Direct numerical simulation of nucleation and three-dimensional, diffusion-controlled growth

Direct numerical simulations, using a boundary integral method, are used to investigate nucleation followed by diffusion-limited growth during electrochemical deposition. Results are compared to three published models. For instantaneous nucleation, the theories are in good agreement with simulations. Errors are more significant for finite nucleation rates for two published theories, while the theory of Mirkin and Nilov is in very good agreement with simulations. The evolution in time of the standard deviation in cluster size due to the apparently random nature in space and time of nucleation is presented. The advantages and possible extensions of the simulation approach are also discussed. (C) 2001 The Electrochemical Society. [DOI: 10.1149/1.1365144] All rights reserved.