Remarks on some open problems in phase-field modelling of solidification

Philosophical Magazine

Volumn 91, Issue 1, 2011, Pages 25-44

  Plapp, Mathis ^a  

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

Author keywords

grain boundary motion; nucleation; phase field models; polycrystals; solidification

Indexed keywords

ANTI-TRAPPING CURRENTS; EQUATION OF MOTION; FIELD MODEL; GRAIN BOUNDARY MOTIONS; IN-PHASE; INTERFACE EFFECT; MODELLING APPROACHES; OPEN PROBLEMS; ORIENTATION FIELDS; PHASE-FIELD APPROACHES; PHASE-FIELD MODELS; POLYCRYSTALLINE; POLYCRYSTALLINE SOLIDIFICATION; QUANTITATIVE DESCRIPTION; STANDARD PROCEDURES; THIN-INTERFACE LIMIT;

EQUATIONS OF MOTION; GRAIN BOUNDARIES; GRAIN SIZE AND SHAPE; NUCLEATION; POLYCRYSTALS; SOLIDIFICATION;

PHASE INTERFACES;

EID: 78249239780     PISSN: 14786435     EISSN: 14786443     Source Type: Journal    
DOI: 10.1080/14786435.2010.486757     Document Type: Article

References (61)

1. W. J. Boettinger, J. A. Warren, C. Beckermann and A. Karma, Annu. Rev. Mater. Res. 32(2002) p. 163.
2. L. Q. Chen, Annu. Rev. Mater. Res. 32(2002) p. 113.
3. L. Gránásy, T. Pusztai and J. A. Warren, J. Phys. Cond. Mat. 16(2004) p. R1205.
4. M. Plapp, J. Cryst. Growth 303(2007) p. 49.
5. I. Singer-Loginova and H. M. Singer, Rep. Prog. Phys. 71(2008) p. 106501.
6. I. Steinbach, Model. Simul. Mater. Sci. Eng. 17(2009) p. 073001.
7. H. Emmerich, Adv. Phys. 57(2008) p. 1.
8. A. Karma and W. J. Rappel, Phys. Rev. e 53(1996) p. R3017.
9. A. Karma and W. J. Rappel, Phys. Rev. e 57(1998) p. 4323.
10. J. Bragard, A. Karma, Y. Y. Lee and M. Plapp, Interface Sci. 10(2002) p. 121.
11. A. Karma, Y. H. Lee and M. Plapp, Phys. Rev. e 61(2000) p. 3996.
12. N. Provatas, N. Goldenfeld and J. Dantzig, J. Comput. Phys. 148(1999) p. 265.
13. R. F. Almgren, SIAM J. Appl. Math. 59(1999) p. 2086.
14. A. Karma, Phys. Rev. Lett. 87(2001) 115701.
15. B. Echebarria, R. Folch, A. Karma and M. Plapp, Phys. Rev. e 70(2004) p. 061604.
16. R. Folch and M. Plapp, Phys. Rev. e 68(2003) p. R010602.
17. R. Folch and M. Plapp, Phys. Rev. e 72(2005) p. 011602.
18. S. G. Kim, Acta Mater. 55(2007) p. 4391.
19. A. Gopinath, R. C. Armstrong and R. A. Brown, J. Cryst. Growth 291(2006) p. 272.
20. M. Ohno and K. Matsuura, Phys. Rev. e 79(2009) p. 031603.
21. T. Ducousso, Étude de la solidification dirigée par la méthode du champ de phase: comparaison théorie-expérience pour un alliage binaire dilué, PhD thesis, Université Paul Cézanne, Marseille, France, 2009.
22. P. L. Kapitza, Zh. Eksp. Teor. Fiz. 11(1941) p. 1.
23. P. Maugis and G. Martin, Phys. Rev. B 49(1994) p. 11580.
24. E. T. Swartz and R. O. Pohl, Rev. Mod. Phys. 61(1989) p. 605.
25. P. E. Wolf, D. O. Edwards and S. Balibar, J. Low Temp. Phys. 51(1983) p. 489.
26. J. L. Barrat and F. Chiaruttini, Mol. Phys. 101(2003) p. 1605.
27. L. Xue, P. Keblinski, S. R. Phillpot, S. U. S. Choi and J. A. Eastman, J. Chem. Phys. 118(2003) p. 337.
28. I. Steinbach, F. Pezzolla, B. Nestler, M. Seeßelberg, R. Prieler, G. J. Schmitz and J. L. L. Rezende, Physica D 94(1996) p. 135.
29. D. Fan and L. Q. Chen, Acta Mater. 45(1997) p. 611.
30. H. Garcke, B. Nestler and B. Stoth, SIAM J. Appl. Math. 60(1999) p. 295.
31. I. Steinbach and F. Pezzolla, Physica D 134(1999) p. 385.
32. N. Moelans, B. Blanpain and P. Wollants, Phys. Rev. B 78(2008) p. 024113.
33. J. Eiken, B. Böttger and I. Steinbach, Phys. Rev. e 73(2006) p. 066122.
34. L. Vanherpe, N. Moelans, B. Blanpain and S. Vandewalle, Phys. Rev. e 76(2007) p. 056702.
35. R. Kobayashi, J. A. Warren and W. C. Carter, Physica D 140(2000) p. 141.
36. J. A. Warren, R. Kobayashi, A. E. Lobovsky and W. C. Carter, Acta Mater. 51(2003) p. 6035.
37. T. Pusztai, G. Bortel and L. Gránásy, Europhys. Lett. 71(2005) p. 131.
38. R. Kobayashi and J. A. Warren, Physica A 356(2005) p. 127.
39. J. Mellenthin, Phase-field modelling of polycrystalline solidification, PhD thesis, École Polytechnique, Palaiseau, France, 2007.
40. P.-G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed., Clarendon Press, Oxford, 1993.
41. E. Kröner, Continuum Theory of Defects, in Les Houches Session XXXV, R. Balian, M. Kléman and J. P. Poirier, eds., North Holland, Amsterdam, 1981, p. 215.
42. Y. Wang and J. Li, Acta Mater. 58(2010) p. 1212.
43. H. Henry, J. Mellenthin and M. Plapp (2010); unpublished.
44. K. A. Wu and P. Voorhees (2010); unpublished.
45. K. R. Elder and M. Grant, Phys. Rev. e 70(2004) p. 051605.
46. M. Upmanyu, D. J. Srolovitz, A. E. Lobkovsky, J. A. Warren and W. C. Carter, Acta Mater. 54(2006) p. 1707.
47. L. Gránásy, T. Pusztai, G. Tegze, J. A. Warren and J. F. Douglas, Phys. Rev. e 72(2005) 011605.
48. L. Gránásy, T. Pusztai, J. A. Warren, J. F. Douglas, T. Börzsönyi and V. Ferreiro, Nature Mater. 2(2003) p. 92.
49. A. Karma and W. J. Rappel, Phys. Rev. e 60(1999) p. 3614.
50. T. Börzsönyi, T. Toth-Katona, A. Buka and L. Granasy, Phys. Rev. Lett. 83(1999) p. 2853.
51. T. Börzsönyi, T. Tóth-Katona, A. Buka and L. Gránasy, Phys. Rev. e 62(2000) p. 7817.
52. L. Gránásy, T. Börzsönyi and T. Pusztai, Phys. Rev. Lett. 88(2002) p. 206105.
53. R. Siquieri and H. Emmerich, Phil. Mag. Lett. 87(2007) p. 829.
54. L. Gránásy, T. Pusztai, D. Saylor and J. A. Warren, Phys. Rev. Lett. 98(2007) p. 035703.
55. J. A. Warren, T. Pusztai, L. Környei and L. Gránásy, Phys. Rev. B 79(2009) p. 014204.
56. G. I. Toth and L. Gránásy, J. Chem. Phys. 127(2007) p. 074709.
57. G. I. Toth and L. Gránásy, J. Chem. Phys. 127(2007) p. 074710.
58. G. Parisi, Statistical Field Theory, Westview Press, Boulder, 1998.
59. J. Borrill and M. Gleiser, Nuclear Physics B 483(1997) p. 416.
60. Q. Bronchart, Y. le Bouar and A. Finel, Phys. Rev. Lett. 100(2008) p. 015702.
61. J. J. Hoyt, M. Asta and A. Karma, Mat. Sci. Eng. R 41(2003) p. 121.