  We have investigated the effect of mass contrast on alloy phonon scattering
in mass-substituted Lennard-Jones crystals. By calculating the mass-difference
phonon scattering rate using a modal analysis method based on molecular
dynamics, we have identified the applicability and limits of the widely-used
mass-difference perturbation model in terms of magnitude and sign of the mass
difference. The result of a phonon -mode-dependent analysis reveals that the
critical phonon frequency, above which the mass-difference perturbation theory
fails, decreases with the magnitude of the mass difference independently of its
sign. This gives rise to a critical mass contrast, above which the
mass-difference perturbation model noticeably underestimates the lattice
thermal conductivity.
