Continuum Mechanics and Thermodynamics

, Volume 29, Issue 4, pp 895–911 | Cite as

Modelling of grain boundary dynamics using amplitude equations

  • Claas HüterEmail author
  • Jörg Neugebauer
  • Guillaume Boussinot
  • Bob Svendsen
  • Ulrich Prahl
  • Robert Spatschek
Original Article


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.


Amplitude equations Grain rotation Coupled motion Nonlinear elasticity 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Claas Hüter
    • 1
    Email author
  • Jörg Neugebauer
    • 1
  • Guillaume Boussinot
    • 2
    • 3
  • Bob Svendsen
    • 4
    • 5
  • Ulrich Prahl
    • 6
  • Robert Spatschek
    • 1
  1. 1.Computational Materials DesignMax Planck Institut für EisenforschungDüsseldorfGermany
  2. 2.Access e.V.RWTH Aachen UniversityAachenGermany
  3. 3.Research CenterPeter-Grünberg InstituteJülichGermany
  4. 4.Microstructure Physics and Alloy DesignMax Planck Institut für EisenforschungDüsseldorfGermany
  5. 5.Material MechanicsRWTH Aachen UniversityAachenGermany
  6. 6.Department of Ferrous MetallurgyRWTH Aachen UniversityAachenGermany

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