Effect of Adsorbate Diffusion on the Dendritic Morphology of Electrodeposited Films

We study the formation of deposits with dendritic morphology using numerical simulations of a model of electrodeposition and diffusion of the adsorbed material. The model considers a diffusive flux of cations in solution, the instantaneous adsorption and reaction in contact with the film surface, and random walks of mobile atoms on that surface, with a maximum of G hops per atom and a detachment probability ϵ per neighbor at the current position. For low temperature or large current, which corresponds to small G, the deposits are similar to the diffusion-limited aggregates growing from the flat electrode; for high temperature or very small current, which is represented by large G or ϵ, the deposits have thick rounded columns with sporadic ramification. In these conditions, the growth direction is controlled by the orientation of the electrode and of the cation flux. For the balanced conditions of adsorbate diffusion and current (typically 102 ≲ G ≲ 104 and ϵ ≲ 0.1, but also for larger G and very small ϵ), the films have a hierarchical dendritic morphology with the shape of maple leaves. The dendrite tips propagate in directions forming 45° with the electrode and are formed by three concurrent terraces, as a consequence of the simulations in a simple cubic lattice. The average dendrite size increases as a power law of G and is consequently expected to decrease with the applied current. The lowest energy configurations (terraces) are shown to be stable within the timescale of crystallization of an atomic layer, but the weakly bonded atoms have sufficiently large mobility to create those configurations. Thus, the dendritic morphology depends on the interplay between the energetics of the crystal and the electric current, which may help the interpretation of dendrite growth with other crystalline structures. The dendrite shape obtained here resembles those observed in some electrodeposited films of gold, zinc, and palladium, and the effect of the electric current on the dendrite size agrees with the observations in the electrodeposition of silver and gold. Assuming that the adsorbate diffusion is thermally activated, we propose that the average dendrite size is a ratio between an Arrhenius factor and a power law of the current; this suggests a method to estimate the microscopic energy barrier of diffusion, which may differ from the macroscopic activation energy