-    KALSILITE     -    KAlSiO4

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 RRUFF, entry #R060801 

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:  173  P6_3 
Lattice parameters (Å):  5.1520  5.1520  8.6621 
Angles (°):  90.0  90.0  120.0 

Symmetry (theoretical): 

Space group:  173  P6_3 
Lattice parameters (Å):  4.9357  4.9365  8.5724 
Angles (°):  90.0  90.0  120.0 

Cell contents: 

Number of atoms:  14 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

K:  0.9999  0.0001  0.2489 
Al:  0.3332  0.6666  0.0551 
Si:  0.3335  0.6669  0.4389 
O:  0.3332  0.6667  0.2528 
O:  0.6467  0.0141  0.9967 
K:  0.0001  0.9999  0.7489 
Al:  0.6668  0.3334  0.5551 
Si:  0.6665  0.3331  0.9389 
O:  0.6668  0.3333  0.7528 
O:  0.6327  0.6469  0.4966 
O:  0.9851  0.6320  0.9969 
O:  0.3533  0.9859  0.4967 
O:  0.3673  0.3531  0.9966 
O:  0.0149  0.3680  0.4969 
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): 

K: 1.0721 0.0077 0.0001 
-0.0077 1.0720 -0.0000 
0.0000 0.0001 1.0998 
Eig. Value: 1.0721 1.0720 1.0998 
Al: 2.5820 -0.2281 -0.0005 
0.2281 2.5823 0.0004 
-0.0004 0.0006 2.5856 
Eig. Value: 2.5820 2.5822 2.5857 
Si: 2.9849 0.2301 -0.0003 
-0.2313 2.9848 -0.0005 
0.0009 -0.0002 3.0195 
Eig. Value: 2.9855 2.9843 3.0195 
O: -1.1523 -0.0003 -0.0006 
0.0003 -1.1524 -0.0006 
-0.0006 -0.0005 -2.8347 
Eig. Value: -1.1523 -1.1524 -2.8347 
O: -1.3309 0.1008 -0.0428 
0.1072 -2.3260 0.3590 
-0.0403 0.4489 -1.2901 
Eig. Value: -1.3202 -2.4759 -1.1510 
K: 1.0721 0.0077 -0.0001 
-0.0077 1.0720 0.0000 
-0.0000 -0.0001 1.0998 
Eig. Value: 1.0721 1.0720 1.0998 
Al: 2.5820 -0.2281 0.0005 
0.2281 2.5823 -0.0004 
0.0004 -0.0006 2.5856 
Eig. Value: 2.5820 2.5822 2.5857 
Si: 2.9849 0.2301 0.0003 
-0.2313 2.9848 0.0005 
-0.0009 0.0002 3.0195 
Eig. Value: 2.9855 2.9843 3.0195 
O: -1.1523 -0.0003 0.0006 
0.0003 -1.1524 0.0006 
0.0006 0.0005 -2.8347 
Eig. Value: -1.1523 -1.1524 -2.8347 
O: -2.1680 0.3763 -0.3324 
0.3825 -1.4907 0.1426 
-0.4088 0.1895 -1.2898 
Eig. Value: -2.4769 -1.3208 -1.1509 
O: -1.9878 -0.4865 -0.2896 
-0.4791 -1.6701 -0.2174 
-0.3684 -0.2602 -1.2903 
Eig. Value: -2.4765 -1.3207 -1.1509 
O: -1.3309 0.1008 0.0428 
0.1072 -2.3260 -0.3590 
0.0403 -0.4489 -1.2901 
Eig. Value: -1.3202 -2.4759 -1.1510 
O: -2.1680 0.3763 0.3324 
0.3825 -1.4907 -0.1426 
0.4088 -0.1895 -1.2898 
Eig. Value: -2.4769 -1.3208 -1.1509 
O: -1.9878 -0.4865 0.2896 
-0.4791 -1.6701 0.2174 
0.3684 0.2602 -1.2903 
Eig. Value: -2.4765 -1.3207 -1.1509 
Atom type 

Dielectric tensors: 

 
Ɛ2.3472 0.0000 0.0000 
0.0000 2.3470 0.0000 
0.0000 0.0000 2.3136 
Eig. Value: 2.3473 2.3469 2.3136 
Refractive index (N): 1.5321 0.0000 0.0000 
0.0000 1.5320 0.0000 
0.0000 0.0000 1.5210 
Eig. Value: 1.5321 1.5320 1.5210 
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