Introductory lecture. Clusters, melting, freezing and phase transitions

The nature of the equilibrium between liquid-like and solid-like clusters is reviewed, in terms of the conditions under which sharp transitions may or may not occur. These conditions may be expressed in terms of characteristics of the potential surface of the cluster. The connection between solid–liquid phase equilibrium of clusters and the first-order melting and freezing transition of bulk matter is discussed, both in terms of how the sharp melting point of bulk matter evolves from the corresponding temperature of larger and larger clusters, and in terms of the connection between the finite range of solid–liquid coexistence of clusters and the range within which metastable supercooled or suerheated bulk material may exist.