On the Becker/Döring theory of nucleation of liquid droplets in solids

Journal of Statistical Physics

Volumn 123, Issue 1, 2006, Pages 55-87

  Dreyer, Wolfgang ^a   Duderstadt, Frank ^a  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

Elasticity; GaAs; Kinetics of phase transitions; Nucleation; Surface stress

Indexed keywords

EID: 33646469866     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-006-9024-z     Document Type: Article

References (44)

1. J. M. Bail, J. Carr, and O. Penrose, The Becker-Döring cluster equations: Basic properties and asymptotic behaviour of solutions. Commun. Math. Phy. 104:657-692 (1986).
2. W. Band, Dissociation treatment of condensing systems. J. Chem. Phy. 7:324-326 (1939).
3. R. Becker and W. Döring, Kinetische Behandlung der Keimbildung in übersättigten Dämpfen. Annalen der Physik (5. Folge) 24:719-752 (1935).
4. J. J. Burton, Nucleation theory, Statistical Mechanics, Part A: Equilibrium Techniques (Berne, B. J. ed.), Plenum Press, New York pp. 195-234 (1977).
5. J. Carr, D. B. Duncan, and C. H. Walshaw, Numerical approximation of a metastable system. IMA J. Numer. Anal. 15(4):505-521 (1995).
6. R. Clausius, Über eine veränderte Form des zweiten Hauptsatzes der mechanischen Wärmetheorie Poggendorf's Annalen XCIII:481 (1854),
7. (also in: Phil. Mag. 4th Ser. Vol. XII:81;
8. Journ. de Liouville t. XX:63.
9. W. Dreyer and F. Duderstadt, On the modelling of semi-insulating GaAs including surface tension and bulk stresses. WIAS-Preprint 995, (2004).
10. W. Dreyer and F. Duderstadt, On the dynamics of the thermodynamic consistent Becker-Döring model. in preparation.
11. W. Dreyer, F. Duderstadt, and S. Qamar, Diffusion in the vicinity of an evolving spherical arsenic droplet. WIAS-Preprint 996 (2004).
12. Dreyer, F. Duderstadt, St. Eichler, and M. Jurisch, Stress analysis and bending tests for GaAs wafer. WIAS-Preprint 897 (2003).
13. F. Duderstadt, Anwendung der von Kármán'sehen Plattentheorie und der Hertz'sehen Pressung für die Spannungsanalyse zur Biegung von GaAs- Wafern im modifizierten Doppelringtest, PhD thesis, Technical University Berlin 2003, also published as WIAS-Report, no. 24.
14. D. B. Duncanand A. R. Soheili, Approximating the Becker-Döring cluster equations, Appl. Numer. Mark. 37(1-2):1-29 (2001).
15. L. Farkas, Keimbildungsgeschwindigkeit in übersättigten Dämpfen. Zeitschrift für physikalische Chemie 125:236-242 (1927).
16. J. I. Frenkel, Journal experimentalnoi i teoreticheskoi fisiki 9(8):952-962 (1939),
17. also in Englisch: A general theory of heterophase fluctuations and pretransition phenomena. J. Chem. Phy. 7:538-547 (1939).
18. J. I. Frenkel, Isgatelstwo akagemii nauk SSSR, Moscow (1945)
19. (second corrected and extended edition in English: Kinetic theory of liquids, Oxford University Press, Oxford (1946), reprint: Dover, New York (1955);
20. German translation of the first edition, corrected and translated by H. Friedrich, W. Ludwig and F. R. Bachmann: Kinetische Theorie der Flüssigkeiten, Deutscher Verlag der Wissenschaften. Berlin (1957)).
21. J. W. Gibbs, On the equilibrium of heterogeneous substances. Transactions of the Connecticut Academy of Arts and Sciences, Third Series XVI(96):343-524 (1878).
22. M. Herrmann, B. Niethammer, and M. Naldzhieva, On a thermodynamically consistent modification of the Becker-Döring equations. MATHEON-Preprint 228 (2005), submitted to Physica D.
23. D. Kashchiev, Nucleation, Butterworth-Heinemann Oxford (2000).
24. F. Kuhrt, Das Tröpfchenmodell realer Gase. Zeitschrift für Physik 131:185-204 (1952).
25. F. Kuhrt, Das Tröpfchenmodell übersättigter realer Gase. Zeitschrift für Physik 131:204-214 (1952).
26. I. M. Lifshitz and V. V. Slyozov, Kinetics of precipitation from supersaturated solid solutions, J. Phys. Chem. Sol 19:35-50 (1961).
27. J. Lothe and G. M. Pound, Reconsiderations of Nucleation Theory. J. Chem. Phy. 36(8):2080-2085 (1962).
28. I. Müller, Thermodynamics, Interaction of Mechanics and Mathematics Series, Pitman Advanced Publishung Program, Boston (1985).
29. I. Müller, Grundzüge der Thermodynamik, 3. ed., Springer, Berline (2001) 1. Auflage (1994).
30. B. Niethammer, On the Dynamics of the Becker-Döring Equations, Habilitation Thesis, University of Bonn, Bonn (2002).
31. B. Niethammer, On the Evolution of Large Clusters in the Becker-Döring ModelJ. Nonlinear Sci. 13(1):115-155 (2003).
32. O. Penrose, Metastable states for the Becker-Döring cluster equations. Commun. Math. Phy. 124:515-541 (1989).
33. O. Penrose, The Becker-Döring equations at large times and their connection with the ESW theory of coarsening. Commun. Math. Phy. 189(1/2):305-320 (1997).
34. O. Penrose and A. Buhagiar. Kinetics of nucleation in lattice gas models: Microscopic theory and simulation compared. J. Stat. Phy. 30:219-241 (1983).
35. O. Penrose and J. E. Lebowitz, Towards a rigorous molecular theory of metastability, Fluctuation Phenomena (E. W. Montroll and J. L. Lebowitz, eds.), Studies in Statical Mechanics, vol. VII, North-Holland, pp. 293-340 (1979).
36. O. Penrose, J. L. Lebowitz, J. Marro, M. Kalos, and J. Tobochnik, Kinetics of a first-order phase transition: Computer simulations and theory. J. Stat. Phy. 34:399-426 (1984).
37. H. Reiss and J. L. Katz, Resolution of the Translation-Rotation Paradox of Irreversible Condensation. J. Chem. Phy. 46(7):2496-2499 (1967).
38. W. Thomson, On the equilibrium of vapour at a curved surface of liquid. Proc. Roy. Soc. 7(63) (1870).
39. M. Volmer, Über Keimbildung und Keimwirkung als Spezialfälle der heterogen Katalyse. Zeitschrift für Elektrochemie 35(9):555-561 (1929).
40. M. Volmer, Kinetik der Phasenbildung, Verlag von Theodor Steinkopff, Dresden (1939),
41. (English translation: Kinetics of phase formation, Clearinghouse for Federal and Technical Information, ATI No. 81935 [F-TS-7068-RE].
42. M. Volmer and H. Flood, Zeitschrift für physikalische Chemie, Abt. A, 170:237 (1934).
43. M. Volmer and A. Weber, Keimbildung in übersättigten Gebilden, Zeitschrift für physikalische Chemie, Abt. A 119:277-301 (1926).
44. C. Wagner, Theorie der Alterung von Niederschlägen durch Umlösen. Zeitschrift für Elektrochemie 65:581-594 (1961).