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Quantifying Uncertainty from Mass-Peak Overlaps in Atom Probe Microscopy

Published online by Cambridge University Press:  14 February 2019

Andrew J. London Open the ORCID record for Andrew J. London [Opens in a new window]
Andrew J. London*
Affiliation:
United Kingdom Atomic Energy Authority, Culham Science Centre, Abingdon, Oxon, OX14 3DB, UK
*
Author for correspondence: Andrew J. London, E-mail: [email protected]
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Abstract

There are many sources of random and systematic error in composition quantification by atom probe microscopy, often, however, only statistical error is reported. Significantly larger errors can occur from the misidentification of ions and overlaps or interferences of peaks in the mass spectrum. These overlaps can be solved using maximum likelihood estimation (MLE), improving the accuracy of the result, but with an unknown effect on the precision. An analytical expression for the uncertainty of the MLE solution is presented and it is demonstrated to be much more accurate than the existing methods. In one example, the commonly used error estimate was five times too small.

Literature results containing overlaps most likely underestimate composition uncertainty because of the complexity of correctly dealing with stochastic effects and error propagation. The uncertainty depends on the amount of overlapped intensity, for example being ten times worse for the CO/Fe overlap than the Cr/Fe overlap. Using the methods described here, accurate estimation of error, and the minimization of this could be achieved, providing a key milestone in quantitative atom probe. Accurate estimation of the composition uncertainty in the presence of overlaps is crucial for planning experiments and scientific interpretation of the measurements.

Keywords

APTatom probe tomographyconfidence intervaldecompositionerror barsmass spectrum analysismaximum likelihoodoverlap solvingpeak deconvolution
Type
Data Analysis
Information
Microscopy and Microanalysis , Volume 25 , Special Issue 2: Atom Probe Tomography and Microscopy APT&M 2018 , April 2019 , pp. 378 - 388
Copyright
Copyright © Microscopy Society of America 2019 

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References

Akaike, H (1974). A new look at the statistical model identification. IEEE Trans Autom Control 19(6), 716–723.Google Scholar
Anderson, G (1976). Error propagation by the Monte Carlo method in geochemical calculations. Geochim Cosmochim Acta 40(12), 1533–1538.Google Scholar
Berglund, M & Wieser, ME (2011). Isotopic compositions of the elements 2009 (IUPAC technical report). Pure Appl Chem 83(2), 397–410.Google Scholar
Burnham, KP & Anderson, DR (2003). Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. Springer Science & Business Media. New York: Springer-Verlag.Google Scholar
Cox, MG & Siebert, BRL (2006). The use of a Monte Carlo method for evaluating uncertainty and expanded uncertainty. Metrologia 43(4), S178–S188.Google Scholar
Danoix, F, Grancher, G, Bostel, A & Blavette, D (2007 a). Standard deviations of composition measurements in atom probe analyses. Part I: Conventional 1D atom probe. Ultramicroscopy 107(9), 734–738.Google Scholar
Danoix, F, Grancher, G, Bostel, A & Blavette, D (2007 b). Standard deviations of composition measurements in atom probe analyses. Part II: 3D atom probe. Ultramicroscopy 107(9), 739–743.Google Scholar
Efron, B (1979). Bootstrap methods: Another look at the jackknife. Ann Statist 7(1), 1–26.Google Scholar
Ferrige, AG, Seddon, MJ, Jarvis, S, Skilling, J & Aplin, R (1991). Maximum entropy deconvolution in electrospray mass spectrometry. Rapid Commun Mass Spectrom 5(8), 374–377.Google Scholar
Gault, B, Moody, MP, Cairney, J & Ringer, S (2012). Atom Probe Microscopy, vol. 160. New York: Springer-Verlag, ISBN: 978-1-4614-3435-1..Google Scholar
Gault, B, Saxey, DW, Ashton, MW, Sinnott, SB, Chiaramonti, AN, Moody, MP & Schreiber, DK (2016). Behavior of molecules and molecular ions near a field emitter. New J Phys 18(3), 033031.Google Scholar
Geyer, CJ (2013). Asymptotics of maximum likelihood without the LLN or CLT or sample size going to infinity. In Advances in Modern Statistical Theory and Applications: A Festschrift in Honor of Morris L. Eaton, Jones, G. and Shen, X. (Eds.), pp. 1–24. Collections, Volume 10, Beachwood, OH: Institute of Mathematical Statistics.Google Scholar
Haley, D, Choi, P & Raabe, D (2015). Guided mass spectrum labeling in atom probe tomography. Ultramicroscopy 159, Part 2, 338–345.Google Scholar
Hansen, PC, Pereyra, V & Scherer, G (2013). Least Squares Data Fitting with Applications. Baltimore, MD: JHU Press.Google Scholar
Hudson, D, Smith, G & Gault, B (2011). Optimisation of mass ranging for atom probe microanalysis and application to the corrosion processes in Zr alloys. Ultramicroscopy 111(6), 480–486.10.1016/j.ultramic.2010.11.007Google Scholar
Hyde, J, Burke, M, Gault, B, Saxey, D, Styman, P, Wilford, K & Williams, T (2011). Atom probe tomography of reactor pressure vessel steels: An analysis of data integrity. Ultramicroscopy 111(6), 676–682.Google Scholar
Johnson, L, Thuvander, M, Stiller, K, Odén, M & Hultman, L (2013). Blind deconvolution of time-of-flight mass spectra from atom probe tomography. Ultramicroscopy 132, 60–64.10.1016/j.ultramic.2013.03.015Google Scholar
Kelly, TF (2011). Kinetic-energy discrimination for atom probe tomography: Review article. Microsc Microanal 17(1), 1–14.Google Scholar
Kelly, TF & Larson, DJ (2000). Local electrode atom probes. Mater Charact 44(1–2), 59–85.10.1016/S1044-5803(99)00055-8Google Scholar
Kelly, TF & Larson, DJ (2012). The second revolution in atom probe tomography. MRS bulletin 37(2), 150–158.Google Scholar
Larson, DJ, Prosa, TJ, Ulfig, RM, Geiser, BP & Kelly, TF (2013). Local Electrode Atom Probe Tomography: A User's Guide. New York: Springer-Verlag, ISBN: 978-1-4614-8720-3.Google Scholar
Lehmann, E & Casella, G (1998). Theory of point estimation (Springer texts in statistics), by E. L. Lehmann, George Casella. New York: Springer-Verlag. ISBN 0-387-985026.Google Scholar
Li, Y, Choi, P, Borchers, C, Westerkamp, S, Goto, S, Raabe, D & Kirchheim, R (2011). Atomic-scale mechanisms of deformation-induced cementite decomposition in pearlite. Acta Mater 59(10), 3965–3977.Google Scholar
Liu, J, Wu, C & Tsong, TT (1991). Measurement of the atomic site specific binding energy of surface atoms of metals and alloys. Surf Sci 246(1–3), 157–162.Google Scholar
London, AJ, Haley, D & Moody, MP (2017). Single-ion deconvolution of mass peak overlaps for atom probe microscopy. Microsc Microanal 23(2), 300–306.Google Scholar
London, AJ, Lozano-Perez, S, Moody, MP, Amirthapandian, S, Panigrahi, BK, Sundar, CS & Grovenor, CRM (2015 a). Quantification of oxide particle composition in model oxide dispersion strengthened steel alloys. Ultramicroscopy 159(2), 360–367.Google Scholar
London, AJ, Santra, S, Amirthapandian, S, Panigrahi, BK, Sarguna, RM, Balaji, S, Vijay, R, Sundar, CS, Lozano-Perez, S & Grovenor, CRM (2015 b). Effect of Ti and Cr on dispersion, structure and composition of oxide nano-particles in model ODS alloys. Acta Mater 97, 223–233.Google Scholar
Marquis, EA (2008). Core/shell structures of oxygen-rich nanofeatures in oxidedispersion strengthened Fe–Cr alloys. Appl Phys Lett 93(18), 181904.Google Scholar
Meisenkothen, F, Steel, EB, Prosa, TJ, Henry, KT & Kolli, RP (2015). Effects of detector dead-time on quantitative analyses involving boron and multi-hit detection events in atom probe tomography. Ultramicroscopy 159, 101–111.Google Scholar
Miller, MK, Cerezo, A, Hetherington, MG & Smith, GDW (1996). Atom Probe Field ion Microscopy. Oxford: Oxford Science Publications, ISBN: 978-0-19-851387-2.Google Scholar
Müller, EW, Panitz, JA & McLane, SB (1968). The atom-probe field ion microscope. Rev Sci Instrum 39(1), 83–86.Google Scholar
Neyman, J (1937). Outline of a theory of statistical estimation based on the classical theory of probability. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 236(767), 333–380.Google Scholar
Pawitan, Y (2001). In all Likelihood: Statistical Modelling and Inference Using Likelihood. Oxford, UK: Oxford University Press.Google Scholar
Philippe, T, Duguay, S & Blavette, D (2010). Clustering and pair correlation function in atom probe tomography. Ultramicroscopy 110(7), 862–865.Google Scholar
Sha, W, Chang, L, Smith, G, Cheng, L & Mittemeijer, E (1992). Some aspects of atom-probe analysis of Fe–C and Fe–N systems. Surf Sci 266(1), 416–423.Google Scholar
Thuvander, M (2016). On the accuracy of compositional quantification for atom probe tomography. Microsc Microanal 22(S3), 642–643.Google Scholar
Thuvander, M, Weidow, J, Angseryd, J, Falk, L, Liu, F, Sonestedt, M, Stiller, K & Andren, H-O (2011). Quantitative atom probe analysis of carbides. Ultramicroscopy 111(6), 604–608. Special Issue: 52nd International Field Emission Symposium.Google Scholar
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