First Principles Validation of Energy Barriers in Ni$_{75}$Al$_{25}$

Abstract

Precipitates in Nickel-based superalloys form during heat treatment on a time scale inaccessible to direct molecular dynamics simulation, but could be studied using kinetic Monte Carlo (KMC). This requires reliable values for the barrier energies separating distinct configurations over the trajectory of the system. In this study, we validate vacancy migration barriers found with the Activation-Relaxation Technique nouveau (ARTn) method in partially ordered Ni$_{75}$Al$_{25}$ with a monovacancy using published potentials for the atomic interactions against first-principles methods. In a first step, we confirm that the ARTn barrier energies agree with those determined with the nudged elastic band (NEB) method. As the number of atoms used in those calculations is too great for direct ab initio calculations, we then cut the cell size to 255 atoms, thus controlling finite size effects. We then use the plane-wave density functional theory (DFT) code CASTEP and its inbuilt NEB method in the smaller cells. This provides us with a continuous validation chain from first principles to kinetic Monte Carlo simulations with interatomic potentials. We then evaluate the barrier energies of five further interatomic potentials with NEB, demonstrating that none yields these with sufficient reliability for KMC simulations, with some of them failing completely. This is a first step towards quantifying the errors incurred in KMC simulations of precipitate formation and evolution.