Aluminium's polycrystalline longitudinal sound speed is

PHYSICS · Multi-part · 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 Elastic waves and the vibrating chain

Problem

v_s=6420\,\mathrm{m\,s^{-1}}

, its nearest-neighbour spacing is

a=2.864\,\mathrm{\mathring{A}}

, and one aluminium atom has mass

26.98\,\mathrm{u}

(take

1\,\mathrm{u}=1.6605\times10^{-27}\,\mathrm{kg}

). The measured longitudinal frequency at the cube-edge zone boundary, at room temperature, is about

9.5\,\mathrm{THz}

. ((a)) Fix aluminium's one-spring bond stiffness

K

from the sound speed. ((b)) Predict the chain's highest frequency

\nu_{\rm max}

. ((c)) Express the miss against the measured value as a ratio, and say, as Section 4.6 did for copper, whether one spring along one line is an adequate model.

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