Nanoclusters in bcc-Fe containing vacancies, copper and nickel: Structure and energetics

Highlights: → Fe-Cu-Ni model alloys for RPV steels. → Atomistic simulation, mainly MMC and MD simulations. → Finding the most stable configurations of defect clusters. → Energetics of clusters, formation and binding energies. → Size dependence of monomer binding energy formula as input for OKMC methods. - Abstract: The most stable atomic configuration of coherent nanoclusters in bcc-Fe formed by vacancies, Cu and Ni as well as the corresponding energetics are determined by on-lattice simulated annealing and subsequent off-lattice relaxation. An interatomic potential recently designed for investigations of radiation-induced effects in the ternary Fe-Cu-Ni system is used in the atomistic simulations. Ternary vlCumNin clusters show a core-shell structure with vacancies in the core coated by a shell of Cu atoms, followed by a shell of Ni atoms. In binary CumNin clusters the Cu core is covered by a shell of Ni atoms. On the contrary, binary vlNin clusters consist of a pure vacancy cluster surrounded by an agglomeration of Ni atoms. The latter is similar to a pure Ni cluster (Nin) and consists of Ni atoms at the second nearest neighbor distance. Because of this special arrangement of atoms vlNin and Nin are also called quasi-clusters. In all clusters investigated Ni atoms may be nearest neighbors of Cu atoms but never nearest neighbors of vacancies or other Ni atoms. The atomic configurations found can be understood by the peculiarities of the binding between vacancies, Cu, Ni and Fe atoms. The structure obtained for CumNin clusters is in agreement with previous theoretical results and with indications from measurements while for the other clusters reference data are not available. It is shown that the presence of Ni atoms promotes the nucleation of clusters containing vacancies and Cu. This is in agreement with experimental observations and with recent results of atomic kinetic Monte Carlo simulations. Based on the specific atomic structure of the clusters and the capillary model, compact and rather accurate analytical formulae for the total binding energy have been derived from the results of the atomistic simulations. Other important energetic characteristics of clusters, e.g. monomer or dimer binding energies, can be easily obtained from these analytical expressions and can be used in rate theory or object kinetic Monte Carlo simulations of nanocluster evolution.