  Heat transfer at the interface between two materials is becoming increasingly
important as the size of electronic devices shrinks. Most studies concentrate
on the interfacial thermal conductance between either crystalline-crystalline
or amorphous-amorphous materials. Here, we investigate the interfacial thermal
conductance at crystalline-amorphous interfaces using non-equilibrium molecular
dynamics simulations. Specifically, gold and two different materials, silicon
and silica, in both their crystalline and amorphous structures, have been
considered. The findings reveal that the interfacial thermal conductance
between amorphous structures and gold is found to be $300 \%$ higher as
compared to crystalline structures for both planar and rough interfaces
($\approx$ 152 MW/m$^2$K for gold-amorphous silicon and $\approx$ 56 MW/m$^2$K
for gold-crystalline silicon). This threefold increase could not be captured by
the diffuse mismatch model, neither be explained by phonon localization at the
interface. We relate the increase of interfacial heat transfer to the
enhancement of the interface bonding and the atomic displacements
cross-correlations of low frequency phonons at the crystalline-amorphous
interfaces. This study calls for the systematic experimental determination of
the interfacial thermal conductance between amorphous materials and metals.
