| Brillouin Zone |
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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 . 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 ''n''-th 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 , a French physicist. SEE ALSO REFERENCES
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