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

Abstract

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.

Classification of apatite structures via topological data analysis: a framework for a ‘Materials Barcode’ representation of structure maps

“…Persistent homology (PH) is the most commonly used method in TDA, which captures topological features in the high-dimensional data, such as connected components, loops, and holes, at multiple scales. All TDA methods treat high-dimension data as a point cloud 26 – 31 . PH maps a set X of points in the high-dimensional space associated with a distance function.…”

Morphological analysis of 3d atom probe data using Minkowski functionals

“…We can then compute the loglikelihood of the measurement (equation 11). If the loglikelihood is increasing, we can iterate, using f i in place off i to compute the kernel ( equations 19,18 ), then using equations 20,21 to update f i again, until the maximum log-likelihood is found. By this iterative scheme we find a smoothed concentration field f i which preserves the atom count and maximises the likelihood of having measured f i .…”

“…* 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].…”

Data-centric science for materials innovation

“…There are many examples of this, such as the analysis of hyperspectral image data obtained by transmission electron microscopy, 42,43 and topological data analysis of atom probe tomography images. 44 A high-throughput synthesis (thin films) and characterization approach with composition and temperature gradients across the substrate has been systematically conducted and the outputs are stored in the highthroughput experimental materials (HTEMs) database (www.htem.nrel.gov). 45 Linking such data to theory and the related assessment of accuracy of measurements in HTS can help in making combinatorial libraries become a source of generating reference data.…”