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