Temperature Dependence of Stability of Copper Clusters

Abstract

Abstract Previously we have determined the lowest-energy structures and full vibrational spectra of Cu N with N up to 150 atoms by means of an unbiased-structure-optimization approach combined with the analytical formulas of the embedded-atom total-energy method and the harmonic superposition approximation. Here, we extend the earlier T = 0 studies to T ≠ 0 and present the equilibrium thermodynamic properties of copper clusters with N from 2 to 150. Thereby, we calculate the Helmholtz free energy quantum mechanically and examine it as a function of temperature and cluster size. It is shown, that the impact of entropic effects on the stability of the copper clusters is rather small for temperatures less than 300 K, which is about the bulk Debye temperature. For larger temperatures, the influence of the vibrational entropy on the cluster stability becomes stronger so that with increasing temperature the stability of some clusters (most often low-symmetrical) is increased and that of others (most often high-symmetrical) is reduced. For the first time, we demonstrate the existence of new magic copper clusters at elevated temperatures. These have the sizes 80, 88, 104, and 125 and will be called the temperature-dependent magic clusters.