A Model for Characteristic X-Ray Emission in Electron Probe Microanalysis Based on the (Filtered) Spherical Harmonic () Method for Electron Transport
| Autor: | Jonas Bünger, Silvia Richter, Manuel Torrilhon |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Microscopy and Microanalysis. 28:454-468 |
| ISSN: | 1435-8115 1431-9276 |
| DOI: | 10.1017/s1431927622000083 |
| Popis: | Classical $k$-ratio models, for example, ZAF and $\phi ( \rho z)$, used in electron probe microanalysis (EPMA) assume a homogeneous or multilayered material structure, which essentially limits the spatial resolution of EPMA to the size of the interaction volume where characteristic X-rays are produced. We present a new model for characteristic X-ray emission that avoids assumptions on the material structure to not restrict the resolution of EPMA a priori. Our model bases on the spherical harmonic ($P_{\rm N}$) approximation of the Boltzmann equation for electron transport in continuous slowing down approximation. $P_{\rm N}$ models have a simple structure, are hierarchical in accuracy and well-suited for efficient adjoint-based gradient computation, which makes our model a promising alternative to classical models in terms of improving the resolution of EPMA in the future. We present results of various test cases including a comparison of the $P_{\rm N}$ model to a minimum entropy moment model as well as Monte-Carlo (MC) trajectory sampling, a comparison of $P_{\rm N}$-based $k$-ratios to $k$-ratios obtained with MC, a comparison with experimental data of electron backscattering yields as well as a comparison of $P_{\rm N}$ and MC based on characteristic X-ray generation in a three-dimensional material probe with fine structures. |
| Databáze: | OpenAIRE |
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