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

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. Ternary v_l Cu_m Ni_n 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 Cu_m Ni_n clusters the Cu core is covered by a shell of Ni atoms. On the contrary, binary v_l Ni_n clusters consist of a pure vacancy cluster surrounded by an agglomeration of Ni atoms. The latter is similar to a pure Ni cluster (Ni_n) and consists of Ni atoms at the second nearest neighbor distance. In all clusters investigated Ni atoms may be nearest neighbors of Cu atoms but never nearest neighbors of vacancies or other Ni atoms. The structure obtained for Cu_m Ni_n 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 recent theoretical results Compact and rather accurate analytical formulae for the total binding energy have been derived from the results of the atomistic simulations. These relations can be used in rate theory or object kinetic Monte Carlo simulations of nanocluster evolution.