-    CROCOITE     -    PbCrO4

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. Tetter norm-conserving pseudopotential for Cr. 

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):  7.1200  7.4300  6.7900 
Angles (°):  90  102.42  90 

Symmetry (theoretical): 

Space group:  14  P2_1/n 
Lattice parameters (Å):  7.0193  7.3464  6.7203 
Angles (°):  90  102.70  90 

Cell contents: 

Number of atoms:  24 
Number of atom types: 
Chemical composition: 

Atomic positions (theoretical):

Pb:  0.2228  0.1448  0.3995 
Cr:  0.2016  0.1659  0.8808 
O:  0.0277  0.0987  0.6799 
O:  0.1217  0.3504  0.9851 
O:  0.2476  0.5064  0.4366 
O:  0.3914  0.2154  0.7782 
Pb:  0.2772  0.6448  0.1005 
Cr:  0.2984  0.6659  0.6192 
O:  0.4723  0.5987  0.8201 
O:  0.3783  0.8504  0.5149 
O:  0.2524  0.0064  0.0634 
O:  0.1086  0.7154  0.7218 
Pb:  0.7772  0.8552  0.6005 
Cr:  0.7984  0.8341  0.1192 
O:  0.9723  0.9013  0.3201 
O:  0.8783  0.6496  0.0149 
O:  0.7524  0.4936  0.5634 
O:  0.6086  0.7846  0.2218 
Pb:  0.7228  0.3552  0.8995 
Cr:  0.7016  0.3341  0.3808 
O:  0.5277  0.4013  0.1799 
O:  0.6217  0.1496  0.4851 
O:  0.7476  0.9936  0.9366 
O:  0.8914  0.2846  0.2782 
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): 

Pb: 3.7026 -0.0619 0.1559 
-0.0227 3.8637 -0.0123 
-0.0231 0.8162 4.0536 
Eig. Value: 3.7313 3.5159 4.3727 
Cr: 2.7986 -0.0610 -0.2152 
-0.0994 3.2314 0.2012 
0.1509 -0.3495 3.7042 
Eig. Value: 2.7820 3.2362 3.7160 
O: -1.5659 -0.6571 -0.8184 
-0.8511 -1.2019 -0.7501 
-1.3422 -0.9469 -2.6734 
Eig. Value: -1.0191 -0.6081 -3.8140 
O: -1.6046 0.5578 0.2050 
0.6500 -2.9110 -1.0140 
0.2870 -1.1662 -0.9826 
Eig. Value: -1.3938 -3.6135 -0.4909 
O: -0.5154 -0.2013 0.2486 
-0.0916 -2.2781 -1.0727 
0.1098 -1.4192 -2.7526 
Eig. Value: -0.4501 -1.3117 -3.7843 
O: -2.8153 -0.7500 0.4241 
-0.7399 -0.7042 0.0307 
0.8176 0.1608 -1.3491 
Eig. Value: -3.2543 -0.4553 -1.1591 
Pb: 3.7026 0.0619 0.1559 
0.0227 3.8637 0.0123 
-0.0231 -0.8162 4.0536 
Eig. Value: 3.7313 3.5159 4.3727 
Cr: 2.7986 0.0610 -0.2152 
0.0994 3.2314 -0.2012 
0.1509 0.3495 3.7042 
Eig. Value: 2.7820 3.2362 3.7160 
O: -1.5659 0.6571 -0.8184 
0.8511 -1.2019 0.7501 
-1.3422 0.9469 -2.6734 
Eig. Value: -1.0191 -0.6081 -3.8140 
O: -1.6046 -0.5578 0.2050 
-0.6500 -2.9110 1.0140 
0.2870 1.1662 -0.9826 
Eig. Value: -1.3938 -3.6135 -0.4909 
O: -0.5154 0.2013 0.2486 
0.0916 -2.2781 1.0727 
0.1098 1.4192 -2.7526 
Eig. Value: -0.4501 -1.3117 -3.7843 
O: -2.8153 0.7500 0.4241 
0.7399 -0.7042 -0.0307 
0.8176 -0.1608 -1.3491 
Eig. Value: -3.2543 -0.4553 -1.1591 
Pb: 3.7026 -0.0619 0.1559 
-0.0227 3.8637 -0.0123 
-0.0231 0.8162 4.0536 
Eig. Value: 3.7313 3.5159 4.3727 
Cr: 2.7986 -0.0610 -0.2152 
-0.0994 3.2314 0.2012 
0.1509 -0.3495 3.7042 
Eig. Value: 2.7820 3.2362 3.7160 
O: -1.5659 -0.6571 -0.8184 
-0.8511 -1.2019 -0.7501 
-1.3422 -0.9469 -2.6734 
Eig. Value: -1.0191 -0.6081 -3.8140 
O: -1.6046 0.5578 0.2050 
0.6500 -2.9110 -1.0140 
0.2870 -1.1662 -0.9826 
Eig. Value: -1.3938 -3.6135 -0.4909 
O: -0.5154 -0.2013 0.2486 
-0.0916 -2.2781 -1.0727 
0.1098 -1.4192 -2.7526 
Eig. Value: -0.4501 -1.3117 -3.7843 
O: -2.8153 -0.7500 0.4241 
-0.7399 -0.7042 0.0307 
0.8176 0.1608 -1.3491 
Eig. Value: -3.2543 -0.4553 -1.1591 
Pb: 3.7026 0.0619 0.1559 
0.0227 3.8637 0.0123 
-0.0231 -0.8162 4.0536 
Eig. Value: 3.7313 3.5159 4.3727 
Cr: 2.7986 0.0610 -0.2152 
0.0994 3.2314 -0.2012 
0.1509 0.3495 3.7042 
Eig. Value: 2.7820 3.2362 3.7160 
O: -1.5659 0.6571 -0.8184 
0.8511 -1.2019 0.7501 
-1.3422 0.9469 -2.6734 
Eig. Value: -1.0191 -0.6081 -3.8140 
O: -1.6046 -0.5578 0.2050 
-0.6500 -2.9110 1.0140 
0.2870 1.1662 -0.9826 
Eig. Value: -1.3938 -3.6135 -0.4909 
O: -0.5154 0.2013 0.2486 
0.0916 -2.2781 1.0727 
0.1098 1.4192 -2.7526 
Eig. Value: -0.4501 -1.3117 -3.7843 
O: -2.8153 0.7500 0.4241 
0.7399 -0.7042 -0.0307 
0.8176 -0.1608 -1.3491 
Eig. Value: -3.2543 -0.4553 -1.1591 
Atom type 

Dielectric tensors: 

 
Ɛ5.0925 0.0000 0.0000 
0.0000 5.3057 0.0000 
0.0000 0.0000 6.3080 
Eig. Value: 5.0925 5.3057 6.3080 
Refractive index (N): 2.2567 0.0000 0.0000 
0.0000 2.3034 0.0000 
0.0000 0.0000 2.5116 
Eig. Value: 2.2567 2.3034 2.5116 
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