Three dimensional cluster analysis for atom probe tomography using Ripley's K-function and machine learning.

Area of Science:

• Materials Science
• Computational Materials Science
• Data Science

Background:

• Accurate quantification of spatial clustering is crucial for understanding material properties.
• Ripley's K-function (K(r)) is a statistical tool for measuring spatial correlation in point patterns.
• Existing methods for cluster quantification can be subjective and less robust.

Purpose of the Study:

• To develop and validate a machine learning approach using K(r) metrics for accurate cluster size and density estimation.
• To apply this novel method to experimental data for characterizing nanoscale clusters in alloys.

Main Methods:

• Utilized simulated 3D point patterns with spherical clusters of varying sizes.
• Developed machine learning models trained on K(r)-derived metrics.
• Applied the trained models to experimental atom probe tomography (APT) data of MgZn clusters in an aluminum alloy.

Main Results:

• Machine learning models achieved over 90% accuracy, with errors within 11% for cluster size and 18% for intra-cluster density in simulations.
• K(r)-based estimates for MgZn clusters in an aluminum alloy were more accurate, consistent, and robust than those from the maximum separation algorithm.

Conclusions:

• Ripley's K-function combined with machine learning provides an accurate, repeatable, and objective method for quantifying material clustering.
• This approach enhances the characterization of microstructural features and their impact on material properties.