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Heating rate effects in the transient nucleation problem.

The matched asymptotic (singular perturbation) treatment of the nucleation equation [V. A. Shneidman, Sov. Phys. Tech. Phys. 32, 76 (1987); 33, 1338 (1988)] is modified to include finite heating rate effects, which follow the isothermal transient stage. Despite the complicated mathematical structure of the discrete Becker-Doring equation, the obtained analytical solution is shown to be accurate numerically. The described situation is typical for two-step annealing crystallization studies and can lead to reinterpretation of some of the classical experiments.