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

J. Chem. Phys. 131, 164115 (2009); doi:10.1063/1.3254322

Published 29 October 2009

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Vitaly A. Shneidman
Department of Physics, New Jersey Institute of Technology, Newark, New Jersey 07102, USA
A typical nucleation-growth process is considered: a system is quenched into a supersaturated state with a small critical radius r<sub>*</sub><sup>-</sup> 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<sub>*</sub><sup>+</sup>. 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<sub>*</sub><sup>+</sup>, 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, lambda related to tn, and Lambda=r<sub>*</sub><sup>+</sup>/r<sub>*</sub><sup>-</sup>. 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[zeta−ezeta], with zeta[proportional]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. ©2009 American Institute of Physics
History: Received 18 June 2009; accepted 5 October 2009; published 29 October 2009
Permalink: http://link.aip.org/link/?JCPSA6/131/164115/1
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KEYWORDS and PACS

Keywords
PACS
  • 64.60.qj
    Studies of nucleation in specific substances (phase transitions)
  • 64.70.-p
    Specific phase transitions
  • 81.40.Gh
    Other heat and thermomechanical treatments
  • YEAR: 2009

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PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
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