Wigner-Seitz cell

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created: 2021-10-31 02:27:55
modified: 2022-01-10 04:13:04

A primitive cell which has been constructed by applying Voronoi decomposition to a crystal lattice. In other words: the set of points in space that are closer to the given lattice point than to any other lattice points.

It can be shown that it is a primitive cell, so it has the same volume of any other primitive cell and the cell spans the entire direct space without leaving any gaps or holes.

The Wigner-Seitz cell of a reciprocal lattice is called the Brillouin zone.


The Wigner-Seitz cell in 2D for different angles

Construction a Wigner-Seitz cell