A graph-theoretic approach for characterization of precipitates from atom probe tomography data

Atom Probe Tomography (APT) represents a revolutionary characterization tool that allows direct-space three-dimensional, atomic-scale resolution imaging along with the chemical identities of each detected atom. Quantitative analysis of APT data to perform characterization of precipitates in alloys gives clear insights into the structure-property relationships and helps in achieving the larger goal of materials-by-design. Most techniques currently used to extract precipitate topology and interface information from APT data are efficient; however, they are based on homogenization of the rich point cloud data which is inherently lossy. Furthermore, these methods require a specified, usually heuristic, concentration-level to draw iso-contours in order to extract characteristics of the precipitate topology. These twin issues of homogenization and heuristics are compelling rationale for the development of a robust, scalable, heuristic-free, graph-based framework, which we call Graph methods for Precipitate Topology Characterization (GraPTop). This framework is motivated by the equivalence between a 3D point cloud data of atoms and an undirected, weighted, labeled graph. By considering the 3D point cloud data as an undirected, weighted, labeled graph, we leverage powerful graph-based algorithms to identify the local topology of precipitates without the necessity of any heuristics. Since GraPTop is based on nearly linear-complexity graph-algorithms, it is scalable to extremely large datasets. Furthermore, the performance of this framework is insensitive to the complexity of the geometry or the number of the precipitates in the point cloud data. We showcase this framework by analyzing several regions of interest in a point cloud Al-Mg-Sc (Aluminium-Magnesium-Scandium) specimen APT data and extract several interesting measures describing the precipitate topology like area, volume, and nonconvexity.