Efficient sampling and representation of the grain boundary geometry and composition space: atomistic simulation meets statistical methodology
Mechanical Properties of Metallic Materials and their Microstructural Origins
Final Report Abstract
To fully explore modern methods of data-based materials science extensive data on materials’ microstructures are needed. One important class of elements of microstructures are their internal interfaces, at which two different regions of crystals with different orientation, composition, and/or lattice structure meet. Grain boundaries, an example of the first category, have a significant influence on the material’s mechanical and functional properties. They can be manipulated via solute segregation, leading to changes in grain boundary energy, mobility, structure, and cohesion. In this project we advance data based materials science by establishing a selective and efficient high-throughput computational framework to determine such grain boundary energies via atomistic simulations. We have developed the necessary algorithm by making use of “design of experiment” approaches and recent developments in modelling grain boundary structures. In contrast to conventional highthroughput calculations, the new design of experiment techniques in combination with nonparametric estimation is capable of identifying and evaluating the most critical regions of the grain boundary parameter space on its own. The resulting scheme can be used to provide grain boundary energies as a function geometry as input for thermodynamic and kinetic, as well as micromechanical modelling. Furthermore, the insights will contribute to a more efficient planning of simulations and experiments for investigations of other multidimensional, non-linear relationships as well.
Publications
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Asymptotic equivalence for nonparametric regression with dependent errors: Gauss–Markov processes. Annals of the Institute of Statistical Mathematics, 74(6), 1163-1196.
Dette, Holger & Kroll, Martin
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Efficient Prediction of Grain Boundary Energies from Atomistic Simulations via Sequential Design. Advanced Theory and Simulations, 5(7).
Kroll, Martin; Schmalofski, Timo; Dette, Holger & Janisch, Rebecca
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Towards active learning: A stopping criterion for the sequential sampling of grain boundary degrees of freedom. Materialia, 31, 101865.
Schmalofski, Timo; Kroll, Martin; Dette, Holger & Janisch, Rebecca
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Effects of mechanical stress, chemical potential, and coverage on hydrogen solubility during hydrogen-enhanced decohesion of ferritic steel grain boundaries: A first-principles study. Physical Review Materials, 8(7).
Azócar Guzmán, Abril & Janisch, Rebecca
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Optimal designs for regression on Lie groups
Chakraborty, S., Dette, H. & Kroll, M.
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Sampling of the multidimensional parameter space of grain boundary energies with atomistic simulations and statistical methods. PhD thesis, Ruhr-University Bochum
Schmalofski, T.
