Superficial segregation in nanoparticles: from facets to infinite surfaces

We compare the superficial segregations of the Cu-Ag system for a nanoparticle and for surfaces that are structurally equivalent to each of its facet. Based on a lattice-gas model and within a mean-field formalism, we derive segregation isotherms at various temperatures in the canonical ensemble, i.e., for a given overall solute concentration, and in the semigrand canonical ensemble, i.e., for a given bulk solute concentration. If both processes are very similar for high temperatures, they differ substantially at lower temperatures. Due to the finite-size effect and the indirect coupling between facets and edges, the relative position of the phase transitions of the facets and the corresponding surfaces is inversed when displayed as a function of the solute bulk concentration. Moreover, we show that working in the semigrand canonical ensemble is a much more efficient way to study this phenomenon, although nanoparticles are "canonical" objects in essence.