On the applicability of the classical nucleation theory in an Ising system

Journal of Chemical Physics

Volumn 111, Issue 15, 1999, Pages 6932-6941

  Shneidman, V A ^a   Jackson, K A ^a   Beatty, K M ^a  

^a University of Arizona   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001423356     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.479985     Document Type: Article

References (82)

1. M. Volmer and A. Weber, Z. Phys. Chem. (Munich) 119, 227 (1926).
2. A. Einstein, Ann. Phys. (Leipzig) 33, 1275 (1910).
3. F. F. Abraham, Homogeneous Nucleation Theory (Academic, New York, 1974).
4. P. Debenedetti, Metastable Liquids (Princeton University Press, Princeton, NJ, 1996).
5. R. M. Westewelt, Phys. Status Solidi B 74, 727 (1976); 76, 31 (1976); I. M. Fishman, Usp. Fiz. Nauk 155, 329 (1987).
6. R. M. Westewelt, Phys. Status Solidi B 74, 727 (1976); 76, 31 (1976); I. M. Fishman, Usp. Fiz. Nauk 155, 329 (1987).
7. R. M. Westewelt, Phys. Status Solidi B 74, 727 (1976); 76, 31 (1976); I. M. Fishman, Usp. Fiz. Nauk 155, 329 (1987).
8. L. Farkas, Z. Phys. Chem. (Munich) 125, 236 (1927); R. Becker and W. Döring, Ann. Phys. (N.Y.) 24, 719 (1935); Ya. B. Zeldovich, Ann. Phys. (N.Y.) 18, 1 (1943); J. Frenkel, Kinetic Theory of Liquids (Oxford University Press, Oxford, 1946).
9. L. Farkas, Z. Phys. Chem. (Munich) 125, 236 (1927); R. Becker and W. Döring, Ann. Phys. (N.Y.) 24, 719 (1935); Ya. B. Zeldovich, Ann. Phys. (N.Y.) 18, 1 (1943); J. Frenkel, Kinetic Theory of Liquids (Oxford University Press, Oxford, 1946).
10. L. Farkas, Z. Phys. Chem. (Munich) 125, 236 (1927); R. Becker and W. Döring, Ann. Phys. (N.Y.) 24, 719 (1935); Ya. B. Zeldovich, Ann. Phys. (N.Y.) 18, 1 (1943); J. Frenkel, Kinetic Theory of Liquids (Oxford University Press, Oxford, 1946).
11. L. Farkas, Z. Phys. Chem. (Munich) 125, 236 (1927); R. Becker and W. Döring, Ann. Phys. (N.Y.) 24, 719 (1935); Ya. B. Zeldovich, Ann. Phys. (N.Y.) 18, 1 (1943); J. Frenkel, Kinetic Theory of Liquids (Oxford University Press, Oxford, 1946).
12. E. M. Lifshits and L. P. Pitaevskii, Physical Kinetics (Pergamon, New York, 1981), Sec. 99.
13. G. Ruppeiner, Rev. Mod. Phys. 67, 605 (1995).
14. G. Wilemski, J. Chem. Phys. 103, 1119 (1995).
15. D. W. Oxtoby and P. R. Harrowell, J. Chem. Phys. 96, 3834 (1992); Y. C. Shen and D. W. Oxtoby, ibid. 104, 4233 (1996); Phys. Rev. Lett. 77, 3585 (1996).
16. D. W. Oxtoby and P. R. Harrowell, J. Chem. Phys. 96, 3834 (1992); Y. C. Shen and D. W. Oxtoby, ibid. 104, 4233 (1996); Phys. Rev. Lett. 77, 3585 (1996).
17. D. W. Oxtoby and P. R. Harrowell, J. Chem. Phys. 96, 3834 (1992); Y. C. Shen and D. W. Oxtoby, ibid. 104, 4233 (1996); Phys. Rev. Lett. 77, 3585 (1996).
18. L. Onsager, Phys. Rev. 65, 117 (1944).
19. B. M. McCoy and T. T. Wu, The Two-Dimensional Ising Model (Harvard University Press, Cambridge, MA, 1973).
20. R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic, New York, 1982).
21. C. Domb, Adv. Phys. 9, 149 (1960).
22. J. D. Weeks, G. H. Gilmer, and H. J. Leamy, Phys. Rev. Lett. 31, 549 (1973).
23. M. Hasenbusch and K. Pinn, Physica A 203, 189 (1994).
24. K. Kawasaki, "Kinetics of Ising models," in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, New York, 1972), Vol. 2, pp. 443-501.
25. Applications of the Monte Carlo Method in Statistical Physics, 2ed., edited by K. Binder (Springer-Verlag, New York, 1987).
26. K. Binder and D. Stauffer, Adv. Phys. 25, 343 (1976).
27. J. Marro, J. L. Lebowitz, and M. H. Kalos, Phys. Rev. Lett. 43, 282 (1979).
28. D. Stauffer, A. Coniglio, and D. W. Heermann, Phys. Rev. Lett. 49, 1299 (1982); D. Stauffer, Int. J. Mod. Phys. C 3, 1059 (1992); Physica A 244, 344 (1997); M. Acharyya and D. Stauffer, Eur. Phys. J. B 5, 571 (1998).
29. D. Stauffer, A. Coniglio, and D. W. Heermann, Phys. Rev. Lett. 49, 1299 (1982); D. Stauffer, Int. J. Mod. Phys. C 3, 1059 (1992); Physica A 244, 344 (1997); M. Acharyya and D. Stauffer, Eur. Phys. J. B 5, 571 (1998).
30. D. Stauffer, A. Coniglio, and D. W. Heermann, Phys. Rev. Lett. 49, 1299 (1982); D. Stauffer, Int. J. Mod. Phys. C 3, 1059 (1992); Physica A 244, 344 (1997); M. Acharyya and D. Stauffer, Eur. Phys. J. B 5, 571 (1998).
31. D. Stauffer, A. Coniglio, and D. W. Heermann, Phys. Rev. Lett. 49, 1299 (1982); D. Stauffer, Int. J. Mod. Phys. C 3, 1059 (1992); Physica A 244, 344 (1997); M. Acharyya and D. Stauffer, Eur. Phys. J. B 5, 571 (1998).
32. D. Stauffer and J. Kertesz, Physica A 177, 381 (1991).
33. D. W. Heerman and W. Klein, Phys. Rev. B 27, 1732 (1983); Phys. Rev. Lett. 50, 1062 (1983).
34. D. W. Heerman and W. Klein, Phys. Rev. B 27, 1732 (1983); Phys. Rev. Lett. 50, 1062 (1983).
35. H. M. Duiker and P. D. Beale, Phys. Rev. B 41, 490 (1990).
36. P. A. Rikvold, H. Tomita, S. Miyashita, and S. W. Sides, Phys. Rev. E 49, 5080 (1994).
37. V. A. Shneidman, K. A. Jackson, and K. M. Beatty, Phys. Rev. B 59, 3579 (1999).
38. R. A. Ramos, P. A. Rikvold, and M. A. Novotny, Phys. Rev. B 59, 9053 (1999).
39. J. P. Marchand and P. A. Martin, Physica A 127A, 681 (1984).
40. R. Kotecky and E. Olivieri, J. Stat. Phys. 70, 1121 (1993).
41. E. J. Neves and R. H. Schonmann, Commun. Math. Phys. 137, 209 (1991); Probab. Theory Relat. Fields 91, 331 (1992); R. H. Schonmann, Commun. Math. Phys. 161, 1 (1994); R. H. Schonmann and S. B. Shlosman, ibid. 194, 389 (1998).
42. E. J. Neves and R. H. Schonmann, Commun. Math. Phys. 137, 209 (1991); Probab. Theory Relat. Fields 91, 331 (1992); R. H. Schonmann, Commun. Math. Phys. 161, 1 (1994); R. H. Schonmann and S. B. Shlosman, ibid. 194, 389 (1998).
43. E. J. Neves and R. H. Schonmann, Commun. Math. Phys. 137, 209 (1991); Probab. Theory Relat. Fields 91, 331 (1992); R. H. Schonmann, Commun. Math. Phys. 161, 1 (1994); R. H. Schonmann and S. B. Shlosman, ibid. 194, 389 (1998).
44. E. J. Neves and R. H. Schonmann, Commun. Math. Phys. 137, 209 (1991); Probab. Theory Relat. Fields 91, 331 (1992); R. H. Schonmann, Commun. Math. Phys. 161, 1 (1994); R. H. Schonmann and S. B. Shlosman, ibid. 194, 389 (1998).
45. E. Stoll, K. Binder, and T. Schneider, Phys. Rev. B 6, 2777 (1972).
46. K. Binder, Phys. Rev. B 15, 4425 (1977).
47. M. E. Fisher, Physics (Long Island City, N.Y.) 3, 255 (1967).
48. V. A. Shneidman, Physica A 190, 145 (1992).
49. H. L. Richards, S. W. Sides, M. A. Novotny, and P. A. Rikvold, J. Magn. Magn. Mater. 150, 37 (1995).
50. J. S. Langer, Ann. Phys. (N.Y.) 54, 258 (1969); ibid. 65, 53 (1971).
51. J. S. Langer, Ann. Phys. (N.Y.) 54, 258 (1969); ibid. 65, 53 (1971).
52. C. Rottman and M. Wortis, Phys. Rev. B 24, 6274 (1981).
53. R. K. Zia and J. E. Avron, Phys. Rev. B 25, 2042 (1982).
54. P. G. van Dongen and M. H. Ernst, J. Stat. Phys. 37, 301 (1984).
55. G. H. Gilmer, Mater. Sci. Eng. 65, 15 (1984); K. A. Jackson, G. H. Gilmer, and D. E. Tëmkin, Phys. Rev. Lett. 75, 2530 (1995); K. A. Jackson et al., J. Cryst. Growth 163, 461 (1996); K. M. Beatty and K. A. Jackson, ibid. 174, 28 (1997).
56. G. H. Gilmer, Mater. Sci. Eng. 65, 15 (1984); K. A. Jackson, G. H. Gilmer, and D. E. Tëmkin, Phys. Rev. Lett. 75, 2530 (1995); K. A. Jackson et al., J. Cryst. Growth 163, 461 (1996); K. M. Beatty and K. A. Jackson, ibid. 174, 28 (1997).
57. G. H. Gilmer, Mater. Sci. Eng. 65, 15 (1984); K. A. Jackson, G. H. Gilmer, and D. E. Tëmkin, Phys. Rev. Lett. 75, 2530 (1995); K. A. Jackson et al., J. Cryst. Growth 163, 461 (1996); K. M. Beatty and K. A. Jackson, ibid. 174, 28 (1997).
58. G. H. Gilmer, Mater. Sci. Eng. 65, 15 (1984); K. A. Jackson, G. H. Gilmer, and D. E. Tëmkin, Phys. Rev. Lett. 75, 2530 (1995); K. A. Jackson et al., J. Cryst. Growth 163, 461 (1996); K. M. Beatty and K. A. Jackson, ibid. 174, 28 (1997).
59. K. M. Beatty, Ph.D. dissertation, University of Arizona, 1997.
60. A. Coniglio and W. Klein, J. Phys. A 13, 2775 (1980).
61. C. N. Yang and T. D. Lee, Phys. Rev. 87, 404 (1952); 87, 410 (1999).
62. C. N. Yang and T. D. Lee, Phys. Rev. 87, 404 (1952); 87, 410 (1999).
63. M. E. Fisher and A. E. Ferdinand, Phys. Rev. Lett. 19, 169 (1967).
64. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
65. L. Onsager, Nuovo Cimento Suppl. 6, 261 (1949).
66. C. N. Yang, Phys. Rev. 85, 808 (1952).
67. M. J. Lowe and D. J. Wallace, J. Phys. A 13, L381 (1980); C. K. Harris, Physica A 17, 1767 (1984); C. C. Günther, P. A. Rikvold, and M. A. Novotny, ibid. 212, 194 (1994).
68. M. J. Lowe and D. J. Wallace, J. Phys. A 13, L381 (1980); C. K. Harris, Physica A 17, 1767 (1984); C. C. Günther, P. A. Rikvold, and M. A. Novotny, ibid. 212, 194 (1994).
69. M. J. Lowe and D. J. Wallace, J. Phys. A 13, L381 (1980); C. K. Harris, Physica A 17, 1767 (1984); C. C. Günther, P. A. Rikvold, and M. A. Novotny, ibid. 212, 194 (1994).
70. C. Rottman and M. Wortis, Phys. Rep. 103, 59 (1984).
71. J. L. Katz, Pure Appl. Chem. 64, 1661 (1992).
72. S. Ono and S. Kondo, Molecular Theory of Surface Tension (Springer, Berlin, 1960).
73. A. Laaksonen and R. McGraw, Europhys. Lett. 35, 367 (1996).
74. R. Baxter (private communication); a more detailed study of the interfacial tension for a triangular lattice is given in R. K. Zia, J. Stat. Phys. 45, 801 (1986).
75. R. Baxter (private communication); a more detailed study of the interfacial tension for a triangular lattice is given in R. K. Zia, J. Stat. Phys. 45, 801 (1986).
76. P. James, Phys. Chem. Glasses 15, 95 (1974); V. Fokin, A. Kalinina, and V. Filipovich, Fiz. Khim. Stekla 3, 122 (1977); J. Deubener, R. Brükner, and M. Sternizke, J. Non-Cryst. Solids 163, 1 (1993).
77. P. James, Phys. Chem. Glasses 15, 95 (1974); V. Fokin, A. Kalinina, and V. Filipovich, Fiz. Khim. Stekla 3, 122 (1977); J. Deubener, R. Brükner, and M. Sternizke, J. Non-Cryst. Solids 163, 1 (1993).
78. P. James, Phys. Chem. Glasses 15, 95 (1974); V. Fokin, A. Kalinina, and V. Filipovich, Fiz. Khim. Stekla 3, 122 (1977); J. Deubener, R. Brükner, and M. Sternizke, J. Non-Cryst. Solids 163, 1 (1993).
79. V. A. Shneidman, K. A. Jackson, and K. M. Beatty, J. Cryst. Growth (submitted).
80. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipies in C (Cambridge University Press, Cambridge, 1988).
81. O. Penrose and J. Lebowitz, in Studies in Statistical Mechanics, Vol. VII, edited by E. Montrol and J. Lebowitz (North-Holland, Amsterdam, 1979); J. Ball, J. Carr, and O. Penrose, Commun. Math. Phys. 104, 657 (1986).
82. O. Penrose and J. Lebowitz, in Studies in Statistical Mechanics, Vol. VII, edited by E. Montrol and J. Lebowitz (North-Holland, Amsterdam, 1979); J. Ball, J. Carr, and O. Penrose, Commun. Math. Phys. 104, 657 (1986).