A surface curvature oscillation model for vapour-liquid-solid growth of periodic one-dimensional nanostructures.

While the vapour-liquid-solid process has been widely used for growing one-dimensional nanostructures, quantitative understanding of the process is still far from adequate. For example, the origins for the growth of periodic one-dimensional nanostructures are not fully understood. Here we observe that morphologies in a wide range of periodic one-dimensional nanostructures can be described by two quantitative relationships: first, inverse of the periodic spacing along the length direction follows an arithmetic sequence; second, the periodic spacing in the growth direction varies linearly with the diameter of the nanostructure. We further find that these geometric relationships can be explained by considering the surface curvature oscillation of the liquid sphere at the tip of the growing nanostructure. The work reveals the requirements of vapour-liquid-solid growth. It can be applied for quantitative understanding of vapour-liquid-solid growth and to design experiments for controlled growth of nanostructures with custom-designed morphologies.