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Encyclopedia > First Brillouin zone

In mathematics and solid state physics, the first Brillouin zone is the primitive cell in the reciprocal lattice in momentum space. It is found by the same method as for the Wigner-Seitz cell in the Bravais lattice.


Taking the 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.


Its importance is that every momentum allowed for the electrons in a crystal is included in a 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.


The concept of a Brillouin zone was developed by Leon Brillouin, a French physicist.


  Results from FactBites:
 
Brillouin zone - Wikipedia, the free encyclopedia (303 words)
In mathematics and solid state physics, the first Brillouin zone is the primitive cell in the reciprocal lattice in momentum space.
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.
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.
Fermi Surfaces and Brillouin Zones (411 words)
This is a sketch of the construction of the first four Brillouin zones for a square lattice.
The first Brillouin zone for a point in a lattice is the set of points that are closer to the point than the Bragg "plane" of any point.
In constructing the Brillouin zones for a point it is expeditent to first determine the nearest neighbors, the next nearest neighbors and so on.
  More results at FactBites »


 

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