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Thermoelectric properties of half-Heusler $\mathrm{ZrNiPb}$ by using first principles calculations

We investigate electronic structures and thermoelectric properties of recent synthetic half-Heusler $\mathrm{ZrNiPb}$ by using generalized gradient approximation (GGA) and GGA plus spin-orbit coupling (GGA+SOC). Calculated results show that $\mathrm{ZrNiPb}$ is a indirect-gap semiconductor. Within the constant scattering time approximation, semi-classic transport coefficients are performed through solving Boltzmann transport equations. It is found that the SOC has more obvious influence on power factor in p-type doping than in n-type doping, leading to a detrimental effect in p-type doping. These can be explained by considering the SOC influences on the valence bands and conduction bands near the Fermi level. The lattice thermal conductivity as a function of temperature is calculated, and the corresponding lattice thermal conductivity is 14.5 $\mathrm{W m^{-1} K^{-1}}$ at room temperature. By comparing the experimental transport coefficients with calculated ones, the scattering time is attained for 0.333 $\times$ $10^{-14}$ s. Finally, the thermoelectric figure of merit $ZT$ can be attained, and the $ZT$ value can be as high as 0.30 at high temperature by choosing appropriate doping level. It is possible to reduce lattice thermal conductivity by point defects and boundaries, and make half-Heusler $\mathrm{ZrNiPb}$ become potential candidate for efficient thermoelectricity.