Strain field fluctuation effects on lattice thermal conductivity of $ZrNiSn$-based thermoelectric compounds

We present a model calculation of the lattice thermal conductivity of $ZrNiSn$-based half-Heusler thermoelectric compounds for temperatures where phonon scattering is dominated by Umklapp and point defect scattering. The difference in mass between impurity and host atoms dominates point defect scattering for alloying $Hf$ on the $Zr$ sublattice, whereas differences in size and interatomic coupling forces between impurity and host atoms dominate point defect scattering for alloying $Pd$ on the $Ni$ sublattice. Because $Pt$ is heavier and larger than $Pd$⁠, we predict that $Pt$ will further reduce lattice thermal conductivity when alloyed on the $Ni$ sublattice of these half-Heusler compounds.