High Speed Matrix Corrections for Quantitative X-ray Microanalysis Based on Monte Carlo Simulated K-Ratio Intensities

Abstract Due to recent advances in modeling the production of characteristic X-rays, Monte Carlo simulation of electron–solid interactions can provide improved quantitative estimates of X-ray intensities for both homogeneous and heterogeneous interaction volumes. In the case of homogeneous materials, these modeled X-ray intensities can predict with excellent accuracy, matrix corrections for arbitrary compositions, arbitrary emission lines, and electron energies. By pre-calculating these Monte Carlo X-ray intensities for pure element standards and a range of compositions of binary systems, we can derive matrix corrections for complex compositions in real-time by parameterizing these k-ratios as the so-called alpha factors. This method allows one to perform Monte Carlo-based bulk matrix corrections in seconds for arbitrary and complex compositions (with two or more elements), by combining these binary alpha factors using the so-called beta expression. We are systematically calculating X-ray intensities for 11 compositions from 1 to 99 wt% for binary pairs of all emitters and absorbers in the periodic table, for the main emission lines (Kα, Kβ, Lα, Lβ, Mα, and Mβ) at beam energies from 5 to 50 keV, using Monte Carlo calculations based on a modified PENELOPE electron-photon transport code, although any other Monte Carlo software could also be utilized. Comparison of k-ratios calculated with the proposed method and experimental k-ratios from the Pouchou and Pichoir database suggest improvements over typical φ(ρz) methods. Additional comparisons with k-ratio measurements from more complex compositions would be ideal, but our testing of the additivity of the beta equation suggests that arbitrary compositions can be handled as well, except in cases of extreme fluorescence or absorption.