Parametric representation and stochastic 3D modeling of grain microstructures in polycrystalline materials using random marked tessellations

• Applicant: Professor Dr. Volker Schmidt
• Subject Area: Mathematics ; Experimental Condensed Matter Physics
• Term: from 2017 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 322917577

• Final Report Year: 2021

Final Report Abstract

The main goal of the German-Czech research project was to develop a flexible platform for the stochastic analysis, modeling and simulation of 3D grain microstructures, using tools from stochastic geometry. This was motivated by the fact that, in many cases, the 3D microstructure of polycrystalline materials significantly influences their physical properties. In a close cooperation between mathematicians and physicists from Ulm University, Charles Uni- versity in Prague and the Czech Academy of Sciences, we investigated several experimental datasets from various polycrystalline materials such as aluminum alloys, a nickel-titanium alloy and others. The first step in such an investigation is usually to identify individual grains through image segmentation where we developed new techniques in particular one based on machine learning. After the grains have been identified, it was possible to perform statistic analyses regarding geo- metrical and crystallographic aspects of different material samples. The micromechanical properties of these samples have also been investigated. For this, tessellations where one cell corresponds to exactly one grain are a very helpful tool. We developed new ways to fit these to experimental data including tessellations with curved boundaries. Based on this, it is possible to compute the curvatures of grain boundaries more accurately than before. Stochastic microstructure models are a powerful tool to understand spatial dependencies. They also provide the possibility to generate artificial microstructures, which can be used for investigations of the physical properties of a material without the need of additional time- and resource-consuming experimental measurements. During the project, we worked on theoretical tools which allow an easier development of these models and published a new framework for stochastic models, which we employed on an aluminum alloy. We also developed a multi-scale stochastic model for the polycrystalline particles in cathodes of lithium ion batteries. In this way, significant progress has been achieved in the development of mathematical meth- ods for processing, analysis and modeling of tomographic image data which reconstruct the 3D microstructure of polycrystalline materials. The results obtained in this project will be used as a basis for our future research in, e.g., virtual materials testing where a large range of virtual microstructures, so-called digital twins, is generated from spatial stochastic models to quantify microstructure-property relationships of polycrystalline materials.

Publications

• Description of the 3D morphology of grain boundaries in aluminum alloys using tessellation models generated by ellipsoids. Image Analysis & Stereology 36, 5–13 (2017)
  O Šedivý, JM Dake, CE Krill III, V Schmidt, A Jäger
  
• Data-driven selection of tessellation models describing polycrystalline microstructures. Journal of Statistical Physics 127, 1223–1246 (2018)
  O Šedivý, D Westhoff, J Kopeček, CE Krill III, V Schmidt
  
• Estimation of geodesic tortuosity and constrictivity in stationary random closed sets. Scandinavian Journal of Statistics 46, 848–884 (2019)
  M Neumann, C Hirsch, J Staněk, V Beneš, V Schmidt
  
• Machine learning techniques for the segmentation of tomographic image data of functional materials. Frontiers in Materials 6, 145 (2019)
  O Furat, M Wang, M Neumann, L Petrich, M Weber, CE Krill III, V Schmidt
  
• Microstructure changes in HPT-processed copper occurring at room temperature. Materials Characterization 151, 602–611 (2019)
  P Král, J Staněk, L Kunčická, F Seitl, L Petrich, V Schmidt, V Beneš, V Sklenička
  
• Reconstruction of grains in polycrystalline materials from incomplete data using Laguerre tessellation. Microscopy and Microanalysis 25, 743–752 (2019)
  L Petrich, J Staněk, M Wang, D Westhoff, L Heller, P Šittner, CE Krill III, V Beneš, V Schmidt
  
• Analysis of polycrystalline microstructure of AlMgSc alloy observed by 3D EBSD. Image Analysis & Stereology 39, 1–11 (2020)
  J Kopeček, J Staněk, S Habr, F Seitl, L Petrich, V Schmidt, V Beneš
  
• Numerical microstructure model of NiTi wire reconstructed from 3D-XRD data. Modelling and Simulation in Materials Science and Engineering 28, 055007 (2020)
  L Heller, I Karafítová, L Petrich, Z Pawlas, P Shayanfard, V Beneš, V Schmidt, P Šittner
  
• Exploration of Gibbs-Laguerre tessellations for three-dimensional stochastic modeling. Methodology and Computing in Applied Probability 23 (2021)
  F Seitl, L Petrich, J Staněk, CE Krill III, V Schmidt, V Beneš
  
• Mapping the architecture of single lithium ion electrode particles in 3D, using electron backscatter diffraction and machine learning segmentation. Journal of Power Sources 483, 229148 (2021)
  O Furat, DP Finegan, D Diercks, F Usseglio-Viretta, K Smith, V Schmidt