- Brillouin zone
In
mathematics andsolid state physics , the first Brillouin zone is a uniquely definedprimitive cell of thereciprocal lattice in thefrequency domain . It is found by the same method as for theWigner-Seitz cell in theBravais lattice . The importance of the Brillouin zone stems from theBloch 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.Taking surfaces at the same distance from one element of the lattice and its neighbours, the
volume included is the first Brillouin zone. 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 theVoronoi cell around the origin of the reciprocal lattice.There are also second, third, "etc.", Brillouin zones, corresponding to a sequence of disjoint regions (all with the same volume) at increasing distances from the origin, but these are used more rarely. As a result, the "first" Brillouin zone is often called simply the "Brillouin zone". (In general, the "n"-th Brillouin zone consist of the set of points that can be reached from the origin by crossing "n" − 1 Bragg planes.)
A related concept is that of the irreducible Brillouin zone, which is the first Brillouin zone reduced by all of the symmetries in the
point group of the lattice.The concept of a Brillouin zone was developed by
Leon Brillouin (1889-1969), a French physicist.Critical points
Several points of high symmetry are of special interest – these are called critical points. [Harald Ibach & Hans Lüth, "Solid-State Physics, An Introduction to Principles of Materials Science", corrected second printing of the second edition, 1996, Springer-Verlag, ISBN 3-540-58573-7]
ee also
*
period lattice
*fundamental domain References
* Charles Kittel, "Introduction to Solid State Physics" (Wiley: New York, 1996).
* Neil W. Ashcroft and N. David Mermin, "Solid State Physics" (Harcourt: Orlando, 1976).
*Léon Brillouin " [http://gallica.bnf.fr/ark:/12148/bpt6k31445 Les électrons dans les métaux et le classement des ondes de de Broglie correspondantes] " Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences, 191, 292 (1930). (original article)External links
* [http://www2.sjsu.edu/faculty/watkins/brillouin.htm Brillouin Zone simple lattice diagrams by Thayer Watkins]
* [http://phycomp.technion.ac.il/~nika/brillouin_zones.html Brillouin Zone 3d lattice diagrams by Technion.]
Wikimedia Foundation. 2010.
