-    PARAKELDYSHITE     -    Na2ZrSi2O7

 

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:  P-1 
Lattice parameters (Å):  6.6600  8.8300  5.4200 
Angles (°):  92.75  94.25  72.33 

Symmetry (theoretical): 

Space group:  P-1 
Lattice parameters (Å):  6.4351  8.7176  5.3822 
Angles (°):  92.60  94.32  71.03 

Cell contents: 

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

Atomic positions (theoretical):

Na:  0.8911  0.1066  0.2630 
Na:  0.3479  0.4929  0.7585 
Zr:  0.2947  0.2735  0.2193 
Si:  0.6532  0.1455  0.7751 
Si:  0.9407  0.3363  0.6817 
O:  0.2808  0.0438  0.1746 
O:  0.8926  0.1626  0.7122 
O:  0.4903  0.2137  0.5394 
O:  0.5795  0.2477  0.0288 
O:  0.0026  0.3294  0.3960 
O:  0.1331  0.3399  0.8818 
O:  0.2841  0.5162  0.2852 
Na:  0.1089  0.8934  0.7370 
Na:  0.6521  0.5071  0.2415 
Zr:  0.7053  0.7265  0.7807 
Si:  0.3468  0.8545  0.2249 
Si:  0.0593  0.6637  0.3183 
O:  0.7192  0.9562  0.8254 
O:  0.1074  0.8374  0.2878 
O:  0.5097  0.7863  0.4606 
O:  0.4205  0.7523  0.9712 
O:  0.9974  0.6706  0.6040 
O:  0.8669  0.6601  0.1182 
O:  0.7159  0.4838  0.7148 
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): 

Na: 1.1643 -0.0114 0.0201 
0.0284 1.0196 0.0567 
0.0335 0.0442 1.0625 
Eig. Value: 1.1739 0.9859 1.0865 
Na: 1.1210 0.0752 0.0209 
0.0603 1.0731 -0.0004 
-0.0153 0.0108 1.0835 
Eig. Value: 1.1692 1.0251 1.0833 
Zr: 4.5827 -0.3583 0.4068 
0.0235 5.2339 -0.1017 
-0.3533 -0.3247 5.5665 
Eig. Value: 4.5416 5.1620 5.6796 
Si: 3.3063 -0.1905 -0.2548 
0.2214 3.8133 -0.3560 
0.2350 -0.0377 3.5183 
Eig. Value: 3.3057 3.9123 3.4199 
Si: 3.2833 0.4872 -0.3526 
-0.4977 3.3221 -0.0125 
0.3502 0.0420 3.6314 
Eig. Value: 3.2826 3.3221 3.6321 
O: -1.2999 -0.2604 -0.0002 
-0.6507 -3.7017 0.0050 
-0.0407 -0.0544 -1.2352 
Eig. Value: -1.2074 -3.7855 -1.2438 
O: -2.4714 -0.7331 0.3628 
-0.5762 -1.9782 0.1695 
0.0289 0.0575 -1.3342 
Eig. Value: -2.9558 -1.5267 -1.3014 
O: -1.7772 0.4164 -0.9636 
0.3437 -1.4844 0.6573 
-1.0573 0.6324 -3.1006 
Eig. Value: -1.2692 -1.2127 -3.8803 
O: -2.2160 0.1846 0.7325 
0.2074 -1.5243 -0.3708 
0.8428 -0.4385 -2.3644 
Eig. Value: -1.5862 -1.3251 -3.1934 
O: -2.2625 0.1528 0.8923 
0.3537 -1.4001 -0.2572 
0.9728 -0.1719 -2.4429 
Eig. Value: -1.4357 -1.3245 -3.3453 
O: -1.7798 0.2062 -0.9428 
0.3444 -1.3203 0.4941 
-0.9852 0.4428 -3.0238 
Eig. Value: -1.2592 -1.1904 -3.6744 
O: -1.6507 0.0312 0.0786 
0.1417 -3.0530 -0.2841 
-0.0113 -0.2026 -1.3611 
Eig. Value: -1.6465 -3.0930 -1.3254 
Na: 1.1643 -0.0114 0.0201 
0.0284 1.0196 0.0567 
0.0335 0.0442 1.0625 
Eig. Value: 1.1739 0.9859 1.0865 
Na: 1.1210 0.0752 0.0209 
0.0603 1.0731 -0.0004 
-0.0153 0.0108 1.0835 
Eig. Value: 1.1692 1.0251 1.0833 
Zr: 4.5827 -0.3583 0.4068 
0.0235 5.2339 -0.1017 
-0.3533 -0.3247 5.5665 
Eig. Value: 4.5416 5.1620 5.6796 
Si: 3.3063 -0.1905 -0.2548 
0.2214 3.8133 -0.3560 
0.2350 -0.0377 3.5183 
Eig. Value: 3.3057 3.9123 3.4199 
Si: 3.2833 0.4872 -0.3526 
-0.4977 3.3221 -0.0125 
0.3502 0.0420 3.6314 
Eig. Value: 3.2826 3.3221 3.6321 
O: -1.2999 -0.2604 -0.0002 
-0.6507 -3.7017 0.0050 
-0.0407 -0.0544 -1.2352 
Eig. Value: -1.2074 -3.7855 -1.2438 
O: -2.4714 -0.7331 0.3628 
-0.5762 -1.9782 0.1695 
0.0289 0.0575 -1.3342 
Eig. Value: -2.9558 -1.5267 -1.3014 
O: -1.7772 0.4164 -0.9636 
0.3437 -1.4844 0.6573 
-1.0573 0.6324 -3.1006 
Eig. Value: -1.2692 -1.2127 -3.8803 
O: -2.2160 0.1846 0.7325 
0.2074 -1.5243 -0.3708 
0.8428 -0.4385 -2.3644 
Eig. Value: -1.5862 -1.3251 -3.1934 
O: -2.2625 0.1528 0.8923 
0.3537 -1.4001 -0.2572 
0.9728 -0.1719 -2.4429 
Eig. Value: -1.4357 -1.3245 -3.3453 
O: -1.7798 0.2062 -0.9428 
0.3444 -1.3203 0.4941 
-0.9852 0.4428 -3.0238 
Eig. Value: -1.2592 -1.1904 -3.6744 
O: -1.6507 0.0312 0.0786 
0.1417 -3.0530 -0.2841 
-0.0113 -0.2026 -1.3611 
Eig. Value: -1.6465 -3.0930 -1.3254 
Atom type 

Dielectric tensors: 

 
Ɛ2.9423 -0.0196 0.0153 
-0.0196 3.0856 -0.0516 
0.0153 -0.0516 3.1555 
Eig. Value: 2.9394 3.0591 3.1850 
Refractive index (N): 1.7153 0.1401 0.1238 
0.1401 1.7566 0.2272 
0.1238 0.2272 1.7764 
Eig. Value: 1.7145 1.7490 1.7847 
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