Coarsening kinetics of fractal-like grain boundaries

A novel coarsening regime for serrated or rugged grain boundaries in single-phase polycrystalline materials is presented. The coarsening is characterized by a smoothing of the initially rough grain boundaries, where the time law of the smoothing kinetics, measured e.g. by the evolution of the profile roughness rho of the grain boundaries, is given by the power law rho approximate to t((1-D))(s)/2. D-S (with 1 less than or equal to D-S less than or equal to 2) is the initially fractal dimension of the grain boundaries as it can be determined by the application of the concepts of fractal geometry to micrographs of plane sections of the grain ensemble. The time law is derived by an analytic model of selfsimilar boundary coarsening based on the phenomenological assumption of a curvature driven relaxation of fractal-like grains. By application of optical and scanning electron microscopy over a wide range of magnifications, the model is tested experimentally by the measurement of the coarsening kinetics of initially fractal-like grain boundaries in pure Zinc during isothermal annealing. Additionally, a Monte Carlo simulation of the thermal relaxation of two-dimensional initially fractal grains is performed. The results of the simulation confirm the assumptions of the phenomenological model and are in good agreement with the annealing experiments.