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 gapof ∼0.54 eV. Thisis found to be inadequate to explain the experimental data. The better explanation of experimental Seebeck coefficientis done by consideringof 0.18 eV which suggests the non-stoichiometry and/or disorder in the sample. In the calculation ofand other TE properties temperature dependence on chemical potential is included. In order to look for the possible enhanced TE properties obtainable in ZrNiSn withof ∼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 × 10cmand ∼1.5 × 10cm, respectively. The maximum figure of meritcalculated 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%. Theare 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() of ∼7.8 × 10Kcalculated 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.