Subscale Inversion of X-Ray Emission in Electron Probe Microanalysis Based on Deterministic Transport Equations

• Applicants: Dr. Silvia Richter; Professor Dr. Manuel Torrilhon
• Subject Area: Thermodynamics and Kinetics as well as Properties of Phases and Microstructure of Materials ; Mechanical Properties of Metallic Materials and their Microstructural Origins ; Physical Chemistry of Solids and Surfaces, Material Characterisation
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 466010736

The investigation of material properties and the development of new materials heavily rely on the characterization of their microstructure. A critical aspect of the characterization is to measure the distribution of the different chemical elements present inside a material. A wellestablished characterization technique is the electron probe microanalysis (EPMA), in which an electron beam interacts with the material causing the emission of x-rays characteristic to the local composition. This technique has the unique advantage to provide accurate quantitative information about the composition of a sample at the micrometer to nanometer scale, while allowing the investigation of a macroscopic sampling area. Although successful, the reconstruction technique used in EPMA is based on the assumption that the sample is homogeneous within the interaction volume of the electron beam, hence, typically the structures of interest must be bigger than the interaction volume in order to be analyzed. Therefore, to apply the quantification procedures to even smaller scales it is necessary to derive fast and accurate mathematical and numerical models of electron-x-ray-matter interactions in complex geometries and inhomogeneous material below the interaction volume. In the first part of this project the usual approaches by simple analytical models or Monte-Carlo simulations have been replaced by the description of electron scattering following the Boltzmann transport equation and its approximation by moment equations. The reduced model is given by a deterministic system of partial differential equation and can be solved efficiently without noise. The newly proposed project contains a modelling and an experimental part. The deterministic model will be used to solve the inverse problem of the reconstruction using efficient adjoint-based optimization methods. The reconstruction requires sufficient data aquisition and this will be developed in a series of controlled experiments using artificial and real-world samples. Additionally, a reconstruction based on Monte-Carlo simulations will be coupled to the deterministic model to increase physical accuracy when needed.

• DFG Programme: Research Grants