Phonon dispersion or scattering: Pitfalls of the Callaway model analyzing the lattice thermal conductivity

The Callaway model is widely used as an experimentalist's tool to analyze the lattice thermal conductivity kl. We here investigate, how deviations from the implicitly assumed linear phonon dispersion relation affect kl. As an example, we show for the half-Heusler system (Hf,Zr,Ti)NiSn that relying on the Callaway model in its simplest form can easily result in a misinterpretation of experimental values by assigning the low measured kl with unphysically strong phonon scattering in these materials. Instead, we demonstrate that similar low values of kl are achieved by implementing a semi-empirical phonon dispersion into the Callaway model, which leads to far better quantitative agreement with both theoretical and experimental values.