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

TL;DR

This study uses first-principles calculations to analyze how alloy composition and phonon mode nature influence the lattice thermal conductivity of Ti$_x$Zr$_y$Hf$_{1-x-y}$NiSn half-Heusler alloys, revealing optimal compositions and the potential of nanostructuring for further reduction.

Contribution

It provides a detailed first-principles analysis of alloy composition effects on thermal conductivity, highlighting the importance of phonon mode nature and mass-disorder scattering in thermoelectric materials.

Findings

Lowest thermal conductivity at Ti$_x$Hf$_{1-x}$NiSn compositions.

Shallow minimum at Ti$_{0.5}$Hf$_{0.5}$NiSn with $rac{3.2}{4.1}$ W/mK.

Nanostructuring can reduce thermal conductivity by up to 42%.

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.