Detecting 3D spatial clustering of particles in nanocomposites based on cross-sectional images

Metal matrix nanocomposites (MMNCs) are high-strength and lightweight materials with great potential in automotive, aerospace, and many other industries. A uniform distribution of nanoparticles in the metal matrix is critical for achieving high-quality MMNCs; hence, nonuniformity of the particle distribution in MMNCs needs to be detected for quality improvement. For this purpose, this article investigates the problem of three-dimensional (3D) clustering detection based on statistical modeling and analysis of the number of nanoparticles on microscopic cross-sectional images of MMNC specimens. Under a 3D distributional model, the probability distributions of the number of particles on an image under both uniform and nonuniform nanoparticle distributions are derived. Based on the results, a hypothesis test is proposed for detecting the existence of clustering. The performance of the method under various parameter settings is investigated. Finally, the method is applied to images from a real MMNC fabrication process. This article has supplementary material available online. © 2014 American Statistical Association and the American Society for Quality.