Refining spatial distribution maps for atom probe tomography via data dimensionality reduction methods.

Area of Science:

• Materials Science
• Data Analysis
• Nanotechnology

Background:

• Spatial distribution maps (SDMs) are crucial for analyzing atomic structures.
• Understanding covariance in interatomic frequency distributions within SDMs is challenging.
• Existing methods may not fully capture subtle atomic structural details.

Purpose of the Study:

• To develop a mathematical framework for analyzing covariance in SDM data.
• To identify and utilize structurally relevant singular vectors (SRSVs) for enhanced structural information extraction.
• To refine SDMs for improved three-dimensional atom probe tomography (3D APT).

Main Methods:

• Application of singular value decomposition (SVD) to SDM data.
• Identification of singular vectors capturing covariance within SDM datasets.
• Extraction of information from z-SDMs using SRSVs to capture interplanar atomic structure.
• Classification of SDM slices into relevant information, noise, and aberrations.

Main Results:

• Obtained singular vectors that effectively capture covariance in SDM data.
• Identified SRSVs that provide insights into atomic plane offsets and neighborhood covariance.
• Developed refined z-SDMs capable of distinguishing structural information from noise and aberrations.
• Constructed refined xy-SDMs yielding enhanced structural details for 3D APT.

Conclusions:

• The SVD-based framework and SRSVs offer a robust method for analyzing atomic structure in SDMs.
• Refined SDMs improve the accuracy and interpretability of data in 3D atom probe tomography.
• This approach enhances the extraction of meaningful structural information from complex nanoscale datasets.