Detecting and extracting clusters in atom probe data: a simple, automated method using Voronoi cells

The analysis of the formation of clusters in solid solutions is one of the most common uses of atom probe tomography. Here, we present a method where we use the Voronoi tessellation of the solute atoms and its geometric dual, the Delaunay triangulation to test for spatial/chemical randomness of the solid solution as well as extracting the clusters themselves. We show how the parameters necessary for cluster extraction can be determined automatically, i.e. without user interaction, making it an ideal tool for the screening of datasets and the pre-filtering of structures for other spatial analysis techniques. Since the Voronoi volumes are closely related to atomic concentrations, the parameters resulting from this analysis can also be used for other concentration based methods such as iso-surfaces.