-    JOHACHIDOLITE     -    CaAlB3O7

The crystal structure is fully relaxed (both unit cell parameters and atomic positions under symmetry constraints) starting from an experimental structure similar to the one reported in 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):  7.7518  7.7518  4.3895 
Angles (°):  90  90  66.80 

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:  0.1248  0.1248  0.4196 
B:  0.2500  0.2500  0.3938 
O:  0.1168  0.1168  0.7447 
O:  0.2076  0.9375  0.2596 
Ca:  0.0000  0.5000  0.0000 
Al:  0.5000  0.5000  0.0000 
B:  0.3752  0.3752  0.4196 
O:  0.3832  0.3832  0.7447 
O:  0.2924  0.5625  0.2596 
B:  0.6248  0.6248  0.5804 
B:  0.7500  0.7500  0.6062 
O:  0.6168  0.6168  0.2553 
O:  0.4375  0.7076  0.7404 
B:  0.8752  0.8752  0.5804 
O:  0.8832  0.8832  0.2553 
O:  0.0625  0.7924  0.7404 
Al:  0.7500  0.2500  0.5000 
O:  0.7924  0.0625  0.7404 
O:  0.7076  0.4375  0.7404 
O:  0.5625  0.2924  0.2596 
O:  0.9375  0.2076  0.2596 
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: 1.9547 0.0000 -0.2388 
0.0003 2.2808 0.0000 
-0.0404 0.0000 2.3715 
Eig. Value: 1.9122 2.2808 2.4139 
Al: 2.2630 -0.0004 -0.0001 
0.0006 3.4961 -0.3149 
-0.0000 -0.5715 3.9312 
Eig. Value: 2.2630 3.2199 4.2074 
Al: 3.3481 0.0146 0.0001 
-0.0001 2.7256 0.0001 
0.0000 -0.0000 2.1884 
Eig. Value: 3.3482 2.7255 2.1884 
B: 1.8967 -0.0007 0.0001 
0.0017 1.7290 0.9121 
-0.0000 -0.3814 1.5096 
Eig. Value: 1.8966 1.9064 1.3322 
B: 0.1478 -0.0001 0.0000 
0.0031 0.1780 0.0001 
-0.0000 0.0000 0.5453 
Eig. Value: 0.1477 0.1781 0.5453 
O: -1.5965 -0.0009 0.0000 
-0.0003 -2.2902 0.5734 
-0.0000 0.9058 -2.8043 
Eig. Value: -1.5965 -1.7643 -3.3303 
O: -2.0713 0.2768 0.0330 
0.2489 -1.8884 -0.2047 
-0.1122 -0.0069 -1.6096 
Eig. Value: -2.2595 -1.7735 -1.5363 
Ca: 1.9537 -0.0000 0.2386 
-0.0012 2.2808 -0.0004 
0.0404 0.0000 2.3715 
Eig. Value: 1.9114 2.2808 2.4138 
Al: 2.2630 0.0003 -0.0000 
0.0006 3.4973 0.3147 
-0.0000 0.5715 3.9312 
Eig. Value: 2.2630 3.2209 4.2076 
B: 1.8967 0.0008 -0.0000 
0.0017 1.7315 -0.9119 
0.0000 0.3814 1.5096 
Eig. Value: 1.8966 1.9081 1.3331 
O: -1.5965 0.0007 0.0003 
-0.0003 -2.2878 -0.5728 
-0.0000 -0.9058 -2.8043 
Eig. Value: -1.5965 -1.7629 -3.3292 
O: -2.0722 0.2782 -0.0332 
0.2475 -1.8862 0.2044 
0.1122 0.0069 -1.6096 
Eig. Value: -2.2594 -1.7726 -1.5360 
B: 1.8972 0.0008 0.0001 
0.0018 1.7464 -0.9086 
0.0000 0.3807 1.5089 
Eig. Value: 1.8972 1.9172 1.3382 
B: -0.0439 -0.0001 0.0000 
0.0030 0.1509 0.0001 
-0.0000 0.0000 0.5279 
Eig. Value: -0.0440 0.1509 0.5279 
O: -1.5751 0.0007 0.0004 
-0.0003 -2.2921 -0.5716 
-0.0000 -0.9060 -2.8047 
Eig. Value: -1.5751 -1.7664 -3.3304 
O: -2.0476 -0.2832 0.0335 
-0.2517 -1.8919 0.2071 
-0.1115 0.0066 -1.6089 
Eig. Value: -2.2501 -1.7657 -1.5327 
B: 1.8972 -0.0007 0.0001 
0.0018 1.7440 0.9088 
-0.0000 -0.3807 1.5089 
Eig. Value: 1.8972 1.9155 1.3374 
O: -1.5751 -0.0008 -0.0000 
-0.0003 -2.2946 0.5721 
-0.0000 0.9060 -2.8047 
Eig. Value: -1.5751 -1.7678 -3.3315 
O: -2.0485 -0.2846 -0.0337 
-0.2530 -1.8941 -0.2074 
0.1115 -0.0066 -1.6089 
Eig. Value: -2.2527 -1.7660 -1.5328 
Al: 3.3482 -0.0147 0.0001 
-0.0015 2.7256 0.0001 
0.0000 -0.0000 2.1884 
Eig. Value: 3.3483 2.7255 2.1884 
O: -2.0475 0.2834 0.0336 
0.2504 -1.8930 -0.2063 
-0.1115 -0.0066 -1.6089 
Eig. Value: -2.2499 -1.7662 -1.5334 
O: -2.0484 0.2848 -0.0338 
0.2491 -1.8909 0.2060 
0.1115 0.0066 -1.6089 
Eig. Value: -2.2496 -1.7654 -1.5332 
O: -2.0713 -0.2767 0.0329 
-0.2501 -1.8873 0.2055 
-0.1122 0.0069 -1.6096 
Eig. Value: -2.2597 -1.7730 -1.5356 
O: -2.0722 -0.2781 -0.0331 
-0.2515 -1.8895 -0.2058 
0.1122 -0.0069 -1.6096 
Eig. Value: -2.2623 -1.7733 -1.5357 
Atom type 

Dielectric tensors: 

 
Ɛ133.9006 0.0000 0.0000 
0.0000 25.5593 0.0000 
0.0001 0.0001 14.9921 
Eig. Value: 133.9006 25.5593 14.9921 
Refractive index (N): 11.5715 0.0000 0.0000 
0.0000 5.0556 0.0000 
0.0078 0.0092 3.8720 
Eig. Value: 11.5715 5.0556 3.8720 
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