Melting and surface tension in microclusters

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Abstract
Approximate partition functions are constructed from approximate quantum mechanical models of near‐rigid, solidlike and nonrigid, liquidlike clusters. The Helmholtz free energies are evaluated for these clusters as functions of temperature T and cluster size N. The thermodynamic temperatures of melting, at which the free energies of the two forms are equal, match well with the melting temperatures determined from classical simulations of Ar clusters. Moreover, the effective coexistence ranges of temperature for solid‐ and liquidlike forms are approximately the same as the range of ‘‘supercooling’’ and ‘‘superheating’’ found in molecular dynamics computations of Ar. The surface tension is determined from an expansion of the free energy in powers of N −1/3. The concept of melting in small clusters, as a transition from a near‐rigid, small‐amplitude vibrator to a nonrigid molecule capable of frequent passage from one local equilibrium geometry to another, is related to the recent proposal by Stillinger and Weber of the nature of the melting transition.