Lattice thermal conductivity of Ti${}_x$Zr${}_y$Hf${}_{1-x-y}$NiSn half-Heusler alloys calculated from first principles: Key role of nature of phonon modes

Abstract

In spite of their relatively high lattice thermal conductivity ${\kappa }_{\ell }$, the XNiSn (X=Ti, Zr or Hf) half-Heusler compounds are good thermoelectric materials. Previous studies have shown that ${\kappa }_{\ell }$ can be reduced by sublattice-alloying on the X-site. To cast light on how the alloy composition affects ${\kappa }_{\ell }$, 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 Ti${}_x$Zr${}_y$Hf${}_{1-x-y}$NiSn phase diagram. The lowest lattice thermal conductivity is found for the Ti${}_x$Hf${}_{1-x}$NiSn compositions; in particular, there is a shallow minimum centered at Ti${}_{0.5}$Hf${}_{0.5}$NiSn with ${\kappa }_l$ 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, Ti${}_{0.5}$Hf${}_{0.5}$NiSn with a grain size of $L=100$ nm experiences a 42\% reduction of ${\kappa }_{\ell }$ compared to that of the single crystal.

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• Electronic and phonon contributions to the Thermoelectric properties of newly discovered half-Heusler alloys XHfPb (X= Ni, Pd, and Pt)
• Uncertainty quantification in first-principles predictions of phonon properties and lattice thermal conductivity
• Discarded gems: Thermoelectric performance of materials with band gap emerging at the hybrid-functional level