The Gibbs method extended to nanothermodynamics and exemplified by evaluations of the surface, line, and point excess energies for icosahedral metal nanoclusters

Abstract

The Gibbs method of surface excesses was extended to nanosized objects and exemplified by evaluations of the specific (per unit area) surface excess energies of Ih nanoclusters of fcc metals (Ag, Au, Cu, Ni, Pb, and Pt), the specific (per unit length) line energies of edges of Ih nanoclusters, and excess point energies of their vertices. In particular, for this purpose, an original interpretation of the Gibbs equimolecular surface concept has been employed. To perform all the above-mentioned evaluations, the extended Gibbs method was combined with the nearest neighbor interaction model. The results of our evaluations of the specific surface energy agree with the experimental values of the specific surface energy for corresponding solid bulk fcc metals. Then, we have found that the values of the specific excess line energy of the Ih nanocluster edges are positive and fall in order of magnitude within the range of 10−10 to 10−9 J/m, which agrees with the available evaluations for other types of linear boundaries. The vertex point energy was found to be on the order of 10−20 J and positive as well. A hypothesis is put forward that the positivity of the excess energies of the edges and vertices results in their instability, i.e., in a trend for the formation of a more rounded shape of polyhedral nanoparticles, especially in the vicinity of their melting temperatures. In addition, some molecular dynamics results on Ih metal nanoclusters are discussed. For Au and Pt Ih nanoclusters, the theoretically calculated values of the specific surface energy are compared with those obtained by combining the Gibbs method with our molecular dynamics results on the size dependence of the potential term into the specific (per atom) internal energy of Ih nanoparticles.