Single-Ion Deconvolution of Mass Peak Overlaps for Atom Probe Microscopy

Interfacial excess of solutes across phase boundaries using atom probe microscopy

Three-dimensional elemental mapping in atom probe microscopy provides invaluable insights into the structure and composition of interfaces in materials. Quasi-atomic resolution facilitates access to the solute decoration of grain boundaries, advancing the knowledge on local segregation and depletion phenomena. More recent developments unlocked three-dimensional mapping of the interfacial excess across grain boundaries. Such detailed understanding of the local structure and composition of these interfaces enabled advancements in processing methods and material development. However, many engineering alloys, such as Ni-based superalloys, have much more complex microstructures with various solutes and precipitates in close proximity to grain boundaries. The complex interaction of grain boundary segregation and grain boundary precipitates requires precise compositional control. However, abrupt changes in solute solubility across phase boundaries obscure the interfacial excess in proximity to grain boundaries. Therefore, this study provides a methodological framework of the quantitative characterization of phase boundaries in proximity to grain boundaries using atom probe microscopy. The detailed mass spectrum ranging of MC, M23C6, and M6C carbides is explored in order to achieve satisfactory compositional information. Proximity histograms and correlating concentration difference profiles determine the interface location, where a Gibbs dividing surface is not accessible. This enables reliable direct calculation of the interfacial excess across phase boundaries. Intuitively interpretable and quantitative 'interface plots' are introduced, and showcased for phase boundaries between γ-matrix, γ' precipitates, GB-γ', MC, M23C6, and M6C carbides. The presented framework advances access to the local composition in proximity to grain boundaries and may be applicable to other engineering alloys or materials with functional properties.

Learning Atom Probe Tomography time-of-flight peaks for mass-to-charge ratio spectrometry

In laser-assisted atom probe tomography, an important goal is to reconstruct the mass-to-charge ratio, (m/z), spectrum due to various ion species. In general, the probability mass function (pmf) associated with the time-of-flight (TOF) spectrum produced by each ion species is unknown and varies from species-to-species. Moreover, measuring pmfs for distinct ion species in calibration experiments is not practical. Here, we present a mixture model method to determine TOF pmfs that can vary from peak-to-peak. In this approach, we determine weights of candidate pmfs with a maximum likelihood method. In a proof-of-principle study, we apply our method to a TOF spectrum acquired from a silicon sample and determine intensity estimates of singly charged isotopes of silicon.

Solving Peak Overlaps for Proximity Histogram Analysis of Complex Interfaces for Atom Probe Tomography Data

Atom probe tomography is a powerful tool for investigating nanostructures such as interfaces and nanoparticles in material science. Advanced analysis tools are particularly useful for analyzing these nanostructures characterized very often by curved shapes. However, these tools are very limited for complex materials with non-negligible peak overlaps in their respective mass-to-charge ratio spectra. Usually, an analyst solves peak overlaps in the bulk regions, but the behavior at interfaces is rarely considered. Therefore, in this work, we demonstrate how the proximity histogram generated for a specific interface can be corrected by using the natural abundances of isotopes. This leads to overlap-solved proximity histograms with a resolution of up to 0.1 nm. This work expands on previous work that showed the advantage of a maximum-likelihood peak overlap solving. The corrected proximity histograms together with the maximum-likelihood peak overlap algorithm were implemented in a user-friendly software suite called EPOSA.

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.

Processing APT Spectral Backgrounds for Improved Quantification

We describe a method to estimate background noise in atom probe tomography (APT) mass spectra and to use this information to enhance both background correction and quantification. Our approach is mathematically general in form for any detector exhibiting Poisson noise with a fixed data acquisition time window, at voltages varying through the experiment. We show that this accurately estimates the background observed in real experiments. The method requires, as a minimum, the z-coordinate and mass-to-charge-state data as input and can be applied retrospectively. Further improvements are obtained with additional information such as acquisition voltage. Using this method allows for improved estimation of variance in the background, and more robust quantification, with quantified count limits at parts-per-million concentrations. To demonstrate applications, we show a simple peak detection implementation, which quantitatively suppresses false positives arising from random noise sources. We additionally quantify the detectability of 121-Sb in a standardized-doped Si microtip as (1.5 × 10−5, 3.8 × 10−5) atomic fraction, α = 0.95. This technique is applicable to all modes of APT data acquisition and is highly general in nature, ultimately allowing for improvements in analyzing low ionic count species in datasets.

Exploring the accuracy of isotopic analyses in atom probe mass spectrometry

Atom probe tomography (APT) can theoretically deliver accurate chemical and isotopic analyses at a high level of sensitivity, precision, and spatial resolution. However, empirical APT data often contain significant biases that lead to erroneous chemical concentration and isotopic abundance measurements. The present study explores the accuracy of quantitative isotopic analyses performed via atom probe mass spectrometry. A machine learning-based adaptive peak fitting algorithm was developed to provide a reproducible and mathematically defensible means to determine peak shapes and intensities in the mass spectrum for specific ion species. The isotopic abundance measurements made with the atom probe are compared directly with the known isotopic abundance values for each of the materials. Even in the presence of exceedingly high numbers of multi-hit detection events (up to 80%), and in the absence of any deadtime corrections, our approach produced isotopic abundance measurements having an accuracy consistent with values limited predominantly by counting statistics.

Enhancing Element Identification by Expectation-Maximization Method in Atom Probe Tomography

This paper describes an alternative way to assign elemental identity to atoms collected by atom probe tomography (APT). This method is based on Bayesian assignation of label through the expectation-maximization method (well known in data analysis). Assuming the correct shape of mass over charge peaks in mass spectra, the probability of each atom to be labeled as a given element is determined, and is used to enhance data visualization and composition mapping in APT analyses. The method is particularly efficient for small count experiments with a low signal to noise ratio, and can be used on small subsets of analyzed volumes, and is complementary to single-ion decomposition methods. Based on the selected model and experimental examples, it is shown that the method enhances our ability to observe and extract information from the raw dataset. The experimental case of the superimposition of the Si peak and N peak in a steel is presented.

A Gas-Phase Reaction Cell for Modern Atom Probe Systems

In this work, we demonstrate a new system for the examination of gas interactions with surfaces via atom probe tomography. This system provides capability of examining the surface and subsurface interactions of gases with a wide range of specimens, as well as a selection of input gas types. This system has been primarily developed to aid the investigation of hydrogen interactions with metallurgical samples, to better understand the phenomenon of hydrogen embrittlement. In its current form, it is able to operate at pressures from 10-6 to 1000 mbar (abs), can use a variety of gasses, and is equipped with heating and cryogenic quenching capabilities. We use this system to examine the interaction of hydrogen with Pd, as well as the interaction of water vapor and oxygen in Mg samples.

Quantification Challenges for Atom Probe Tomography of Hydrogen and Deuterium in Zircaloy-4

Analysis and understanding of the role of hydrogen in metals is a significant challenge for the future of materials science, and this is a clear objective of recent work in the atom probe tomography (APT) community. Isotopic marking by deuteration has often been proposed as the preferred route to enable quantification of hydrogen by APT. Zircaloy-4 was charged electrochemically with hydrogen and deuterium under the same conditions to form large hydrides and deuterides. Our results from a Zr hydride and a Zr deuteride highlight the challenges associated with accurate quantification of hydrogen and deuterium, in particular associated with the overlap of peaks at a low mass-to-charge ratio and of hydrogen/deuterium containing molecular ions. We discuss possible ways to ensure that appropriate information is extracted from APT analysis of hydrogen in zirconium alloy systems that are important for nuclear power applications.

Quantifying Uncertainty from Mass-Peak Overlaps in Atom Probe Microscopy

There are many sources of random and systematic error in composition quantification by atom probe microscopy, often, however, only statistical error is reported. Significantly larger errors can occur from the misidentification of ions and overlaps or interferences of peaks in the mass spectrum. These overlaps can be solved using maximum likelihood estimation (MLE), improving the accuracy of the result, but with an unknown effect on the precision. An analytical expression for the uncertainty of the MLE solution is presented and it is demonstrated to be much more accurate than the existing methods. In one example, the commonly used error estimate was five times too small.Literature results containing overlaps most likely underestimate composition uncertainty because of the complexity of correctly dealing with stochastic effects and error propagation. The uncertainty depends on the amount of overlapped intensity, for example being ten times worse for the CO/Fe overlap than the Cr/Fe overlap. Using the methods described here, accurate estimation of error, and the minimization of this could be achieved, providing a key milestone in quantitative atom probe. Accurate estimation of the composition uncertainty in the presence of overlaps is crucial for planning experiments and scientific interpretation of the measurements.

Resolving mass spectral overlaps in atom probe tomography by isotopic substitutions - case of TiSi15N

Mass spectral overlaps in atom probe tomography (APT) analyses of complex compounds typically limit the identification of elements and microstructural analysis of a material. This study concerns the TiSiN system, chosen because of severe mass-to-charge-state ratio overlaps of the ¹⁴N⁺ and ²⁸Si²⁺ peaks as well as the ¹⁴N₂⁺ and ²⁸Si⁺ peaks. By substituting ¹⁴N with ¹⁵N, mass spectrum peaks generated by ions composed of one or more N atoms will be shifted toward higher mass-to-charge-state ratios, thereby enabling the separation of N from the predominant Si isotope. We thus resolve thermodynamically driven Si segregation on the nanometer scale in cubic phase Ti_1-xSi_x¹⁵N thin films for Si contents 0.08 ≤ x ≤ 0.19 by APT, as corroborated by transmission electron microscopy. The APT analysis yields a composition determination that is in good agreement with energy dispersive X-ray spectroscopy and elastic recoil detection analyses. Additionally, a method for determining good voxel sizes for visualizing small-scale fluctuations is presented and demonstrated for the TiSiN system.