Quantum growth refers to the phenomena in which the quantum mechanically confined motion of electrons in metallic wires, islands, and films determines their overall structural stability as well as their physical and chemical properties. Yet to date, there has been a lack of a unified understanding of quantum growth with respect to the dimensionality of the nanostructures as well as the valency of the constituent atoms. Based on a first-principles approach, we investigate the stability of nanowires, nanoislands, and ultrathin films of prototypical metal elements. We reveal that the Friedel oscillations generated at the edges (or surfaces) of the nanostructures cause corresponding oscillatory behaviors in their stability, leading to the existence of highly preferred lengths (or thicknesses). Such magic lengths of the nanowires are further found to depend on both the number of valence electrons and the radial size, with the oscillation period monotonously increasing for alkali and group IB metals, and monotonously decreasing for transition and group IIIA-VA metals. When the radial size of the nanowires increases to reach ∼10 Å, the systems equivalently become nanosize islands, and the oscillation period saturates to that of the corresponding ultrathin films. These findings offer a generic perspective of quantum growth of different classes of metallic nanostructures.
Keywords: Friedel oscillations; quantum growth; radial size; valence electrons.