On the binding energies and configurations of vacancy and copper–vacancy clusters in bcc Fe–Cu:a computational study

Abstract

Vacancy and copper–vacancy clusters in bcc Fe–Cu alloys have been studied using a combination of metropolis Monte Carlo (MMC) and molecular dynamics (MD) techniques, to investigate their lowest energy configurations and corresponding binding energies, for sizes up to a few hundreds of elements (∼2 nm). Two different many-body interatomic potentials were used to perform the calculations, in order to assess the robustness of the results 1, 2. Empirical expressions for the binding energies, of immediate use in kinetic Monte Carlo (KMC) or rate theory (RT) models, have been obtained. It is observed that vacancy clusters are three-dimensional cavities whose shape is primarily determined by a criterion of maximisation of the number of first and second nearest neighbour pairs. Copper atoms, when present, tend to coat an inner vacancy cluster, while remaining first nearest neighbours to each other. The inner vacancy cluster, when completely coated, tends to be as close as possible to the surface of the hollow precipitate. These findings are consistent with previous experimental and computational work. The binding energy of these complexes is a monotonously growing function of the ratio number of vacancies to number of copper atoms. Pure copper precipitates appear to follow a loose criterion of maximisation of first nearest neighbour pairs. While the two interatomic potentials used in this work provide largely similar values for the binding energies and comparable configurations, some differences are found and discussed. Subtle differences observed in comparison with ab initio calculations are also discussed.