An order statistic approach for inference of the size distribution of 3D particle clusters in metal matrix nanocomposites

Metal matrix nanocomposites (MMNCs) become popular in recent decades due to their superior properties over traditional materials, like high strength and light weight. They are fabricated by dispersing nanoparticles into molten metal matrix. If nanoparticles are not well dispersed and form clusters in the metal matrix, the mechanical properties of the MMNC would be greatly affected. It is crucially important and useful if the size of three-dimensional (3D) clusters in the metal matrix can be extracted for process characterization. This paper proposes a novel approach based on order statistic theory to infer the size distribution of 3D particle clusters based on their two-dimensional (2D) cross-sectional microscopic images. The novelty of this idea is that it utilizes information from only the few largest 2D clusters, hence eliminating the practical difficulties in correctly identifying and accurately measuring the radii of small clusters. The joint probability distribution of the l largest 2D cluster radii is linked to the distribution of the 3D cluster size, based on which then maximum likelihood estimation (MLE) method is used to infer the 3D cluster size distribution. Extensive simulation studies and real cases have demonstrated the effectiveness, efficiency and robustness of the proposed approach compared to the existing methods.