Higher order approximations in the Shi-Seinfeld-Okuyama description of transient nucleation》.pdfVIP

Scripta METALLURGICA Vol. 29, pp. 1535-1540, 1993 Pergamon Press Ltd. et MATERIALIA Printed in the U.S.A. All rights reserved HIGHER ORDERAPPROXIMATIONS INTHESHI-SE~FELD-OKUYAMA DESCRIPTION OFTRANSIENT NUCLEATION J. J. Hoyt and G. Sundar Department of Mechanical and Materials Engineering Washington State University Pullman, WA 99164 (Received September 6, 1993) .Introduction The nucleation rate, that is the rate of formation of droplets of a stable phase within a supersaturated parent phase, can be found by first solving the Fokker-Planck equation for the time dependent droplet size distribution. It is a straightforward matter to derive the steady state nucleation rate but behavior during the transient regime is much more difficult to obtain. Although numerical computations are possible [ 1], an accurate analytical description of the time dependent nucleation rate has eluded physicists and metallurgists for many years [1]. Recent progress has been made by Trinkhaus and Yoo (TY) [2] who solved for the cluster size distribution using a Greens function technique. Shi, Seinfeld and Okuyama (SSO) [3] (see also Shi and Seinfeld [4-7]) recognized that, for most physical systems, a transition layer about the critical droplet size exists and thus a singular perturbation technique