  Recently, an anisotropic Debye model [Dames et al., Physical Review B 87, 12
(2013)] was proposed for calculations of the interfacial thermal conductance
and the minimum thermal conductivity of graphite-like layered materials.
Despite successes of the model in explaining heat transport mechanisms in
layered materials (e.g., phonon focusing in highly anisotropic materials), the
anisotropic Debye model assumes a phonon dispersion with unrealistic speeds of
sounds especially for the flexural (ZA) phonons and overestimated cutoffs for
all phonon branches. The deficiencies lead to substantially underestimated
phonon irradiation for low-frequency phonons. Here, we develop an anisotropic
model with truncated linear dispersion that resembles the real phonon
dispersion, using speeds of sounds derived from elastic constants and cutoff
frequencies derived from Brillouin zone boundaries. We also employ a piecewise
linear function for the ZA phonons. Our model correctly calculates the phonon
irradiation over a wide temperature range, verifying the accuracy of our
model.We compare calculations of our and the Dames models to measurements of
thermal conductivity of graphite and thermal conductance of metal/graphite
interfaces, and find that the two models differ significantly for heat
transport across the basal planes in graphite even at high temperatures. Our
work thus provides a convenient analytical tool to study the phonon transport
properties in layered materials.
