1.2103 -2.3924 
F: -1.1359 -0.3162 0.1760 
-0.3221 -1.1483 0.1530 
0.1873 0.1536 -1.0128 
Eig. Value: -0.8183 -1.5631 -0.9156 
Al: 2.9354 -0.0564 0.0972 
0.0028 3.0015 0.0752 
-0.1596 0.0372 3.0832 
Eig. Value: 2.9249 2.9748 3.1205 
O: -1.7635 -0.2935 0.4335 
-0.2846 -1.5232 -0.0471 
0.4664 -0.0250 -2.0309 
Eig. Value: -1.7148 -1.2103 -2.3924 
F: -1.1359 0.3162 -0.1760 
0.3221 -1.1483 0.1530 
-0.1873 0.1536 -1.0128 
Eig. Value: -0.8183 -1.5631 -0.9156 
Al: 2.9354 0.0564 0.0972 
-0.0028 3.0015 -0.0752 
-0.1596 -0.0372 3.0832 
Eig. Value: 2.9249 2.9748 3.1205 
O: -1.7635 0.2935 0.4335 
0.2846 -1.5232 0.0471 
0.4664 0.0250 -2.0309 
Eig. Value: -1.7148 -1.2103 -2.3924 
F: -1.1359 -0.3162 -0.1760 
-0.3221 -1.1483 -0.1530 
-0.1873 -0.1536 -1.0128 
Eig. Value: -0.8183 -1.5631 -0.9156 
Al: 2.9354 -0.0564 -0.0972 
0.0028 3.0015 -0.0752 
0.1596 -0.0372 3.0832 
Eig. Value: 2.9249 2.9748 3.1205 
O: -1.7635 -0.2935 -0.4335 
-0.2846 -1.5232 0.0471 
-0.4664 0.0250 -2.0309 
Eig. Value: -1.7148 -1.2103 -2.3924 
F: -1.1359 0.3162 0.1760 
0.3221 -1.1483 -0.1530 
0.1873 -0.1536 -1.0128 
Eig. Value: -0.8183 -1.5631 -0.9156 
Atom type 

Dielectric tensors: 

 
Ɛ2.6884 0.0000 0.0000 
0.0000 2.6981 0.0000 
0.0000 0.0000 2.7158 
Eig. Value: 2.6884 2.6981 2.7158 
Refractive index (N): 1.6396 0.0000 0.0000 
0.0000 1.6426 0.0000 
0.0000 0.0000 1.6480 
Eig. Value: 1.6396 1.6426 1.6480 
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