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.
Shneidman
Vitaly A
VA
Department of Physics, New Jersey Institute of Technology, Newark, New Jersey 07102, USA.