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Application of the Inverse Monte Carlo Method to Energy-Dispersive X-Ray Fluorescence

  • A.M. Yacout (a1) and W.L. Dunn (a1)

Abstract

The feasibility of utilizing the Inverse Monte Carlo (IMC) method to determine elemental amounts in homogeneous samples from energy-dispersive X-ray fluorescence (EDXRF) measurements has been investigated. IMC is a novel application of standard Monte Carlo that, in principle, allows a rather large class of inverse problems to be solved noniteratively, in the sense that the simulation is not repeated. IMC is implemented by hypothesizing values for the unknown parameters, executing a direct Monte Carlo simulation using these values and scoring the results with factors that contain the unknown parameters. By equating the resulting Monte Carlo estimators to the known measured responses, a system of algebraic equations is formed that may be soluble by standard numerical techniques. Advantages of IMC include the facts that it can be applied to complex (e.g., multidimensional) problems and that it is relatively efficient since the simulation is performed only once. In the EDXRF case, simplified assumptions have been used to construct an approximate IMC solution. The model provides a means to determine the elemental amounts in an unknown sample by treating the unknown composition as a perturbation around the composition of a fixed "reference" sample that contains the same elements as the unknown sample. Primary and secondary X-rays are included in the model. The resulting system of algebraic equations is nonlinear and solutions are obtained via an approximation. Since the model is based on correlated sampling techniques, several unknown samples can be modeled simultaneously provided that they contain the same elements and their compositions are sufficiently close to that of the assumed reference sample. Direct Monte Carlo was used to generate the relative intensities for eighteen different samples in a ternary (Ni-Fe-Cr) system; these results were then used in the IMC model to recover the sample weight fractions. Excellent results were obtained, demonstrating the feasibility of the approach.

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References

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Application of the Inverse Monte Carlo Method to Energy-Dispersive X-Ray Fluorescence

  • A.M. Yacout (a1) and W.L. Dunn (a1)

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