The usefulness of integral mean curvature measurements in the study of the kinetics of coarsening

Abstract

Coarsening kinetics are often studied in terms of an asymptotic solution to the basic growth/dissolution rate equation. In this “asymptotic state” all properties of the particle size distribution become qualitatively invariant with time except for a scale factor. Therefore, as long as this state is presumed to exist, it is unnecessary to measure the size distribution of the particles. Among the properties that pertain to the entire paniculate ensemble are the volume (Vv), the interfacial area(Sv), and the integral mean curvature(Mv)per unit volume of the aggregate. Of these,Vv does not change significantly during coarsening butSv andMv do, and are easy to measure unambiguously on plane sections. A strategy is outlined for deriving the relationship betweenSv andMv and their time dependence for any arbitrary rate equation and its attendant asymptotic solution. This strategy is then illustrated for three selected coarsening theories. The measurement ofSv andMv, which is less tedious than that of size distributions, is shown to be sufficient for distinguishing the merits of the theory under consideration as long as scale factor coarsening is presumed to exist.