Statistical Relationship between Three- and Two-Dimensional Spatial Distributions of Dispersed Phases

Abstract

We defined 3-dimensional local number, LN3D, 2-dimensional local number, LN2D, and their probability distribution to describe the spatial distribution of second phase particles, and then suggested the statistical relationship of probability distributions between LN2D and LN3D concerning uniform random and clustering spatial distributions. The relationship was validated by computer experiments using particles of overlap permissive spheres, and was applied to the real microstructures of Al-10 vol%SiC composites. Using the relationship, probability distributions of either LN3D or LN2D could be predicted from the measured relative frequency distributions of another dimension in computer experiments with satisfactory accuracy. Using the relationship, the probability distributions of LN3D was approximately predicted from the relative frequency distributions of LN2D that were obtained by measurements of spatial distributions of SiC particles in Al-SiC composites.