| Depending on the plating conditions, surfaces produced by electrodeposition can be smooth and lustrous or rough and granular. Upon prolonged electrodeposition the latter often evolve into dendrites, thereby imposing severe limitations on plating and battery applications. This technologically important phenomenon has so far been treated mostly empirically.;Morphological instability analysis applied to the initiation stage where minute surface perturbations evolve into dendritic precursors, explains why certain surfaces remain smooth during electrodeposition whereas others evolve dendrites. It is determined that electrodeposition carried under practical conditions will always lead to roughness evolution, yet because of the long induction time observed when operating below a critical overpotential, a pseudo-stable region, in which no roughness will evolve at appreciable rates, is defined. The critical overpotential strongly depends on the reversibility of the system, however, is relatively insensitive to concentration or flow rate variations.;The constant propagation velocity of the paraboloidal shaped tips is modelled in the propagation stage by applying both the maximum tip velocity and the marginal stability criteria. A critical overpotential for roughness propagation is defined. Combining the induction time, the critical overpotential and the propagation rate yields the complete growth history of roughness elements in electrochemical systems.;The density of the roughness elements is determined by considering the interaction between the two-dimensional diffusion fields associated with adjacent growth sites. The optimal spacing is found to be about equal to the mass transport boundary layer thickness.;In the present work, a comprehensive quantitative model, taking into account the combined effects of transport by diffusion and convection, reaction kinetics and the surface energy, has been derived. The model analyzes the growth of roughness elements in terms of three stages: initiation, transition and propagation.;The distribution of roughness elements over extended electrodes subject to non-uniform flow and potential fields is determined, indicating that severe localized dendritic growth may occur already at current densities well below the limiting current, particularly near the edge.;Experimental measurements performed in electrodeposition of copper and zinc, and reported observations in the literature, are in excellent agreement with the theoretical predictions. |
