-    PLAGIOCLASE     -    (Na,Ca)(Si,Al)4O8

ANORTHITE - Theoretical structure, term in the plagioclase series treated as ideal solid solution using alchemical pseudopotentials. 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:     
Lattice parameters (Å):       
Angles (°):       

Symmetry (theoretical): 

Space group:     
Lattice parameters (Å):  7.6353  7.3880  6.9699 
Angles (°):  106.1  100.6  115.0 

Cell contents: 

Number of atoms:  26 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Ca:  0.2364  0.2944  0.0936 
Si:  0.8426  0.1637  0.2198 
Si:  0.1861  0.8197  0.2316 
Si:  0.5624  0.7872  0.3197 
Si:  0.8018  0.5669  0.3623 
O:  0.8695  0.1231  0.9811 
O:  0.5798  0.5618  0.2777 
O:  0.6963  0.9079  0.1855 
O:  0.9516  0.6818  0.2361 
O:  0.7438  0.3133  0.3015 
O:  0.3088  0.6782  0.2074 
O:  0.0889  0.2839  0.3751 
O:  0.3389  0.0554  0.4292 
Ca:  0.7636  0.7056  0.9064 
Si:  0.1574  0.8363  0.7802 
Si:  0.8139  0.1803  0.7684 
Si:  0.4376  0.2128  0.6803 
Si:  0.1982  0.4331  0.6377 
O:  0.1305  0.8769  0.0189 
O:  0.4202  0.4382  0.7223 
O:  0.3037  0.0921  0.8145 
O:  0.0484  0.3182  0.7639 
O:  0.2562  0.6867  0.6985 
O:  0.6912  0.3218  0.7926 
O:  0.9111  0.7161  0.6249 
O:  0.6611  0.9446  0.5708 
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: 2.3434 0.0029 0.0595 
-0.0270 2.2865 0.0820 
0.0268 0.0882 2.3246 
Eig. Value: 2.4052 2.2082 2.3410 
Si: 2.8442 0.2408 0.0049 
0.0688 2.6427 0.1349 
-0.0455 0.1097 2.8937 
Eig. Value: 2.8910 2.5215 2.9682 
Si: 2.8113 -0.2463 0.0149 
-0.0733 2.8249 -0.0828 
0.0397 -0.1297 3.0436 
Eig. Value: 2.6502 2.9135 3.1161 
Si: 2.8721 -0.1518 0.1445 
-0.1189 2.9525 0.0757 
0.1266 0.0926 2.7529 
Eig. Value: 2.9206 3.0544 2.6025 
Si: 2.7438 0.0426 -0.0364 
0.0546 3.1339 -0.0504 
0.0615 0.0012 2.8377 
Eig. Value: 2.7355 3.1416 2.8383 
O: -1.5394 -0.0619 0.4450 
-0.0797 -1.4554 0.1818 
0.4702 0.1670 -2.3110 
Eig. Value: -1.3258 -1.4241 -2.5558 
O: -1.5687 0.0787 -0.2325 
0.1081 -2.3736 0.1434 
-0.2375 0.1353 -1.3290 
Eig. Value: -1.6797 -2.4109 -1.1808 
O: -2.3503 -0.2517 0.2503 
-0.2344 -1.3663 -0.1783 
0.2977 -0.1572 -1.4607 
Eig. Value: -2.4617 -1.1323 -1.5833 
O: -2.3415 0.3215 0.3293 
0.2845 -1.3688 0.0616 
0.3620 0.0425 -1.5144 
Eig. Value: -2.5295 -1.1939 -1.5014 
O: -1.4308 -0.4014 -0.1160 
-0.3837 -2.2201 -0.3053 
-0.1034 -0.2880 -1.3058 
Eig. Value: -1.2713 -2.4681 -1.2173 
O: -1.5432 0.3127 -0.2548 
0.2704 -2.2440 0.0856 
-0.2697 0.0499 -1.3376 
Eig. Value: -1.6051 -2.3733 -1.1465 
O: -1.4363 0.1877 -0.1861 
0.2456 -1.4315 0.1270 
-0.2566 0.1480 -2.2644 
Eig. Value: -1.5601 -1.2135 -2.3586 
O: -1.4046 -0.0739 -0.4226 
-0.1149 -1.3807 -0.2751 
-0.4718 -0.2596 -2.3296 
Eig. Value: -1.2220 -1.3153 -2.5775 
Ca: 2.3434 0.0029 0.0595 
-0.0270 2.2865 0.0820 
0.0268 0.0882 2.3246 
Eig. Value: 2.4052 2.2082 2.3410 
Si: 2.8442 0.2408 0.0049 
0.0688 2.6427 0.1349 
-0.0455 0.1097 2.8937 
Eig. Value: 2.8910 2.5215 2.9682 
Si: 2.8113 -0.2463 0.0149 
-0.0733 2.8249 -0.0828 
0.0397 -0.1297 3.0436 
Eig. Value: 2.6502 2.9135 3.1161 
Si: 2.8721 -0.1518 0.1445 
-0.1189 2.9525 0.0757 
0.1266 0.0926 2.7529 
Eig. Value: 2.9206 3.0544 2.6025 
Si: 2.7438 0.0426 -0.0364 
0.0546 3.1339 -0.0504 
0.0615 0.0012 2.8377 
Eig. Value: 2.7355 3.1416 2.8383 
O: -1.5394 -0.0619 0.4450 
-0.0797 -1.4554 0.1818 
0.4702 0.1670 -2.3110 
Eig. Value: -1.3258 -1.4241 -2.5558 
O: -1.5687 0.0787 -0.2325 
0.1081 -2.3736 0.1434 
-0.2375 0.1353 -1.3290 
Eig. Value: -1.6797 -2.4109 -1.1808 
O: -2.3503 -0.2517 0.2503 
-0.2344 -1.3663 -0.1783 
0.2977 -0.1572 -1.4607 
Eig. Value: -2.4617 -1.1323 -1.5833 
O: -2.3415 0.3215 0.3293 
0.2845 -1.3688 0.0616 
0.3620 0.0425 -1.5144 
Eig. Value: -2.5295 -1.1939 -1.5014 
O: -1.4308 -0.4014 -0.1160 
-0.3837 -2.2201 -0.3053 
-0.1034 -0.2880 -1.3058 
Eig. Value: -1.2713 -2.4681 -1.2173 
O: -1.5432 0.3127 -0.2548 
0.2704 -2.2440 0.0856 
-0.2697 0.0499 -1.3376 
Eig. Value: -1.6051 -2.3733 -1.1465 
O: -1.4363 0.1877 -0.1861 
0.2456 -1.4315 0.1270 
-0.2566 0.1480 -2.2644 
Eig. Value: -1.5601 -1.2135 -2.3586 
O: -1.4046 -0.0739 -0.4226 
-0.1149 -1.3807 -0.2751 
-0.4718 -0.2596 -2.3296 
Eig. Value: -1.2220 -1.3153 -2.5775 
Atom type 

Dielectric tensors: 

 
Ɛ2.5835 0.0000 0.0122 
0.0000 2.6038 0.0182 
0.0122 0.0182 2.6077 
Eig. Value: 2.5731 2.5970 2.6249 
Refractive index (N): 1.6073 -0.0000 0.1105 
-0.0000 1.6136 0.1348 
0.1105 0.1348 1.6148 
Eig. Value: 1.6041 1.6115 1.6202 
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