Abstract
Within the last decades significant improvements in the spatial resolution of electron probe microanalysis (EPMA) were obtained by instrumental enhancements. In contrast, the quantification procedures essentially remained unchanged. As the classical procedures assume either homogeneity or a multi-layered structure of the material, they limit the spatial resolution of EPMA. The possibilities of improving the spatial resolution through more sophisticated quantification procedures are therefore almost untouched. We investigate a new analytical model (M1-model) for the quantification procedure based on fast and accurate modelling of electron-X-ray-matter interactions in complex materials using a deterministic approach to solve the electron transport equations. We outline the derivation of the model from the Boltzmann equation for electron transport using the method of moments with a minimum entropy closure and present first numerical results for three different test cases (homogeneous, thin film and interface). Taking Monte Carlo as a reference, the results for the three test cases show that the M1-model is able to reproduce the electron dynamics in EPMA applications very well. Compared to classical analytical models like XPP and PAP, the M1-model is more accurate and far more flexible, which indicates the potential of deterministic models of electron transport to further increase the spatial resolution of EPMA.
Highlights
Electron probe microanalysis (EPMA) provides a popular method to obtain quantitative information about the chemical composition of heterogeneous materials, fine structures and grains in metals and alloys
Taking Monte Carlo as a reference, the results for the three test cases show that the M1-model is able to reproduce the electron dynamics in electron probe microanalysis (EPMA) applications very well
We take results obtained from Monte Carlo (MC) simulations as reference solutions since this method can model the electron transport most accurately
Summary
Electron probe microanalysis (EPMA) provides a popular method to obtain quantitative information about the chemical composition of heterogeneous materials, fine structures and grains in metals and alloys. It poses an inverse problem, as the chemical concentrations are not measured directly, but have to be reconstructed from intensity measurements of X-rays. The experimental intensities are normalised to so-called k-ratios kExp and the simulation of a forward model provides computed k-ratios kM(c) that depend on one or more assumed elemental concentration fields c(x) inside the probe. The inverse problem [1,2] consists of finding the concentration c∗ that minimises the error between the experimental and simulated k-ratios kM.
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