Mathematical techniques for quantitative elemental analysis by energy dispersive X-ray fluorescence

Recent interest in the use of automated or semi-automated energy dispersive X-ray fluorescence analysis has created the need for improved mathematical techniques and computer software for use with this type of analysis. A review is given on the present state of the development of mathematical techniques necessary for implementing: (1) the least-squares method for the determination of characteristic elemental X-ray intensities and (2) the use of the Monte Carlo method for extending the fundamental parameters approach to radioisotope and X-ray machine exciting sources for the determination of elemental amounts. In (1) after the description of the basic least squares method its application to X-ray spectra is discussed, further the minimization of pulse pile-up distortion by mathematical modelling and the modelling of nonlinear component intensities are treated. In the second part the extension of fundamental parameters methods by Monte Carlo simulation and the sample heterogeneity effects are discussed. (T.G.)