Dynamical polygonization below the cellular-bifurcation threshold in thin-sample directional solidification

Physical Review B - Condensed Matter and Materials Physics

Volumn 66, Issue 5, 2002, Pages 541021-5410210

  Bottin Rousseau, Sabine ^a   Akamatsu, Silvère ^a   Faivre, Gabriel ^a  

^a INSTITUT DES NANOSCIENCES DE PARIS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALLOY;

ARTICLE; CRYSTALLIZATION; DIFFUSION; GEOMETRY; MODEL; PHYSICAL PHENOMENA; SOLID; THEORY;

EID: 0036695677     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevB.66.054102     Document Type: Article

References (37)

1. J.W. Rutter and B. Chalmers, Can. J. Phys. 31, 15 (1953).
2. W.W. Mullins and R.F. Sekerka, J. Appl. Phys. 35, 444 (1964).
3. D.J. Wollkind and L.A. Segel, Philos. Trans. R. Soc. London, Ser. A 268a, 351 (1970); B. Caroli, C. Caroli, and B. Roulet, J. Phys. (Paris) 43, 1767 (1982).
4. D.J. Wollkind and L.A. Segel, Philos. Trans. R. Soc. London, Ser. A 268a, 351 (1970); B. Caroli, C. Caroli, and B. Roulet, J. Phys. (Paris) 43, 1767 (1982).
5. W. Losert, B.Q. Shi, and H.Z. Cummins, Proc. Natl. Acad. Sci. U.S.A. 95, 431 (1998).
6. S.R. Coriell and R.F. Sekerka, J. Cryst. Growth 19, 285 (1973).
7. L.H. Ungar and R.A. Brown, Phys. Rev. B 30, 3993 (1984).
8. For an introduction to the physics of lattice defects, see D. Hull, Introduction to Dislocations (Pergamon Press, Oxford, 1975). Subboundaries (or low-angle grain boundaries) are made of two-dimensional periodic arrays of dislocations devoid of long-range stresses. Polygonization is the generic name of the rearrangement processes giving rise to subboundaries.
9. G. Grange, C. Jourdan, J. Gastaldi, and B. Billia, J. Phys. III 4, 293 (1994).
10. K.A. Jackson and J.D. Hunt, Acta Metall. 13, 1212 (1965).
11. H.M. Hawthorne and J.N. Sherwood, Trans. Faraday Soc. 66, 1783 (1970). These authors showed that the mechanical properties of the nonfaceted transparent "plastic" organic crystals are similar to those of metals of the same crystal structure (fcc, in our case) at the same reduced temperature (absolute temperature divided by the melting temperature).
12. S. de Cheveigné, C. Guthmann, and M.-M. Lebrun, J. Phys. (Paris) 47, 2095 (1986). Also see M.-M. Lebrun, Thesis, Université Paris 7, 1987.
13. S. de Cheveigné, C. Guthmann, and M.-M. Lebrun, J. Phys. (Paris) 47, 2095 (1986). Also see M.-M. Lebrun, Thesis, Université Paris 7, 1987.
14. S. Akamatsu, G. Faivre, and T. Ihle, Phys. Rev. E 51, 4751 (1995).
15. S. Akamatsu and G. Faivre, Phys. Rev. E 58, 3302 (1998).
16. M. Ginibre, S. Akamatsu, and G. Faivre, Phys. Rev. E 56, 780 (1997).
17. D.P. Woodruff, The Solid-Liquid Interface (Cambridge University Press, Cambridge, 1973). Also see R. Kikuchi and J.W. Cahn, Phys. Rev. 21, 1893 (1985).
18. D.P. Woodruff, The Solid-Liquid Interface (Cambridge University Press, Cambridge, 1973). Also see R. Kikuchi and J.W. Cahn, Phys. Rev. 21, 1893 (1985).
19. P. Kopczynski, W.-J. Rappel, and A. Karma, Phys. Rev. E 55, 1282 (1997).
20. H. Jamgotchian, R. Trivedi, and B. Billia, Phys. Rev. E 47, 4313 (1993).
21. J. Mergy, G. Faivre, C. Guthmann, and R. Mellet, J. Cryst. Growth 134, 353 (1993).
22. S. Akamatsu and G. Faivre, J. Phys. 16, 5037 (1996).
23. Grain coarsening involves the whole GB network of the solid. The lateral displacements of the GB grooves that we observe along the front are part of this process. They occur during directional solidification as well as at rest.
24. W.A. Tiller, K.A. Jackson, J.W. Rutter, and B. Chalmers, Acta Metall. 1, 428 (1953).
25. For an introduction to the theory of the Mullins-Sekerka bifurcation, see B. Caroli, C. Caroli and B. Roulet, in Solids Far from Equilibrium, edited by C. Godrèche (Cambridge University Press, Cambridge, 1992).
26. R.J. Schaefer, M.E. Glicksman, and J.D. Ayers, Philos. Mag. 32, 725 (1975).
27. M. Gündüz and J.D. Hunt, Acta Metall. 33, 1651 (1985).
28. K.A. Jackson, Philos. Mag. 7, 1615 (1962).
29. B. Chalmers, Principles of Solidification (Krieger, Huntington, NY, 1977).
30. S. Akamatsu, S. Moulinet, and G. Faivre, Metall. Mater. Trans. A 32, 2039 (2001).
31. E. Billig, Proc. R. Soc. London, Ser. A 235, 37 (1956).
32. An externally applied stress can provoke an Asaro-Tiller-Grinfeld instability of the front in a dislocation-free crystal [see I. Cantat, K. Kassner, C. Misbah and H. Müller-Krumbhaar, Phys. Rev. E 58, 6027 (1998)]. The present study suggests that, in a ductile crystal, such a stress would simply result in an enhancement of the dynamical polygonization.
33. J.D. Verhoeven and E.D. Gibson, J. Cryst. Growth 11, 39 (1971).
34. K.A. Jackson and J.D. Hunt, Trans. AIME 236, 1129 (1966).
35. J.S. Langer, Phys. Rev. Lett. 44, 1023 (1980).
36. W. Datye and J.S. Langer, Phys. Rev. B 24, 4155 (1981).
37. M. Plapp and A. Karma, Phys. Rev. E 60, 6865 (1999).