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Brillouin zoneIn mathematics and solid state physics, the first Brillouin zone is a uniquely defined primitive cell of the reciprocal lattice in the frequency domain. It is found by the same method as for the WignerSeitz cell in the Bravais lattice. The importance of the Brillouin zone stems from the Bloch wave description of waves in a periodic medium, in which it is found that the solutions can be completely characterized by their behavior in a single Brillouin zone. Additional recommended knowledgeTaking 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 kspace that can be reached from the origin without crossing any Bragg plane. There are also second, third, etc., Brillouin zones, corresponding to a sequence of disjoint regions (all with the same volume) at increasing distances from the origin, but these are used more rarely. As a result, the first Brillouin zone is often called simply the Brillouin zone. (In general, the nth Brillouin zone consist of the set of points that can be reached from the origin by crossing n − 1 Bragg planes.) A related concept is that of the irreducible Brillouin zone, which is the first Brillouin zone reduced by all of the symmetries in the point group of the lattice. The concept of a Brillouin zone was developed by Leon Brillouin (18891969), a French physicist. Critical pointsSeveral points of high symmetry are of special interest – these are called critical points.^{[1]}
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Brillouin_zone". A list of authors is available in Wikipedia. 