Effective medium formulation for phonon transport analysis of nanograined polycrystals

For many research fields, it has been a challenge to accurately predict the lattice thermal conductivity of nanograined polycrystals, where the structure size becomes comparable or smaller than phonon mean free paths (MFPs). Although this can be achieved by advanced techniques such as phonon Monte Carlo simulations, they are generally complicated and can be very time-consuming especially when frequency-dependent phonon MFPs are considered. In this work, we apply the effective medium approach to phonon transport studies of polycrystals, which yields identical results as phonon Monte Carlo simulations in both frequency-dependent and frequency-independent analysis. The formulation can also be modified to consider additional factors, including grain boundaries with an additional interface layer, in-grain substructures, and grain size variation. This work provides a simple but accurate model for thermal studies of general polycrystals.