-    GROSSITE     -    CaAl4O7

 

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):  6.7945  4.6898  2.8740 
Angles (°):  90  106.83  90 

Symmetry (theoretical): 

Space group:  15  C2/c 
Lattice parameters (Å):  7.8215  7.8215  5.4351 
Angles (°):  75.52  104.47  111.01 

Cell contents: 

Number of atoms:  24 
Number of atom types:  3 
Chemical composition:  0 

Atomic positions (theoretical):

Ca:  0.8175  0.8175  0.2500 
Al:  0.2519  0.9216  0.2977 
Al:  0.5611  0.3227  0.2440 
O:  0.5317  0.5317  0.2500 
O:  0.1575  0.9278  0.5494 
O:  0.3767  0.1372  0.1567 
O:  0.6394  0.2545  0.5824 
Al:  0.9216  0.2519  0.2023 
Al:  0.3227  0.5611  0.2560 
O:  0.9278  0.1575  0.9506 
O:  0.1372  0.3767  0.3433 
O:  0.2545  0.6394  0.9176 
Ca:  0.1825  0.1825  0.7500 
Al:  0.7481  0.0784  0.7023 
Al:  0.4389  0.6773  0.7560 
O:  0.4683  0.4683  0.7500 
O:  0.8425  0.0722  0.4506 
O:  0.6233  0.8628  0.8433 
O:  0.3606  0.7455  0.4176 
Al:  0.0784  0.7481  0.7977 
Al:  0.6773  0.4389  0.7440 
O:  0.0722  0.8425  0.0494 
O:  0.8628  0.6233  0.6567 
O:  0.7455  0.3606  0.0824 
Atom type  X  Y  Z 

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: 2.0746 0.0000 0.0759 
0.0000 2.3067 0.0000 
0.0721 0.0000 2.3483 
Eig. Value: 2.0559 2.3067 2.3671 
Al: 2.4555 -0.1534 0.0536 
-0.1178 2.4566 -0.1055 
0.0673 -0.0324 2.5918 
Eig. Value: 2.3203 2.5003 2.6833 
Al: 2.6173 -0.0501 0.0257 
-0.0202 2.4398 -0.0065 
0.0236 -0.0659 2.8200 
Eig. Value: 2.6193 2.4306 2.8271 
O: -2.0963 0.0000 -0.0833 
-0.0000 -1.5317 -0.0000 
-0.0210 -0.0000 -1.8758 
Eig. Value: -2.1080 -1.5317 -1.8641 
O: -1.6883 -0.0175 0.2040 
-0.0105 -1.5855 0.2870 
0.2035 0.2762 -2.0242 
Eig. Value: -1.6482 -1.4209 -2.2290 
O: -1.3159 0.1486 -0.1414 
0.1593 -2.3591 0.0268 
-0.1479 0.0392 -1.6391 
Eig. Value: -1.2448 -2.3852 -1.6841 
O: -2.0577 0.3097 -0.1382 
0.2780 -1.3393 -0.1798 
-0.1720 -0.1474 -1.9847 
Eig. Value: -2.2086 -1.1809 -1.9922 
Al: 2.4555 0.1534 0.0536 
0.1178 2.4566 0.1055 
0.0673 0.0324 2.5918 
Eig. Value: 2.3203 2.5003 2.6833 
Al: 2.6173 0.0501 0.0257 
0.0202 2.4398 0.0065 
0.0236 0.0659 2.8200 
Eig. Value: 2.6193 2.4306 2.8271 
O: -1.6883 0.0175 0.2040 
0.0105 -1.5855 -0.2870 
0.2035 -0.2762 -2.0242 
Eig. Value: -1.6482 -1.4209 -2.2290 
O: -1.3159 -0.1486 -0.1414 
-0.1593 -2.3591 -0.0268 
-0.1479 -0.0392 -1.6391 
Eig. Value: -1.2448 -2.3852 -1.6841 
O: -2.0577 -0.3097 -0.1382 
-0.2780 -1.3393 0.1798 
-0.1720 0.1474 -1.9847 
Eig. Value: -2.2086 -1.1809 -1.9922 
Ca: 2.0746 -0.0000 0.0759 
-0.0000 2.3067 -0.0000 
0.0721 0.0000 2.3483 
Eig. Value: 2.0559 2.3067 2.3671 
Al: 2.4555 -0.1534 0.0536 
-0.1178 2.4566 -0.1055 
0.0673 -0.0324 2.5918 
Eig. Value: 2.3203 2.5003 2.6833 
Al: 2.6173 -0.0501 0.0257 
-0.0202 2.4398 -0.0065 
0.0236 -0.0659 2.8200 
Eig. Value: 2.6193 2.4306 2.8271 
O: -2.0963 0.0000 -0.0833 
0.0000 -1.5317 0.0000 
-0.0210 -0.0000 -1.8758 
Eig. Value: -2.1080 -1.5317 -1.8641 
O: -1.6883 -0.0175 0.2040 
-0.0105 -1.5855 0.2870 
0.2035 0.2762 -2.0242 
Eig. Value: -1.6482 -1.4209 -2.2290 
O: -1.3159 0.1486 -0.1414 
0.1593 -2.3591 0.0268 
-0.1479 0.0392 -1.6391 
Eig. Value: -1.2448 -2.3852 -1.6841 
O: -2.0577 0.3097 -0.1382 
0.2780 -1.3393 -0.1798 
-0.1720 -0.1474 -1.9847 
Eig. Value: -2.2086 -1.1809 -1.9922 
Al: 2.4555 0.1534 0.0536 
0.1178 2.4566 0.1055 
0.0673 0.0324 2.5918 
Eig. Value: 2.3203 2.5003 2.6833 
Al: 2.6173 0.0501 0.0257 
0.0202 2.4398 0.0065 
0.0236 0.0659 2.8200 
Eig. Value: 2.6193 2.4306 2.8271 
O: -1.6883 0.0175 0.2040 
0.0105 -1.5855 -0.2870 
0.2035 -0.2762 -2.0242 
Eig. Value: -1.6482 -1.4209 -2.2290 
O: -1.3159 -0.1486 -0.1414 
-0.1593 -2.3591 -0.0268 
-0.1479 -0.0392 -1.6391 
Eig. Value: -1.2448 -2.3852 -1.6841 
O: -2.0577 -0.3097 -0.1382 
-0.2780 -1.3393 0.1798 
-0.1720 0.1474 -1.9847 
Eig. Value: -2.2086 -1.1809 -1.9922 
Atom type  X  Y  Z 

Dielectric tensors: 

 X Y Z 
Ɛ∞: 2.7048 0.0000 0.0352 
0.0000 2.6688 0.0000 
0.0352 0.0000 2.7896 
Eig. Value: 2.6921 2.6688 2.8023 
Refractive index (N): 1.6446 -0.0000 0.1877 
-0.0000 1.6336 -0.0000 
0.1877 -0.0000 1.6702 
Eig. Value: 1.6408 1.6336 1.6740 
Ɛ0: 0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 
0.0000 0.0000 0.0000 
Eig. Value: 0.0000 0.0000 0.0000