-    DURANGITE     -    NaAlFAsO4

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:  15  C2/c 
Lattice parameters (Å):  6.5300  8.4600  7.0000 
Angles (°):  90.0  115.2  90.0 

Symmetry (theoretical): 

Space group:  15  C2/c 
Lattice parameters (Å):  5.3012  5.3012  6.8930 
Angles (°):  74.8  105.2  75.2 

Cell contents: 

Number of atoms:  16 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Na:  0.6714  0.6714  0.2500 
Al:  0.0000  0.0000  0.0000 
As:  0.3133  0.3133  0.2500 
O:  0.6377  0.2361  0.4209 
O:  0.3083  0.0942  0.1102 
F:  0.9331  0.9331  0.2500 
Al:  0.0000  0.0000  0.5000 
O:  0.2361  0.6377  0.0791 
O:  0.0942  0.3083  0.3898 
Na:  0.3286  0.3286  0.7500 
As:  0.6867  0.6867  0.7500 
O:  0.3623  0.7639  0.5791 
O:  0.6917  0.9058  0.8898 
F:  0.0669  0.0669  0.7500 
O:  0.7639  0.3623  0.9209 
O:  0.9058  0.6917  0.6102 
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): 

Na: 1.1370 -0.0000 -0.0670 
-0.0000 1.0858 -0.0000 
-0.1220 0.0000 1.0527 
Eig. Value: 1.1984 1.0858 0.9914 
Al: 3.1402 -0.6745 -0.1291 
-0.6084 3.3576 0.2125 
0.5498 0.3264 3.1071 
Eig. Value: 2.4318 3.9064 3.2668 
As: 3.2347 0.0000 0.4767 
0.0000 3.3835 -0.0000 
0.2321 -0.0000 3.4351 
Eig. Value: 2.9666 3.3835 3.7032 
O: -1.8045 -0.4844 -0.5045 
-0.5047 -1.5830 -0.2907 
-0.5776 -0.2842 -1.5096 
Eig. Value: -2.5515 -1.2719 -1.0737 
O: -1.4366 0.2982 0.1895 
0.2589 -1.8236 -0.4553 
0.1157 -0.4964 -1.4858 
Eig. Value: -1.3247 -2.2781 -1.1431 
F: -1.0298 0.0000 0.3493 
0.0000 -1.0139 0.0000 
0.2640 -0.0000 -1.6042 
Eig. Value: -0.8969 -1.0139 -1.7371 
Al: 3.1402 0.6745 -0.1291 
0.6084 3.3576 -0.2125 
0.5498 -0.3264 3.1071 
Eig. Value: 2.4318 3.9064 3.2668 
O: -1.8045 0.4844 -0.5045 
0.5047 -1.5830 0.2907 
-0.5776 0.2842 -1.5096 
Eig. Value: -2.5515 -1.2719 -1.0737 
O: -1.4366 -0.2982 0.1895 
-0.2589 -1.8236 0.4553 
0.1157 0.4964 -1.4858 
Eig. Value: -1.3247 -2.2781 -1.1431 
Na: 1.1370 -0.0000 -0.0670 
-0.0000 1.0858 0.0000 
-0.1220 0.0000 1.0527 
Eig. Value: 1.1984 1.0858 0.9914 
As: 3.2347 -0.0000 0.4767 
-0.0000 3.3835 -0.0000 
0.2321 0.0000 3.4351 
Eig. Value: 2.9666 3.3835 3.7032 
O: -1.8045 -0.4844 -0.5045 
-0.5047 -1.5830 -0.2907 
-0.5776 -0.2842 -1.5096 
Eig. Value: -2.5515 -1.2719 -1.0737 
O: -1.4366 0.2982 0.1895 
0.2589 -1.8236 -0.4553 
0.1157 -0.4964 -1.4858 
Eig. Value: -1.3247 -2.2781 -1.1431 
F: -1.0298 0.0000 0.3493 
-0.0000 -1.0139 0.0000 
0.2640 -0.0000 -1.6042 
Eig. Value: -0.8969 -1.0139 -1.7371 
O: -1.8045 0.4844 -0.5045 
0.5047 -1.5830 0.2907 
-0.5776 0.2842 -1.5096 
Eig. Value: -2.5515 -1.2719 -1.0737 
O: -1.4366 -0.2982 0.1895 
-0.2589 -1.8236 0.4553 
0.1157 0.4964 -1.4858 
Eig. Value: -1.3247 -2.2781 -1.1431 
Atom type 

Dielectric tensors: 

 
Ɛ2.7484 0.0000 0.0273 
0.0000 2.8584 0.0000 
0.0273 0.0000 2.8115 
Eig. Value: 2.7383 2.8584 2.8216 
Refractive index (N): 1.6578 -0.0000 0.1651 
-0.0000 1.6907 -0.0000 
0.1651 -0.0000 1.6767 
Eig. Value: 1.6548 1.6907 1.6798 
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