Quantitative investigation of cellular growth in directional solidification by phase-field simulation

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 84, Issue 4, 2011, Pages

  Wang, Zhijun ^a   Wang, Jincheng ^a   Li, Junjie ^a   Yang, Gencang ^a   Zhou, Yaohe ^a  

^a NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL METHOD; ANALYTICAL MODEL; CELLULAR GROWTH; CELLULAR INTERACTION; DOUBLONS; LOWER LIMITS; OSCILLATORY INSTABILITY; PHASE FIELDS; PHASE-FIELD MODELS; PHASE-FIELD SIMULATION; PULLING VELOCITY; QUANTITATIVE INVESTIGATION; SYSTEMATIC INVESTIGATIONS; TIP RADIUS; TIP SPLITTING; UPPER LIMITS;

MATHEMATICAL MODELS; SOLIDIFICATION; UNDERCOOLING;

COMPUTER SIMULATION;

EID: 80054986200     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.84.041604     Document Type: Article

References (42)

1. J. S. Langer, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.52.1 52, 1 (1980).
2. B. Billia and R. Trivedi, Handbook of Crystal Growth, Vol. 1, Chap. 14 (Elsevier, Amsterdam, 1993).
3. M. Kerszberg, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.27.3909 27, 3909 (1983).
4. M. J. Bennett and R. A. Brown, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.39.11705 39, 11705 (1989).
5. D. A. Kessler and H. Levine, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.41.3197 41, 3197 (1990).
6. P. Kopczynski, W. J. Rappel, and A. Karma, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.77.3387 77, 3387 (1996).
7. P. Kurowski, C. Guthmann, and S. de Cheveigné, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.42.7368 42, 7368 (1990).
8. S. Z. Lu and J. D. Hunt, J. Cryst. Growth JCRGAE 0022-0248 10.1016/0022-0248(92)90006-5 123, 17 (1992). (Pubitemid 23564105)
9. A. Pocheau and M. Georgelin, J. Cryst. Growth JCRGAE 0022-0248 10.1016/S0022-0248(99)00335-8 206, 215 (1999);
10. A. Pocheau and M. Georgelin, J. Cryst. Growth JCRGAE 0022-0248 10.1016/S0022-0248(02)02234-0 250, 100 (2003).
11. V. Laxmanan, Scripta Mater. 1359-6462 10.1016/S1359-6462(98)00038-4 38, 1289 (1998).
12. H. Jamgotchian, R. Trivedi, and B. Billia, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.47.4313 47, 4313 (1993).
13. K. Kassner, C. Misbah, H. Müller-Krumbhaar, and A. Valance, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.49.5477 49, 5477 (1994).
14. M. Georgelin and A. Pocheau, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.2698 79, 2698 (1997).
15. M. H. Burden and J. D. Hunt, J. Cryst. Growth 0022-0248 10.1016/0022-0248(74)90127-4 22, 109 (1974).
16. V. Laxmanan, Acta Metall. 0001-6160 10.1016/0001-6160(85)90197-X 33, 1037 (1985). (Pubitemid 15565271)
17. R. Trivedi, J. Cryst. Growth JCRGAE 0022-0248 10.1016/0022-0248(80)90157- 8 49, 219 (1980).
18. J. D. Hunt, Solidification of Casting of Metals, Book 192 (The Metals Society, London, 1979), p. 3.
19. W. Kurz and D. J. Fisher, Fundamentals of Solidification, 4th ed., Chap. 3 (Trans Tech Publications, Switzerland, 1998).
20. R. Trivedi and K. Somboonsuk, Mater. Sci. Eng. MSCEAA 0025-5416 10.1016/0025-5416(84)90200-3 65, 65 (1984). (Pubitemid 14602880)
21. W. J. Boettinger, J. A. Warren, C. Beckermann, and A. Karma, Ann. Rev. Mater. Res. 1531-7331 10.1146/annurev.matsci.32.101901.155803 23, 163 (2002). (Pubitemid 34992569)
22. A. A. Wheeler, W. J. Boettinger, and G. B. McFadden, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.45.7424 45, 7424 (1992);
23. A. A. Wheeler, W. J. Boettinger, and G. B. McFadden, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.47.1893 47, 1893 (1993).
24. A. Karma and W.-J. Rappel, Phys. Rev. E 1539-3755 10.1103/PhysRevE.53. R3017 53, R3017 (1996);
25. A. Karma and W.-J. Rappel, Phys. Rev. E 1539-3755 10.1103/PhysRevE.57. 4323 57, 4323 (1998).
26. S. G. Kim, W. T. Kim, and T. Suzuki, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.60.7186 60, 7186 (1999).
27. B. Echebarria, R. Folch, A. Karma, and M. Plapp, Phys. Rev. E 1539-3755 10.1103/PhysRevE.70.061604 70, 061604 (2004). (Pubitemid 40219639)
28. W. J. Boettinger and J. A. Warren, J. Cryst. Growth 0022-0248 10.1016/S0022-0248(98)01063-X 200, 583 (1999).
29. Z. Bi and R. F. Sekerka, J. Cryst. Growth 0022-0248 10.1016/S0022- 0248(01)01893-0 237, 138 (2002). (Pubitemid 34544238)
30. C. W. Lan, C. J. Shih, and W. T. Hsu, J. Cryst. Growth 0022-0248 10.1016/j.jcrysgro.2003.12.032 264, 379 (2004).
31. C. W. Lan, C. J. Shih, and M. H. Lee, Acta Mater. ACMAFD 1359-6454 10.1016/j.actamat.2005.01.034 53, 2285 (2005). (Pubitemid 40467387)
32. T. Takaki, T. Fukuoka, and Y. Tomita, J. Cryst. Growth 0022-0248 10.1016/j.jcrysgro.2005.05.064 283, 263 (2005). (Pubitemid 41235420)
33. Z. J. Wang, J. C. Wang, and G. C. Yang, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.3081634 94, 061920 (2009).
34. Z. J. Wang, J. C. Wang, and G. C. Yang, Scr. Mater. SCMAF7 1359-6462 10.1016/j.scriptamat.2009.07.033 61, 915 (2009).
35. S. Gurevich, A. Karma, M. Plapp, and R. Trivedi, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.011603 81, 011603 (2010).
36. T. F. Bower, H. D. Brody, and M. C. Flemings, Trans. AIME 236, 624 (1965).
37. P. Pelcé and A. Pumir, J. Cryst. Growth JCRGAE 0022-0248 10.1016/0022-0248(85)90310-0 73, 337 (1985).
38. W. Huang, X. Geng, and Y. Zhou, J. Cryst. Growth JCRGAE 0022-0248 10.1016/0022-0248(93)90015-O 134, 105 (1993).
39. J. A. Warren and J. S. Langer, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.47.2702 47, 2702 (1993).
40. J. C. Ramirez and C. Beckermann, Acta Mater. ACMAFD 1359-6454 10.1016/j.actamat.2004.12.021 53, 1721 (2005). (Pubitemid 40245692)
41. K. Somboonsuk, J. T. Mason, and R. Trivedi, Metall. Trans. A 10.1007/BF02644688 15A, 967 (1984).
42. R. Trivedi, Shan Liu, and S. Williams, Nat. Mater. 1476-1122 10.1038/nmat749 1, 157 (2002).