The Brillouin zone reference article from the English Wikipedia on 24-Apr-2004
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Brillouin zone

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In mathematics and solid state physics the first Brillouin zone is defined as the Wigner-Seitz primitive cell in the reciprocal lattice.

Another definition is: the set of points in k space that can be reached from the origin without crossing any Bragg plane.

General: the nth Brillouin zone consist of the set of points that can be reached from the origin by crossing n-1 Bragg planes.

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