  Phonon transmission across interfaces of dissimilar materials has been
studied intensively in the recent years by using atomistic simulation tools
owing to its importance in determining the effective thermal conductivity of
nanostructured materials. Atomistic Green's function (AGF) method with
interatomic force constants from the first-principles (FP) calculations has
evolved to be a promising approach to study phonon transmission in many not
well-studied material systems. However, the direct FP calculation for
interatomic force constants becomes infeasible when the system involves atomic
disorder. Mass approximation is usually used, but its validity has not been
tested. In this paper, we employ the higher-order force constant model to
extract harmonic force constants from the FP calculations, which originates
from the virtual crystal approximation but considers the local force-field
difference. As a feasibility demonstration of the proposed method that
integrates higher-order force constant model from the FP calculations with the
AGF, we study the phonon transmission in the Mg2Si/Mg2Si1-xSnx systems. When
integrated with the AGF, the widely-used mass approximation is found to
overpredict phonon transmission across Mg2Si/Mg2Sn interface. The difference
can be attributed to the absence of local strain field-induced scattering in
the mass approximation, which makes the high-frequency phonons less scattered.
The frequency-dependent phonon transmission across an interface between a
crystal and an alloy, which often appears in high efficiency "nanoparticle in
alloy" thermoelectric materials, is studied. The interfacial thermal resistance
across Mg2Si/Mg2Si1-xSnx interface is found to be weakly dependent on the
composition of Sn when the composition x is less than 40%, but increases
rapidly when it is larger than 40% due to the transition of high-frequency
phonon DOS in Mg2Si1-xSnx alloys.
