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

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±0.06. The number of deposits (trees) of size s is also found to scale as $n_s$∼$s^{\mathrm{-}\tau }$ with τapeq21.54. 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.