The Wigner-Seitz Method

CONSTRUCTION OF WIGNER-SEITZ CELLS

To create a Wigner-Seitz cell simply complete the following steps.

Choose any lattice site as the origin.
Starting at the origin draw vectors to all neighbouring lattice points.
Construct a plane perpendicular to and passing through the midpoint of each vector.
The area enclosed by these planes is the Wigner-Seitz cell.

Construction of the Wigner-Seitz cell for the simple cubic lattice and the body centred lattice are illustrated in ‘Simple Cubic W-S Cells’ and ‘Body Centred Cubic W-S Cell’ respectively.

The Wigner-Seitz cells have the following characteristics:

Wigner-Seitz cells associated with all lattice points are identical in size, shape and orientation as follows with the translational symmetry of the lattice.
When stacked the Wigner-Seitz cells fill all space.
The Wigner-Seitz cell is a polyhedron.
The Wigner-Seitz cell has the full point symmetry of its lattice point.

Prepared by Laura Malcolm -- last update : March 27, 1997