Uncovering design principles for amorphous-like heat conduction using two-channel lattice dynamics

The physics of heat conduction puts practical limits on many technological fields such as energy production, storage, and conversion. It is now widely appreciated that the phonon-gas model does not describe the full vibrational spectrum in amorphous materials, since this picture likely breaks down at higher frequencies. A two-channel heat conduction model, which uses harmonic vibrational states and lattice dynamics as a basis, has recently been shown to capture both crystal-like (phonon-gas channel) and amorphous-like (diffuson channel) heat conduction. While materials design principles for the phonon-gas channel are well established, similar understanding and control of the diffuson channel is lacking. In this work, in order to uncover design principles for the diffuson channel, we study structurally-complex crystalline Yb₁₄ (Mn,Mg)Sb₁₁, a champion thermoelectric material above 800 K, experimentally using inelastic neutron scattering and computationally using the two-channel lattice dynamical approach. Our results show that the diffuson channel indeed dominates in Yb₁₄MnSb₁₁ above 300 K. More importantly, we demonstrate a method for the rational design of amorphous-like heat conduction by considering the energetic proximity phonon modes and modifying them through chemical means. We show that increasing (decreasing) the mass on the Sb-site decreases (increases) the energy of these modes such that there is greater (smaller) overlap with Yb-dominated modes resulting in a higher (lower) thermal conductivity. This design strategy is exactly opposite of what is expected when the phonon-gas channel and/or common analytical models for the diffuson channel are considered, since in both cases an increase in atomic mass commonly leads to a decrease in thermal conductivity. This work demonstrates how two-channel lattice dynamics can not only quantitatively predict the relative importance of the phonon-gas and diffuson channels, but also lead to rational design strategies in materials where the diffuson channel is important.