Rock salt's diatomic chain has repeat length

PHYSICS · Subjective · Fermi University Physics · Oscillations, Waves & Acoustics · Condensed Matter, Materials & Soft Matter · Lattice dynamics and thermal properties of solids

Condensed Matter Physics, Ch Two atoms in the cell: acoustic and optical branches

Problem

Rock salt's diatomic chain has repeat length a=5.64 A˚a=5.64\ \mathrm{\mathring{A}}. (a) Using the Brillouin zone convention of Chapter 2, find the wavevector at the zone boundary of this chain. (b) Using vg=dω/dqv_g=\mathrm{d}\omega/\mathrm{d}q applied to the general formula ω±2(q)=K(1M1+1M2)[1±1−4M1M2sin⁡2(qa/2)(M1+M2)2]\omega_\pm^2(q)=K\left(\frac1{M_1}+\frac1{M_2}\right)\left[1\pm\sqrt{1-\dfrac{4M_1M_2\sin^2(qa/2)}{(M_1+M_2)^2}}\right] of this chapter, show that vg=0v_g=0 for both branches at that same wavevector, and connect this to the standing-wave argument of Chapter 4.

Browse the problem library