Unified derivation of phase-field models for alloy solidification from a grand-potential functional

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

Volumn 84, Issue 3, 2011, Pages

  Plapp, Mathis ^a  

^a LABORATOIRE DE PHYSIQUE DE LA MATIÈRE CONDENSÉE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALLOY SOLIDIFICATION; CONCENTRATION FIELDS; DIFFUSE INTERFACE; DYNAMICAL VARIABLES; ENERGY FUNCTIONALS; INTERFACE THICKNESS; INTERMEDIATE STATE; LOCAL COMPOSITIONS; MACROSCOPIC PROPERTIES; PHASE FIELDS; PHASE-FIELD MODELS; PURE SUBSTANCES;

ALLOYING; ALLOYS; NUMERICAL METHODS; PHASE DIAGRAMS; SOLIDIFICATION; FREE ENERGY; INTERFACE STATES; MATHEMATICAL MODELS;

PHASE INTERFACES;

EID: 80053045884     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.84.031601     Document Type: Article

References (40)

1. A. Karma and W.-J. Rappel, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.57.4323 57, 4323 (1998).
2. W. J. Boettinger, J. A. Warren, C. Beckermann, and A. Karma, Annu. Rev. Mater. Res. ARMRCU 1531-7331 10.1146/annurev.matsci.32.101901.155803 32, 163 (2002). (Pubitemid 34992569)
3. M. Plapp, J. Cryst. Growth JCRGAE 0022-0248 10.1016/j.jcrysgro.2006.12. 064 303, 49 (2007). (Pubitemid 46550501)
4. I. Steinbach, Modell. Simul. Mater. Sci. Eng. MSMEEU 0965-0393 10.1088/0965-0393/17/7/073001 17, 073001 (2009).
5. J. S. Langer, in Directions in Condensed Matter Physics, edited by, G. Grinstein, and, G. Mazenko, (World Scientific, Singapore, 1986), p. 165.
6. G. Caginalp, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.39.5887 39, 5887 (1989).
7. R. Kobayashi, Physica D PDNPDT 0167-2789 10.1016/0167-2789(93)90120-P 63, 410 (1993).
8. A. Karma and A. Sarkissian, Metall. Mater. Trans. A MMTAEB 1073-5623 10.1007/BF02648952 27, 635 (1996).
9. A. Karma, Y. H. Lee, and M. Plapp, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.61.3996 61, 3996 (2000).
10. A. A. Wheeler, W. J. Boettinger, and G. B. McFadden, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.45.7424 45, 7424 (1992).
11. G. Caginalp and W. Xie, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.48.1897 48, 1897 (1993).
12. J. A. Warren and W. J. Boettinger, Acta Metall. Mater. AMATEB 0956-7151 10.1016/0956-7151(94)00285-P 43, 689 (1995).
13. J. Ni and C. Beckermann, Metall. Trans. B AMATEB 0360-2141 10.1007/BF02651234 22, 349 (1991).
14. J. Tiaden, B. Nestler, H.-J. Diepers, and I. Steinbach, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(97)00226-1 115, 73 (1998).
15. C. Beckermann, H.-J. Diepers, I. Steinbach, A. Karma, and X. Tong, J. Comput. Phys. JCTPAH 0021-9991 10.1006/jcph.1999.6323 154, 468 (1999).
16. S. G. Kim, W. T. Kim, and T. Suzuki, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.60.7186 60, 7186 (1999).
17. B. Echebarria, R. Folch, A. Karma, and M. Plapp, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.70.061604 70, 061604 (2004). (Pubitemid 40219639)
18. J. C. Ramirez, C. Beckermann, A. Karma, and H.-J. Diepers, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.69.051607 69, 051607 (2004).
19. J. S. Langer, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.52.1 52, 1 (1980).
20. W. Losert, D. A. Stillman, H. Z. Cummins, P. Kopczyński, W.-J. Rappel, and A. Karma, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.58.7492 58, 7492 (1998).
21. M. Plapp and M. Dejmek, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2003-10078-2 65, 276 (2004). (Pubitemid 38069273)
22. R. Folch and M. Plapp, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.72. 011602 72, 011602 (2005). (Pubitemid 41521209)
23. A. Karma, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.115701 87, 115701 (2001).
24. S. G. Kim, Acta Mater. ACMAFD 1359-6454 10.1016/j.actamat.2007.04.004 55, 4391 (2007). (Pubitemid 46977810)
25. O. Penrose and P. C. Fife, Physica D PDNPDT 0167-2789 10.1016/0167-2789(90)90015-H 43, 44 (1990).
26. S.-L. Wang, R. F. Sekerka, A. A. Wheeler, B. T. Murray, S. R. Coriell, R. J. Braun, and G. B. McFadden, Physica D PDNPDT 0167-2789 10.1016/0167-2789(93) 90189-8 69, 189 (1993).
27. G. J. Fix, in Free Boundary Problems: Theory and Applications, edited by, A. Fasano, and, M. Primicerio, (Piman, Boston, 1983), p. 580.
28. J. B. Collins and H. Levine, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.31.6119 31, 6119 (1985).
29. R. Evans, Adv. Phys. ADPHAH 0001-8732 10.1080/00018737900101365 28, 143 (1979).
30. M. Conti, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.64.051601 64, 051601 (2001).
31. M. Conti and M. Fermani, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.67.026117 67, 026117 (2003).
32. J. S. Langer, in Solids Far From Equilibrium, edited by, C. Godrèche, (Edition Aléa Saclay, Cambridge, UK, 1992), p. 297.
33. L. S. Darken, Trans. AIME 175, 184 (1948).
34. C. Tong, M. Greenwood, and N. Provatas, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.064112 77, 064112 (2008).
35. R. Folch and M. Plapp, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.68. 010602 68, 010602 (R) (2003).
36. M. J. Aziz, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.329867 53, 1158 (1982). (Pubitemid 12476851)
37. J. Eiken, B. Böttger, and I. Steinbach, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.73.066122 73, 066122 (2006). (Pubitemid 43938079)
38. Y. Sun and C. Beckermann, Physica D PDNPDT 0167-2789 10.1016/j.physd. 2004.09.003 198, 281 (2004).
39. Y. Sun and C. Beckermann, Physica D PDNPDT 0167-2789 10.1016/j.physd. 2008.06.010 237, 3089 (2008).
40. D. M. Anderson, G. B. McFadden, and A. A. Wheeler, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(99)00109-8 135, 175 (2000).