Surface Segregation in Bimetallic Clusters: Statistical-Mechanical Modeling Using Cluster Site Energies

Abstract

A five-state statistical-mechanical model is employed in the present study of surface segregation in 201-atom bimetallic clusters having truncated cubo-octahedral shape. The model uses ideal entropy of mixing and assumes zero heat of mixing. Surface segregation is studied via direct minimization of the free energy without performing Monte Carlo simulations. The effects of size mismatch between atoms of different type are included via a new empirical formula, based upon dimensional scaling arguments, leading to an increase in the surface fraction of larger atoms. We used the corrected effective medium potentials to generate the site energies (interaction energy per atom) used in the model. A complete list of site energies for nine fcc metals is presented for 201-, 586-, 1289-atom clusters and semi-infinite surfaces. In particular, the corner and edge site energies are found to be independent of cluster size. The model reproduced qualitatively the surface and edge-comer segregation results for 11 50%-50% bimetallic clusters generated by atomistic simulations at 600 K that we reported earlier. The remaining difference in results between the model and the simulations is attributed to the effect of nonzero heats of mixing. For systems with very large (> 12%) lattice-size mismatch such as Ni-Ag and Cu-Ag, the distortion from the perfect lattice structure is significant according to the simulations; thus, simple modeling involving a few well-defined states is problematic.