Morphology: From sharp interface to phase field models

Journal of Crystal Growth

Volumn 264, Issue 4, 2004, Pages 530-540

  Sekerka, Robert F ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

A1. Computer simulation; A1. Crystal morphology; A1. Morphological stability; A1. Phase field

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; CAPILLARITY; COMPUTER SIMULATION; CRYSTALS; INTERFACES (MATERIALS); MATHEMATICAL MODELS; MELTING; MICROSCOPIC EXAMINATION; PRECIPITATION (CHEMICAL);

CRYSTAL MORPHOLOGY; MORPHOLOGICAL STABILITY; PHASE-FIELD;

CRYSTAL GROWTH;

EID: 1842430848     PISSN: 00220248     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcrysgro.2003.12.033     Document Type: Conference Paper

References (76)

1. Walter E. Kingston (Ed.), Conyers Herring, surface tension as a motivation for sintering, The Physics of Powder Metallurgy, a symposium held at Bayside, L.I. New York, 24-26 August, 1949, McGraw-Hill, New York 1951, p. 143.
2. R. Gomer, C. S. Smith (Eds.), Conyers Herring, the use of classical macroscopic concepts in surface-energy problems, Structure and Properties of Solid Surfaces, a Conference Arranged by the National Research Council, Lake Geneva, WI, September 1952, University of Chicago Press, Chicago, 1953, p. 5.
3. Ivantsov G.P. Dokl. Akad. Nauk SSSR. 58:1947;567 G. Horvay, (English Transl., General Electric Research Report No. 60-RL-(2511M), Schenectady, NY, 1960).
4. Ivantsov G.P. Dokl. Akad. Nauk SSSR. 58:1947;567 G. Horvay, (English Transl., General Electric Research Report No. 60-RL-(2511M), Schenectady, NY, 1960).
5. Ivantsov G.P. Dokl. Akad. Nauk SSSR. 83:1952;573.
6. Horvay G., Cahn J.W. Acta Metal. 9:1961;695.
7. Ham F.S. Quart. J. Appl. Math. 17:1959;137.
8. Canright D., H. Davis S. Metal. Trans. 20A:1989;225.
9. R.F. Sekerka, Shun-Lien Wang, Moving phase boundary problems, in: H.I. Aaronson (Ed.), Lectures on the Theory of Phase Transformations, 2nd Edition, TMS, Warrendale, 1999, p. 231.
10. Chernov A.A. Sov. Phys. Crystallogr. 8:1964;401.
11. F.C. Frank, On the kinematic theory of crystal growth and dissolution processes, in: R.H. Doremus, B.W. Roberts, D. Turnbull (Eds.), Growth and Perfection in Crystals, Wiley, New York, 1958, p. 411.
12. Hoffman D.W., Cahn J.W. Surf. Sci. 31:1972;368.
13. Cahn J.W., Hoffman D.W. Acta. Metall. 22:1974;1205.
14. Angenent S., Gurtin M.E. Arch. Ration. Mech. Anal. 108:1989;323.
15. Yokoyama Etsuro, Sekerka R.F. J. Crystal Growth. 125:1992;389.
16. Mullins W.W., Sekerka R.F. J. Appl. Phys. 34:1963;323.
17. Langer J.S., Müller-Krumbhaar H. J. Crystal Growth. 42:1977;11.
18. Langer J.S., Sekerka R.F., Fujioka T. J. Crystal Growth. 44:1978;414.
19. Barbieri A., Langer J.S. Phys Rev. A39:1989;5314.
20. Ben Amar M., Pelcé P. Phys. Rev. A39:1989;4263.
21. Y. Pomeau, M. Ben Amar, Dendritic growth and related topics, in: C. Godrèche (Ed.), Solids Far From Equilibrium, Cambridge University Press, Cambridge, 1992, p. 365.
22. Mullins W.W., Sekerka R.F. J. Appl. Phys. 35:1964;444.
23. S.R. Coriell, G.B. McFadden, Morphological stability, in: D.T.J. Hurle (Ed.), Handbook of Crystal Growth 1a Fundamentals, Transport and Stability, North-Holland, Amsterdam, 1993, p. 785.
24. J.S. Langer, August 1978, unpublished notes.
25. Collins J.B., Levine H. Phys. Rev. B31:1985;6119.
26. J.S. Langer, in: G. Grinstein, G. Mazenko (Eds.), Directions in Condensed Matter Physics, World Scientific, Singapore, 1986, p. 165.
27. Cahn J.W., Hilliard J.E. J. Chem. Phys. 28:1958;258.
28. Wang S-L., Sekerka R.F., Wheeler A.A., Murray B.T., Coriell S.R., Braun R.J., McFadden G.B. Physica D. 69:1993;189.
29. McFadden G.B., Wheeler A.A., Anderson D.M. Physica D. 144:2000;154.
30. Karma A., Rappel W.-J. Phys. Rev. E. 53:1996;3017.
31. McFadden G.B., Wheeler A.A., Braun R.J., Coriell S.R., Sekerka R.F. Phys. Rev. E48:1993;2016.
32. Wheeler A.A., McFadden G.B. Eur. J. Appl. Math. 7:1996;367.
33. Wheeler A.A., McFadden G.B. Proc. Roy. Soc. London A. 453:1997;1611.
34. R.F. Sekerka, Fundamentals of phase field theory, in: K. Sato, Y. Furukawa, K. Nakajima (Eds.), Advances in Crystal Growth Research, Elsevier, Amsterdam, 2001, p. 21.
35. Wheeler A.A., Boettinger W.J., McFadden G.B. Phys. Rev. A. 45:1992;7424.
36. A.A. Wheeler, W.J. Boettinger, in: M.E. Gurtin, G.B. McFadden, (Eds.), On the Evolution of Phase Boundaries, The IMA Volumes in Mathematics and its Applications, Vol. 43, Springer, Berlin, 1992, p. 127.
37. Wheeler A.A., Boettinger W.J., McFadden G.B. Phys. Rev. E. 47:1993;1893.
38. W.J. Boettinger, A.A. Wheeler, G.B. McFadden, R. Kobayashi, in: S.P. Marsh, C.S. Pande (Eds.), Modeling of Coarsening and Grain Growth, TMS, Warrendale, 1993, p. 45.
39. Bi Z., Sekerka R.F. Physica A. 261:1998;95.
40. Charach Ch., Fife P.C. SIAM. J. Appl. Math. 58:1998;1826.
41. Charach Ch., Fife P.C. Open Syst. Inform. Dyn. 5:1998;99.
42. Warren J.A., Boettinger W.J. Acta Metall. Mater. 43:1995;689.
43. Conti M. Phys. Rev. E. 56:1997;3197.
44. J.A. Warren, W.J. Boettinger, in: M. Cross, J. Campbell (Eds.), Modeling of Casting, Welding and Advanced Solidification Processes, Vol. VII, TMS, Warrendale, 1995, p. 601.
45. J.A. Warren, W.J. Boettinger, in: J. Beach, H. Jones (Eds.), Solidification Processing, Department of Engineering Materials, University of Sheffeld, UK, 1997, p. 422.
46. Bi Zhiqiang, F. Sekerka R. J. Crystal Growth. 127-239:2002;138.
47. Gurtin M.E., Polignone D., Viñals J. Math. Models Meth. Appl. Sci. 6:1996;815.
48. Anderson D.M., McFadden G.B. Phys. Fluids. 9:1997;1870.
49. Anderson D.M., McFadden G.B., Wheeler A.A. Annu. Rev. Fluid Mech. 30:1998;139.
50. Anderson D.M., McFadden G.B., Wheeler A.A. Physica D. 135:2000;175.
51. R.F. Sekerka, Z. Bi, Phase field model of multicomponent alloy with hydrodynamics, in: M.K. Smith, M.J. Mixis, G.B. McFadden, G.P. Neitzel, D.R. Canright (Eds.), Interfaces for the Twenty-First Century, Imperial College Press, London, 2001, p. 147.
52. Anderson D.M., McFadden G.B., Wheeler A.A. Physica D. 2711:2001;1.
53. D.M. Anderson, G.B. McFadden, A.A. Wheeler, A phase-field model of solidification with convection: numerical simulations, in: M.K. Smith, M.J. Mixis, G.B. McFadden, G.P. Neitzel, D.R. Canright (Eds.), Interfaces for the Twenty-First Century, Imperial College Press, London, 2001, p. 131.
54. Tönhardt R., Amberg G. J. Crystal Growth. 194:1998;406.
55. Tönhardt R., Amberg G. J. Crystal Growth. 213:2000;161.
56. Tönhardt R., Amberg G. Phys. Rev. E62:2000;828.
57. Beckermann C., Diepers H.J., Steinbach I., Karma A., Tong X. J. Comput. Phys. 154:1999;468.
58. Boettinger W.J., Warren J.A., Beckermann C., Karma A. Annu. Rev. Mater. Res. 32:2002;163.
59. Braun R.A., Murray B.T. J. Crystal Growth. 174:1997;41.
60. Provatas N., Goldenfeld N., Dantzig J. J. Comput. Phys. 148:1999;265.
61. Schmidt A. J. Comput. Phys. 125:1996;293.
62. Provatas N., Goldenfeld N. J. Dantzig, Phys. Rev. Lett. 80:1998;3308.
63. Jeong Jun-Ho, Goldenfeld N., Dantzig J.A. Phys. Rev. E64:2001;41602.
64. Karma A., Plapp M. Phys. Rev. Lett. 84:2000;1740.
65. Karma A., H. Lee Youngyih, Plapp M. Phys. Rev. E. 61:2000;3996.
66. Boettinger W.J., Wheeler A.A., Murray B.T., McFadden G.B. Mater. Sci. Eng. A. 178:1994;217.
67. Conti M. Phys. Rev. E. 55:1997;701.
68. Conti M. Phys. Rev. E. 55:1997;765.
69. Ahmad N.A., Wheeler A.A., Boettinger B.J., McFadden G.B. Phys. Rev. E. 58:1998;3436.
70. Charach Ch., Chen C.K., Fife P.C. J. Stat. Phys. 95:1999;1141.
71. Charach Ch., Fife P.C. J. Crystal Growth. 198/199:1999;1267.
72. McFadden G.B., Wheeler A.A., Anderson D.M. Physica D. 144:2000;154.
73. Karma A. Phys. Rev. Lett. 87:2001;115701.
74. Kobayashi R., Warren J.A., Carter W.C. Physics D. 140:2000;141.
75. Kassner K., Misbah C., Müller J., Kappey J., Kohlert P. J. Crystal Growth. 225:2001;289.
76. Gránásy L., Börzsönyi T., Pusztai T. J. Crystal Growth. 237-239:2002;1813.