UC Berkeley

Atom Probe Tomography (APT) is a powerful analytical technique for 3D characterization of materials at the atomic scale which has been widely used to study irradiation induced features. However, the accuracy and reliability of the atom probe reconstruction and post-processing methods such as cluster analysis is often neglected. In an effort to account for both of these limitations we introduce a two-step method for quantifying the quality of an atom probe reconstruction and the resulting secondary analysis.

First, we developed a pointwise measure of uncertainty for APT data based on linear error propagation. This approach provide a systematic way of estimating the uncertainty in the atom positions and the most influential reconstruction parameters. The pointwise uncertainty measure can be used to assess the local quality of APT data and govern alternate reconstruction directions which minimize uncertainty. Furthermore, focusing the error analysis not on resolution but on parameter and coordinate uncertainty enables error to be propagated through complex processes such as the measurement of isotopically enriched thin films.

Second, we developed a method which extends monte-carlo consensus clustering from K-based clustering algorithms to density-based clustering algorithms. In doing so a measure of relative stability is introduced to describe the ambiguity of clustering observed in an APT sample and automate the selection of the distance parameter for DBSCAN (Density-based spatial clustering of applications with noise). Our approach uses Monte-Carlo perturbation statistics, and thus could be linked to use the pointwise uncertainty established in the first part of this work, to generate alternate atom probe datasets and then apply DBSCAN to each of these datasets. In doing so the sample size for which to calculate grows in magnitude enabling more thorough post-clustering filtration methods with which to extract clusters from high-noise scenarios. We use statistical methods to analyze the results and determine the optimal DBSCAN parameters that maximize the clustering performance and minimize the uncertainty.

The efficacy and utility of pointwise error propagation is demonstrated through a case study on the measurement of an isotopically enriched iron thin film while our novel clustering algorithm, Density-based Monte-Carlo Consensus Clustering (DMC3), is benchmarked against a round robin study on binary Fe-Cu systems with an emphasis on irradiation induced hardening. Our approaches provides a quantitative and objective way of assessing the quality of APT data and improving the reliability of APT data analysis.