Site-specific average atomic concentrations computed for systems of Rh-Cu, Ni-Cu and Rh-Ni-Cu icosahedral and cuboctahedral free nanoclusters of different sizes by the “free-energy concentration expansion method” are used for evaluating pertinent cluster thermodynamic functions. Compared to stable surface segregated “magic-number” structures, at intermediate overall compositions the cluster system is expected to separate into these “phases.” A Schottky-type heat-capacity anomaly is predicted and attributed to atomic exchange (e.g., desegregation) excitation processes. Its measurement can elucidate the cluster segregation energetics.