Stability of Some Ternary 13-Atom Icosahedral Clusters Assessed with Geometric, Electronic, and Thermodynamic Criteria

Abstract

Superatoms are clusters with physical or chemical properties that bear certain similarities to atoms. We calculated equilibrium geometries and properties using spin-polarized density functional theory (DFT) within the generalized gradient approximation (PBE). We also performed Ab Initio Molecular Dynamics (AIMD) simulations in the NVT ensemble with a Nosé-Hoover thermostat. In addition, Monte Carlo simulations with a potential fitted to DFT were carried out to assess a number of clusters as possible superatoms. The clusters we studied have a chemical composition AB2C10, where A, B, and C are metals, and a structure derived from that of a 13-atom icosahedron. We adopt an operational definition of superatom to assess clusters. According to this definition, superatoms should have (i) a quasispherical equilibrium geometry and (ii) a set of valence orbitals delocalized over the cluster; (iii) they should maintain these two attributes at elevated temperatures (mechanical and thermal stability); and (iv) they should be thermodynamically favored relative to similar clusters. By these criteria, Sn3Y10, CrSn2Zr10, and possibly CrSn2Ti10 can be classified as “superatoms”. We show that cluster stability arises from (i) the intrinsic stability of the C 10 fragment; (ii) its interaction energy with the three “dopant atoms”; and (iii) compatible atomic sizes of the three elements. Clusters such as CrSn2Ti10 and CrSn2Zr10 exhibit an optimal balance among these contributions. They have a high effective coordination, an absence of very low vibrational frequencies, a favorable ratio of their elements’ cohesive energy, and exceptional thermal resilience, with melting temperatures that are well above the weighted average of their elements’ bulk melting points. Electronic analysis shows that CrSn2Ti10 and CrSn2Zr10 display discrete density-of-states features and partial electron delocalization, consistent with superatomic behavior. These electronic properties vanish as the clusters approach the melting point and undergo structural distortion. We show the importance of looking at several, often interrelated, properties in assessing possible superatoms.