-    FRESNOITE     -    Ba2TiSi2O8

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:  100  P4bm 
Lattice parameters (Å):  8.5200  8.5200  5.2100 
Angles (°):  90  90  90 

Symmetry (theoretical): 

Space group:  100  P4bm 
Lattice parameters (Å):  8.4458  8.4458  5.0746 
Angles (°):  90  90  90 

Cell contents: 

Number of atoms:  26 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Ba:  0.3271  0.8271  0.0041 
Si:  0.1282  0.6282  0.5207 
Ti:  0.0000  0.0000  0.5452 
O:  0.0000  0.5000  0.6410 
O:  0.1255  0.6255  0.2096 
O:  0.2933  0.5771  0.6555 
O:  0.0000  0.0000  0.2104 
Ba:  0.1729  0.3271  0.0041 
Si:  0.3718  0.1282  0.5207 
O:  0.5000  0.0000  0.6410 
O:  0.3745  0.1255  0.2096 
O:  0.4229  0.2933  0.6555 
Ba:  0.8271  0.6729  0.0041 
Si:  0.6282  0.8718  0.5207 
Ti:  0.5000  0.5000  0.5452 
O:  0.6255  0.8745  0.2096 
O:  0.7933  0.9229  0.6555 
O:  0.5000  0.5000  0.2104 
Ba:  0.6729  0.1729  0.0041 
Si:  0.8718  0.3718  0.5207 
O:  0.8745  0.3745  0.2096 
O:  0.7067  0.4229  0.6555 
O:  0.0771  0.7933  0.6555 
O:  0.9229  0.2067  0.6555 
O:  0.5771  0.7067  0.6555 
O:  0.2067  0.0771  0.6555 
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): 

Ba: 2.8163 0.1754 0.0356 
0.1754 2.8163 0.0356 
0.0182 0.0182 2.6721 
Eig. Value: 2.9962 2.6409 2.6677 
Si: 3.3990 -0.2067 0.1251 
-0.2067 3.3990 0.1251 
0.0145 0.0145 2.9655 
Eig. Value: 3.6056 3.2293 2.9286 
Ti: 4.4162 -0.0968 0.0000 
0.0968 4.4162 -0.0000 
0.0000 0.0000 3.1409 
Eig. Value: 4.4162 4.4162 3.1409 
O: -2.3311 -0.7332 0.0000 
-0.7332 -2.3311 0.0000 
0.0000 -0.0000 -1.6406 
Eig. Value: -1.5979 -3.0643 -1.6406 
O: -1.7506 -0.0967 -0.0006 
-0.0967 -1.7506 -0.0006 
-0.0144 -0.0144 -2.1224 
Eig. Value: -1.8468 -1.6539 -2.1228 
O: -3.1384 0.6042 0.0273 
0.6539 -1.8255 -0.1176 
0.0939 -0.0929 -1.4758 
Eig. Value: -3.3959 -1.6125 -1.4313 
O: -1.0867 0.0063 -0.0000 
-0.0063 -1.0867 -0.0000 
0.0000 -0.0000 -2.6275 
Eig. Value: -1.0867 -1.0867 -2.6275 
Ba: 2.8163 -0.1754 -0.0356 
-0.1754 2.8163 0.0356 
-0.0182 0.0182 2.6721 
Eig. Value: 2.9962 2.6409 2.6677 
Si: 3.3990 0.2067 -0.1251 
0.2067 3.3990 0.1251 
-0.0145 0.0145 2.9655 
Eig. Value: 3.6056 3.2293 2.9286 
O: -2.3311 0.7332 0.0000 
0.7332 -2.3311 0.0000 
-0.0000 -0.0000 -1.6406 
Eig. Value: -1.5979 -3.0643 -1.6406 
O: -1.7506 0.0967 0.0006 
0.0967 -1.7506 -0.0006 
0.0144 -0.0144 -2.1224 
Eig. Value: -1.6539 -1.8468 -2.1228 
O: -1.8255 -0.6539 0.1176 
-0.6042 -3.1384 0.0273 
0.0929 0.0939 -1.4758 
Eig. Value: -1.6125 -3.3959 -1.4313 
Ba: 2.8163 -0.1754 0.0356 
-0.1754 2.8163 -0.0356 
0.0182 -0.0182 2.6721 
Eig. Value: 2.9962 2.6409 2.6677 
Si: 3.3990 0.2067 0.1251 
0.2067 3.3990 -0.1251 
0.0145 -0.0145 2.9655 
Eig. Value: 3.6056 3.2293 2.9286 
Ti: 4.4162 0.0968 -0.0000 
-0.0968 4.4162 -0.0000 
-0.0000 0.0000 3.1409 
Eig. Value: 4.4162 4.4162 3.1409 
O: -1.7506 0.0967 -0.0006 
0.0967 -1.7506 0.0006 
-0.0144 0.0144 -2.1224 
Eig. Value: -1.6539 -1.8468 -2.1228 
O: -3.1384 -0.6042 0.0273 
-0.6539 -1.8255 0.1176 
0.0939 0.0929 -1.4758 
Eig. Value: -3.3959 -1.6125 -1.4313 
O: -1.0867 -0.0063 -0.0000 
0.0063 -1.0867 -0.0000 
-0.0000 0.0000 -2.6275 
Eig. Value: -1.0867 -1.0867 -2.6275 
Ba: 2.8163 0.1754 -0.0356 
0.1754 2.8163 -0.0356 
-0.0182 -0.0182 2.6721 
Eig. Value: 2.9962 2.6409 2.6677 
Si: 3.3990 -0.2067 -0.1251 
-0.2067 3.3990 -0.1251 
-0.0145 -0.0145 2.9655 
Eig. Value: 3.6056 3.2293 2.9286 
O: -1.7506 -0.0967 0.0006 
-0.0967 -1.7506 0.0006 
0.0144 0.0144 -2.1224 
Eig. Value: -1.8468 -1.6539 -2.1228 
O: -3.1384 0.6042 -0.0273 
0.6539 -1.8255 0.1176 
-0.0939 0.0929 -1.4758 
Eig. Value: -3.3959 -1.6125 -1.4313 
O: -1.8255 0.6539 -0.1176 
0.6042 -3.1384 0.0273 
-0.0929 0.0939 -1.4758 
Eig. Value: -1.6125 -3.3959 -1.4313 
O: -1.8255 0.6539 0.1176 
0.6042 -3.1384 -0.0273 
0.0929 -0.0939 -1.4758 
Eig. Value: -1.6125 -3.3959 -1.4313 
O: -1.8255 -0.6539 -0.1176 
-0.6042 -3.1384 -0.0273 
-0.0929 -0.0939 -1.4758 
Eig. Value: -1.6125 -3.3959 -1.4313 
O: -3.1384 -0.6042 -0.0273 
-0.6539 -1.8255 -0.1176 
-0.0939 -0.0929 -1.4758 
Eig. Value: -3.3959 -1.6125 -1.4313 
Atom type 

Dielectric tensors: 

 
Ɛ3.4937 0.0000 0.0000 
0.0000 3.4937 0.0000 
0.0000 0.0000 3.3664 
Eig. Value: 3.4937 3.4937 3.3664 
Refractive index (N): 1.8692 0.0000 0.0000 
0.0000 1.8692 0.0000 
0.0000 0.0000 1.8348 
Eig. Value: 1.8692 1.8692 1.8348 
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