Non-equilibrium vacancy formation energies in metastable alloys - A case study of Ti_(0.5)Al_(0.5)N

摘要

In this study, we present a computational technique to investigate non-equilibrium vacancies in metastable alloys. In contrast to equilibrium materials, calculation of the energy of removing an alloying atom requires a finite size configurational correction. We explain that in metastable alloys the vacancy formation energy is defined up to an arbitrary constant. We argue that in non-equilibrium alloys no statistical considerations are required and there is a distribution of the vacancy formation energy with large variation. We show for the example of Ti0.5Al0.5N that the configuration correction is significant. Using cluster expansion, we demonstrate the major importance of the first two metallic coordination shells in Ti0.5Al0.5N. We introduce a three-dimensional representation of the energies of removing Ti and Al atoms as a function of number of Al atoms in the neighboring shells and we predict the metal atom vacancy formation energy in arbitrary local chemical environments. Neglecting the interactions between the vacant sites and assuming their simultaneous occurrence, we show how to extract information about the energy cost of a vacancy concentration in metastable alloys. We conclude that in metastable disordered alloys vacancies should occur in local environments that correspond to the lowest formation energies rather than distributed statistically. (C) 2016 Elsevier Ltd. All rights reserved.