Identifying structural and energetic trends in isovalent core-shell nanoalloys as a function of composition and size mismatch.

We locate the putative global minimum structures of Na(x)Cs(55-x) and Li(x)Cs(55-x) nanoalloys through combined empirical potential and density functional theory calculations, and compare them to the structures of 55-atom Li-Na and Na-K nanoalloys obtained in a recent paper [A. Aguado and J. M. López, J. Chem. Phys. 133, 094302 (2010)]. Alkali nanoalloys are representative of isovalent metallic mixtures with a strong tendency towards core-shell segregation, and span a wide range of size mismatches. By comparing the four systems, we analyse how the size mismatch and composition affect the structures and relative stabilities of these mixtures, and identify useful generic trends. The Na-K system is found to possess a nearly optimal size mismatch for the formation of poly-icosahedral (pIh) structures with little strain. In systems with a larger size mismatch (Na-Cs and Li-Cs), frustration of the pIh packing induces for some compositions a reconstruction of the core, which adopts instead a decahedral packing. When the size mismatch is smaller than optimal (Li-Na), frustration leads to a partial amorphization of the structures. The excess energies are negative for all systems except for a few compositions, demonstrating that the four mixtures are reactive. Moreover, we find that Li-Cs and Li-Na mixtures are more reactive (i.e., they have more negative excess energies) than Na-K and Na-Cs mixtures, so the stability trends when comparing the different materials are exactly opposite to the trends observed in the bulk limit: the strongly non-reactive Li-alkali bulk mixtures become the most reactive ones at the nanoscale. For each material, we identify the magic composition x(m) which minimizes the excess energy. x(m) is found to increase with the size mismatch due to steric crowding effects, and for Li(x)Cs(55-x) the most stable cluster has almost equiatomic composition. We advance a simple geometric packing rule that suffices to systematize all the observed trends in systems with large size mismatch (Na-K, Na-Cs, and Li-Cs). As the size mismatch is reduced, however, electron shell effects become more and more important and contribute significantly to the stability of the Li-Na system.