Effect of Grain Boundaries on the Lattice Thermal Transport Properties of Insulating Materials: A Predictive Model

Abstract

We present two theoretical models to predict the lattice thermal conductivity degradation of insulating materials at high temperature (above one‐third of the Debye temperature). This degradation is due to the presence of grains, with known sizes and shapes, inducing thermal resistance at their boundaries. The first model is derived directly from the kinetic theory of gases (KTG). The formulation of the second is based on a localized continuum model (LCM), assuming phonon Umklapp scattering and the Debye approximation of phonon density of state. The two proposed models are purely predictive, as no experimental information related to the grain size dependence of the thermal conductivity is necessary for the parameterization of the models. The predictive accuracy of the two proposed models is tested on several different types of electrically insulating compounds. Although the model derived from the KTG is similar to the well‐known Kapitza thermal resistance formalism, it fails to predict the grain size dependence of the lattice thermal conductivity. The one derived from a LCM is a new formalism predicting, with good accuracy, the lattice thermal conductivity as a function of the average grain size. It is applicable for microstructures with a grain size typically above 20–50 nm.