Using the Callaway Model to Deduce Relevant Phonon Scattering Processes: The Importance of Phonon Dispersion

The thermal conductivity $\kappa$ of a material is an important parameter in many different applications. Optimization strategies of $\kappa$ often require insight into the dominant phonon scattering processes of the material under study. The Callaway model is widely used as an experimentalist's tool to analyze the lattice part of the thermal conductivity, $\kappa_l$. Here, we investigate how deviations from the implicitly assumed linear phonon dispersion relation affect $\kappa_l$ and in turn conclusions regarding the relevant phonon scattering processes. As an example, we show for the half-Heusler system (Hf,Zr,Ti)NiSn, that relying on the Callaway model in its simplest form has earlier resulted in a misinterpretation of experimental values by assigning the low measured $\kappa_l$ with unphysically strong phonon scattering in these materials. Instead, we propose an implementation of more realistic phonon dispersion curves, combined with empirical expressions for typical phonon scattering processes, which leads to far better quantitative agreement with both theoretical and experimental values. This method can easily be extended to other materials with known phonon dispersion relations.