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Modelling of grain boundary dynamics using amplitude equations

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Abstract

We discuss the modelling of grain boundary dynamics within an amplitude equations description, which is derived from classical density functional theory or the phase field crystal model. The relation between the conditions for periodicity of the system and coincidence site lattices at grain boundaries is investigated. Within the amplitude equations framework, we recover predictions of the geometrical model by Cahn and Taylor for coupled grain boundary motion, and find both \({\langle100\rangle}\) and \({\langle110\rangle}\) coupling. No spontaneous transition between these modes occurs due to restrictions related to the rotational invariance of the amplitude equations. Grain rotation due to coupled motion is also in agreement with theoretical predictions. Whereas linear elasticity is correctly captured by the amplitude equations model, open questions remain for the case of nonlinear deformations.

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Authors and Affiliations

  1. Computational Materials Design, Max Planck Institut für Eisenforschung, 40237, Düsseldorf, Germany

    Claas Hüter, Jörg Neugebauer & Robert Spatschek

  2. Access e.V., RWTH Aachen University, 52072, Aachen, Germany

    Guillaume Boussinot

  3. Research Center, Peter-Grünberg Institute, 52425, Jülich, Germany

    Guillaume Boussinot

  4. Microstructure Physics and Alloy Design, Max Planck Institut für Eisenforschung, 40237, Düsseldorf, Germany

    Bob Svendsen

  5. Material Mechanics, RWTH Aachen University, 52062, Aachen, Germany

    Bob Svendsen

  6. Department of Ferrous Metallurgy, RWTH Aachen University, 52056, Aachen, Germany

    Ulrich Prahl

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  1. Claas Hüter
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Correspondence to Claas Hüter.

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Communicated by Ralf Müller.

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Hüter, C., Neugebauer, J., Boussinot, G. et al. Modelling of grain boundary dynamics using amplitude equations. Continuum Mech. Thermodyn. 29, 895–911 (2017). https://doi.org/10.1007/s00161-015-0424-7

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