Solidification loops in the phase diagram of nanoscale alloy particles: from a specific example towards a general vision

Interface contributions as well as size confinement effects need to be taken into account into the description of phase equilibria and phase transformations in nanoscale systems. Here, a modified Gibbsian thermodynamic approach has been suggested to describe the solidification of a nano-sized liquid alloy droplet and the equilibrium states in the two-phase region of the phase diagram. Cu–Ni has been chosen as a model system due to the availability of thermodynamic data. This description shows for the first time the occurrence of solidification loops at the size-dependent temperature–composition phase diagram for the isolated Cu–Ni nano-droplet, showing two-phase equilibrium states for droplet radii of 25 and 40 nm, i.e. well within the size domain of nanoparticles that are, for example, used for applications in additive manufacturing. Furthermore, the current results show quantitatively that these equilibrium loops that are specific for the nano-sized systems do not coincide with the solubility curve. It leads to the new “solidification loop” concept concerning the phase diagram introduced in the paper. The isolated liquid Cu–Ni nanoscale droplet can actually crystallize along different trajectories, whereas the dominant transition type is comparable to homogeneous nucleation that proceeds from the inner part of the droplet towards the surface: the newly formed phase after initial nucleation is a Ni-rich crystal with a Cu-rich liquid shell. The decrease in the nanoparticle size causes the decrease in the solidification temperature and the temperature width of the phase transition, the increase in the solubility limit and the concentration width of the solidification loop as well as a change in the shape and slope of the equilibrium curves of the two-phase region of the phase diagram. For larger droplets, the size-dependent phase diagram approaches the well-known bulk phase diagram.