The number of atoms created with the Supercell tool

Introduction:

We take the examples of P,B and FCC lattices in cubic structures and the different space groups related.

A-Elements:

1-P lattice: Polonium   a=3.359 A°   Space group number: 221




2-B lattice: Chromium   a=2.91 A°   Space group number: 229

3-F lattice:  Copper   a=3.615 A°   Space group number: 225

B-Binary compounds:

1-P lattice: Cesium Chloride   a=4.123 Å   Space group number: 221

2-B lattice:  

...........

3-F lattice:  Sodium Chloride   a=3.615 A°   Space group number: 225

Supercell creation: The supercell will break the symmetry 

The supercell operation P 1x1x1  makes all the sites inequivalent.

The AxAxA operation leads to the creation of the multiplied number AxAxA/1 for P lattice, AxAxA/2 for B lattice and AxAxA/4 for F lattice.

A-Elements:

The P 2x2x2 supercell will give 2x2x2/1 (=8) times for every site. The B 2x2x2 supercell will give 2x2x2/2 (=4) times for very site. The 2x2x2 supercell will give 2x2x2/4 (=2) times for every site.

The P 4x4x4 supercell will give 4x4x4/1 (=64) times for every site. The B 4x4x4 supercell will give 4x4x4/2 (=32) times for every site. The 4x4x4/4 (=16) times for every site.

B-Binary compounds:

The same thing will happens to the binary compounds and we deal with the binary compound as a cobmination of 2 element compounds (or 2 parts) and apply the rules to every part.

Example:

Supercell calculations on TiC

This example shows you how to create a supercell of TiC, which could be used to simulate a TiC-surface or vacancies, impurities or core-holes for X-ray absorption / ELNES spectroscopy. I'll describe the procedure using Unix and WIEN2k commands in an xterm, but of course you can do the same in w2web.

Create a new directory, copy the original TiC struct file into it and run supercell program:

  mkdir super
  cd super
  cp ../TiC/TiC.struct .
  x supercell

Specify ``TiC.struct'', a ``2x2x2'' supercell, ``F'' lattice (this will create a cell with 16 atoms, you can also create 32 or 64 atom cells using B or P lattice type

Illustration for 1 site: