Determination of spherical grain size from the average area of intersection in Ostwald ripening

Abstract

When the size distribution of spherical grains is a one-parameter function, the average of the spatial diameter D can be calculated either from the average of the circular intersect area A or from the average of the linear intersect length l . The conversion factors from A to D are here calculated for the diffusion- and reaction-controlled grain size distributions in the theory of Ostwald ripening developed by Lifshitz, Slyozov, and Wagner (LSW). In the alloy of spherical Co grains dispersed in liquid Cu, the value D converted from the measured A agrees well with that obtained from l . It is therefore possible to determine the average sphere diameter simply by counting the total number of grains on intersect planes if the size distribution agrees with the LSW theory.