-    VATERITE     -    CaCO3

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:  15  C2/c 
Lattice parameters (Å):  12.1700  7.1200  9.4700 
Angles (°):  90  118.37  90 

Symmetry (theoretical): 

Space group:  15  C2/c 
Lattice parameters (Å):  6.9700  6.9700  9.4178 
Angles (°):  68.61  111.38  119.49 

Cell contents: 

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

Atomic positions (theoretical):

Ca:  0.5000  0.0000  0.0000 
Ca:  0.3453  0.1925  0.4987 
C:  0.5885  0.2041  0.2646 
C:  0.9530  0.9530  0.2500 
O:  0.5460  0.3441  0.1401 
O:  0.6379  0.2355  0.4019 
O:  0.9103  0.8217  0.3817 
O:  0.5822  0.0242  0.2540 
O:  0.1345  0.1345  0.2500 
Ca:  0.0000  0.5000  0.5000 
Ca:  0.1925  0.3453  0.0013 
C:  0.2041  0.5885  0.2354 
O:  0.3441  0.5460  0.3599 
O:  0.2355  0.6379  0.0981 
O:  0.8217  0.9103  0.1183 
O:  0.0242  0.5822  0.2460 
Ca:  0.6547  0.8075  0.5013 
C:  0.4115  0.7959  0.7354 
C:  0.0470  0.0470  0.7500 
O:  0.4540  0.6559  0.8599 
O:  0.3621  0.7645  0.5981 
O:  0.0897  0.1783  0.6183 
O:  0.4178  0.9758  0.7460 
O:  0.8655  0.8655  0.7500 
Ca:  0.8075  0.6547  0.9987 
C:  0.7959  0.4115  0.7646 
O:  0.6559  0.4540  0.6401 
O:  0.7645  0.3621  0.9019 
O:  0.1783  0.0897  0.8817 
O:  0.9758  0.4178  0.7540 
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: 2.1823 0.0958 -0.2596 
0.1115 2.3223 0.1869 
0.0676 -0.0498 2.5237 
Eig. Value: 2.0952 2.3762 2.5568 
Ca: 2.2716 0.0283 0.1762 
0.0376 2.1973 0.0845 
-0.0383 -0.0366 2.5169 
Eig. Value: 2.2631 2.1847 2.5379 
C: 2.2097 -1.0354 0.0129 
-1.0268 1.0966 -0.0036 
0.0396 -0.0240 3.2386 
Eig. Value: 2.8228 0.4814 3.2407 
C: 0.4927 0.0000 -0.0743 
-0.0000 2.8007 0.0000 
-0.0565 -0.0000 3.2453 
Eig. Value: 0.4912 2.8007 3.2468 
O: -1.3163 0.1425 -0.6232 
0.1390 -1.1595 0.3588 
-0.5626 0.3180 -2.2027 
Eig. Value: -1.0085 -1.0770 -2.5930 
O: -1.2466 0.1322 0.5011 
0.1221 -1.1272 -0.3034 
0.4804 -0.2929 -2.2398 
Eig. Value: -1.0430 -1.0537 -2.5170 
O: -1.0656 -0.0205 0.0315 
-0.0119 -1.3371 0.6564 
0.0204 0.6217 -2.2543 
Eig. Value: -1.0651 -1.0090 -2.5829 
O: -1.8237 0.6428 0.0678 
0.6358 -1.1234 -0.0438 
0.0452 -0.0134 -1.3082 
Eig. Value: -2.2069 -0.7446 -1.3037 
O: -0.7330 0.0000 0.0012 
-0.0000 -2.2164 -0.0000 
0.0196 0.0000 -1.2698 
Eig. Value: -0.7328 -2.2164 -1.2700 
Ca: 2.1823 -0.0958 -0.2596 
-0.1115 2.3223 -0.1869 
0.0676 0.0498 2.5237 
Eig. Value: 2.0952 2.3762 2.5568 
Ca: 2.2716 -0.0283 0.1762 
-0.0376 2.1973 -0.0845 
-0.0383 0.0366 2.5169 
Eig. Value: 2.2631 2.1847 2.5379 
C: 2.2097 1.0354 0.0129 
1.0268 1.0966 0.0036 
0.0396 0.0240 3.2386 
Eig. Value: 2.8228 0.4814 3.2407 
O: -1.3163 -0.1425 -0.6232 
-0.1390 -1.1595 -0.3588 
-0.5626 -0.3180 -2.2027 
Eig. Value: -1.0085 -1.0770 -2.5930 
O: -1.2466 -0.1322 0.5011 
-0.1221 -1.1272 0.3034 
0.4804 0.2929 -2.2399 
Eig. Value: -1.0430 -1.0537 -2.5170 
O: -1.0656 0.0205 0.0315 
0.0119 -1.3371 -0.6564 
0.0204 -0.6217 -2.2543 
Eig. Value: -1.0651 -1.0090 -2.5829 
O: -1.8237 -0.6428 0.0678 
-0.6358 -1.1234 0.0438 
0.0452 0.0134 -1.3082 
Eig. Value: -2.2069 -0.7446 -1.3037 
Ca: 2.2716 0.0283 0.1762 
0.0376 2.1973 0.0845 
-0.0383 -0.0366 2.5169 
Eig. Value: 2.2631 2.1847 2.5379 
C: 2.2097 -1.0354 0.0129 
-1.0268 1.0966 -0.0036 
0.0396 -0.0240 3.2386 
Eig. Value: 2.8228 0.4814 3.2407 
C: 0.4927 0.0000 -0.0743 
-0.0000 2.8007 0.0000 
-0.0565 -0.0000 3.2453 
Eig. Value: 0.4912 2.8007 3.2468 
O: -1.3163 0.1425 -0.6232 
0.1390 -1.1595 0.3588 
-0.5626 0.3180 -2.2027 
Eig. Value: -1.0085 -1.0770 -2.5930 
O: -1.2466 0.1322 0.5011 
0.1221 -1.1272 -0.3034 
0.4804 -0.2929 -2.2398 
Eig. Value: -1.0430 -1.0537 -2.5170 
O: -1.0656 -0.0205 0.0315 
-0.0119 -1.3371 0.6564 
0.0204 0.6217 -2.2543 
Eig. Value: -1.0651 -1.0090 -2.5829 
O: -1.8237 0.6428 0.0678 
0.6358 -1.1234 -0.0438 
0.0452 -0.0134 -1.3082 
Eig. Value: -2.2069 -0.7446 -1.3037 
O: -0.7330 0.0000 0.0012 
-0.0000 -2.2164 -0.0000 
0.0196 0.0000 -1.2698 
Eig. Value: -0.7328 -2.2164 -1.2700 
Ca: 2.2716 -0.0283 0.1762 
-0.0376 2.1973 -0.0845 
-0.0383 0.0366 2.5169 
Eig. Value: 2.2631 2.1847 2.5379 
C: 2.2097 1.0354 0.0129 
1.0268 1.0966 0.0036 
0.0396 0.0240 3.2386 
Eig. Value: 2.8228 0.4814 3.2407 
O: -1.3163 -0.1425 -0.6232 
-0.1390 -1.1595 -0.3588 
-0.5626 -0.3180 -2.2027 
Eig. Value: -1.0085 -1.0770 -2.5930 
O: -1.2466 -0.1322 0.5011 
-0.1221 -1.1272 0.3034 
0.4804 0.2929 -2.2399 
Eig. Value: -1.0430 -1.0537 -2.5170 
O: -1.0656 0.0205 0.0315 
0.0119 -1.3371 -0.6564 
0.0204 -0.6217 -2.2543 
Eig. Value: -1.0651 -1.0090 -2.5829 
O: -1.8237 -0.6428 0.0678 
-0.6358 -1.1234 0.0438 
0.0452 0.0134 -1.3082 
Eig. Value: -2.2069 -0.7446 -1.3037 
Atom type 

Dielectric tensors: 

 
Ɛ2.4567 0.0000 0.0000 
0.0000 2.4619 0.0000 
0.0098 0.0000 2.8414 
Eig. Value: 2.4566 2.4619 2.8415 
Refractive index (N): 1.5674 0.0000 0.0000 
0.0000 1.5691 0.0000 
0.0991 0.0000 1.6856 
Eig. Value: 1.5674 1.5691 1.6857 
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