-    TSUMOITE     -    BiTe

 

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:  164  P-3m1 
Lattice parameters (Å):  2.3406  2.3406  12.7013 
Angles (°):  90.0  90.0  120.0 

Symmetry (theoretical): 

Space group:  164  P-3m1 
Lattice parameters (Å):  4.2956  4.2956  23.0433 
Angles (°):  90.0  90.0  120.0 

Cell contents: 

Number of atoms:  12 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Bi:  0.0000  0.0000  0.1243 
Bi:  0.3333  0.6667  0.2923 
Bi:  0.6667  0.3333  0.4640 
Te:  0.3333  0.6667  0.0510 
Te:  0.6667  0.3333  0.2088 
Te:  0.0000  0.0000  0.3664 
Bi:  0.0000  0.0000  0.8757 
Bi:  0.6667  0.3333  0.7077 
Bi:  0.3333  0.6667  0.5360 
Te:  0.6667  0.3333  0.9490 
Te:  0.3333  0.6667  0.7912 
Te:  0.0000  0.0000  0.6336 
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): 

Bi: 11.1782 -1.0055 -1.4967 
-1.0055 10.0171 0.8641 
-1.4393 0.8310 6.6984 
Eig. Value: 12.2741 9.4366 6.1831 
Bi: 8.9121 -0.4038 -1.1774 
-0.4038 8.4457 0.6798 
-0.7413 0.4280 6.7461 
Eig. Value: 9.5785 8.2126 6.3129 
Bi: -0.7740 0.3401 0.8503 
0.3401 -0.3813 -0.4909 
0.3064 -0.1769 -0.5391 
Eig. Value: -1.4565 -0.1850 -0.0529 
Te: -6.7243 0.6086 -0.0232 
0.6086 -6.0216 0.0134 
0.9485 -0.5476 -1.8541 
Eig. Value: -7.1298 -5.6702 -1.8000 
Te: -9.8966 0.7666 1.7663 
0.7666 -9.0114 -1.0198 
1.0422 -0.6017 -8.7637 
Eig. Value: -11.3541 -8.5689 -7.7487 
Te: -2.6953 -0.3059 0.0808 
-0.3059 -3.0485 -0.0466 
-0.1165 0.0673 -2.2877 
Eig. Value: -2.5206 -3.2251 -2.2859 
Bi: 11.1782 -1.0055 -1.4967 
-1.0055 10.0171 0.8641 
-1.4393 0.8310 6.6984 
Eig. Value: 12.2741 9.4366 6.1831 
Bi: 8.9121 -0.4038 -1.1774 
-0.4038 8.4457 0.6798 
-0.7413 0.4280 6.7461 
Eig. Value: 9.5785 8.2126 6.3129 
Bi: -0.7740 0.3401 0.8503 
0.3401 -0.3813 -0.4909 
0.3064 -0.1769 -0.5391 
Eig. Value: -1.4565 -0.1850 -0.0529 
Te: -6.7243 0.6086 -0.0232 
0.6086 -6.0216 0.0134 
0.9485 -0.5476 -1.8541 
Eig. Value: -7.1298 -5.6702 -1.8000 
Te: -9.8966 0.7666 1.7663 
0.7666 -9.0114 -1.0198 
1.0422 -0.6017 -8.7637 
Eig. Value: -11.3541 -8.5689 -7.7487 
Te: -2.6953 -0.3059 0.0808 
-0.3059 -3.0485 -0.0466 
-0.1165 0.0673 -2.2877 
Eig. Value: -2.5206 -3.2251 -2.2859 
Atom type 

Dielectric tensors: 

 
Ɛ135.1169 -38.7137 -34.4192 
-38.7137 90.4142 19.8719 
-34.4192 19.8719 72.2527 
Eig. Value: 173.1271 68.0628 56.5939 
Refractive index (N): 11.6240 -6.2220 -5.8668 
-6.2220 9.5086 4.4578 
-5.8668 4.4578 8.5002 
Eig. Value: 13.1578 8.2500 7.5229 
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