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In this work we calculate the thermoelectric figure of merit of XHfPb (X= Ni,Pd, and Pt) by computing the both the power factor and the lattice thermalconductivity by first principles. We make reasonable approximations: we use theConstant Relaxation Time Approximation (CRTA) to compute the electron transportcontribution and the modified Debye-Callaway model to calculate the thermallattice conductivity. We also report the dielectric properties of thesesemiconductors and the mode Gr\"uneisen parameters. Not surprisingly we findthat the average Gr\"uneisen coefficient correlates with the tehrmalconductivity. Next, we consider a realistic relaxation time $\tau$ and carrierconcentration $n$ from experimental data on ZrHfPb and obtain the figure ofmerit $ZT$ as a function of temperature. Our main finding is that despite thePt is isoelectronic with Ni and Pd, the $ZT$ of PtHfPb is larger and behavesdifferently from the other two materials, suggesting that PtHfPb is bettersuited for high temperature thermoelectric generators.

Electronic and phonon contributions to the Thermoelectric properties of newly discovered half-Heusler alloys XHfPb (X= Ni, Pd, and Pt)