Self-epitaxial nucleation origin of fractal aggregation

The self-epitaxial nucleation and growth origin of the formation and transf ormation of crystalline fractal pattern is identified for the first time. T wo universal parameters, so-called relative elemental branching period <(l) over tilde > and the anisotropy or structural match parameter m, are intro duced to describe the pattern transformation. These two parameters can be p redicted according to our model. Fractal patterns arise when <(l) over tild e >less than or equal to 1. Fractal patterns have a strong anisotropy (m -- > 1) at relatively low surface supersaturations, and a very weak anisotropy (m -->-1) at high surface supersaturations. The theoretic results are in e xcellent agreement with experiments. (C) 2000 American Institute of Physics . [S0021-9606(00)72133-7].