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Brillouin zone (Read 2448 times)
Gerrit-Jan Linker
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Brillouin zone
19.08.09 at 12:34:43
Brillouin zone
The first Brillouin zone is a uniquely defined primitive cell in reciprocal space.
The boundaries of this cell are given by planes related to points on the reciprocal lattice.
First Brioullin zone: k=0 .. π/a
k=0 is called the zone center, also called the gamma point.
The points k=π/a are called zone edges.
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.  
When k=0 all monomer MO's are "in phase"
When k=π/a all monomer MO's are "out-of-phase"
Above, "in-phase" means that two unit cells can be obtained using direct translation. "Out-of-phase" indicates a change of sign accompanying the translation.
The range of energies spanned by a band in the first Brillouin zone is called the dispersion of the band. The higher the dispersion the higher the intercell interaction.
See also:
Wave vector
Critical points in the Brioullin zone
Modern Physical Organic Chemistry, Anslyn
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« Last Edit: 26.10.10 at 11:38:10 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
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