The reduction of vibrational contributions to thermal transport and the search for material classes with intrinsically low lattice thermal conductivities are at the heart of thermoelectric research. Both engineering the heat transport of known thermoelectrics and searching for new material candidates is guided by understanding the physics of low thermal conduction. Spectral analytical models (e.g., the Callaway model) for propagating phonon transport have proved to be a powerful tool for interpreting experimental results and providing metrics for materials design. Now, however, it is known that another mechanism of phonon heat transport can occur in complex crystalline materials. Called diffusons, they describe the non-propagating atomic scale random-walk of thermal energy between energetically proximal phonon modes. While analytical models exist to describe both transport behaviors independently, an analytical model accounting for both transport channels simultaneously is necessary to interpret and design so-called 2-channel thermal transport. In this work, we propose an analytical 2-channel transport model that partitions the vibrational density of states into two transport regimes and subsequently accounts for both transport mechanisms. The model is then used to explain the experimental thermal conductivities of the solid solution series Ag9-xGa1-xGexSe6. In this series, substitution leads to the stabilization of a highly vacant Ag+ substructure, which is expected to induce strong point-defect phonon scattering. While the propagating phonons are strongly scattered at low temperatures, the diffuson channel is apparently unaffected. By establishing materials design metrics for 2-channel thermal transport from analytical theory, experimental investigations of materials with astonishingly low lattice thermal conductivities can now be better guided and informed.
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