Size effects on the phase diagrams of nanoparticles of various shapes

It is known that the melting point and other phase transitions in nanoparticles vary with their size. Some crystal phases also appear preferentially in nanoparticles. These also depend on the chemical environment and the encapsulation of nanosystems. Although their shape is usually considered to be spherical-like, nanoparticles of various shapes (disks, rods, etc.) may be prepared experimentally. It is shown that, in the limit where thermodynamical arguments remain valid, the phase diagrams of nanoparticles are a function of both their size and shape. This is demonstrated for various geometrical figures. The implications for the modelling of processes involving nanoparticles are discussed.