-    TUGTUPITE     -    Na4BeAlSi4O12Cl

 

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:  82  I-4 
Lattice parameters (Å):  8.6400  8.6400  8.8730 
Angles (°):  90  90  90 

Symmetry (theoretical): 

Space group:  82  I-4 
Lattice parameters (Å):  7.5504  7.5504  7.5504 
Angles (°):  110.22  110.22  107.97 

Cell contents: 

Number of atoms:  23 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Al:  0.2500  0.7500  0.5000 
Be:  0.7500  0.2500  0.5000 
Si:  0.7499  0.5085  0.2668 
O:  0.5808  0.5970  0.2856 
O:  0.6839  0.9977  0.3828 
O:  0.2871  0.5671  0.5768 
Na:  0.3890  0.3463  0.3623 
Cl:  0.0000  0.0000  0.0000 
Si:  0.2416  0.4831  0.7332 
O:  0.3114  0.2952  0.7144 
O:  0.6149  0.3011  0.6172 
O:  0.9904  0.7104  0.4232 
Na:  0.9840  0.0267  0.6377 
Si:  0.4915  0.7584  0.2415 
O:  0.4030  0.6886  0.9839 
O:  0.0023  0.3851  0.6862 
O:  0.4329  0.0096  0.7200 
Na:  0.6537  0.0160  0.0427 
Si:  0.5169  0.2501  0.7585 
O:  0.7048  0.4192  0.0161 
O:  0.6989  0.3161  0.3138 
O:  0.2896  0.7129  0.2800 
Na:  0.9733  0.6110  0.9573 
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): 

Al: 2.4712 0.2132 -0.0000 
-0.2132 2.4712 -0.0000 
-0.0000 0.0000 2.9385 
Eig. Value: 2.4712 2.4712 2.9385 
Be: 1.8912 -0.1130 0.0000 
0.1130 1.8912 -0.0000 
0.0000 -0.0000 2.1497 
Eig. Value: 1.8912 1.8912 2.1497 
Si: 2.9579 -0.0336 -0.1733 
0.0263 3.3165 0.0383 
0.2139 0.0076 2.8722 
Eig. Value: 2.9624 3.3177 2.8665 
O: -1.9082 0.8787 0.0242 
0.8606 -2.0419 0.0994 
-0.0337 0.0388 -1.1528 
Eig. Value: -1.0773 -2.8490 -1.1767 
O: -1.8196 -0.0124 -0.6509 
-0.0380 -1.1880 -0.0503 
-0.5998 -0.1091 -1.8785 
Eig. Value: -1.2450 -1.1616 -2.4795 
O: -1.2406 -0.0029 0.0749 
0.0332 -1.8007 0.6994 
0.1088 0.6329 -1.9164 
Eig. Value: -1.2910 -1.1369 -2.5298 
Na: 1.0241 0.0111 -0.0431 
0.0081 1.0252 -0.0044 
-0.0519 -0.0018 1.0629 
Eig. Value: 0.9910 1.0255 1.0957 
Cl: -1.0117 -0.0016 -0.0000 
0.0016 -1.0117 -0.0000 
0.0000 0.0000 -1.0379 
Eig. Value: -1.0117 -1.0117 -1.0379 
Si: 2.9579 -0.0336 0.1733 
0.0263 3.3165 -0.0383 
-0.2139 -0.0076 2.8722 
Eig. Value: 2.9624 3.3177 2.8665 
O: -1.9082 0.8787 -0.0242 
0.8606 -2.0419 -0.0994 
0.0337 -0.0388 -1.1528 
Eig. Value: -1.0773 -2.8490 -1.1767 
O: -1.8196 -0.0124 0.6509 
-0.0380 -1.1880 0.0503 
0.5998 0.1091 -1.8785 
Eig. Value: -1.2450 -1.1616 -2.4795 
O: -1.2406 -0.0029 -0.0749 
0.0332 -1.8007 -0.6994 
-0.1088 -0.6329 -1.9164 
Eig. Value: -1.2910 -1.1369 -2.5298 
Na: 1.0241 0.0111 0.0431 
0.0081 1.0252 0.0044 
0.0519 0.0018 1.0629 
Eig. Value: 0.9910 1.0255 1.0957 
Si: 3.3165 -0.0263 -0.0383 
0.0336 2.9579 -0.1733 
-0.0076 0.2139 2.8722 
Eig. Value: 3.3177 2.9624 2.8665 
O: -2.0419 -0.8606 -0.0994 
-0.8787 -1.9082 0.0242 
-0.0388 -0.0337 -1.1528 
Eig. Value: -2.8490 -1.0773 -1.1767 
O: -1.1880 0.0380 0.0503 
0.0124 -1.8196 -0.6509 
0.1091 -0.5998 -1.8785 
Eig. Value: -1.1616 -1.2450 -2.4795 
O: -1.8007 -0.0332 -0.6994 
0.0029 -1.2406 0.0749 
-0.6329 0.1088 -1.9164 
Eig. Value: -1.1369 -1.2910 -2.5298 
Na: 1.0252 -0.0081 0.0044 
-0.0111 1.0241 -0.0431 
0.0018 -0.0519 1.0629 
Eig. Value: 1.0255 0.9910 1.0957 
Si: 3.3165 -0.0263 0.0383 
0.0336 2.9579 0.1733 
0.0076 -0.2139 2.8722 
Eig. Value: 3.3177 2.9624 2.8665 
O: -2.0419 -0.8606 0.0994 
-0.8787 -1.9082 -0.0242 
0.0388 0.0337 -1.1528 
Eig. Value: -2.8490 -1.0773 -1.1767 
O: -1.1880 0.0380 -0.0503 
0.0124 -1.8196 0.6509 
-0.1091 0.5998 -1.8785 
Eig. Value: -1.1616 -1.2450 -2.4795 
O: -1.8007 -0.0332 0.6994 
0.0029 -1.2406 -0.0749 
0.6329 -0.1088 -1.9164 
Eig. Value: -1.1369 -1.2910 -2.5298 
Na: 1.0252 -0.0081 -0.0044 
-0.0111 1.0241 0.0431 
-0.0018 0.0519 1.0629 
Eig. Value: 1.0255 0.9910 1.0957 
Atom type 

Dielectric tensors: 

 
Ɛ2.2994 0.0000 0.0000 
0.0000 2.2994 0.0000 
0.0000 0.0000 2.3103 
Eig. Value: 2.2994 2.2994 2.3103 
Refractive index (N): 1.5164 0.0000 0.0000 
0.0000 1.5164 0.0000 
0.0000 0.0000 1.5200 
Eig. Value: 1.5164 1.5164 1.5200 
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