Monte Carlo Simulation of Characteristic Secondary Fluorescence in Electron Probe Microanalysis of Homogeneous Samples Using the Splitting Technique

Abstract

Electron probe microanalysis (EPMA) is based on the comparison of characteristic intensities induced by monoenergetic electrons. When the electron beam ionizes inner atomic shells and these ionizations cause the emission of characteristic X-rays, secondary fluorescence can occur, originating from ionizations induced by X-ray photons produced by the primary electron interactions. As detectors are unable to distinguish the origin of these characteristic X-rays, Monte Carlo simulation of radiation transport becomes a determinant tool in the study of this fluorescence enhancement. In this work, characteristic secondary fluorescence enhancement in EPMA has been studied by using the splitting routines offered by PENELOPE 2008 as a variance reduction alternative. This approach is controlled by a single parameter NSPLIT, which represents the desired number of X-ray photon replicas. The dependence of the uncertainties associated with secondary intensities on NSPLIT was studied as a function of the accelerating voltage and the sample composition in a simple binary alloy in which this effect becomes relevant. The achieved efficiencies for the simulated secondary intensities bear a remarkable improvement when increasing the NSPLIT parameter; although in most cases an NSPLIT value of 100 is sufficient, some less likely enhancements may require stronger splitting in order to increase the efficiency associated with the simulation of secondary intensities.

Bremsstrahlung enhancement in electron probe microanalysis for homogeneous samples using Monte Carlo simulation

“…The variance reduction technique of interaction forcing offered by the penelope package was chosen. The obtained results for primary and secondary intensities follow the same trend that those previously obtained by using the splitting technique (Petaccia et al ., ); however, the assessed bremsstrahlung correction factors F bear quite smaller errors.…”

“…These distributions are equivalent to those obtained using another variance reduction technique, i.e. splitting (Kahn & Harris, ), which have proved to provide adequate values for the characteristic fluorescence correction factors (Petaccia et al ., ). It can be seen that the uncertainties are slightly lower in the case of interaction forcing.…”

“…It can be seen that the uncertainties are slightly lower in the case of interaction forcing. However, it is worth emphasizing that interaction forcing allows to simultaneously obtain primary intensities with small errors, whereas with splitting two separate simulations are needed to achieve reasonable uncertainties, since primary photons must be simulated with no splitting (Petaccia et al ., ). Nevertheless, primary intensities obtained following the strategy suggested in this previous work bear uncertainties much larger than those achieved with interaction forcing, as displayed in Figure , despite the rather longer CPU time devoted (96 h against 24 h).…”

“…The program penslab from 2003 penelope distribution was modified to classify all kinds of enhancement (Petaccia et al ., ); this new code was updated to fulfil the penelope 2008 requirements, and take advantage of the variance reduction techniques offered by this distribution. For this study, the possibility of using interaction forcing was included in order to take into account secondary fluorescence by bremsstrahlung photons.…”

PENEPMA: a Monte Carlo programme for the simulation of X-ray emission in EPMA

“…Examples of recent applications of PENEPMA or PENELOPE in EPMA include the study of secondary fluorescence effects in bulk samples and near phase boundaries [31,32], the analysis of inclusions in steel [33], the simulation of energy-dispersive spectra for automated materials identification [34,35], the determination of the detector efficiency for standard-less analysis [36] or the examination of carbon contamination effects in high-resolution EPMA [37].…”