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Embracing Uncertainty: Modeling Uncertainty in EPMA—Part II

Published online by Cambridge University Press:  17 February 2021

Nicholas W.M. Ritchie
Nicholas W.M. Ritchie*
Affiliation:
Surface and Microanalysis Science, NIST, Gaithersburg, MD 20899, USA
*
*Author for correspondence: Nicholas W.M. Ritchie, E-mail: [email protected]
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Abstract

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.

Keywords

compositionEPMAmatrix correctionmeasurement optimizationuncertainty
Type
Software and Instrumentation
Information
Microscopy and Microanalysis , Volume 27 , Issue 1 , February 2021 , pp. 74 - 89
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of the Microscopy Society of America

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References

Armstrong, JT (1995). CITZAF — A package of correction programs for the quantitative electron microbeam X-ray-analysis of thick polished materials, thin-films, and particles. Microbeam Anal 4, 177–200.Google Scholar
Armstrong, JT, Donovan, J & Carpenter, P (2013). CALCZAF, TRYZAF and CITZAF: The use of multi-correction-algorithm programs for estimating uncertainties and improving quantitative X-ray analysis of difficult specimens. Microsc Microanal 19, 812–813.CrossRefGoogle Scholar
Bastin, GF, Dijkstra, JM & Heijligers, HJM (1998). PROZA96: An improved matrix correction program for electron probe microanalysis, based on a double Gaussian approach. X-Ray Spectrom 27, 3–10.3.0.CO;2-L>CrossRefGoogle Scholar
Castaing, R (1951). Application des sondes électronique à une méthode d'analyse ponctuelle chimique et cristallographique. PhD Thesis. University of Paris, Publication ONERA No. 55 (1952).Google Scholar
Chantler, CT (1995). Theoretical form factor, attenuation, and scattering tabulation for Z=1–92 from E=1–10 eV to E=0.4–1.0 MeV. J Phys Chem Ref Data 24, 71–643.CrossRefGoogle Scholar
Chantler, CT (2000). Detailed tabulation of atomic form factors, photoelectric absorption and scattering cross section, and mass attenuation coefficients in the vicinity of absorption edges in the soft X-ray (z = 30 − −36, z = 60 − −89, e = 0.1 − −10 keV), addressing convergence issues of earlier work. J Phys Chem Ref Data 29, 597–1048.CrossRefGoogle Scholar
Chantler, CT, Olsen, K, Dragoset, RA, Chang, J, Kishore, AR, Kotochigova, SA & Zucker, DS (2005). X-ray form factor, attenuation and scattering tables. Tech. Rep., National Institute of Standards and Technology, Gaithersburg, MD. Available at http://physics.nist.gov/ffast (retrieved May 1, 2007).Google Scholar
Coulon, J & Zeller, C (1973). Theoretical determination of backscattering factor in X-ray emission microanalysis. C R Hebd Seances Acad Sci Ser B 276, 215–218.Google Scholar
ISO/JCGM (2008). JCGM:101 – Supplement 1 to the “Guide to the Expression of Uncertainty in Measurement” – Propagation of Distributions Using a Monte Carlo Method. Tech. Rep., BIPM, IEC and IFCC, ILAC and ISO, IUPAC and IUPAP, OIML.Google Scholar
ISO/JCGM (2011). JCGM:102 – Evaluation of Measurement Data – Supplement 2 to the “Guide to the Expression of Uncertainty in Measurement” – Extension to Any Number of Output Quantities. Tech. Rep., BIPM, IEC and IFCC, ILAC and ISO, IUPAC and IUPAP, OIML.Google Scholar
Llovet, X, Fernandez-Varea, J, Sempau, J & Salvat, F (2005). Monte Carlo simulation of X-ray emission using the general-purpose code PENELOPE. Surf Interface Anal 37, 1054–1058.CrossRefGoogle Scholar
Pouchou, JL & Pichoir, F (1984). A new model for quantitative X-ray-microanalysis: Application to the analysis of homogeneous samples. Rech Aerosp, 167–192.Google Scholar
Pouchou, JL & Pichoir, F (1985). Performance extension of quantitative X-ray-microanalysis. Mem Etud Sci Rev Metall 82, 498–498.Google Scholar
Pouchou, JL & Pichoir, F (1986). Very high elements X-ray-microanalysis – Recent models of quantification. J Microsc Spectrosc Electron 11, 229–250.Google Scholar
Pouchou, JL & Pichoir, F (1991). Quantitative analysis of homogeneous or stratified microvolumes applying the model ‘PAP’. In Electron Probe Quantitation, Heinrich K & Newbury D (Eds.), pp. 31–75. Springer. Available at http://www.ebook.de/de/product/3835664/electron˙probe˙quantitation.html.Google Scholar
Reed, SJB (1993). Electron Probe Microanalysis, 2nd ed. Cambridge: Cambridge University Press.Google Scholar
Ritchie, N & Scott, J (2006). Visualizing electron and X-ray transport in complex three-dimensional samples using NISTMonte. Scanning 28, 109.Google Scholar
Ritchie, NW (2020). Embracing uncertainty: Modeling the standard uncertainty in electron probe microanalysis–Part I. Microsc Microanal 26, 1–15.CrossRefGoogle Scholar
Ritchie, NWM (2005). A new Monte Carlo application for complex sample geometries. Surf Interface Anal 37, 1006–1011.CrossRefGoogle Scholar
Salvat, F, Llovet, X, Fernandez-Varea, JM & Sempau, J (2006). Monte Carlo simulation in electron probe microanalysis. Comparison of different simulation algorithms. Microchim Acta 155, 67–74.CrossRefGoogle Scholar
Springer, G (1976). Iterative procedures in electron probe analysis corrections. X-ray Spectrom 5, 88–91.CrossRefGoogle Scholar
Wegstein, A (1958). Accelerating convergence of iterative processes. Commun ACM 1. https://doi.org/10.1145/368861.368871.CrossRefGoogle Scholar