Accessible Unlicensed Requires Authentication Published by Oldenbourg Wissenschaftsverlag February 15, 2016

Temperature Dependence of Stability of Copper Clusters

Valeri G. Grigoryan and Michael Springborg


Previously we have determined the lowest-energy structures and full vibrational spectra of CuN 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.


On the occasion of the appearance of this Festschrift, one of us (VGG) thanks sincerely Prof. Michael Springborg for giving him the opportunity to work in his research group for many years, for guidance in scientific and teaching matters, for introducing in current topics, for great ideas and fruitful discussions, and of course, for very friendly and cordial relations throughout the whole time.

Received: 2015-11-10
Accepted: 2016-1-22
Published Online: 2016-2-15
Published in Print: 2016-5-28

©2016 Walter de Gruyter Berlin/Boston