In mathematics and solid state physics, the first Brillouin zone is the primitive cell in the reciprocal lattice in momentum space. It is found by the same method as for the Wigner-Seitz cell in the Bravais lattice.
Taking the surfaces at the same distance from one element of the lattice and its neighbours, the volume included is the first Brillouin zone. Another definition is as the set of points in k-space that can be reached from the origin without crossing any Bragg plane.
Its importance is that every momentum allowed for the electrons in a crystal is included in a Brillouin zone. In general, the n-th Brillouin zone consist of the set of points that can be reached from the origin by crossing n − 1 Bragg planes.
The concept of a Brillouin zone was developed by Leon Brillouin, a French physicist.
See also