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

Abstract

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.

Keywords:

• 3D Markov field
• clusters
• cluster hardening
• age hardening
• aluminium alloys
• microscopy
• atom probe

Acknowledgements

The authors are grateful for financial support from the Australian Research Council, which partly sponsored this work. A.V. Ceguerra is grateful for a Commonwealth Scientific and Industrial Research Organisation (CSIRO) top-up scholarship, and to Dr. Mahnaz Jahedi and colleagues at the CSIRO Materials Science and Engineering (CMSE) and the CSIRO Light Metals Flagship. The authors are grateful for scientific and technical input and support from the Australian Microscopy & Microanalysis Research Facility (AMMRF) node at The University of Sydney. Particular thanks for fruitful discussions are extended to Messrs. P.V. Liddicoat and D.J. Haley at the University of Sydney, Dr. Tomoyuki Honma now at Nagaoka University of Technology, Japan, and staff from Imago Scientific Instruments.