Brillouin Zones
AimsBefore you startIntroductionReciprocal lattice vectorsBrillouin Zone constructionThe general case in three dimensionsZone foldingExamples of Brillouin Zones in Three DimensionsSummaryQuestionsGoing furtherTLP creditsTLP contentsShow all contentViewing and downloading resourcesAbout the TLPsTerms of useFeedbackCredits Print this page
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Introduction
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.