A new example of the diffusion-limited aggregation: Ni–Cu film patterns

The mechanism of the growth of the dendrites in the Ni–Cu films is studied by comparing them with the aggregates obtained by Monte Carlo (MC) simulations according to the diffusion-limited aggregation (DLA) model. The films were grown by electrodeposition. The structural analysis of the films carried out using the x-ray diffraction showed that the films have a face-centered cubic structure. Scanning electron microscope (SEM) was used for morphological observations and the film compositions were determined by energy dispersive x-ray spectroscopy. The observed SEM images are compared with the patterns obtained by MC simulations according to DLA model in which the sticking probability, P between the particles is used as a parameter. For all samples between the least and the densest aggregates in the films, the critical exponents of the density–density correlation functions, α were within the interval 0.160 ± 0.005–0.124 ± 0.006, and the fractal dimensions, Df, varies from 1.825 ± 0.006 to 1.809 ± 0.008 according to the method of two-point correlation function. These values are also verified by the mass-radius method. The pattern with α and Df within these intervals was obtained by MC simulations to DLA model while the sticking probability, P was within the interval from 0.35 to 0.40 obtained by varying P (1–0.001). The results showed that the DLA model in this binary system is a possible mechanism for the formation of the ramified pattern of Ni–Cu within the Ni-rich base part of the Ni–Cu films due to the diffusive characteristics of Cu.