Thermodynamics of phase-separating nanoalloys: Single particles and particle assemblies

The aim of this paper is to investigate the consequences of finite-size effects on the thermodynamics of nanoparticle assemblies and isolated particles. We consider a binary phase-separating alloy with a negligible atomic size mismatch, and equilibrium states are computed using off-lattice Monte Carlo simulations in several thermodynamic ensembles. First, a semi-grand-canonical ensemble is used to describe infinite assemblies of particles with the same size. When decreasing the particle size, we obtain a significant decrease of the solid/liquid transition temperatures as well as a growing asymmetry of the solid-state miscibility gap related to surface segregation effects. Second, a canonical ensemble is used to analyze the thermodynamic equilibrium of finite monodisperse particle assemblies. Using a general thermodynamic formulation, we show that a particle assembly may split into two subassemblies of identical particles. Moreover, if the overall average canonical concentration belongs to a discrete spectrum, the subassembly concentrations are equal to the semi-grand-canonical equilibrium ones. We also show that the equilibrium of a particle assembly with a prescribed size distribution combines a size effect and the fact that a given particle size assembly can adopt two configurations. Finally, we have considered the thermodynamics of an isolated particle to analyze whether a phase separation can be defined within a particle. When studying rather large nanoparticles, we found that the region in which a two-phase domain can be identified inside a particle is well below the bulk phase diagram, but the concentration of the homogeneous core remains very close to the bulk solubility limit.