-    LUESHITE     -    NaNbO3

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):  5.4043  5.4224  7.6510 
Angles (°):  90  90  90 

Symmetry (theoretical): 

Space group:  62  Pbnm 
Lattice parameters (Å):  5.3778  5.4906  7.6898 
Angles (°):  90  90  90 

Cell contents: 

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

Atomic positions (theoretical):

Na:  0.9917  0.0382  0.2500 
Nb:  0.5000  0.0000  0.0000 
O:  0.0853  0.4786  0.2500 
O:  0.7041  0.2940  0.0443 
Na:  0.4917  0.4618  0.7500 
Nb:  0.0000  0.5000  0.0000 
O:  0.5853  0.0214  0.7500 
O:  0.2041  0.2060  0.9557 
Na:  0.0083  0.9618  0.7500 
Nb:  0.5000  0.0000  0.5000 
O:  0.9147  0.5214  0.7500 
O:  0.2959  0.7060  0.5443 
Na:  0.5083  0.5382  0.2500 
Nb:  0.0000  0.5000  0.5000 
O:  0.4147  0.9786  0.2500 
O:  0.7959  0.7940  0.4557 
O:  0.2959  0.7060  0.9557 
O:  0.7959  0.7940  0.0443 
O:  0.7041  0.2940  0.4557 
O:  0.2041  0.2060  0.5443 
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: 1.0114 0.0344 -0.0000 
0.0724 1.0255 0.0000 
-0.0000 -0.0000 1.0429 
Eig. Value: 0.9645 1.0723 1.0429 
Nb: 8.2959 1.0390 1.4319 
-1.0274 8.5575 0.0059 
-1.3096 -0.3430 8.3218 
Eig. Value: 8.3285 8.6469 8.1999 
O: -1.6233 0.1513 -0.0000 
-0.1448 -1.5534 -0.0000 
-0.0000 0.0000 -6.0237 
Eig. Value: -1.6235 -1.5533 -6.0237 
O: -3.8420 -2.2729 0.0213 
-2.3481 -4.0148 -0.0328 
0.0131 -0.0253 -1.6705 
Eig. Value: -1.6010 -6.2405 -1.6857 
Na: 1.0114 -0.0344 -0.0000 
-0.0724 1.0255 -0.0000 
-0.0000 0.0000 1.0429 
Eig. Value: 0.9645 1.0723 1.0429 
Nb: 8.2959 -1.0390 -1.4319 
1.0274 8.5575 0.0059 
1.3096 -0.3430 8.3218 
Eig. Value: 8.3285 8.6469 8.1999 
O: -1.6233 -0.1513 -0.0000 
0.1448 -1.5534 0.0000 
-0.0000 -0.0000 -6.0237 
Eig. Value: -1.6235 -1.5533 -6.0237 
O: -3.8420 2.2729 -0.0213 
2.3481 -4.0148 -0.0328 
-0.0131 -0.0253 -1.6705 
Eig. Value: -1.6010 -6.2405 -1.6857 
Na: 1.0114 0.0344 0.0000 
0.0724 1.0255 -0.0000 
0.0000 0.0000 1.0429 
Eig. Value: 0.9645 1.0723 1.0429 
Nb: 8.2959 1.0390 -1.4319 
-1.0274 8.5575 -0.0059 
1.3096 0.3430 8.3218 
Eig. Value: 8.3285 8.6469 8.1999 
O: -1.6233 0.1513 0.0000 
-0.1448 -1.5534 0.0000 
0.0000 -0.0000 -6.0237 
Eig. Value: -1.6235 -1.5533 -6.0237 
O: -3.8420 -2.2729 -0.0213 
-2.3481 -4.0148 0.0328 
-0.0131 0.0253 -1.6705 
Eig. Value: -1.6010 -6.2405 -1.6857 
Na: 1.0114 -0.0344 0.0000 
-0.0724 1.0255 0.0000 
0.0000 -0.0000 1.0429 
Eig. Value: 0.9645 1.0723 1.0429 
Nb: 8.2959 -1.0390 1.4319 
1.0274 8.5575 -0.0059 
-1.3096 0.3430 8.3218 
Eig. Value: 8.3285 8.6469 8.1999 
O: -1.6233 -0.1513 0.0000 
0.1448 -1.5534 -0.0000 
0.0000 0.0000 -6.0237 
Eig. Value: -1.6235 -1.5533 -6.0237 
O: -3.8420 2.2729 0.0213 
2.3481 -4.0148 0.0328 
0.0131 0.0253 -1.6705 
Eig. Value: -1.6010 -6.2405 -1.6857 
O: -3.8420 -2.2729 0.0213 
-2.3481 -4.0148 -0.0328 
0.0131 -0.0253 -1.6705 
Eig. Value: -1.6010 -6.2405 -1.6857 
O: -3.8420 2.2729 -0.0213 
2.3481 -4.0148 -0.0328 
-0.0131 -0.0253 -1.6705 
Eig. Value: -1.6010 -6.2405 -1.6857 
O: -3.8420 -2.2729 -0.0213 
-2.3481 -4.0148 0.0328 
-0.0131 0.0253 -1.6705 
Eig. Value: -1.6010 -6.2405 -1.6857 
O: -3.8420 2.2729 0.0213 
2.3481 -4.0148 0.0328 
0.0131 0.0253 -1.6705 
Eig. Value: -1.6010 -6.2405 -1.6857 
Atom type 

Dielectric tensors: 

 
Ɛ5.6339 0.0000 0.0000 
0.0000 5.7776 0.0000 
0.0000 0.0000 5.5007 
Eig. Value: 5.6339 5.7776 5.5007 
Refractive index (N): 2.3736 0.0000 0.0000 
0.0000 2.4037 0.0000 
0.0000 0.0000 2.3454 
Eig. Value: 2.3736 2.4037 2.3454 
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