Ostwald Ripening and Relaxation in Dendritic Structures

Abstract

The development of microstructures in cast materials is described as a sequence of processes, among which are dendritic growth and coarsening. Dendritic evolution is analyzed first as the deterministic formation of the tip and its neighborhood, followed by the incubation of stochastic events, including Ostwald ripening and coalescence. Mean-field theories of coarsening are discussed briefly, and the problem of relating classical coarsening of convex spherical particles to that of highly branched dendritic interfaces is shown to be resolved by considering the distribution of chemical potentials over the solid-liquid surface. Experiments relying on stereological measurements yield kinetic coarsening experiments in reasonable agreement with the statistical theories. The influence of volume fraction on the coarsening kinetics is shown to affect the rate constant, which increases about four-fold when the solid fraction rises to 50 pct, but the coarsening exponent remains at the classical value of 1/3. Attempts to measure mean-field intensive thermodynamic properties such as temperature and concentration during dendritic coarsening yield consistent kinetics, although the precise relationships of these mean-field quantities to the stereological parameters are not yet established. The application of morphological scaling laws is stressed throughout, as a fundamental method to predict cast structures in more complex materials.