An anisotropic model for the minimum thermal conductivity

Abstract

The Cahill-Pohl/Einstein model of minimum phonon thermal conductivity (κmin), which assumes isotropic material properties, is widely successful as the lower limit for fully dense amorphous and disordered materials. However, measurements of disordered highly anisotropic layered WSe2 [Chiritescu et al., Science 315, 351 (2007)] fall below the isotropic κmin limit by at least a factor of four. Here, we generalize the isotropic κmin to be anisotropic, suitable for both layered and chain-like materials with any anisotropy ratio. We obtain compact algebraic expressions in limiting temperature regimes for heat transfer along both c-axis (κmin−c) and ab-plane (κmin−ab). Applying this framework to the disordered layered WSe2 with no free parameters brings the theoretical κmin−c back in line with the experimental results. The anisotropic corrections result from both a phonon focusing effect and a first Brillouin zone truncation effect.