Use of differential operators in the Monte Carlo-library least-squares method for X-ray fluorescence applications

For the simulation of Energy Dispersive X-Ray Fluorescence (EDXRF) analyzers, a Monte Carlo X-ray transport code CEARXRF has been developed. CEARXRF can simulate various complicated analyzer geometries by the use of HERMETOR, a general geometry package, and all three major X-ray interactions with atoms. Incoherent scattering, coherent scattering, photoelectric absorption, and all the possible emission lines of K and L X-rays following photoelectric absorption are modeled in the code.;The incoherently scattered photon energy model has been improved to reflect Doppler broadening effects due to bound electron momentum through the use of Compton profile data as suggested by Namito. The improved incoherent scattering model showed very good agreement with measurements.;Differential operators have been implemented into CEARXRF to provide differential responses (up to second order with cross terms and third order without cross terms) to elements in a reference sample. With a Taylor series expansion of the reference response and its derivatives, responses for any sample whose composition is near the reference sample can be calculated.;As an improvement to the original Monte Carlo - Library Least-Squares method (MCLLS) which is based on linear combinations of elemental libraries, a new MCLLS approach with differential spectra and Taylor expansion up to second order has been suggested. The new second order Taylor series expansion MCLLS is applied to simulated spectra and generally gives better results than the original linear MCLLS approach. However, when the initial guess deviates from the actual composition greatly, the second order Taylor expansion generally gives a worse result than the original linear MCLLS.;Independent of the CEARXRF code and the new MCLLS approach, a Monte Carlo pulse pile-up simulation code CEARPPU has been developed. The simulated pulse piled-up spectra match measurements well. Pulse pile-up distortion of measured spectra is unavoidable in real applications due to high radiation counting rates. For these cases, CEARPPU can provide simulated results for real observed measurement counting rates. The simulated results can be directly compared with measurement to give analytical information of the sample of interest.