Predicting the elastic, phonon and thermodynamic properties of cubic HfNiX (X = Ge and Sn) Half Heulser alloys: a DFT study

In this work, details density functional theory calculations were performed to obtain the electronic, elastic, phonon and thermodynamic properties of half-Heusler alloys HfNiX (X = Ge and Sn). The PBE functional as implemented in Projector augmented-wave (PAW) pseudopotentials was used for all the calculations. From our results, we reported the energy gap of 0.38 eV for HfNiSn and 0.61 eV for HfNiGe indicating the semiconductor property of these compounds. Also, the mechanical and elastical stabilities of these compounds were confirmed from the comparison of the elastic constants of these compounds with conditions for stabilities. Although the phonon dispersion curves for HfNiGe and HfNiSn are similar with splitting at the Γ point, the shift in their frequency was as a result of the mass different in Ge and Sn. The phonon dispersion curve predicts the dynamically stabilities of these half-Heusler alloys. From the thermodynamic properties of these compounds, it was revealed that these compounds are soft at low temperature, but at a high temperature they tend to be hard materials. Our calculations showed that these two compounds are mechanically, elastically and dynamically stable as cubic half-Heusler alloys.