-    SULFUR     -    S12

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 Zeitschrift ruer Anorganische ind Allgemeine Chemie (1950) (DE) (1981) 476, p171-p178 

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:  58  Pnnm 
Lattice parameters (Å):  4.7250  9.1040  14.5320 
Angles (°):  90  90  90 

Symmetry (theoretical): 

Space group:  58  Pnnm 
Lattice parameters (Å):  4.3240  8.8504  14.2063 
Angles (°):  90  90  90 

Cell contents: 

Number of atoms:  24 
Number of atom types:  1 
Chemical composition:  0 

Atomic positions (theoretical):

S:  0.0000  0.0000  0.2693 
S:  0.2576  0.1349  0.3568 
S:  0.0124  0.3290  0.3833 
S:  0.2447  0.2100  0.0000 
S:  0.7424  0.8651  0.3568 
S:  0.9876  0.6710  0.3833 
S:  0.7553  0.7900  0.0000 
S:  0.5000  0.5000  0.2307 
S:  0.2424  0.6349  0.1432 
S:  0.4876  0.8290  0.1167 
S:  0.2553  0.7100  0.5000 
S:  0.7576  0.3651  0.1432 
S:  0.5124  0.1710  0.1167 
S:  0.7447  0.2900  0.5000 
S:  0.0000  0.0000  0.7307 
S:  0.7424  0.8651  0.6432 
S:  0.9876  0.6710  0.6167 
S:  0.2576  0.1349  0.6432 
S:  0.0124  0.3290  0.6167 
S:  0.5000  0.5000  0.7693 
S:  0.7576  0.3651  0.8568 
S:  0.5124  0.1710  0.8833 
S:  0.2424  0.6349  0.8568 
S:  0.4876  0.8290  0.8833 
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): 

S: -0.0207 0.4811 -0.0000 
0.1228 0.0425 -0.0000 
-0.0000 -0.0000 -0.0408 
Eig. Value: -0.2926 0.3145 -0.0408 
S: 0.1095 -0.0077 0.1155 
-0.1866 -0.0963 0.2356 
0.4722 0.1779 -0.2161 
Eig. Value: 0.2841 0.0264 -0.5134 
S: -0.0837 -0.1353 -0.4271 
0.2333 0.2403 -0.0794 
-0.2779 0.0670 0.2642 
Eig. Value: -0.3055 0.2390 0.4872 
S: -0.0309 -0.0273 0.0000 
-0.2301 -0.3306 -0.0000 
0.0000 0.0000 -0.0552 
Eig. Value: 0.0168 -0.3783 -0.0552 
S: 0.1095 -0.0077 -0.1155 
-0.1866 -0.0963 -0.2356 
-0.4722 -0.1779 -0.2161 
Eig. Value: 0.2841 0.0264 -0.5134 
S: -0.0837 -0.1353 0.4271 
0.2333 0.2403 0.0794 
0.2779 -0.0670 0.2642 
Eig. Value: -0.3055 0.2390 0.4872 
S: -0.0309 -0.0273 -0.0000 
-0.2301 -0.3306 -0.0000 
0.0000 0.0000 -0.0552 
Eig. Value: 0.0168 -0.3783 -0.0552 
S: -0.0207 -0.4811 -0.0000 
-0.1228 0.0425 -0.0000 
-0.0000 -0.0000 -0.0408 
Eig. Value: -0.2926 0.3145 -0.0408 
S: 0.1095 0.0077 0.1155 
0.1866 -0.0963 -0.2356 
0.4722 -0.1779 -0.2161 
Eig. Value: 0.2841 0.0264 -0.5134 
S: -0.0837 0.1353 -0.4271 
-0.2333 0.2403 0.0794 
-0.2779 -0.0670 0.2642 
Eig. Value: -0.3055 0.2390 0.4872 
S: -0.0309 0.0273 0.0000 
0.2301 -0.3306 -0.0000 
0.0000 0.0000 -0.0552 
Eig. Value: 0.0168 -0.3783 -0.0552 
S: 0.1095 0.0077 -0.1155 
0.1866 -0.0963 0.2356 
-0.4722 0.1779 -0.2161 
Eig. Value: 0.2841 0.0264 -0.5134 
S: -0.0837 0.1353 0.4271 
-0.2333 0.2403 -0.0794 
0.2779 0.0670 0.2642 
Eig. Value: -0.3055 0.2390 0.4872 
S: -0.0309 0.0273 -0.0000 
0.2301 -0.3306 0.0000 
0.0000 -0.0000 -0.0552 
Eig. Value: 0.0168 -0.3783 -0.0552 
S: -0.0207 0.4811 -0.0000 
0.1228 0.0425 0.0000 
-0.0000 0.0000 -0.0408 
Eig. Value: -0.2926 0.3145 -0.0408 
S: 0.1095 -0.0077 0.1155 
-0.1866 -0.0963 0.2356 
0.4722 0.1779 -0.2161 
Eig. Value: 0.2841 0.0264 -0.5134 
S: -0.0837 -0.1353 -0.4271 
0.2333 0.2403 -0.0794 
-0.2779 0.0670 0.2642 
Eig. Value: -0.3055 0.2390 0.4872 
S: 0.1095 -0.0077 -0.1155 
-0.1866 -0.0963 -0.2356 
-0.4722 -0.1779 -0.2161 
Eig. Value: 0.2841 0.0264 -0.5134 
S: -0.0837 -0.1353 0.4271 
0.2333 0.2403 0.0794 
0.2779 -0.0670 0.2642 
Eig. Value: -0.3055 0.2390 0.4872 
S: -0.0207 -0.4811 0.0000 
-0.1228 0.0425 -0.0000 
0.0000 -0.0000 -0.0408 
Eig. Value: -0.2926 0.3145 -0.0408 
S: 0.1095 0.0077 0.1155 
0.1866 -0.0963 -0.2356 
0.4722 -0.1779 -0.2161 
Eig. Value: 0.2841 0.0264 -0.5134 
S: -0.0837 0.1353 -0.4271 
-0.2333 0.2403 0.0794 
-0.2779 -0.0670 0.2642 
Eig. Value: -0.3055 0.2390 0.4872 
S: 0.1095 0.0077 -0.1155 
0.1866 -0.0963 0.2356 
-0.4722 0.1779 -0.2161 
Eig. Value: 0.2841 0.0264 -0.5134 
S: -0.0837 0.1353 0.4271 
-0.2333 0.2403 -0.0794 
0.2779 0.0670 0.2642 
Eig. Value: -0.3055 0.2390 0.4872 
Atom type  X  Y  Z 

Dielectric tensors: 

 X Y Z 
Ɛ∞: 5.3126 0.0000 0.0000 
-0.0000 7.3769 -0.0000 
0.0000 -0.0000 6.5177 
Eig. Value: 5.3126 7.3769 6.5177 
Refractive index (N): 2.3049 0.0000 0.0000 
-0.0000 2.7160 -0.0000 
0.0000 -0.0000 2.5530 
Eig. Value: 2.3049 2.7160 2.5530 
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