Skip to main content

An Experimental Assessment of Continuum Models of Dendritic Growth

  • Chapter
Growth and Form

Part of the book series: NATO ASI Series ((NSSB,volume 276))

Abstract

Experimental evidence pertinent to theories of needle crystals (dendrites) based on continuum models is reviewed and assessed critically. Some predictions, such as the dependence of the growth state on crystalline anisotropy, have not been convincingly demonstrated, and the models may not be appropriate in all cases, for example when kinetic effects are important. On the other hand, the continuum models provide an internally consistent explanation for many of the observations, including some related to sidebranching.

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 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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. D.A. Kessler, J. Koplik, and H. Levine, Adv. Phys. 37, 255 (1988).

    Article  ADS  Google Scholar 

  2. J.S. Langer, in Chance and Matter, ed. by J. Souletie, J. Vannimenus, and R. Stora (Elsevier, New York, 1987), p. 629

    Google Scholar 

  3. J.S. Langer, Science 243, 1150 (1989).

    Article  ADS  Google Scholar 

  4. P. Pelcé, Dynamics of Curved Fronts (Academic Press, New York, 1988).

    MATH  Google Scholar 

  5. For a general review from a materials science perspective see W. Kurz and R. Trivedi, Acta Meta U. Mater. 38, 1 (1990).

    Article  Google Scholar 

  6. A. Dougherty, P.D. Kaplan, and J.P. Gollub, Phys. Rev. Lett. 58, 1652 (1987).

    Article  ADS  Google Scholar 

  7. S.-C. Huang and M.E. Glicksman, Acta Metall. 29, 701 and 717 (1981).

    Article  Google Scholar 

  8. Y. Sawada, A. Dougherty, and J.P. Gollub, Phys. Rev. Lett. 56, 1260 (1986).

    Article  ADS  Google Scholar 

  9. F. Argoul, A. Arneodo, and G. Grasseau, Phys. Rev. Lett. 61, 2558 (1988).

    Article  ADS  Google Scholar 

  10. P. Oswald, J. Phys. France 49, 1083 (1988).

    Article  Google Scholar 

  11. W.W. Mullins and R.F. Sekerka, J. Appl. Phys. 34, 323 (1963)

    Article  ADS  Google Scholar 

  12. W.W. Mullins and R.F. Sekerka, J. Appl. Phys. 35, 444 (1964).

    Article  ADS  Google Scholar 

  13. H. Chou and H.Z. Cummins, Phys. Rev. Lett. 61, 173 (1988).

    Article  ADS  Google Scholar 

  14. V. Pines, M. Zlatkowski, and A. Chait, Phys. Rev. A 42, 6129 and 6137 (1990).

    Article  ADS  Google Scholar 

  15. D.A. Kessler and H. Levine, Phys. Rev. A 33, 3352 (1986).

    Article  ADS  Google Scholar 

  16. A. Barbieri and J.S. Langer, Phys. Rev. A 39, 5314 (1989).

    Article  ADS  Google Scholar 

  17. J.S. Langer, Phys. Rev. A 36, 3350 (1987).

    Article  ADS  Google Scholar 

  18. Y. Saito, G. Goldbeck-Wood, and H. Müller-Krumbhaar, Phys. Rev. Lett. 58, 1541 (1987)

    Article  ADS  Google Scholar 

  19. Y. Saito, G. Goldbeck-Wood, and H. Müller-Krumbhaar, Phys. Rev. A 38, 2148 (1988).

    Article  ADS  Google Scholar 

  20. D. Kessler, in Proceedings of the Conference on Asymptotics Beyond All Orders, ed. by S. Tanveer (Plenum, 1991), to appear. A different approach to the effect of non-axisymmetry on state selection has been given by Y. Miata, S.H. Tirmizi, and M.E. Glicksman, “Dendritic growth with interfacial energy anisotropy,” J. Cryst. Growth (1991), to appear.

    Google Scholar 

  21. M.E. Glicksman and N.B. Singh, J. Cryst. Growth 98, 277 (1989).

    Article  ADS  Google Scholar 

  22. J.H. Bilgram, M. Firmann, and E. Hürlimann, J. Cryst. Growth 96, 175 (1989).

    Article  ADS  Google Scholar 

  23. A. Dougherty and J.P. Gollub, Phys. Rev. A 38, 3043 (1988).

    Article  ADS  Google Scholar 

  24. A. Dougherty, Surface tension anisotropy and the dendritic growth of pivalic acid, J. Cryst. Growth (1991), in press.

    Google Scholar 

  25. J. Maurer, B. Perrin, and P. Tabeling, Three dimensional structure of NH4Br dendrites growing out of a gel (1990), preprint.

    Google Scholar 

  26. M. Ben Amar, private communication.

    Google Scholar 

  27. X.W. Qian and H.Z. Cummins, Phys. Rev. Lett. 64, 3038 (1990).

    Article  ADS  Google Scholar 

  28. P. Bouissou, A. Chiffaudel, B. Perin, and P. Tabeling, Europhys. Lett. 13, 89 (1990).

    Article  ADS  Google Scholar 

  29. S.-K. Chan, H.-H. Reimer, and M. Kahlweit, J. Cryst. Growth 32, 303 (1976).

    Article  ADS  Google Scholar 

  30. E. Brener and H. Levine, Phys. Rev. A 43, 883 (1991).

    Article  ADS  Google Scholar 

  31. J. Maurer, P. Bouissou, B. Perrin, and P. Tabeling, Europhys. Lett. 8, 67 (1988).

    Article  ADS  Google Scholar 

  32. M. Ben Amar and Y. Pomeau, Europhys. Lett. 6, 609 (1988).

    Article  ADS  Google Scholar 

  33. E. Raz, S.G. Lipson, and E. Polturak, Phys. Rev. A 40, 1088 (1989).

    Article  ADS  Google Scholar 

  34. E. Raz, S.G. Lipson, and E. Ben-Jacob, Meta-ordering observed during dendritic growth of ammonium chloride crystals in thin layers (1990), preprint.

    Google Scholar 

  35. R.-F. Xiao, J.I.D. Alexander, and F. Rosenberger, Phys. Rev. A 38, 2447 (1988)

    Article  ADS  Google Scholar 

  36. R.-F. Xiao, J.I.D. Alexander, and F. Rosenberger, J. Cryst. Growth 100, 313 (1990).

    Article  ADS  Google Scholar 

  37. R. Pieters and J.S. Langer, Phys. Rev. Lett. 56, 1948 (1986).

    Article  ADS  Google Scholar 

  38. M. Barber, A. Barbieri, and J.S. Langer, Phys. Rev. A 36, 3340 (1987).

    Article  ADS  Google Scholar 

  39. D.A. Kessler and H. Levine, Europhys. Lett. 4, 215 (1987).

    Article  ADS  Google Scholar 

  40. B. Caroli, C. Caroli, and B. Roulet, J. Phys. Paris 48, 1423 (1987).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Plenum Press, New York

About this chapter

Cite this chapter

Gollub, J.P. (1991). An Experimental Assessment of Continuum Models of Dendritic Growth. In: Amar, M.B., Pelcé, P., Tabeling, P. (eds) Growth and Form. NATO ASI Series, vol 276. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-1357-1_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-1357-1_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-1359-5

  • Online ISBN: 978-1-4684-1357-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics