-    JOHACHIDOLITE     -    CaAlB3O7

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:  67  Cmma 
Lattice parameters (Å):  7.9670  11.7230  4.3718 
Angles (°):  90  90  90 

Symmetry (theoretical): 

Space group:  67  Cmma 
Lattice parameters (Å):  7.3343  7.3343  4.2299 
Angles (°):  90  90  63.80 

Cell contents: 

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

Atomic positions (theoretical):

Ca:  0.5000  0.0000  0.0000 
Al:  0.0000  0.0000  0.0000 
Al:  0.2500  0.7500  0.5000 
B:  0.1270  0.1270  0.4074 
B:  0.2500  0.2500  0.4067 
O:  0.1183  0.1183  0.7420 
O:  0.2219  0.9325  0.2430 
Ca:  0.0000  0.5000  0.0000 
Al:  0.5000  0.5000  0.0000 
B:  0.3730  0.3730  0.4074 
O:  0.3817  0.3817  0.7420 
O:  0.2781  0.5675  0.2430 
B:  0.6270  0.6270  0.5926 
B:  0.7500  0.7500  0.5933 
O:  0.6183  0.6183  0.2580 
O:  0.4325  0.7219  0.7570 
B:  0.8730  0.8730  0.5926 
O:  0.8817  0.8817  0.2580 
O:  0.0675  0.7781  0.7570 
Al:  0.7500  0.2500  0.5000 
O:  0.7781  0.0675  0.7570 
O:  0.7219  0.4325  0.7570 
O:  0.5675  0.2781  0.2430 
O:  0.9325  0.2219  0.2430 
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: 1.6878 -0.0000 -0.1536 
0.0002 2.3477 0.0000 
-0.2932 0.0000 2.3864 
Eig. Value: 1.6224 2.3477 2.4517 
Al: 2.3220 -0.0000 0.0000 
0.0002 3.4266 -0.3521 
-0.0000 -0.3317 3.7240 
Eig. Value: 2.3220 3.2025 3.9481 
Al: 3.2545 0.0000 -0.0000 
-0.0003 2.9242 -0.0000 
0.0000 -0.0000 2.1368 
Eig. Value: 3.2545 2.9242 2.1368 
B: 1.8429 -0.0016 0.0006 
-0.0045 1.5572 1.0110 
-0.0000 -0.1292 1.3590 
Eig. Value: 1.8429 1.9101 1.0062 
B: 0.3491 0.0032 -0.0000 
0.1633 0.4838 -0.0000 
0.0000 0.0000 0.5262 
Eig. Value: 0.3094 0.5235 0.5262 
O: -1.5955 0.0002 0.0003 
-0.0267 -2.4734 0.5108 
-0.0000 0.7766 -2.5411 
Eig. Value: -1.5951 -1.8630 -3.1519 
O: -2.0315 0.2331 -0.0157 
0.1056 -1.8416 -0.1659 
-0.0501 -0.1115 -1.6024 
Eig. Value: -2.1343 -1.8241 -1.5171 
Ca: 1.6878 -0.0000 0.1536 
0.0002 2.3477 0.0000 
0.2932 -0.0000 2.3864 
Eig. Value: 1.6224 2.3477 2.4517 
Al: 2.3220 -0.0000 0.0000 
0.0002 3.4266 0.3521 
0.0000 0.3317 3.7240 
Eig. Value: 2.3220 3.2025 3.9481 
B: 1.8429 -0.0016 -0.0006 
-0.0045 1.5572 -1.0110 
0.0000 0.1292 1.3590 
Eig. Value: 1.8429 1.9101 1.0062 
O: -1.5955 0.0002 -0.0003 
-0.0267 -2.4734 -0.5108 
-0.0000 -0.7766 -2.5411 
Eig. Value: -1.5951 -1.8630 -3.1519 
O: -2.0395 0.2380 0.0157 
0.0928 -1.8336 0.1659 
0.0501 0.1115 -1.6024 
Eig. Value: -2.1345 -1.8247 -1.5164 
B: 1.8414 0.0000 -0.0000 
-0.0021 1.5546 -1.0119 
-0.0000 0.1293 1.3590 
Eig. Value: 1.8414 1.9088 1.0048 
B: 0.4534 0.0000 -0.0000 
-0.0037 0.4890 -0.0000 
0.0000 0.0000 0.5268 
Eig. Value: 0.4533 0.4891 0.5268 
O: -1.6045 0.0000 -0.0000 
-0.0122 -2.4732 -0.5113 
-0.0000 -0.7765 -2.5411 
Eig. Value: -1.6044 -1.8625 -3.1520 
O: -2.0395 -0.2380 -0.0157 
-0.1161 -1.8336 0.1659 
-0.0502 0.1115 -1.6023 
Eig. Value: -2.1447 -1.8168 -1.5140 
B: 1.8414 0.0000 -0.0000 
-0.0021 1.5546 1.0119 
0.0000 -0.1293 1.3590 
Eig. Value: 1.8414 1.9088 1.0048 
O: -1.6045 0.0000 -0.0000 
-0.0122 -2.4732 0.5113 
-0.0000 0.7765 -2.5411 
Eig. Value: -1.6044 -1.8625 -3.1520 
O: -2.0395 -0.2380 0.0157 
-0.1161 -1.8336 -0.1659 
0.0502 -0.1115 -1.6023 
Eig. Value: -2.1447 -1.8168 -1.5139 
Al: 3.2542 0.0108 -0.0000 
-0.0000 2.9068 -0.0000 
-0.0000 -0.0000 2.1368 
Eig. Value: 3.2543 2.9067 2.1368 
O: -2.0409 0.2320 -0.0157 
0.1206 -1.8398 -0.1659 
-0.0502 -0.1115 -1.6023 
Eig. Value: -2.1467 -1.8207 -1.5156 
O: -2.0489 0.2369 0.0157 
0.1078 -1.8318 0.1659 
0.0502 0.1115 -1.6023 
Eig. Value: -2.1470 -1.8211 -1.5149 
O: -2.0298 -0.2376 -0.0157 
-0.1317 -1.8342 0.1659 
-0.0501 0.1115 -1.6024 
Eig. Value: -2.1447 -1.8096 -1.5121 
O: -2.0298 -0.2376 0.0157 
-0.1317 -1.8342 -0.1659 
0.0501 -0.1115 -1.6024 
Eig. Value: -2.1447 -1.8096 -1.5120 
Atom type 

Dielectric tensors: 

 
Ɛ140.7673 0.0000 0.0000 
-0.0000 15.5089 0.0000 
0.0000 0.0000 12.7617 
Eig. Value: 140.7673 15.5089 12.7617 
Refractive index (N): 11.8645 0.0000 0.0000 
-0.0000 3.9381 0.0012 
0.0009 0.0012 3.5724 
Eig. Value: 11.8645 3.9381 3.5724 
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