Abstract
The idea of φ(ρz) equations and the depth distribution of x-ray intensities as a basis for the quantitative correction of measured x-ray intensities goes back to the origins of electron probe microanalysis. φ(ρz) is the characteristic x-ray intensity generated in a thin layer dρz at depth ρz in the specimen relative to intensity generated in an identical layer dρz, isolated in space. Castaing [1] first suggested that you could write the measured k-ratio in terms of φ(ρz) equations as:
where subscripts s and A refer to specimen and pure element A, respectively, μ is the mass absorption coefficient, with subscript referring to characteristic line and superscript the absorber. ρz represents the mass depth in the specimen. Ψ is the x-ray take-off angle. Castaing (with Descamps) [2] also demonstrated that is was possible to measure φ(ρz) curves using a sandwich sample technique (fig. 1). The advantage of the φ(ρz) equation is its relative simplicity in concept and the fact that the major corrections of absorption, atomic number and characteristic fluorescence can be explicitly written. The equation for the fraction of x rays which escape from the specimen, f(χ), the absorption correction is
where μ sA is the mass absorption coefficient for the characteristic x rays of element A in the specimen. The combined factor μ cscΨ is the so-called absorption parameter χ. The numerator is simply the number of x rays which escape from the specimen while the denominator represents the total number of x rays generated in the specimen.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Castaing, R. (1960), Advances in Electronics and Electron Physics, Vol. XIII, Marton, L., ed., Academic Press, New York, 317.
Castaing, R. and Descamps, J. (1955), J. Phys. et Radium 16, 304.
Brown, J. D., Ph.D. (1966), Thesis, University of Maryland, College Park, MD, 167.
Castaing, R. and Henoc J. (1966), X-Ray Optics and Microanalysis, Castaing, R., Descamps, P. and Philibert, J., eds., Hermann, Paris, 120.
Brown, J. D. and Parobek, L. (1972), Proc. 6th Int. Conf. X-Ray Optics and Microanalysis, Shinoda, G., Kohra, K., and Ichinokawa, T., eds., U. of Tokyo Press, Tokyo, 163.
Buchner, A. R. and Pitsch, W. (1971), Z. Metallkunde 62, 393.
Buchner, A. R. and Pitsch, W. (1972), Z. Metallkunde 63, 398.
Rehbach, W. and Karduck, P. (1987), Proc. 11th Int. Conf. X-Ray Optics and Microanalysis, Brown, J. D. and Packwood, R. H., eds., UWO Graphics Serv., London, Ontario, Canada, 244.
Criss, J. W. (1968), NBS Spec. Publ. 298, 53.
Wittry, D. B., (1957), Ph.D. Thesis, California Institute of Technology.
Kyser, D. F. (1972), Proc. 6th Int. Conf. X-Ray Optics and Microanalysis, Shinoda, G., Kohra, K., and Ichinokawa, T., eds., 147.
Parobek, L. and Brown, J. D. (1978), X-Ray Spectr. 7, 26.
Brown, J. D. and Robinson, W. H. (1979), Microbeam Analysis, 238.
Packwood, R. H. and Brown, J. D. (1981), X-Ray Spectr. 10, 138.
Brown, J. D. and Packwood, R. H. (1982), X-Ray Spectr. 11, 187.
Packwood, R. H. and Brown, J. D. (1980), Microbeam Analysis, 45.
Bastin, G. F. and Heijligers, H. J. M. (1984 and 1985 ), Internal Reports, Univ. of Technology, Eindhoven, ISBN, 90–6819–002–4 and 90–6819–006–7.
Bastin, G. F., Heijligers, H. J. M., and van Loo, F. J. J. (1984), Scanning 6, 58.
Bastin, G. F., Heijligers, H. J. M. (1986), X-Ray Spectr. 15, 143.
Tirira Saa, J. H., Del Giorgio, M. A., and Riveros, J. A. (1987), X-Ray Spectr. 16, 255.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media New York
About this chapter
Cite this chapter
Brown, J.D. (1991). φ(ρz) Equations for Quantitative Analysis. In: Heinrich, K.F.J., Newbury, D.E. (eds) Electron Probe Quantitation. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2617-3_5
Download citation
DOI: https://doi.org/10.1007/978-1-4899-2617-3_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-2619-7
Online ISBN: 978-1-4899-2617-3
eBook Packages: Springer Book Archive