A New Method for Dead Time Calibration and a New Expression for Correction of WDS Intensities for Microanalysis.

Observed photon count rates must be corrected for detector dead time effects for accurate quantification, especially at high count rates. We present the "constant k-ratio" method, a new approach for calibrating dead time for wavelength dispersive spectrometers by measuring k-ratios as a function of beam current. The method is based on the observation that for a given emission line at a specific take-off angle and electron beam energy, the intensity ratio from two materials containing the element should remain constant as a function of beam current, if the dead time calibration is accurate. The method has the advantage that it does not rely on the linearity of the beam current picoammeter, yet also allows the analyst to evaluate the picoammeter linearity, another critical parameter in EPMA calibration. By simultaneously comparing k-ratios for all spectrometers, one can also ascertain k-ratio consensus, essential for inter-laboratory comparisons. We also introduce improved dead time expressions and provide best practices on how to perform these instrument calibrations using this new "constant k-ratio" method. These improvements enable quantitative analysis of major and minor elements with high accuracy at high beam currents, simultaneously with trace elements with high sensitivity, for point analyses and X-ray mapping.

Assessing the Accuracy of Mass Attenuation Coefficients for Soft X-ray EPMA.

The use of soft X-rays in electron probe microanalysis (EPMA) has gained renewed interest over the past decades due to the advent of new detector technologies. Because X-ray absorption is the dominant correction for soft X-rays, a reliable set of mass attenuation coefficients (MACs) is needed for accurate composition determination. Although several MAC tabulations cover the soft X-ray range, the accuracy of such tabulations below 1 keV is not firmly established. In this study, we assess the accuracy of MAC tabulations in the soft X-ray region by comparing tabulated values for Be, B, C, N, O, and F Kα X-rays with experimental data available in the literature. We find that the 1993 semi-empirical MAC compilation of Henke et al. [(1993). Low-energy X-ray interaction coefficients: Photoabsorption, scattering, transmission and reflection at E=50-30000 eV, Z=1-92. Atom Data Nucl Data Tables54, 181-342] and the more recent theoretical MAC calculations of Sabbatucci and Salvat [(2016). Theory and calculation of the atomic photoeffect. Rad Phys Chem121, 122-140] perform slightly better than the rest of the considered tabulations. The Sabbatucci-Salvat dataset also provides the best agreement with the few existing experimental measurements for Al L2,3M X-rays.

An Improved Average Atomic Number Calculation for Estimating Backscatter and Continuum Production in Compounds.

It is often assumed that electron backscatter and continuum (bremsstrahlung) productions emitted from electron-solid interactions during X-ray microanalysis in compounds can be extrapolated from pure element observations by means of the assumption of average atomic number, or Z-bar (Z¯). For pure elements the average Z is equal to the atomic number, but this direct approach fails for compounds. The use of simple atomic fractions yields completely spurious results, and while the commonly used mass fraction Z averaging produces fairly reasonable results, we know from physical considerations that the mass of the neutron plays only a negligible role in such interactions below ∼1 MeV. Therefore, including the mass or atomic weight in such calculations can only introduce further errors in these models. We present an expression utilizing atomic fractions of the atomic numbers of the elements in the compound (Z fraction), with an exponent to account for the variation in nuclear screening as a function of the element Z value.

Electron Probe Microanalysis of Transition Metals using L lines: The Effect of Self-absorption.

Electron microprobe-based quantitative compositional measurement of first-row transition metals using their L$\alpha$ X-ray lines is hampered by, among other effects, self-absorption. This effect, which occurs when a broad X-ray line is located close to a broad absorption edge, is not accounted for by matrix corrections. To assess the error due to neglecting self-absorption, we calculate the L$\alpha$ X-ray intensity emitted from metallic Fe, Ni, Cu, and Zn targets, assuming a Lorentzian profile for the X-ray line and taking into account the energy dependence of the mass absorption coefficient near the absorption edge. We find that calculated X-ray intensities depart increasingly, for increasing electron beam energy, from those obtained assuming a narrow X-ray line and a single fixed absorption coefficient (conventional approach), with a maximum deviation of $\sim$15% for Ni and of $\sim$10% for Fe. In contrast, X-ray intensities calculated for metallic Zn and Cu do not differ significantly from those obtained using the conventional approach. The implications of these results for the analysis of transition-metal compounds by electron probe microanalysis as well as strategies to account for self-absorption effects are discussed.

ϕ(ρz) Distributions in Bulk and Thin-Film Samples for EPMA. Part 2: BadgerFilm: A New Thin-Film Analysis Program.

Since the 1960s, thicknesses and compositions of thin-film specimens have been determined by using the nondestructive technique of electron probe microanalysis. This approach, refined in the 1990s, is based upon models of the ionization depth distribution, the so-called ϕ(ρz) distribution, and is capable of analyzing layered specimens. Most of these quantification models have led to commercial programs. However, these programs may have possible limitations: some may not be directly compatible with modern computers, they often are "black boxes" making it difficult to assess the reliability of the results, and they are sometimes expensive enough to restrain many labs from purchasing them. We present a user-friendly, free, open-source program, BadgerFilm, implementing a documented ϕ(ρz) model and algorithms allowing the quantification of stratified samples. The program has the ability to calculate absolute X-ray intensities that can be directly compared with Monte Carlo simulations. We give a detailed explanation for the operation of the employed ϕ(ρz) model in thin films. A wide range of detailed Monte Carlo simulations and experimental data have been used to evaluate and validate the accuracy of the implemented algorithms. BadgerFilm demonstrated excellent quantification results for the films and in many cases for the substrates.

ϕ(ρz) Distributions in Bulk and Thin Film Samples for EPMA. Part 1: A Modified ϕ(ρz) Distribution for Bulk Materials, Including Characteristic and Bremsstrahlung Fluorescence.

Electron probe microanalysis is a nondestructive technique widely used to determine the elemental composition of bulk samples. This was extended to layered specimens, with the development of appropriate software. The traditional quantification method requires the use of matrix correction procedures based upon models of the ionization depth distribution, the so-called ϕ(ρz) distribution. Most of these models have led to commercial quantification programs but only few of them allow the quantification of layered specimens. Therefore, we developed BadgerFilm, a free open-source thin film program available to the general public. This program implements a documented ϕ(ρz) model as well as algorithms to calculate fluorescence in bulk and thin film samples. Part 1 of the present work aims at describing the operation of the implemented ϕ(ρz) distribution model and validating its implementation against experimental measurements and Monte Carlo simulations on bulk samples. The program has the ability to predict absolute X-ray intensities that can be directly compared to Monte Carlo simulations. We demonstrate that the implemented model works very well for bulk materials. And as will be shown in Part 2, BadgerFilm predictions for thin film specimens are also shown to be in good agreements with experimental and Monte Carlo results.

Quantitative Measurement of Iron-Silicides by EPMA Using the Fe Lα and Lß X-ray Lines: A New Twist to an Old Approach.

The recent availability of Schottky-type field emission electron microprobes provides incentive to consider analyzing micrometer-sized features. Yet, to quantify sub-micrometer-sized features, the electron interaction volume must be reduced by decreasing accelerating voltage. However, the K lines of the transition elements (e.g., Fe) then cannot be excited, and the L lines must be used. The Fe Lα1,2 line is the most intense of the L series but bonding effects change its atomic parameters because it involves a valence band electron transition. For successful traditional electron probe microanalysis, the mass absorption coefficient (MAC) must be accurately known, but the MAC of Fe Lα1,2 radiation by Fe atoms varies from one Fe-compound to another and is not well known. We show that the conventional method of measuring the MAC by an electron probe cannot be used in close proximity to absorption edges, making its accurate determination impossible. Fortunately, we demonstrate, using a set of Fe-silicide compounds, that it is possible to derive an accurate calibration curve, for a given accelerating voltage and takeoff angle, which can be used to quantify Fe in Fe-silicide compounds. The calibration curve can be applied to any spectrometer without calibration and gives accurate quantification results.

Standardless Quantification of Heavy Elements by Electron Probe Microanalysis.

Absolute Mα and Mß X-ray intensities were measured for the elements Pt, Au, Pb, U, and Th by electron impact for energies ranging from 6 to 38 keV. Experimental data were obtained by measuring the X-ray intensity emitted from bulk samples with an electron microprobe using high-resolution wavelength-dispersive spectrometers. Recorded X-ray intensities were converted into absolute X-ray yields by evaluation of the detector efficiency and then compared with X-ray intensities calculated by means of Monte Carlo simulations. Simulated Mα and Mß X-ray intensities were found to be in good agreement with the measurements, allowing their use in standardless quantification methods. A procedure and a software program were developed to accurately obtain virtual standard values. Standardless quantifications of Pb and U were tested on standards of PbS, PbTe, PbCl2, vanadinite, and UO2.