The free-energy concentration expansion method (FCEM), originally derived for the theoretical prediction of surface segregation in the presence of short-range order in binary alloys [1], is an attractive tool for elucidating multicomponent nanocluster compositional structural phenomena [2] that are inaccessible by current experimental techniques. FCEM computations in conjunction with coordination-dependent energetic parameters were accomplished for Ni-Cu-Pd, Ni-Cu-Rh and Ni-Cu-Al nanocluster systems, containing up to 923 atoms with icosahedral and truncated octahedral shapes. The first two exhibit site-specific, sequentially competitive surface segregation of Cu/Pd and Cu/Ni, respectively, with resultant core separation of Ni and of Rh. Yet, remarkable differences, governed by the opposite hetero-atomic interactions, were noted in the surface segregated compositional patterns: "mixed" Cu/Pd ordering for Ni-Cu-Pd, and "demixed" order for Ni-Cu-Rh. The computations predict also in-surface rearrangement transitions reflecting the interplay of segregation and order. For Ni-Cu-Al, the much stronger Ni-Al interactions are manifested in compositional ordering that extends into the cluster core. Based on the FCEM data, thermodynamic properties such as the cluster mixing entropy and free-energy were computed for the three systems. The Ni-Cu-Rh clusters, with all-repulsive hetero-atomic interactions, were found to separate into three kinds of clusters, having different "magic number" compositions. Critical temperatures of inter-cluster compositional separation, computed for the Rh-Cu system, depend on both the cluster size and shape. Likewise, computations of the configurational contribution to the heat capacity vs. temperature reveal desegregation related characteristic features, which depend distinctly on the cluster size and shape.
[1] M. Polak and L. Rubinovich, Surf. Sci. Rep. 38, 127 (2000).
[2] L. Rubinovich and M. Polak, Phys. Rev. B 69, 155405 (2004).

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