A Concept of Local Coordination Number for the Characterization of Solute Clusters within Atom Probe Tomography Data

Identifying clusters of solute atoms in a matrix of solvent atoms helps to understand precipitation phenomena in alloys, for example, during the age hardening of certain aluminum alloys. Atom probe tomography datasets can deliver such information, provided that appropriate cluster identification routines are available. We investigate algorithms based on the local composition of the neighborhood of solute atoms and compare them with traditional approaches based on the local solute number density, such as the maximum separation distance method. For an ideal solid solution, the pair correlation functions of the kth nearest solute atom in the coordination number representation are derived, and the percolation threshold and the size distribution of clusters are studied. A criterion for selecting optimal control parameters based on maximizing the phase separation by the degree of clustering is proposed for a two-phase system. A map of phase compositions accessible for cluster analysis is constructed. The coordination number approach reduces the influence of density variations commonly observed in atom probe tomography data. Finally, a practical cluster analysis technique applied to the early stages of aluminum alloy aging is described.