A wavevector lies outside the first Brillouin zone

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Lattice dynamics and thermal properties of solids

Condensed Matter Physics, Ch Elastic waves and the vibrating chain

Problem

A wavevector

q=1.7\,\pi/a

lies outside the first Brillouin zone. Using copper's chain spacing

a=2.556\,\mathrm{\mathring{A}}

, ((a)) find the equivalent wavevector inside the first zone,

-\pi/a<q\le\pi/a

, and ((b)) confirm that

|\sin(qa/2)|

takes the same value for both, so that they sit at the same point on the dispersion curve.

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