Complete statistical thermodynamics of the cluster solid-liquid transition

A constant (N,P,T) statistical method is developed for a finite-size system. A scaling variable a is introduced to describe the size of the system following the method used for the bulk system. The histograms of the Boltzmann distribution function f(${\mathit{E}}_{\mathit{c}}$,V;T,P) (${\mathit{E}}_{\mathit{c}}$ and V being the configuration energy and the volume) for a 55-atom cluster bound by Lennard-Jones pair potentials are calculated at several (T,P) values by Monte Carlo (MC) simulations. From the density of states Ω(${\mathit{E}}_{\mathit{c}}$,V) constructed from the MC results, important thermodynamical quantities are then obtained. In the phase-transition region, f(${\mathit{E}}_{\mathit{c}}$,V;T,P) shows a bimodal distribution on the (${\mathit{E}}_{\mathit{c}}$,V) plane indicated by a ‘‘twin-peak’’ structure. The full phase equilibrium, including volume or pressure changes, of a cluster is explored in a systematic manner, and thus a complete picture of the phase diagram of a cluster is presented.