Thermoelectric properties, efficiency and thermal expansion of ZrNiSn half-Heusler by first-principles calculations

In this work, we try to understand the experimental thermoelectric (TE) properties of a ZrNiSn sample with DFT and semiclassical transport calculations using SCAN functional. SCAN and mBJ provide the same band gap Eg of ∼0.54 eV. This Eg is found to be inadequate to explain the experimental data. The better explanation of experimental Seebeck coefficient S is done by considering Eg of 0.18 eV which suggests the non-stoichiometry and/or disorder in the sample. In the calculation of S and other TE properties temperature dependence on chemical potential is included. In order to look for the possible enhanced TE properties obtainable in ZrNiSn with Eg of ∼0.54 eV, power factor and optimal carrier concentrations are calculated. The optimal electron and hole concentrations required to attain highest power factors are ∼7.6 × 1019 cm−3 and ∼1.5 × 1021 cm−3, respectively. The maximum figure of merit ZT calculated at 1200 K for n-type and p-type ZrNiSn are ∼0.5 and ∼0.6, respectively. The % efficiency obtained for n-type ZrNiSn is ∼4.2% while for p-type ZrNiSn is ∼5.1%. The ZT are expected to be further enhanced to ∼1.1 (n-type) and ∼1.2 (p-type) at 1200 K by doping with heavy elements for thermal conductivity reduction. The phonon properties are also studied by calculating dispersion, total and partial density of states. The calculated Debye temperature of 382 K is in good agreement with experimental value of 398 K. The thermal expansion behaviour in ZrNiSn is studied under quasi-harmonic approximation. The average linear thermal expansion coefficient αave(T) of ∼7.8 × 10−6 K−1 calculated in our work is quite close to the experimental values. The calculated linear thermal expansion coefficient will be useful in designing the thermoelectric generators for high temperature applications.