MONTE CARLO SIMULATION OF THE X-RAY FLUORESCENCE SPECTRA FROM MULTIELEMENT HOMOGENEOUS AND HETEROGENEOUS SAMPLES (CUBIC SPLINES)

A Monte Carlo model that predicts the entire photon spectrum for energy-dispersive X-ray fluorescence (EDXRF) analyzers excited by radioisotope sources from multielement samples is developed and demonstrated. The components of the photon spectrum resulting from the model are: (1) the characteristic primary, secondary, and tertiary X rays, both K(,(alpha)) and K(,(beta)) from the unscattered source photons; (2) the characteristic X rays as specified in (1) from the scattered source photons; (3) the characteristic X rays excited by characteristic X rays scattered in the sample; and (4) the back-scattered source photons from single, double, and multiple scatters in the sample.;Benchmark results were obtained by applying the detector response function for the Si(Li) detector to the photon spectra obtained from the code to generate the entire pulse-height spectra for standard samples of known compositions. Experimental pulse-height spectra obtained for the standard samples were in excellent agreement with the calculated benchmark values.;A previous Monte Carlo model that uses the simple assumption of spherical homogeneous particles to approximate sample heterogeneities has been modified to improve the execution time requirements for the heterogeneous sample case. A new technique for photon tracking is used and has been shown to dramatically reduce the computational time requirements (by over 60%).;A computer code, called NCSMCXF, based on this model has been developed. The code is capable of handling up to 20 elements per sample and provides a detailed account of the intensities of the different X rays and the backscattered source photons per unit source photon as well as a summary of the relative intensities from all the elements present in the sample. It also provides the photon pulse-height spectrum in up to 2048 energy channels. The code is made efficient in computation requirements, both time and storage, by using cubic spline representations for the cross sections, coherent and incoherent scattering cumulative distribution functions, and Compton profiles for the incoherent scattering. The code has built-in criteria that eliminate the unnecessary computations of negligible secondary, and tertiary X rays.