General effective medium formulation for thermal analysis of a polycrystal - The influence of partially specular phonon transmission across grain boundaries

In this work, we extend the previous effective medium formulation on phonon transport within a polycrystal to more general cases by further considering partially specular phonon transmission across grain boundaries, in addition to the diffuse grain-boundary scattering of phonons. Such specular phonon transmission normally becomes important at cryogenic temperatures to facilitate the grain-boundary phonon transport, whereas the diffuse scattering is dominant above room temperature. This extension enables accurate thermal analysis of a polycrystal over the full temperature range. The new formulation yields identical results as phonon Monte Carlo simulations considering frequency-dependent phonon mean free paths. Literature data of different polycrystals are analyzed with this simple but accurate formulation. At low temperatures, the temperature dependence of the lattice thermal conductivity highly depends on the employed frequency-dependent phonon specularity of grain boundaries.