Extracting features buried within high density atom probe point cloud data through simplicial homology

Srinivasan, Srikant; Kaluskar, Kaustubh; Broderick, Scott; Rajan, Krishna

doi:10.1016/j.ultramic.2015.04.009

Cited by 4 publications

(4 citation statements)

References 22 publications

(21 reference statements)

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“…Thus, a circle and a square have the same topology although they are geometrically different. Such qualitative geometric features can be represented by simplicial complexes, which are combinatorial objects that can represent spaces and separate the topology of a space from its geometry [62]. Simplicial homology is a process that provides information about the simplicial complex by the number of cycles (a type of hole) it contains.…”

Section: Topological Analysis For Defining Morphology Of Precipitatesmentioning

confidence: 99%

“…As discussed earlier and expanded upon in our prior work [62], the persistence of different topological features can be recorded as barcodes, which we now group according to each Betti number. The horizontal axis represents the parameter ɛ or the range of connectivity among points in the point cloud while the vertical axis captures the number of topological components present in the point cloud at each interval of ɛ.…”

Section: Topological Analysis For Defining Morphology Of Precipitatesmentioning

confidence: 99%

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Topological Data Analysis for the Characterization of Atomic Scale Morphology from Atom Probe Tomography Images

2018

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Atom probe tomography (APT) represents a revolutionary characterization tool for materials that combine atomic imaging with a time-of-flight (TOF) mass spectrometer to provide direct space three-dimensional, atomic scale resolution images of materials with the chemical identities of hundreds of millions of atoms. It involves the controlled removal of atoms from a specimen's surface by field evaporation and then sequentially analyzing them with a position sensitive detector and TOF mass spectrometer. A paradox in APT is that while on the one hand, it provides an unprecedented level of imaging resolution in three dimensions, it is very difficult to obtain an accurate perspective of morphology or shape outlined by atoms of similar chemistry and microstructure. The origins of this problem are numerous, including incomplete detection of atoms and the complexity of the evaporation fields of atoms at or near interfaces. Hence, unlike scattering techniques such as electron microscopy, interfaces appear diffused, not sharp. This, in turn, makes it challenging to visualize and quantitatively interpret the microstructure at the "meso" scale, where one is interested in the shape and form of the interfaces and their associated chemical gradients. It is here that the application of informatics at the nanoscale and statistical learning methods plays a critical role in both defining the level of uncertainty and helping to make quantitative, statistically objective interpretations where heuristics often dominate. In this chapter, we show how the tools of Topological Data Analysis provide a new and powerful tool in the field of nanoinformatics for materials characterization.

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Section: Topological Analysis For Defining Morphology Of Precipitatesmentioning

confidence: 99%

Section: Topological Analysis For Defining Morphology Of Precipitatesmentioning

confidence: 99%

Topological Data Analysis for the Characterization of Atomic Scale Morphology from Atom Probe Tomography Images

2018

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“…Other analyses of this material for different objectives are provided in the literature. [35][36][37] …”

Section: B Experimental Detailsmentioning

confidence: 99%

Impact of extreme electrical fields on charge density distributions in Al3Sc alloy

Loyola

Peralta

Broderick

et al. 2016

Journal of Vacuum Science &Amp; Technology A: Vacuum, Surfaces, and Films

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In this study, the authors investigated how extreme electrical fields affect charge distribution of metallic surfaces and bond character at the moment of evaporation. The surface structure and neighborhood chemistry were also studied as a function of various field evaporation pathways. Density functional theory (DFT) was used to model the surface bonding and charge distribution and then correlate the DFT results with experimental results by comparing the calculated evaporation fields with atom probe tomography measurements. The evaporation fields of different surface neighborhood chemistries in L12-Al3Sc were calculated, with the Sc atoms occupying the corners of a cubic unit cell and the Al atoms occupying the face centers. Al-Al surface atoms are found via DFT to be more likely to evaporate as dimers because of the Al-Al shared charge density. In contrast, Al-Sc evaporates as single ions due to the increased density localized around the Sc atom. This difference in evaporation behavior correlates with the resistance to degradation under extreme fields. This work allows better interpretation of the atom probe data by clarifying the relationship between different evaporation events and the role of surface and subsurface chemistry.

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“…* daniel.mason@ukaea.uk Methods related to topology have previously been applied in APM, to define clusters [14] and for the analysis of segregation [15]. Measurements of the topology have been made using the Euler characteristic for spinodal decomposition [16] as well as for feature extraction [17,18].…”

Section: Introductionmentioning

confidence: 99%

Morphological analysis of 3d atom probe data using Minkowski functionals

Mason¹,

London²

2020

Ultramicroscopy

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We present a morphological analysis of atom probe data of nanoscale microstructural features, using methods developed by the astrophysics community to describe the shape of superclusters of galaxies. We describe second-phase regions using Minkowski functionals, representing the regions' volume, surface area, mean curvature and Euler characteristic. The alloy data in this work show microstructures that can be described as sponge-like, filament-like, plate-like, and sphere-like at different concentration levels, and we find quantitative measurements of these features. To reduce user decision-making in constructing isosurfaces and to enhance the accuracy of the analysis a maximum likelihood based denoising filter was developed. We show that this filter performs significantly better than a simple Gaussian smoothing filter. We also interpolate the data using natural cubic splines, to refine voxel sizes and to refine the surface. We demonstrate that it is possible to find a mathematically well-defined, quantitative description of microstructure from atomistic datasets, to sub-voxel resolution, without user-tuneable parameters.

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Extracting features buried within high density atom probe point cloud data through simplicial homology

Cited by 4 publications

References 22 publications

Topological Data Analysis for the Characterization of Atomic Scale Morphology from Atom Probe Tomography Images

Topological Data Analysis for the Characterization of Atomic Scale Morphology from Atom Probe Tomography Images

Impact of extreme electrical fields on charge density distributions in Al3Sc alloy

Morphological analysis of 3d atom probe data using Minkowski functionals

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