Brillouin zone


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Brillouin zone

In the propagation of any type of wave motion through a crystal lattice, the frequency is a periodic function of wave vector k . This function may be complicated by being multivalued; that is, it may have more than one branch. Discontinuities may also occur. In order to simplify the treatment of wave motion in a crystal, a zone in k -space is defined which forms the fundamental periodic region, such that the frequency or energy for a k outside this region may be determined from one of those in it. This region is known as the Brillouin zone (sometimes called the first or the central Brillouin zone). It is usually possible to restrict attention to k values inside the zone. Discontinuities occur only on the boundaries. If the zone is repeated indefinitely, all k -space will be filled. Sometimes it is also convenient to define larger figures with similar properties which are combinations of the first zone and portions of those formed by replication. These are referred to as higher Brillouin zones.

The central Brillouin zone for a particular solid type is a solid which has the same volume as the primitive unit cell in reciprocal space, that is, the space of the reciprocal lattice vectors, and is of such a shape as to be invariant under as many as possible of the symmetry operations of the crystal. See Crystallography

Brillouin zone

[brēy·wan ¦zōn]
(solid-state physics)
A fundamental region of wave vectors in the theory of the propagation of waves through a crystal lattice; any wave vector outside this region is equivalent to some vector inside it.
References in periodicals archive ?
An example of this phenomenon occurs in Solid State Physics where the translational symmetry of atoms in a solid resulting from the regular lattice spacing, is equivalent to an effective sampling of the atoms of the solid and gives rise to the Brillouin zone for which the valid values of k are governed by (35).
This is called the reduced zone scheme and [pi]/a is called the Brillouin zone boundary [21, see p.
The shape of the border of the first irreducible Brillouin zone in the wavenumbers space is drawn in the inset of the figure.
Because eight permutations of the wave vector in the (111) direction exist, there are eight L sub-band ellipsoids with centers located near the boundary of the first Brillouin zone.
Appendix V Brillouin Zones, Vibration Modes, and Raman Spectra of Typical Ordinary and Semiconducting Crystals
are the positive branches or Brillouin zones of interest and [k.