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.

Acknowledgements

Fruitful discussions with C.S. Becquart, C. Domain, and A. Legris regarding the interpretation of these results and the relevant workplan are acknowledged. Special thanks to F. Djurabekova who revised some of the original data for binding energies of small clusters, thereby reducing the number of possible mistakes. This work was started as convention between SCK•CEN and ULB in the framework of the international REVE initiative; it was later partially funded by the Belgian Federal Scientific Policy Office, in the framework of the co-operation agreement between Belgium and Argentina (contract BL/52/A01), and partially by the PERFECT IP (contract F160-CT-2003-508840).

Notes

§On leave from: A.F. Ioffe Physico-Technical Institute of the RAS, Polytechnicheskaya Str. 26, 194021 St. Petersburg (Russia).

†Note that for very small clusters the linear interpolation is as good as any other. Even up to N _V ∼ 30 the exponent of the interpolating power law is still larger than 2/3 (around 0.75). Only well above size 30 the surface effect becomes predominant and a 2/3 exponent clearly starts providing the best fit.

†Note, however, that the global picture may be partially modified if a binding energy between 2 nn Cu–V pairs was foreseen by the used interatomic potential, consistently with ab initio results.

Additional information

Notes on contributors

D. Kulikov§

§On leave from: A.F. Ioffe Physico-Technical Institute of the RAS, Polytechnicheskaya Str. 26, 194021 St. Petersburg (Russia).