Lattice thermal conductivity ofTixZryHf1−x−yNiSnhalf-Heusler alloys calculated from first principles: Key role of nature of phonon modes

In spite of their relatively high lattice thermal conductivity ${\ensuremath{\kappa}}_{\ensuremath{\ell}}$, the $X\mathrm{NiSn}$ ($X=\text{Ti}$, Zr, or Hf) half-Heusler compounds are good thermoelectric materials. Previous studies have shown that ${\ensuremath{\kappa}}_{\ensuremath{\ell}}$ can be reduced by sublattice alloying on the $X$ site. To cast light on how the alloy composition affects ${\ensuremath{\kappa}}_{\ensuremath{\ell}}$, we study this system using the phonon Boltzmann-transport equation within the relaxation time approximation in conjunction with density functional theory. The effect of alloying through mass-disorder scattering is explored using the virtual crystal approximation to screen the entire ternary ${\mathrm{Ti}}_{x}{\mathrm{Zr}}_{y}{\mathrm{Hf}}_{1\ensuremath{-}x\ensuremath{-}y}\mathrm{NiSn}$ phase diagram. The lowest lattice thermal conductivity is found for the ${\mathrm{Ti}}_{x}{\mathrm{Hf}}_{1\ensuremath{-}x}\mathrm{NiSn}$ compositions; in particular, there is a shallow minimum centered at ${\mathrm{Ti}}_{0.5}{\mathrm{Hf}}_{0.5}\mathrm{NiSn}$ with ${\ensuremath{\kappa}}_{\ensuremath{\ell}}$ taking values between 3.2 and 4.1 W/mK when the Ti content varies between 20% and 80%. Interestingly, the overall behavior of mass-disorder scattering in this system can only be understood from a combination of the nature of the phonon modes and the magnitude of the mass variance. Mass-disorder scattering is not effective at scattering acoustic phonons of low energy. By using a simple model of grain boundary scattering, we find that nanostructuring these compounds can scatter such phonons effectively and thus further reduce the lattice thermal conductivity; for instance, ${\mathrm{Ti}}_{0.5}{\mathrm{Hf}}_{0.5}\mathrm{NiSn}$ with a grain size of $L=100$ nm experiences a 42% reduction of ${\ensuremath{\kappa}}_{\ensuremath{\ell}}$ compared to that of the single crystal.