Theory of time-dependent nucleation and growth during a rapid quench

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Abstract

Phase transformation via the nucleation and growth mechanism during a rapid cooling (quench) of a glass-forming liquid or melt is considered. Traditional approaches here are based on the quasi-steady-state (QSS) approximation for nucleation and the assumption of a size-independent growth. However, the QSS approach becomes invalid if the dimensionless rate of the barrier change, n = - τ∂(W*/kT)/∂t (τ is the inner time scale of the nucleation process) is not vanishingly small. For such "strongly time-dependent" situations an asymptotic (singular perturbation) technique of matching the time- and size-dependent nucleation and growth solutions is elaborated, and an explicit expression to describe the distribution function of large particles is derived. Formally, the results can be reproduced by the QSS approximation with the steady-state nucleation rate multiplied by an n-dependent factor. Analytical treatment is tested against numerically exact solutions of the nucleation (Becker-Döring) and growth equations.

Original languageEnglish (US)
Pages (from-to)9772-9781
Number of pages10
JournalThe Journal of Chemical Physics
Volume103
Issue number22
DOIs
StatePublished - Jan 1 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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