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.

The 50th anniversary of the application of electron probe microanalysis (EPMA) to the Earth Sciences provides an opportunity for an assessment of the state-of-the-art of the technique. Stemming from the introduction of the first automated instruments, the latest developments of EPMA and some typical applications are reviewed with an eye to the future. The most noticeable recent technical achievements such as the field-emission electron gun, the latest generation of energy and wavelength dispersive spectrometers, and the development of analytical methods based on new sets of first principle data obtained by the use of sophisticated computer codes, allow for the extension of the method to the analysis of trace elements, ultra-light elements (down to Li), small particles, and thin films, with a high degree of accuracy and precision and within a considerably reduced volume of interaction. A number of working examples and a thorough list of references provide the reader with a working knowledge of the capabilities and limitations of EPMA today.

An algorithm for the simulation of bremsstrahlung emission by fast electrons using numerical cross sections is described. It is based on natural factorization of the double-differential cross section and on the fact that the intrinsic angular distribution of photons with a given energy can be very closely approximated by a Lorentz-boosted dipole distribution. The parameters of this angular distribution vary smoothly with the atomic number of the target atom and with the energies of the projectile’s electron and the photon emitted. Results from simulations of thick-target bremsstrahlung are compared with experimental data.

A correction procedure is proposed to account for the effect of secondary X-ray fluorescence near grain boundaries in electron microprobe analysis. The procedure is based on the Monte Carlo simulation method, which is used to calculate the X-ray spectrum emitted by the mineral couple (i.e., the mineral of interest with the neighboring mineral). The contribution of secondary fluorescence from the neighboring mineral, which appears in the simulated spectrum in a natural way, is then subtracted from the measured k-ratio and thereafter conventional matrix corrections are applied. The Monte Carlo simulation algorithm used is largely based on the general-purpose simulation package PENELOPE. In order to assess the reliability of this code, simulated “apparent” element profiles are compared with electron microprobe measurements found in the literature, in which the effect of secondary fluorescence was characterized and the reliability of the different assumptions underlying the proposed procedure is discussed. Finally, the procedure is used to assess data from the olivine-clinopyroxene thermobarometer in a spinel lherzolite xenolith. The application of the secondary fluorescence correction leads to: (1) higher systematic pressure estimations than those obtained from uncorrected data, with lower uncertainties; and (2) a better agreement between the olivine-clinopyroxene temperature estimations and those estimated using the two-pyroxene thermometer. Estimated P-T conditions indicate a decompressional path with a slight decrease in temperature from core to crystal rim. However, if the effect of secondary fluorescence is not taken into account, an apparent heating event is observed.

We describe a semi-analytical method for the fast calculation of secondary fluorescence in electron probe microanalysis of material couples. The calculation includes contributions from primary K-, L- and M-shell characteristic x-rays and bremsstrahlung photons. The required physical interaction parameters (subshell partial cross sections, attenuation coefficients, etc) are extracted from the database of the Monte Carlo simulation code system PENELOPE. The calculation makes use of the intensities of primary photons released in interactions of beam electrons and secondary electrons. Since these intensities are not readily available and do not allow analytical calculation, they are generated from short Monte Carlo simulation runs. The reliability of the proposed calculation method has been assessed by comparing calculated, distance-dependent k-ratios with experimental data available in the literature and with results from simulations with PENELOPE. Numerical results are found to be in close agreement with both simulated and experimental data.