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 Boltzmanns 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.
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