An anisotropic model for the minimum thermal conductivity

The Cahill-Pohl/Einstein model of minimum phonon thermal conductivity (kappa(min)), 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 kappa(min) limit by at least a factor of four. Here, we generalize the isotropic kappa(min) 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 (kappa(min-c)) and ab-plane (kappa(min-ab)). Applying this framework to the disordered layered WSe2 with no free parameters brings the theoretical kappa(min-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. (C) 2015 AIP Publishing LLC.