The Application of the OPTICS Algorithm to Cluster Analysis in Atom Probe Tomography Data

Atom probe tomography (APT) is a powerful technique to characterize buried three-dimensional nanostructures in a variety of materials. Accurate characterization of those nanometer-scale clusters and precipitates is of great scientific significance to understand the structure–property relationships and the microstructural evolution. The current widely used cluster analysis method, a variant of the density-based spatial clustering of applications with noise algorithm, can only accurately extract clusters of the same atomic density, neglecting several experimental realities, such as density variations within and between clusters and the nonuniformity of the atomic density in the APT reconstruction itself (e.g., crystallographic poles and other field evaporation artifacts). This clustering method relies heavily on multiple input parameters, but ideal selection of those parameters is challenging and oftentimes ambiguous. In this study, we utilize a well-known cluster analysis algorithm, called ordering points to identify the clustering structures, and an automatic cluster extraction algorithm to analyze clusters of varying atomic density in APT data. This approach requires only one free parameter, and other inputs can be estimated or bounded based on physical parameters, such as the lattice parameter and solute concentration. The effectiveness of this method is demonstrated by application to several small-scale model datasets and a real APT dataset obtained from an oxide-dispersion strengthened ferritic alloy specimen.