  Thermal management is extremely important for designing high-performance
devices. The lattice thermal conductivity of materials is strongly dependent on
the structural defects at different length scales, particularly point defects
like vacancies, line defects like dislocations, and planar defects such as
grain boundaries. Traditionally, the McKelvey-Shockley phonon Boltzmann's
transport equation (BTE) method combined with molecular dynamics simulations
has been widely used to evaluate the phonon mean free paths (MFPs) in defective
systems. However, this method can only provide the aggregate MFPs of the whole
sample. It is, therefore, challenging to extract the MFPs in the different
regions with different thermal properties. In this study, the 1D
McKelvey-Shockley phonon BTE method was extended to model inhomogeneous
materials, where the effect of defects on the phonon MFPs is explicitly
obtained. Then, the method was used to study the phonon interactions with the
core structure of an edge dislocation. The phonon MFPs in the dislocation core
were obtained and consistent with the analytical model such that high frequency
phonons are likely to be scattered in this area. This method not only advances
the knowledge of phonon-dislocation scattering but also shows the potential to
investigate phonon transport behaviors in more complicated materials.
