(a) Confirm that the zone-boundary wavelength, , satisfies Bragg's law at normal…

PHYSICS · Subjective · 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) Confirm that the zone-boundary wavelength, λ=2a\lambda=2a, satisfies Bragg's law 2dsin⁡θ=nλ2d\sin\theta=n\lambda at normal incidence (θ=90∘\theta=90^\circ, n=1n=1) on planes spaced aa apart. (b) The reciprocal lattice of a one-dimensional chain of spacing aa consists of points spaced G=2π/aG=2\pi/a apart (Chapter 2), and the first Brillouin zone extends from the origin to half the distance to the nearest such point. Show that the zone-boundary wavevector q=π/aq=\pi/a found in Section 4.5 is exactly G/2G/2, and say what this confirms about the boundary.

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