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Phase-field modeling of surface diffusion

  • Klaus Kassner , Robert Spatschek and Clemens Gugenberger
Published/Copyright: June 11, 2013
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International Journal of Materials Research
From the journal International Journal of Materials Research Volume 101 Issue 4

Abstract

In the classical description of surface diffusion, transport on a curved interface is associated with the Laplace – Beltrami operator acting on a chemical potential (difference). An early attempt to model surface diffusion via the phase-field approach goes back to Cahn, Elliott and Novick-Cohen; they use a scalar mobility approaching zero in the bulk. Similar models have been proposed first on the basis of heuristic ideas and then underpinned by asymptotic analysis. As it turns out, most of these analyses suffer from a subtle flaw, due not to a miscalculation but rather to early termination of the calculation. The asymptotic analysis provides all the equations desired for the correct sharp-interface limit. Unfortunately, it provides an additional equation, which is one restriction too many. Consequences for dynamical simulations of this kind of model are explored numerically. We construct two models based on the introduction of a tensorial mobility that approximate known sharp-interface equations without adding undesired constraints. Numerical simulations suggest superior performance of the new models in at least some situations.

Keywords: Surface diffusion; Computational techniques; Phase-field model; Tensorial mobility
* Correspondence address, Prof. Dr. Klaus Kassner, Otto-von-Guericke-Universität Magdeburg, Postfach 41 20, D-39016 Magdeburg. Tel.: +49 391 6 71 87 99, Fax: +49 391 6 71 12 05. E-mail:

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Received: 2009-10-9
Accepted: 2010-1-27
Published Online: 2013-06-11
Published in Print: 2010-04-01

© 2010, Carl Hanser Verlag, München

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  1. Contents
  2. Contents
  3. Editorial
  4. Second Symposium on Phase-Field Modelling in Materials Science
  5. Basic
  6. Phase-field modeling of surface diffusion
  7. Elastic and plastic effects on solid-state transformations: A phase field study
  8. Elastic interactions in phase-field crystal models: numerics and postprocessing
  9. Phase-field modeling of solute trapping: comparative analysis of parabolic and hyperbolic models
  10. Multi-phase field study of the equilibrium state of multi-junctions
  11. Numerical study on the evolution of stress distribution in cellular microstructures
  12. Effect of surface charges on the polarization distribution in ferroelectric nanotubes
  13. Efficient and reliable finite element techniques for phase field models
  14. Applied
  15. Phase-field simulation of microstructure formation in technical magnesium alloys
  16. Phase-field modelling of gas porosity formation during the solidification of aluminium
  17. Application of the phase-field method in predicting gas bubble microstructure evolution in nuclear fuels
  18. Simulation of reaction-diffusion phenomena occurring between Ir coating and Ni–Al alloy substrate using phase-field model
  19. Phase-field simulation of γ(A1) + γ′(L12) + γ′′(D022) three-phase microstructure formation in Ni-base superalloys
  20. Phase field modelling of austenite formation from ultrafine ferrite–carbide aggregates in Fe–C
  21. Phase field simulation of austenite grain growth in the HAZ of microalloyed linepipe steel
  22. Dual-scale phase-field simulation of grain growth upon reheating of a microalloyed line pipe steel
  23. Phase field simulation of grain growth with grain boundary segregation
  24. Notification
  25. DGM News
https://doi.org/10.3139/146.110294
Keywords for this article
Surface diffusion; Computational techniques; Phase-field model; Tensorial mobility

Articles in the same Issue

  1. Contents
  2. Contents
  3. Editorial
  4. Second Symposium on Phase-Field Modelling in Materials Science
  5. Basic
  6. Phase-field modeling of surface diffusion
  7. Elastic and plastic effects on solid-state transformations: A phase field study
  8. Elastic interactions in phase-field crystal models: numerics and postprocessing
  9. Phase-field modeling of solute trapping: comparative analysis of parabolic and hyperbolic models
  10. Multi-phase field study of the equilibrium state of multi-junctions
  11. Numerical study on the evolution of stress distribution in cellular microstructures
  12. Effect of surface charges on the polarization distribution in ferroelectric nanotubes
  13. Efficient and reliable finite element techniques for phase field models
  14. Applied
  15. Phase-field simulation of microstructure formation in technical magnesium alloys
  16. Phase-field modelling of gas porosity formation during the solidification of aluminium
  17. Application of the phase-field method in predicting gas bubble microstructure evolution in nuclear fuels
  18. Simulation of reaction-diffusion phenomena occurring between Ir coating and Ni–Al alloy substrate using phase-field model
  19. Phase-field simulation of γ(A1) + γ′(L12) + γ′′(D022) three-phase microstructure formation in Ni-base superalloys
  20. Phase field modelling of austenite formation from ultrafine ferrite–carbide aggregates in Fe–C
  21. Phase field simulation of austenite grain growth in the HAZ of microalloyed linepipe steel
  22. Dual-scale phase-field simulation of grain growth upon reheating of a microalloyed line pipe steel
  23. Phase field simulation of grain growth with grain boundary segregation
  24. Notification
  25. DGM News
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