# Wigner-Seitz cell

The **Wigner-Seitz cell** (after Eugene Paul Wigner and Frederick Seitz ) describes a special, primitive cell of a crystal lattice that is defined by a clear construction specification. The Wigner-Seitz cell contains only one grid point and that in its center. All locations inside the Wigner-Seitz cell are closer to this grid point than to the neighboring grid points. Their counterpart in the reciprocal lattice is the first Brillouin zone .

For the construction one chooses a grid point and bisects all connecting lines to all other points by normal planes , i. H. by levels on which the connecting lines are each vertical. By drawing in the center perpendicular (or plane in 3D ) to all points of a crystal lattice, an area (or volume in 3D) is obtained around the lattice point. The geometric body that is bounded by the normal planes is the Wigner-Seitz cell.

This is the starting point for the description of numerous mechanical and electrical properties of solids .

The Wigner-Seitz cell is the three-dimensional special case of a Voronoi cell for crystal lattices. In this respect, the Voronoi theory provides the mathematical description and thus also a wealth of algorithms for its handling.

## literature

- Neil W. Ashcroft, N. David Mermin: Solid State Physics . 2nd Edition. Oldenbourg, Munich 2005, ISBN 3-486-57720-4 .

## Individual evidence

- ↑ Wigner, Seitz, On the constitution of metallic sodium, Phys. Review, Volume 43, 1933, pp. 804-810, Volume 46, 1934, pp. 509-524.