Model of grain refinement in solidification of undercooled melts

International Journal of Non-Equiulibrium Processing

Volumn 11, Issue 2, 1998, Pages 201-233

  Karma, Alain ^a  

^a NORTHEASTERN UNIVERSITY   (United States)

Author keywords

Capillary forces; Critical undercooling; Dendrite fragmentation; Grain refinement; Solute supersaturation

Indexed keywords

COOLING; DIFFUSION IN SOLIDS; MATHEMATICAL MODELS; METALLOGRAPHIC MICROSTRUCTURE; MORPHOLOGY; SOLIDIFICATION; SUPERSATURATION;

UNDERCOOLING;

LIQUID METALS;

EID: 0032647151     PISSN: 13689290     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (45)

1. J.L. WALKER, in The Physical Chemistry of Process Metallurgy, ed. G.R. St. Pierre, Interscience, New York, 1959, Part 2, p. 845.
2. J.W. WALKER, cited in B. Chalmers: Principles of Solidification, New York, 1964.
3. T.Z. KATTAMIS and M.C. FLEMINGS, Metall. Trans., 1970, 1, 1449;
4. J. Cryst. Growth, 1976, 34, 215.
5. G.E. AMAYA, J.A. PATCHETT and G.J. ABBASCHIAN, in Grain Refinement in Castings and Welds, eds G.J. Abbaschian and S.A. David, AIME 1982, p. 51.
6. G.J. ABBASCHIAN and M.C. FLEMINGS, Metall. Trans., 1983, 14A, 1147-1157.
7. A. MUNITZ and G.J. ABBASCHIAN, in Undercooled Alloy Phases, ed. E.W. Collings and C.C. Koch, AIME, Warrendale, PA, 1986, p. 23.
8. R. WILLNECKER, D.M. HERLACH and B. FEUERBACHER, Appl. Phys. Lett., 1990, 56, 324.
9. D.M. HERLACH, R.F. COCHRANE, I. EGRY, H.J. FECHT and A.L. GREER, Int. Mater. Rev., 1993, 38, 273.
10. M. SCHWARZ, A. KARMA, K. ECKLER and D.M. HERLACH, Phys. Rev. Lett., 1994, 73, 1380-83.
11. H. ECKLER, M. SCHWARZ, A. KARMA and D.M. HERLACH, Materials Science Forum, 1996, 215-326, 45.
12. F. GÄRTNER, A.F. NORMAN, A.L. GREER, A. ZAMBON, E. RAMOUS, K. ECKLER and D.M. HERLACH, Acta Mater., 1997, 45, 51.
13. K. ECKLER, A.F. NORMAN, F. GÄRTNER, A.L. GREER and D.M. HERLACH, J. Cryst. Growth, 1997, 173, 528.
14. R. WILLNECKER, G.-P. GÖRLER and G. WILDE, Mater. Sci. Eng., 1997, A226-228, 439.
15. F. GÄRTNER, S.A. MOIR, A.F. NORMAN, A.L. GREER and D.M. HERLACH, Mater. Sci. Eng. A, 1997, 226-228, 307.
16. S.A. MOIR, K. ECKLER and D.M. HERLACH, Acta Mater., 1998, 46, 4029..
17. R.F. COCHRANE, S.E. BATTERSBY and A.M. MULLIS, in Solidification 1998, eds S.P. Marsh, J.A. Dantzig, R. Trivedi, W. Hofmeister, M.G. Chu, E.J. Lavernia and J.-H. Chun, The Mineral, Metals and Materials Society, 1998, p. 246-254.
18. R.F. COCHRANE, S.E. BATTERSBY and A.M. MULLIS, in Solidification 1998, eds S.P. Marsh, J.A. Dantzig, R. Trivedi, W. Hofmeister, M.G. Chu, E.J. Lavernia and J.-H. Chun, The Mineral, Metals and Materials Society, 1998, p. 223-232.
19. M. SCHWARZ, Ph.D Thesis, Bochum University, Germany, 1998.
20. G. HORVAY, Proc. 4th National Congress on Appl. Mech., ASME, 1962, 1315.
21. R.F. COCHRANE, D.M. HERLACH and B. FEUERBACHER, Mater. Sci. Eng., 1991, A133, 706.
22. A.M. MULLIS and R.F. COCHRANE, J. Appl. Phys, 1997, 82, 3783.
23. For reviews see: J.S. Langer, in Chance and Matter, Lectures on the Theory of Pattern Formation, Les Houches Summer School, Les Houches, 1986, eds J. Souletie, J. Vannimenus, and R. Stora, North Holland, New York, 1987, pp. 629-711;
24. D. Kessler, J. Koplik, and H. Levine, Adv. Phys., 1998, 37, 255.
25. D.M. MATSON, in Solidification 1998, eds. S.P. Marsh, J.A. Dantzig, R. Trivedi, W. Hofmeister, M.G. Chu, E.J. Lavernia, and J.-H. Chun, The Mineral, Metals and Materials Society, 1998, p. 233-245.
26. K.A. JACKSON, J.D. HUNT, D.R. UHLMANN and T.P. SEWARD, Trans. TMS-AIME, 1966, 236, p. 149-158.
27. S.P. MARSH and M.E. GLICKSMAN, Metall. Trans., 1996, 27A, 557.
28. M.J. AZIZ, J. Appl. Phys., 1982, 53, 1158.
29. H.E. CLINE, Acta Metall., 1971, 19, 481.
30. W.W. MULLINS and R.F. SEKERKA, J. Appl. Phys., 1964, 35, 444.
31. R.F. SEKERKA and T.F. MARINIS, Proceedings of the International Conference on Solid-Solid Phase Transformations, TMS-AIME, Warrendale, Pa., 1983, p. 67-84.
32. R.F. MARINIS and R.F. SEKERKA, Proceedings of the Conference on In Situ Composites - III, Materials Research Society Annual Meeting, Boston, Mass., November 1978, eds J.L. Walter, M.F. Gigliotti, B.F. Oliver, H. Bibring, Ginn Custom Publishing, Lexington, MA, 1979, p. 86-94.
33. R. WILLNECKER, D.M. HERLACH and B. FEUERBACHER, Phys. Rev. Lett., 1989, 62, 2707.
34. K. ECKLER, R.F. COCHRANE, D.M. HERLACH, B. FEUERBACHER and M. JURISCH, Phys. Rev. B, 1992, 45, 5019.
35. J. LIPTON, W. KURZ and R. TRIVEDI, Acta Metall., 1987, 35, 957;
36. J. LIPTON, W. KURZ and R. TRIVEDI, Acta Metall., 1987, 35, 965.
37. A. KARMA and W.J. RAPPEL, Phys. Rev. Lett., 1996, 77, 4050;
38. Phys. Rev. E, 1998, 57, 4323-49.
39. Y. LEE, Ph.D Thesis, Northeastern University, Boston (1998).
40. D.M. HERLACH, R. WILLNECKER and F. GILLESSEN, Proc. 4th Europ. Symp. Materials Science under Microgravity, European Space Agency Report No. ESA SP-222, 1984, p. 399.
41. M.J. AZIZ, J. Appl. Phys., 1982, 53, 1158.
42. E.A. BRENER and V.I. MEL'NIKOV, Adv. Phys., 1991, 40, 53.
43. X. TONG, C. BECKERMANN and A. KARMA, in Proc. Conf. on Modeling of Casting, Welding and Advanced Solidification VIII, eds. B.G. Thomas, C. Beckerman and I. Ohnaka, TMS, Warrendale, PA, 1998.
44. A.A. WHEELER, W.J. BOETTINGER and G.B. McFADDEN, Phys. Rev. E, 1993, 47, 1893.
45. A. AHMAD, A.A. WHEELER, W.J. BOETTINGER and G.B. McFADDEN, "Solute Trapping and Solute Drag in a Phase Field Model of Rapid Solidification", Phys. Rev. E, submitted.