-    BISMITE     -    Bi2O3

 

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:  14  P2_1/c 
Lattice parameters (Å):  5.8486  8.1661  7.5097 
Angles (°):  90.0  113.0  90.0 

Symmetry (theoretical): 

Space group:  14  P2_1/c 
Lattice parameters (Å):  5.7210  8.4798  7.3843 
Angles (°):  90.0  112.8  90.0 

Cell contents: 

Number of atoms:  20 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Bi:  0.5192  0.1712  0.3628 
Bi:  0.0503  0.0340  0.7807 
O:  0.7718  0.3137  0.7087 
O:  0.2315  0.0481  0.1268 
O:  0.2665  0.0250  0.5040 
Bi:  0.4808  0.6712  0.1372 
Bi:  0.9497  0.5340  0.7193 
O:  0.2282  0.8137  0.7913 
O:  0.7685  0.5481  0.3732 
O:  0.7335  0.5250  0.9960 
Bi:  0.4808  0.8288  0.6372 
Bi:  0.9497  0.9660  0.2193 
O:  0.2282  0.6863  0.2913 
O:  0.7685  0.9519  0.8732 
O:  0.7335  0.9750  0.4960 
Bi:  0.5192  0.3288  0.8628 
Bi:  0.0503  0.4660  0.2807 
O:  0.7718  0.1863  0.2087 
O:  0.2315  0.4519  0.6268 
O:  0.2665  0.4750  0.0040 
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: 4.1740 0.4930 0.0314 
0.7402 3.3401 0.3324 
0.0225 -0.2434 4.1058 
Eig. Value: 4.5064 3.0121 4.1015 
Bi: 4.1618 -0.9095 0.0321 
-0.7270 3.3907 -0.1334 
0.1049 0.2548 4.7466 
Eig. Value: 4.6726 2.8676 4.7589 
O: -2.9770 -0.8146 0.5069 
-0.3198 -2.9687 -0.4949 
0.5270 -0.3636 -2.0106 
Eig. Value: -3.5437 -2.9032 -1.5094 
O: -2.7093 -0.8926 -0.2340 
-0.8245 -1.6855 -0.5402 
-0.3396 -0.6055 -3.5700 
Eig. Value: -2.8441 -1.1423 -3.9783 
O: -2.6495 -0.0157 -0.3363 
-0.1031 -2.0766 0.4320 
-0.3148 0.7434 -3.2719 
Eig. Value: -2.6052 -1.7967 -3.5961 
Bi: 4.1740 -0.4930 0.0314 
-0.7402 3.3401 -0.3324 
0.0225 0.2434 4.1058 
Eig. Value: 4.5064 3.0121 4.1015 
Bi: 4.1618 0.9095 0.0321 
0.7270 3.3907 0.1334 
0.1049 -0.2548 4.7466 
Eig. Value: 4.6726 2.8676 4.7589 
O: -2.9770 0.8146 0.5069 
0.3198 -2.9687 0.4949 
0.5270 0.3636 -2.0106 
Eig. Value: -3.5437 -2.9032 -1.5094 
O: -2.7093 0.8926 -0.2340 
0.8245 -1.6855 0.5402 
-0.3396 0.6055 -3.5700 
Eig. Value: -2.8441 -1.1423 -3.9783 
O: -2.6495 0.0157 -0.3363 
0.1031 -2.0766 -0.4320 
-0.3148 -0.7434 -3.2719 
Eig. Value: -2.6052 -1.7967 -3.5961 
Bi: 4.1740 0.4930 0.0314 
0.7402 3.3401 0.3324 
0.0225 -0.2434 4.1058 
Eig. Value: 4.5064 3.0121 4.1015 
Bi: 4.1618 -0.9095 0.0321 
-0.7270 3.3907 -0.1334 
0.1049 0.2548 4.7466 
Eig. Value: 4.6726 2.8676 4.7589 
O: -2.9770 -0.8146 0.5069 
-0.3198 -2.9687 -0.4949 
0.5270 -0.3636 -2.0106 
Eig. Value: -3.5437 -2.9032 -1.5094 
O: -2.7093 -0.8926 -0.2340 
-0.8245 -1.6855 -0.5402 
-0.3396 -0.6055 -3.5700 
Eig. Value: -2.8441 -1.1423 -3.9783 
O: -2.6495 -0.0157 -0.3363 
-0.1031 -2.0766 0.4320 
-0.3148 0.7434 -3.2719 
Eig. Value: -2.6052 -1.7967 -3.5961 
Bi: 4.1740 -0.4930 0.0314 
-0.7402 3.3401 -0.3324 
0.0225 0.2434 4.1058 
Eig. Value: 4.5064 3.0121 4.1015 
Bi: 4.1618 0.9095 0.0321 
0.7270 3.3907 0.1334 
0.1049 -0.2548 4.7466 
Eig. Value: 4.6726 2.8676 4.7589 
O: -2.9770 0.8146 0.5069 
0.3198 -2.9687 0.4949 
0.5270 0.3636 -2.0106 
Eig. Value: -3.5437 -2.9032 -1.5094 
O: -2.7093 0.8926 -0.2340 
0.8245 -1.6855 0.5402 
-0.3396 0.6055 -3.5700 
Eig. Value: -2.8441 -1.1423 -3.9783 
O: -2.6495 0.0157 -0.3363 
0.1031 -2.0766 -0.4320 
-0.3148 -0.7434 -3.2719 
Eig. Value: -2.6052 -1.7967 -3.5961 
Atom type 

Dielectric tensors: 

 
Ɛ6.0780 0.0000 0.1392 
0.0000 5.4756 0.0000 
0.1392 0.0000 6.0257 
Eig. Value: 6.1935 5.4756 5.9103 
Refractive index (N): 2.4654 -0.0000 0.3731 
-0.0000 2.3400 -0.0000 
0.3731 -0.0000 2.4547 
Eig. Value: 2.4887 2.3400 2.4311 
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