Two different magic number behaviors in supported metal clusters, which contain several to hundreds of atoms, are revealed on a series of fcc(001) metal surfaces based on the calculations with the tight-binding potential. The magic number sequence persists on some surfaces while gradually disappears on the others with the increasing cluster size. A theory is proposed to explain these behaviors in terms of atomic interactions. We find in surprise that the different magic number behaviors are triggered by the relatively weak adatom–adatom interactions between next nearest-neighbor (NNN) atoms, although the closed shell of the magic cluster is enhanced by nearest-neighbor interactions. For an attractive NNN interaction, the closed shell of the magic cluster is gradually destabilized and eventually broken, leading to the disappearance of the magic number sequence with increasing cluster size. For a repulsive one, the closed shell and magic number sequence persists. Besides, our theory also allows a good understanding of the equilibrium shape of Cu islands on the Cu(001) surface.
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