The first Brillouin zone is a fundamental cell in reciprocal space. For a one-dimensional lattice of spacing , one conventional choice is
A Bragg point is a crystal momentum at which two plane waves differing by a reciprocal lattice vector are degenerate. A periodic potential mixes the waves there, producing an avoided crossing and opening a band gap.
The reciprocal lattice of a two-dimensional triangular Bravais lattice is triangular, so its Wigner-Seitz cell is a regular hexagon. Opposite boundary points are identified modulo reciprocal-lattice translations, and the six corners fall into two inequivalent classes of three corners each, conventionally denoted and .
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A Brillouin zone is a fundamental concept in solid-state physics and crystallography that describes the momentum space (or reciprocal space) of a crystal lattice. It is defined as a specific volume in reciprocal space that contains all the unique momentum states of electrons (or other particles) in a periodic crystal structure due to the periodic arrangement of atoms.