-    HERDERITE     -    CaBe(PO4)F

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/a 
Lattice parameters (Å):  5.1859  4.0641  2.5401 
Angles (°):  90.0  90.1  90.0 

Symmetry (theoretical): 

Space group:  14  P2_1/a 
Lattice parameters (Å):  9.7332  7.6783  4.8347 
Angles (°):  90.0  91.0  90.0 

Cell contents: 

Number of atoms:  32 
Number of atom types:  5 
Chemical composition:  0 

Atomic positions (theoretical):

Ca:  0.0000  0.3293  0.1118 
Be:  0.9966  0.3366  0.4114 
P:  0.5413  0.0817  0.2678 
O:  0.4746  0.0416  0.3943 
O:  0.2476  0.4554  0.2828 
O:  0.6445  0.1933  0.3428 
O:  0.6767  0.1474  0.1037 
F:  0.3470  0.3230  0.4037 
Ca:  0.2227  0.1707  0.6118 
Be:  0.0034  0.1634  0.9114 
P:  0.4587  0.4183  0.7678 
O:  0.5254  0.4584  0.8943 
O:  0.7524  0.0446  0.7828 
O:  0.3555  0.3067  0.8428 
O:  0.3233  0.3526  0.6037 
F:  0.6530  0.1770  0.9037 
Ca:  0.7773  0.6707  0.8882 
Be:  0.0034  0.6634  0.5886 
P:  0.4587  0.9183  0.7322 
O:  0.5254  0.9584  0.6057 
O:  0.7524  0.5446  0.7172 
O:  0.3555  0.8067  0.6572 
O:  0.3233  0.8526  0.8963 
F:  0.6530  0.6770  0.5963 
Ca:  0.7773  0.8293  0.3882 
Be:  0.9966  0.8366  0.0886 
P:  0.5413  0.5817  0.2322 
O:  0.4746  0.5416  0.1057 
O:  0.2476  0.9554  0.2172 
O:  0.6445  0.6933  0.1572 
O:  0.6767  0.6474  0.3963 
F:  0.3470  0.8230  0.0963 
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: 2.2891 -0.0251 -0.0235 
-0.0507 2.2665 0.0966 
-0.0417 -0.0533 2.5600 
Eig. Value: 2.3112 2.2383 2.5662 
Be: 2.0592 -0.0274 0.0646 
0.0009 2.0650 0.0731 
-0.0025 0.0946 1.4008 
Eig. Value: 2.0562 2.0799 1.3888 
P: 3.6588 -0.0472 0.0146 
-0.0272 3.4988 -0.0103 
0.0979 -0.1696 3.0127 
Eig. Value: 3.6758 3.5015 2.9930 
O: -1.4032 0.1577 -0.2594 
0.1369 -1.6380 0.5765 
-0.2361 0.5300 -1.7153 
Eig. Value: -1.3327 -1.1055 -2.3183 
O: -2.1854 0.4017 0.4009 
0.4283 -1.3977 0.0321 
0.3967 -0.0142 -1.3019 
Eig. Value: -2.4778 -1.3623 -1.0449 
O: -2.0371 -0.3424 -0.3069 
-0.3858 -1.4216 -0.2093 
-0.3519 -0.1769 -1.4853 
Eig. Value: -2.3696 -1.2389 -1.3355 
O: -1.4308 0.4452 0.2396 
0.4964 -2.3668 -0.1580 
0.2199 -0.0861 -1.1815 
Eig. Value: -1.3623 -2.5917 -1.0252 
F: -0.9506 0.0755 -0.1299 
0.0542 -1.0062 -0.0450 
-0.0822 -0.0295 -1.2894 
Eig. Value: -0.8785 -1.0467 -1.3209 
Ca: 2.2891 0.0251 -0.0235 
0.0507 2.2665 -0.0966 
-0.0417 0.0533 2.5600 
Eig. Value: 2.3112 2.2383 2.5662 
Be: 2.0592 0.0274 0.0646 
-0.0009 2.0650 -0.0731 
-0.0025 -0.0946 1.4008 
Eig. Value: 2.0562 2.0799 1.3888 
P: 3.6588 0.0472 0.0146 
0.0272 3.4988 0.0103 
0.0979 0.1696 3.0127 
Eig. Value: 3.6758 3.5015 2.9930 
O: -1.4032 -0.1577 -0.2594 
-0.1369 -1.6380 -0.5765 
-0.2361 -0.5300 -1.7153 
Eig. Value: -1.3327 -1.1055 -2.3183 
O: -2.1854 -0.4017 0.4009 
-0.4283 -1.3977 -0.0321 
0.3967 0.0142 -1.3019 
Eig. Value: -2.4778 -1.3623 -1.0449 
O: -2.0371 0.3424 -0.3069 
0.3858 -1.4216 0.2093 
-0.3519 0.1769 -1.4853 
Eig. Value: -2.3696 -1.2389 -1.3355 
O: -1.4308 -0.4452 0.2396 
-0.4964 -2.3668 0.1580 
0.2199 0.0861 -1.1815 
Eig. Value: -1.3623 -2.5917 -1.0252 
F: -0.9506 -0.0755 -0.1299 
-0.0542 -1.0062 0.0450 
-0.0822 0.0295 -1.2894 
Eig. Value: -0.8785 -1.0467 -1.3209 
Ca: 2.2891 -0.0251 -0.0235 
-0.0507 2.2665 0.0966 
-0.0417 -0.0533 2.5600 
Eig. Value: 2.3112 2.2383 2.5662 
Be: 2.0592 -0.0274 0.0646 
0.0009 2.0650 0.0731 
-0.0025 0.0946 1.4008 
Eig. Value: 2.0562 2.0799 1.3888 
P: 3.6588 -0.0472 0.0146 
-0.0272 3.4988 -0.0103 
0.0979 -0.1696 3.0127 
Eig. Value: 3.6758 3.5015 2.9930 
O: -1.4032 0.1577 -0.2594 
0.1369 -1.6380 0.5765 
-0.2361 0.5300 -1.7153 
Eig. Value: -1.3327 -1.1055 -2.3183 
O: -2.1854 0.4017 0.4009 
0.4283 -1.3977 0.0321 
0.3967 -0.0142 -1.3019 
Eig. Value: -2.4778 -1.3623 -1.0449 
O: -2.0371 -0.3424 -0.3069 
-0.3858 -1.4216 -0.2093 
-0.3519 -0.1769 -1.4853 
Eig. Value: -2.3696 -1.2389 -1.3355 
O: -1.4308 0.4452 0.2396 
0.4964 -2.3668 -0.1580 
0.2199 -0.0861 -1.1815 
Eig. Value: -1.3623 -2.5917 -1.0252 
F: -0.9506 0.0755 -0.1299 
0.0542 -1.0062 -0.0450 
-0.0822 -0.0295 -1.2894 
Eig. Value: -0.8785 -1.0467 -1.3209 
Ca: 2.2891 0.0251 -0.0235 
0.0507 2.2665 -0.0966 
-0.0417 0.0533 2.5600 
Eig. Value: 2.3112 2.2383 2.5662 
Be: 2.0592 0.0274 0.0646 
-0.0009 2.0650 -0.0731 
-0.0025 -0.0946 1.4008 
Eig. Value: 2.0562 2.0799 1.3888 
P: 3.6588 0.0472 0.0146 
0.0272 3.4988 0.0103 
0.0979 0.1696 3.0127 
Eig. Value: 3.6758 3.5015 2.9930 
O: -1.4032 -0.1577 -0.2594 
-0.1369 -1.6380 -0.5765 
-0.2361 -0.5300 -1.7153 
Eig. Value: -1.3327 -1.1055 -2.3183 
O: -2.1854 -0.4017 0.4009 
-0.4283 -1.3977 -0.0321 
0.3967 0.0142 -1.3019 
Eig. Value: -2.4778 -1.3623 -1.0449 
O: -2.0371 0.3424 -0.3069 
0.3858 -1.4216 0.2093 
-0.3519 0.1769 -1.4853 
Eig. Value: -2.3696 -1.2389 -1.3355 
O: -1.4308 -0.4452 0.2396 
-0.4964 -2.3668 0.1580 
0.2199 0.0861 -1.1815 
Eig. Value: -1.3623 -2.5917 -1.0252 
F: -0.9506 -0.0755 -0.1299 
-0.0542 -1.0062 0.0450 
-0.0822 0.0295 -1.2894 
Eig. Value: -0.8785 -1.0467 -1.3209 
Atom type  X  Y  Z 

Dielectric tensors: 

 X Y Z 
Ɛ∞: 2.5654 0.0000 0.0000 
0.0000 2.5455 0.0000 
0.0000 0.0000 2.4674 
Eig. Value: 2.5654 2.5455 2.4674 
Refractive index (N): 1.6017 -0.0000 -0.0000 
-0.0000 1.5955 -0.0000 
-0.0000 -0.0000 1.5708 
Eig. Value: 1.6017 1.5955 1.5708 
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