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The size and structure of spatial molecular and atomic clustering cansignificantly impact material properties and is therefore important toaccurately quantify. Ripley's K-function (K(r)), a measure of spatialcorrelation, can be used to perform such quantification when the materialsystem of interest can be represented as a marked point pattern. This workdemonstrates how machine learning models based on K(r)-derived metrics canaccurately estimate cluster size and intra-cluster density in simulated threedimensional (3D) point patterns containing spherical clusters of varying size;over 90% of model estimates for cluster size and intra-cluster density fallwithin 11% and 18% error of the true values, respectively. These K(r)-basedsize and density estimates are then applied to an experimental APTreconstruction to characterize MgZn clusters in a 7000 series aluminum alloy.We find that the estimates are more accurate, consistent, and robust to userinteraction than estimates from the popular maximum separation algorithm. UsingK(r) and machine learning to measure clustering is an accurate and repeatableway to quantify this important material attribute.

Using Ripley's K-function to Characterize Clustering In 3-Dimensional Point Patterns With a Case Study in Atom Probe Tomography