Simulation of an X-RAY Fluorescence Experiment for Gold Assaying With Photon Interaction Probability and Moments Model

An interaction probability model is used to model the Energy Dispersive X-Ray Fluorescent (EDXRF) response from a given gold sample to determine the purity (or karatage) of gold. The application of this model is considered for estimating experimental results using a spectrometer with a X-Ray source of 18.6 keV which counts L-shell fluorescence in gold. In the elementary model, Compton scattering is largely ignored as it forms an insignificant contribution compared with photoelectric absorption in the energies of interest. The model is used to infer the “average depth” to which this analysis can be expected to provide reliable results, since ‘depth profiling’ is a major limitation of XRF. This model is further strengthened by carrying out a ‘deep-penetration’ analysis for the energy-dependent photon transport equation with the moments method. The first four moments are computed and used to obtain the spatial profile for the energy-dependent photon flux in the vicinity of L-shell phenomena. This analysis is useful to understand the contribution from interaction phenomena deeper within the material. For validation of depth profile, 2 gold-coated discs of thickness 10 microns and 40 microns were analyzed on the same XRF spectrometer. Transport theory depth-profiling results were validated from detection of the nickel-silver substrate of the discs.