Lithium fluoride also crystallises in the rock-salt structure

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

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

Problem

Lithium fluoride also crystallises in the rock-salt structure, with

M_{\rm Li}=6.94\ \mathrm{u}

M_{\rm F}=19.00\ \mathrm{u}

, repeat length

a=4.02\ \mathrm{\mathring{A}}

, and a measured sound speed along a cube edge of

v_s=6600\ \mathrm{m\,s^{-1}}

. (a) Fix

K

from this sound speed, and predict lithium fluoride's zone-centre optical frequency and wavelength. (b) The measured infrared absorption of lithium fluoride sits at

32.0\ \mu\mathrm{m}

. Find the percentage by which the chain's prediction misses this line, and say whether the chain predicts too high or too low a frequency. (c) This miss is noticeably larger than rock salt's

12

per cent. Using the chapter's own comment on what the single spring constant leaves out, suggest one reason the single-spring model might do less well for lithium fluoride's light, tightly held ions than for rock salt's heavier ones.

Browse the problem library