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Secondary Fluorescence of 3D Heterogeneous Materials Using a Hybrid Model

Published online by Cambridge University Press:  27 May 2020

Yu Yuan Open the ORCID record for Yu Yuan [Opens in a new window] ,
Hendrix Demers ,
Xianglong Wang  and
Raynald Gauvin
Yu Yuan
Affiliation:
Department of Mining and Materials Engineering, McGill University, M.H. Wong Building, 3610 Rue University, Montreal, Quebec, CanadaH3A 0C5
Hendrix Demers
Affiliation:
Centre d'excellence en électrification des transports et stockage d’énergie, IREQ, 1800 Boulevard Lionel-Boulet, Varennes, Québec, CanadaJ3X 1S1
Xianglong Wang
Affiliation:
Department of Mining and Materials Engineering, McGill University, M.H. Wong Building, 3610 Rue University, Montreal, Quebec, CanadaH3A 0C5
Raynald Gauvin*
Affiliation:
Department of Mining and Materials Engineering, McGill University, M.H. Wong Building, 3610 Rue University, Montreal, Quebec, CanadaH3A 0C5
*
*Author for correspondence: Raynald Gauvin, E-mail: raynald.gauvin@mcgill.ca
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Abstract

In electron probe microanalysis or scanning electron microscopy, the Monte Carlo method is widely used for modeling electron transport within specimens and calculating X-ray spectra. For an accurate simulation, the calculation of secondary fluorescence (SF) is necessary, especially for samples with complex geometries. In this study, we developed a program, using a hybrid model that combines the Monte Carlo simulation with an analytical model, to perform SF correction for three-dimensional (3D) heterogeneous materials. The Monte Carlo simulation is performed using MC X-ray, a Monte Carlo program, to obtain the 3D primary X-ray distribution, which becomes the input of the analytical model. The voxel-based calculation of MC X-ray enables the model to be applicable to arbitrary samples. We demonstrate the derivation of the analytical model in detail and present the 3D X-ray distributions for both primary and secondary fluorescence to illustrate the capability of our program. Examples for non-diffusion couples and spherical inclusions inside matrices are shown. The results of our program are compared with experimental data from references and with results from other Monte Carlo codes. They are found to be in good agreement.

Keywords

3D heterogeneous materials3D X-ray distributionMonte Carlosecondary fluorescence
Type
Software and Instrumentation
Information
Microscopy and Microanalysis , Volume 26 , Issue 3 , June 2020 , pp. 484 - 496
Copyright
Copyright © Microscopy Society of America 2020

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References

Armigliato, A, Desalvo, A & Rosa, R (1982). A Monte Carlo code including an X-ray characteristic fluorescence correction for electron probe microanalysis of a thin film on a substrate. J Phys D Appl Phys 15(10), L121.CrossRefGoogle Scholar
Armstrong, JT & Buseck, PR (1985). A general characteristic fluorescence correction for the quantitative electron microbeam analysis of thick specimens, thin films and particles. X-Ray Spectrom 14(4), 172–182.CrossRefGoogle Scholar
Bastin, G, Van Loo, F, Vosters, P & Vrolijk, J (1984). An iterative procedure for the correction of secondary fluorescence effects in electron-probe microanalysis near phase boundaries. Spectrochim Acta B At Spectrosc 39(12), 1517–1522.CrossRefGoogle Scholar
Bastin, G, Van Loo, F, Vosters, P & Vrolljk, J (1983). A correction procedure for characteristic fluorescence encountered in microprobe analysis near phase boundaries. Scanning 5(4), 172–183.CrossRefGoogle Scholar
Bote, D & Salvat, F (2008). Calculations of inner-shell ionization by electron impact with the distorted-wave and plane-wave Born approximations. Phys Rev A 77(4), 042701.CrossRefGoogle Scholar
Browning, R, Li, TZ, Chui, B, Ye, J, Pease, RFW, Czyżewski, Z & Joy, DC (1994). Empirical forms for the electron/atom elastic scattering cross sections from 0.1 to 30 keV. J Appl Phys 76(4), 2016–2022.CrossRefGoogle Scholar
Casnati, E, Tartari, A & Baraldi, C (1982). An empirical approach to K-shell ionisation cross section by electrons. J Phys B At Mol Phys 15(1), 155.CrossRefGoogle 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(1), 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 keV–10 keV), addressing convergence issues of earlier work. J Phys Chem Ref Data 29(4), 597–1056.CrossRefGoogle Scholar
Chantler, CT, Olsen, K, Dragoset, RA, Kishore, AR, Kotochigova, SA & Zucker, DS (2005). X-Ray Form Factor, Attenuation and Scattering Tables (version 2.1). Gaithersburg, MD: National Institute of Standards and Technology. Available at http://physics.nist.gov/ffast (March 16, 2005).Google Scholar
Cox, M, Love, G & Scott, V (1979). A characteristic fluorescence correction for electron-probe microanalysis of thin coatings. J Phys D Appl Phys 12(9), 1441.CrossRefGoogle Scholar
Czyżewski, Z, MacCallum, DON, Romig, A & Joy, DC (1990). Calculations of Mott scattering cross section. J Appl Phys 68(7), 3066–3072.CrossRefGoogle Scholar
Escuder, J, Salvat, F, Llovet, X & Donovan, J (2010). Numerical correction for secondary fluorescence across phase boundaries in EPMA. In IOP Conference Series: Materials Science and Engineering, Vol. 7, p. 012008. Bristol: IOP Publishing.Google Scholar
Gauvin, R, Lifshin, E, Demers, H, Horny, P & Campbell, H (2006). Win X-ray: A new Monte Carlo program that computes X-ray spectra obtained with a scanning electron microscope. Microsc Microanal 12(1), 49–64.CrossRefGoogle ScholarPubMed
Gauvin, R & Michaud, P (2009). MC X-Ray, a new Monte Carlo program for quantitative X-ray microanalysis of real materials. Microsc Microanal 15(S2), 488–489.CrossRefGoogle Scholar
Goldstein, JI, Newbury, DE, Echlin, P, Joy, DC, Romig, AD Jr., Lyman, CE, Fiori, C & Lifshin, E (1992). Scanning Electron Microscopy and X-Ray Microanalysis: A Text for Biologists, Materials Scientists, and Geologists. New York: Plenum Press.CrossRefGoogle Scholar
Goldstein, JI, Newbury, DE, Michael, JR, Ritchie, NW, Scott, JHJ & Joy, DC (2017). Scanning Electron Microscopy and X-ray Microanalysis. New York: Springer.Google Scholar
Henoc, M, Maurice, MF & Zemskoff, MA (1969). Phenomenes de fluorescence aux limites de phases. Vth International Congress on X-Ray Optics and Microanalysis/V, pp. 187–192. Internationaler Kongreß für Röntgenoptik und Mikroanalyse/Ve Congrès International sur l'Optique des Rayons X et la Microanalyse. New York: Springer.Google Scholar
Hovington, P, Drouin, D & Gauvin, R (1997). CASINO: A new Monte Carlo code in C language for electron beam interaction—Part I: Description of the program. Scanning 19(1), 1–14.CrossRefGoogle Scholar
Kirkpatrick, P & Wiedmann, L (1945). Theoretical continuous X-ray energy and polarization. Phys Rev 67(11–12), 321.CrossRefGoogle Scholar
Llovet, X & Galan, G (2003). Correction of secondary X-ray fluorescence near grain boundaries in electron microprobe analysis: Application to thermobarometry of spinel lherzolites. Am Mineral 88(1), 121–130.CrossRefGoogle Scholar
Llovet, X, Pinard, P, Donovan, J & Salvat, F (2012). Secondary fluorescence in electron probe microanalysis of material couples. J Phys D Appl Phys 45(22), 225301.CrossRefGoogle Scholar
Llovet, X & Salvat, F (2017). PENEPMA: A Monte Carlo program for the simulation of X-ray emission in electron probe microanalysis. Microsc Microanal 23(3), 634–646.CrossRefGoogle ScholarPubMed
Llovet, X, Valovirta, E & Heikinheimo, E (2000). Monte Carlo simulation of secondary fluorescence in small particles and at phase boundaries. Microchim Acta 132(2), 205–212.CrossRefGoogle Scholar
Myklebust, RL & Newbury, DE (1995). Monte Carlo modeling of secondary x-ray fluorescence across phase boundaries in electron probe microanalysis. Scanning 17(4), 235–242.CrossRefGoogle Scholar
Pfeiffer, A, Schiebl, C & Wernisch, J (1996). Continuous fluorescence correction in electron probe microanalysis applying an electron scattering model. X-Ray Spectrom 25(3), 131–137.3.0.CO;2-0>CrossRefGoogle Scholar
Powell, CJ, Jablonski, A, Salvat, F & Lee, AY (2016). NIST electron elastic-scattering cross-section database. Version 4, 0. (No. Natl Std. Ref. Data Series (NIST NSRDS)-64).Google Scholar
Ritchie, NW (2009). Spectrum simulation in DTSA-II. Microsc Microanal 15(5), 454–468.CrossRefGoogle ScholarPubMed
Ritchie, NW (2017). Efficient simulation of secondary fluorescence via NIST DTSA-II Monte Carlo. Microsc Microanal 23(3), 618–633.CrossRefGoogle ScholarPubMed
Salvat, F, Jablonski, A & Powell, CJ (2005). ELSEPA—Dirac partial-wave calculation of elastic scattering of electrons and positrons by atoms, positive ions and molecules. Comput Phys Commun 165(2), 157–190.CrossRefGoogle Scholar
Schreiber, T & Wims, A (1982). Relative intensity factors for K. L and M shell x-ray lines. X-Ray Spectrom 11(2), 42–45.CrossRefGoogle Scholar
Seltzer, SM & Berger, MJ (1986). Bremsstrahlung energy spectra from electrons with kinetic energy 1 keV–10 GeV incident on screened nuclei and orbital electrons of neutral atoms with Z = 1–100. At Data Nucl Data Tables 35(3), 345–418.CrossRefGoogle Scholar
Valovirta, E, Erlach, S, Llovet, X & Heikinheimo, E (2001). EPMA of metal-metal diffusion couples at high temperature. In EMAS 2001 – 7th European Workshop on Modern Developments and Applications in Microbeam Analysis. European Microbeam Analysis Society.Google Scholar
Waldo, R (1991). A characteristic x-ray fluorescence correction for thin-film analysis by electron microprobe. Microbeam Anal 45, 45–53.Google Scholar
Youhua, H, Yuencai, H & Jiaguang, C (1988). The calculation equations of characteristic fluorescence for multi-layer films. J Phys D Appl Phys 21(7), 1221.CrossRefGoogle Scholar
Yuan, Y, Demers, H, Brodusch, N & Gauvin, R (2016). X-ray emission from thin films on a substrate – Experiments and simulations. Microsc Microanal 22(S3), 400–401.CrossRefGoogle Scholar
Yuan, Y, Demers, H, Rudinsky, S & Gauvin, R (2019). Secondary fluorescence correction for characteristic and bremsstrahlung X-rays using Monte Carlo X-ray depth distributions applied to bulk and multilayer materials. Microsc Microanal 25(1), 92–104.CrossRefGoogle ScholarPubMed