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Description
The phonon Boltzmann equation developed by Peierls describes the heat conduction in solids in terms of the dynamics of interacting phonon wave-packets. This picture holds true only in a perfectly pure and infinite crystal. Several methods have been recently developed to solve this equation in a numerically exact way, allowing to determine the thermal conductivity of crystals.
Introducing disorder, it is possible to reach a point where the phonon wave-packets do not propagate far enough to sample the crystal periodicity, rendering impossible to attribute them a wave vector or a group velocity. In this regime, the theory developed by Allen and Feldman applies.
The thermal transport in Si/Ge alloys is studied using these two approaches at variance of the composition.
