The Becker-Döring equations at large times and their connection with the LSW theory of coarsening

Journal of Statistical Physics

Volumn 89, Issue 1-2, 1997, Pages 305-320

  Penrose, O ^a  

^a HERIOT WATT UNIVERSITY   (United Kingdom)

Author keywords

Asymptotics; Becker D ring equations; Cluster kinetics; Kinetics of phase transitions; Lifshitz Slyozov theory; Ostwald ripening

Indexed keywords

EID: 0031256457     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02770767     Document Type: Article

References (24)

1. A. J. Ardell, The mechanics of phase transitions in crystalline solids, Institute of metals monograph Series, vol. 33, (London, 1969), page 111.
2. A. J. Ardell and R. B. Nicholson, J. Phys. Chem. Solids 27:1793-1804 (1966).
3. J. M. Ball, J. Carr and O. Penrose, Commun. Math. Phys. 104:657-692 (1986). The Becker-Döring cluster equations: basic properties and asymptotic behavior of solutions.
4. R. Becker and W. Döring, Ann. Phys. (Leipzig) 24:719-752 (1935). Kinetische Behandlung der Keimbildung in übersättigten Dämpfen.
5. A Buhagiar, Kinetics of phase segregation in a quenched alloy, Thesis, Open University, Milton Keynes. U.K. (1980).
6. J. J. Burton, Nucleation theory. pp. 195-234 of Statistical Mechanics, Part A: Equilibrium techniques, edited by B. J. Berne, Plenum, 1977.
7. J. Carr and O. Penrose, unpublished.
8. A. DeMasi and E. Presutti, Mathematical methods for hydrodynamic limits, Springer lecture notes in mathematics, no. 1501. Berlin/Heidelberg, 1991.
9. P. Fratzl and O. Penrose, Phys. Rev. B, to appear (1997). Competing mechanisms for precipitate coarsening in phase separation with vacancy dynamics.
10. 0.33.
11. F. Leyvraz and H. R. Tschudi, J. Phys A: Math. Gen. 14:3389-3405 (1981). Singularities in the kinetics of coagulation processes.
12. I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Sol. 19:35-50 (1961). Kinetics of precipitation from supersaturated solid solutions.
13. E. M. Hendriks, M. H. Ernst, and R. M. Ziff, J. Stat. Phys. 31:519-563 (1983). Coagulation equations with gelation.
14. S. C. Hardy and P. W. Voorhees, Metall. Trans. 19A:2713-2721 (1988). Ostwald ripening in a system with a high volume fraction of coarsening phase.
15. R. Pego, Proc. Roy. Soc. Lond. A 422: 261-278 (1989). Front migration in the nonlinear Cahn-Hilliard equation.
16. O. Penrose and A. Buhagiar, J. Stat. Phys. 30:219-241 (1983). Kinetics of nucleation in a lattice gas model: microscopic theory and simulation compared.
17. O. Penrose, J. L. Lebowitz, J. Marro, M. H. Kalos, and A. Sur, J. Stat. Phys. 19:243-267 (1978). Growth of Clusters in a First-order Phase Transition.
18. J. R. Rubinstein, P. Sternberg, and J. B. Keller, SIAM J. Appl. Math. 49:116-133 (1989). Fast reaction, slow diffusion, and curve shortening.
19. P. W. Voorhees, J. Stat. Phys. 38:231-252 (1985). The theory of Ostwald ripening.
20. P. W. Voorhees, Ann. Rev. Mater. Sci. 22:197-215 (1992).
21. J. Velazquez, preprint (1997). The Becker Döring equations and the Lifshitz-Slyozov theory of coarsening.
22. C. Wagner, Z. Elektrochem. 65:581-591 (1961).
23. 3Ga precipitates in aged Ni Ga alloys.
24. S. Q. Xiao and P. Haasen, Acta Met. Mat. 39:651-659 (1991). HREM investigation of homogeneous decomposition in a Ni-12 at % Al alloy.