Application of the Least-Squares Method to the Analysis of XRF Spectral Intensities from Atmospheric Particulates Collected on Filters

Abstract

The least-squares method with complete component library spectra is applied to the quantitative analysis of X-ray fluorescence spectral intensities. An approach is outlined for application to the general case of thick homogeneous samples at high counting rates, A simplified approach can be taken with the more specific case represented, by atmospheric particulates collected on filters. The details and sample results of this approach for this specific case are given for an energy dispersive X-ray fluorescence analyzer. The results indicate that the least-squares method as developed and applied here is valid and should prove generally useful to X-ray analysts.

Monte Carlo modelling of gamma-ray stopping efficiencies of Geiger–Müller counters

“…al. [5] in which the feasibility of utilizing a PGNAA analyzer for determining the amounts of individual components of a multiphase flow was demonstrated, the so-called Monte Carlo library least-squares (MCLLS) approach [25][26][27] was used for the subsequent inverse quantitative analyses. Briefly, it can be mentioned that the MCLLS approach is used in order to take advantage of the information contained within the entire prompt gamma-ray spectrum of the sample by assuming that the total count rate in the total prompt gamma-ray spectrum of any sample can be given as the sum of the products of the amounts and the library spectrum of each constituent of the sample.…”

The complete spectral response for EDXRF systems—calculation by Monte Carlo and analysis applications. 1—homogeneous samples

“…Rayleigh or coherent scattering is characterized by changes in direction with virtually no energy loss. The differential scattering cross section for this interaction is (1) where (rO2/2)(1+cos2 8) is the cross section for Thompson scattering from a free electron, and F(q, z ) is the atomic form factor which represents the probability that the recoil momentum q is tranferred to the z orbital electrons with no energy absorption. F(q, z ) is available as a tabulated function of the incident photon energy Eo and scattering angle f3.…”