Brillouin zones | Reciprocal Lattice
Brillouin zones
In Ewald construction we find that all the k values for which the reciprocal lattice points intersect the Ewald space are Bragg reflected. Let us now construct a locus of all values of k that can be Bragg reflected.
Let us construct Brillouin zones for a simple square lattice of side a. The primitive translational vectors for this lattice are
This equation represents a family of straight lines in the kx and ky plane.
The four lines are plotted in the fig. All k vector originating at the origin and terminating on these lines will produce Bragg's reflection. Besides this set of lines, some other set of lines also.
The form of the Brillouin zone in three dimensions is evaluated.
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