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The Time Lag in Transient Nucleation

Published online by Cambridge University Press:  26 February 2011

David T. Wu
David T. Wu*
Affiliation:
Division of Applied Sciences, Harvard University, Cambridge, MA 02138
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Abstract

The time lag in transient nucleation was originally introduced to characterize the temporal evolution of the nucleation current in the simplest possible way. Previous attempts to calculate the time lag have relied mainly on either the approximate solution of the continuous Fokker-Planck equation or the numerical solution of the discrete rate equations. It is shown that the exact time lag can be calculated using a different method which requires knowledge only of the initial and the steady-state cluster populations.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 205: Symposium F – Kinetics of Phase Transformations , 1990 , 411
Copyright
Copyright © Materials Research Society 1992

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References

References and Notes

1 Becker, R. and Döring, W., Ann. Phys. 24, 719 (1935).Google Scholar
2 “k+1/2” is used to index the current for reasons of symmetry. The consequences of this convention are discussed in Wu, D. T., submitted to J. Chem. Phys.Google Scholar
3 See Goodrich, F. C., Proc. R. Soc. London A 277, 167 (1964) and J. L. Katz and M. D. Donohue, Adv. Chem. Phys. 4Q, 137 (1979) for physical construction of N' when the backward rate constant a is unknown.Google Scholar
4 Frenkel, J. I., The Kinetic Theory of Liquids (Oxford Univ. Press, London, 1946).Google Scholar
5 Zeldovich, J. B., Acta Physicochim. URSS 18, 1 (1943).Google Scholar
6 There are many possible choices for the effective diffusion coefficient, each one leading to a distinct continuum approximation. For instance, Frenkel used D(x+i/2). See ref. 2 for details. 7 For a review see K. F. Kelton, A. L. Greer, C. V. Thompson, J. Chem. Phys. 79, 6261 (1983).Google Scholar
8 Courtney, W. G., J. Chem. Phys. 36, 2009 (1962).Google Scholar
9 Abraham, F. F., J. Chem. Phys. 51, 1632 (1969).Google Scholar
10 Ref. 7.Google Scholar
11 Wu, D. T., submitted to J. Chem. Phys.Google Scholar