A germanium crystal at has a measured lattice thermal conductivity

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 Thermal expansion and lattice thermal conductivity

Problem

A germanium crystal at 300 K300\,\mathrm{K} has a measured lattice thermal conductivity κ=60 W m−1K−1\kappa = 60\,\mathrm{W\,m^{-1}K^{-1}}, a heat capacity per unit volume cV=1.73×106 J m−3K−1c_V = 1.73\times10^6\,\mathrm{J\,m^{-3}K^{-1}}, a branch-averaged sound speed v=5400 m s−1v = 5400\,\mathrm{m\,s^{-1}} and a lattice constant a=5.658 A˚a = 5.658\,\mathrm{\mathring{A}}. Extract the phonon mean free path ℓ\ell, in nanometres and in lattice constants.

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