-    Na2Mg(SO4)2     -    Na2Mg(SO4)2

 

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):  10.1010  8.2400  8.7300 
Angles (°):  90.0  114.640  90.0 

Symmetry (theoretical): 

Space group:  15  C2/c 
Lattice parameters (Å):  6.4236  6.4236  9.5494 
Angles (°):  66.31  113.69  100.99 

Cell contents: 

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

Atomic positions (theoretical):

Mg:  0.1021  0.1021  0.2500 
Na:  0.3932  0.6762  0.0213 
S:  0.6379  0.9980  0.3470 
O:  0.7708  0.0501  0.4973 
O:  0.4318  0.1349  0.2568 
O:  0.5775  0.7545  0.3890 
O:  0.7714  0.0681  0.2397 
Na:  0.6762  0.3932  0.4787 
S:  0.9980  0.6379  0.1530 
O:  0.0501  0.7708  0.0027 
O:  0.1349  0.4318  0.2432 
O:  0.7545  0.5775  0.1110 
O:  0.0681  0.7714  0.2603 
Mg:  0.8979  0.8979  0.7500 
Na:  0.6068  0.3238  0.9787 
S:  0.3621  0.0020  0.6530 
O:  0.2292  0.9499  0.5027 
O:  0.5682  0.8651  0.7432 
O:  0.4225  0.2455  0.6110 
O:  0.2286  0.9319  0.7603 
Na:  0.3238  0.6068  0.5213 
S:  0.0020  0.3621  0.8470 
O:  0.9499  0.2292  0.9973 
O:  0.8651  0.5682  0.7568 
O:  0.2455  0.4225  0.8890 
O:  0.9319  0.2286  0.7397 
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: 2.2824 -0.1195 -0.0218 
-0.1195 2.2328 0.0178 
0.0301 -0.0245 2.3134 
Eig. Value: 2.3801 2.1355 2.3130 
Na: 1.1805 0.0524 0.0208 
0.0600 1.0104 0.0452 
-0.0362 -0.0038 1.1103 
Eig. Value: 1.1974 0.9895 1.1143 
S: 3.6119 -0.0235 -0.1154 
0.0842 3.1681 -0.1326 
-0.0215 0.0326 3.4057 
Eig. Value: 3.6367 3.1574 3.3917 
O: -1.0279 -0.0832 -0.1349 
-0.0821 -1.1760 -0.4800 
-0.1748 -0.5459 -2.0748 
Eig. Value: -1.0064 -0.9414 -2.3309 
O: -2.0158 0.3697 -0.4455 
0.3361 -1.0757 0.1991 
-0.4486 0.2336 -1.2008 
Eig. Value: -2.3459 -0.9126 -1.0338 
O: -0.9968 -0.1647 0.0440 
-0.1769 -2.0337 0.2902 
0.0165 0.2190 -0.9945 
Eig. Value: -0.9723 -2.1195 -0.9333 
O: -1.9882 -0.1425 0.6778 
-0.1496 -0.9143 0.1134 
0.6633 0.0938 -1.4026 
Eig. Value: -2.4480 -0.8928 -0.9644 
Na: 0.9950 0.0215 -0.0400 
0.0139 1.1958 -0.0295 
-0.0036 0.0362 1.1103 
Eig. Value: 0.9895 1.1974 1.1143 
S: 3.1744 -0.0066 0.1064 
-0.1144 3.6057 0.1400 
-0.0363 0.0144 3.4057 
Eig. Value: 3.1574 3.6367 3.3917 
O: -1.1369 -0.1047 0.4425 
-0.1058 -1.0669 0.2296 
0.4990 0.2821 -2.0748 
Eig. Value: -0.9414 -1.0064 -2.3309 
O: -1.2550 0.4941 -0.2855 
0.5277 -1.8365 0.3957 
-0.3199 0.3917 -1.2008 
Eig. Value: -0.9126 -2.3459 -1.0338 
O: -1.9229 -0.3692 -0.2752 
-0.3569 -1.1077 -0.1021 
-0.2111 -0.0606 -0.9945 
Eig. Value: -2.1195 -0.9723 -0.9333 
O: -0.9006 0.0762 0.0267 
0.0833 -2.0020 -0.6867 
0.0430 -0.6685 -1.4026 
Eig. Value: -0.8928 -2.4480 -0.9644 
Mg: 2.2824 -0.1195 -0.0218 
-0.1195 2.2328 0.0178 
0.0301 -0.0245 2.3134 
Eig. Value: 2.3801 2.1355 2.3130 
Na: 1.1805 0.0524 0.0208 
0.0600 1.0104 0.0452 
-0.0362 -0.0038 1.1103 
Eig. Value: 1.1974 0.9895 1.1143 
S: 3.6119 -0.0235 -0.1154 
0.0842 3.1681 -0.1326 
-0.0215 0.0326 3.4057 
Eig. Value: 3.6367 3.1574 3.3917 
O: -1.0279 -0.0832 -0.1349 
-0.0821 -1.1760 -0.4800 
-0.1748 -0.5459 -2.0748 
Eig. Value: -1.0064 -0.9414 -2.3309 
O: -2.0158 0.3697 -0.4455 
0.3361 -1.0757 0.1991 
-0.4486 0.2336 -1.2008 
Eig. Value: -2.3459 -0.9126 -1.0338 
O: -0.9968 -0.1647 0.0440 
-0.1769 -2.0337 0.2902 
0.0165 0.2190 -0.9945 
Eig. Value: -0.9723 -2.1195 -0.9333 
O: -1.9882 -0.1425 0.6778 
-0.1496 -0.9143 0.1134 
0.6633 0.0938 -1.4026 
Eig. Value: -2.4480 -0.8928 -0.9644 
Na: 0.9950 0.0215 -0.0400 
0.0139 1.1958 -0.0295 
-0.0036 0.0362 1.1103 
Eig. Value: 0.9895 1.1974 1.1143 
S: 3.1744 -0.0066 0.1064 
-0.1144 3.6057 0.1400 
-0.0363 0.0144 3.4057 
Eig. Value: 3.1574 3.6367 3.3917 
O: -1.1369 -0.1047 0.4425 
-0.1058 -1.0669 0.2296 
0.4990 0.2821 -2.0748 
Eig. Value: -0.9414 -1.0064 -2.3309 
O: -1.2550 0.4941 -0.2855 
0.5277 -1.8365 0.3957 
-0.3199 0.3917 -1.2008 
Eig. Value: -0.9126 -2.3459 -1.0338 
O: -1.9229 -0.3692 -0.2752 
-0.3569 -1.1077 -0.1021 
-0.2111 -0.0606 -0.9945 
Eig. Value: -2.1195 -0.9723 -0.9333 
O: -0.9006 0.0762 0.0267 
0.0833 -2.0020 -0.6867 
0.0430 -0.6685 -1.4026 
Eig. Value: -0.8928 -2.4480 -0.9644 
Atom type 

Dielectric tensors: 

 
Ɛ2.2671 0.0000 0.0000 
0.0000 2.2669 0.0000 
0.0000 0.0000 2.2806 
Eig. Value: 2.2668 2.2654 2.2824 
Refractive index (N): 1.5057 0.0000 0.0000 
0.0000 1.5056 0.0000 
0.0000 0.0000 1.5102 
Eig. Value: 1.5056 1.5051 1.5108 
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