  In spite of their importance for understanding phonon transport phenomena in
thin films and polycrystalline solids, the effects of boundary roughness
scattering on phonon specularity and coherence are poorly understood because
there is no general method for predicting their dependence on phonon momentum,
frequency, branch and boundary morphology. Using the recently formulated
atomistic S-matrix method, we develop a theory of boundary roughness scattering
to determine the mode-resolved phonon coherence and specularity parameters from
the scattering amplitudes. To illustrate the theory, we apply it to phonon
scattering in realistic nonsymmetric graphene grain boundary (GB) models
derived from atomic structure predictions. The method is validated by comparing
its predictions with frequency-resolved results from lattice dynamics-based
calculations. We prove that incoherent scattering is almost perfectly
diffusive. We show that phonon scattering at the graphene GB is not diffuse
although coherence and specularity are significantly reduced for
long-wavelength flexural acoustic phonons. Our approach can be generalized to
other atomistic boundary models.
