Computational Representation of Wigner-Seitz Cell

Abstract

Wigner-Seitz cell, theprimitive cell in reciprocal space was constructed computationally by joining the perpendicular bisectors of the line between the concerned point and its nearest neighbours. First of all, arrays of lattice points were constructed and the mid-point was identified. Then all the nearest points of the mid-point were joined and then perpendicular bisectors were drawn. At the last step, all the bisected points were joined to its adjacent lattice to form a closed region encompassing the mid-point. The innermost region is called the Wigner-Seitz cell in direct lattice and Brillouin zone in reciprocal lattice