Atom Probe Tomography Data Research Articles

Machine learning assisted crystallographic reconstruction from atom probe tomographic images

Atom probe tomography (APT) is a powerful technique for three-dimensional (3D) atomic-scale imaging, enabling the accurate analysis on the compositional distribution at the nanoscale. How to accurately reconstruct crystallographic information from APT data, however, is still a great challenge due to the intrinsic nature of the APT technique. In this paper, we propose a novel approach that consists of the modified forward simulation process and the backward machine learning process to recover the tested crystal from APT data. The high-throughput forward simulations on Al single crystals of different orientations generate 10 000 original 3D images and data augmentation is implemented on the original images, resulting in 100 000 3D images. The big data allows the development of deep learning models and three deep learning algorithms of Convolutional Neural Network (CNN), Vision Transformer (ViT), and Variational Autoencoder (VAE) are used in the backward process. After training, the ViT model performs superior than the CNN and VAE models, which can recover the crystalline orientation outstandingly, as evaluated by the coefficient of determinationR2and the Mean Percent Error (MPE), viz.,R2= 0.93 and MPE = 0.43%,R2= 0.97 and MPE = 0.35%, andR2= 0.93 and MPE = 0.77% for the rotation anglesϕ,ψandθ, respectively, on the test dataset. The present work clearly demonstrates the capability of deep learning models in the recovery of the tested crystals from APT data, thereby paving the way for the further development of large artificial intelligent models of APT.

Crystallographic Dependence of Field Evaporation Energy Barrier in Metals Using Field Evaporation Energy Loss Spectroscopy Mapping.

Atom probe tomography data are composed of a list of coordinates of the reconstructed atoms in the probed volume. The elemental identity of each atom is derived from time-of-flight mass spectrometry, with no local chemical information readily available. In this study, we use a data processing technique referred to as field evaporation energy loss spectroscopy (FEELS), which analyzes the tails of mass peaks. FEELS was used to extract critical energetic parameters that are related to the activation energy for atoms to escape from the surface under intense electrostatic field and dependent of the path followed by the departing atoms. We focused our study on pure face-centered cubic metals. We demonstrate that the energetic parameters can be mapped in two-dimensional with nanometric resolution. A dependence on the considered crystallographic planes is observed, with sets of planes of low Miller indices showing a lower sensitivity to the field. The temperature is also an important parameter in particular for aluminum, which we attribute to an energetic transition between two paths of field evaporation between 25 and 60 K close to (002) pole. This paper shows that the information that can be retrieved from the measured energy loss of surface atoms is important both experimentally and theoretically.

Towards Establishing Best Practice in the Analysis of Hydrogen and Deuterium by Atom Probe Tomography.

As hydrogen is touted as a key player in the decarbonization of modern society, it is critical to enable quantitative hydrogen (H) analysis at high spatial resolution and, if possible, at the atomic scale. H has a known deleterious impact on the mechanical properties (strength, ductility, toughness) of most materials that can hinder their use as part of the infrastructure of a hydrogen-based economy. Enabling H mapping including local hydrogen concentration analyses at specific microstructural features is essential for understanding the multiple ways that H affect the properties of materials including embrittlement mechanisms and their synergies. In addition, spatial mapping and quantification of hydrogen isotopes is essential to accurately predict tritium inventory of future fusion power plants thus ensuring their safe and efficient operation. Atom probe tomography (APT) has the intrinsic capability to detect H and deuterium (D), and in principle the capacity for performing quantitative mapping of H within a material's microstructure. Yet, the accuracy and precision of H analysis by APT remain affected by complex field evaporation behavior and the influence of residual hydrogen from the ultrahigh vacuum chamber that can obscure the signal of H from within the material. The present article reports a summary of discussions at a focused workshop held at the Max-Planck Institute for Sustainable Materials in April 2024. The workshop was organized to pave the way to establishing best practices in reporting APT data for the analysis of H. We first summarize the key aspects of the intricacies of H analysis by APT and then propose a path for better reporting of the relevant data to support interpretation of APT-based H analysis in materials.

Machine Learning-Enabled Tomographic Imaging of Chemical Short-Range Atomic Ordering.

In solids, chemical short-range order (CSRO) refers to the self-organization of atoms of certain species occupying specific crystal sites. CSRO is increasingly being envisaged as a lever to tailor the mechanical and functional properties of materials. Yet quantitative relationships between properties and the morphology, number density, and atomic configurations of CSRO domains remain elusive. Herein, it is showcased how machine learning-enhanced atom probe tomography (APT) can mine the near-atomically resolved APT data and jointly exploit the technique's high elemental sensitivity to provide a 3D quantitative analysis of CSRO in a CoCrNi medium-entropy alloy. Multiple CSRO configurations are revealed, with their formation supported by state-of-the-art Monte-Carlo simulations. Quantitative analysis of these CSROs allows establishing relationships between processing parameters and physical properties. The unambiguous characterization of CSRO will help refine strategies for designing advanced materials by manipulating atomic-scale architectures.

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.

Considerations for using Calibration Curves to Infer Oxide Stoichiometry from Atom Probe Tomography Data

Considerations for using Calibration Curves to Infer Oxide Stoichiometry from Atom Probe Tomography Data

Unraveling the potential of Cu addition and cluster hardening in Al-Mg-Si alloys

With the aim of further exploiting the trade-off between formability and strength in Al alloys, this study addresses the influence of Cu in Al-Mg-Si alloys that achieve simultaneously high strength and high ductility via cluster hardening. The study carefully examines the mechanical properties and strain hardening behavior of various Mg/Si ratios with and without Cu and compares the effects of pre-aging and atypical long-term low-temperature aging treatments at 100°C to conventional heat treatments. Interestingly, in all cases adding Cu improved ductility. In the extremal case cluster hardening plus the addition of Cu quadruples elongation, while keeping yield strength similar to the classical T6 state. The results of the study are discussed with a focus on the dense distribution of clusters and partial hardening phases based on atom probe tomography data. Most importantly, the cluster-hardened alloys exhibit pronounced strain-hardening properties, which we evaluate using a Kocks-Mecking approach in combination with a microstructural analysis in the pre-aging and long-term aging condition. The key finding of the study involves the role of Cu in refining clusters/precipitates, where it causes a substantial increase in number density and volume fraction. This refinement, in combination with strain-induced clustering, contributes significantly to improving the alloys’ overall mechanical performance and underlines the central role of Cu in tailoring microstructural features, especially in alloys primarily strengthened by clusters.

A Machine Learning based Workflow to Quantify Atom Probe Tomography Data

A Machine Learning based Workflow to Quantify Atom Probe Tomography Data

Spatial Ranging and Volume Segmentation of Atom Probe Tomography Data

Spatial Ranging and Volume Segmentation of Atom Probe Tomography Data

Atom Probe Tomography Investigation of Clustering in Model P2O5-Doped Borosilicate Glasses for Nuclear Waste Vitrification.

Atom probe tomography (APT) has been utilized to investigate the microstructure of two model borosilicate glasses designed to understand the solubility limits of phosphorous pentoxide (P2O5). This component is found in certain high-level radioactive defence wastes destined for vitrification, where phase separation can potentially lead to a number of issues relating to the processing of the glass and its long-term chemical and structural stability. The development of suitable focused ion beam (FIB)-preparation routes and APT analysis conditions were initially determined for the model glasses, before examining their detailed microstructures. In a 3.0 mol% P2O5-doped glass, both visual inspection and sensitive statistical analysis of the APT data show homogeneous microstructures, while raising the content to 4.0 mol% initiates the formation of phosphorus-enriched nanoscale precipitates. This study confirms the expected inhomogeneities and phase separation of these glasses and offers routes to characterizing these at near-atomic scale resolution using APT.

A MATLAB Toolbox for Findable, Accessible, Interoperable, and Reusable Atom Probe Data Science.

Atom probe tomography (APT) data analytics have traditionally been based on manual analytics by researchers. As newer atom probes together with focused ion beam-based specimen preparation have opened APT to many more materials, yielding much more complex mass spectra, building up a systematic understanding of the pathway from raw data to final interpretation has increasingly become important. This demands a system in which the data and treatment can be traced, ideally by any interested party. Such an approach of findable, accessible, interoperable, and reusable (FAIR) data and analysis policies is becoming increasingly important, not just in APT. In this paper, we present a toolbox, written in MATLAB, which allows the user to store the raw and processed data in a standardized FAIR format (hierarchical data format 5) and process the data in a largely scriptable environment to minimize manual user input. This allows for the experiment data to be interchanged without owner explanations and the analysis to be reproduced. We have devised a metadata scheme that is extensible to other experiments in the materials science domain. With this toolbox, collective knowledge can be built up, and a large number of data sets can be analyzed in a fully automated fashion.

Estimation of the Electric Field in Atom Probe Tomography Experiments Using Charge State Ratios.

Kingham [(1982). The post-ionization of field evaporated ions: A theoretical explanation of multiple charge states. Surf Sci116(2), 273-301] provided equations for the probability of observing higher charge states in atom probe tomography (APT) experiments. These "Kingham curves" have wide application in APT, but cannot be analytically transformed to provide the electric field in terms of the easily measured charge state ratio (CSR). Here we provide a numerical scheme for the calculation of Kingham curves and the variation in electric field with CSR. We find the variation in electric field with CSR is well described by a simple two- or three-parameter equation, and the model is accurate to most elements and charge states. The model is applied to experimental APT data of pure aluminium and a microalloyed steel, demonstrating that the methods described in this work can be easily applied to a variety of APT problems to understand electric field variations.

Towards a new impact geochronometer: Deformation microstructures and U-Pb systematics of shocked xenotime

Shock-deformation microstructures in xenotime have been proposed to record diagnostic evidence for meteorite impacts. Evaluating the potential for impact-induced U-Pb age resetting of the various microstructures that form in shocked xenotime remains largely unexplored. In this study, we investigate the U-Pb systematics of shocked xenotime from three impact structures, including Vredefort (South Africa), Santa Fe (New Mexico, USA), and Araguainha (Brazil). Xenotime at these sites is found in shocked granite, impact melt rock, and as detrital grains, and preserves a range of impact-induced microstructures, including planar fractures, planar deformation bands, deformation twins, and polycrystalline neoblastic grains. Microstructures in xenotime were characterised by electron backscatter diffraction (EBSD) and then targeted for U-Pb geochronology. Secondary ion mass spectrometry (SIMS) and correlated atom probe tomography (APT) were used to determine age and element mobility mechanisms at micrometer- to nanometer-scale. At the precision of SIMS spots, grain areas characterised by lattice deformation microstructures do not show evidence of U-Pb system resetting. In contrast, some grains with neoblastic textures were found to yield impact ages, with U-Pb disturbance correlating to the extent of grain recrystallisation. The APT data showed nanoscale compositional heterogeneities in the form of Pb*-Ca enriched clusters, dislocations arrays, and grain boundaries, the latter with higher concentration of trace elements such as Si, Mg, Ca, Na, Cl, and Al. Combining microstructural, geochronological and nanoscale characterisation, this study demonstrates that neoblastic microstructures can yield accurate impact ages. Shocked xenotime with neoblastic texture is the most reliable geochronometer for dating impact events.

Quantifying free energies through local composition fluctuations in binary solid solutions: A proof-of-concept study using atomistic embedded-atom simulations

While thermodynamic fluctuation theory has been extensively utilized in liquids for decades to obtain direct thermodynamic information, such as Gibbs free energies, from local composition fluctuations, this study presents an extension of the theory for its application in solids. It is demonstrated that composition fluctuations in solids are influenced by an additional elastic work term, which is specific to solids and encompasses liquids as a special case. To verify the extended fluctuation model, atomistic simulations were conducted on an exemplary Cu–Ni embedded-atom system. Monte Carlo simulations were performed in the semi-grandcanonical ensemble at a fixed temperature, covering the entire composition range. Composition fluctuations within a subvolume were monitored over time and statistically analyzed in terms of the variance. The atomistic results exhibit perfect agreement with the predictions derived from the extended model. This methodology has primarily been developed for the analysis of experimental atom probe tomography data, which provides three-dimensional chemical information with sub-nanometer precision. This technique enables the direct measurement of local composition fluctuations, facilitating the extraction of thermodynamic information from any allowed temperature–composition pair in the phase diagram.

Influence of high‐strain deformation on major element mobility in garnet: Nanoscale evidence from atom probe tomography

AbstractGarnet is a common rock‐forming mineral that occurs in a variety of rock types and over a wide range of pressure (P)–temperature (T) conditions in the Earth's lithosphere. Because garnet is considered a high‐strength mineral stable across an extensive range of conditions (1–25 GPa, <300–2000°C), it is generally accepted that garnets can retain their microstructures and chemical composition during deformation and metamorphism. Therefore, garnet is commonly used as a geothermobarometer and geochronometer to provide P–T and timing constraints on tectonic events. Herein, we study garnet from an eclogite facies mylonite (central Australia) to investigate the mechanisms of element mobility during high‐strain deformation under relatively dry, lower crustal conditions. Electron backscatter diffraction (EBSD) and electron channelling contrast imaging (ECCI) reveal evidence of crystal plasticity associated with brittle deformation in the form of heterogeneous misorientation patterns and low‐angle grain boundaries developed over length scales of 20–50 μm in the rims of garnet porphyroclasts. Atom probe tomography (APT) analysis of a low‐angle grain boundary within a highly strained portion of a clast shows Ca enrichment and Mg depletion along dislocations, whereas APT data along the rim of a mostly undeformed clast reveal a homogeneous distribution of garnet major components in the specimen matrix with the exception of Ca, Fe and Mg enrichment within a healed microfracture. The above‐mentioned results suggest that under relatively dry conditions, crystal plasticity enhances bulk element mobility via pipe diffusion, highlighting the importance of deformation‐induced microstructures on element mobility, with important implications for the robust and reliable use of garnet as a petrological tool.

On the Use of a Cluster Identification Method and a Statistical Approach for Analyzing Atom Probe Tomography Data for GP Zones in Al-Zn-Mg(-Cu) Alloys.

Early-stage clustering in two Al-Mg-Zn(-Cu) alloys has been investigated using atom probe tomography and transmission electron microscopy. Cluster identification by the isoposition method and a statistical approach based on the pair correlation function have both been applied to estimate the cluster size, composition, and volume fraction from atom probe data sets. To assess the accuracy of the quantification of clusters of different mean sizes, synthesized virtual data sets were used, accounting for a simulated degraded spatial resolution. The quality of the predictions made by the two complementary methods is discussed, considering the experimental and simulated data sets.

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.

High-resolution chemical and structural characterization of the native oxide scale on a Mg-based alloy

The structure and composition of the native oxide forming on the basal plane (0001) of the magnesium-based alloy Mg-2Al-0.1Ca was investigated by combining scanning transmission electron microscopy (STEM) and atom probe tomography (APT). While STEM measurements demonstrated the growth of a (111) MgO oxide layer with 3–4 nm thickness on the basal (0001) plane of the atom probe specimen, APT data further revealed the formation of an aluminum-rich region between bulk magnesium and the native oxide. The aluminum enrichment of up to ∼20 at% at the interface is consistent with an inward growth of the oxide scale.

Evidence of Xe-incorporation in the bubble superlattice in irradiated U-Mo fuel

For years, researchers have reported competing ideas on the formation of fission gas bubble superlattices in metallic fuels, which was postulated to be comprised of elemental xenon (Xe) atoms. However, the chemical and physical arrangement of these elements within this gas bubble superlattice had not been verified. In this contribution, Xe was chemically profiled using atomic resolution scanning transmission electron microscopy (STEM) and atom probe tomography (APT) techniques in irradiated uranium-molybdenum (U-Mo) fuels. These complementary techniques provide conclusive evidence of Xe presence in the bubble superlattice up to fission densities of 4.5 × 1021 fissions/cm3 and give a quantitative assessment of Xe content within the bubble superlattice. Based on the results of simultaneous imaging and spectroscopy using STEM, the chemical composition of the Xe bubble superlattice was measured and found to be up to 8±1.3 atomic %. APT data complemented STEM findings on Xe distribution in irradiated U-Mo fuel sample. This study provides conclusive evidence that Xe is not only present within an atomically arranged bubble superlattice but provides fundamental insight into the physical state of Xe in low enriched U-Mo monolithic fuel.

Is it meaningful to quantify vacancy concentrations of nanolamellar (Ti,Al)N thin films based on laser-assisted atom probe data?

Recently, it was proposed to quantify vacancy concentrations based on laser-assisted atom probe tomography (APT) data for a (Ti,Al)N film with a nanolamellar architecture, grown by chemical vapor deposition. To determine, whether vacancy concentrations can be reliably estimated based on APT data, we systematically compare measurements with an ultraviolet (UV) as well as a green laser to ion beam analysis data. First, monolithic TiN and AlN films, which are stoichiometric within the measurement uncertainties of ion beam analysis, are investigated. In case of TiN an electric field strength of 39.4 V nm−1 and a nitrogen content of 49.0 at.%, consistent with ion beam analysis data, is obtained with both lasers, when using pulse energies of 5 pJ (UV laser) and 0.1 nJ (green laser). However, significant differences can be observed for monolithic AlN as nitrogen contents from 41.9 to 35.8 at.% and 48.4 to 41.4 at.% are measured, depending on variations of the pulse energies of the UV and green laser, respectively. In order to mimic a nanolamellar architecture for correlative compositional analysis by ion beam analysis and laser-assisted APT, a TiN/AlN/TiN trilayer film is synthesized and significant deviations with respect to the nitrogen content are evident for the AlN layer. While the average nitrogen concentration from ion beam analysis is 51 at.%, nitrogen contents from laser-assisted APT data are only 38 at.% (UV laser) or 41 at.% (green laser). Hence, the nitrogen content of the AlN layer is underestimated from laser-assisted APT data by at least 10 and up to 13 at.% and this significant discrepancy cannot be explained by the measurement uncertainties. Thus, the here presented data emphasize that it is not meaningful to quantify vacancy concentrations of nanolamellar (Ti,Al)N thin films solely based on atom probe data, since the measurement accuracy depends on the field evaporation conditions.