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Brillouin zone

In mathematics and solid state physics, the first Brillouin zone is a uniquely defined primitive cell in reciprocal space. In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice is broken up into Brillouin zones. The boundaries of this cell are given by planes related to points on the reciprocal lattice. The importance of the Brillouin zone stems from the description of waves in a periodic medium given by Bloch's theorem, in which it is found that the solutions can be completely characterized by their behavior in a single Brillouin zone.

Critical points
, a truncated octahedron, showing symmetry labels for high symmetry lines and points Several points of high symmetry are of special interest – these are called critical points. Other lattices have different types of high-symmetry points. They can be found in the illustrations below for both three- and two-dimensional lattices. Brillouin zone types in 3D Brillouin zone types in 2D In two dimensions, the number of Bravais lattices reduces to five. In the following illustration, the corresponding Brillouin zones are delimited by red lines. For each lattice, the irreducible Brillouin zone is highlighted (blue) in accordance with the definitions of the symmetry points given in Refs. and . ==See also==
Source: Wikipedia ↗
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