-    LAZULITE     -    MgAl2(PO4)2(OH)2

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:  14  P2_1/c 
Lattice parameters (Å):  7.1440  7.2780  7.2280 
Angles (°):  90  120.51  90 

Symmetry (theoretical): 

Space group:  14  P2_1/c 
Lattice parameters (Å):  7.7518  7.7518  4.3895 
Angles (°):  90  120.26  90 

Cell contents: 

Number of atoms:  34 
Number of atom types:  5 
Chemical composition:  0 

Atomic positions (theoretical):

Mg:  0.0000  0.0000  0.0000 
Al:  0.7335  0.2668  0.0099 
P:  0.2490  0.3897  0.2425 
O:  0.8001  0.0214  0.1182 
O:  0.6945  0.4975  0.9025 
O:  0.0424  0.2693  0.1129 
O:  0.4394  0.2363  0.8808 
O:  0.7374  0.1443  0.7607 
H:  0.6008  0.4321  0.1957 
Mg:  0.0000  0.5000  0.5000 
Al:  0.2665  0.7668  0.4901 
P:  0.7510  0.8897  0.2575 
O:  0.1999  0.5214  0.3818 
O:  0.3055  0.9975  0.5975 
O:  0.9576  0.7693  0.3871 
O:  0.5606  0.7363  0.6192 
O:  0.2626  0.6443  0.7393 
H:  0.3992  0.9321  0.3043 
Al:  0.2665  0.7332  0.9901 
P:  0.7510  0.6103  0.7575 
O:  0.1999  0.9786  0.8818 
O:  0.3055  0.5025  0.0975 
O:  0.9576  0.7307  0.8871 
O:  0.5606  0.7637  0.1192 
O:  0.2626  0.8557  0.2393 
H:  0.3992  0.5679  0.8043 
Al:  0.7335  0.2332  0.5099 
P:  0.2490  0.1103  0.7425 
O:  0.8001  0.4786  0.6182 
O:  0.6945  0.0025  0.4025 
O:  0.0424  0.2307  0.6129 
O:  0.4394  0.2637  0.3808 
O:  0.7374  0.3557  0.2607 
H:  0.6008  0.0679  0.6957 
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): 

Mg: 2.1293 -0.0455 -0.0046 
-0.0244 2.1788 0.0345 
-0.1211 0.1123 1.9759 
Eig. Value: 2.1132 2.2320 1.9387 
Al: 3.2087 0.2040 -0.0135 
0.2819 3.1821 0.0126 
0.2146 -0.2488 3.0736 
Eig. Value: 3.4389 2.8465 3.1790 
P: 3.6885 0.0585 0.1457 
0.0279 3.5502 0.0152 
0.0649 0.0504 3.3016 
Eig. Value: 3.7293 3.5378 3.2731 
O: -1.6561 -0.3404 0.3942 
-0.3900 -1.9450 0.5513 
0.4055 0.5911 -1.5814 
Eig. Value: -1.4080 -2.6487 -1.1258 
O: -1.7254 -0.3616 0.2918 
-0.2961 -1.8565 0.5426 
0.2777 0.5879 -1.5132 
Eig. Value: -1.4889 -2.5143 -1.0918 
O: -2.0315 -0.4688 -0.5532 
-0.4511 -1.6901 -0.4083 
-0.5898 -0.4200 -1.4835 
Eig. Value: -2.7459 -1.3706 -1.0885 
O: -1.8734 -0.4351 -0.5492 
-0.4381 -1.5331 -0.3940 
-0.5612 -0.3665 -1.5331 
Eig. Value: -2.5974 -1.2347 -1.1076 
O: -1.5574 -0.1106 0.1256 
-0.0737 -1.3437 0.0108 
0.1552 0.0119 -1.7091 
Eig. Value: -1.5048 -1.3051 -1.8002 
H: 0.8821 -0.1726 0.1610 
-0.1402 0.5467 -0.0526 
0.0936 -0.0306 0.4572 
Eig. Value: 0.9780 0.4860 0.4219 
Mg: 2.1293 0.0455 -0.0046 
0.0244 2.1788 -0.0345 
-0.1211 -0.1123 1.9759 
Eig. Value: 2.1132 2.2320 1.9387 
Al: 3.2087 -0.2040 -0.0135 
-0.2819 3.1821 -0.0126 
0.2146 0.2488 3.0736 
Eig. Value: 3.4389 2.8465 3.1790 
P: 3.6885 -0.0585 0.1457 
-0.0279 3.5502 -0.0152 
0.0649 -0.0504 3.3016 
Eig. Value: 3.7293 3.5378 3.2731 
O: -1.6561 0.3404 0.3942 
0.3900 -1.9450 -0.5513 
0.4055 -0.5911 -1.5814 
Eig. Value: -1.4080 -2.6487 -1.1258 
O: -1.7254 0.3616 0.2918 
0.2961 -1.8565 -0.5426 
0.2777 -0.5879 -1.5132 
Eig. Value: -1.4889 -2.5143 -1.0918 
O: -2.0315 0.4688 -0.5532 
0.4511 -1.6901 0.4083 
-0.5898 0.4200 -1.4835 
Eig. Value: -2.7459 -1.3706 -1.0885 
O: -1.8734 0.4351 -0.5492 
0.4381 -1.5331 0.3940 
-0.5612 0.3665 -1.5331 
Eig. Value: -2.5974 -1.2347 -1.1076 
O: -1.5574 0.1106 0.1256 
0.0737 -1.3437 -0.0108 
0.1552 -0.0119 -1.7091 
Eig. Value: -1.5048 -1.3051 -1.8002 
H: 0.8821 0.1726 0.1610 
0.1402 0.5467 0.0526 
0.0936 0.0306 0.4572 
Eig. Value: 0.9780 0.4860 0.4219 
Al: 3.2087 0.2040 -0.0135 
0.2819 3.1821 0.0126 
0.2146 -0.2488 3.0736 
Eig. Value: 3.4389 2.8465 3.1790 
P: 3.6885 0.0585 0.1457 
0.0279 3.5502 0.0152 
0.0649 0.0504 3.3016 
Eig. Value: 3.7293 3.5378 3.2731 
O: -1.6561 -0.3404 0.3942 
-0.3900 -1.9450 0.5513 
0.4055 0.5911 -1.5814 
Eig. Value: -1.4080 -2.6487 -1.1258 
O: -1.7254 -0.3616 0.2918 
-0.2961 -1.8565 0.5426 
0.2777 0.5879 -1.5132 
Eig. Value: -1.4889 -2.5143 -1.0918 
O: -2.0315 -0.4688 -0.5532 
-0.4511 -1.6901 -0.4083 
-0.5898 -0.4200 -1.4835 
Eig. Value: -2.7459 -1.3706 -1.0885 
O: -1.8734 -0.4351 -0.5492 
-0.4381 -1.5331 -0.3940 
-0.5612 -0.3665 -1.5331 
Eig. Value: -2.5974 -1.2347 -1.1076 
O: -1.5574 -0.1106 0.1256 
-0.0737 -1.3437 0.0108 
0.1552 0.0119 -1.7091 
Eig. Value: -1.5048 -1.3051 -1.8002 
H: 0.8821 -0.1726 0.1610 
-0.1402 0.5467 -0.0526 
0.0936 -0.0306 0.4572 
Eig. Value: 0.9780 0.4860 0.4219 
Al: 3.2087 -0.2040 -0.0135 
-0.2819 3.1821 -0.0126 
0.2146 0.2488 3.0736 
Eig. Value: 3.4389 2.8465 3.1790 
P: 3.6885 -0.0585 0.1457 
-0.0279 3.5502 -0.0152 
0.0649 -0.0504 3.3016 
Eig. Value: 3.7293 3.5378 3.2731 
O: -1.6561 0.3404 0.3942 
0.3900 -1.9450 -0.5513 
0.4055 -0.5911 -1.5814 
Eig. Value: -1.4080 -2.6487 -1.1258 
O: -1.7254 0.3616 0.2918 
0.2961 -1.8565 -0.5426 
0.2777 -0.5879 -1.5132 
Eig. Value: -1.4889 -2.5143 -1.0918 
O: -2.0315 0.4688 -0.5532 
0.4511 -1.6901 0.4083 
-0.5898 0.4200 -1.4835 
Eig. Value: -2.7459 -1.3706 -1.0885 
O: -1.8734 0.4351 -0.5492 
0.4381 -1.5331 0.3940 
-0.5612 0.3665 -1.5331 
Eig. Value: -2.5974 -1.2347 -1.1076 
O: -1.5574 0.1106 0.1256 
0.0737 -1.3437 -0.0108 
0.1552 -0.0119 -1.7091 
Eig. Value: -1.5048 -1.3051 -1.8002 
H: 0.8821 0.1726 0.1610 
0.1402 0.5467 0.0526 
0.0936 0.0306 0.4572 
Eig. Value: 0.9780 0.4860 0.4219 
Atom type  X  Y  Z 

Dielectric tensors: 

 X Y Z 
Ɛ∞: 2.8146 0.0000 0.0336 
0.0000 2.7470 0.0000 
0.0336 0.0000 2.6884 
Eig. Value: 2.8230 2.7470 2.6800 
Refractive index (N): 1.6777 0.0000 0.1833 
0.0000 1.6574 0.0000 
0.1833 0.0000 1.6396 
Eig. Value: 1.6802 1.6574 1.6371 
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