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A quantification model which uses standard X-ray spectra collected from bulk materials to determine the composition and mass thickness of single-layer and multilayer unsupported thin films is presented. The multivariate model can be iteratively solved for single layers in which each element produces at least one visible characteristic X-ray line. The model can be extended to multilayer thin films in which each element is associated with only one layer. The model may sometimes be solved when an element is present in multiple layers if additional information is added in the form of independent k-ratios or model assumptions. While the algorithm is suitable for any measured k-ratios, it is particularly well suited to energy-dispersive X-ray spectrometry where the bulk standard spectra can be used to deconvolve peak interferences in the thin-film spectra. The algorithm has been implemented and made available in the Open Source application National Institute of Standards and Technology DTSA-II. We present experimental data and Monte Carlo simulations supporting the quantification model.
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It can be useful to register (or align) two sets of particle data measured from the same physical sample. However, if the two data sets were collected at different translational or rotational offsets, finding the optimal registration can be a challenge. We will present an algorithm that efficiently determines the rotation and translational offset that best registers (in a least-squares sense) the corresponding particles in two or more data sets measured from the same sample. This algorithm can be used to merge two data sets that have been collected on overlapping but otherwise distinct regions on the sample. Alternatively, it can be used to overlay data sets that have been collected on the same sample area to compare replicate data for quality control and measurement efficiency purposes.
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Electron-excited X-ray microanalysis with energy-dispersive spectrometry (EDS) proceeds through the application of the software that extracts characteristic X-ray intensities and performs corrections for the physics of electron and X-ray interactions with matter to achieve quantitative elemental analysis. NIST DTSA-II is an open-access, fully documented, and freely available comprehensive software platform for EDS quantification, measurement optimization, and spectrum simulation. Spectrum simulation with DTSA-II enables the prediction of the EDS spectrum from any target composition for a specified electron dose and for the solid angle and window parameters of the EDS spectrometer. Comparing the absolute intensities for measured and simulated spectra reveals correspondence within ±25% relative to K-shell and L-shell characteristic X-ray peaks in the range of 111 keV. The predicted M-shell intensity exceeds the measured value by a factor of 1.42.2 in the range 13 keV. The X-ray continuum (bremsstrahlung) generally agrees within ±10% over the range of 110 keV. Simulated EDS spectra are useful for developing an analytical strategy for challenging problems such as estimating trace detection levels.
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NeXL is a collection of Julia language packages (libraries) for X-ray microanalysis data processing. NeXLCore provides basic atomic and X-ray physics data and models including support for microanalysis-related data types for materials and k-ratios. NeXLMatrixCorrection provides algorithms for matrix correction and iteration. NeXLSpectrum provides utilities and tools for energy-dispersive X-ray spectrum and hyperspectrum analysis including display, manipulation, and fitting. NeXL is integrated with the Julia language infrastructure. NeXL builds on the Gadfly plotting library and the DataFrames tabular data library. When combined with the DrWatson package, NeXL can provide a highly reproducible environment in which to process microanalysis data. Data availability and reproducible data analysis are two keys to scientific reproducibility. Not only should readers of journal articles have access to the data, they should also be able to reproduce the analysis steps that take the data to final results. This paper will both discuss the NeXL framework and provide examples of how it can used for reproducible data analysis.
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NIST DTSA-II is a free, open access, and fully-documented comprehensive software platform for electron-excited X-ray microanalysis with energy dispersive spectrometry (EDS), including tools for quantification, measurement optimization, and spectrum simulation. EDS simulation utilizes a Monte Carlo electron trajectory simulation that includes characteristic and continuum X-ray generation, self-absorption, EDS window absorption, and energy-to-charge conversion leading to peak broadening. Spectra are simulated on an absolute basis considering electron dose and spectrometer parameters. Simulated and measured spectra agree within ± 25% relative for K-shell and L-shell characteristic X-ray peaks from 1 to 11 keV, while the predicted M-shell intensity was found to exceed the measured value by a factor of 1.4-2.2 from 1 to 3 keV. The X-ray continuum (bremsstrahlung) intensity agreed within ± 10% over the photon energy range from 1 to 10 keV for elements from boron to bismuth. Simulated spectra can be used to develop analytical strategy, such as assessing detection of trace constituents.
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Quantification of electron-exited X-ray spectra following the standards-based "k-ratio" (unknown/standard intensity) protocol with corrections for "matrix effects" (electron energy loss and backscattering, X-ray absorption, and secondary X-ray fluorescence) is a well-established method with a record of rigorous testing and extensive experience. Two recent studies by Gopon et al. working in the FeSi system and Llovet et al. working in the NiSi system have renewed interest in studying the accuracy of measurements made using L-shell X-ray peaks. Both have reported unexpectedly large deviations in analytical accuracy when analyzing intermetallic compounds when using the low photon energy Fe or Ni L-shell X-ray peaks with pure element standards and wavelength-dispersive X-ray spectrometry. This study confirms those observations on the Ni-based intermetallic compounds using energy-dispersive X-ray spectrometry and extends the study of analysis with low photon energy L-shell peaks to a wide range of elements, Ti to Se. Within this range of elements, anomalies in analytical accuracy have been found for Fe, Co, and Ge in addition to Ni. For these elements, the use of compound standards instead of pure elements usually resulted in significantly improved analytical accuracy. However, compound standards do not always provide satisfactory accuracy as is demonstrated for L-shell peak analysis in the FeS system: FeS and FeS2 unexpectedly do not provide good accuracy when used as mutual standards.
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This, the second in a series of articles present a new framework for considering the computation of uncertainty in electron excited X-ray microanalysis measurements, will discuss matrix correction. The framework presented in the first article will be applied to the matrix correction model called "Pouchou and Pichoir's Simplified Model" or simply "XPP." This uncertainty calculation will consider the influence of beam energy, take-off angle, mass absorption coefficient, surface roughness, and other parameters. Since uncertainty calculations and measurement optimization are so intimately related, it also provides a starting point for optimizing accuracy through choice of measurement design.
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Standard Reference Material (SRM) 2806: Medium Test Dust in Hydraulic Fluid represents a series of reference materials certified by the National Institute of Standards and Technology (NIST) used to calibrate liquid-borne optical (or automatic) particle counters applied in a wide range of industrial, aerospace, and military applications. The series, including SRM 2806b, and SRM 2806d, was manufactured for NIST by IFTS, Institut de la Filtration et des Techniques Séparatives International Filter Testing Services, in France. An important factor for the acceptance of the material for certification was the degree of bottle-to-bottle homogeneity, which was evaluated by both IFTS and NIST. A statistical graphics methodology was developed that provided immediate visual as well as quantitative statistical metrics with which to characterize the SRM. This NIST-developed approach was used in four studies to assess the homogeneity of the material during both its production stage and its finished bottled-product stage. IFTS performed measurements using an optical particle counter for on-line quality assurance and sampled 40 bottles of the finished 400 bottle series to determine homogeneity from the particle size distribution. NIST also determined the particle size distribution of the finished material and performed microscopy to look for possible contaminant material in the suspension. An accelerated aging experiment was conducted on both materials (2806b and 2806d) to verify their stability.
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This is the first in a series of articles which present a new framework for computing the standard uncertainty in electron excited X-ray microanalysis measurements. This article will discuss the framework and apply it to a handful of simple, but useful, subcomponents of the larger problem. Subsequent articles will handle more complex aspects of the measurement model. The result will be a framework in which sophisticated and practical models of the uncertainty for real-world measurements. It will include many long overlooked contributions like surface roughness and coating thickness. The result provides more than just error bars for our measurements. It also provides a framework for measurement optimization and, ultimately, the development of an expert system to guide both the novice and expert to design more effective measurement protocols.
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2018 marked the 50th anniversary of the introduction of energy dispersive X-ray spectrometry (EDS) with semiconductor detectors to electron-excited X-ray microanalysis. Initially useful for qualitative analysis, EDS has developed into a fully quantitative analytical tool that can match wavelength dispersive spectrometry for accuracy in the determination of major (mass concentration C > 0.1) and minor (0.01 ≤ C ≤ 0.1) constituents, and useful accuracy can extend well into the trace (0.001 < C < 0.01) constituent range even when severe peak interference occurs. Accurate analysis is possible for low atomic number elements (B, C, N, O, and F), and at low beam energy, which can optimize lateral and depth spatial resolution. By recording a full EDS spectrum at each picture element of a scan, comprehensive quantitative compositional mapping can also be performed.
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When analyzing an unknown by electron-excited energy dispersive X-ray spectrometry, with the entire periodic table possibly in play, how does the analyst discover minor and trace constituents when their peaks are overwhelmed by the intensity of an interfering peak(s) from a major constituent? In this paper, we advocate for and demonstrate an iterative analytical approach, alternating qualitative analysis (peak identification) and standards-based quantitative analysis with peak fitting. This method employs two "tools": (1) monitoring of the "raw analytical total," which is the sum of all measured constituents as well as any such as oxygen calculated by the method of assumed stoichiometry, and (2) careful inspection of the "peak fitting residual spectrum" that is constructed as part of the quantitative analysis procedure in the software engine DTSA-II (a pseudo-acronym) from the National Institute of Standards and Technology. Elements newly recognized after each round are incorporated into the next round of quantitative analysis until the limits of detection are reached, as defined by the total spectrum counts.
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The evolution of the energy dispersive spectrometer (EDS) from the lithium-drifted silicon detector [Si(Li)] to the silicon drift detector (SDD) has created new opportunities in the field of electron probe X-ray microanalysis. The SDD permits operation at significantly higher count rates than the Si(Li) and also provides a more stable energy scale. X-ray spectra captured by EDS can now be analyzed qualitatively or quantitatively under the same beam conditions as used for wavelength dispersive spectrometry (WDS). Standards-based quantitative EDS (SB-Quant-EDS) can thus provide analyses that are accurate and precise for an ever growing number of materials measurement problems. In this study, we analyze NIST research glasses with "known" nominal concentrations of titanium (Ti) and vanadium (V) to evaluate the external reproducibility of the SB-Quant-EDS technique in the presence of severe peak overlaps. We additionally analyze several naturally occurring oxide minerals by WDS and EDS simultaneously and evaluate the outputs of these two methods when quantifying the same analytical volume within the sample.
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Secondary fluorescence, the final term in the familiar matrix correction triumvirate Z·A·F, is the most challenging for Monte Carlo models to simulate. In fact, only two implementations of Monte Carlo models commonly used to simulate electron probe X-ray spectra can calculate secondary fluorescence-PENEPMA and NIST DTSA-II a (DTSA-II is discussed herein). These two models share many physical models but there are some important differences in the way each implements X-ray emission including secondary fluorescence. PENEPMA is based on PENELOPE, a general purpose software package for simulation of both relativistic and subrelativistic electron/positron interactions with matter. On the other hand, NIST DTSA-II was designed exclusively for simulation of X-ray spectra generated by subrelativistic electrons. NIST DTSA-II uses variance reduction techniques unsuited to general purpose code. These optimizations help NIST DTSA-II to be orders of magnitude more computationally efficient while retaining detector position sensitivity. Simulations execute in minutes rather than hours and can model differences that result from detector position. Both PENEPMA and NIST DTSA-II are capable of handling complex sample geometries and we will demonstrate that both are of similar accuracy when modeling experimental secondary fluorescence data from the literature.
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Scanning electron microscopy with energy-dispersive spectrometry has been applied to the analysis of various materials at low-incident beam energies, E 0≤5 keV, using peak fitting and following the measured standards/matrix corrections protocol embedded in the National Institute of Standards and Technology Desktop Spectrum Analyzer-II analytical software engine. Low beam energy analysis provides improved spatial resolution laterally and in-depth. The lower beam energy restricts the atomic shells that can be ionized, reducing the number of X-ray peak families available to the analyst. At E 0=5 keV, all elements of the periodic table except H and He can be measured. As the beam energy is reduced below 5 keV, elements become inaccessible due to lack of excitation of useful characteristic X-ray peaks. The shallow sampling depth of low beam energy microanalysis makes the technique more sensitive to surface compositional modification due to formation of oxides and other reaction layers. Accurate and precise analysis is possible with the use of appropriate standards and by accumulating high count spectra of unknowns and standards (>1 million counts integrated from 0.1 keV to E 0).
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Electron-excited X-ray microanalysis performed with scanning electron microscopy and energy-dispersive spectrometry (EDS) has been used to measure trace elemental constituents of complex multielement materials, where "trace" refers to constituents present at concentrations below 0.01 (mass fraction). High count spectra measured with silicon drift detector EDS were quantified using the standards/matrix correction protocol embedded in the NIST DTSA-II software engine. Robust quantitative analytical results for trace constituents were obtained from concentrations as low as 0.000500 (mass fraction), even in the presence of significant peak interferences from minor (concentration 0.01≤C≤0.1) and major (C>0.1) constituents. Limits of detection as low as 0.000200 were achieved in the absence of peak interference.
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A new material has been certified to become Standard Reference Material (SRM) 2806b - Medium Test Dust in Hydraulic Fluid. SRM 2806b consists of trace polydisperse, irregularly shaped mineral dust particles suspended in hydraulic fluid. The certified values of SRM 2806b are the projected area circular-equivalent diameters of the collected dust particles from the hydraulic fluid. The dimensional measurements were determined from the area of the collected dust particles using images obtained from automated scanning electron microscopy (SEM) followed by image analysis. An automated SEM and an automated image analysis software allowed the processing of over 29 million particles. The dimensional calibration of the SEM images (actual length per pixel and thus the actual projected diameters) are traceable to the NIST Line Scale Interferometer (LSI) through a NIST calibrated Geller MRS-4XY pitch standard. The certified diameters are correlated with the numeric concentration of particles greater than each diameter, referred to as the cumulative number size distribution. SRM 2806b is intended to be used to calibrate liquid-borne optical particle counters in conjunction with the reference method ISO 11171:2010.