Hierarchical density-based cluster analysis framework for atom probe tomography data

Abstract

Atom probe tomography (APT) has enabled the direct visualization of solute clusters. However one of the main analysis methods used by the APT community, i.e. the maximum separation method, often suffers from subjective parametric selection and limited applicability. To address the need for more robust and versatile analysis tools, a framework based on hierarchical density-based cluster analysis is implemented. Cluster analysis begins with the HDBSCAN algorithm to conservatively segment the datasets into regions containing clusters and a matrix or noise region. The stability of each cluster and the probability that an atom belongs to a cluster are quantified. Each clustered region is further analyzed by the DeBaCl algorithm to separate and refine clusters present in the sub-volumes. Finally, the k-nearest neighbor algorithm may be used to re-assign matrix atoms to clusters, based on their probability values. Four mandatory parameters are required for this cluster analysis approach. However, the selection of an appropriate value for only one of these parameters, i.e. a rough estimate of the minimum cluster size, is essential. The improved performance of the method was evaluated by analyzing four synthetic APT datasets and comparing the outcome with the commonly-used maximum separation method. Codes and data are made available through GitHub.

Keywords: Atom probe tomography; Cluster search; DeBaCl; Density-based clustering; HDBSCAN; Level set tree.