Mechanisms for potential oscillations and synchronizing self-organized formation of ordered dendrite structures, which is an important example of morphogenesis in Laplacian fields, were studied using Sn, Zn, Cu, and Pb electrodeposition. Electron backscattering diffraction (EBSD) experiments showed that Sn latticework as a typical example of the ordered dendrite structures grew in an epitaxial mode in particular directions from the Sn electrode surface. In situ optical and phase-contrast microscopic inspection showed that the Sn latticework growth as well as the concentration profile for deposited Sn(II) ions near the growing front oscillated in synchronization with the potential oscillation, which led to formation of a highly ordered Sn latticework structure. Similar behavior was observed in other electrodeposition systems. On the basis of these results, a general mechanism for the potential oscillations and synchronized formation of the ordered dendrite structures was proposed, in which autocatalytic crystal growth, passivation in flat surfaces of dendrites, and depletion of deposited metal ions in the electrolyte near and inside the dendrites played the key roles. Numerical calculations by use of a modified coupled map lattice (CML) model confirmed the validity of the mechanism. The clarification of the general mechanism has enabled us to classify all the oscillatory dendrite growth, including reported ones by other research groups, into three types (type-I, type-II, and type-III), which will serve for preparation of designed and controlled micro-and nanostructures at solid surfaces.

Strikingly well-ordered Sn latticeworks, standing perpendicular to the substrate, are formed spontaneously in oscillatory electrodeposition. Cooperation of various processes, such as needle formation by autocatalytic crystal growth, cuboid formation under a reaction-limited condition, and autocatalytic oxidation at closest-packed surfaces, enabled the self-organization of the latticeworks. The mechanism is generally applicable to deposition of other metals such as Zn, Pb, and Cu. The present work has opened a promising, unique field toward the formation of highly ordered 3-D micro- or nanostructures at solid surfaces.

Electrodeposition of zinc ͑Zn͒ from a strongly alkaline Zn͑II͒ solution showed a potential oscillation in the region of the current density exceeding the diffusion-limited one, accompanied by the formation of dendrites with a stacked wafer structure. Scanning electron microscopic inspection showed that the dendrites changed their shape periodically in synchronization with the potential oscillation from thick hexagonal wafers on the negative potential side to thin maple-leaf-like wafers on the positive potential side and inversely. In situ electrochemical quartz crystal microbalance measurements revealed that the rate of Zn deposition also oscillated in synchronization with the oscillation. A mechanism is proposed to explain the oscillation and the dendrite formation by taking into account coupling of autocatalytic Zn-crystal growth, in close relation with Mullins-Sekerka instability, and autocatalytic surface oxidation at the close packed crystal faces leading to surface passivation.