Brillouin zone

A primitive cell in reciprocal space that represents distinct wave vectors of a periodic crystal lattice. Its first zone is the Wigner–Seitz cell of the reciprocal lattice.

Reciprocal lattice: A lattice in reciprocal space whose vectors encode the periodicity of a crystal lattice. The Brillouin zone is a primitive cell of this lattice.
Bragg plane: A plane in reciprocal space where waves associated with lattice-related wave vectors satisfy a Bragg-reflection condition. Bragg planes form the boundaries of the first zone.
Electronic band structure: The allowed electron energies in a solid as functions of crystal momentum. Band diagrams commonly plot energies across the first Brillouin zone.
Primitive cell: A smallest-volume cell whose lattice translations reproduce an entire periodic lattice. Many primitive cells tile reciprocal space, but the first zone has a symmetry-centered construction.
Reciprocal space: A space of wave vectors used to describe spatial periodicity and diffraction. The zone partitions this space into equivalent regions.
Bragg reflection: Coherent scattering from periodic planes that redirects waves when their phase conditions reinforce. At zone boundaries, crystal waves can be strongly reflected by the lattice.
Band structure: The relation between energy and wave vector for allowed excitations in a periodic material. The zone supplies the standard wave-vector domain for periodic solids.
Conventional cell: A lattice cell chosen to display crystal symmetry clearly, not necessarily with minimum volume. Its reciprocal counterpart need not match the first Brillouin zone's shape.
Crystal lattice: An infinite periodic arrangement of points representing the translational symmetry of a crystal. Its periodicity determines the geometry of the reciprocal lattice.
Bragg's law: The relation between wavelength, diffraction angle, and plane spacing for constructive X-ray or wave scattering. Its diffraction condition underlies the reciprocal-space boundary construction.

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