Many materials undergo modifications to both structure and chemistry during electron bombardment in an electron probe microanalyzer (EPMA). This results in changes to the emitted X-ray intensities by various physical processes including heating, breaking of molecular bonds, ionization, volatilization and sputtering, subsurface static charging and subsequent mobility of the measured elements. Most of these processes are proportional to the degree and duration of electron beam exposure (analytical time, acceleration voltage, beam current, and beam focus) and to the thermal and electrical conductivity of the analyzed material. Therefore, quantitative accuracy is dependent upon correction schemes that monitor changes in X-ray emission over time, a process called Time Dependent Intensity (TDI) corrections. This paper investigates various applications of TDI corrections and demonstrates that accurate point analyses can be obtained with such corrections. Moreover, the combination of replicate X-ray mapping with a TDI correction can produce precise and accurate quantitative element maps for beam-sensitive materials, expanding the range of materials and analytical conditions suitable for EPMA applications.

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.

Abstract Estimates of the oxidation states of magmas are important to current investigations of the geochemical characteristics of their source regions and of evolved magmatic series created during differentiation. One means of achieving such estimates is to capitalize on compositions of coexisting cubic and rhombohedral Fe-Ti oxides determined by electron microprobe. A combination of experimental calibration points and thermodynamic modeling provides a basis for translating such compositions into T-ƒO2 values. This has been done until recently by estimating Fe3+/ΣFe on the basis of charge balance and stoichiometry by the method of Droop (1987), after matrix corrections of X-ray intensity data have been performed, as EPMA cannot be used routinely to distinguish different elemental valence states, much less accurately quantify abundances of Fe3+ and Fe2+. The traditional approach of undertaking post-data-reduction calculations falls short of attaining the best possible quantitative results. The tactical choice of not accounting for light elements that have not been explicitly analyzed prior to matrix corrections of X-ray intensity data leads to systematic errors in reported oxide abundances for measured elements. This article addresses one such issue, the oxygen associated with Fe3+ (hereafter “excess oxygen”), on the basis of coexisting Fe-Ti oxides from Andean lavas. A new software routine in probe for EPMA (PFE) uses an iterative calculation scheme to calculate amounts of excess oxygen that would not be considered if all iron were assumed to be ferrous and then applies this excess oxygen during matrix corrections. The PFE approach reveals that Fe-concentrations have been underestimated, universally, in these minerals because O atoms absorb FeKα radiation: discrepancies increase as total Fe and Fe3+/Fe2+, hence excess oxygen, increase. Analyses of the most Fe-rich cubic oxide compositions in this data set have ~6 wt% excess oxygen and ~1 wt% more FeO+Fe2O3 than would be reported without incorporating the impact of excess oxygen in matrix corrections. Minor to negligible differences in other elements are also observed. These effects are not because excess oxygen is directly attributed to these elements, although some may be present in multiple valence states, as matrix corrections are undertaken on the basis of the conventional assumptions that they occur as Cr3+, V3+, Mn2+, Mg2+, Ca2+, and Si4+. Rather, variably small increases in total Fe propagate through the matrix corrections for other elements, and these differences may be recorded as minor increases or decreases in some concentrations, depending on the particular element and the amount of change in Fe-concentration. Fe3+/ΣFe in analyses produced with the PFE routine are essentially identical to those determined in the traditional mode, as cation proportions calculated on the basis of charge balance and stoichiometry, with the method of Droop (1987), is a necessary step. The new method: (1) provides more accurate concentrations, mainly for Fe and Ti; (2) is applicable to any mineral containing ferric iron (subject to stoichiometric constraints); (3) provides more accurate analytical totals, which can be advantageous for evaluating analytical quality; and (4) does not impact estimates of oxidation state. Oxygen fugacities and temperatures determined with the model of Ghiorso and Evans (2008) are essentially unchanged.

The chemistry of erupted minerals and melts are commonly used to determine the pressures, temperatures and H2O contents of magma storage regions beneath volcanic centres. In turn, these estimates are vital for hazard assessment, to understand the formation of critical metal deposits, and to inform models of continental crust formation. In the last few decades, more than 100 empirical and thermodynamic expressions have been calibrated using measurements of phases in experimental studies where these intensive parameters are known. By collating these different models into a computationally-efficient, open-source Python3 package, Thermobar, we can critically assess the performance of thermobarometers in igneous systems, and propagate analytical errors. When we apply published models for different mineral equilibrium to a new experimental dataset not used in model calibration, we find that stated errors vastly underestimate the true uncertainty when these workflows are applied to natural systems.Specifically, we find that realistic calculation workflows involving Clinopyroxene (Cpx) equilibrium (e.g., iterating pressure and temperature) have uncertainties spanning the entire crust in most tectonic settings. Using Thermobar functions to propagate analytical error using Monte Carlo simulations, we suggest that these large errors result from imprecise analyses of minor elements such as Na in experimental (and natural) Cpx. Common analytical conditions used for Cpx yield highly correlated pressure-temperature arrays spanning the entire crust, which have been incorrectly interpreted as trancrustal storage in natural systems. Insuffucient analyses of each phase in experimental products means that this analytical error is not sufficiently mediated by averaging, so reported mineral compositions deviate from the true phase composition. This impacts thermobarometer calibration, as well as assessment of these methods using test experimental datasets.Overall, we demonstrate that the development of Python3 infrastructure for common quantitative workflows in volcanology is vital to allow rigorous error assessment and model intercomparison; such assessments simply aren’t feasible using traditional tools (e.g., Excel workbooks). Specific changes to analytical, experimental and model calibration workflows (e.g., higher beam currents and count times in Na) will be essential to produce a more robust dataset to calibrate and test the next generation of more precise and accurate Cpx-based barometers. In turn, this will enable more rigorous investigation of magma storage geometries in a variety of tectonic settings (e.g., distinguishing true transcrustal storage vs. storage in discrete reservoirs).

Journal Article The Holy Trinity of Microanalysis: Standards, K-ratios and Physics Get access John Donovan, John Donovan CAMCOR, University of Oregon, Eugene, Oregon, USA Search for other works by this author on: Oxford Academic Google Scholar Aurélien Moy, Aurélien Moy Department of Geoscience, University of Wisconsin-Madison, Wisconsin, USA Search for other works by this author on: Oxford Academic Google Scholar Will Nachlas, Will Nachlas Department of Geoscience, University of Wisconsin-Madison, Wisconsin, USA Search for other works by this author on: Oxford Academic Google Scholar John Fournelle John Fournelle Department of Geoscience, University of Wisconsin-Madison, Wisconsin, USA Search for other works by this author on: Oxford Academic Google Scholar Microscopy and Microanalysis, Volume 29, Issue Supplement_1, 1 August 2023, Pages 243–244, https://doi.org/10.1093/micmic/ozad067.109 Published: 22 July 2023

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.

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Abstract While much progress has been made in electron-probe microanalysis (EPMA) to improve the accuracy of point analysis, the same level of attention has not always been applied to the quantification of wavelength-dispersive spectrometry (WDS) X-ray intensity maps at the individual pixel level. We demonstrate that the same level of rigor applied in traditional point analysis can also be applied to the quantification of pixels in X-ray intensity maps, along with additional acquisition and quantitative processing procedures to further improve accuracy, precision, and mapping throughput. Accordingly, X-ray map quantification should include pixel-level corrections for WDS detector deadtime, corrections for changes in beam current (beam drift), changes in standard intensities (standard drift), high-accuracy removal of background intensities, quantitative matrix corrections, quantitative correction of spectral interferences, and, if required, time-dependent corrections (for beam and/or contamination sensitive materials). The purpose of quantification at the pixel level is to eliminate misinterpretation of intensity artifacts, inherent in raw X-ray intensity signals, that distort the apparent abundance of an element. Major and minor element X-ray signals can contain significant artifacts due to absorption and fluorescence effects. Trace element X-ray signals can contain significant artifacts where phases with different average atomic numbers produce different X-ray continuum (bremsstrahlung) intensities, or where a spectral interference, even an apparently minor one, can produce a false-positive intensity signal. The methods we propose for rigorous pixel quantification require calibration of X-ray intensities on the instrument using standard reference materials, as we already do for point analysis that is then used to quantify multiple X-ray maps, and thus the relative time overhead associated with such pixel-by-pixel quantification is small. Moreover, the absolute time overhead associated with this method is usually less than that required for quantification using manual calibration curve methods while resulting in significantly better accuracy. Applications to geological, synthetic, or engineering materials are numerous as quantitative maps not only show compositional 2D variation of fine-grained or finely zoned structures but also provide very accurate quantitative analysis, with precision approaching that of a single point analysis, when multiple-pixel averaging in compositionally homogeneous domains is utilized.

Historically, many EPMA labs have neglected to measure all of the elements present in some samples, either because it was impossible or difficult to acquire low energy/long wavelength X-ray lines, or because they could be assumed to be present and correctly accounted for by stoichiometric apportionment and post-processing outside the matrix correction. With the availability of layered synthetic diffractors since the late 1980s, it became possible, with attention to detail, to quantify B, C, N, O and F [1]. It has been 24 years since Tingle et al [2] pointed out the importance of including "missing" oxygen in EPMA measurements, and there is the need to remind our community of this not insignificant aspect of EPMA, especially as new generations of microanalysts learn the technique. We present four examples where the inclusion of ALL elements is essential for accurate and complete correctionof matrix effects: carbonate minerals, hydrous minerals, hydrous carbonates, and borate minerals.

Electron probe microanalysis (EPMA), whether by wavelength-dispersive spectrometer or energy dispersive spectrometer, is a method for measuring the composition of a material. However, EPMA is an indirect technique. The fundamental measurand in EPMA is the X-ray intensity. Materials are compared through the ratio of X-ray intensities measured under similar conditions on the unknown and a standard – called the k-ratio. The k-ratio is converted to a measure of composition through an implicit multivariate measurement model [1], called matrix correction, in which we compute the anticipated k-ratio for a specified element and X-ray line in a specified material and compare it with the measured k-ratio. The estimated composition is adjusted through a non-linear optimization process, called iteration, until the computed k-ratio equals the measured k-ratio.

Journal Article Including the Oxidation State of Iron to Improve Matrix Corrections in EPMA Analyses Get access Emma Bullock, Emma Bullock Carnegie Institution for Science, Washington, District of Columbia, United States Search for other works by this author on: Oxford Academic Google Scholar Andrew Locock, Andrew Locock University of Alberta, Edmonton, Alberta, Canada Search for other works by this author on: Oxford Academic Google Scholar Anette von der Handt, Anette von der Handt University of Minnesota, Minneapolis, Minnesota, United States Search for other works by this author on: Oxford Academic Google Scholar John Fournelle, John Fournelle University of Wisconsin, Madison, Madison, Wisconsin, United States Search for other works by this author on: Oxford Academic Google Scholar Michael Dungan, Michael Dungan University of Oregon, Eugene, Oregon, United States Search for other works by this author on: Oxford Academic Google Scholar John Donovan John Donovan University of Oregon, Eugene, Oregon, United States Search for other works by this author on: Oxford Academic Google Scholar Microscopy and Microanalysis, Volume 26, Issue S2, 1 August 2020, Pages 1876–1877, https://doi.org/10.1017/S1431927620019674 Published: 01 August 2020

We present results from 25 hydrothermal quartz growth experiments, all conducted at 800 degrees C and 1 kbar but with varying starting materials and run times, to address discrepancies between calibrations of the titanium-in-quartz (TitaniQ) thermobarometer. In our experiments, a gold capsule is loaded with silica glass, water, and either rutile or anatase as the TiO2 source. In most experiments, there is also a large quartz seed crystal contained in an open inner capsule. The use of rutile versus anatase has a significant influence on the (re)crystallization pathways of the SiO2 and TiO2 components. When rutile is used, quartz overgrowths have abundant open cavities and complex zonations. The rutile does not completely dissolve because rutile is the stable TiO2 polymorph, and yet, new rutile forms at the quartz seed-overgrowth interface and on the outer surface of quartz crystals. This suggests crystallization of quartz near Omega(rut) similar to 1, but wide-ranging Ti concentrations and zonations in quartz are indicative of kinetic effects. When powdered anatase is used, the quartz overgrowths look markedly different, lacking the open cavities and instead exhibiting step edges and terraces. The Ti concentrations in quartz from these experiments are also wide-ranging but reach larger values. Our results span the range of previous calibrations and indicate that Ti concentrations in quartz are sensitive to the TiO2/SiO2 ratio of the fluid as opposed to the absolute concentration (or activity) of dissolved TiO2. We present a kinetic model for quartz and rutile growth from a fluid where the input parameters are the initial degrees of supersaturation with respect to quartz and rutile, the total reactive surface area, and rate constants that link the degree of supersaturation to net precipitation rates. The model can explain many of the salient features of our experimental results, as well as those from previous studies, but requires that the rate constant multiplied by the reactive surface area for rutile is less than that of quartz, and that rutile solubility depends on the SiO2 concentration of the fluid, as documented in the recent literature. Complete quartz-rutile equilibrium may not have been established in any of the experimental studies, but low-pressure experiments with slowly grown quartz seem to be more reliable than extrapolations from high-pressure experiments for thermobarometry of shallow natural systems. (C) 2020 Elsevier Ltd. All rights reserved.

Journal Article A Modified Mean Atomic Number Background Correction Using Off-Peak Interpolated Measurements Get access Omero Orlandini, Omero Orlandini University of Texas at Austin, Austin, Texas, United States Search for other works by this author on: Oxford Academic Google Scholar John Donovan, John Donovan University of Oregon, Eugene, Oregon, United States Search for other works by this author on: Oxford Academic Google Scholar Benjamin Hanson Benjamin Hanson Corning Research and Development Corp., Corning, New York, United States Search for other works by this author on: Oxford Academic Google Scholar Microscopy and Microanalysis, Volume 26, Issue S2, 1 August 2020, Pages 508–509, https://doi.org/10.1017/S1431927620014889 Published: 01 August 2020

Electron microprobe trace element analysis is a significant challenge. Due to the low net intensity of peak measurements, the accuracy and precision of such analyses relies critically on background measurements, and on the accuracy of any pertinent peak interference corrections. A linear regression between two points selected at appropriate background positions is a classical approach for electron probe microanalysis (EPMA). However, this approach neglects the accurate assessment of background curvature (exponential or polynomial), and the presence of background interferences, a hole in the background, or an absorption edge can dramatically affect the results if underestimated or ignored. The acquisition of a quantitative wavelength-dispersive spectrometry (WDS) scan over the spectral region of interest remains a reasonable option to determine the background intensity and curvature from a fitted regression of background portions of the scan, but this technique can be time consuming and retains an element of subjectivity, as the analyst has to select areas in the scan which appear to represent background. This paper presents a new multi-point background (MPB) method whereby the background intensity is determined from up to 24 background measurements from wavelength positions on either side of analytical lines. This method improves the accuracy and precision of trace element analysis in a complex matrix through careful regression of the background shape, and can be used to characterize the background over a large spectral region covering several elements to be analyzed. The overall efficiency improves as systematic WDS scanning is not required to assess background interferences. The method is less subjective compared to methods that rely on WDS scanning, including selection of two interpolation points based on WDS scans, because "true" backgrounds are selected through an exclusion method of possible erroneous backgrounds. The first validation of the MPB method involves blank testing to ensure the method can accurately measure the absence of an element. The second validation involves the analysis of U-Th-Pb in several monazite reference materials of known isotopic age. The impetus for the MPB method came from efforts to refine EPMA monazite U-Th-Pb dating, where it was recognized that background errors resulting from interference or strong background curvature could result in errors of several tens of millions of years on the calculated date. Results obtained on monazite reference materials using two different microprobes, a Cameca SX-100 Ultrachron and a JEOL JXA-8230, yield excellent agreement with ages obtained by isotopic methods (Thermal Ionization Mass Spectrometry [TIMS], Sensitive High-Resolution Ion MicroProbe [SHRIMP], or Secondary Ion Mass Spectrometry [SIMS]). Finally, the MPB method can be used to model the background over a large spectrometer range to improve the accuracy of background measurement of minor and trace elements acquired on a same spectrometer, a method called the shared background measurement. This latter significantly improves the accuracy of minor and trace element analysis in complex matrices, as demonstrated by the analysis of Rare Earth Elements (REE) in REE-silicates and phosphates and of trace elements in scheelite.