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## Wigner-Seitz cellThe ## Additional recommended knowledge## DefinitionThe Wigner-Seitz cell around a lattice point is defined as the locus of points in space, which are closer to that lattice point than to any of the other lattice points. It can be shown mathematically that a Wigner-Seitz Cell is a primitive cell spanning the entire Bravais lattice without leaving any gaps or holes. ## Constructing the cellThe cell may be chosen by first picking a lattice point. Then, lines are drawn to all nearby (closest) lattice points. At the midpoint of each line, another line is drawn normal to each of the first set of lines. In the case of a three-dimensional lattice, a perpendicular plane is drawn at the midpoint of the lines between the lattice points. By using this method, the smallest area (or volume) is enclosed in this way and is called the ## General mathematical conceptThe general mathematical concept embodied in a Wigner-Seitz cell is more commonly called a Voronoi cell. Though the Wigner-Seitz cell in itself is not of paramount importance in direct space, it is extremely important in the reciprocal space. The Wigner-Seitz cell in the reciprocal space is called the Brillouin zone, which contains the information about whether a material will be a conductor, semi-conductor or an insulator. Categories: Condensed matter physics | Crystallography | Mineralogy |

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Wigner-Seitz_cell". A list of authors is available in Wikipedia. |