  Phonon transmission across epitaxial interfaces is studied within the lattice
dynamic approach. The transmission shows weak dependence on frequency for the
lattice wave with a fixed angle of incidence. The dependence on azimuth angle
is found to be related to the symmetry of the boundary interface. The
transmission varies smoothly with the change of the incident angle. A critical
angle of incidence exists when the phonon is incident from the side with large
group velocities to the side with low ones. No significant mode conversion is
observed among different acoustic wave branches at the interface, except when
the incident angle is near the critical value. Our theoretical result of the
Kapitza conductance $G_{K}$ across the Si-Ge (100) interface at temperature
$T=200 $K is $4.6\times10^{8} {\rm WK}^{-1}{\rmm}^{-2}$. A scaling law $G_K
\propto T^{2.87}$ at low temperature is also reported. Based on the features of
transmission obtained within lattice dynamic approach, we propose a simplified
formula for thermal conductanceacross the epitaxial interface. A reasonable
consistency is found between the calculated values and the experimentally
measured ones.
