Structure and size-dependent vibrational and thermal properties of Ni clusters: A systematic ab initio approach

Abstract

There is scarce information on the vibrational and thermal properties of small Ni clusters. Here, the outcomes of ab initio spin-polarized density functional theory calculations on the size and geometry effects upon the vibrational and thermal properties of Nin (n = 13 and 55) clusters, are discussed. For theses clusters a comparison is presented between the closed shell symmetric octahedral (Oh) and the icosahedral (Ih) geometries. The results indicate that the Ih isomers are lower in energy. Besides, ab initio molecular dynamics runs at T = 300K show that Ni13 and Ni55 clusters transform from their initial Oh geometries towards the corresponding Ih ones. For Ni13, we also consider the lowest energy less symmetric layered 1-3-6-3 structure, and the cuboid, recently observed experimentally for Pt13, which is competitive in energy but is unstable, as phonon analysis reveals. We calculate their vibrational density of states (νDOS) and heat capacity, and compare with the Ni FCC bulk counterpart. The characteristic features of the νDOS curves of these clusters are interpreted in terms of the clusters’ sizes, the interatomic distance contractions, the bond order values as well as the internal pressure and strains of the clusters. We find that the softest possible frequency of the clusters is size and structure-dependent, being the smallest for the Oh ones. We identify mostly shear, tangential type displacements involving mainly surface atoms for the lowest frequency of the spectra of both Ih and Oh isomers. For the maximum frequencies of these clusters the central atom shows anti-phase movements against groups of nearest neighbor atoms. An excess of heat capacity at low temperatures with respect to the bulk is found, while at high temperatures a constant limiting value, close but lower to the Dulong and Petit value, is determined.