Phase transitions in clusters

Abstract

General concepts of cluster phase transitions are reviewed as well as the cluster behavior near the melting point. Configuration excitation determines the nature of the cluster phase transitions, but a significant contribution to the entropy jump is given by thermal motion of atoms that allows one to characterize the phase transition through thermal atom motion in the Lindemann and other criteria. The phase coexistence near the melting point is the peculiarity of not large clusters. The void concept of phase transitions with a void as an elementary configuration excitation allows one to describe the phase transition for clusters and macroscopic atomic systems. Phase transitions in metal clusters resemble those in clusters with pairwise atomic interactions, but their numerical parameters are other because of a large number of isomers and an additional electron degree of freedom. Cluster models are convenient for the analysis of macroscopic atomic systems. They allow us to understand the nature of glassy transitions and the reason of absence of a stable infinite crystal lattice for gases at zero temperature and high pressure.

Ions in liquid metal clusters

“…For convenience, we assume that coexistence of phases is observable in the range [26] According to formula (10), given that the basic temperature dependence for the ratio of populations of the liquid and solid states p(T ) has the form p(T ) ∼ exp(−�E/T ), we find the width of the observable coexistence range (10) of the solid and liquid phases δT m i.e., we assume δT m ≪ T m , and the solid and liquid phases coexist in observable quantities within the temperature range from T m − δT m up to T m + δT m . Table 1 contains the temperature range δT .…”

Entropy and Phase Coexistence in Clusters: Metals vs. Nonmetals

“…Figure 8. The entropy jump at melting of the 13-atom Lennard-Jones cluster [22,23]. Closed circles are obtained from the results of computer simulation of the isolated 13-atom Lennard-Jones cluster [6], and open circles correspond to the isothermal 13-atom Lennard-Jones cluster [7].…”

“…The largest contribution to the variation of the entropy is determined by thermal motion of atoms in the liquid aggregate state. The entropy jump for the 13-atom Lennard-Jones cluster under isothermal conditions is given in Figure 8 [22,23]. These values are obtained on the basis of probabilities that a cluster is located in the liquid or solid states; these, in turn, emerge from molecular dynamics simulations of this cluster under adiabatic [6] and isothermal [7] conditions.…”

“…For definiteness, we arbitrarily take the range of observable phase coexistence to be [23] 10 ≥ p ≥ 0.1…”

“…That such ranges exist was demonstrated both in early simulations and in the experiments cited above. However, apart from one early discussion based on a continuum-capillarity model [21], the conditions and constraints that allow the coexistence ranges to be wide enough to be detectable had not been identified until very recently [22,23].…”