Analytical models for phonon mean free path in polycrystalline nanostructures based on mean square displacement

Abstract

In this study, a numerical simulation method and analytical models for predicting the boundary scattering mean free path (MFP) of phonons in polycrystalline nanostructures are developed. The grain morphologies are assumed to be approximately equiaxed, i.e., forbidding needle-like or pancake-like morphologies. Adapting a technique from rarefied gas dynamics, the method evaluates the MFP from the mean square displacements of phonons that experience random motion and interface collisions in nanostructures. We confirm that the MFP in simple cubic polycrystalline nanostructures obtained by the simulations agrees with that reported in a previous study; this result supports the validity of the method. Two analytical models for high and low interfacial transmission probabilities at the crystal interfaces are also derived by considering the mean square displacements. We find that the grain-boundary intercept length distribution of polycrystalline structures is an essential parameter for determining this boundary scattering MFP. These analytical models reproduce the MFPs in simple cubic and Voronoi diagram polycrystalline nanostructures calculated by the numerical simulations. This result indicates that the boundary scattering MFP of phonons in polycrystalline nanostructures can be obtained once the intercept length distribution is evaluated, without any additional numerical simulations.