Anisotropy-driven dynamics of cellular fronts in directional solidification in thin samples

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 58, Issue 3, 1998, Pages 3302-3315

  Akamatsu, Silvère ^a   Faivre, Gabriel ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; CRYSTAL GROWTH; CRYSTAL IMPURITIES; CRYSTAL ORIENTATION; CRYSTAL SYMMETRY; NUMERICAL METHODS; ORGANOMETALLICS; PHASE TRANSITIONS; SOLIDIFICATION; SURFACE TENSION;

CELLULAR GROWTH; CELLULAR THRESHOLD VELOCITY; INTERFACIAL ANISOTROPY; RESIDUAL IMPURITY EFFECTS;

MOLECULAR DYNAMICS;

EID: 0032159643     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.58.3302     Document Type: Article

References (64)

1. K. A. Jackson and J. D. Hunt, Acta Metall. 13, 1212 (1965).AMETAR
2. W. W. Mullins and R. F. Sekerka, J. Appl. Phys. 35, 444 (1964).
3. See also D. J. Wollkind and L. A. Segel, Philos. Trans. R. Soc. London, Ser. A 268, 351 (1970)
4. and B. Caroli,C. Caroli, and B. Roulet, in Solids Far from Equilibrium, edited by C. Godréche (Cambridge University Press, Cambridge, England, 1992).
5. See, for instance, G. P. Ivantsov [Dokl. Akad. Nauk SSSR 58, 567 (1947)] for dendritic growth,
6. J. W. Rutter and B. Chalmers [Can. J. Phys. 31, 15 (1953)] for cellular growth, and
7. C. Zener [Trans. AIME 167, 550 (1946)] for lamellar eutectic growth.TAIMAF
8. The kinetic coefficient is defined as β=ΔTk/V, where ΔTk is the difference between the actual and the equilibrium value of the undercooling at the interface. When the solid-liquid interface is rough, ΔTk is a linear function of V, and β is independent of V.
9. Several valuable reviews on the theory of dendritic growth are available, for instance, those by J. S. Langer, in Chance and Matter, edited by J. Souletie, J. Vannimenus, and R. Stora (Elsevier, Amsterdam, 1987)
10. D. A. Kessler, J. Koplik, and H. Levine, Adv. Phys. 37, 255 (1988)
11. H. Müller-Krumbhaar and W. Kurz, Phase Transformation in Materials, edited by P. Haasen (VCH-Verlag, Weinheim, 1991)
12. Y. Pomeau and M. Ben Amar, in Solids Far from Equilibrium, edited by C. Godrèche (Cambridge University Press, Cambridge, England, 1992).
13. E. A. Brener, H. Müller-Krumbhaar, and D. E. Temkin, Europhys. Lett. 17, 535 (1992).EULEEJ
14. T. Ihle and H. Müller-Krumbhaar, Phys. Rev. Lett. 70, 3083 (1993)
15. T. Ihle and H. Müller-Krumbhaar, Phys. Rev. E 49, 2972 (1994).PLEEE8
16. R. Kupferman, D. A. Kessler, and E. Ben-Jacob, Physica A 213, 451 (1995).PHYADX
17. S. Akamatsu, G. Faivre, and T. Ihle, Phys. Rev. E 51, 4751 (1995).PLEEE8
18. R. Trivedi, V. Seetharaman, and M. A. Eshelman, Metall. Trans. 22A, 585 (1991).MTTABN
19. S. R. Coriell and R. F. Sekerka, J. Cryst. Growth 34, 157 (1976).JCRGAE
20. M. Bennett, K. Tsiveriotis, and R. A. Brown, Phys. Rev. B 45, 9562 (1992).PRBMDO
21. W.-J. Rappel and H. Riecke, Phys. Rev. A 45, 846 (1992).PLRAAN
22. P. Coullet and G. Iooss, Phys. Rev. Lett. 64, 866 (1990).PRLTAO
23. J. T. Gleeson and P. Cladys, Phys. Rev. Lett. 66, 236 (1991).PRLTAO
24. S. de Cheveigné and C. Guthmann, J. Phys. I 2, 193 (1992).JPGCE8
25. H. Jamgotchian, R. Trivedi, and B. Billia, Phys. Rev. E 47, 4313 (1993).PLEEE8
26. M. Georgelin, Thèse de Doctorat, Université d’Aix-Marseille I (1997)
27. M. Georgelin and A. Pocheau, Phys. Rev. E 57, 3189 (1998).PLEEE8
28. M. Georgelin and A. Pocheau, Phys. Rev. Lett. 79, 2698 (1997).PRLTAO
29. W. L. Kaukler and J. W. Rutter, in In Situ Composites, edited by F. D. Lemkey, H. E. Cline, and M. McLean (Elsevier, Amsterdam, 1982), p. 305.
30. J. Mergy, G. Faivre, C. Guthmann, and R. Mellet, J. Cryst. Growth 134, 353 (1993).JCRGAE
31. T. Ihle and S. Akamatsu (unpublished). The found values are β0≈5×10-3 K s μm-1, and ɛk≈0.1. Numerical results show that kinetic effects predominate over capillary effects for any reasonable value of the anisotropy coefficient of γ. This is probably due to the high value (≈20) of the ratio Dβ0/ΔT0d0(see text for definitions).
32. P. Kurowski, C. Guthmann, and S. de Cheveigné, Phys. Rev. A 42, 7368 (1990).PLRAAN
33. K. Brattkus and C. Misbah, Phys. Rev. Lett. 64, 1925 (1990). The limited extent of the weakly nonlinear range is due to the fact that d0/lth≪1 (for a definition, see the text) in our system, as is usually the case in directional solidification.PRLTAO
34. S.-K. Chan, H.-H. Reimer, and M. Kahlweit, J. Cryst. Growth 32, 303 (1976).JCRGAE
35. E. A. Brener and V. I. Mel’nikov, Adv. Phys. 40, 53 (1991).ADPHAH
36. J. C. LaCombe, M. B. Koss, V. E. Fradkov, and M. E. Glicksman, Phys. Rev. E 52, 2778 (1995); PLEEE8
37. U. Bisang and J. H. Bilgram, Phys. Rev. Lett. 75, 3898 (1995).PRLTAO
38. A. Classen, C. Misbah, H. Müller-Krumbhaar, and Y. Saito, Phys. Rev. A 43, 6920 (1991).PLRAAN
39. Y. Saito, C. Misbah, and H. Müller-Krumbhaar, Phys. Rev. Lett. 63, 2377 (1989).PRLTAO
40. T. Okada and Y. Saito, Phys. Rev. E 54, 650 (1996).PLEEE8
41. S. Akamatsu and T. Ihle, Phys. Rev. E 56, 4479 (1997).PLEEE8
42. P. Kopczynski, W. J. Rappel, and A. Karma, Phys. Rev. Lett. 77, 3387 (1996).PRLTAO
43. M. Ginibre, S. Akamatsu, and G. Faivre, Phys. Rev. E 56, 780 (1997).PLEEE8
44. S. Akamatsu and G. Faivre, J. Phys. I 6, 503 (1996).JPGCE8
45. Image processing was made with the NIH-Image software on a Power Macintosh computer. NIH Image is a public domain program developed at the U.S. National Institutes of Health and available from the Internet by anonymous FTP from zippy.nimh.nih.gov or on floppy disk from the National Technical Information Service, Springfield, Virginia, part number PB95-500195GEI.
46. V. G. Smith, W. A. Tiller, and J. W. Rutter, Can. J. Phys. 33, 723 (1955).
47. See also J. A. Warren and J. S. Langer, Phys. Rev. A 47, 2702 (1993)
48. B. Caroli, C. Caroli, and L. Ramirez-Piscina, J. Cryst. Growth 132, 377 (1993).JCRGAE
49. The solidification dynamics of our system at V close to Vc(V/Vc-1≈0.1) seems to be dominated by three-dimensional effects involving wetting forces at the glass plates, which may be sensitive to residual impurities (unpublished observations). These effects become unimportant as soon as the amplitude of the cells is large compared to the sample thickness.
50. P. Kurowski, S. de Cheveigné, G. Faivre, and C. Guthmann, J. Phys. (France) 50, 3007 (1989).JOPQAG
51. W. Huang, X. Geng, and Y. Zhou, J. Cryst. Growth 134, 105 (1993).JCRGAE
52. W. Losert, B. Q. Shi, and H. Z. Cummins, Proc. Natl. Acad. Sci. USA 95, 431 (1998); PNASA6
53. Proc. Natl. Acad. Sci. USAW. LosertB. Q. ShiH. Z. Cummins95, 439 (1998).
54. B. Caroli, C. Caroli, G. Faivre, and J. Mergy, J. Cryst. Growth 118, 135 (1992).JCRGAE
55. P. Kopczynski, W-J. Rappel, and A. Karma, Phys. Rev. Lett. 79, 2698 (1997).PRLTAO
56. See, e.g., F. Giorgiutti and L. Limat, Physica D 103, 590 (1997).PDNPDT
57. G. Faivre and J. Mergy, Phys. Rev. A 45, 7320 (1992)
58. Phys. Rev. AG. FaivreJ. Mergy46, 963 (1992).
59. A. J. Simon, J. Bechhoefer, and A. Libchaber, Phys. Rev. Lett. 61, 2574 (1988).
60. See also J. M. Flesselles, A. J. Simon, and A. J. Libchaber, Adv. Phys. 40, 1 (1991).ADPHAH
61. P. Coullet, R. E. Goldstein, and G. H. Gunaratne, Phys. Rev. Lett. 63, 1954 (1989).
62. See also S. Fauve, S. Douady, and O. Thual, J. Phys. II 1, 311 (1991)
63. S. FauveS. DouadyO. ThualPhys. Rev. Lett. 65, 385 (1990)
64. B. Caroli, C. Caroli, and S. Fauve, J. Phys. I 2, 281 (1992). JPGCE8