SCALING LAWS IN THERMAL RELAXATION OF FRACTAL AGGREGATES

We study shape relaxation of a two-dimensional fractal aggregate, duri ng annealing after the rapid crystallization on a substrate. The edge length of the aggregate decreases with time in a power law with the ex ponent (d - 1 - D)/(beta + 1), where d = 2 is the spatial dimension, D is the fractal dimension and beta depends on the relaxation mechanism as to be 3, 2 and 1 for edge diffusion, surface diffusion and edge ki netics, respectively. With Monte Carlo simulation, we confirm the pred icted exponents for the diffusion-limited aggregation with two differe nt diffusion mechanisms.