Skip to main content

Diffuse Interface Model for Microstructure Evolution

  • Chapter
  • First Online:
Advances in Solid State Physics

Part of the book series: Advances in Solid State Physics ((ASSP,volume 42))

  • 773 Accesses

Abstract

A phase-field model for a general class of multi-phase metallic alloys is proposed which describes both, multi-phase solidification phenomena as well as polycrystalline grain structures. The model serves as a computational method to simulate the motion and kinetics of multiple phase boundaries and enables the visualization of the diffusion processes and of the phase transitions in multi-phase systems. Numerical simulations are presented which illustrate the capability of the phase-field model to recover a variety of complex experimental growth structures. In particular, the phase-field model can be used to simulate microstructure evolutions in eutectic, peritectic and monotectic alloys. In addition, polycrystalline grain structures with effects such as wetting, grain growth, symmetry properties of adjacent triple junctions in thin film samples and stability criteria at multiple junctions are described by phase-field simulations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. S. Langer, private communication.

    Google Scholar 

  2. O. Penrose and P. C. Fife, Physica D 43, 44 (1990).

    Article  Google Scholar 

  3. S-L Wang, R. F. Sekerka, A. A. Wheeler, B. T. Murray, S. R. Coriell, R. J. Braun, G. B. McFadden, Physica D 69, 189 (1993).

    Article  CAS  Google Scholar 

  4. G. Caginalp, Phys. Rev. A 39, 5887 (1989).

    Article  Google Scholar 

  5. A. A. Wheeler and G. B. McFadden, Eur. J. Appl. Math. 7, 369 (1996).

    Article  Google Scholar 

  6. A. Karma and W.-J. Rappel, Phys. Rev. E 53, R3017 (1996).

    Article  CAS  Google Scholar 

  7. A. A. Wheeler, W. J. Boettinger, G. B. McFadden, Phys. Rev. A 45, 7424 (1992); A. A. Wheeler, W. J. Boettinger, G. B. McFadden, Phys. Rev. E 47, 1893 (1993); J. A. Warren and W. J. Boettinger, Acta. metall. mater. 43, 689 (1994). 209

    Article  CAS  Google Scholar 

  8. R. Kobayashi, Bull. Jpn. Soc. Ind. Appl. Math. 1, 22 (1991); R. Kobayashi, Physica D 63, 410 (1993); R. Kobayashi, Experimental Math 3, 60 (1994).

    Google Scholar 

  9. S-L. Wang and R. F. Sekerka, J. Comp. Phys. 127, 110 (1996).

    Article  Google Scholar 

  10. N. Provatas, N. Goldenfeld, and J. Dantzig, Phys. Rev. Lett. 80, 3308 (1998)

    Article  CAS  Google Scholar 

  11. Long-Qing Chen and Wei Young, Phys. Rev. B 50, 15752 (1994); Long-Qing Chen, Scr. Metall. Mater. 32, 115 (1995).

    Article  CAS  Google Scholar 

  12. I. Steinbach, F. Pezzolla, B. Nestler, J. Rezende, M. Seesselberg and G. J. Schmitz, Physica D 94, 135 (1996).

    Article  Google Scholar 

  13. B. Nestler and A. A. Wheeler, Phys. Rev. E 57, 2602 (1998).

    Article  CAS  Google Scholar 

  14. R. Kobayashi, J. A. Warren, and W.C. Carter, Physica D 119, 415 (1998).

    Article  CAS  Google Scholar 

  15. H. Garcke, B. Nestler and B. Stoth, Physica D 115, 87 (1998); H. Garcke, B. Nestler and B. Stoth, SIAM Journal on Applied Mathematics 60, 295 (1999); H. Garcke, B. Nestler and B. Stoth, J. Interfaces and Free Boundary Problems 1, 175 (1999); H. Garcke and B. Nestler, Mathematical Models and Methods in Applied Sciences 10, 895 (2000).

    Article  CAS  Google Scholar 

  16. B. Nestler and A. A. Wheeler, Phys. Rev. E 57, 2602 (1998); B. Nestler and A. A. Wheeler, Physica D 138, 114 (2000); B. Nestler, A. A. Wheeler, L. Ratke, C. Stöcker, Physica D 141, 133 (2000).

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Nestler, B. (2002). Diffuse Interface Model for Microstructure Evolution. In: Kramer, B. (eds) Advances in Solid State Physics. Advances in Solid State Physics, vol 42. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45618-X_16

Download citation

  • DOI: https://doi.org/10.1007/3-540-45618-X_16

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42907-4

  • Online ISBN: 978-3-540-45618-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics