Vacancy formation energies in concentrated solid solutions: from atomistic simulations to thermodynamics

Abstract

A method to calculate the vacancy formation energy in disordered alloys is presented. Classical molecular statics coupled with statistical mechanical concepts are used to produce a relatively simpler approach when compared to other more lengthy calculation methods of the literature. For disordered alloys one should note that, i) the vacancy is not a unique defect but possesses a distribution of energies depending on its local chemical environment, and ii) it is physically inconsistent to associate the empty site with the species of the missing atom. Usually, calculations involve comparing boxes with and without the defect, which must be compensated to possess the same number of atoms across species, thus issue ii) is likely to be present to some extent. To our knowledge, this observation has never been analysed in detail and, moreover, has been the source of some confusion in the literature. The method here developed handles both complexities in a consistent manner. For testing purposes, three model systems are considered: i) various rigid lattice AB alloys with nearest neighbour interaction parameters, ii) an fcc equimolar FeNi alloy, and iii) a bcc U-10wt%Mo alloy. Overall, we obtain a reasonable comparison in the temperature ranges tested, but close to order/disorder transformations.