-    KOTTIGITE     -    Zn3(AsO4)28H2O

 

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:  12  C2/m 
Lattice parameters (Å):  12.2960  11.3130  6.1140 
Angles (°):  90  105.21  90 

Symmetry (theoretical): 

Space group:  12  C2/m 
Lattice parameters (Å):  0.5292  0.5292  0.5292 
Angles (°):  80.83  99.16  74.75 

Cell contents: 

Number of atoms:  37 
Number of atom types:  4 
Chemical composition:  0 

Atomic positions (theoretical):

Zn:  0.0000  0.0000  0.0000 
Zn:  0.3831  0.3831  0.0000 
As:  0.3138  0.6862  0.3800 
O:  0.1475  0.8525  0.3974 
O:  0.4123  0.5877  0.7287 
O:  0.4438  0.7725  0.2091 
O:  0.2118  0.0167  0.8138 
O:  0.6398  0.8143  0.7115 
H:  0.8002  0.0405  0.3566 
H:  0.6864  0.0624  0.0385 
H:  0.4162  0.1846  0.4899 
H:  0.2398  0.1921  0.2774 
As:  0.6862  0.3138  0.6200 
O:  0.8525  0.1475  0.6026 
O:  0.5877  0.4123  0.2713 
O:  0.7725  0.4438  0.7909 
O:  0.0167  0.2118  0.1862 
O:  0.8143  0.6398  0.2885 
H:  0.0405  0.8002  0.6434 
H:  0.0624  0.6864  0.9615 
H:  0.1846  0.4162  0.5101 
H:  0.1921  0.2398  0.7226 
Zn:  0.6169  0.6169  0.0000 
O:  0.5562  0.2275  0.7909 
O:  0.7882  0.9833  0.1862 
O:  0.3602  0.1857  0.2885 
H:  0.1998  0.9595  0.6434 
H:  0.3136  0.9376  0.9615 
H:  0.5838  0.8154  0.5101 
H:  0.7602  0.8079  0.7226 
O:  0.2275  0.5562  0.2091 
O:  0.9833  0.7882  0.8138 
O:  0.1857  0.3602  0.7115 
H:  0.9595  0.1998  0.3566 
H:  0.9376  0.3136  0.0385 
H:  0.8154  0.5838  0.4899 
H:  0.8079  0.7602  0.2774 
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): 

Zn: 2.5563 0.0000 0.3844 
0.0000 1.9547 0.0000 
0.1521 0.0000 2.3837 
Eig. Value: 2.7518 1.9547 2.1882 
Zn: 2.1604 0.0000 -0.2069 
0.0000 2.1551 -0.0000 
-0.2615 0.0000 2.6138 
Eig. Value: 2.0611 2.1551 2.7130 
As: 3.6607 -0.0000 0.1098 
-0.0000 2.7152 -0.0000 
0.1783 0.0000 3.3986 
Eig. Value: 3.7243 2.7152 3.3349 
O: -2.5294 0.0000 0.1494 
-0.0000 -1.1156 0.0000 
0.0744 0.0000 -1.8082 
Eig. Value: -2.5464 -1.1156 -1.7912 
O: -1.4428 0.0000 -0.5134 
0.0000 -1.1507 -0.0000 
-0.4931 -0.0000 -2.5153 
Eig. Value: -1.2436 -1.1507 -2.7144 
O: -1.6563 -0.2153 0.0194 
-0.1727 -1.5868 0.2176 
0.0093 0.3587 -1.7600 
Eig. Value: -1.6741 -1.3061 -2.0229 
O: -1.3988 0.0896 -0.0641 
0.2332 -1.3002 0.0706 
-0.1657 -0.0858 -1.6053 
Eig. Value: -1.4687 -1.1674 -1.6682 
O: -0.9159 -0.0841 -0.1599 
-0.1233 -1.5905 -0.1452 
-0.1366 -0.1198 -1.1453 
Eig. Value: -0.8413 -1.6541 -1.1562 
H: 0.5444 -0.3734 -0.5010 
-0.1942 0.5998 0.3838 
-0.3260 0.4633 0.9841 
Eig. Value: 0.2819 0.3305 1.5158 
H: 0.8603 -0.0320 0.6240 
-0.1752 0.3369 -0.1492 
0.6535 -0.0399 0.9822 
Eig. Value: 0.2759 0.3249 1.5786 
H: 0.3878 0.0397 0.1295 
0.0028 0.7247 0.4672 
0.0748 0.3675 0.7500 
Eig. Value: 0.4115 0.2861 1.1649 
H: 0.6151 0.2844 0.0865 
0.4342 1.0252 0.1767 
0.1038 0.1517 0.3539 
Eig. Value: 0.4064 1.2730 0.3147 
As: 3.6607 -0.0000 0.1098 
-0.0000 2.7152 -0.0000 
0.1783 0.0000 3.3986 
Eig. Value: 3.7243 2.7152 3.3349 
O: -2.5294 0.0000 0.1494 
-0.0000 -1.1156 0.0000 
0.0744 0.0000 -1.8082 
Eig. Value: -2.5464 -1.1156 -1.7912 
O: -1.4428 0.0000 -0.5134 
-0.0000 -1.1507 -0.0000 
-0.4931 -0.0000 -2.5153 
Eig. Value: -1.2436 -1.1507 -2.7144 
O: -1.6563 0.2153 0.0194 
0.1727 -1.5868 -0.2176 
0.0093 -0.3587 -1.7600 
Eig. Value: -1.6741 -1.3061 -2.0229 
O: -1.3988 -0.0896 -0.0641 
-0.2332 -1.3002 -0.0706 
-0.1657 0.0858 -1.6053 
Eig. Value: -1.4687 -1.1674 -1.6682 
O: -0.9159 0.0841 -0.1599 
0.1233 -1.5905 0.1452 
-0.1366 0.1198 -1.1453 
Eig. Value: -0.8413 -1.6541 -1.1562 
H: 0.5444 0.3734 -0.5010 
0.1942 0.5998 -0.3838 
-0.3260 -0.4633 0.9841 
Eig. Value: 0.2819 0.3305 1.5158 
H: 0.8603 0.0320 0.6240 
0.1752 0.3369 0.1492 
0.6535 0.0399 0.9822 
Eig. Value: 0.2759 0.3249 1.5786 
H: 0.3878 -0.0397 0.1295 
-0.0028 0.7247 -0.4672 
0.0748 -0.3675 0.7500 
Eig. Value: 0.4115 0.2861 1.1649 
H: 0.6151 -0.2844 0.0865 
-0.4342 1.0252 -0.1767 
0.1038 -0.1517 0.3539 
Eig. Value: 0.4064 1.2730 0.3147 
Zn: 2.1604 0.0000 -0.2069 
0.0000 2.1551 0.0000 
-0.2615 0.0000 2.6138 
Eig. Value: 2.0611 2.1551 2.7130 
O: -1.6563 -0.2153 0.0194 
-0.1727 -1.5868 0.2176 
0.0093 0.3587 -1.7600 
Eig. Value: -1.6741 -1.3061 -2.0229 
O: -1.3988 0.0896 -0.0641 
0.2332 -1.3002 0.0706 
-0.1657 -0.0858 -1.6053 
Eig. Value: -1.4687 -1.1674 -1.6682 
O: -0.9159 -0.0841 -0.1599 
-0.1233 -1.5905 -0.1452 
-0.1366 -0.1198 -1.1453 
Eig. Value: -0.8413 -1.6541 -1.1562 
H: 0.5444 -0.3734 -0.5010 
-0.1942 0.5998 0.3838 
-0.3260 0.4633 0.9841 
Eig. Value: 0.2819 0.3305 1.5158 
H: 0.8603 -0.0320 0.6240 
-0.1752 0.3369 -0.1492 
0.6535 -0.0399 0.9822 
Eig. Value: 0.2759 0.3249 1.5786 
H: 0.3878 0.0397 0.1295 
0.0028 0.7247 0.4672 
0.0748 0.3675 0.7500 
Eig. Value: 0.4115 0.2861 1.1649 
H: 0.6151 0.2844 0.0865 
0.4342 1.0252 0.1767 
0.1038 0.1517 0.3539 
Eig. Value: 0.4064 1.2730 0.3147 
O: -1.6563 0.2153 0.0194 
0.1727 -1.5868 -0.2176 
0.0093 -0.3587 -1.7600 
Eig. Value: -1.6741 -1.3061 -2.0229 
O: -1.3988 -0.0896 -0.0641 
-0.2332 -1.3002 -0.0706 
-0.1657 0.0858 -1.6053 
Eig. Value: -1.4687 -1.1674 -1.6682 
O: -0.9159 0.0841 -0.1599 
0.1233 -1.5905 0.1452 
-0.1366 0.1198 -1.1453 
Eig. Value: -0.8413 -1.6541 -1.1562 
H: 0.5444 0.3734 -0.5010 
0.1942 0.5998 -0.3838 
-0.3260 -0.4633 0.9841 
Eig. Value: 0.2819 0.3305 1.5158 
H: 0.8603 0.0320 0.6240 
0.1752 0.3369 0.1492 
0.6535 0.0399 0.9822 
Eig. Value: 0.2759 0.3249 1.5786 
H: 0.3878 -0.0397 0.1295 
-0.0028 0.7247 -0.4672 
0.0748 -0.3675 0.7500 
Eig. Value: 0.4115 0.2861 1.1649 
H: 0.6151 -0.2844 0.0865 
-0.4342 1.0252 -0.1767 
0.1038 -0.1517 0.3539 
Eig. Value: 0.4064 1.2730 0.3147 
Atom type  X  Y  Z 

Dielectric tensors: 

 X Y Z 
Ɛ∞: 2.9625 0.0000 0.0504 
0.0000 2.8585 0.0000 
0.0504 0.0000 3.0875 
Eig. Value: 2.9447 2.8585 3.1052 
Refractive index (N): 1.7212 0.0000 0.2245 
0.0000 1.6907 0.0000 
0.2245 0.0000 1.7571 
Eig. Value: 1.7160 1.6907 1.7622 
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