Kapitza conductance and phonon scattering at grain boundaries by simulation

We use a nonequilibrium molecular-dynamics method to compute the Kapitza resistance of three twist grain boundaries in silicon, which we find to increase significantly with increasing grain boundary energy, i.e., with increasing structural disorder at the grain boundary. The origin of this Kapitza resistance is analyzed directly by studying the scattering of packets of lattice vibrations of well-defined polarization and frequency from the grain boundaries. We find that scattering depends strongly on the wavelength of the incident wave packet. In the case of a high-energy grain boundary, the scattering approaches the prediction of the diffuse mismatch theory at high frequencies, i.e., as the wavelength becomes comparable to the lattice parameter of the bulk crystal. We discuss the implications of our results in terms of developing a general model of scattering probabilities that can be applied to mesoscale models of heat transport in polycrystalline systems.