Atom Probe Tomography Datasets Research Articles

Developing the Metrology for Atomic Level Spatial Distribution and Local Chemistry Analysis of in-Situ Dopants By Atom Probe Tomography

We present a metrology for analyzing the spatial distribution and local chemistry of in-situ dopants using Atom Probe Tomography (APT). Our approach integrates a 'local composition method' with a Kolmogorov-Smirnov test on a 3D APT dataset to evaluate spatial inhomogeneity. This methodology was applied to a nanometer scale in-situ highly boron-doped silicon germanium layer. By subdividing the dopant-dopant local composition distribution into three, its influence on the localized chemical environment was determined. Our findings reveal an inhomogeneous spatial distribution for the dopant and the Si/Ge atoms. Our results demonstrate the potential for linking at an atomic-scale the epitaxial growth conditions of dopants and the matrix elements to a device performance.

A Concept of Local Coordination Number for the Characterization of Solute Clusters within Atom Probe Tomography Data.

Identifying clusters of solute atoms in a matrix of solvent atoms helps to understand precipitation phenomena in alloys, for example, during the age hardening of certain aluminum alloys. Atom probe tomography datasets can deliver such information, provided that appropriate cluster identification routines are available. We investigate algorithms based on the local composition of the neighborhood of solute atoms and compare them with traditional approaches based on the local solute number density, such as the maximum separation distance method. For an ideal solid solution, the pair correlation functions of the kth nearest solute atom in the coordination number representation are derived, and the percolation threshold and the size distribution of clusters are studied. A criterion for selecting optimal control parameters based on maximizing the phase separation by the degree of clustering is proposed for a two-phase system. A map of phase compositions accessible for cluster analysis is constructed. The coordination number approach reduces the influence of density variations commonly observed in atom probe tomography data. Finally, a practical cluster analysis technique applied to the early stages of aluminum alloy aging is described.

Scalable substrate development for aqueous sample preparation for atom probe tomography.

Reliable and consistent preparation of atom probe tomography (APT) specimens from aqueous and hydrated biological specimens remains a significant challenge. One particularly difficult process step is the use of a focused ion beam (FIB) instrument for preparing the required needle-shaped specimen, typically involving a "lift-out" procedure of a small sample of material. Here, two alternative substrate designs are introduced that enable using FIB only for sharpening, along with example APT datasets. The first design is a laser-cut FIB-style half-grid close to those used for transmission-electron microscopy, that can be used in a grid holder compatible with APT pucks. The second design is a larger, standalone self-supporting substrate called a "crown," with several specimen positions that self-aligns in APT pucks, prepared by electrical discharge machining (EDM). Both designs are made nanoporous, to provide strength to the liquid-substrate interface, using chemical and vacuum dealloying. We select alpha brass a simple, widely available, lower-cost alternative to previously proposed substrates. We present the resulting designs, APT data, and provide suggestions to help drive wider community adoption. Lay Description Atom probe tomography (APT) maps the composition of solid materials in three dimensions with sub-nanometre resolution. Preparation of specimens from aqueous specimens remains a significant challenge. To aid with preparation, we introduce here two substrate designs that can hold suitable volumes of liquid for freezing, prior to shaping the final specimen into a sharp needle for APT by using cryogenic focused ion beam milling. We also describe the complete setup that we designed for handling these substrates, including dedicated sample holders. Both substrates are made nanoporous, to provide strength to the liquid-substrate interface, using chemical and vacuum dealloying of alpha brass a simple, widely available, low-cost material. We finally showcase APT data and provide suggestions to help drive wider community adoption. This article is protected by copyright. All rights reserved.

Revealing in-plane grain boundary composition features through machine learning from atom probe tomography data

Grain boundaries (GBs) are planar lattice defects that govern the properties of many types of polycrystalline materials. Hence, their structures have been investigated in great detail. However, much less is known about their chemical features, owing to the experimental difficulties to probe these features at the atomic length scale inside bulk material specimens. Atom probe tomography (APT) is a tool capable of accomplishing this task, with an ability to quantify chemical characteristics at near-atomic scale. Using APT data sets, we present here a machine-learning-based approach for the automated quantification of chemical features of GBs. We trained a convolutional neural network (CNN) using twenty thousand synthesized images of grain interiors, GBs, or triple junctions. Such a trained CNN automatically detects the locations of GBs from APT data. Those GBs are then subjected to compositional mapping and analysis, including revealing their in-plane chemical decoration patterns. We applied this approach to experimentally obtained APT data sets pertaining to three case studies, namely, Ni-P, Pt-Au, and Al-Zn-Mg-Cu alloys. In the first case, we extracted GB specific segregation features as a function of misorientation and coincidence site lattice character. Secondly, we revealed interfacial excesses and in-plane chemical features that could not have been found by standard compositional analyses. Lastly, we tracked the temporal evolution of chemical decoration from early-stage solute GB segregation in the dilute limit to interfacial phase separation, characterized by the evolution of complex composition patterns. This machine-learning-based approach provides quantitative, unbiased, and automated access to GB chemical analyses, serving as an enabling tool for new discoveries related to interface thermodynamics, kinetics, and the associated chemistry-structure-property relations.

Assessment of Local Observation of Atomic Ordering in Alloys via the Radial Distribution Function: A Computational and Experimental Approach

As a powerful analytical technique, atom probe tomography (APT) has the capacity to acquire the spatial distribution of millions of atoms from a complex sample. However, extracting information at the Ångstrom-scale on atomic ordering remains a challenge due to the limits of the APT experiment and data analysis algorithms. The development of new computational tools enable visualization of the data and aid understanding of the physical phenomena such as disorder of complex crystalline structures. Here, we report progress towards this goal using two steps. We describe a computational approach to evaluate atomic ordering in the crystal structure by generating radial distribution functions (RDF). Atomic ordering is rendered as the Fractional Cumulative Radial Distribution Function (FCRDF) which allows for greater visibility of local compositions at short range in the structure. Further, we accommodate in the analysis additional parameters such as uncertainty in the atomic coordinates and the atomic abundance to ascertain short-range ordering in APT data sets. We applied the FCRDF analysis to synthetic and experimental APT data sets for Ni3Al. The ability to observe a signal of atomic ordering consistent with the known L12 crystal structure is heavily dependent on spatial uncertainty, irrespective of abundance. Detection of atomic ordering is subject to an upper limit of spatial uncertainty of atoms described with Gaussian distributions with a standard deviation of 1.3 Å. The FCRDF analysis was also applied to the APT data set for a six-component alloy, Al1.3CoCrCuFeNi. In this case, we are currently able to visualize elemental segregation at the nanoscale, though unambiguous identification of atomic ordering at the Ångstrom (nearest-neighbor) scale remains a goal.

Open and strong-scaling tools for atom-probe crystallography: high-throughput methods for indexing crystal structure and orientation.

Volumetric crystal structure indexing and orientation mapping are key data processing steps for virtually any quantitative study of spatial correlations between the local chemical composition features and the microstructure of a material. For electron and X-ray diffraction methods it is possible to develop indexing tools which compare measured and analytically computed patterns to decode the structure and relative orientation within local regions of interest. Consequently, a number of numerically efficient and automated software tools exist to solve the above characterization tasks. For atom-probe tomography (APT) experiments, however, the strategy of making comparisons between measured and analytically computed patterns is less robust because many APT data sets contain substantial noise. Given that sufficiently general predictive models for such noise remain elusive, crystallography tools for APT face several limitations: their robustness to noise is limited, and therefore so too is their capability to identify and distinguish different crystal structures and orientations. In addition, the tools are sequential and demand substantial manual interaction. In combination, this makes robust uncertainty quantification with automated high-throughput studies of the latent crystallographic information a difficult task with APT data. To improve the situation, the existing methods are reviewed and how they link to the methods currently used by the electron and X-ray diffraction communities is discussed. As a result of this, some of the APT methods are modified to yield more robust descriptors of the atomic arrangement. Also reported is how this enables the development of an open-source software tool for strong scaling and automated identification of a crystal structure, and the mapping of crystal orientation in nanocrystalline APT data sets with multiple phases.

Materials Fingerprinting Classification

Significant progress in many classes of materials could be made with the availability of experimentally-derived large datasets composed of atomic identities and three-dimensional coordinates. Methods for visualizing the local atomic structure, such as atom probe tomography (APT), which routinely generate datasets comprised of millions of atoms, are an important step in realizing this goal. However, state-of-the-art APT instruments generate noisy and sparse datasets that provide information about elemental type, but obscure atomic structures, thus limiting their subsequent value for materials discovery. The application of a materials fingerprinting process, a machine learning algorithm coupled with topological data analysis, provides an avenue by which here-to-fore unprecedented structural information can be extracted from an APT dataset. As a proof of concept, the material fingerprint is applied to high-entropy alloy APT datasets containing body-centered cubic (BCC) and face-centered cubic (FCC) crystal structures. A local atomic configuration centered on an arbitrary atom is assigned a topological descriptor, with which it can be characterized as a BCC or FCC lattice with near perfect accuracy, despite the inherent noise in the dataset. This successful identification of a fingerprint is a crucial first step in the development of algorithms which can extract more nuanced information, such as chemical ordering, from existing datasets of complex materials. Program summaryProgram Title: Materials FingerprintingCPC Library link to program files:https://doi.org/10.17632/2fhch3x85m.1Developer's repository link:https://github.com/maroulaslab/Materials-FingerprintingLicensing provisions: GPLv3Programming language: PythonSupplementary material: A user manual and examples are provided with the source code in the GitHub repository.Nature of problem: Atom probe tomography provides sub-nanometer resolution of a material, but due to noise and sparsity introduced by the process, the crystal structure of a material cannot presently be determined from the resulting data.Solution method: Our Materials Fingerprinting library presents a topologically informed machine learning methodology to classify the lattice structure of a material from atomic probe tomography data. We create persistence diagrams from small neighborhoods centered at each atom in the resulting APT data and use the summary statistics of a novel metric on the space of persistence diagrams as features for a classification algorithm.

On strong-scaling and open-source tools for analyzing atom probe tomography data

The development of strong-scaling computational tools for high-throughput methods with an open-source code and transparent metadata standards has successfully transformed many computational materials science communities. While such tools are mature already in the condensed-matter physics community, the situation is still very different for many experimentalists. Atom probe tomography (APT) is one example. This microscopy and microanalysis technique has matured into a versatile nano-analytical characterization tool with applications that range from materials science to geology and possibly beyond. Here, data science tools are required for extracting chemo-structural spatial correlations from the reconstructed point cloud. For APT and other high-end analysis techniques, post-processing is mostly executed with proprietary software tools, which are opaque in their execution and have often limited performance. Software development by members of the scientific community has improved the situation but compared to the sophistication in the field of computational materials science several gaps remain. This is particularly the case for open-source tools that support scientific computing hardware, tools which enable high-throughput workflows, and open well-documented metadata standards to align experimental research better with the fair data stewardship principles. To this end, we introduce paraprobe, an open-source tool for scientific computing and high-throughput studying of point cloud data, here exemplified with APT. We show how to quantify uncertainties while applying several computational geometry, spatial statistics, and clustering tasks for post-processing APT datasets as large as two billion ions. These tools work well in concert with Python and HDF5 to enable several orders of magnitude performance gain, automation, and reproducibility.

Revealing Solute Clusters in Coalescence by Atom Probe Tomography Analysis.

Experimentally revealing dynamic evolution and growth behavior of small solute clusters in alloys remains a technical challenge. To date, the coalescence of the solute clusters has seldom been experimentally addressed. To address the challenge, we used atom probe tomography (APT) to access boundary information of solute clusters and identify those in close contact. By systematically investigating the population and size evolution of the clusters in close contact with aging time, we unveiled important information regarding the clusters in coalescence with the exsitu experimental technique. In this work, the maximum separation method was employed to identify clusters in APT datasets of naturally aged Al–Zn–Mg alloy. Coalescence was found to significantly contribute to the growth of small clusters and remained predominant for the formation and growth of large Guinier–Preston II ${\rm \lpar G}{\rm P}_{{\eta }^{\prime}}\rpar$ zones after 3 months aging.

Towards model-driven reconstruction in atom probe tomography

Reconstructions in atom probe tomography (APT) are plagued by image distortions arising from changes in the specimen geometry throughout the experiment. The simplistic and inaccurate geometrical assumptions that underpin the conventional reconstruction approach account for much of this distortion. Here we extend our previous work of modelling APT experiments using level set methods to three dimensions (3D). This model is used to generate and subsequently reconstruct synthetic APT datasets from electron tomography (ET) of an multiphase specimen. Finally, we apply our model to the reconstruction of an experimental field-effect transistor (finFET) dataset. This model-driven reconstruction successfully reduces density distortions compared to conventional methods. By combining prior knowledge about the specimen geometry from sources such as ET, such an approach promises new distortion correcting APT reconstruction applicable to complex specimen geometries.

Objective identification of local spatial structure for material characterization

AbstractObjective tools for characterizing materials at the atomic level are often difficult to develop because of the size or structure of the data. Atom probe tomography (APT) is a measurement tool that maps the location and type of atoms in materials in three‐dimensions (3D), producing data sets with potentially billions of observations. In this work, we present a set of spatial statistics methods developed to test the null hypotheses of no global spatial association; no local spatial association; and no local spatial cross‐correlation and apply these for the first time to APT data. The empirical and modeled covariogram and Moran's I can be used to study the global structure of a spatially referenced atomic element. The local indicator of spatial association (LISA) identifies volumes where high levels of values (hot spots) or low levels of values (cold spots) of elemental clustering exist. The local indicator of spatial cross‐correlation (LISC) reports where simultaneously high levels or low levels of two atomic elements occur. For each test statistic at each location, an associated p‐value is produced that can be used to weigh the evidence in favor of spatial clustering. The size of APT data sets presents some challenges, so the effect of weight functions and neighborhood selection on the computation and significance of the test statistics are discussed, and the issue of multiple statistical testing is also considered. These methods are illustrated using an APT data set with atomic percentages reported in voxels binned to 1 nm3.

Interpreting nanovoids in atom probe tomography data for accurate local compositional measurements

Quantifying chemical compositions around nanovoids is a fundamental task for research and development of various materials. Atom probe tomography (APT) and scanning transmission electron microscopy (STEM) are currently the most suitable tools because of their ability to probe materials at the nanoscale. Both techniques have limitations, particularly APT, because of insufficient understanding of void imaging. Here, we employ a correlative APT and STEM approach to investigate the APT imaging process and reveal that voids can lead to either an increase or a decrease in local atomic densities in the APT reconstruction. Simulated APT experiments demonstrate the local density variations near voids are controlled by the unique ring structures as voids open and the different evaporation fields of the surrounding atoms. We provide a general approach for quantifying chemical segregations near voids within an APT dataset, in which the composition can be directly determined with a higher accuracy than STEM-based techniques.

Using alpha hulls to automatically and reproducibly detect edge clusters in atom probe tomography datasets

An automated way to accurately and reproducibly identify edge clusters within atom probe tomography datasets has been developed. The alpha-hull algorithm is used to generate a concave alpha-shape around an atom probe dataset. Information from core-linkage cluster searches is used, in combination with the calculated alpha-shape, to determine which clusters are on the edge of the dataset.The potential effects that not removing edge clusters may have on calculated cluster sizes, number densities and compositions is discussed. The viability of the methodology is demonstrated via application to real datasets, one of which was a non-standard shape.The sensitivity of the method to user parameter selection is explored. Sampling fractions >0.1% and an alpha value, used to make the alpha shape, greater than twice the maximum measured nearest neighbour distance were found to be suitable.

Characterization of nano-sized precipitation and dislocations and the correlation with mechanical properties of a low alloy TRIP-aided steel

The present work focuses on structure-property correlation in a new low alloy multi-phase microstructure steel engineered with retained austenite via Cu alloying plus a three-step heat treatment, namely, intercritical annealing, intercritical tempering and sub-critical tempering of an as hot rolled structure. Particular attention was paid to characterizing nano-sized precipitates and dislocations after the three-step heat treatment by atom probe tomography (APT) and transmission electron microscopy (TEM), in order to establish their respective contribution to the yield strength. Cu-rich atomic clusters and ultra-fine precipitates were obtained in intercritical ferrite after the three-step heat treatment. The average radius of clusters and precipitates was 1.3±0.4 nm and 5.6±0.7 nm, respectively. The number density of clusters and precipitates was estimated as 2.55 × 1023 m-3 and 1.68 × 1021 m-3, respectively. The strength contribution from clusters and precipitates was ~72 MPa and ~101 MPa, respectively, assuming the number density of the APT dataset to represent the whole material. In addition, a large number of dislocations were observed in the intercritical ferrite by TEM study. The average density of dislocations was measured to be ~1.66 × 1014 ± 7.12 × 1013 m-2, which contributed ~250 MPa to yield strength according to the Bailey–Hirsch relationship.

A Precise Method for Analysis of Elemental Distribution Inside Solute Clusters.

A procedure to analyze the elemental concentration distribution inside solute clusters after detection of clusters from atom probe tomography data set was proposed. We developed a code which can directly illustrate an average concentration profile inside a cluster even in the case of including various sizes of ellipsoidal clusters. The profile can be with respect to absolute distance and includes errors in each data point. The reliability of the developed code was verified by analyzing an artificial cluster model which has inhomogeneous elemental distribution. It was found that the precise estimation of cluster centroids is important and that the preferable conditions for targeting clusters are a detection efficiency of over 20%, over 30 atoms in a cluster on average, and over 100 atoms for each concentration data point.

Spatial distribution of substitutional Mn-As clusters in ferromagnetic (Zn,Sn,Mn)As2 thin films revealed by image reconstruction of atom probe tomography data

The ferromagnetic transition in (Zn,Sn,Mn)As2 thin films is explained in terms of magnetic percolation in a Mn-As clustering network. We first studied the relationship between the spatial distribution of Mn-As clusters and the Curie temperature (TC). The local atomic structure was reconstructed from datasets of atomic positions in (Zn,Sn,Mn)As2 obtained by atom probe tomography (APT). To probe the local atomic structure and the magnetic properties of Mn-As clusters in ZnSnAs2 thin films, we investigated molecular beam epitaxially grown (Zn,Sn,Mn)As2 samples doped with 2.1 and 3.6 at. % Mn. Representative regions with a low and high Mn concentration were extracted from APT datasets. Mn-As clusters containing 2-36 Mn atoms were identified in regions of high Mn concentration. We also obtained a correlation between TC and Mn-As clustering that was consistent with not only the experimental results but also first-principles calculations using the mean-field approximation.

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

Atom probe tomography (APT) has enabled the direct visualization of solute clusters. However one of the main analysis methods used by the APT community, i.e. the maximum separation method, often suffers from subjective parametric selection and limited applicability. To address the need for more robust and versatile analysis tools, a framework based on hierarchical density-based cluster analysis is implemented. Cluster analysis begins with the HDBSCAN algorithm to conservatively segment the datasets into regions containing clusters and a matrix or noise region. The stability of each cluster and the probability that an atom belongs to a cluster are quantified. Each clustered region is further analyzed by the DeBaCl algorithm to separate and refine clusters present in the sub-volumes. Finally, the k-nearest neighbor algorithm may be used to re-assign matrix atoms to clusters, based on their probability values. Four mandatory parameters are required for this cluster analysis approach. However, the selection of an appropriate value for only one of these parameters, i.e. a rough estimate of the minimum cluster size, is essential. The improved performance of the method was evaluated by analyzing four synthetic APT datasets and comparing the outcome with the commonly-used maximum separation method. Codes and data are made available through GitHub.

An Automated Computational Approach for Complete In-Plane Compositional Interface Analysis by Atom Probe Tomography.

We introduce an efficient, automated computational approach for analyzing interfaces within atom probe tomography datasets, enabling quantitative mapping of their thickness, composition, as well as the Gibbsian interfacial excess of each solute. Detailed evaluation of an experimental dataset indicates that compared with the composition map, the interfacial excess map is more robust and exhibits a relatively higher resolution to reveal compositional variations. By field evaporation simulations with a predefined emitter mimicking the experimental dataset, the impact of trajectory aberrations on the measurement of the thickness, composition, and interfacial excess of the decorated interface are systematically analyzed and discussed.

DF-Fit: A Robust Algorithm for Detection of Crystallographic Information in Atom Probe Tomography Data

We report on a new algorithm for the detection of crystallographic information in three-dimensional, as retained in atom probe tomography (APT), with improved robustness and signal detection performance. The algorithm is underpinned by one-dimensional distribution functions (DFs), as per existing algorithms, but eliminates an unnecessary parameter as compared to current methods.By examining traditional DFs in an automated fashion in real space, rather than using Fourier transform approaches, we utilize an error metric based upon the expected value for a spatially random distribution for detecting crystallography. We show cases where the metric is able to successfully obtain orientation information, and show that it can function with high levels of additive and displacive background noise. We additionally compare this metric to Fourier transform methods, showing fewer artifacts when examining simulated datasets. An extension of the approach is used to aid the automatic detection of high-quality data regions within an entire dataset, albeit with a large increase in computational cost.This extension is demonstrated on acquired aluminum and tungsten APT datasets, and shown to be able to discern regions of the data which have relatively improved spatial data quality. Finally, this program has been made available for use in other laboratories undertaking their own analyses.

Composition Metrology of Ternary Semiconductor Alloys Analyzed by Atom Probe Tomography

Ternary semiconductor alloys based on the AyB1–yC stoichiometry are widely employed in electronic devices, and their composition plays a key role in band gap engineering of heterostructures. We have studied the crucial issue of accuracy in composition measurements of AlyGa1–yN and MgyZn1–yO alloys using atom probe tomography (APT). The results indicate a similar behavior for both nitride and oxide systems. A correct site fraction y is measured at low field conditions, while Ga and Zn preferentially evaporate at high field, yielding an overestimation of y. Furthermore, APT data sets exhibit local biases depending on the distribution of the electrostatic field at the specimen surface. We estimate the detection efficiencies for each species and interpret the results through a model describing preferential evaporation in simple terms.