Fractal structure and cluster statistics of zinc-metal trees de- posited on a line electrode

Abstract

Zinc-metal ``trees'' are grown two dimensionally from a line electrode by electrodeposition. The deposits, which consist of trees of all sizes, bear close resemblance to the patterns of two-dimensional (d=2) diffusion-limited deposition on a one-dimensional (${d}_{b}$=1) substrate computer simulated first by Meakin. The fractal nature of the deposits is confirmed with the fractal dimension ${d}_{f}$(2,1)=0.70\ifmmode\pm\else\textpm\fi{}0.06. The number of deposits (trees) of size s is also found to scale as ${n}_{s}$\ensuremath{\sim}${s}^{\mathrm{\ensuremath{-}}\ensuremath{\tau}}$ with \ensuremath{\tau}apeq21.54. These values are in excellent agreement with the theoretical values calculated for the case of the diffusion-limited deposition with d=2 and ${d}_{b}$=1 and with the large-scale computer-simulation results.