Brillouin zone [SEP] named after
the irreducible Brillouin zone, which is the first Brillouin zone reduced by all of the symmetries in the point group of the lattice (point group of the crystal).
The concept of a Brillouin zone was developed by Léon Brillouin (1889–1969), a French physicist.
Critical 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.
See also.
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Umklapp scattering
In crystalline materials, Umklapp scattering (also U-process or Umklapp process) is a scattering process that results in a wave vector (usually written "k") which falls outside the first Brillouin zone. If a material is periodic, it has a Brillouin zone, and any point outside the first Brillouin zone can also be expressed as a point inside the zone. So, the wave vector is then mathematically transformed to a point inside the first Brillouin zone. This transformation allows for scattering processes which would