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Wigner–Seitz cell

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The Wigner–Seitz cell, named after Eugene Wigner and Frederick Seitz, is a type of Voronoi cell used in the study of crystalline material in solid-state physics.The unique property of a crystal is that its atoms are arranged in a regular 3-dimensional array called a lattice. All the properties attributed to crystalline materials stem from this highly ordered structure. Such a structure exhibits discrete translational symmetry. In order to model and study such a periodic system, one needs a mathematical "handle" to describe the symmetry and hence draw conclusions about the material properties consequent to this symmetry. The Wigner–Seitz cell is a means to achieve this.A Wigner–Seitz cell is an example of another kind of Primitive cell. The primitive unit cell (or simply primitive cell) is a special case of unit cell which has only one lattice point combined and shared by eight other primitive cells. It is the most "primitive" cell one can construct, and it is a parallelepiped. The general unit cell has an integral number of lattice points. The simple cubic lattice is the only primitive unit cell conventionally. The body centered cubic (BCC) and face centered cubic (FCC) lattices are simply unit cells, not primitive. The general mathematical concept behind the primitive cell is termed the fundamental domain or the Voronoi cell. The primitive cell of the reciprocal lattice in momentum space is called the Brillouin zone.