Lattice dynamics and thermodynamic investigation of MNiSn (M = Hf, Ti and Zr) Half-Heusler compounds: Density functional theory approach

Abstract First-principles calculations have been performed using density functional theory, within the generalized gradient approximation implemented in quantum espresso, to compute the structural properties of MNiSn where (M = Hf, Ti and Zr) half-Heusler alloys. The optimized lattice constants for the three compounds agree more with experimental values when compared to other theoretical results despite its overestimation. The calculated elastic constants from the linear fit of stress strain relationship affirm the elastic stability of these alloys. Density functional perturbation theory was adopted in the investigation of their lattice dynamics and the positive frequency observed across the entire brillouin zone of the phonon dispersion spectra is a strong indication of dynamical stability of these compounds. The computed phonon density of states display the allowed frequencies at every point across the entire brillouin zone and also, it was the essential information used in computing the thermodynamic properties within the harmonic approximation. The thermodynamic properties for the three alloys were studied between 0 K and 1000 K in order to minimize the potential effect of an harmonicity, the results show that the internal energies and entropies increase while the vibrational energies decrease with increasing temperature, and the specific heat capacities at constant volume increase significantly between the temperature range of 0–200 K while slight increment were observed at higher temperature until they approaches asymptotic limit of 73.8 Jmol−1K.