  The new model of phonon transmission across the interface between two
crystals is proposed featured by taking into account the mismatch of crystal
lattices. It has been found that the mismatch of lattices results in phonon
scattering at the interface even in the absence of defects. As it has been
shown, at the normal incidence, longitudinally polarized phonons have much
larger transmission coefficient than that of transversely polarized phonons,
excluding the special resonance cases. For the quasi one-dimensional case the
exact solution has been obtained.
