Compositional structures and thermodynamic properties of Pd-Cu, Rh-Pd, and Rh-Pd-Cu nanoclusters computed by a combined free-energy concentration expansion method and tight-binding approach

Abstract

The statistical-mechanical free-energy concentration expansion method in conjunction with tight-binding elemental bonding energetics are used in atomistic modeling of alloy cluster compositional structures. The study focuses on three systems of 923-atom cuboctahedron clusters, Pd-Cu, Rh-Pd, and Rh-Pd-Cu, each capable of inter-cluster atomic exchange. At low temperatures, cluster core ordering and surface mixed-type ordering are predicted for Pd-Cu compositional ``magic-number'' clusters, whereas the system of Rh-Pd clusters tends to separate into clusters exhibiting demixed order. In the former case, slight deviations from magic-number compositions strongly affect segregation levels. At high temperatures, Pd-Cu clusters exhibit surface segregation that affects order-disorder transitions, and at even higher temperatures a surface desegregation process, all of which are reflected in characteristic Schottky-type configurational heat capacity versus $T$ curves. Comparing Pd-Cu with Rh-Pd-Cu reveals distinct ternary alloying effects. The role of surface induced bond energy variations in segregation related order-disorder transitions is demonstrated.