Approximate Models for the Lattice Thermal Conductivity of Alloy Thermoelectrics

Thermoelectric generators (TEGs) convert waste heat to electricity and are a leading contender for improving energy efficiency at a range of scales. Ideal TE materials show a large Seebeck effect, high electrical conductivity, and low thermal conductivity. Alloying is a widely-used approach to engineering the heat transport in TEs, but despite many successes the underlying mechanisms are poorly understood. In previous work, first-principles modelling has successfully been used to study the thermodynamics of alloy formation and to investigate its effect on the electronic structure and phonon spectrum. However, it has so far only been possible to examine qualitatively the impact of alloying on the lattice thermal conductivity. In this work, we develop and test two new approaches to addressing this. The constant relaxation-time approximation (CRTA) assumes the primary effect of alloying is on the phonon group velocities, and allows the thermal conductivity to be calculated assuming a suitable constant lifetime. Alternatively, setting the three-phonon interaction strengths to a constant further enables an assessment of how changes to the phonon frequency spectrum influence the lifetimes. We test both approaches for the Pnma Sn(S_1-xSe_x) alloy system and are able to account for the substantially-reduced thermal conductivity measured in experiments.