Constraints, iteration schemes and convergence criteria for concentration calculations in X-ray fluorescence spectrometry with the use of fundamental parameter methods

A set of computer programs for X-ray fluorescence calculations, based on fundamental parameter methods, was developed in which some new combinations of mathematical refinement procedures were tested together with new target functions and iteration stop criteria. The results show that practical needs cannot be fulfilled with a single-universal method and a strategy is given to deal with the following situations: (1) not all elements present in the sample have been measured; (2) the mass thickness of the sample is not known and/or has to be determined together with the composition of the sample; and (3) the only unmeasured element is oxygen. If the optimal method is chosen, the results for the major constituents are accurate to better than 1%. For minor constituents, the accuracy is generally of the order of a few percent.