-    AKERMANITE     -    Ca2MgSi2O7

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:  113  P-42_1m 
Lattice parameters (Å):  7.8338  7.8338  5.0082 
Angles (°):  90  90  90 

Symmetry (theoretical): 

Space group:  113  P-42_1m 
Lattice parameters (Å):  7.8435  7.8435  4.9958 
Angles (°):  90  90  90 

Cell contents: 

Number of atoms:  24 
Number of atom types:  4 
Chemical composition:  0 

Atomic positions (theoretical):

Ca:  0.3336  0.1664  0.5070 
Mg:  0.0000  0.0000  0.0000 
Si:  0.1397  0.3603  0.9345 
O:  0.5000  0.0000  0.1844 
O:  0.1387  0.3613  0.2537 
O:  0.0809  0.1867  0.7885 
Ca:  0.8336  0.3336  0.4930 
Si:  0.6397  0.1397  0.0655 
O:  0.0000  0.5000  0.8156 
O:  0.6387  0.1387  0.7463 
O:  0.8133  0.0809  0.2115 
Ca:  0.1664  0.6664  0.4930 
Mg:  0.5000  0.5000  0.0000 
Si:  0.3603  0.8603  0.0655 
O:  0.3613  0.8613  0.7463 
O:  0.4191  0.6867  0.2115 
Ca:  0.6664  0.8336  0.5070 
Si:  0.8603  0.6397  0.9345 
O:  0.8613  0.6387  0.2537 
O:  0.9191  0.8133  0.7885 
O:  0.3133  0.4191  0.7885 
O:  0.6867  0.5809  0.7885 
O:  0.1867  0.9191  0.2115 
O:  0.5809  0.3133  0.2115 
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): 

Ca: 2.2120 -0.2246 -0.1263 
-0.2246 2.2120 0.1263 
-0.0095 0.0095 2.4311 
Eig. Value: 2.5299 1.9874 2.3378 
Mg: 2.0540 -0.0322 -0.0000 
0.0322 2.0540 0.0000 
-0.0000 0.0000 1.4856 
Eig. Value: 2.0540 2.0540 1.4856 
Si: 2.7165 -0.0597 0.0249 
-0.0597 2.7165 -0.0249 
-0.0435 0.0435 2.7960 
Eig. Value: 2.7696 2.6568 2.8026 
O: -1.9905 -0.7899 0.0000 
-0.7899 -1.9905 -0.0000 
0.0000 -0.0000 -1.4745 
Eig. Value: -1.2006 -2.7804 -1.4745 
O: -1.4461 0.0595 -0.0181 
0.0595 -1.4461 0.0181 
0.0159 -0.0159 -2.1634 
Eig. Value: -1.3866 -1.5056 -2.1634 
O: -1.5668 -0.0906 -0.0115 
-0.1912 -1.9473 -0.2128 
-0.0010 -0.1129 -1.5346 
Eig. Value: -1.5494 -2.0425 -1.4569 
Ca: 2.2120 0.2246 0.1263 
0.2246 2.2120 0.1263 
0.0095 0.0095 2.4311 
Eig. Value: 2.5299 1.9874 2.3378 
Si: 2.7165 0.0597 -0.0249 
0.0597 2.7165 -0.0249 
0.0435 0.0435 2.7960 
Eig. Value: 2.7696 2.6568 2.8026 
O: -1.9905 0.7899 0.0000 
0.7899 -1.9905 -0.0000 
-0.0000 0.0000 -1.4745 
Eig. Value: -1.2006 -2.7804 -1.4745 
O: -1.4461 -0.0595 0.0181 
-0.0595 -1.4461 0.0181 
-0.0159 -0.0159 -2.1634 
Eig. Value: -1.3866 -1.5056 -2.1634 
O: -1.9473 0.1912 -0.2128 
0.0906 -1.5668 0.0115 
-0.1129 0.0010 -1.5346 
Eig. Value: -2.0425 -1.5494 -1.4569 
Ca: 2.2120 0.2246 -0.1263 
0.2246 2.2120 -0.1263 
-0.0095 -0.0095 2.4311 
Eig. Value: 2.5299 1.9874 2.3378 
Mg: 2.0540 0.0322 0.0000 
-0.0322 2.0540 0.0000 
0.0000 -0.0000 1.4856 
Eig. Value: 2.0540 2.0540 1.4856 
Si: 2.7165 0.0597 0.0249 
0.0597 2.7165 0.0249 
-0.0435 -0.0435 2.7960 
Eig. Value: 2.7696 2.6568 2.8026 
O: -1.4461 -0.0595 -0.0181 
-0.0595 -1.4461 -0.0181 
0.0159 0.0159 -2.1634 
Eig. Value: -1.3866 -1.5056 -2.1634 
O: -1.5668 0.0906 -0.0115 
0.1912 -1.9473 0.2128 
-0.0010 0.1129 -1.5346 
Eig. Value: -1.5494 -2.0425 -1.4569 
Ca: 2.2120 -0.2246 0.1263 
-0.2246 2.2120 -0.1263 
0.0095 -0.0095 2.4311 
Eig. Value: 2.5299 1.9874 2.3378 
Si: 2.7165 -0.0597 -0.0249 
-0.0597 2.7165 0.0249 
0.0435 -0.0435 2.7960 
Eig. Value: 2.7696 2.6568 2.8026 
O: -1.4461 0.0595 0.0181 
0.0595 -1.4461 -0.0181 
-0.0159 0.0159 -2.1634 
Eig. Value: -1.3866 -1.5056 -2.1634 
O: -1.5668 -0.0906 0.0115 
-0.1912 -1.9473 0.2128 
0.0010 0.1129 -1.5346 
Eig. Value: -1.5494 -2.0425 -1.4569 
O: -1.9473 -0.1912 0.2128 
-0.0906 -1.5668 0.0115 
0.1129 0.0010 -1.5346 
Eig. Value: -2.0425 -1.5494 -1.4569 
O: -1.9473 -0.1912 -0.2128 
-0.0906 -1.5668 -0.0115 
-0.1129 -0.0010 -1.5346 
Eig. Value: -2.0425 -1.5494 -1.4569 
O: -1.9473 0.1912 0.2128 
0.0906 -1.5668 -0.0115 
0.1129 -0.0010 -1.5346 
Eig. Value: -2.0425 -1.5494 -1.4569 
O: -1.5668 0.0906 0.0115 
0.1912 -1.9473 -0.2128 
0.0010 -0.1129 -1.5346 
Eig. Value: -1.5494 -2.0425 -1.4569 
Atom type  X  Y  Z 

Dielectric tensors: 

 X Y Z 
Ɛ∞: 2.7167 0.0000 0.0000 
0.0000 2.7167 0.0000 
0.0000 0.0000 2.7294 
Eig. Value: 2.7167 2.7167 2.7294 
Refractive index (N): 1.6483 0.0000 0.0000 
0.0000 1.6483 0.0000 
0.0000 0.0000 1.6521 
Eig. Value: 1.6483 1.6483 1.6521 
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