-    METAVARISCITE     -    AlPO4.2H2O

 

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/n 
Lattice parameters (Å):  5.1780  9.5140  8.4540 
Angles (°):  90.0  90.3  90.0 

Symmetry (theoretical): 

Space group:  14  P2_1/n 
Lattice parameters (Å):  5.0607  9.5198  8.2031 
Angles (°):  90.0  91.6  90.0 

Cell contents: 

Number of atoms:  48 
Number of atom types:  4 
Chemical composition:  0 

Atomic positions (theoretical):

Al:  0.4036  0.3218  0.2932 
P:  0.9072  0.1400  0.1794 
O:  0.1807  0.1697  0.2557 
O:  0.8742  0.2114  0.0136 
O:  0.6972  0.2005  0.2911 
O:  0.8785  0.9803  0.1655 
O:  0.1108  0.4360  0.2771 
O:  0.4469  0.3509  0.0713 
H:  0.1614  0.5370  0.2543 
H:  0.9220  0.4345  0.3111 
H:  0.3098  0.3350  0.9839 
H:  0.6162  0.3124  0.0293 
Al:  0.0964  0.8218  0.2068 
P:  0.5928  0.6400  0.3206 
O:  0.3193  0.6697  0.2443 
O:  0.6258  0.7114  0.4864 
O:  0.8028  0.7005  0.2089 
O:  0.6215  0.4803  0.3345 
O:  0.3892  0.9360  0.2229 
O:  0.0531  0.8509  0.4287 
H:  0.3386  0.0370  0.2457 
H:  0.5780  0.9345  0.1889 
H:  0.1902  0.8350  0.5161 
H:  0.8838  0.8124  0.4707 
Al:  0.5964  0.6782  0.7068 
P:  0.0928  0.8600  0.8206 
O:  0.8193  0.8303  0.7443 
O:  0.1258  0.7886  0.9864 
O:  0.3028  0.7995  0.7089 
O:  0.1215  0.0197  0.8345 
O:  0.8892  0.5640  0.7229 
O:  0.5531  0.6491  0.9287 
H:  0.8386  0.4630  0.7457 
H:  0.0780  0.5655  0.6889 
H:  0.6902  0.6650  0.0161 
H:  0.3838  0.6876  0.9707 
Al:  0.9036  0.1782  0.7932 
P:  0.4072  0.3600  0.6794 
O:  0.6807  0.3303  0.7557 
O:  0.3742  0.2886  0.5136 
O:  0.1972  0.2995  0.7911 
O:  0.3785  0.5197  0.6655 
O:  0.6108  0.0640  0.7771 
O:  0.9469  0.1491  0.5713 
H:  0.6614  0.9630  0.7543 
H:  0.4220  0.0655  0.8111 
H:  0.8098  0.1650  0.4839 
H:  0.1162  0.1876  0.5293 
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): 

Al: 3.1625 0.0896 -0.0181 
0.0824 3.2283 0.2839 
-0.1252 0.1353 3.1259 
Eig. Value: 3.2081 3.3955 2.9130 
P: 3.3959 0.0115 0.1825 
-0.1871 3.5284 0.1786 
-0.0061 -0.0613 3.4426 
Eig. Value: 3.2828 3.5742 3.5099 
O: -2.3123 -0.2550 -0.4672 
-0.1437 -1.7058 -0.1985 
-0.3565 -0.2090 -1.2145 
Eig. Value: -2.5289 -1.6544 -1.0494 
O: -1.3442 0.2871 -0.0840 
0.2811 -1.3917 0.2684 
0.0061 0.3509 -2.4859 
Eig. Value: -1.0580 -1.5860 -2.5777 
O: -1.9750 0.5398 0.3065 
0.5699 -1.4281 -0.2871 
0.3796 -0.2509 -1.7765 
Eig. Value: -2.5602 -1.0789 -1.5404 
O: -1.5946 -0.0964 0.0236 
0.0635 -2.4737 0.0179 
0.0429 0.0262 -1.0316 
Eig. Value: -1.5962 -2.4744 -1.0293 
O: -1.8213 -0.2117 0.1722 
0.0916 -1.5359 0.0302 
0.0736 0.0382 -0.8181 
Eig. Value: -1.8491 -1.5239 -0.8022 
O: -1.3374 0.1365 0.0092 
0.2031 -0.9429 -0.0907 
-0.2144 0.0160 -1.5340 
Eig. Value: -1.3624 -0.8722 -1.5797 
H: 0.7349 0.6035 -0.0628 
0.4811 1.2810 -0.1441 
-0.0351 -0.0854 0.3066 
Eig. Value: 0.4039 1.6267 0.2920 
H: 1.4758 -0.1776 -0.2173 
-0.3140 0.4672 0.0736 
-0.1243 0.0362 0.3582 
Eig. Value: 1.5591 0.4132 0.3289 
H: 0.5770 0.1081 0.2522 
0.1055 0.3544 0.0181 
0.4012 0.0853 1.1687 
Eig. Value: 0.4766 0.3013 1.3222 
H: 1.0387 -0.4502 -0.0969 
-0.4953 0.6189 0.0210 
-0.0419 -0.0502 0.4584 
Eig. Value: 1.3489 0.2959 0.4713 
Al: 3.1625 -0.0896 -0.0181 
-0.0824 3.2283 -0.2839 
-0.1252 -0.1353 3.1259 
Eig. Value: 3.2081 3.3955 2.9130 
P: 3.3959 -0.0115 0.1825 
0.1871 3.5283 -0.1786 
-0.0061 0.0613 3.4426 
Eig. Value: 3.2828 3.5742 3.5099 
O: -2.3123 0.2550 -0.4672 
0.1437 -1.7059 0.1985 
-0.3565 0.2090 -1.2145 
Eig. Value: -2.5289 -1.6544 -1.0494 
O: -1.3442 -0.2871 -0.0840 
-0.2811 -1.3917 -0.2684 
0.0061 -0.3509 -2.4859 
Eig. Value: -1.0580 -1.5860 -2.5777 
O: -1.9750 -0.5398 0.3065 
-0.5699 -1.4281 0.2871 
0.3796 0.2509 -1.7765 
Eig. Value: -2.5602 -1.0789 -1.5404 
O: -1.5946 0.0964 0.0236 
-0.0635 -2.4737 -0.0179 
0.0429 -0.0262 -1.0316 
Eig. Value: -1.5962 -2.4743 -1.0293 
O: -1.8213 0.2117 0.1722 
-0.0916 -1.5359 -0.0302 
0.0736 -0.0382 -0.8181 
Eig. Value: -1.8491 -1.5239 -0.8022 
O: -1.3374 -0.1365 0.0092 
-0.2031 -0.9429 0.0907 
-0.2144 -0.0160 -1.5340 
Eig. Value: -1.3625 -0.8722 -1.5797 
H: 0.7349 -0.6035 -0.0628 
-0.4811 1.2810 0.1441 
-0.0351 0.0854 0.3066 
Eig. Value: 0.4039 1.6267 0.2920 
H: 1.4758 0.1776 -0.2173 
0.3140 0.4672 -0.0736 
-0.1243 -0.0362 0.3582 
Eig. Value: 1.5591 0.4132 0.3289 
H: 0.5770 -0.1081 0.2522 
-0.1055 0.3544 -0.0181 
0.4012 -0.0853 1.1687 
Eig. Value: 0.4766 0.3013 1.3222 
H: 1.0387 0.4502 -0.0969 
0.4953 0.6189 -0.0210 
-0.0419 0.0502 0.4584 
Eig. Value: 1.3489 0.2959 0.4713 
Al: 3.1625 0.0896 -0.0181 
0.0824 3.2283 0.2839 
-0.1252 0.1353 3.1259 
Eig. Value: 3.2081 3.3955 2.9130 
P: 3.3959 0.0115 0.1825 
-0.1871 3.5284 0.1786 
-0.0061 -0.0613 3.4426 
Eig. Value: 3.2828 3.5742 3.5099 
O: -2.3123 -0.2550 -0.4672 
-0.1437 -1.7058 -0.1985 
-0.3565 -0.2090 -1.2145 
Eig. Value: -2.5289 -1.6544 -1.0494 
O: -1.3442 0.2871 -0.0840 
0.2811 -1.3917 0.2684 
0.0061 0.3509 -2.4859 
Eig. Value: -1.0580 -1.5860 -2.5777 
O: -1.9750 0.5398 0.3065 
0.5699 -1.4281 -0.2871 
0.3796 -0.2509 -1.7765 
Eig. Value: -2.5602 -1.0789 -1.5404 
O: -1.5946 -0.0964 0.0236 
0.0635 -2.4737 0.0179 
0.0429 0.0262 -1.0316 
Eig. Value: -1.5962 -2.4744 -1.0293 
O: -1.8213 -0.2117 0.1722 
0.0916 -1.5359 0.0302 
0.0736 0.0382 -0.8181 
Eig. Value: -1.8491 -1.5239 -0.8022 
O: -1.3374 0.1365 0.0092 
0.2031 -0.9429 -0.0907 
-0.2144 0.0160 -1.5340 
Eig. Value: -1.3624 -0.8722 -1.5797 
H: 0.7349 0.6035 -0.0628 
0.4811 1.2810 -0.1441 
-0.0351 -0.0854 0.3066 
Eig. Value: 0.4039 1.6267 0.2920 
H: 1.4758 -0.1776 -0.2173 
-0.3140 0.4672 0.0736 
-0.1243 0.0362 0.3582 
Eig. Value: 1.5591 0.4132 0.3289 
H: 0.5770 0.1081 0.2522 
0.1055 0.3544 0.0181 
0.4012 0.0853 1.1687 
Eig. Value: 0.4766 0.3013 1.3222 
H: 1.0387 -0.4502 -0.0969 
-0.4953 0.6189 0.0210 
-0.0419 -0.0502 0.4584 
Eig. Value: 1.3489 0.2959 0.4713 
Al: 3.1625 -0.0896 -0.0181 
-0.0824 3.2283 -0.2839 
-0.1252 -0.1353 3.1259 
Eig. Value: 3.2081 3.3955 2.9130 
P: 3.3959 -0.0115 0.1825 
0.1871 3.5283 -0.1786 
-0.0061 0.0613 3.4426 
Eig. Value: 3.2828 3.5742 3.5099 
O: -2.3123 0.2550 -0.4672 
0.1437 -1.7059 0.1985 
-0.3565 0.2090 -1.2145 
Eig. Value: -2.5289 -1.6544 -1.0494 
O: -1.3442 -0.2871 -0.0840 
-0.2811 -1.3917 -0.2684 
0.0061 -0.3509 -2.4859 
Eig. Value: -1.0580 -1.5860 -2.5777 
O: -1.9750 -0.5398 0.3065 
-0.5699 -1.4281 0.2871 
0.3796 0.2509 -1.7765 
Eig. Value: -2.5602 -1.0789 -1.5404 
O: -1.5946 0.0964 0.0236 
-0.0635 -2.4737 -0.0179 
0.0429 -0.0262 -1.0316 
Eig. Value: -1.5962 -2.4743 -1.0293 
O: -1.8213 0.2117 0.1722 
-0.0916 -1.5359 -0.0302 
0.0736 -0.0382 -0.8181 
Eig. Value: -1.8491 -1.5239 -0.8022 
O: -1.3374 -0.1365 0.0092 
-0.2031 -0.9429 0.0907 
-0.2144 -0.0160 -1.5340 
Eig. Value: -1.3625 -0.8722 -1.5797 
H: 0.7349 -0.6035 -0.0628 
-0.4811 1.2810 0.1441 
-0.0351 0.0854 0.3066 
Eig. Value: 0.4039 1.6267 0.2920 
H: 1.4758 0.1776 -0.2173 
0.3140 0.4672 -0.0736 
-0.1243 -0.0362 0.3582 
Eig. Value: 1.5591 0.4132 0.3289 
H: 0.5770 -0.1081 0.2522 
-0.1055 0.3544 -0.0181 
0.4012 -0.0853 1.1687 
Eig. Value: 0.4766 0.3013 1.3222 
H: 1.0387 0.4502 -0.0969 
0.4953 0.6189 -0.0210 
-0.0419 0.0502 0.4584 
Eig. Value: 1.3489 0.2959 0.4713 
Atom type  X  Y  Z 

Dielectric tensors: 

 X Y Z 
Ɛ∞: 2.6651 0.0000 0.0000 
0.0000 2.5466 0.0000 
0.0000 0.0000 2.5364 
Eig. Value: 2.6652 2.5466 2.5363 
Refractive index (N): 1.6325 -0.0000 -0.0000 
-0.0000 1.5958 -0.0000 
-0.0000 -0.0000 1.5926 
Eig. Value: 1.6325 1.5958 1.5926 
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