Vibrational Entropy Stabilizes Distorted Half-Heusler Structures

First-principles methods have been extensively used for prediction of half-Heusler (HH) phases for a wide range of functional properties. However, in some cases, suggested stable HHs are observed to be distorted phases (P63mc or Pnma) in experiments. We examine the impact of vibrational entropy on the thermodynamics of HH and competing low-symmetry phases by performing phonon calculations. We find that, in general, the lower symmetry phases have larger vibrational entropies, favoring their stability at higher temperatures. The high vibrational entropy of the distorted phase possibly comes from the weak bonding associated with larger atom motion, which leads to a large phonon density of states at low frequency. Our work explains the discrepancy between first-principles predictions and experimental phase stability and emphasizes the important effect of including vibrational entropy on the phase stability.