page_title: Brillouin zone
section_title: See also
hierarchical_section_title: Brillouin zone / See also
caption_attribution_description: English: Selected area electron diffraction (SAED) pattern of a thick Si specimen with many diffusely-scattered 100keV electrons, and a beam direction nearly parallel to the Si&lt;111&gt; zone. The λ ≈ 0.0370 Å electron-wavelength makes the radius 1/λ Ewald-sphere nearly planar on the scale of the inner-star radius g220 ≡ 1/d220 ≈ 1/1.92Å, and the beam half-angle facilitates weak excitation of many Bragg-reflections even though no reflections are at the Bragg-condition (where a Kikuchi-band in the star-pattern e.g. of width θscatt = 2θBragg = 2asin[λ/(2d220)] ≈ 19.2 mrad would have been shifted to intersect both the incident beam's central dot and a diffraction spot). These electrons either had enough leptonic-imagination by themselves to construct the 2D Wigner-Seitz cell[1] (lattice-point bisectors) for this reciprocal-lattice slice, or else Brillouin-zone surfaces in a crystal are so real that they can be directly imaged. What do you think?
context_page_description: In mathematics and solid state physics, the first Brillouin zone is a uniquely defined primitive cell in reciprocal space. In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice is broken up into Brillouin zones. The boundaries of this cell are given by planes related to points on the reciprocal lattice. The importance of the Brillouin zone stems from the Bloch wave description of waves in a periodic medium, in which it is found that the solutions can be completely characterized by their behavior in a single Brillouin zone.
  The first Brillouin zone is the locus of points in reciprocal space that are closer to the origin of the reciprocal lattice than they are to any other reciprocal lattice points. Another definition is as the set of points in k-space that can be reached from the origin without crossing any Bragg plane. Equivalently, this is the Voronoi cell around the origin of the reciprocal lattice.
  There are also second, third, etc., Brillouin zones, corresponding to a sequence of disjoint regions at increasing distances from the origin, but these are used less frequently.
context_section_description: Fundamental pair of periods
  Fundamental domain
caption: Brillouin-zone construction by selected area diffraction, using 300 keV electrons.
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