A polycrystalline

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 Thermal expansion and lattice thermal conductivity

Problem

A polycrystalline, chemical-vapour-deposited diamond film used as a heat spreader has a lower measured conductivity than single-crystal diamond, κ=1200 W m−1K−1\kappa = 1200\,\mathrm{W\,m^{-1}K^{-1}} at 300 K300\,\mathrm{K}, within the 10001000 to 2000 W m−1K−12000\,\mathrm{W\,m^{-1}K^{-1}} range quoted for CVD diamond. Its heat capacity per unit volume and sound speed are the same as bulk diamond's, cV=1.8×106 J m−3K−1c_V = 1.8\times10^6\,\mathrm{J\,m^{-3}K^{-1}} and v=1.3×104 m s−1v = 1.3\times10^4\,\mathrm{m\,s^{-1}}, and its lattice constant is a=3.57 A˚a = 3.57\,\mathrm{\mathring{A}}. ((a)) Find the film's phonon mean free path, in nanometres and in lattice constants. ((b)) Section 7.6 quotes single-crystal diamond's mean free path as 260 nm260\,\mathrm{nm}. By what factor is the film's mean free path shorter, and what does that tell you about what limits it?

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