Breakdown of the Hume−Rothery Rules in Sub-Nanometer-Sized Ta-Containing Bimetallic Small Clusters

The Hume-Rothery rules are empirical rules to predict the solid solubility of metals. We examined whether the rules hold for sub-nanometer-sized small particles. We prepared bimetallic cluster ions in the gas phase by a double laser ablation technique. Taking advantage of the magic compositions of the bimetallic cluster ions relating to the distinguished stabilities, the coalescence or the segregation of Ta and another element in the sub-nanometer-sized clusters was discussed. It was found that W, Nb, and Mo readily coalesce with Ta, while Ag, Al, Au, Co, Cu, Fe, Hf, Ni, Pt, Ti, and V are segregated from Ta. On the basis of these results, we concluded that the Hume-Rothery rules do not hold for sub-nanometer-sized particles.