Quantitative phase-field modeling for dilute alloy solidification involving diffusion in the solid

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

Volumn 79, Issue 3, 2009, Pages

  Ohno, Munekazu ^a   Matsuura, Kiyotaka ^a  

^a HOKKAIDO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ALLOYING; CRYSTALLIZATION; DIFFUSION; PHASE INTERFACES; SOLIDIFICATION;

ANTI-TRAPPING CURRENTS; ARBITRARY VALUES; CONVERGENCE TESTS; DIFFUSIVITIES; DILUTE ALLOYS; EXCELLENT PERFORMANCE; INTERFACE EFFECTS; INTERFACE THICKNESS; INTERPOLATING FUNCTIONS; ISOTHERMAL DENDRITES; PHASE-FIELD MODELING; PHASE-FIELD MODELS; SOLIDIFICATION PROCESS; SPURIOUS EFFECTS;

ASYMPTOTIC ANALYSIS;

EID: 63249092680     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.031603     Document Type: Article

References (49)

1. A. Karma, Encyclopedia of Materials Science and Technology (Elsevier, Oxford, 2001);
2. L.-Q. Chen, Annu. Rev. Mater. Sci. 32, 113 (2002); 10.1146/annurev. matsci.32.112001.132041
3. W. J. Boettinger, J. A. Warren, C. Beckermann, and A. Karma, Annu. Rev. Mater. Sci. 32, 163 (2002); 10.1146/annurev.matsci.32.101901.155803
4. M. Ode, S. G. Kim and T. Suzuki, ISIJ Int. 41, 1076 (2001). 10.2355/isijinternational.41.1076
5. A. Jacot and M. Rappaz, Acta Mater. 50, 1909 (2002); 10.1016/S1359- 6454(01)00442-6
6. W. Wang, P. D. Lee, and M. McLean, Acta Mater. 51, 2971 (2003);
7. J. A. Sethian and J. Strain, J. Comput. Phys. 98, 231 (1992); 10.1016/0021-9991(92)90140-T
8. R. Almgren, J. Comput. Phys. 106, 337 (1993).
9. R. Kobayashi, Physica D 63, 410 (1993); 10.1016/0167-2789(93)90120-P
10. G. B. McFadden, A. A. Wheeler, R. J. Braun, S. R. Coriell, and R. F. Sekerka, Phys. Rev. E 48, 2016 (1993); 10.1103/PhysRevE.48.2016
11. A. A. Wheeler, B. T. Murray, and R. J. Schaefer, Physica D 66, 243 (1993); 10.1016/0167-2789(93)90242-S
12. S.-L. Wang, R. F. Sekerka, A. A. Wheeler, B. T. Murray, S. R. Coriell, R. J. Braun, and G. B. McFadden, Physica D 69, 189 (1993). 10.1016/0167-2789(93) 90189-8
13. A. A. Wheeler, W. J. Boettinger, and G. B. McFadden, Phys. Rev. A 45, 7424 (1992); 10.1103/PhysRevA.45.7424
14. A. A. Wheeler, W. J. Boettinger, and G. B. McFadden, Phys. Rev. E 47, 1893 (1993); 10.1103/PhysRevE.47.1893
15. A. Karma, Phys. Rev. E 49, 2245 (1994); 10.1103/PhysRevE.49.2245
16. J. A. Warren and W. J. Boettinger, Acta Metall. Mater. 43, 689 (1995). 10.1016/0956-7151(94)00285-P
17. I. Steinbach, F. Pezzola, B. Nestler, M. Seeßelberg, R. Prieler, G. J. Schmitz and J. L. L. Rezende, Physica D 94, 135 (1996); 10.1016/0167- 2789(95)00298-7
18. J. Tiaden, B. Nestler, H. J. Diepers and I. Steinbach, Physica D 115, 73 (1998); 10.1016/S0167-2789(97)00226-1
19. I. Steinbach and F. Pezzolla, Physica D 134, 385 (1999); 10.1016/S0167-2789(99)00129-3
20. B. Neslter, A. A. Wheeler, and H. Gracke, Comput. Mater. Sci. 26, 111 (2003); 10.1016/S0927-0256(02)00407-X
21. S. G. Kim, W. T. Kim, T. Suzuki, and M. Ode, J. Cryst. Growth 261, 38 (2004); 10.1016/j.jcrysgro.2003.09.017
22. B. Boettger, J. Eiken, and I. Steinbach, Acta Mater. 54, 2697 (2006); 10.1016/j.actamat.2006.02.008
23. R. S. Qin, E. R. Wallach, and R. C. Thomson, J. Cryst. Growth 279, 163 (2005); 10.1016/j.jcrysgro.2005.02.005
24. J. Eiken, B. Bottger, and I. Steinbach, Phys. Rev. E 73, 066122 (2006). 10.1103/PhysRevE.73.066122
25. G. Caginalp, Phys. Rev. A 39, 5887 (1989). 10.1103/PhysRevA.39.5887
26. S.-L. Wang and R. F. Sekerka, Phys. Rev. E 53, 3760 (1996). 10.1103/PhysRevE.53.3760
27. A. Karma and W.-J. Rappel, Phys. Rev. E 53, R3017 (1996); 10.1103/PhysRevE.53.R3017
28. A. Karma and W.-J. Rappel, Phys. Rev. E 57, 4323 (1998). 10.1103/PhysRevE.57.4323
29. S. G. Kim, W. T. Kim, and T. Suzuki, Phys. Rev. E 60, 7186 (1999). 10.1103/PhysRevE.60.7186
30. R. F. Almgren, SIAM J. Appl. Math. 59, 2086 (1999). 10.1137/ S0036139997330027
31. A. Karma, Phys. Rev. Lett. 87, 115701 (2001). 10.1103/PhysRevLett.87. 115701
32. B. Echebarria, R. Folch, A. Karma, and M. Plapp, Phys. Rev. E 70, 061604 (2004). 10.1103/PhysRevE.70.061604
33. J. C. Ramirez, C. Beckermann, A. Karma, and H.-J. Diepers, Phys. Rev. E 69, 051607 (2004). 10.1103/PhysRevE.69.051607
34. M. Greenwood, M. Haataja, and N. Provatas, Phys. Rev. Lett. 93, 246101 (2004); 10.1103/PhysRevLett.93.246101
35. C. W. Lan and C. J. Shih, Phys. Rev. E 69, 031601 (2004); 10.1103/PhysRevE.69.031601
36. J. C. Ramirez and C. Beckermann, Acta Mater. 53, 1721 (2005); 10.1016/j.actamat.2004.12.021
37. A. Badillo and C. Beckermann, Acta Mater. 54, 2015 (2006); 10.1016/j.actamat.2005.12.025
38. C. Tong, M. Greenwood, and N. Provatas, Phys. Rev. B 77, 064112 (2008). 10.1103/PhysRevB.77.064112
39. R. Folch and M. Plapp, Phys. Rev. E 68, 010602 (R) (2003); 10.1103/PhysRevE.68.010602
40. R. Folch and M. Plapp, Phys. Rev. E 72, 011602 (2005); 10.1103/PhysRevE.72.011602
41. H. Emmerich and R. Siquieri, J. Phys.: Condens. Matter 18, 11121 (2006); 10.1088/0953-8984/18/49/006
42. M. Plapp, J. Cryst. Growth 303, 49 (2007); 10.1016/j.jcrysgro.2006.12.064
43. R. Siquieri and H. Emmerich, Philos. Mag. Lett. 87, 829 (2007). 10.1080/09500830701397586
44. S. G. Kim, Acta Mater. 55, 4391 (2007). 10.1016/j.actamat.2007.04.004
45. W. Kurz and D. J. Fisher, Fundamentals of Solidification (Trans Tech, Aedermannsdorf, Switzerland, 1992).
46. A. Gopinath, R. C. Armstrong, and R. A. Brown, J. Cryst. Growth 291, 272 (2006). 10.1016/j.jcrysgro.2006.03.001
47. R. Folch, J. Casademunt, A. Hernández-Machado, and L. Ramírez-Piscina, Phys. Rev. E 60, 1724 (1999); 10.1103/PhysRevE.60.1724
48. K. R. Elder, M. Grant, N. Provatas, and J. M. Kosterlitz, Phys. Rev. E 64, 021604 (2001). 10.1103/PhysRevE.64.021604
49. A. Barbieri and J. S. Langer, Phys. Rev. A 39, 5314 (1989). 10.1103/PhysRevA.39.5314