Dynamical equilibrium in nanoalloys

Using Monte Carlo simulations on a lattice-gas model, we study the segregation isotherm of a cluster made of thousands of atoms for a system that tends to phase separate, e.g., Cu-Ag. We show that the Ag segregation involves the vertices first, then the edges and finally the (111) and (100) facets. In these facets, the segregation starts on the outer shells, leading to a heterogeneous chemical composition. When the nominal Ag concentration (or the chemical potential difference delta(mu)c between Ag and Cu), is increased a dynamical equilibrium replaces the progressive evolution of the segregation towards the core of the facets: the whole facet oscillates between one pseudo Ag-pure state and another one corresponding to a rather Cu-pure core surrounded by Ag-enriched outer shells. A remarkable consequence is that very different concentrations can be observed for facets of equivalent orientation. This dynamical equilibrium occurs in a delta(mu) range that is very close to the critical value delta(mu)c associated with the first-order phase transition of the Fowler-Guggenheim type that affects the surfaces of semi-infinite alloys. These results, which have been obtained in the grand-canonical ensemble, can also be derived in the canonical ensemble due to a sufficient number of facets that behave with each other as a reservoir.