Theory of lattice thermal conductivity

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Abstract
It is shown that on a plausible approximation the three-phonon contribution to the lattice thermal resistivity can be described in terms of simple exponential decays toward a set of terminal distributions, one for each reciprocal lattice vector. The result of this is to produce an Umklapp-process drift term in the steady-state distribution as well as a Normal-process drift. The Callaway result follows when Umklapp processes are negligible. For a perfect infinite lattice a correction to the single mode relaxation time result of more than a factor of three greater than the Callaway correction is predicted.