On the geometry and thermodynamics of nanoclusters

Abstract

It is proposed that the volume, surface, and radii of nanoclusters be determined by Delaunay tesselation. Argon, silver, zinc, and iron clusters with total numbers of atoms ranging from 13 to 1415 are investigated by means of molecular dynamics (MD) along with the different potentials of interparticle interactions using the embedded atom model (EAM). The cluster surface area is defined as the sum of the surface areas of Delaunay simplexes. A formula that accurately describes the atomic volumes of clusters is proposed. The geometric characteristics, numbers of surface atoms, sphericity, energy, and entropy of specific clusters are calculated via MD. It is shown that the number of surface atoms for a given cluster size depends substantially on the material due to variations in the looseness of surface layers. The distribution of kinetic energy over atoms and parts of clusters is not uniform and deviates by ∼1/N. It is found that the dependence of energy U on the cluster size is linear in the (U/N, N−1/3) coordinate system (where N is the number of atoms) for all investigated cases. The behaviors of entropy and the effective Gibbs energy are similar, so specific surface characteristics need not be determined when calculating excess characteristics. The specific excess surface energy per unit area, determined from the MD data on clusters, grows by several tens of percent when their size falls from N = 1415 to 13. In all of the investigated cases, nanoclusters are stable at any size. The melting point depression of nanoclusters is proportional to N−1/3 and can be calculated from the MD data.