[B._Beckhoff,_et_al.]_Handbook_of_Practical_X-Ray_(b-ok.org).pdf

The concept of influence coefficients is used to

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The concept of influence coefficients is used to describe the relationship between count rates and concentrations in a way that directly reveals the effect of the matrix on the count rates from the analyte element (Sect. 5.3). The general principle is that the “ideal” calibration curve is assumed to be in principle linear, however affected by matrix effects and thereby distorted (i.e., made nonlinear). By applying corresponding counteracting “corrections,” the experimental curve is again linearized. The coefficients, which account for the extent of these (mathematical) corrections for each matrix element, are called empirical or theoretical influence coefficients , respectively, depending on the method of their determination. The accuracy of empirical methods (where the influence coefficients are determined by measuring standards) can be very high and is only limited by experimental issues (mainly the repeatability and reproducibility of the measurements and the specimen preparation procedure) and the quality of standards (reliability of the provided data and a close similarity of their com- position and preparatory method to that of the unknown material). In prac- tice, it is often difficult (and expensive) to maintain the required quality and sometimes impossible to obtain or manufacture the standard specimens. Theoretical influence coefficient methods are based on the classical set of FPs and their accuracy is comparable to that of any other FP method. Since the main time-consuming step is the computation of the influence coefficients, routine analysis with precomputed sets of coefficients is very fast. Compared to the empirical parameter method, the accuracy can be similar if the same set of standards is used. The high long-term stability of modern instruments allows precalibration for all elements in the factory with simple drift corrections on site. Analysis can thereby be carried out without actual standards (Sect. 5.7). Monte Carlo methods are sometimes employed for analyses of inhomoge- neous materials and for studying complex indirect excitation effects, such as
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5 Quantitative Analysis 311 the excitation of light elements by photo-electrons and Auger-electrons. They are by their nature an FP method, but based on a statistical description of interactions rather than on a deterministic equation system. A brief introduc- tion to the principles of the method is given in Sect. 5.8. An important aspect of any analytical task is to estimate the resulting error in view of the chosen methodology (achievable trueness and precision) and the probable statistical error made in an individual measurement (Sect. 5.9). Following the demands of modern industrial networks for precise crite- ria, rules, guidelines, and definitions, internationally accepted standards have been set up not only for materials and manufacturing processes but also for analytical procedures. An introduction to standardized methods in XRF, as they are used for example in the petrochemical industry and in the cement industries, is given in Sect. 5.10.
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