MONTE-CARLO TESTING OF THE STATISTICAL-ANALYSIS OF NUCLEATION DATA

A method is proposed for experimentally determining the magnitude of t he preexponential and exponential factors in the nucleation rate equat ion. The method is a modification of a statistical approach developed by Skripov, which allows nucleation data, such as a collection of unde rcoolings prior to nucleation, to be analyzed to yield quantitative in formation on the nucleation rate equation. Three expressions for the n ucleation rate equation (Fisher-Turnbull Spaepen-Turnbull, and Thompso n-Spaepen) were used to generate probability distributions of nucleati on events as a function of temperature. The probability density functi ons generated from these expressions differ for the homogeneous nuclea tion case when normalized to a common mode undercooling. However, for common mode undercoolings in the heterogeneous regime (approximately 1 5% T-m undercooling) the resulting probability distributions are quite similar. To test the approach and evaluate the uncertainty of the sta tistical analysis, nucleation data sets were simulated by a Monte Carl o technique. For data sets of 100 experimental runs, the uncertainty i n the exponential factor and the log of the preexponential factor is 1 0% if temperature measurement is exact. The implications of temperatur e measurement uncertainty were evaluated numerically. (C) 1998 Acta Me tallurgica Inc.