Elementary models of the "flux driven anti-ripening" during nanobelt growth

A stirring solution hydrothermal approach is widely used to rationally grow elongated oxide nanostructures with controllable aspect ratios. Depending on the synthesis conditions, the following are observed: (i) no nanostructure formation (the system exists as a pure liquid), (ii) formation of nanostructure starting from a critical powder/initial volume of the liquid solution, and (iii) monotonic increase in the nanostructure's aspect ratio (towards asymptotic value) with stirring rate. Despite these experimental observations, the theoretical understanding of the process is limited. Herein, using an athermal ballistic atomic jump model, we develop a phenomenological theory of nanostructure growth under different stirring rates, demonstrating the conditions necessary for breaking the equilibrium Wulff shape, the formation of elongated one-dimensional structures, and explaining regimes (i-iii) reported experimentally. Moreover, the comparison of the phenomenological models without and with the account of ripening effects in the open ensemble of nanowires under stirring provides the theoretical guidance for the controllable growth of elongated nanostructures by the stirring solution hydrothermal approach.