Rationalizing phonon dispersion for lattice thermal conductivity of solids

Lattice thermal conductivity (kappa(L)) is one of the most fundamental properties of solids. The acoustic-elastic-wave assumption, proposed by Debye (Debye P. Ann Phys 1912; 344: 789-839), has led to linear phonon dispersion being the most common approximation for understanding phonon transport over the past century. Such an assumption does not take into account the effect of a periodic boundary condition on the phonon dispersion, originating from the nature of periodicity on atomic arrangements. Driven by modern demands on the thermal functionality of materials, with kappa(L) ranging from ultra-low to ultra-high, any deviation from the Debye approximation in real materials becomes more and more significant. This work takes into account the periodic boundary condition, and therefore rationalizes the phonon dispersion to be more realistic. This significantly improves the precision for quickly predicting kappa(L) without any fitting parameters, as demonstrated in hundreds of materials, and offers a theoretical basis rationalizing kappa(L) to be lower than the minimum currently accepted based on the Debye dispersion. This work paves the way for designing solids with expected kappa(L) and particularly inspires the advancement of low-kappa(L) materials for thermal energy applications.