Potassium chloride crystallises in the rock-salt structure

PHYSICS · Multi-part · 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

Potassium chloride crystallises in the rock-salt structure, with

M_{\rm K}=39.10\ \mathrm{u}

M_{\rm Cl}=35.45\ \mathrm{u}

and repeat length

a=6.29\ \mathrm{\mathring{A}}

. Sound travels along a cube edge of potassium chloride at

v_s=4490\ \mathrm{m\,s^{-1}}

. ((a)) Following the procedure of this chapter's worked example, fix the chain's force constant

K

from this sound speed. ((b)) Predict the frequency and wavelength of potassium chloride's zone-centre optical mode, and compare with the measured infrared absorption at

63.5\ \mu\mathrm{m}

. ((c)) State briefly why an ionic crystal such as potassium chloride can absorb infrared light at this one frequency, when a metal made of one kind of atom cannot.

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