Relative edge energy in the stability of transition metal nanoclusters of different motifs

Abstract

When a structure is reduced to a nanometer scale, the proportion of the lowly-coordinated edge atoms increases significantly, which can play a crucial role in determining both their geometric and electronic properties, as demonstrated by the recently established generalized Wulff construction principle [S. F. Li, et al., Phys. Rev. Lett., 2013, 111, 115501]. Consequently, it is of great interest to clarify quantitatively the role of the edge atoms that dominate the motifs of these nanostructures. In principle, establishing an effective method valid for determining the absolute value of the surface energy and particularly the edge energy for a given nanostructure is expected to resolve such a problem. However, hitherto, it is difficult to obtain the absolute edge energy of transition metal clusters, particularly when their sizes approach the nanometer regime. In this paper, taking Ru nanoclusters as a prototypical example, our first-principles calculations introduce the concept of relative edge energy (REE), reflecting the net edge atom effect over the surface (facet) atom effect, which is fairly powerful to quasi-quantitatively estimate the critical size at which the crossover occurs between different configurations of a given motif, such as from an icosahedron to an fcc nanocrystal. By contrast, the bulk effect should be re-considered to rationalize the power of the REE in predicting the relative stability of larger nanostructures between different motifs, such as fcc-like and hcp-like nanocrystals.