An analysis is presented of measured and calculated cross sections for inner-shell ionization by electron impact. We describe the essentials of classical and semiclassical models and of quantum approximations for computing ionization cross sections. The emphasis is on the recent formulation of the distorted-wave Born approximation by Bote and Salvat [Phys. Rev. A 77, 042701 (2008)] that has been used to generate an extensive database of cross sections for the ionization of the K shell and the L and M subshells of all elements from hydrogen to einsteinium (Z = 1 to Z = 99) by electrons and positrons with kinetic energies up to 1 GeV. We describe a systematic method for evaluating cross sections for emission of x rays and Auger electrons based on atomic transition probabilities from the Evaluated Atomic Data Library of Perkins et al. [Lawrence Livermore National Laboratory, UCRL-ID-50400, 1991]. We made an extensive comparison of measured K-shell, L-subshell, and M-subshell ionization cross sections and of Lα x-ray production cross sections with the corresponding calculated cross sections. We identified elements for which there were at least three (for K shells) or two (for L and M subshells) mutually consistent sets of cross-section measurements and for which the cross sections varied with energy as expected by theory. The overall average root-mean-square deviation between the measured and calculated cross sections was 10.9% and the overall average deviation was −2.5%. This degree of agreement between measured and calculated ionization and x-ray production cross sections was considered to be very satisfactory given the difficulties of these measurements.

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Conventional electron-probe microanalysis has an X-ray analytical spatial resolution on the order of 1-4 μm width/depth. Many of the naturally occurring Fe-Si compounds analyzed in this study are smaller than 1 μm in size, requiring the use of lower accelerating potentials and nonstandard X-ray lines for analysis. Problems with the use of low-energy X-ray lines (soft X-rays) of iron for quantitative analyses are discussed and a review is given of the alternative X-ray lines that may be used for iron at or below 5 keV (i.e., accelerating voltage that allows analysis of areas of interest <1 μm). Problems include increased sensitivity to surface effects for soft X-rays, peak shifts (induced by chemical bonding, differential self-absorption, and/or buildup of carbon contamination), uncertainties in the mass attenuation coefficient for X-ray lines near absorption edges, and issues with spectral resolution and count rates from the available Bragg diffractors. In addition to the results from the traditionally used Fe Lα line, alternative approaches, utilizing Fe Lβ, and Fe Ll-η lines, are discussed.

Results from measurements of K-shell ionization cross sections of the elements Cr, Ni and Cu by electron impact with energies in the range 6.5-40 keV are presented. Cross sections were obtained by measuring characteristic x-rays emitted from (1-6 nm thick) films of the studied elements deposited on self-supporting carbon backing films. The procedure yields relative cross sections with uncertainties of the order of 2%. Transformation to absolute units increases the uncertainties to about 10%. Our results are compared with those from other groups and with two calculations based on the first Born approximation, which include corrections for exchange, Coulomb and relativistic effects. A simple empirical formula that accurately describes the energy dependence of the measured cross sections is provided.

We present results from measurements of L␣ x-ray production cross sections of the elements W, Pt, and Au by impact of electrons with energies in the range 10-30 keV. The cross sections were obtained by measuring L␣ x-ray intensities emitted from very thin films of the studied elements deposited on thick carbon substrates. The directional and energy spreading of the electron beam within the active film and the x-ray enhancement due to electron backscattering from the substrate were accounted for by means of Monte Carlo simulation. Recorded x-ray intensities were converted to absolute x-ray production cross sections by using two different methods; the first employs measured values of the sample thickness and the number of incident electrons and estimated detector efficiencies; the second is based on a comparison between measured and calculated bremsstrahlung intensities. Experimental data are compared with the results of simple analytical formulas of common use in practical electron probe microanalysis, with calculated cross sections obtained from the distorted-wave Born approximation and with other experimental data available in the literature.