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Brillouin Zones and Fundamental Regions
Author(s) -
Jones G. A.,
Landsberg P. T.
Publication year - 1985
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221280228
Subject(s) - brillouin zone , reciprocal lattice , lattice (music) , reciprocal , mathematics , geometry , physics , theoretical physics , mathematical analysis , quantum mechanics , philosophy , linguistics , diffraction , acoustics
The n ‐th Brillouin zone is defined to be the set of points in reciprocal space which have the origin as their (not necessarily unique) n ‐th nearest lattice‐point. From this definition it is shown that (a) all zones have equal volumes and (b) each zone can be translated into the first zone so as to fill it exactly by translating different pieces of the zone by appropriate reciprocal lattice‐vectors. The argument, being purely geometrical, does not require appeal to periodic boundary conditions, the Schrödinger equation or similar results from the physics of the solid state. A connection with the more general “fundamental regions” is also pointed out.