Electron microscopy
Partial, Integral and Total Cross-Sections
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Table 955. Partial, integral and total cross-sections for inner-shell ionization.

  Partial cross-section Integral cross-section Total cross-section [2-9]

A partial cross-section specifies the probability of a specific shell scattering through angles up to a specific angle and with energy losses covering an energy range above an ionization energy [1]


Computed using the Born approximation for elements of low atomic number bombarded by electrons of energy >30 keV, based on a hydrogenic model with Zener screening constant. [1]
The model is consistent with Auger, X-ray and energy-loss measurements. [1]

Note that for large collection angles, the partial ionization cross-section, σ(β,Δ), becomes the total ionization cross-section, σ(Δ). The measurement of the total scattering cross section can be done using unfiltered images, i.e. on a microscope not equipped with an energy filter or EELS spectrometer. [10]









[1] R. F. Egerton, K-shell ionization cross-sections for use in microanalysis, 4(2), (1979) 169-179.
[2] E.H.S. Burhop, Proc. Cambr. Phil. Soc. 36 (1940) 43.
[3] A.M. Arthurs and B.L. Moiseiwitsch, Proc. Roy. Soc. A247(1958) 550.
[4] M. Gryzinski, Phys. Rev. A138 (1965) 336.
[5] M.R.H. Rudge and S.B. Schwartz, Proc. Phys. Soc. 88 (1966) 563.
[6] H. Kolbenstvedt, J. Appl. Phys. 38 (1967) 4785.
[7] E.J. McGuire, Phys. Rev. 175 (1968) 20; Plays. Rev. A3 (1971) 267.
[8] S.T. Manson, Phys. Rev. A6 (1972) 1013.
[9] R.D. Leapman, P. Rez and D.F. Mayers, in: Proc. 9th Int. Congr. Electron Microscopy, ed. J.M. Sturgess, (Microscopical Society of Canada, Toronto, 1978) p. 526.
[10] Huai-Ruo Zhang, Ray F. Egertona, Marek Malac, Local thickness measurement through scattering contrast and electron energy-loss spectroscopy, Micron, 43 (2012) 8-15.