Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-27T23:11:15.190Z Has data issue: false hasContentIssue false

Embracing Uncertainty: Modeling the Standard Uncertainty in Electron Probe Microanalysis—Part I

Published online by Cambridge University Press:  21 May 2020

Nicholas W. M. Ritchie*
Affiliation:
Microanalysis Group, Materials Measurement Science Division, National Institute of Standards and Technology, Gaithersburg, MD20899-8371, USA
*
*Author for correspondence: Nicholas W. M. Ritchie, E-mail: [email protected]
Get access

Abstract

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.

Type
Software and Instrumentation
Copyright
Copyright © Microscopy Society of America 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allaz, JM, Williams, ML, Jercinovic, MJ, Goemann, K & Donovan, J (2019). Multipoint background analysis: Gaining precision and accuracy in microprobe trace element analysis. Microsc Microanal 25, 3046.CrossRefGoogle ScholarPubMed
Ancey, M, Bastenaire, F & Tixier, R (1977). Statistical control and optimization of X-ray intensity measurements. J Phys D 10, 817830.CrossRefGoogle Scholar
Armstrong, JT (2014). Comparative performance of SDD-EDS and WDS detectors for quantitative analysis of mineral specimens: The next generation electron microprobe. Microsc Microanal 20, 692693.CrossRefGoogle 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, 812813.CrossRefGoogle Scholar
Bastin, GF & Heijligers, HJM (1986). Quantitative electron probe microanalysis of carbon in binary carbides. I—Principles and procedures. X-Ray Spectrom 15, 135141.CrossRefGoogle Scholar
Bullock, ES (2019). A combined WDS, EDS and cathodoluminescence study of carbonate grains in water-rich meteorites. Microsc Microanal 25, 266267.CrossRefGoogle Scholar
Camus, P (2015). Factors affecting WDS performance superiority over EDS. Microsc Microanal 21, 16291630.CrossRefGoogle Scholar
Castaing, R (1952). Application des sondes électronique à une méthode d'analyse ponctuelle chimique et cristallographique. PhD Thesis. University of Paris, ONERA, Paris No. 55 (1952).Google 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, 5971048.CrossRefGoogle Scholar
Criss, J & Birks, L (1966). in McKinley et al. (Eds) The Electron Microprobe, John Wiley, New York, 1966, p. 229. New York: Wiley.Google Scholar
Donovan, JJ, Lowers, HA & Rusk, BG (2011). Improved electron probe microanalysis of trace elements in quartz. Am Mineral 96, 274282.CrossRefGoogle Scholar
Donovan, JJ & Tingle, TN (1995). An improved mean atomic number background correction for quantitative microanalysis. In Microbeam Analysis 1995 – Proceedings of the 29th Annual Conference of the Microbeam Analysis Society, Microbeam Analysis, Breckenridge, CO, August 6–11, 1995, Etz ES (Ed.), pp. 209–210.Google Scholar
Gopon, P, Fournelle, J, Sobol, PE & Llovet, X (2013). Low-voltage electron-probe microanalysis of Fe–Si compounds using soft X-rays. Microsc Microanal 19, 16981708.CrossRefGoogle ScholarPubMed
Heinrich, KF (1981). Electron Beam X-ray Microanalysis. New York: Van Nostrand Reingold.Google Scholar
JCGM (Joint Committee for Guides in Metrology) (2008). Evaluation of Measurement Data – Guide for the Expression of Uncertainty in Measurement. JCGM 100:2008. Geneva: International Organization for Standardization, p. 167.Google Scholar
JCGM (Joint Committee for Guides in Metrology) (2008). Supplement 1 to the “Guide to the Expression of Uncertainty in Measurement” – Propagation of Distributions Using a Monte Carlo Method (BIPM 101:2008). Geneva: International Organization for Standardization.Google Scholar
JCGM (Joint Committee for Guides in Metrology) (2011). Evaluation of Measurement Data – Supplement 2 to the “Guide to the Expression of Uncertainty in Measurement” – Extension to Any Number of Output Quantities (BIPM:102). Geneva: International Organization for Standardization.Google Scholar
Lifshin, E, Doganaksoy, N, Sirois, J & Gauvin, R (1999). Statistical considerations in microanalysis by energy-dispersive spectrometry. Microsc Microanal 4, 598604.CrossRefGoogle Scholar
Llovet, X, Pinard, PT, Heikinheimo, E, Louhenkilpi, S & Richter, S (2016). Electron probe microanalysis of Ni silicides using Ni-L X-ray lines. Microsc Microanal 22, 12331243.CrossRefGoogle ScholarPubMed
Marinenko, RB & Leigh, S (2010). Uncertainties in electron probe microanalysis. In IOP Conference Series: Materials Science and Engineering, vol. 7, p. 012017. IOP Publishing. Bristol, UKCrossRefGoogle Scholar
McNaught, AD & Wilkinson, A (Eds.) (1997 (downloaded March 24, 2020)). IUPAC Compendium of Chemical Terminology. (The “Gold Book”), 2nd ed. Oxford, UK: Blackwell Scientific Publications.Google Scholar
Moran, K & Wuhrer, R (2016). Current state of combined EDS-WDS quantitative X-ray mapping. Microsc Microanal 22, 9293.CrossRefGoogle Scholar
Newbury, DE & Ritchie, NWM (2015). Quantitative electron-excited X-ray microanalysis of borides, carbides, nitrides, oxides, and fluorides with scanning electron microscopy/silicon drift detector energy-dispersive spectrometry (SEM/SDD-EDS) and NIST DTSA-II. Microsc Microanal 21, 1327–1340.CrossRefGoogle Scholar
Newbury, DE & Ritchie, NWM (2016 a). Electron-excited X-ray microanalysis at low beam energy: Almost always an adventure! Microsc Microanal 22, 735753.CrossRefGoogle ScholarPubMed
Newbury, DE & Ritchie, NWM (2016 b). Measurement of trace constituents by electron-excited X-ray microanalysis with energy-dispersive spectrometry. Microsc Microanal 22, 520535.CrossRefGoogle ScholarPubMed
Newbury, DE & Ritchie, NWM (2018). An iterative qualitative–quantitative sequential analysis strategy for electron-excited X-ray microanalysis with energy dispersive spectrometry: Finding the unexpected needles in the peak overlap haystack. Microsc Microanal 24, 350373.CrossRefGoogle ScholarPubMed
Newville, M (2004). Fundamentals of XAFS, vol. 78. USA: Consortium for Advanced Radiation Sources, University of Chicago. Available at http://xafsorg.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, S & Mason, P (1967). in Transactions of The Second National Conference on Electron Microprobe Analysis, Boston, Mass., June 14–16, 1967 as referenced by [Springer, 1976] .Google Scholar
Ritchie, NWM & Newbury, DE (2012). Uncertainty estimates for electron probe X-ray microanalysis measurements. Anal Chem 84, 99569962.CrossRefGoogle ScholarPubMed
Springer, G (1976). Iterative procedures in electron probe analysis corrections. X-Ray Spectrom 5, 8891.CrossRefGoogle Scholar
Terborg, R & Richter, S (2019). Analysis and quantification of transition metal borides with WDS and EDS. Microsc Microanal 25, 17661767.CrossRefGoogle Scholar
Thompson, K (2018). Advances in SDD-based EDS and comparisons to WDS for light element sensitivity. Microsc Microanal 24, 754755.CrossRefGoogle Scholar
Tiesinga, E, Mohr, PJ, Newell, DB & Taylor, BN (2019). The 2018 CODATA Recommended Values of the Fundamental Physical Constants (Web Version 8.0). Gaithersburg, MD: National Institute of Standards and Technology. Available at http://physics.nist.gov/constants. Database developed by J Baker, M Douma & S Kotochigova.Google Scholar
Ziebold, TO (1967). Precision and sensitivity in electron microprobe analysis. Anal Chem 39, 858861.CrossRefGoogle Scholar