Simulation study of nucleation in a phase-field model with nonlocal interactions

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 57, Issue 3, 1998, Pages 2610-2617

  Roy, A ^a   Rickman, J M ^b   Gunton, J D ^a   Elder, K R ^c  

^a LEHIGH UNIVERSITY   (United States)

^b Lehigh University   (United States)

^c OAKLAND UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001201263     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.57.2610     Document Type: Article

References (23)

1. J. D. Gunton and M. Droz, Introduction to the Theory of Metastable and Unstable States (Springer-Verlag, Heidelberg, 1983).
2. E. Becker and W. Döring, Ann. Phys. (Leipzig) 24, 719 (1935).ANPYA2
3. K. Binder and D. Stauffer, Adv. Phys. 25, 343 (1976).ADPHAH
4. O. Penrose, in Stochastic Processes in Nonequilibrium Systems, edited by L. Garrido, P. Seglar, and P. J. Shepherd, Lecture Notes in Physics Vol. 84 (Springer-Verlag, Heidelberg, 1978).
5. H. Muller-Krumbhaar, in Monte Carlo Methods in Statistical Physics, edited by K. Binder (Springer-Verlag, Berlin, 1979).
6. J. S. Langer, Ann. Phys. (N.Y.) 54, 258 (1969).APNYA6
7. J. S. Langer and L. A. Turski, Phys. Rev. A 8, 3230 (1973).PLRAAN
8. M. Grant and J. D. Gunton, Phys. Rev. B 32, 7299 (1985).PRBMDO
9. A. Laaksonen and D. W. Oxtoby, J. Chem. Phys. 102, 5803 (1995).JCPSA6
10. Y. C. Shen and D. W. Oxtoby, Phys. Rev. Lett. 77, 3585 (1996).PRLTAO
11. F. Spaepen, Mater. Sci. Eng. A 178, 15 (1994).MSAPE3
12. J. S. Langer and A. J. Schwartz, Phys. Rev. A 21, 948 (1980).PLRAAN
13. P. A. Rikvold, H. Tomita, S. Miyashita, and S. W. Sides, Phys. Rev. E 49, 5080 (1994).PLEEE8
14. P. R. ten Wolde, M. J. Ruiz-Montero, and D. Frenkel, J. Chem. Phys. 104, 9932 (1996).JCPSA6
15. S. Semenovskaya and A. G. Khachaturyan, Physica D 66, 205 (1993).PDNPDT
16. L.-Q. Chen, Y. Wang, and A. G. Khachaturyan, Philos. Mag. Lett. 64, 241 (1991).PMLEEG
17. P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. 49, 435 (1977).RMPHAT
18. In two-dimensional real space G(r→)=2πK0(γ|r→|), where K0 is a modified Bessel function.
19. For notational convenience the renormalized critical radius, eigenvalues and formation free energy will not be denoted with a bar.
20. C. H. Bennett, in Diffusion in Solids: Recent Developments, edited by A. S. Nowick and J. J. Burton (Academic Press, New York, 1975), pp. 73–113.
21. C. Sagui and R. C. Desai, Phys. Rev. E 49, 2225 (1994).PLEEE8
22. As the effective parameters τ¯ and ḡ change as γ changes, it is necessary to vary the field h if one wishes to work at fixed critical droplet size, RC.
23. Given the dimensions of the matrix representation of the operator M, it was necessary to employ an approximation in order to calculate the negative eigenvalues. While the Green function in Eq. (20) leads to many additional couplings in M, one still expects that this approximation is useful since the renormalized interface width ∼τ¯-1/2 is relatively insensitive to γ for the interaction ranges considered here. This expectation was validated by noting that the values of λ0(γ) were quite insensitive to the width of the annular region for a sufficiently large width.