-    GLAUBERITE     -    Na2Ca(SO4)2

Theoretical atomic positions and lattice parameters at experimental volum from 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:  15  C2/c 
Lattice parameters (Å):  10.1580  8.3330  8.5510 
Angles (°):  90  112.333  90 

Symmetry (theoretical): 

Space group:  15  C2/c 
Lattice parameters (Å):  6.5509  6.5509  8.5659 
Angles (°):  73.52  106.47  102.01 

Cell contents: 

Number of atoms:  26 
Number of atom types:  4 
Chemical composition:  0 

Atomic positions (theoretical):

Na:  0.4159  0.6993  0.0582 
Ca:  0.0569  0.0569  0.2500 
S:  0.6003  0.9632  0.3159 
O:  0.4339  0.0984  0.2877 
O:  0.6669  0.9962  0.1573 
O:  0.5185  0.7338  0.3702 
O:  0.7943  0.0316  0.4384 
Na:  0.6993  0.4159  0.4418 
S:  0.9632  0.6003  0.1841 
O:  0.0984  0.4339  0.2123 
O:  0.9962  0.6669  0.3427 
O:  0.7338  0.5185  0.1298 
O:  0.0316  0.7943  0.0616 
Na:  0.5841  0.3007  0.9418 
Ca:  0.9431  0.9431  0.7500 
S:  0.3997  0.0368  0.6841 
O:  0.5661  0.9016  0.7123 
O:  0.3331  0.0038  0.8427 
O:  0.4815  0.2662  0.6298 
O:  0.2057  0.9684  0.5616 
Na:  0.3007  0.5841  0.5582 
S:  0.0368  0.3997  0.8159 
O:  0.9016  0.5661  0.7877 
O:  0.0038  0.3331  0.6573 
O:  0.2662  0.4815  0.8702 
O:  0.9684  0.2057  0.9384 
Atom type  X  Y  Z 

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: 1.0395 0.0580 -0.0272 
0.0758 1.1487 0.1572 
-0.0048 0.0682 1.1167 
Eig. Value: 0.9698 1.2545 1.0806 
Ca: 2.5750 -0.0000 0.1001 
0.0000 2.3592 -0.0000 
0.0238 0.0000 2.2250 
Eig. Value: 2.5856 2.3592 2.2143 
S: 3.3833 0.1179 -0.1878 
0.2777 3.3429 -0.0609 
-0.1109 0.1315 3.0921 
Eig. Value: 3.5789 3.2512 2.9882 
O: -2.2370 -0.3159 -0.1928 
-0.3938 -1.1049 -0.0760 
-0.1624 -0.0690 -0.9634 
Eig. Value: -2.3650 -1.0087 -0.9316 
O: -1.2674 -0.2518 0.4533 
-0.2659 -1.1665 0.2691 
0.4354 0.2517 -1.7106 
Eig. Value: -1.0924 -0.9316 -2.1205 
O: -1.1568 0.3222 -0.0778 
0.3521 -1.8236 0.3232 
-0.0974 0.2503 -1.0003 
Eig. Value: -1.0235 -2.0492 -0.9079 
O: -1.0490 -0.2150 -0.0178 
-0.2500 -1.5763 -0.5131 
-0.0717 -0.6170 -1.6470 
Eig. Value: -1.1688 -0.8935 -2.2099 
Na: 1.0395 -0.0580 -0.0272 
-0.0758 1.1487 -0.1572 
-0.0048 -0.0682 1.1167 
Eig. Value: 0.9698 1.2545 1.0806 
S: 3.3833 -0.1179 -0.1878 
-0.2777 3.3429 0.0609 
-0.1109 -0.1315 3.0921 
Eig. Value: 3.5789 3.2512 2.9882 
O: -2.2370 0.3159 -0.1928 
0.3938 -1.1049 0.0760 
-0.1624 0.0690 -0.9634 
Eig. Value: -2.3650 -1.0087 -0.9316 
O: -1.2674 0.2518 0.4533 
0.2659 -1.1665 -0.2691 
0.4354 -0.2517 -1.7106 
Eig. Value: -1.0924 -0.9316 -2.1205 
O: -1.1568 -0.3222 -0.0778 
-0.3521 -1.8236 -0.3232 
-0.0974 -0.2503 -1.0003 
Eig. Value: -1.0235 -2.0492 -0.9079 
O: -1.0490 0.2150 -0.0178 
0.2500 -1.5763 0.5131 
-0.0717 0.6170 -1.6470 
Eig. Value: -1.1688 -0.8935 -2.2099 
Na: 1.0395 0.0580 -0.0272 
0.0758 1.1487 0.1572 
-0.0048 0.0682 1.1167 
Eig. Value: 0.9698 1.2545 1.0806 
Ca: 2.5750 -0.0000 0.1001 
-0.0000 2.3592 0.0000 
0.0238 0.0000 2.2250 
Eig. Value: 2.5856 2.3592 2.2143 
S: 3.3833 0.1179 -0.1878 
0.2777 3.3429 -0.0609 
-0.1109 0.1315 3.0921 
Eig. Value: 3.5789 3.2512 2.9882 
O: -2.2370 -0.3159 -0.1928 
-0.3938 -1.1049 -0.0760 
-0.1624 -0.0690 -0.9634 
Eig. Value: -2.3650 -1.0087 -0.9316 
O: -1.2674 -0.2518 0.4533 
-0.2659 -1.1665 0.2691 
0.4354 0.2517 -1.7106 
Eig. Value: -1.0924 -0.9316 -2.1205 
O: -1.1568 0.3222 -0.0778 
0.3521 -1.8236 0.3232 
-0.0974 0.2503 -1.0003 
Eig. Value: -1.0235 -2.0492 -0.9079 
O: -1.0490 -0.2150 -0.0178 
-0.2500 -1.5763 -0.5131 
-0.0717 -0.6170 -1.6470 
Eig. Value: -1.1688 -0.8935 -2.2099 
Na: 1.0395 -0.0580 -0.0272 
-0.0758 1.1487 -0.1572 
-0.0048 -0.0682 1.1167 
Eig. Value: 0.9698 1.2545 1.0806 
S: 3.3833 -0.1179 -0.1878 
-0.2777 3.3429 0.0609 
-0.1109 -0.1315 3.0921 
Eig. Value: 3.5789 3.2512 2.9882 
O: -2.2370 0.3159 -0.1928 
0.3938 -1.1049 0.0760 
-0.1624 0.0690 -0.9634 
Eig. Value: -2.3650 -1.0087 -0.9316 
O: -1.2674 0.2518 0.4533 
0.2659 -1.1665 -0.2691 
0.4354 -0.2517 -1.7106 
Eig. Value: -1.0924 -0.9316 -2.1205 
O: -1.1568 -0.3222 -0.0778 
-0.3521 -1.8236 -0.3232 
-0.0974 -0.2503 -1.0003 
Eig. Value: -1.0235 -2.0492 -0.9079 
O: -1.0490 0.2150 -0.0178 
0.2500 -1.5763 0.5131 
-0.0717 0.6170 -1.6470 
Eig. Value: -1.1688 -0.8935 -2.2099 
Atom type  X  Y  Z 

Dielectric tensors: 

 X Y Z 
Ɛ∞: 2.3686 0.0000 0.0000 
0.0000 2.3613 0.0000 
0.0000 0.0000 2.2949 
Eig. Value: 2.3686 2.3613 2.2949 
Refractive index (N): 1.5390 0.0000 0.0000 
0.0000 1.5367 0.0000 
0.0000 0.0000 1.5149 
Eig. Value: 1.5390 1.5367 1.5149 
Ɛ0: 0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 
Eig. Value: 0.0000 0.0000 0.0000