Wigner–Seitz cell

The Wigner -Seitz cell ( to Eugene Paul Wigner and Frederick Seitz ) refers to a special primitive cell of a crystal lattice, which is defined by a unique design provision. The Wigner- Seitz cell contains only one grid point, and indeed in its center. All locations inside the Wigner- Seitz cell are this lattice point than to the neighboring grid points. Their correspondence in the reciprocal lattice, the first Brillouin zone.

For the construction of a grid point is chosen and halved all links to all other points by normal levels, i.e., levels at which the connection lines are perpendicular. By inscribing the central vertical line ( or plane in 3D) to all points of a crystal lattice, we get around the grid point an area ( or volume in 3D). The geometric body which is defined by the normal levels, 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 special case of a three-dimensional Voronoi cell of the crystal lattice. As such, the Voronoi theory provides the mathematical description, and thus also an abundance of algorithms for their handling.