  Interatomic potentials beyond quadratic order provide scattering sources for
phonon transport in lattice. By using a weakly-interacting interface model, we
investigated the relation between the order of interatomic potential and the
multiple-phonon scattering process. We find that high order interatomic
potential not only causes multiple-phonon scattering processes, but also has
significant impacts on elastic phonon scattering processes. Using fourth order
potential as an example, we show that it can significantly affects elastic
phonon scatterings, through the formation of localized phonons. Such impact is
closely related to the correlations of interfacial atoms and it becomes more
significant with increasing temperature. Our work suggests that it is
insufficient to consider only quadratic potential to investigate elastic phonon
transport.
