Rare gas clusters: Solids, liquids, slush, and magic numbers

Abstract

Simulations by constant energy molecular dynamics have been performed for numerous clusters in the size range N=7–33. Detailed investigations have been conducted on the portions of the caloric curves in which the transition between rigid and nonrigid behavior occurs, to study the N dependence of the solid–liquid phase change. Clusters of several sizes display a coexistence of forms, each with a characteristic mean temperature, over a well-defined energy range in the transition region, as had been observed for the Ar13 cluster. Within the coexistence region, the high temperature form is solid-like and the low temperature form behaves in a liquid-like fashion. The caloric curves of state for these clusters take on two-valued forms when averages are calculated for each of the two ‘‘phases’’ separately; the two branches are smooth extensions of the curves from the single phase regions. Clusters of other sizes do not display this clear coexistence of phases, but appear to pass through a ‘‘slush-like’’ state during the melting transition. The coexistence behavior is not a smooth function of N. The clusters Ar13 and Ar19, and to a certain extent Ar7, display high stability properties indicative of magic number behavior.

Effect of Potential Energy Distribution on the Melting of Clusters

“…There has been some controversy concerning the dependence of the simulated thermodynamic properties on the ensemble until the work by Calvo and Labastie [17]. These authors [17] showed that if the sampling of the phase space is accurate enough (a large enough number of MC configurations and MD trajectories), the thermodynamic results are identical in both ensembles because the thermodynamics is determined by the configurational density of states [7,8,17,18].In this Letter, we show that the potential energy distribution of atoms in the clusters can consistently explain many of the important phenomena which occur during phase changes of small clusters, such as the nonmonotonic variation of melting temperature with the size of clusters [3,6,7], the dependence of melting, boiling, and sublimation temperatures on the interatomic potentials [12,13,19], the existence of a surface-melted phase [6,8,11,15,16], and the absence of a premelting peak in heat capacity curves [9,[14][15][16].We have studied the thermodynamic behavior of clusters of metals and nonmetals for the sizes of 12 # n # 34. For the interatomic interactions, we have employed the tight-binding potentials based on the second moment approximation [7,16] for metal clusters (M n , M Ni, Cu, Pd, Ag, Pt, Au, Al, and Pb) and pair potentials for nonmetal clusters.…”

“…As the cluster size decreases, the melting temperature monotonically decreases [4,5]. However, when the cluster size is small enough (# 200 atoms), the melting temperature does not vary monotonically with the size of cluster [3,6,7].…”

“…The weakly bound surface atoms can easily move and form hole-floater structures before the stable internal atoms are involved in melting [16]. The criterion of S $ 1 can also be used to explain the surface melting observed in other clusters modeled by Lennard-Jones potentials [6,8], the inverse-power-based potentials [15], and Gupta potentials [11], for example. The values of S for these clusters are in the range of 1.0 1.7.…”

“…As the cluster size decreases, the melting temperature monotonically decreases [4,5]. However, when the cluster size is small enough (# 200 atoms), the melting temperature does not vary monotonically with the size of cluster [3,6,7].Multimodal heat capacity curves observed in small clusters indicate that thermal energy can be dissipated by a "premelting" mechanism before overall melting [7]. Premelting has been attributed to surface melting [8], partial melting [9], orientational disordering in molecular cluster [10], and isomerization [7,11].…”

“…In this Letter, we show that the potential energy distribution of atoms in the clusters can consistently explain many of the important phenomena which occur during phase changes of small clusters, such as the nonmonotonic variation of melting temperature with the size of clusters [3,6,7], the dependence of melting, boiling, and sublimation temperatures on the interatomic potentials [12,13,19], the existence of a surface-melted phase [6,8,11,15,16], and the absence of a premelting peak in heat capacity curves [9,[14][15][16].…”