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The Tamura model is a particular type of 1$^{\text{st}}$ Born approximationof the phonon-isotope scattering problem. The expression for the mode-resolvedphonon-isotope scattering rates in this model, derived in 1983, is still widelyused in ab initio transport calculations. While the original work emphasizedits applicability to low-energy acoustic phonons only, it has, nevertheless,been also applied to optical phonons in the field of phonon transport. Themodel has the salient feature of being a perturbation theory on top of avirtual crystal background. As such, this approach does not correspond to theproper methodology for solving the phonon-substitution defect problem in therespective limit. Here, we explore three avenues to go beyond the Tamura modeland carry out calculations on a set of common materials to compare thedifferent approaches. This work allows a systematic improvement of thetreatment of phonon-isotope scattering in ab initio phonon transport, whileunifying it with the general phonon-substitution scattering problem.

Beyond the Tamura model of the phonon-isotope scattering