A Unified Understanding of Minimum Lattice Thermal Conductivity

We propose a first-principles model of minimum lattice thermal conductivity ($\kappa_{\rm L}^{\rm min}$) based on a unified theoretical treatment of thermal transport in crystals and glasses. We apply this model to thousands of inorganic compounds and discover a universal behavior of $\kappa_{\rm L}^{\rm min}$ in crystals in the high-temperature limit: the isotropically averaged $\kappa_{\rm L}^{\rm min}$ is independent of structural complexity and bounded within a range from $\sim$0.1 to $\sim$2.6 W/[m$\cdot$K], in striking contrast to the conventional phonon gas model which predicts no lower bound. We unveil the underlying physics by showing that for a given parent compound $\kappa_{\rm L}^{\rm min}$ is bounded from below by a value that is approximately insensitive to disorder, but the relative importance of different heat transport channels (phonon gas versus diffuson) depends strongly on the degree of disorder. Moreover, we propose that the diffuson-dominated $\kappa_{\rm L}^{\rm min}$ in complex and disordered compounds might be effectively approximated by the phonon gas model for an ordered compound by averaging out disorder and applying phonon unfolding. With these insights, we further bridge the knowledge gap between our model and the well-known Cahill-Watson-Pohl (CWP) model, rationalizing the successes and limitations of the CWP model in the absence of heat transfer mediated by diffusons. Finally, we construct graph network and random forest machine learning models to extend our predictions to all compounds within the Inorganic Crystal Structure Database (ICSD), which were validated against thermoelectric materials possessing experimentally measured ultralow $\kappa_{\rm L}$. Our work offers a unified understanding of $\kappa_{\rm L}^{\rm min}$, which can guide the rational engineering of materials to achieve $\kappa_{\rm L}^{\rm min}$.