The structural transition of the Na$_{309}$ clusters

Abstract

Theoretical insights are provided for understanding why the structural changes detected by photoelectronic measurements on the canonical ensemble of clusters Na$_{309}$ do not induce any signal on their experimental specific heat. The cooling down of a collection of these clusters, whose atomic interactions are modeled with the Gupta potential, reveals that Na$_{309}$ has indeed two configurations of enhanced stability. The most stable one is a perfect icosahedral structure (ico configuration), just as was determined by experiments. The candidate derived from the interaction model for the unknown configuration is a kind of hcp variation of the first (ico-hcp configuration). It has more atoms with low coordination, but also more atoms with high coordination. But the difference between the quantities of the first ones is greater than the difference between the amounts of the second ones, causing a slight loss of the cluster cohesion. Additionally, the properties of an ensemble of Na$_{309}$ clusters in thermodynamic equilibrium were determined. The comparison between theoretical and experimental results shows that the model only reproduces the properties of the solid–solid transition. However, its predictions for the melting and premelting are wrong. We suggest that both failures could be consequences of only one elementary fault: the underestimation of the cohesion of the atoms with low coordination. This source of error of the model would not affect the description of the structural transition, since this transformation is essentially caused by clusters made up of atoms with high coordination. In spite of its mistakes, the model allowed to determine for the first time a candidate for the unknown solid phase of these clusters. This structure, as well as the elementary fault suggested for the model, must be confirmed by ab-initio calculations.