  It is widely assumed in the literature that the specularity parameters for
phonon transmission (forward scattering) and reflection (backward scattering)
at a boundary are identical, i.e., the statistical distributions of the
transition probabilities between an incident phonon and the range of outgoing
phonon modes are the same for both transmission and reflection. However, it is
hypothesized by Li and McGaughey that separate specularity parameters are
needed to describe the behavior of transmitted and reflected phonons in
superlattices and polycrystalline materials correctly. We test this hypothesis
by analyzing the mode-resolved specularity parameters computed separately for
transmission and reflection processes at a graphene grain boundary. Our results
show that backward scattering is considerably more diffuse than forward
scattering at most frequencies and polarizations, providing strong evidence for
Li and McGaughey's hypothesis, and shed new light on how surfaces and
interfaces modify phonon transport within and between domains in nanostructured
materials.
