TY - JOUR
T1 - Transformations of the distribution of nuclei formed in a nucleation pulse
T2 - Interface-limited growth
AU - Shneidman, Vitaly A.
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
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U2 - 10.1063/1.3254322
DO - 10.1063/1.3254322
M3 - Article
C2 - 19894935
AN - SCOPUS:72049089876
SN - 0021-9606
VL - 131
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
IS - 16
M1 - 164115
ER -