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A new formalism is proposed to correct with accuracy the matrix effects in x‐ray fluorescence (XRF) analysis. It has been deduced from Sherman's equations and includes a new algorithm between concentration and intensity, theoretically exact, and explicit expressions permitting the calculation of αij and ρij coefficients that correct for absorption and enhancement effects, respectively. In other words, the concept of correction coefficients is established on a solid theoretical basis. In the second part, it will be shown how to adapt this new formalism to practical situations. From an estimate of composition calculated by the Claisse–Quintin algorithm and an appropriate calibration, the new algorithm is used to refine the estimated composition for greater accuracy. This last approach is equivalent to the ‘fundamental parameters’ method but is presented in a simpler version adaptable to any mini‐computer.

In Part 1, a new formalism was proposed to correct with accuracy the matrix effects in XRF analysis. In this paper it is shown how to adapt this new formalism to practical situations. From an estimate of composition calculated by the Claisse–Quintin algorithm and an appropriate calibration, the new algorithm is used to refine the estimated composition for greater accuracy. This last approach is equivalent to the ‘fundamental parameters’ method but is presented in a simpler version adaptable to any mini‐computer.

Different calibration procedures for the determination of major and trace elements by XRF analysis are presented and discussed. Empirical calibration curves comparing intensities with concentrations can be used for the analysis of samples with limited variations of the matrix composition. However, a general‐purpose calibration procedure that is applicable to a larger variety of matrix types and covering wider ranges of the analyte concentration is usually more desirable. This paper presents practical and simple calibration procedures for the determination of major and trace elements that will allow one to adapt any mathematical model to any set of experimental data while producing the maximum of accuracy in the final results. It is also shown how to calculate from multi‐element standards a practical intensity of the pure analyte, thus eliminating the requirement for a pure analyte specimen.