Transformations of the distribution of nuclei formed in a nucleation pulse: Interface-limited growth

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Abstract

A typical nucleation-growth process is considered: a system is quenched into a supersaturated state with a small critical radius r- * and is allowed to nucleate during a finite time interval tn, after which the supersaturation is abruptly reduced to a fixed value with a larger critical radius r+*. The size-distribution of nucleated particles f (r,t) further evolves due to their deterministic growth and decay for r larger or smaller than r+, respectively. A general analytic expressions for f (r,t) is obtained, and it is shown that after a large growth time t this distribution approaches an asymptotic shape determined by two dimensionless parameters, λ related to tn, and = r+*/r-*. This shape is strongly asymmetric with an exponential and double-exponential cutoffs at small and large sizes, respectively, and with a broad near-flat top in case of a long pulse. Conversely, for a short pulse the distribution acquires a distinct maximum at r= rmax (t) and approaches a universal shape exp [ξ- eξ], with ξ α r rmax, independent of the pulse duration. General asymptotic predictions are examined in terms of Zeldovich-Frenkel nucleation model where the entire transient behavior can be described in terms of the Lambert W function. Modifications for the Turnbull-Fisher model are also considered, and analytics is compared with exact numerics. Results are expected to have direct implementations in analysis of two-step annealing crystallization experiments, although other applications might be anticipated due to universality of the nucleation pulse technique.

Original languageEnglish (US)
Article number164115
JournalJournal of Chemical Physics
Volume131
Issue number16
DOIs
StatePublished - 2009

All Science Journal Classification (ASJC) codes

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

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