The Maximum Separation Cluster Analysis Algorithm for Atom-Probe Tomography: Parameter Determination and Accuracy

AbstractAtom-probe tomography is a materials characterization method ideally suited for the investigation of clustering and precipitation phenomena. To distinguish the clusters from the surrounding matrix, the maximum separation algorithm is widely employed. However, the results of the cluster analysis strongly depend on the parameters used in the algorithm and hence, a wrong choice of parameters leads to erroneous results, e.g., for the cluster number density, concentration, and size. Here, a new method to determine the optimum value of the parameter dmax is proposed, which relies only on information contained in the measured atom-probe data set. Atom-probe simulations are employed to verify the method and to determine the sensitivity of the maximum separation algorithm to other input parameters. In addition, simulations are used to assess the accuracy of cluster analysis in the presence of trajectory aberrations caused by the local magnification effect. In the case of Cu-rich precipitates (Cu concentration 40–60 at% and radius 0.25–1.0 nm) in a bcc Fe–Si–Cu matrix, it is shown that the error in concentration is below 10 at% and the error in radius is <0.15 nm for all simulated conditions, provided that the correct value for dmax, as determined with the newly proposed method, is employed.

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Resolving the Morphology of Niobium Carbonitride Nano-Precipitates in Steel Using Atom Probe Tomography

Microscopy and Microanalysis ◽

10.1017/s1431927614012872 ◽

2014 ◽

Vol 20 (4) ◽

pp. 1100-1110 ◽

Cited By ~ 16

Author(s):

Andrew J. Breen ◽

Kelvin Y. Xie ◽

Michael P. Moody ◽

Baptiste Gault ◽

Hung-Wei Yen ◽

...

Keyword(s):

Electron Microscopy ◽

Atom Probe Tomography ◽

Atom Probe ◽

Niobium Carbonitride ◽

Surrounding Matrix ◽

Transmission Electron ◽

A New Technique ◽

Insight Into ◽

Reconstructed Data ◽

Magnification Effect

AbstractAtom probe is a powerful technique for studying the composition of nano-precipitates, but their morphology within the reconstructed data is distorted due to the so-called local magnification effect. A new technique has been developed to mitigate this limitation by characterizing the distribution of the surrounding matrix atoms, rather than those contained within the nano-precipitates themselves. A comprehensive chemical analysis enables further information on size and chemistry to be obtained. The method enables new insight into the morphology and chemistry of niobium carbonitride nano-precipitates within ferrite for a series of Nb-microalloyed ultra-thin cast strip steels. The results are supported by complementary high-resolution transmission electron microscopy.

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The Application of the OPTICS Algorithm to Cluster Analysis in Atom Probe Tomography Data

Microscopy and Microanalysis ◽

10.1017/s1431927618015386 ◽

2019 ◽

Vol 25 (2) ◽

pp. 338-348 ◽

Cited By ~ 4

Author(s):

Jing Wang ◽

Daniel K. Schreiber ◽

Nathan Bailey ◽

Peter Hosemann ◽

Mychailo B. Toloczko

Keyword(s):

Cluster Analysis ◽

Atom Probe Tomography ◽

Spatial Clustering ◽

Atom Probe ◽

Atomic Density ◽

Scale Model ◽

Small Scale ◽

Physical Parameters ◽

Structure Property ◽

Ferritic Alloy

AbstractAtom probe tomography (APT) is a powerful technique to characterize buried three-dimensional nanostructures in a variety of materials. Accurate characterization of those nanometer-scale clusters and precipitates is of great scientific significance to understand the structure–property relationships and the microstructural evolution. The current widely used cluster analysis method, a variant of the density-based spatial clustering of applications with noise algorithm, can only accurately extract clusters of the same atomic density, neglecting several experimental realities, such as density variations within and between clusters and the nonuniformity of the atomic density in the APT reconstruction itself (e.g., crystallographic poles and other field evaporation artifacts). This clustering method relies heavily on multiple input parameters, but ideal selection of those parameters is challenging and oftentimes ambiguous. In this study, we utilize a well-known cluster analysis algorithm, called ordering points to identify the clustering structures, and an automatic cluster extraction algorithm to analyze clusters of varying atomic density in APT data. This approach requires only one free parameter, and other inputs can be estimated or bounded based on physical parameters, such as the lattice parameter and solute concentration. The effectiveness of this method is demonstrated by application to several small-scale model datasets and a real APT dataset obtained from an oxide-dispersion strengthened ferritic alloy specimen.

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PosgenPy: An Automated and Reproducible Approach to Assessing the Validity of Cluster Search Parameters in Atom Probe Tomography Datasets

Microscopy and Microanalysis ◽

10.1017/s1431927621012368 ◽

2021 ◽

pp. 1-10

Author(s):

Przemysław Klupś ◽

Daniel Haley ◽

Andrew J. London ◽

Hazel Gardner ◽

James Famelton ◽

...

Keyword(s):

Atom Probe Tomography ◽

Spatial Clustering ◽

Atom Probe ◽

Parameter Selection ◽

Material System ◽

Number Density ◽

Cluster Number ◽

Simulated Material ◽

Parameter Values ◽

Selection Of

One of the main capabilities of atom probe tomography (APT) is the ability to not only identify but also characterize early stages of precipitation at length scales that are not achievable by other techniques. One of the most popular methods to identify nanoscale clustering in APT data, based on the density-based spatial clustering of applications with noise (DBSCAN), is used extensively in many branches of research. However, it is common that not all of the steps leading to the selection of certain parameters used in the analysis are reported. Without knowing the rationale behind parameter selection, it may be difficult to compare cluster parameters obtained by different researchers. In this work, a simple open-source tool, PosgenPy, is used to justify cluster search parameter selection via providing a systematic sweep through parameter values with multiple randomizations to minimize a false-positive cluster ratio. The tool is applied to several different microstructures: a simulated material system and two experimental datasets from a low-alloy steel . The analyses show how values for the various parameters can be selected to ensure that the calculated cluster number density and cluster composition are accurate.

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

Ultramicroscopy ◽

10.1016/j.ultramic.2020.113151 ◽

2021 ◽

Vol 220 ◽

pp. 113151

Author(s):

Galen B. Vincent ◽

Andrew P. Proudian ◽

Jeramy D. Zimmerman

Keyword(s):

Machine Learning ◽

Cluster Analysis ◽

Atom Probe Tomography ◽

Three Dimensional ◽

Atom Probe ◽

Ripley’S K Function ◽

Ripley’S K ◽

Ripley's K ◽

K Function

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Hierarchical density-based cluster analysis framework for atom probe tomography data

Ultramicroscopy ◽

10.1016/j.ultramic.2019.01.011 ◽

2019 ◽

Vol 200 ◽

pp. 28-38 ◽

Cited By ~ 12

Author(s):

I. Ghamarian ◽

E.A. Marquis

Keyword(s):

Cluster Analysis ◽

Atom Probe Tomography ◽

Atom Probe ◽

Analysis Framework ◽

Tomography Data

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Atom Probe Tomography Interlaboratory Study on Clustering Analysis in Experimental Data Using the Maximum Separation Distance Approach

Microscopy and Microanalysis ◽

10.1017/s1431927618015581 ◽

2019 ◽

Vol 25 (2) ◽

pp. 356-366 ◽

Cited By ~ 7

Author(s):

Yan Dong ◽

Auriane Etienne ◽

Alex Frolov ◽

Svetlana Fedotova ◽

Katsuhiko Fujii ◽

...

Keyword(s):

Experimental Data ◽

Group Analysis ◽

Atom Probe ◽

Separation Distance ◽

Interlaboratory Study ◽

304 Stainless Steel ◽

Published Data ◽

Local Concentration ◽

Cluster Number ◽

Maximum Separation

AbstractWe summarize the findings from an interlaboratory study conducted between ten international research groups and investigate the use of the commonly used maximum separation distance and local concentration thresholding methods for solute clustering quantification. The study objectives are: to bring clarity to the range of applicability of the methods; identify existing and/or needed modifications; and interpretation of past published data. Participants collected experimental data from a proton-irradiated 304 stainless steel and analyzed Cu-rich and Ni–Si rich clusters. The datasets were also analyzed by one researcher to clarify variability originating from different operators. The Cu distribution fulfills the ideal requirements of the maximum separation method (MSM), namely a dilute matrix Cu concentration and concentrated Cu clusters. This enabled a relatively tight distribution of the cluster number density among the participants. By contrast, the group analysis of the Ni–Si rich clusters by the MSM was complicated by a high Ni matrix concentration and by the presence of Si-decorated dislocations, leading to larger variability among researchers. While local concentration filtering could, in principle, tighten the results, the cluster identification step inevitably maintained a high scatter. Recommendations regarding reporting, selection of analysis method, and expected variability when interpreting published data are discussed.

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Atom Probe Reconstruction With a Locally Varying Emitter Shape

Microscopy and Microanalysis ◽

10.1017/s1431927618015350 ◽

2018 ◽

Vol 25 (2) ◽

pp. 280-287 ◽

Cited By ~ 2

Author(s):

Daniel Beinke ◽

Guido Schmitz

Keyword(s):

Atom Probe Tomography ◽

Local Density ◽

Atom Probe ◽

Radial Symmetry ◽

Reconstruction Technique ◽

Reconstruction Method ◽

New Approach ◽

Surrounding Matrix ◽

Projection Approach ◽

Point Projection

AbstractAn improved reconstruction method for atom probe tomography is presented. In this approach, the curvature of the field emitter is variable, in contrast to the conventional reconstruction technique. The information about the tip shape at different stages of the reconstruction is directly extracted from the local density of events on the detector. To this end, the detector and the tip surface are split into different segments. According to the density distribution of events observed on the detector, the size of the corresponding segment on the tip surface is calculated, yielding an emitter profile which is not necessarily spherical. The new approach is demonstrated for emitter structures with radial symmetry that contain a spherical precipitate with a substantially lower or higher evaporation field compared to the surrounding matrix. A comparison to the conventional point projection approach is made.

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