-    WALSTROMITE     -    Ca2BaSi3O9

 

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:  P-1 
Lattice parameters (Å):  3.5630  5.0886  3.5577 
Angles (°):  69.6  102.3  96.9 

Symmetry (theoretical): 

Space group:  P-1 
Lattice parameters (Å):  6.6598  9.5265  6.6281 
Angles (°):  69.9  102.6  97.0 

Cell contents: 

Number of atoms:  30 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Ca:  0.2693  0.5085  0.7589 
Ca:  0.4388  0.8272  0.9449 
Ba:  0.0495  0.8502  0.3203 
Si:  0.0947  0.2212  0.1508 
Si:  0.2321  0.4813  0.2843 
Si:  0.4404  0.1972  0.5138 
O:  0.2313  0.2593  0.9691 
O:  0.8984  0.1195  0.1004 
O:  0.0423  0.3707  0.1972 
O:  0.3733  0.5561  0.1074 
O:  0.1278  0.5858  0.3654 
O:  0.3569  0.3565  0.5074 
O:  0.6152  0.2363  0.3707 
O:  0.5088  0.0900  0.7557 
O:  0.2288  0.1244  0.3920 
Ca:  0.7307  0.4915  0.2411 
Ca:  0.5612  0.1728  0.0551 
Ba:  0.9505  0.1498  0.6797 
Si:  0.9053  0.7788  0.8492 
Si:  0.7679  0.5187  0.7157 
Si:  0.5596  0.8028  0.4862 
O:  0.7687  0.7407  0.0309 
O:  0.1016  0.8805  0.8996 
O:  0.9577  0.6293  0.8028 
O:  0.6267  0.4439  0.8926 
O:  0.8722  0.4142  0.6346 
O:  0.6431  0.6435  0.4926 
O:  0.3848  0.7637  0.6293 
O:  0.4912  0.9100  0.2443 
O:  0.7712  0.8756  0.6080 
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): 

Ca: 2.3918 0.1339 -0.0646 
0.0708 2.1951 -0.0747 
-0.0471 -0.1232 2.3994 
Eig. Value: 2.5149 2.1317 2.3398 
Ca: 2.4047 -0.0620 -0.0795 
-0.0144 2.2729 -0.0387 
-0.0967 -0.0114 2.3669 
Eig. Value: 2.4769 2.2389 2.3287 
Ba: 2.5254 -0.1990 0.1350 
-0.1978 2.9267 0.0637 
0.0995 0.1312 2.5968 
Eig. Value: 2.3551 3.0137 2.6801 
Si: 2.5459 0.0396 0.2159 
0.1061 2.9188 0.2639 
0.0832 0.1710 3.1442 
Eig. Value: 2.5092 2.7874 3.3123 
Si: 2.7922 -0.1508 -0.0383 
-0.0807 3.2677 0.0671 
-0.0318 0.0902 2.8216 
Eig. Value: 2.7599 3.3091 2.8126 
Si: 3.1345 -0.1154 0.1673 
-0.1454 2.8716 -0.0719 
0.3963 -0.1263 2.8268 
Eig. Value: 3.3564 2.8190 2.6576 
O: -1.8446 -0.1367 0.1058 
-0.1384 -1.5167 0.0003 
0.2628 0.0260 -1.9802 
Eig. Value: -1.7580 -1.4609 -2.1226 
O: -1.8356 -0.1236 -0.1593 
-0.1541 -1.9007 -0.0255 
-0.1487 -0.0814 -1.7112 
Eig. Value: -1.7775 -2.0675 -1.6026 
O: -1.5481 -0.0045 -0.0836 
-0.0479 -2.2266 -0.5726 
-0.0926 -0.5352 -1.5959 
Eig. Value: -1.5576 -2.5531 -1.2600 
O: -1.8194 -0.1629 0.2687 
-0.2189 -1.6184 0.2015 
0.2652 0.1566 -1.7569 
Eig. Value: -2.1791 -1.4947 -1.5209 
O: -1.6673 0.4111 0.1707 
0.4782 -2.1544 -0.3266 
0.1601 -0.2614 -1.6238 
Eig. Value: -1.4034 -2.5418 -1.5004 
O: -1.5943 0.5489 -0.1629 
0.5309 -2.2519 0.1932 
-0.1637 0.1768 -1.5821 
Eig. Value: -1.2805 -2.6119 -1.5359 
O: -2.1350 -0.0779 0.1920 
-0.0384 -1.4717 0.0655 
0.0040 0.1150 -1.8137 
Eig. Value: -2.1720 -1.4477 -1.8008 
O: -1.5747 0.0391 -0.0863 
0.0116 -1.7036 0.3511 
-0.0678 0.3262 -2.0065 
Eig. Value: -1.5702 -1.4792 -2.2353 
O: -1.7755 -0.1398 -0.5809 
-0.1614 -1.6087 -0.0964 
-0.6228 -0.0542 -2.0856 
Eig. Value: -1.2913 -1.6026 -2.5759 
Ca: 2.3918 0.1339 -0.0646 
0.0708 2.1951 -0.0747 
-0.0471 -0.1232 2.3994 
Eig. Value: 2.5149 2.1317 2.3398 
Ca: 2.4047 -0.0620 -0.0795 
-0.0144 2.2729 -0.0387 
-0.0967 -0.0114 2.3669 
Eig. Value: 2.4769 2.2389 2.3287 
Ba: 2.5254 -0.1990 0.1350 
-0.1978 2.9267 0.0637 
0.0995 0.1312 2.5968 
Eig. Value: 2.3551 3.0137 2.6801 
Si: 2.5459 0.0396 0.2159 
0.1061 2.9188 0.2639 
0.0832 0.1710 3.1442 
Eig. Value: 2.5092 2.7874 3.3123 
Si: 2.7922 -0.1508 -0.0383 
-0.0807 3.2677 0.0671 
-0.0318 0.0902 2.8216 
Eig. Value: 2.7599 3.3091 2.8126 
Si: 3.1345 -0.1154 0.1673 
-0.1454 2.8716 -0.0719 
0.3963 -0.1263 2.8268 
Eig. Value: 3.3564 2.8190 2.6576 
O: -1.8446 -0.1367 0.1058 
-0.1384 -1.5167 0.0003 
0.2628 0.0260 -1.9802 
Eig. Value: -1.7580 -1.4609 -2.1226 
O: -1.8356 -0.1236 -0.1593 
-0.1541 -1.9007 -0.0255 
-0.1487 -0.0814 -1.7112 
Eig. Value: -1.7775 -2.0675 -1.6026 
O: -1.5481 -0.0045 -0.0836 
-0.0479 -2.2266 -0.5726 
-0.0926 -0.5352 -1.5959 
Eig. Value: -1.5576 -2.5531 -1.2600 
O: -1.8194 -0.1629 0.2687 
-0.2189 -1.6184 0.2015 
0.2652 0.1566 -1.7569 
Eig. Value: -2.1791 -1.4947 -1.5209 
O: -1.6673 0.4111 0.1707 
0.4782 -2.1544 -0.3266 
0.1601 -0.2614 -1.6238 
Eig. Value: -1.4034 -2.5418 -1.5004 
O: -1.5943 0.5489 -0.1629 
0.5309 -2.2519 0.1932 
-0.1637 0.1768 -1.5821 
Eig. Value: -1.2805 -2.6119 -1.5359 
O: -2.1350 -0.0779 0.1920 
-0.0384 -1.4717 0.0655 
0.0040 0.1150 -1.8137 
Eig. Value: -2.1720 -1.4477 -1.8008 
O: -1.5747 0.0391 -0.0863 
0.0116 -1.7036 0.3511 
-0.0678 0.3262 -2.0065 
Eig. Value: -1.5702 -1.4792 -2.2353 
O: -1.7755 -0.1398 -0.5809 
-0.1614 -1.6087 -0.0964 
-0.6228 -0.0542 -2.0856 
Eig. Value: -1.2913 -1.6026 -2.5759 
Atom type 

Dielectric tensors: 

 
Ɛ2.9242 -0.0282 0.0248 
-0.0282 2.9612 0.0134 
0.0248 0.0134 2.9512 
Eig. Value: 2.8948 2.9654 2.9765 
Refractive index (N): 1.7014 0.0000 0.0000 
0.0000 1.7220 0.0000 
0.0000 0.0000 1.7253 
Eig. Value: 1.7014 1.7220 1.7253 
Ɛ010.8459 0.0000 0.0000 
0.0000 8.3535 0.0000 
0.0000 0.0000 8.3712 
Eig. Value: 0.0000 0.0000 0.0000