Impact of short-range repulsive interactions between nuclei on the evolution of a phase transformation

Journal of Chemical Physics

Volumn 114, Issue 2, 2001, Pages 915-922

  Tong, W S ^a   Rickman, J M ^b   Barmak, K ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b Lehigh University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COALESCENCE; COMPUTER SIMULATION; GROWTH KINETICS; MICROSTRUCTURE; NUCLEATION;

INTERNUCLEAR SEPARATIONS; REPULSIVE INTERACTIONS;

PHASE TRANSITIONS;

EID: 0035127709     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1331568     Document Type: Article

References (28)

1. J. D. Gunton and M. Droz, Introduction to the Theory of Metastable and Unstable States (Springer-Verlag, New York, 1983).
2. M. Avrami, J. Chem. Phys. 7, 1103 (1939).
3. A. N. Kolmogorov, Bull. Acad. Sci. USSR, Phys. Ser. (Engl. Transl.) 1, 355 (1937).
4. K. Sekimoto, Physica A 135, 328 (1986).
5. H. J. Frost and C. V. Thompson, in Computer Simulation of Microstructural Evolution, edited by D. J. Srolovitz (The Metallurgical Society, Warrendale, PA, 1986), pp. 33-48.
6. J. M. Rickman, W. S. Tong, and K. Barmak, Acta Mater. 45, 1153 (1997).
7. H. J. Frost and C. V. Thompson, Acta Metall. 35, 529 (1987).
8. L.-Q. Chen, Y. Wang, and A. G. Khachaturyan, Philos. Mag. Lett. 64, 241 (1991).
9. S. Semenovskaya and A. G. Khachaturyan, Physica D 66, 205 (1993).
10. A. Roy, J. M. Rickman, J. D. Gunton, and K. R. Elder, Phys. Rev. E 57, 2610 (1998).
11. D. Chae, F. Ree, and T. Ree, J. Chem. Phys. 50, 1581 (1969).
12. See, for example, T. L. Hill, Statistical Mechanics: Principles and Selected Applications (McGraw-Hill, New York, 1956).
13. N. G. vanKampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1992).
14. It is also possible to perform the simulation in the grand-canonical ensemble wherein the number of particles N is variable. This, however, requires one to specify the chemical potential of the system. For simplicity, and because of the equivalence of ensembles in the limit of large N, we have chosen to work in the canonical ensemble here.
15. K. Binder, in Monte Carlo Methods in Statistical Physics, edited by K. Binder (Springer-Verlag, Berlin, 1986), pp. 1-45.
16. J. J. Binney, N. J. Dowrick, A. J. Fisher, and M. E. J. Newman, The Theory of Critical Phenomena: An Introduction to the Renormalization Group (Oxford University Press, Oxford, 1992).
17. D. Chandler, Introduction to Modern Statistical Mechanics (Oxford University Press, Oxford, 1987).
18. W. S. Tong, J. M. Rickman, and K. Barmak, Acta Mater. 47, 435 (1999).
19. It is possible to improve, for example, the BYG representation by using different schemes to truncate the associated hierarchy of equations. See, for example, Y. Uehara, T. Ree, and F. H. Ree, J. Chem. Phys. 70, 1876 (1979).
20. J. G. Kirkwood, E. K. Maun, and B. J. Alder, J. Chem. Phys. 18, 1040 (1950).
21. For the hard-disk system, however, one would expect the Kirkwood approximation to be satisfactory, though not particularly accurate, owing to the importance of short-range interactions in this system (Ref. 11).
22. Inherent in this approximation is the assumption that the region of integration is large. More precisely, the double integral over the pair correlation function leads to an integral over a more complex domain given by the intersection of circular regions of radius G1.
23. W. S. Tong, J. M. Rickman, and K. Barmak, Acta Mater. 48, 1181 (2000).
24. J. A. Barker and D. Henderson, Rev. Mod. Phys. 48, 587 (1976).
25. S. Sengupta, P. Nielaba, and K. Binder, Phys. Rev. E 61, 6294 (2000).
26. J. Tobochnik and G. V. Chester, Phys. Rev. B 25, 6778 (1982).
27. R. Nelson, Probability, Stochastic Processes, and Queueing Theory: The Mathematics of Computer Performance Modeling (Springer-Verlag, New York, 1995).
28. J. W. Cahn, Acta Metall. 4, 449 (1956). Recent work involves the application of a "time cone" approach.