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(Ec,V;T,P) (Ec 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 (Ec,V) constructed from the MC results, important thermodynamical quantities are then obtained. In the phase-transition region, f(Ec,V;T,P) shows a bimodal distribution on the (Ec,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.