Leon Brillouin (1889-1969) first introduced Brillouin Zones in his work on the general properties of periodic structures. The concept and construction of the zones can appear quite abstract, but this is largely a result of their wide range of useful applications.
Brillouin zones are polyhedra in reciprocal space in crystalline materials and are the geometrical equivalent of Wigner-Seitz cells in real space. Physically, Brillouin zone boundaries represent Bragg planes which reflect (diffract) waves having particular wave vectors so that they cause constructive interference.
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