Inferring the Size Distribution of 3D Particle Clusters in Metal Matrix Nanocomposites

Metal matrix nanocomposites (MMNCs) are produced by dispersing reinforcing nanoparticles into metal matrix. It is a type of emerging materials with high strength and light weight and draws significant attentions in recent years. If the particles are not well dispersed, they will form particle clusters in the metal matrix. These clusters will detrimentally impact on the final quality of MMNCs. This paper proposes a statistical approach to estimating the parameters of the size distribution of clusters in MMNCs. One critical challenge is that the clusters are distributed in a three-dimensional (3D) space, while the observations we have are two-dimensional (2D) cross-section microscopic images of these clusters. In the proposed approach, we first derived the probability distribution of the observed sizes of the 2D cross sections of the clusters and then a maximum likelihood estimation (MLE) method is developed to estimate the 3D cluster size distribution. Computational efficient algorithms are also established to make computational load manageable. The case studies based on simulation and real observed data are conducted, which demonstrates the effectiveness of the proposed approach.