Anisotropic Klemens Model for the Thermal Conductivity Tensor and Its Size Effect

With the constraint from Onsager reciprocity relations, here we generalize the Klemens model for intrinsic phonon-phonon scattering from isotropic to anisotropic. Combined with the anisotropic Debye dispersion, this anisotropic Klemens model leads to analytical expressions for heat transfer along both ab-plane (κab) and c-axis (κc), suitable for both layered and chainlike materials with any anisotropy ratio of the dispersion and the scattering. This combination of dispersion and scattering is further applied to the equation of phonon radiative transfer to model heat conduction across anisotropic thin films. The model is compared to experimental κab and κc of bulk graphite at high temperatures (T≥0.1×max(θD,ab,θD,c), where θD,ab and θD,c are the two Debye temperatures), leading to best-fit scattering parameters that capture the harmonic and anharmonic nature of the intra- and inter-layer bonding of graphite. With no further adjusting of these parameters, the anisotropic scattering model performs at least 9 times better than the isotropic one at explaining the experimental κc of graphite thin films. This size effect is further justified by comparing the accumulation function of κc.