 Brillouin zone

The first Brillouin zone is a fundamental cell in reciprocal space. For a one-dimensional lattice of spacing $a$, one conventional choice is

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.