Bimetallic Al–Sn clusters: mixing at the nanoscale

Abstract

Metals which are not miscible in the bulk solid phase can form clusters at the nanoscale, and a typical example is the Al–Sn system. We have investigated the reasons for the enhanced miscibility occurring at the nanoscale. Density functional calculations have been performed for small Al_mSn_n clusters at all compositions when the total number of atoms N = m + n is equal to or smaller than N = 6, and for selected compositions for N = 10 and N = 11. The cohesive energies show that the clusters are energetically stable with respect to the separated atoms. Also, after an Al_mSn_n cluster has formed, its separation into two pure clusters Al_m and Sn_n is energetically forbidden. This justifies the observation that those clusters can form by condensation in gas phase experiments. The different miscibility criteria explored reveal a substantial dependence on the reference state. Between those miscibility criteria, a particularly valuable one consists in studying the substitution reactions in which an Al atom of the gas replaces a Sn atom of the Al_mSn_n cluster to produce Al_m+1Sn_n−1, or a Sn atom replaces an Al atom to produce Al_m−1Sn_n+1. The conclusion is that substitution reactions enriching the clusters in Sn and depleting the cluster in Al are favorable. However, AlSn₁₀ is an exception to this general trend. This is a special cluster. It readily forms by replacing a Sn atom by an Al atom in Sn₁₁. Also, AlSn₁₀ forms easily by adding an Al atom to Sn₁₀. The geometric structures of Sn₁₁ and Sn₁₀ easily reorganize to form AlSn₁₀ accommodating the Al atom inside a Sn cage. The exceptionally stable character of AlSn₁₀ justifies the identification of AlSn₁₀ as a magic cluster with the highest population in the measured mass spectra of this family. Even if Al and Sn can form clusters, the degree of mixing of these two elements in the clusters is modest, and a tendency for segregation of Al and Sn atoms on different parts of the cluster is incipient.