-    LARNITE     -    Ca2SiO4

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:  14  P2_1/c 
Lattice parameters (Å):  5.5041  6.7622  9.3281 
Angles (°):  90.0  94.2  90.0 

Symmetry (theoretical): 

Space group:  14  P2_1/c 
Lattice parameters (Å):  5.5185  6.7781  9.2992 
Angles (°):  90.0  95.3  90.0 

Cell contents: 

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

Atomic positions (theoretical):

Ca:  0.2248  0.3457  0.4322 
Ca:  0.2141  0.9992  0.7001 
Si:  0.2672  0.7802  0.4182 
O:  0.2117  0.0089  0.4392 
O:  0.0149  0.6652  0.3623 
O:  0.4777  0.7495  0.3096 
O:  0.3465  0.6710  0.5726 
Ca:  0.2752  0.8457  0.0678 
Ca:  0.2859  0.4992  0.7999 
Si:  0.2328  0.2802  0.0818 
O:  0.2883  0.5089  0.0608 
O:  0.4851  0.1652  0.1377 
O:  0.0223  0.2495  0.1904 
O:  0.1535  0.1710  0.9274 
Ca:  0.7752  0.6543  0.5678 
Ca:  0.7859  0.0008  0.2999 
Si:  0.7328  0.2198  0.5818 
O:  0.7883  0.9911  0.5608 
O:  0.9851  0.3348  0.6377 
O:  0.5223  0.2505  0.6904 
O:  0.6535  0.3290  0.4274 
Ca:  0.7248  0.1543  0.9322 
Ca:  0.7141  0.5008  0.2001 
Si:  0.7672  0.7198  0.9182 
O:  0.7117  0.4911  0.9392 
O:  0.5149  0.8348  0.8623 
O:  0.9777  0.7505  0.8096 
O:  0.8465  0.8290  0.0726 
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: 2.2475 -0.0491 -0.0256 
-0.0100 2.4905 -0.0040 
-0.0034 0.0389 2.1348 
Eig. Value: 2.2454 2.4950 2.1324 
Ca: 2.3112 -0.0062 0.0500 
-0.0805 2.1747 0.0063 
-0.0265 -0.0562 2.4139 
Eig. Value: 2.3203 2.1604 2.4190 
Si: 2.8685 0.0742 -0.0643 
0.0396 2.8678 -0.0187 
-0.0923 -0.0192 2.5992 
Eig. Value: 2.9396 2.8179 2.5780 
O: -1.5189 0.1508 -0.0140 
0.1628 -2.4411 -0.1353 
-0.0189 -0.1132 -1.4975 
Eig. Value: -1.5245 -2.4817 -1.4513 
O: -2.1658 -0.3112 -0.2089 
-0.3039 -1.7935 -0.1136 
-0.2468 -0.1280 -1.5760 
Eig. Value: -2.4181 -1.6205 -1.4967 
O: -2.0861 0.1002 0.4049 
0.0527 -1.5519 -0.0935 
0.4626 -0.0290 -1.9264 
Eig. Value: -2.4579 -1.5412 -1.5654 
O: -1.6564 0.0962 -0.1421 
0.0889 -1.7464 0.3321 
-0.0746 0.3180 -2.1480 
Eig. Value: -1.6388 -1.5549 -2.3572 
Ca: 2.2475 0.0491 -0.0256 
0.0100 2.4905 0.0040 
-0.0034 -0.0389 2.1348 
Eig. Value: 2.2454 2.4950 2.1324 
Ca: 2.3112 0.0062 0.0500 
0.0805 2.1747 -0.0063 
-0.0265 0.0562 2.4139 
Eig. Value: 2.3203 2.1604 2.4190 
Si: 2.8685 -0.0742 -0.0643 
-0.0396 2.8678 0.0187 
-0.0923 0.0192 2.5992 
Eig. Value: 2.9396 2.8179 2.5780 
O: -1.5189 -0.1508 -0.0140 
-0.1628 -2.4411 0.1353 
-0.0189 0.1132 -1.4975 
Eig. Value: -1.5245 -2.4817 -1.4513 
O: -2.1658 0.3112 -0.2089 
0.3039 -1.7935 0.1136 
-0.2468 0.1280 -1.5760 
Eig. Value: -2.4181 -1.6205 -1.4967 
O: -2.0861 -0.1002 0.4049 
-0.0527 -1.5519 0.0935 
0.4626 0.0290 -1.9264 
Eig. Value: -2.4579 -1.5412 -1.5654 
O: -1.6564 -0.0962 -0.1421 
-0.0889 -1.7464 -0.3321 
-0.0746 -0.3180 -2.1480 
Eig. Value: -1.6388 -1.5549 -2.3572 
Ca: 2.2475 -0.0491 -0.0256 
-0.0100 2.4905 -0.0040 
-0.0034 0.0389 2.1348 
Eig. Value: 2.2454 2.4950 2.1324 
Ca: 2.3112 -0.0062 0.0500 
-0.0805 2.1747 0.0063 
-0.0265 -0.0562 2.4139 
Eig. Value: 2.3203 2.1604 2.4190 
Si: 2.8685 0.0742 -0.0643 
0.0396 2.8678 -0.0187 
-0.0923 -0.0192 2.5992 
Eig. Value: 2.9396 2.8179 2.5780 
O: -1.5189 0.1508 -0.0140 
0.1628 -2.4411 -0.1353 
-0.0189 -0.1132 -1.4975 
Eig. Value: -1.5245 -2.4817 -1.4513 
O: -2.1658 -0.3112 -0.2089 
-0.3039 -1.7935 -0.1136 
-0.2468 -0.1280 -1.5760 
Eig. Value: -2.4181 -1.6205 -1.4967 
O: -2.0861 0.1002 0.4049 
0.0527 -1.5519 -0.0935 
0.4626 -0.0290 -1.9264 
Eig. Value: -2.4579 -1.5412 -1.5654 
O: -1.6564 0.0962 -0.1421 
0.0889 -1.7464 0.3321 
-0.0746 0.3180 -2.1480 
Eig. Value: -1.6388 -1.5549 -2.3572 
Ca: 2.2475 0.0491 -0.0256 
0.0100 2.4905 0.0040 
-0.0034 -0.0389 2.1348 
Eig. Value: 2.2454 2.4950 2.1324 
Ca: 2.3112 0.0062 0.0500 
0.0805 2.1747 -0.0063 
-0.0265 0.0562 2.4139 
Eig. Value: 2.3203 2.1604 2.4190 
Si: 2.8685 -0.0742 -0.0643 
-0.0396 2.8678 0.0187 
-0.0923 0.0192 2.5992 
Eig. Value: 2.9396 2.8179 2.5780 
O: -1.5189 -0.1508 -0.0140 
-0.1628 -2.4411 0.1353 
-0.0189 0.1132 -1.4975 
Eig. Value: -1.5245 -2.4817 -1.4513 
O: -2.1658 0.3112 -0.2089 
0.3039 -1.7935 0.1136 
-0.2468 0.1280 -1.5760 
Eig. Value: -2.4181 -1.6205 -1.4967 
O: -2.0861 -0.1002 0.4049 
-0.0527 -1.5519 0.0935 
0.4626 0.0290 -1.9264 
Eig. Value: -2.4579 -1.5412 -1.5654 
O: -1.6564 -0.0962 -0.1421 
-0.0889 -1.7464 -0.3321 
-0.0746 -0.3180 -2.1480 
Eig. Value: -1.6388 -1.5549 -2.3572 
Atom type 

Dielectric tensors: 

 
Ɛ2.9998 0.0000 0.0000 
0.0000 3.0214 0.0000 
0.0000 0.0000 2.9430 
Eig. Value: 2.9998 3.0214 2.9430 
Refractive index (N): 1.7320 0.0000 0.0000 
0.0000 1.7382 0.0000 
0.0000 0.0000 1.7155 
Eig. Value: 1.7320 1.7382 1.7155 
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