| The classical theory of nucleation predicts a nucleation rate which varies from near zero to extremely large values over a narrow range of temperature, thus effectively defining the onset of nucleation or cloud point. However, experiments conducted in the 1960's and the early 1970's have shown disagreement between the theoretically predicted and measured cloud points. In particular, these experiments showed that larger supersaturations were required to observe the cloud point than those predicted by the classical theory. In 1980, Langer and Schwartz (LS) proposed a model which predicted that the nucleation time diverges for initial supersaturations higher than those predicted by the classical theory, thereby suggesting an explanation for the paradox.; In order to test the validity of the LS model, small-angle x-ray scattering (SAXS) was used to monitor the decrease in supersaturation with time in Al-Zn alloys following quenches into the metastable miscibility gap. The results demonstrated that the LS model is accurate provided a time-dependent nucleation is included.; Transmission electron microscopy (TEM) was used as an additional tool to further investigate nucleation kinetics in Al-Zn, thereby validating the LS results. The value of the critical undercooling was established by noting the lowest temperature in the miscibility gap at which precipitates were no longer observed.; The time-dependent nucleation was studied in more detail by Shi, Seinfeld and Okuyama (SSO) who employed a singular perturbation technique to solve the Fokker-Planck equation. In the present work, this technique was further extended to examine various aspects of transient nucleation. Three cases are discussed. The first investigates the role of excess vacancies from the high temperature quench in the transient kinetics. The second case examines the effect of a preexisting cluster size distribution formed during the high temperature anneal, on nucleation kinetics. Finally, the SSO model was modified to take into account the monomer depletion that was neglected in their model. |
