Modeling Atom Probe Tomography: A review

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.

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.

Testing the Influence of Laser Pulse Energy and Rate in the Atom Probe Tomography Analysis of Minerals

The use of atom probe tomography (APT) for mineral analysis is contributing to fundamental studies in Earth Sciences. Meanwhile, the need for standardization of this technique is becoming evident. Pending the use of mineral standards, the optimization of analysis parameters is needed to facilitate the study of different mineral groups in terms of data collection and quality. The laser pulse rate and energy are variables that highly affect the atom evaporation process occurring during APT analysis, and their testing is important to forecast mineral behavior and obtain the best possible data. In this study, five minerals representative of major groups (albite, As-pyrite, barite, olivine, and monazite) were analyzed over a range of laser pulse energies (10-50 pJ) and rates (100-250 kHz) to assess output parameter quality and evaluate compositional estimate stoichiometry. Among the studied minerals, As-pyrite, with the higher thermal conductivity and lower band gap, was the most affected by the laser pulse variation. Chemical composition estimates equal or close to the general chemical formula were achieved for monazite and As-pyrite. The analysis of multihit events has proved to be the best strategy to verify the efficacy of the evaporation process and to evaluate the best laser pulse setting for minerals.

Introducing a Dynamic Reconstruction Methodology for Multilayered Structures in Atom Probe Tomography

Atom probe tomography (APT) is a powerful three-dimensional nanoanalyzing microscopy technique considered key in modern materials science. However, progress in the spatial reconstruction of APT data has been rather limited since the first implementation of the protocol proposed by Bas et al. in 1995. This paper proposes a simple semianalytical approach to reconstruct multilayered structures, i.e., two or more different compounds stacked perpendicular to the analysis direction. Using a field evaporation model, the general dynamic evolution of parameters involved in the reconstruction of this type of structure is estimated. Some experimental reconstructions of different structures through the implementation of this method that dynamically accommodates variations in the tomographic reconstruction parameters are presented. It is shown both experimentally and theoretically that the depth accuracy of reconstructed APT images is improved using this method. The method requires few parameters in order to be easily usable and substantially improves atom probe tomographic reconstructions of multilayered structures.

Nanoscale Three-Dimensional Charge Density and Electric Field Mapping by Electron Holographic Tomography

The operation of nanoscale electronic devices is related intimately to the three-dimensional (3D) charge density distributions within them. Here, we demonstrate the quantitative 3D mapping of the charge density and long-range electric field associated with an electrically biased carbon fiber nanotip with a spatial resolution of approximately 5 nm using electron holographic tomography in the transmission electron microscope combined with model-based iterative reconstruction. The approach presented here can be applied to a wide range of other nanoscale materials and devices.

Topology Optimized Prelithiated SiO Anode Materials for Lithium-Ion Batteries

Silicon monoxide (SiO)-based materials have great potential as high-capacity anode materials for lithium-ion batteries. However, they suffer from a low initial coulombic efficiency (ICE) and poor cycle stability, which prevent their successful implementation into commercial lithium-ion batteries. Despite considerable efforts in recent decades, their low ICE and poor cycle stability cannot be resolved at the same time. Here, it is demonstrated that the topological optimization of the prelithiated SiO materials is highly effective in improving both ICE and capacity retention. Laser-assisted atom probe tomography combined with thermogravimetry and differential scanning calorimetry reveals that two exothermic reactions related to microstructural evolution are key in optimizing the domain size of the Si active phase and Li₂ SiO₃ buffer phase, and their topological arrangements in prelithiated SiO materials. The optimized prelithiated SiO, heat-treated at 650 °C, shows higher capacity retention of 73.4% and lower thickness changes of 68% after 300 cycles than those treated at other temperatures, with high ICE of ≈90% and reversible capacity of 1164 mAh g^-1 . Such excellent electrochemical properties of the prelithiated SiO electrode originate from its optimized topological arrangement of active Si phase and Li₂ SiO₃ inactive buffer phase.

A Combinatorial Approach to Reliable Quantitative Analysis of Small Nano-Sized Precipitates: A Case Study with α' Precipitates in Fe-20 at% Cr Alloy

The quantitative characterization of small nano-sized precipitates poses genuine challenges and is often deficient in accuracy due to the inherent limitations inevitably associated with the individual experimental techniques. A convenient solution is to utilize multiple complementary techniques. The present work demonstrates an effective way to reliably quantify nano-sized precipitates using a combination of complementary techniques of atom probe tomography (APT), small angle neutron scattering (SANS), and transmission electron microscopy (TEM). As a case study, the size (radius, r), number density (NP), volume fraction (ϕ), and chemical composition of Cr-rich α′ precipitates are determined in Fe–20 at% Cr alloy, thermally aged at 773 K for 1,000 h. This combinatorial approach utilizes the strength of each technique in such a way that the overall accuracy of quantitative precipitation analysis improves significantly. For example, the superior spatial resolution makes TEM the appropriate technique to estimate the size and size distribution of the precipitates, while APT provides the chemical composition. Similarly, SANS analysis incorporates both the size and the compositional information thus derived independently and provides statiscally averaged quantitative analysis overcoming the field-of-view limitations of both TEM and APT. This combinatorial approach improves the accuracy of quantification and provides the true representation of the microstructure.

Reflections on the Spatial Performance of Atom Probe Tomography in the Analysis of Atomic Neighborhoods

Atom probe tomography (APT) is often introduced as providing “atomic-scale” mapping of the composition of materials and as such is often exploited to analyze atomic neighborhoods within a material. Yet quantifying the actual spatial performance of the technique in a general case remains challenging, as it depends on the material system being investigated as well as on the specimen's geometry. Here, by using comparisons with field-ion microscopy experiments, field-ion imaging and field evaporation simulations, we provide the basis for a critical reflection on the spatial performance of APT in the analysis of pure metals, low alloyed systems and concentrated solid solutions (i.e., akin to high-entropy alloys). The spatial resolution imposes strong limitations on the possible interpretation of measured atomic neighborhoods, and directional neighborhood analyses restricted to the depth are expected to be more robust. We hope this work gets the community to reflect on its practices, in the same way, it got us to reflect on our work.

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.

Community-Driven Methods for Open and Reproducible Software Tools for Analyzing Datasets from Atom Probe Microscopy

Atom probe tomography, and related methods, probe the composition and the three-dimensional architecture of materials. The software tools which microscopists use, and how these tools are connected into workflows, make a substantial contribution to the accuracy and precision of such material characterization experiments. Typically, we adapt methods from other communities like mathematics, data science, computational geometry, artificial intelligence, or scientific computing. We also realize that improving on research data management is a challenge when it comes to align with the FAIR data stewardship principles. Faced with this global challenge, we are convinced it is useful to join forces. Here, we report the results and challenges with an inter-laboratory call for developing test cases for several types of atom probe microscopy software tools. The results support why defining detailed recipes of software workflows and sharing these recipes is necessary and rewarding: Open source tools and (meta)data exchange can help to make our day-to-day data processing tasks become more efficient, the training of new users and knowledge transfer become easier, and assist us with automated quantification of uncertainties to gain access to substantiated results.

Visualization of Collagen-Mineral Arrangement Using Atom Probe Tomography

Bone is a functional material comprised of mainly two phases: an organic collagenous phase and an inorganic mineral phase. Collagen-mineral arrangement has implications for bone function, aging, and disease. However, theories on collagen-mineral arrangement have been confined to studies with low spatial and/or compositional resolution resulting in an extensive debate over the location of mineral with respect to collagen. Herein, a strategy is developed to extract a single mineralized collagen fibril from bone and analyze its composition and structure atom-by-atom with 3D sub-nanometer accuracy and compositional clarity using atom probe tomography (APT). It is shown for the first time a method to probe fibril-level mineralization and collagen-mineral arrangement from an in vivo system with both the spatial and compositional precision required to comment on nanoscale collagen-mineral arrangement. APT of leporine bone shows distinct and helical collagen fibrils with mineralized deposits both encapsulating and incorporated into the collagenous structures. This study demonstrates a novel fibril-level detection method that can be used to probe the composition of bone and contribute new insights to the structure and organization of mineralized materials such as bones and teeth.

Atom probe tomography

Atom probe tomography (APT) provides three-dimensional compositional mapping with sub-nanometre resolution. The sensitivity of APT is in the range of parts per million for all elements, including light elements such as hydrogen, carbon or lithium, enabling unique insights into the composition of performance-enhancing or lifetime-limiting microstructural features and making APT ideally suited to complement electron-based or X-ray-based microscopies and spectroscopies. Here, we provide an introductory overview of APT ranging from its inception as an evolution of field ion microscopy to the most recent developments in specimen preparation, including for nanomaterials. We touch on data reconstruction, analysis and various applications, including in the geosciences and the burgeoning biological sciences. We review the underpinnings of APT performance and discuss both strengths and limitations of APT, including how the community can improve on current shortcomings. Finally, we look forwards to true atomic-scale tomography with the ability to measure the isotopic identity and spatial coordinates of every atom in an ever wider range of materials through new specimen preparation routes, novel laser pulsing and detector technologies, and full interoperability with complementary microscopy techniques.

Analysis of nanoscale fluid inclusions in geomaterials by atom probe tomography: Experiments and numerical simulations

The spatial correlation between defects in crystalline materials and trace element segregation plays a fundamental role in determining the physical and mechanical properties of a material, which is particularly important in naturally deformed materials. Herein, we combine electron backscatter diffraction, electron channelling contrast imaging, scanning transmission electron microscopy and atom probe tomography on a naturally occurring metal sulphide in an attempt to document mechanisms of element segregation in a brittle-dominated deformation regime. Within APT reconstructions, features with a high point density comprising O-rich discs stacked over As-rich spherules are observed. The combined microscopy data allow us to interpret these as nanoscale fluid inclusions. Our observations are confirmed by simulated APT experiments of core-shell particles with a core exhibiting a very low evaporation field and the shell emulating a segregated layer at the inclusion interface. Our data has significant trans-disciplinary implications to the geosciences, the material sciences, and analytical microscopy.

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.

Atom probe tomography can image chemical composition at the nanoscale, but our understanding of how it images voids, or empty spaces, is still lacking. Here, the authors combine atom probe tomography, scanning transmission electron microscopy, and field-evaporation theory to show how voids are imaged and subsequently measured.

3D nanostructural characterisation of grain boundaries in atom probe data utilising machine learning methods

Boosting is a family of supervised learning algorithm that convert a set of weak learners into a single strong one. It is popular in the field of object tracking, where its main purpose is to extract the position, motion, and trajectory from various features of interest within a sequence of video frames. A scientific application explored in this study is to combine the boosting tracker and the Hough transformation, followed by principal component analysis, to extract the location and trace of grain boundaries within atom probe data. Before the implementation of this method, these information could only be extracted manually, which is time-consuming and error-prone. The effectiveness of this method is demonstrated on an experimental dataset obtained from a pure aluminum bi-crystal and validated on simulated data. The information gained from this method can be combined with crystallographic information directly contained within the data, to fully define the grain boundary character to its 5 degrees of freedom at near-atomic resolution in three dimensions. It also enables local atomic compositional and geometric information, i.e. curvature, to be extracted directly at the interface.

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.

Machine-learning-based atom probe crystallographic analysis

Atom probe tomography is known for its accurate compositional analysis at the nanoscale. However, the patterns created by successive hits on the single particle detector during experiments often contain complementary information about the specimen's crystallography, including structure and orientation. This information remains in most cases unexploited because it is, up to now, retrieved predominantly manually. Here, we propose an approach combining image analysis techniques for feature selection and deep-learning to automatically interpret the patterns. Application of unsupervised machine learning techniques allows to build and train a deep neural network, based on a library generated from theoretically known crystallographic angular relationships. This approach enables direct interpretation of the detector hit maps, as shown here on the example of numerous pure-Al, and is robust enough to function under various conditions of base temperature, pulsing mode and pulse fraction. We benchmark our approach against recent attempts to automate the pattern identification via Hough-transform and discuss the current limitations of our approach. This new automated approach renders crystallographic atom probe tomography analysis more efficient, feature-sensitive, robust, user-independent and reliable. With that, deep-learning algorithms show a great potential to give access to combined atom probe crystallographic and compositional analysis to a large community of users.

Wet-chemical etching of atom probe tips for artefact free analyses of nanoscaled semiconductor structures

We introduce an innovative specimen preparation method employing the selectivity of a wet-chemical etching step to improve data quality and success rates in the atom probe analysis of contemporary semiconductor devices. Firstly, on the example of an SiGe fin embedded in SiO₂ we demonstrate how the selective removal of SiO₂ from the final APT specimen significantly improves accuracy and reliability of the reconstructed data. With the oxide removal, we eliminate the origin of shape artefacts, i.e. the formation of a non-hemispherical tip shape, that are typically observed in the reconstructed volume of complex systems. Secondly, using the same approach, we increase success rates to ∼90% for the damage-free, 3D site-specific localization of short (250 nm), vertical Si nanowires at the specimen apex. The impact of the abrupt emitter radius change that is introduced by this specimen preparation method is evaluated as being minor using field evaporation simulation and comparison of different reconstruction schemes. The Ge content within the SiGe fin as well as the 3D boron distribution in the Si NW as resolved by atom probe analysis are in good agreement with TEM/EDS and ToF-SIMS analysis, respectively.

Atom probe tomography analysis of SiGe fins embedded in SiO2: Facts and artefacts

We present atom probe analysis of 40nm wide SiGe fins embedded in SiO₂ and discuss the root cause of artefacts observed in the reconstructed data. Additionally, we propose a simple data treatment routine, relying on complementary transmission electron microscopy analysis, to improve compositional analysis of the embedded SiGe fins. Using field evaporation simulations, we show that for high oxide to fin width ratios the difference in evaporation field thresholds between SiGe and SiO₂ results in a non-hemispherical emitter shape with a negative curvature in the direction across, but not along the fin. This peculiar emitter shape leads to severe local variations in radius and hence in magnification across the emitter apex causing ion trajectory aberrations and crossings. As shown by our experiments and simulations, this translates into unrealistic variations in the detected atom densities and faulty dimensions in the reconstructed volume, with the width of the fin being up to six-fold compressed. Rectification of the faulty dimensions and density variations in the SiGe fin was demonstrated with our dedicated data treatment routine.

Optimizing Atom Probe Analysis with Synchronous Laser Pulsing and Voltage Pulsing

Atom probe has been developed for investigating materials at the atomic scale and in three dimensions by using either high-voltage (HV) pulses or laser pulses to trigger the field evaporation of surface atoms. In this paper, we propose an atom probe setup with pulsed evaporation achieved by simultaneous application of both methods. This provides a simple way to improve mass resolution without degrading the intrinsic spatial resolution of the instrument. The basic principle of this setup is the combination of both modes, but with a precise control of the delay (at a femtosecond timescale) between voltage and laser pulses. A home-made voltage pulse generator and an air-to-vacuum transmission system are discussed. The shape of the HV pulse presented at the sample apex is experimentally measured. Optimizing the delay between the voltage and the laser pulse improves the mass spectrum quality.