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Secondary fluorescence is an inevitable effect that has to be taken into account in any algorithm for quantitative electron probe microanalysis (EPMA) as an additional correction. Moreover, secondary fluorescence worsens spatial resolution of EPMA. Secondary fluorescence is excited both by characteristic radiation and by the X-ray continuum. In most cases the correction is small. There are, however, cases, e.g. the determination of low heavy metal concentration in a light matrix, where the contribution of secondary fluorescence exceeds 10% of the measured X-ray line intensity.
For secondary fluorescence correction the measured X-ray line intensity has to be divided by the correction factor (1+I_flchar/I_p +I_flcont/I_p )≈(1+I_flchar/I_p )(1+I_flcont/I_p ) in order to get those intensity I_p, which is excited only by the primary electrons. I_flchar and I_flcont mean the calculated characteristic and continuums fluorescence intensities. In order to get the intensity of fluorescence radiation, the absorption of the exciting radiation in the specimen, the photoionization probability and the self-absorption of the emitted line must be calculated. The critical quantity is the X-ray yield of the exciting atoms in case of fluorescence by characteristic radiation and the bremsstrahlung yield of the specimen in case of continuum fluorescence. In the former case it is reasonable to apply the same physical model to calculate I_flchar and I_p.
The X-ray intensities of the K-, L- and M-lines of copper, zirconium and tungsten have been measured with an energy-dispersive X-ray spectrometer of known efficiency as function of photon energy. X-ray production efficiencies were determined from the measured intensities for Kα- and L-series of Cu and Zr and for the L- and M-series of W. These data were compared to calculated X-ray production efficiencies based on the widely used matrix correction models of Pouchou and Pichoir (XPP) and Bastin (PROZA96).
Our results indicate that a replacement of the stopping power in the PROZA96 algorithm by expressions of Joy and Jablonski has only a minor influence on the calculated X-ray production efficiencies. In contrast, the modifications of the ionization cross-section show a stronger effect. We replaced the ionization cross-sections for K lines of the PROZA96 algorithm with different models.
The results for L- and M-Lines are different. For the L-lines of Cu the original XPP and PROZA96 models show the best agreement while using the Bote cross-sections result in an overestimation. For the Zr-L and W-L1, -L2, -L3 X-ray production efficiencies, the Bote cross-sections lead to a significant improvement compared to all other models. The original XPP model represents the best agreement for the M5 efficiencies but underestimates the M4 efficiencies.
There is no superior model or modification because the parameter sets in the models need to be aligned to each other. However, using the ionization cross-sections of Bote, which are based on quantum mechanical calculations, show promising results in many cases.