A three-dimensional Markov field approach for the analysis of atomic clustering in atom probe data

Solute clustering is increasingly recognised as a significant characteristic within certain material systems that can be tailored to the optimization of bulk properties and performance. Atom probe tomography (APT) is emerging as a powerful tool for the detection of these nanoscale features; however, complementary to experiment, precise and efficient characterization algorithms are required to identify and characterise these nanoclusters within the potentially massive three-dimensional atomistic APT datasets. In this study, a new three-dimensional Markov field (3DMF) cluster identification algorithm is proposed. The algorithm is based upon an analysis of the direct atomic neighbourhood surrounding each atom, and the only input parameter required utilises known crystallographic properties of the system. Further, an array of statistical approaches has been developed and applied with respect to the results generated by the 3DMF algorithm including: an S N statistic, a two-tailed z-test, a difference measure, the χ2 test, and a direct evaluation of the Warren–Cowley parameter for short-range ordering. Finally, the methodologies have been applied to the characterization of the nanostructural evolution of an Al-1.1Cu-0.5Mg (at.%) alloy subjected to a variety of heat treatments.