Melting and freezing phenomena

Clusters of atoms and molecules lend themselves to the study of phase changes because they are susceptible to the analytic and computational methods appropriate for small systems, yet allow the study of size dependence, even approaching the bulk limit. Clusters not only give insights into the nature of bulk phase transitions,. they have many properties unique to small systems, such as bands of temperature and pressure within which phaselike forms may coexist-not just curves of coexistence. Moreover, more than two phaselike forms may coexist in such bands; in fact, clusters may exhibit phaselike forms that do not exist for bulk matter. These properties of coexistence are the consequence of the small differences between the free energies of the clusters in different, phaselike forms, yet theory predicts that these bands of coexistence have sharp boundaries, due to the disappearance of local stability of each phaselike form. In contrast also to bulk phase equilibrium, coexistence of phaselike forms of clusters and nanoscale particles is a dynamic equilibrium, lie that of chemical isomers. Hence, for clusters to exhibit a particular phase, they must dwell in the region of configuration and phase space appropriate to that phase long enough to establish equilibriumlike properties associated with that phase, and not with the entire configuration or phase space. These phenomena come at the cost of loss of the sharp distinction between ''phase'' and ''component,'' and the inapplicability of the Gibbs phase rule.