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Data-Driven Selection of Tessellation Models Describing Polycrystalline Microstructures

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Abstract

Tessellation models have proven to be useful for the geometric description of grain microstructures in polycrystalline materials. With the use of a suitable tessellation model, the complex morphology of grains can be represented by a small number of parameters assigned to each grain, which not only entails a significant reduction in complexity, but also facilitates the investigation of certain geometric features of the microstructure. However, for a given set of microstructural data, the choice of a particular geometric model is traditionally based on researcher intuition. The model should provide a sufficiently good approximation to the data, while keeping the number of parameters small. In this paper, we discuss general aspects of the process of model selection and suggest several criteria for selecting an appropriate candidate from a certain set of tessellation models. The choice of candidate represents a trade-off between accuracy and complexity of the model. Here, the selected model is used solely to approximate given data samples, but it also provides guidance for developing stochastic tessellation models and generating virtual microstructures. Model fitting is carried out by simulated annealing, applied in a consistent manner to twelve different tessellation models.

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Acknowledgements

This research was funded by the German Science Foundation (DFG) and the Czech Science Foundation (GACR, Project Number 17-00393J). We are grateful to the Japan Synchrotron Radiation Research Institute for the allotment of beam time on beamline BL20XU of SPring-8 (Proposals 2012A1427 and 2013A1506), and we thank Dmitri Molodov of the Institute of Physical Metallurgy and Metal Physics, RWTH Aachen, for providing the Al–1 wt% Mg specimen.

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Authors and Affiliations

  1. Institute of Stochastics, Ulm University, Ulm, Germany

    Ondřej Šedivý, Daniel Westhoff & Volker Schmidt

  2. Institute of Physics, Czech Academy of Sciences, Prague, Czech Republic

    Jaromír Kopeček

  3. Institute of Micro and Nanomaterials, Ulm University, Ulm, Germany

    Carl E. Krill III

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  1. Ondřej Šedivý
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  2. Daniel Westhoff
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  3. Jaromír Kopeček
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  4. Carl E. Krill III
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  5. Volker Schmidt
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Correspondence to Daniel Westhoff.

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Šedivý, O., Westhoff, D., Kopeček, J. et al. Data-Driven Selection of Tessellation Models Describing Polycrystalline Microstructures. J Stat Phys 172, 1223–1246 (2018). https://doi.org/10.1007/s10955-018-2096-8

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  • DOI: https://doi.org/10.1007/s10955-018-2096-8

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