Extracting features buried within high density atom probe point cloud data through simplicial homology

Feature extraction from Atom Probe Tomography (APT) data is usually performed by repeatedly delineating iso-concentration surfaces of a chemical component of the sample material at different values of concentration threshold, until the user visually determines a satisfactory result in line with prior knowledge. However, this approach allows for important features, buried within the sample, to be visually obscured by the high density and volume (~107 atoms) of APT data. This work provides a data driven methodology to objectively determine the appropriate concentration threshold for classifying different phases, such as precipitates, by mapping the topology of the APT data set using a concept from algebraic topology termed persistent simplicial homology. A case study of Sc precipitates in an Al-Mg-Sc alloy is presented demonstrating the power of this technique to capture features, such as precise demarcation of Sc clusters and Al segregation at the cluster boundaries, not easily available by routine visual adjustment.