Abstract
A mathematical model based on a combination of the total addition method (TAM) and limit dilution method (LDM) is proposed. The model shows the hyperbolic behaviour of the experimental data when the X-ray fluorescence intensities are represented versus the addition-dilution factor [ (1 − ƒ n) ƒ n ]. The equation obtained for the chemical system can be split into two terms, which relate directly to the processes of addition of the standard and dilution of the unknown. This equation fits mathematically to a hyperbolic function from which physical parameters and data of analytical interest are obtained for the samples studied. In the proposed model, some parameters are defined which are equivalent to the fluorescence intensity of the analyte in the normalised sample ( I i s), in the standard ( I i p) and the corrected intensity ( I i sc) respectively. These parameters allow determination of the analyte concentration in an unknown and a suitable algorithm is proposed for their calculation. The proposed model is applied to the determination of Zn, Ti and Zr in a synthetic sample, prepared by homogenising the respective metal oxides. The results are in complete agreement with the contents which suggests a good correction of the strong interelement effects typical at these levels of concentration as is demonstrated by a low error in an interval of 0.7–1.2%.
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