Kinetic Monte Carlo approach to Schottky defects in noble metal nanoclusters

Abstract

The vacancy concentration dependence on temperature and diameter of noble metal (gold, silver, and copper) nanoclusters is investigated using a Kinetic Monte Carlo method. Icosahedral and decahedral nanoclusters are studied, with diameters up to 3.73 nm for icosahedral clusters and up to 6.65 nm for decahedral clusters. The cohesive energy is calculated using a coordination number approach, resulting in a linear relation with cluster size. Random Schottky defects are frozen into the clusters at low temperatures (100–600 K) and we find that the vacancy concentration increases with smaller diameters and higher temperatures. We develop a model for this behavior, which explains the temperature and size dependence. This model predicts silver icosahedra to have the highest concentration of vacancies in the clusters studied. Vacancy concentrations are related to the ratio of surface/interior sites based on nearest neighbor calculations. The modified enthalpy and entropy of constant diameter clusters are derived from a logarithmic model for the Gibbs energy. Melting entropy and enthalpy are calculated in this coordination type model and compare well with previously published molecular dynamics results.