The phonon transport properties and the lattice thermal conductivity of silicon germanium alloy crystals have been investigated based on phonon gas model by using classical molecular dynamics simulations. The attenuation of the mode-dependent phonon relaxation time due to alloying and its dependence on the alloy fraction were quantified by projecting the molecular dynamics phase space trajectory onto the normal mode of the alloyed crystal. By empirically approximating the group velocities from the extended dispersion relations, the lattice thermal conductivity was calculated based on the phonon gas model under relaxation time approximation. The obtained reduction in the lattice thermal conductivity caused by alloying agrees well with that of the experiment and direct non-equilibrium molecular dynamics calculations. The phonon-mean-free-path dependent contribution to thermal conductivity suggests that the effect of nanostructuring can have non-monotonic dependence on the alloy fraction.

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