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Using a combination of simulated data and pyrite isotopic reference materials, we have refined a methodology to obtain quantitative δ34S measurements from atom probe tomography (APT) datasets. This study builds on previous attempts to characterize relative 34S/32S ratios in gold-containing pyrite using APT. We have also improved our understanding of the artifacts inherent in laser-pulsed APT of insulators. Specifically, we find the probability of multi-hit detection events increases during the APT experiment, which can have a detrimental effect on the accuracy of the analysis. We demonstrate the use of standardized corrected time-of-flight single-hit data for our isotopic analysis. Additionally, we identify issues with the standard methods of extracting background-corrected counts from APT mass spectra. These lead to inaccurate and inconsistent isotopic analyses due to human variability in peak ranging and issues with background correction algorithms. In this study, we use the corrected time-of-flight single-hit data, an adaptive peak fitting algorithm, and an improved deconvolution algorithm to extract 34S/32S ratios from the S2+ peaks. By analyzing against a standard material, acquired under similar conditions, we have extracted δ34S values to within ±5‰ (1‰ = 1 part per thousand) of the published values of our standards.
Zirconium alloys are common fuel claddings in nuclear fission reactors and are susceptible to the effects of hydrogen embrittlement. There is a need to be able to detect and image hydrogen at the atomic scale to gain the experimental evidence necessary to fully understand hydrogen embrittlement. Through the use of deuterium tracers, atom probe tomography (APT) is able to detect and spatially locate hydrogen at the atomic scale. Previous works have highlighted issues with quantifying deuterium concentrations using APT due to complex peak overlaps in the mass-to-charge-state ratio spectrum between molecular hydrogen and deuterium (H2 and D). In this work, we use new methods to analyze historic and simulated atom probe data, by applying currently available data analysis tools, to optimize solving peak overlaps to improve the quantification of deuterium. This method has been applied to literature data to quantify the deuterium concentrations in a concentration line profile across an α-Zr/deuteride interface.
One of the main capabilities of atom probe tomography (APT) is the ability to not only identify but also characterize early stages of precipitation at length scales that are not achievable by other techniques. One of the most popular methods to identify nanoscale clustering in APT data, based on the density-based spatial clustering of applications with noise (DBSCAN), is used extensively in many branches of research. However, it is common that not all of the steps leading to the selection of certain parameters used in the analysis are reported. Without knowing the rationale behind parameter selection, it may be difficult to compare cluster parameters obtained by different researchers. In this work, a simple open-source tool, PosgenPy, is used to justify cluster search parameter selection via providing a systematic sweep through parameter values with multiple randomizations to minimize a false-positive cluster ratio. The tool is applied to several different microstructures: a simulated material system and two experimental datasets from a low-alloy steel . The analyses show how values for the various parameters can be selected to ensure that the calculated cluster number density and cluster composition are accurate.
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.
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.
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.
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.
We summarize the findings from an interlaboratory study conducted between ten international research groups and investigate the use of the commonly used maximum separation distance and local concentration thresholding methods for solute clustering quantification. The study objectives are: to bring clarity to the range of applicability of the methods; identify existing and/or needed modifications; and interpretation of past published data. Participants collected experimental data from a proton-irradiated 304 stainless steel and analyzed Cu-rich and Ni–Si rich clusters. The datasets were also analyzed by one researcher to clarify variability originating from different operators. The Cu distribution fulfills the ideal requirements of the maximum separation method (MSM), namely a dilute matrix Cu concentration and concentrated Cu clusters. This enabled a relatively tight distribution of the cluster number density among the participants. By contrast, the group analysis of the Ni–Si rich clusters by the MSM was complicated by a high Ni matrix concentration and by the presence of Si-decorated dislocations, leading to larger variability among researchers. While local concentration filtering could, in principle, tighten the results, the cluster identification step inevitably maintained a high scatter. Recommendations regarding reporting, selection of analysis method, and expected variability when interpreting published data are discussed.
The local electrode atom probe (LEAP) has become the primary instrument used for atom probe tomography measurements. Recent advances in detector and laser design, together with updated hit detection algorithms, have been incorporated into the latest LEAP 5000 instrument, but the implications of these changes on measurements, particularly the size and chemistry of small clusters and elemental segregations, have not been explored. In this study, we compare data sets from a variety of materials with small-scale chemical heterogeneity using both a LEAP 3000 instrument with 37% detector efficiency and a 532-nm green laser and a new LEAP 5000 instrument with a manufacturer estimated increase to 52% detector efficiency, and a 355-nm ultraviolet laser. In general, it was found that the number of atoms within small clusters or surface segregation increased in the LEAP 5000, as would be expected by the reported increase in detector efficiency from the LEAP 3000 architecture, but subtle differences in chemistry were observed which are attributed to changes in the way multiple hit detection is calculated using the LEAP 5000.
Due to the intrinsic evaporation properties of the material studied, insufficient mass-resolving power and lack of knowledge of the kinetic energy of incident ions, peaks in the atom probe mass-to-charge spectrum can overlap and result in incorrect composition measurements. Contributions to these peak overlaps can be deconvoluted globally, by simply examining adjacent peaks combined with knowledge of natural isotopic abundances. However, this strategy does not account for the fact that the relative contributions to this convoluted signal can often vary significantly in different regions of the analysis volume; e.g., across interfaces and within clusters. Some progress has been made with spatially localized deconvolution in cases where the discrete microstructural regions can be easily identified within the reconstruction, but this means no further point cloud analyses are possible. Hence, we present an ion-by-ion methodology where the identity of each ion, normally obscured by peak overlap, is resolved by examining the isotopic abundance of their immediate surroundings. The resulting peak-deconvoluted data are a point cloud and can be analyzed with any existing tools. We present two detailed case studies and discussion of the limitations of this new technique.
The functional properties of the high-temperature superconductor Y1Ba2Cu3O7−δ (Y-123) are closely correlated to the exact stoichiometry and oxygen content. Exceeding the critical value of 1 oxygen vacancy for every five unit cells (δ>0.2, which translates to a 1.5 at% deviation from the nominal oxygen stoichiometry of Y7.7Ba15.3Cu23O54−δ) is sufficient to alter the superconducting properties. Stoichiometry at the nanometer scale, particularly of oxygen and other lighter elements, is extremely difficult to quantify in complex functional ceramics by most currently available analytical techniques. The present study is an analysis and optimization of the experimental conditions required to quantify the local nanoscale stoichiometry of single crystal yttrium barium copper oxide (YBCO) samples in three dimensions by atom probe tomography (APT). APT analysis required systematic exploration of a wide range of data acquisition and processing conditions to calibrate the measurements. Laser pulse energy, ion identification, and the choice of range widths were all found to influence composition measurements. The final composition obtained from melt-grown crystals with optimized superconducting properties was Y7.9Ba10.4Cu24.4O57.2.
We explore racial differences in multigenerational living arrangements in 1910, focusing on
trigenerational kin structures. Coresidence across generations represents a public function of
the family, and we observe this across different ages or life-course stages through which
adults came to be at risk for providing simultaneous household support for multiple generations
of kin dependents. Using data from the 1.4 percent 1910 Integrated Public Use Microdata Sample,
our comparisons adjust for marital turnover, including widow(er)hood/divorce and remarriage, as
rates are known to be historically higher among African Americans in this period. Across
subgroups defined by age and sex, we find that African Americans are virtually always as likely
as or more likely than European Americans (of both native and foreign parentage) to live as
grandparents in trigenerational households. Widow(er)hood/divorce generally increased the
likelihood of trigenerational coresidence, while remarriage sometimes increased, sometimes
decreased, and sometimes had no association with this living arrangement. Also, we find that
the life-course staging of household kin support in 1910 differed across race/generation partly
due to different economic and demographic circumstances, suggesting more complexity in kin
support than previously considered. We discuss these findings in relation to the histories of
African American and European American families as well as their implications for future
Many scholars have noted the theoretical importance of remarriage in twentieth-century American life (Burch 1995; Cherlin 1998; Furstenberg 1980; Glick 1980; Thornton 1977; Uhlenberg and Chew 1986), yet few historical studies have examined remarriage in the United States empirically. This gap in the literature is noteworthy for two reasons. First, the turn of the twentieth century seems to have marked a crossover in the remarriage transition of the United States, reflecting changes in the pool of persons eligible to remarry. This transition was characterized by decreases in remarriage resulting from declines in mortality and the probability of widow(er)hood, followed by increases in remarriage resulting from higher divorce rates. The crossover in the transition was likely to have occurred when the pool of eligibles was at or near its nadir. Second, there is ongoing debate about the implications of remarriage for families and individuals (Booth and Dunn 1994), and about the impacts of remarriage on family functions (Cherlin 1978; Cherlin and Furstenberg 1994). In the light of these considerations, we believe it is important to examine remarriage and its consequences in the United States at the turn of the century so that we may better understand the ways that remarriage influences family life and shapes the life course of persons within families (see London and Elman 2001).
Many scholars have noted the theoretical importance of remarriage in
twentieth-century American life (Burch 1995; Cherlin 1998; Furstenberg 1980;
Glick 1980; Thornton 1977; Uhlenberg and Chew 1986), yet few historical studies
have examined remarriage in the United States empirically. This gap in the
literature is noteworthy for two reasons. First, the turn of the twentieth
century seems to have marked a crossover in the remarriage transition of the
United States, reflecting changes in the pool of persons eligible to remarry.
This transition was characterized by decreases in remarriage resulting from
declines inmortality and probability of widow(er)hood, followed by increases in
remarriage resulting from higher divorce rates. The crossover in the transition
was likely to have occurred when the pool of eligibles was at or near its nadir.
Second, there is ongoing debate about the implications of remarriage for
families and individuals (Booth and Dunn 1994), and about the impacts of
remarriage on family functions (Cherlin 1978; Cherlin and Furstenberg 1994). In
the light of these considerations, we believe it is important to examine
remarriage and its consequences in the United States at the turn of the century
so that we may better understand the ways that remarriage influences family life
and shapes the life course of persons within families (see London and Elman
Although individual and personal, names take on their significance in social interaction. Since the context of social interaction changes with immigration, names can be expected to change as well. In this paper, we use information from the Public Use Sample of the 1910 U.S. census to compare the patterns of personal (given) names of first- and second-generation Italian and Jewish immigrants and native-born whites of native parentage, and to examine the association of naming patterns of immigrants with several measures indicating interaction with those outside the ethnic group. Because the information from the census is at a single point in time, we also draw on interviews with elderly Italian and Jewish women in order to provide more direct evidence of change and of the contexts in which this change occurred.
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