Theory of the thermal boundary resistance between dissimilar lattices

Continuum acoustics allows only three different phonons to be reflected and transmitted for each phonon that is incident on an interface between two materials. We show that a lattice-dynamical theory for dissimilar lattices allows more phonons to be generated at the interface since we must introduce a larger unit cell. Numerical examples are given for the thermal boundary conductivity between two fcc crystals. The additional high-frequency phonons are found to carry an appreciable amount of the reflected and transmitted heat.