-    SPODUMENE     -    LiAlSi2O6

 

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:  15  C2/c 
Lattice parameters (Å):  9.4628  8.3882  5.2186 
Angles (°):  90.0  110.2  90.0 

Symmetry (theoretical): 

Space group:  15  C2/c 
Lattice parameters (Å):  6.2451  6.2451  5.1499 
Angles (°):  74.7  105.3  97.4 

Cell contents: 

Number of atoms:  20 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Li:  0.2717  0.2717  0.2500 
Al:  0.9083  0.9083  0.2500 
Si:  0.3881  0.8009  0.2596 
O:  0.1924  0.9752  0.1429 
O:  0.6342  0.9045  0.2973 
O:  0.3369  0.6242  0.0689 
Si:  0.8009  0.3881  0.2404 
O:  0.9752  0.1924  0.3571 
O:  0.9045  0.6342  0.2027 
O:  0.6242  0.3369  0.4311 
Li:  0.7283  0.7283  0.7500 
Al:  0.0917  0.0917  0.7500 
Si:  0.6119  0.1991  0.7404 
O:  0.8076  0.0248  0.8571 
O:  0.3658  0.0955  0.7027 
O:  0.6631  0.3758  0.9311 
Si:  0.1991  0.6119  0.7596 
O:  0.0248  0.8076  0.6429 
O:  0.0955  0.3658  0.7973 
O:  0.3758  0.6631  0.5689 
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): 

Li: 1.0855 -0.0000 0.0870 
-0.0000 1.1471 0.0000 
0.0772 -0.0000 1.1835 
Eig. Value: 1.0389 1.1471 1.2301 
Al: 3.2224 -0.0000 0.0329 
-0.0000 3.0272 0.0000 
0.0240 0.0000 2.9563 
Eig. Value: 3.2254 3.0272 2.9533 
Si: 3.1028 0.2778 -0.1196 
0.1707 3.3332 -0.0615 
-0.1060 0.0997 3.4760 
Eig. Value: 2.9445 3.4399 3.5275 
O: -2.1166 -0.2608 -0.2159 
-0.1667 -1.5381 0.1605 
-0.1791 0.0757 -1.8459 
Eig. Value: -2.2492 -1.3958 -1.8555 
O: -1.6691 -0.5325 -0.0055 
-0.5231 -2.2130 0.0079 
-0.0335 -0.0337 -1.4919 
Eig. Value: -1.3466 -2.5352 -1.4921 
O: -1.4710 0.3268 0.2811 
0.2823 -1.6693 -0.5544 
0.2680 -0.6186 -2.2081 
Eig. Value: -1.2124 -1.4250 -2.7111 
Si: 3.1028 -0.2778 -0.1196 
-0.1707 3.3332 0.0615 
-0.1060 -0.0997 3.4760 
Eig. Value: 2.9445 3.4399 3.5275 
O: -2.1166 0.2608 -0.2159 
0.1667 -1.5381 -0.1605 
-0.1791 -0.0757 -1.8459 
Eig. Value: -2.2492 -1.3958 -1.8555 
O: -1.6691 0.5325 -0.0055 
0.5231 -2.2130 -0.0079 
-0.0335 0.0337 -1.4919 
Eig. Value: -1.3466 -2.5352 -1.4921 
O: -1.4710 -0.3268 0.2811 
-0.2823 -1.6693 0.5544 
0.2680 0.6186 -2.2081 
Eig. Value: -1.2124 -1.4250 -2.7111 
Li: 1.0855 -0.0000 0.0870 
-0.0000 1.1471 0.0000 
0.0772 -0.0000 1.1835 
Eig. Value: 1.0389 1.1471 1.2301 
Al: 3.2224 -0.0000 0.0329 
-0.0000 3.0272 0.0000 
0.0240 0.0000 2.9563 
Eig. Value: 3.2254 3.0272 2.9533 
Si: 3.1028 0.2778 -0.1196 
0.1707 3.3332 -0.0615 
-0.1060 0.0997 3.4760 
Eig. Value: 2.9445 3.4399 3.5275 
O: -2.1166 -0.2608 -0.2159 
-0.1667 -1.5381 0.1605 
-0.1791 0.0757 -1.8459 
Eig. Value: -2.2492 -1.3958 -1.8555 
O: -1.6691 -0.5325 -0.0055 
-0.5231 -2.2130 0.0079 
-0.0335 -0.0337 -1.4919 
Eig. Value: -1.3466 -2.5352 -1.4921 
O: -1.4710 0.3268 0.2811 
0.2823 -1.6693 -0.5544 
0.2680 -0.6186 -2.2081 
Eig. Value: -1.2124 -1.4250 -2.7111 
Si: 3.1028 -0.2778 -0.1196 
-0.1707 3.3332 0.0615 
-0.1060 -0.0997 3.4760 
Eig. Value: 2.9445 3.4399 3.5275 
O: -2.1166 0.2608 -0.2159 
0.1667 -1.5381 -0.1605 
-0.1791 -0.0757 -1.8459 
Eig. Value: -2.2492 -1.3958 -1.8555 
O: -1.6691 0.5325 -0.0055 
0.5231 -2.2130 -0.0079 
-0.0335 0.0337 -1.4919 
Eig. Value: -1.3466 -2.5352 -1.4921 
O: -1.4710 -0.3268 0.2811 
-0.2823 -1.6693 0.5544 
0.2680 0.6186 -2.2081 
Eig. Value: -1.2124 -1.4250 -2.7111 
Atom type 

Dielectric tensors: 

 
Ɛ2.8671 0.0000 0.0000 
0.0000 2.8922 0.0000 
0.0000 0.0000 2.9304 
Eig. Value: 2.8670 2.8922 2.9305 
Refractive index (N): 1.6933 0.0000 0.0000 
0.0000 1.7006 0.0000 
0.0000 0.0000 1.7118 
Eig. Value: 1.6932 1.7006 1.7119 
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