Scaling Laws in Thermal Relaxation of Fractal Aggregates

Abstract

We study shape relaxation of a two-dimensional fractal aggregate, during annealing after the rapid crystallization on a substrate. The edge length of the aggregate decreases with time in a power law with the exponent (d - 1 - D)/(β + 1), where d = 2 is the spatial dimension, D is the fractal dimension and β depends on the relaxation mechanism as to be 3, 2 and 1 for edge diffusion, surface diffusion and edge kinetics, respectively. With Monte Carlo simulation, we confirm the predicted exponents for the diffusion-limited aggregation with two different diffusion mechanisms.