Skip to main content
Log in

Overview of Geometric Effects on Coarsening of Mushy Zones

  • Published:
Metallurgical and Materials Transactions A Aims and scope Submit manuscript

Abstract

An overview is presented of the thermodynamic, kinetic, statistical, and geometric factors that govern phase coarsening in dendritic mushy zones. The coarsening behavior of such systems is best quantified through the kinetics of the decay rate of the specific surface area,S v. The geometry of the complex solid-melt interfaces comprising a mushy zone is described statistically as an areal distribution of local curvature parameters. These parameters capture both the intensive and extensive thermodynamic characteristics of the mushy zone. The effects of local interface shape, negative mean, and Gaussian curvatures and the appearance of inactive lengthscales on the coarsening kinetics of dendritic structures are discussed. The combined contribution of all these geometrical effects yields global coarsening rates for ramified mushy zones that are comparable to those predicted from theory for a collection of spherical particles having the identical volume fraction of solid.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L.A. Meloro: Master’s Thesis, Rensselaer Polytechnic Institute, Troy, NY, 1988.

  2. P.W. Voorhees:J. Status Phys., 1985, vol. 38, pp. 231–52.

    Article  Google Scholar 

  3. ME. Glicksman, R.N. Smith, S.P. Marsh, and R. Kuklinski:Metall. Trans. A, 1992, vol. 23A, pp. 659–67.

    CAS  Google Scholar 

  4. S.P. Marsh and D. Banerjee: inMaterials Processing in the Computer Age II, V.R. Voller, S.P. Marsh, and N. El-Kaddah, eds., TMS, Warrendale, PA, 1994, pp. 105–16.

    Google Scholar 

  5. N. Aikawa and P.W. Voorhees:Phys. Rev. E, 1994, vol. E49, pp. 3860–80.

    Article  Google Scholar 

  6. P.W. Voorhees:Ann. Rev. Mater. Sci., 1992, vol. 22, pp. 197–215.

    Article  CAS  Google Scholar 

  7. W.W. Mullins:J. Appl. Phys., 1986, vol. 59, pp. 1341–49.

    Article  CAS  Google Scholar 

  8. O.M. Todes and W.W. Chruschtschew:J. Physk. Chem., 1947, vol. 21, pp. 301–11.

    CAS  Google Scholar 

  9. I.M. Lifshitz and V.V. Slyozov:J. Phys. Chem. Solids, 1961, vol. 19, pp. 35–50.

    Article  Google Scholar 

  10. C. Wagner:Z Elektrochem, 1961, vol. 65, pp. 581–615.

    CAS  Google Scholar 

  11. K. Tsumuraya and Y. Miyata:Ada Metall., 1983, vol. 31, pp. 437–52.

    Article  CAS  Google Scholar 

  12. S.C. Hardy and P.W. Voorhees:Metall. Trans. A, 1988, vol. 19A, pp. 2713–21.

    CAS  Google Scholar 

  13. A.N. Niemi and T.H. Courtney:J. Mater. Sci., 1981, vol. 16, pp. 226- 36.

    Article  CAS  Google Scholar 

  14. S.P. Marsh: Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, NY, 1989.

  15. S.P. Marsh and M.E. Glicksman: inModeling of Coarsening and Grain Growth, S.P. Marsh and C.S. Pande, eds., TMS, Warrendale, PA, 1993, pp. 1–14.

    Google Scholar 

  16. T.Z. Kattamis, J.C. Coughlin, and M.C. Flemings:Trans. AIME, 1967, vol. 239, pp. 1504–11.

    CAS  Google Scholar 

  17. K.P. Young and D.H. Kirkwood:Metall. Trans. A, 1975, vol. 6A, pp. 197–205.

    Google Scholar 

  18. D.R. Poirer, S. Ganesan, M. Andrews, and P. Ocansey:Mater. Sci. Eng., 1991, vol. A148, pp. 289–97.

    Google Scholar 

  19. N.J. Whisler and T.Z. Kattamis:J. Cryst. Growth, 1972, vol. 15, pp. 20–24.

    Article  Google Scholar 

  20. D.H. Kirkwood:Mater. Sci. Eng., 1985, vol. 73, pp. L1-L4.

    Article  CAS  Google Scholar 

  21. J.J. Reeves and T.Z. Kattamis:Scripta Metall, 1971, vol. 5, pp. 223–29.

    Article  CAS  Google Scholar 

  22. E.E. Underwood:Quantitative Stereology, Addison-Wesley Publishing Company, Reading, MA, 1970.

    Google Scholar 

  23. R.T. DeHoff:Metallography, 1984, vol. 17, pp. 203–08.

    Article  CAS  Google Scholar 

  24. R.T. DeHoff: inTreatise on Materials Science and Technology, H. Herman, ed., Academic Press, New York, NY, 1972, pp. 282–4.

    Google Scholar 

  25. R.T. DeHoff:Acta Metall, 1984, vol. 32, pp. 43–47.

    Article  Google Scholar 

  26. M.M. Lipschutz:Differential Geometry, Schaum Outline Series, McGraw-Hill, New York, NY, 1969, p. 154.

    Google Scholar 

  27. M.E. Glicksman and P.W. Voorhees:Metall. Trans. A, 1984, vol. 15A, pp. 995–1001.

    CAS  Google Scholar 

  28. D. Feijóo and H.E. Exner:J. Cryst. Growth, 1991, vol. 113, pp. 449- 55.

    Article  Google Scholar 

  29. D.A. Drew:S1AM J. Appl. Math, 1990, vol. 50, pp. 649–66.

    Article  Google Scholar 

  30. D.J. Griffiths:Introduction to Electrodynamics, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1981, pp. 56–79.

    Google Scholar 

  31. R.T. DeHoff:Acta Metall. Mater., 1991, vol. 39, pp. 2349–60.

    Article  CAS  Google Scholar 

  32. S.P. Marsh and D. Banerjee: inModeling and Control of Casting and Welding Processes VII, M. Cross and J. Campbell, eds., TMS, Warrendale, PA, 1995, pp. 713–20. $

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This article is based on a presentation made at the “Analysis and Modeling of Solidification” symposium as part of the 1994 Fall meeting of TMS in Rosemont, Illinois, October 2–6, 1994, under the auspices of the TMS Solidification Committee.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marsh, S.P., Glicksman, M.E. Overview of Geometric Effects on Coarsening of Mushy Zones. Metall Mater Trans A 27, 557–567 (1996). https://doi.org/10.1007/BF02648946

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02648946

Keywords

Navigation