Approximate model for calculation of x-ray fluorescence intensity and its use in XRF spectrometry

Abstract

Sherman's fundamental equations were used in deriving an approximate expression for calculating the X-ray fluorescence intensity of elements. The error of approximate calculations relative to the fundamental equations is a few hundredths of 1% if the fluorescent material does not contain elements whose absorption edges are shorter than the wavelength of the analytical line of the measured element. For the three-component Cr-Fe-Ni and Cr-Mn-Fe compositions, the error of calculation is a few tenths of 1% if allowance is made for the dependence of corrections for the presence of the above-mentioned elements on the composition of the material being analyzed. For calculating the x-ray fluorescence intensity of the main elements in iron-nickel and high-temperature alloys, with the dependence of corrections on sample composition taken into account, in rare instances it exceeds 1% relative. Such a low error and the simplicity of the proposed model provided reason enough to employ it in x-ray fluorescence analysis. An algorithm is suggested for deriving element contents, which implies a regression reconciliation of calculated and measured intensities. Such a reconciliation make it possible to take into account the model errors and use in the analysis the analytical line intensities which have been measured but not corrected for the background. The algorithm was checked for validity by comparing results derived from determining the composition with reliable data for the chemical analysis of three-component compositions reported by Rasberry and Heinrich and with certified element contents in five-component alloys reported by Broll. A calculation of the element contents was based on experimental intensities of analytical lines from the cited references. The error of calculation of the element contents by the proposed algorithm was found to be significantly lower than those obtained by the cited authors. The intensities that were not corrected for the background component were used to determine element contents in 50 standard samples of high-alloy steels. Results of analysis are characterized by an acceptable accuracy of determinations.