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A Universal Equation for the Emission Range of X Rays from Bulk Specimens

Published online by Cambridge University Press:  28 September 2007

Raynald Gauvin
Raynald Gauvin
Affiliation:
Department of Mining, Metals and Materials Engineering, McGill University, Montréal, Québec H3A 2B2, Canada
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Abstract

The derivation of a universal equation to compute the range of emitted X rays is presented for homogeneous bulk materials. This equation is based on two fundamental assumptions: the φ(ρz) curve of X-ray generation is constant and the ratio of the emitted to the generated X-ray range is equal to the ratio of the emitted to the generated X-ray intensity. An excellent agreement is observed with data obtained from Monte Carlo simulations of 200,000 electron trajectories in C, Al, Cu, Ag, Au, and an Fe–B alloy with boron weight fractions equal to 0.01, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 0.99, performed with the electron beam energy varied from 1 to 30 keV in 1-keV steps. When the ratio of the generated X-ray range to the photon mean free path is much smaller than one, the emission X-ray range is equal to the generated X-ray range, but when this ratio is much greater than one, the emission X-ray range is constant and is given by the product of the effective photon mean free path multiplied by the sine of the take-off angle.

Keywords

X-ray microanalysisX-ray rangeMonte Carlomodeling
Type
MATERIALS APPLICATIONS
Information
Microscopy and Microanalysis , Volume 13 , Issue 5 , October 2007 , pp. 354 - 357
Copyright
© 2007 Microscopy Society of America

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References

REFERENCES

Anderson, C.A. & Hasler, M.F. (1966). Extension of electron microprobe techniques to biochemistry by the use of long wavelength X-rays. In Proceedings of the Fourth International Conference on X-ray Optics and Microanalysis, Castaing, R., Deschamps, P. & Philibert, J. (Eds.), pp. 310–327. Paris: Hermann.
Bastin, G.F., Dijkstra, J.M. & Heijligers, H.J.M. (1998). PROZA96: An improved matrix correction program for electron probe microanalysis, based on a double Gaussian φ(ρz) approach. X-Ray Spectrom 27, 3–10.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, 49–64.Google Scholar
Henke, B.L., Gullikwa, E.M. & Davies, J.C. (1993). X-ray interactions: Photoabsorption, scattering, transmission and reflection at E = 50–30000 eV, Z = 1–92. At Data Nucl Tables 54, 181–342.Google Scholar
Hovington, P., Drouin, D. & Gauvin, R. (1997a). CASINO: A new Monte Carlo Code in C language for electron beam interaction, Part I: Description of the program. Scanning 19, 1–14.Google Scholar
Hovington, P., Drouin, D., Gauvin, R. & Joy, D.C. (1997b). Parameterization of the range of electrons at low energy using the CASINO Monte Carlo program. Microsc Microanal 3(suppl. 2), 885–886.Google Scholar
Pouchou, J.L. & Pichoir, F. (1991). Quantitative analysis of homogeneous or stratified microvolumes applying the model PAP. In Electron Probe Quantitation, Workshop at the National Bureau of Standards, Gaithersburg, Maryland, 1988, Heinrich, K.F.J. & Newbury, D.E. (Eds.), pp. 31–75. New York: Plenum Press.