Melting of clusters and melting

A model is presented for the melting and freezing behavior of finite clusters. The model has the property---and suggests that some real clusters may so behave---that the rigid, solidlike form is the only thermodynamically stable form below a "freezing" temperature T₅, that the solidlike form may coexist with a nonrigid, liquidlike form within a sharply-bounded range of temperatures between T₅ and a higher "melting" temperature T₌, and that above T₌, only the liquidlike form of cluster is thermodynamically stable. The temperatures T₅ and T₌ are functions of N, the number of particles in the cluster; it is suggested that the traditional melting point is the common temperature to which T₅ (N) and T₌ (N) converge as N.