Three-dimensional local number, LN3D, and two-dimensional local number, LN2D, were defined as the number of gravity centers (GCs) of second phase particles in the measuring sphere and circle with specially determined radiuses, respectively, whose centers were put on GCs of noticed particles. LN3D and LN2D represent local number density including a noticed and its neighboring particles and each particle has a specific value. We suggested the quantitative method to evaluate the particle spatial distribution using the relative frequency distributions of LN3D and LN2D, and this method was examined by computer experiments using overlap permissive spheres. It was shown that randomness of second phase particles was correctly evaluated in 3-and 2-dimensions by this method, and the average and variance of LN3D and LN2D are proper descriptors to evaluate the spatial distribution randomness of second phase particles. It was also shown that spatial distribution randomness of 2-dimensional particles appeared on cut planes of 3-dimensional particles having uniform random arrangement can be evaluated by this method regardless of both the particle volume fraction and the particle size distribution.

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.