Phase-field approach to polycrystalline solidification including heterogeneous and homogeneous nucleation

Journal of Physics Condensed Matter

Volumn 20, Issue 40, 2008, Pages

  Pusztai, Taḿs ^a   Tegze, György ^b   Tóth, Gyula I ^a   Környei, Ĺszló ^a   Bansel, Gurvinder ^b   Fan, Zhungyun ^b   Gŕńsy, Ĺszló ^b  

^a WIGNER RESEARCH CENTRE FOR PHYSICS   (Hungary)

^b BRUNEL UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; PHASE INTERFACES; SOLIDIFICATION;

CRYSTALLOGRAPHIC ORIENTATIONS; EULER-LAGRANGE EQUATIONS; HETEROGENEOUS NUCLEATION; HOMOGENEOUS NUCLEATION; PHASE-FIELD APPROACHES; POLYCRYSTALLINE SOLIDIFICATION; POLYCRYSTALLINE STRUCTURE; QUATERNION REPRESENTATION;

NUCLEATION;

EID: 54749124341     PISSN: 09538984     EISSN: 1361648X     Source Type: Journal    
DOI: 10.1088/0953-8984/20/40/404205     Document Type: Article

References (108)

1. Abramoff M D, Magelhaes P J and Ram S J 2004 Biophotomics Int. 11 36
2. Athreya B P, Goldenfeld N and Dantzig J A 2006 J. Stat. Phys. 125 1019
3. Athreya B P, Goldenfeld N, Dantzig J A, Greenwood M and Provatas N 2007 Phys. Rev. E 76 056706
4. Auer S and Frenkel D 2001a Nature 409 1020
5. Auer S and Frenkel D 2001b Nature 413 71
6. Beltram-Sanchez L and Stefanescu D M 2004 Metall. Mater. Trans. A 35 2471
7. Birnie D P III and Weinberg M C 1995 J. Chem. Phys. 103 3742
8. Boettinger W J, Warren J A, Beckermann C and Karma A 2002 Annu. Rev. Mater. Res. 32 163
9. Börzsönyi T, Tóth-Katona T, Buka and Grnsy L 1999 Phys. Rev. Lett. 83 1853
10. Börzsönyi T, Tóth-Katona T, Buka and Grnsy L 2000 Phys. Rev. E 62 7817
11. Bouissou Ph, Chiffaudel A, Perrin B and Tabeling P 1990 Europhys. Lett. 13 89
12. Broughton J Q and Gilmer G H 1986 J. Chem. Phys. 84 5749
13. Cacciuto A, Auer S and Frenkel D 2003 J. Chem. Phys. 119 7467
14. Cahn J W and Hilliard J E 1958 J. Chem. Phys. 28 258
15. Cahn R V 2001 The Coming of Materials Science (Oxford: Pergamon)
16. Chen L Q 2002 Annu. Rev. Mater. Res. 32 113
17. Cheng Z, Chaikin P M, Zhu J, Russel W B and Meyer W V 2002 Phys. Rev. Lett. 88 015501
18. Christian J W 1981 Transformations in Metals and Alloys (Oxford: Pergamon)
19. Davidchack R L and Laird B B 1998 J. Chem. Phys. 108 9452
20. Davidchack R L and Laird B B 2000 Phys. Rev. Lett. 85 4751
21. Davidchack R L, Morris J R and Laird B B 2006 J. Chem. Phys. 125 094710
22. Diepers H J, Ma D and Steinbach I 2002 J. Cryst. Growth 237-239 149
23. Elder K R and Grant M 2004 Phys. Rev. E 70 051605
24. Elder K R, Katakowski M, Haataja M and Grant M 2002 Phys. Rev. Lett. 88 245701
25. Elder K R, Provatas N, Berry J, Stefanovic P and Grant M 2007 Phys. Rev. B 75 064107
26. Fan D and Chen L Q 1996 Acta Mater. 45 611
27. Folch R and Plapp M 2003 Phys. Rev. E 68 010602
28. Folch R and Plapp M 2005 Phys. Rev. E 72 011602
29. Geil P H 1963 Polymer Single Crystals (New York: Wiley)
30. Goldenfeld N, Athreya B P and Dantzig J A 2005 Phys. Rev. E 72 020601
31. Grnsy L, Börzsönyi T and Pusztai T 2002 Phys. Rev. Lett. 88 206105
32. Grnsy L, Börzsönyi T and Pusztai T 2003c Interface and Transport Dynamics, Computational Modelling (Springer Lecture Notes in Computational Science and Engineering vol 32) ed H Emmerich, B Nestler and M Schreckenberg (Berlin: Springer) p190
33. Grnsy L and Pusztai T 2002 J. Chem. Phys. 117 10121
34. Grnsy L, Pusztai T, Börzsönyi T, Warren J A and Douglas J F 2004b Nat. Mater. 3 635
35. Grnsy L, Pusztai T, Saylor D and Warren J A 2007 Phys. Rev. Lett. 98 035703
36. Grnsy L, Pusztai T, Tegze G, Warren J A and Douglas J F 2005 Phys. Rev. E 72 011605
37. Grnsy L, Pusztai T, Tóth G, Jurek Z, Conti M and Kvamme B 2003a J. Chem. Phys. 119 10376
38. Grnsy L, Pusztai T, Tóth G I, Tegze G, Warren J A and Douglas J F 2006 Phil. Mag. 86 3757
39. Grnsy L, Pusztai T and Warren J A 2004a J. Phys.: Condens. Matter 16 R1205
40. Grnsy L, Pusztai T, Warren J A, Börzsönyi T, Douglas J F and Ferreiro V 2003b Nat. Mater. 2 92
41. Gunton J D, San Miguel M and Sahni P 1983 Phase Transitions and Critical Phenomena vol 8 ed C Domb and J L Lebowitz (London: Academic) p267
42. Howe J M 1996 Phil. Mag. A 74 761
43. Howe J M and Saka H 2004 MRS Bull. 29 951
44. Hoyt J J, Asta M and Karma A 2003 Mater. Sci. Eng. Rep. R 41 121
45. Huisman W J, Peters J F, Zwanenburg M J, de Wries S A, Derry T E, Abernathy D and van der Veen J F 1997 Nature 390 379
46. Hyde S T, Carnerup A M, Larsson A K, Christy A G and Garcia-Ruiz J M 2004 Physica A 339 24
47. Jacot A and Rappaz M 2002 Acta Mater. 50 1909
48. Jarvis D J and Voss D 2005 Mater. Sci. Eng. 413/414 583
49. Jin L-W, Claborn K A, Kurimoto M, Geday M A, Maezawa I, Sohraby F, Estrada M, Kaminsky W and Kahr B 2003 Proc. Natl Acad. Sci. 100 15297
50. Karma A 2001 Phys. Rev. Lett. 87 115701
51. Karma A and Rappel W-J 1999 Phys. Rev. E 60 3614
52. Khan S R, Finlayson B and Hackett R L 1979 Invest. Urol. 17 199
53. Kim S G 2007 Acta Mater. 55 4391
54. Kim S G, Kim W T and Suzuki T 1999 Phys. Rev. E 60 7186
55. Kobayashi R and Warren J A 2005a TMS Lett. 2 1
56. Kobayashi R and Warren J A 2005b Physica A 356 127
57. Kobayashi R, Warren J A and Carter W C 1998 Physica D 119 415
58. Kobayashi R, Warren J A and Carter W C 2000 Physica D 140 141
59. Korn G A and Korn T M 1970 Mathematical Handbook for Scientists and Engineers (New York: McGraw-Hill)
60. Koss M B, LaCombe J C, Chait A, Pines P, Zlatkowski M, Glicksman M E and Kar P 2005 J. Cryst. Growth 279 170
61. Krebs M H R, MacPhee C E, Miller A F, Dunlop I E, Dobson C M and Donald A M 2005 Biophys. J. 88 2013
62. Krill C E and Chen L Q 2002 Acta Mater. 50 3057
63. Laird B B and Haymet A D J 1992 Chem. Rev. 92 1819
64. Lambert C C, Lambert G, Crundwell G and Kantardjieff K 1998 J. Exp. Zool. 282 323
65. Lewis D, Pusztai T, Grnsy L, Warren J and Boettinger W 2004 J. Met. 56 34
66. Li L, Li C Y and Ni C 2006 J. Am. Chem. Soc. 128 1692
67. Li S W, Li X R, Lowengrub J and Glicksman M E 2007 Fluid Dyn. Mater. Process. 2 1
68. Magill J H 2001 J. Mater. Sci. 36 3143
69. Morin B, Elder K R, Sutton M and Grant M 1995 Phys. Rev. Lett. 75 2156
70. Murray B T, Wheeler A A and Glicksman M E 1995 J. Cryst. Growth 154 386
71. Napolitano R E, Meco H and Jung C 2004 J. Met. 56 16
72. Oxtoby D W 1991 Liquids, Freezing and Glass Transition ed J P Hansen et al (Amsterdam: Elsevier) p145
73. Provatas N, Dantzig J A, Athreya B, Chan P, Stefanovic P, Goldenfeld N and Elder K R 2007 J. Met. 59 83
74. Pusztai T and Grnsy L 1998 Phys. Rev. B 57 14110
75. Pusztai T, Bortel G and Grnsy L 2005a Europhys. Lett. 71 131
76. Pusztai T, Bortel G and Grnsy L 2005b Mater. Sci. Eng. A 413/414 412
77. Pusztai T, Bortel G and Grnsy L 2006 Modeling of Casting, Welding and Advanced Solidification Processes-XI ed C A Gandin and M Bellet (Warrendale, PA: The Minerals, Metals and Materials Society) p409
78. Pusztai T, Környei L, Bansel G and Grnsy L 2008 unpublished
79. Qian X and Cummins H Z 1990 Phys. Rev. Lett. 64 3038
80. Ramalingam H, Asta M, van der Walle A and Hoyt J J 2002 Interface Sci. 10 149
81. Schmidt A 1996 J. Comput. Phys. 125 293
82. Shelf C A and Hill C A 2003 J. Cave Karst Studies 65 130
83. Shepilov M P 1990 Sov. Phys. Crystallogr. 35 164
84. Shepilov M P and Baik D S 1994 J. Non-Cryst. Solids 171 141
85. Shih W H, Wang Z Q, Zeng X C and Stroud D 1987 Phys. Rev. A 35 2611
86. Steinbach I, Beckermann C, Kauerauf B, Li Q and Guo J 1999 Acta Mater. 47 971
87. Steinbach I, Pezzola F, Nestler B, Seesselberg M, Prieler M, Schmitz G J and Rezende J L L 1996 Physica D 94 135
88. Tan J and Zabaras N 2006 J. Comput. Phys. 211 36
89. Tan J and Zabaras N 2007 J. Comput. Phys. 226 131
90. Tanaka H 1995 J. Chem. Phys. 103 2361
91. Tanaka H 1996 J. Chem. Phys. 105 10909
92. Tanaka H and Araki T 1998 Phys. Rev. Lett. 81 389
93. Tegze G, Bansel G, Toth G I, Pusztai T, Fan Z and Grnsy L 2008 unpublished
94. Tegze G and Grnsy L 2006 Proc. Modeling of Cating, Welding and Advanced Solidification Processes-XI ed C A Gandin and M Bellet (Warrendale, PA: The Minerals, Metals and Materials Society) p513
95. Tegze G, Pusztai T and Grnsy L 2005 Mater. Sci. Eng. A 413/414 418
96. Tiaden J, Nestler B, Diepers H J and Steinbach I 1998 Physica D 115 73
97. Toxvaerd S 2002 J. Chem. Phys. 117 10303
98. Tryggvason G, Brunner B, Esmaeeli A, Juric D, Al-Rawahi N, Tauber W, Han J, Nas S and Jan Y-J 2001 J. Comput. Phys. 169 708
99. Tupper P F and Grant M 2008 Europhys. Lett. 81 40007
100. van der Veen J F and Reichert H 2004 MRS Bull. 29 958
101. Wang S L, Sekerka R F, Wheeler A A, Murray B T, Coriell S R, Braun R J and McFadden G B 1993 Physica D 69 189
102. Warren J A 2007 personal communication
103. Warren J A, Kobayashi R, Lobkovsky A E and Carter W C 2003 Acta Mater. 51 6035
104. Webb E B, Grest G S and Heine D R 2003 Phys. Rev. Lett. 91 236102
105. Woodhead-Galloway J and Gaskell T 1968 J. Phys. C: Solid State Phys. 1 1472
106. Zacharaissen K E and Hammel H T 1988 Cryobiology 25 143
107. Zhu M-F, Dai T, Lee S-Y and Hong C-P 2008 Comput. Math. Appl. 55 1620
108. Zhu M-F and Hong C-P 2002 Phys. Rev. B 66 155428