-    OLIVINE-Ge     -    Mg2GeO4

The crystal structure is fully relaxed (both unit cell parameters and atomic positions under symmetry constraints) starting from forsterite structure, #w000188 

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:  62  Pnma 
Lattice parameters (Å):       
Angles (°):       

Symmetry (theoretical): 

Space group:  62  Pnma 
Lattice parameters (Å):  4.9032  11.1533  6.3039 
Angles (°):  90  90  90 

Cell contents: 

Number of atoms:  28 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Mg:  0.0000  1.0000  0.0000 
Mg:  0.9929  0.2753  0.2500 
Ge:  0.4356  0.0949  0.2500 
O:  0.7868  0.0919  0.2500 
O:  0.2277  0.4406  0.2500 
O:  0.2668  0.1650  0.0221 
Mg:  0.5000  0.5000  0.0000 
Mg:  0.4929  0.2247  0.7500 
Ge:  0.9356  0.4051  0.7500 
O:  0.2868  0.4081  0.7500 
O:  0.7277  0.0594  0.7500 
O:  0.7668  0.3350  0.9779 
Mg:  0.0000  1.0000  0.5000 
Mg:  0.0071  0.7247  0.7500 
Ge:  0.5644  0.9051  0.7500 
O:  0.2132  0.9081  0.7500 
O:  0.7723  0.5594  0.7500 
O:  0.7332  0.8350  0.5221 
Mg:  0.5000  0.5000  0.5000 
Mg:  0.5071  0.7753  0.2500 
Ge:  0.0644  0.5949  0.2500 
O:  0.7132  0.5919  0.2500 
O:  0.2723  0.9406  0.2500 
O:  0.2332  0.6650  0.4779 
O:  0.7332  0.8350  0.9779 
O:  0.2332  0.6650  0.0221 
O:  0.2668  0.1650  0.4779 
O:  0.7668  0.3350  0.5221 
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): 

Mg: 2.2232 -0.0495 -0.1006 
0.1054 1.6817 0.2869 
0.1771 0.2390 1.9457 
Eig. Value: 2.2401 1.5195 2.0911 
Mg: 1.9259 0.0562 -0.0000 
-0.1033 2.2689 -0.0000 
-0.0000 0.0000 2.0133 
Eig. Value: 1.9243 2.2705 2.0133 
Ge: 3.1295 0.0099 0.0000 
-0.0039 2.7620 -0.0000 
0.0000 0.0000 3.0460 
Eig. Value: 3.1295 2.7619 3.0460 
O: -2.3475 0.0013 0.0000 
-0.0015 -1.4469 -0.0000 
0.0000 -0.0000 -1.5377 
Eig. Value: -2.3475 -1.4469 -1.5377 
O: -1.6633 0.0227 0.0000 
0.1393 -1.9937 0.0000 
-0.0000 0.0000 -1.5762 
Eig. Value: -1.6445 -2.0124 -1.5762 
O: -1.6339 0.0712 0.0134 
0.1101 -1.6360 0.1882 
-0.1029 0.2188 -1.9456 
Eig. Value: -1.5034 -1.6502 -2.0618 
Mg: 2.2232 0.0495 0.1006 
-0.1054 1.6817 0.2869 
-0.1771 0.2390 1.9457 
Eig. Value: 2.2401 1.5195 2.0911 
Mg: 1.9259 -0.0562 0.0000 
0.1033 2.2689 0.0000 
0.0000 0.0000 2.0133 
Eig. Value: 1.9243 2.2705 2.0133 
Ge: 3.1295 -0.0099 0.0000 
0.0039 2.7620 0.0000 
-0.0000 -0.0000 3.0460 
Eig. Value: 3.1295 2.7619 3.0460 
O: -2.3475 -0.0013 -0.0000 
0.0015 -1.4469 0.0000 
-0.0000 0.0000 -1.5377 
Eig. Value: -2.3475 -1.4469 -1.5377 
O: -1.6633 -0.0227 0.0000 
-0.1393 -1.9936 0.0000 
0.0000 -0.0000 -1.5762 
Eig. Value: -1.6445 -2.0124 -1.5762 
O: -1.6339 -0.0712 -0.0134 
-0.1101 -1.6360 0.1882 
0.1029 0.2188 -1.9456 
Eig. Value: -1.5034 -1.6502 -2.0618 
Mg: 2.2232 -0.0495 0.1006 
0.1054 1.6817 -0.2869 
-0.1771 -0.2390 1.9457 
Eig. Value: 2.2401 1.5195 2.0911 
Mg: 1.9259 0.0562 0.0000 
-0.1033 2.2689 -0.0000 
0.0000 -0.0000 2.0133 
Eig. Value: 1.9243 2.2705 2.0133 
Ge: 3.1295 0.0099 0.0000 
-0.0039 2.7620 -0.0000 
-0.0000 0.0000 3.0460 
Eig. Value: 3.1295 2.7619 3.0460 
O: -2.3475 0.0013 0.0000 
-0.0015 -1.4469 0.0000 
0.0000 0.0000 -1.5377 
Eig. Value: -2.3475 -1.4469 -1.5377 
O: -1.6633 0.0227 -0.0000 
0.1393 -1.9937 0.0000 
-0.0000 0.0000 -1.5762 
Eig. Value: -1.6445 -2.0124 -1.5762 
O: -1.6339 0.0712 -0.0134 
0.1101 -1.6360 -0.1882 
0.1029 -0.2188 -1.9456 
Eig. Value: -1.5034 -1.6502 -2.0618 
Mg: 2.2232 0.0495 -0.1006 
-0.1054 1.6817 -0.2869 
0.1771 -0.2390 1.9457 
Eig. Value: 2.2401 1.5195 2.0911 
Mg: 1.9259 -0.0562 -0.0000 
0.1033 2.2689 0.0000 
0.0000 -0.0000 2.0133 
Eig. Value: 1.9243 2.2705 2.0133 
Ge: 3.1295 -0.0099 0.0000 
0.0039 2.7620 0.0000 
0.0000 -0.0000 3.0460 
Eig. Value: 3.1295 2.7619 3.0460 
O: -2.3475 -0.0013 -0.0000 
0.0015 -1.4469 -0.0000 
0.0000 0.0000 -1.5377 
Eig. Value: -2.3475 -1.4469 -1.5377 
O: -1.6633 -0.0227 0.0000 
-0.1393 -1.9936 -0.0000 
-0.0000 -0.0000 -1.5762 
Eig. Value: -1.6445 -2.0124 -1.5762 
O: -1.6339 -0.0712 0.0134 
-0.1101 -1.6360 -0.1882 
-0.1029 -0.2188 -1.9456 
Eig. Value: -1.5034 -1.6502 -2.0618 
O: -1.6339 0.0712 0.0134 
0.1101 -1.6360 0.1882 
-0.1029 0.2188 -1.9456 
Eig. Value: -1.5034 -1.6502 -2.0618 
O: -1.6339 -0.0712 -0.0134 
-0.1101 -1.6360 0.1882 
0.1029 0.2188 -1.9456 
Eig. Value: -1.5034 -1.6502 -2.0618 
O: -1.6339 0.0712 -0.0134 
0.1101 -1.6360 -0.1882 
0.1029 -0.2188 -1.9456 
Eig. Value: -1.5034 -1.6502 -2.0618 
O: -1.6339 -0.0712 0.0134 
-0.1101 -1.6360 -0.1882 
-0.1029 -0.2188 -1.9456 
Eig. Value: -1.5034 -1.6502 -2.0618 
Atom type 

Dielectric tensors: 

 
Ɛ3.1848 0.0000 0.0000 
0.0000 2.9584 0.0000 
0.0000 0.0000 3.0211 
Eig. Value: 3.1848 2.9584 3.0211 
Refractive index (N): 1.7846 0.0000 0.0000 
0.0000 1.7200 0.0000 
0.0000 0.0000 1.7381 
Eig. Value: 1.7846 1.7200 1.7381 
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