Monte Carlo testing of the statistical analysis of nucleation data

• Published in: Acta materialia 1998-03, Vol.46 (6), p.1903-1908
• Main Authors: Hofmeister, W.H, Morton, C.W, Bayuzick, R.J
• Format: Article
• Language: English
• Subjects: Condensed matter: structure, mechanical and thermal properties; Equations of state, phase equilibria, and phase transitions; Exact sciences and technology; Physics; Solid-solid transitions; Specific phase transitions
• ISSN: 1359-6454; 1873-2453
• DOI: 10.1016/S1359-6454(97)00439-4

A method is proposed for experimentally determining the magnitude of the preexponential and exponential factors in the nucleation rate equation. The method is a modification of a statistical approach developed by Skripov, which allows nucleation data, such as a collection of undercoolings prior to nucleation, to be analyzed to yield quantitative information on the nucleation rate equation. Three expressions for the nucleation rate equation (Fisher–Turnbull, Spaepen–Turnbull, and Thompson–Spaepen) were used to generate probability distributions of nucleation events as a function of temperature. The probability density functions generated from these expressions differ for the homogeneous nucleation case when normalized to a common mode undercooling. However, for common mode undercoolings in the heterogeneous regime (approximately 15% T m undercooling) the resulting probability distributions are quite similar. To test the approach and evaluate the uncertainty of the statistical analysis, nucleation data sets were simulated by a Monte Carlo technique. For data sets of 100 experimental runs, the uncertainty in the exponential factor and the log of the preexponential factor is 10% if temperature measurement is exact. The implications of temperature measurement uncertainty were evaluated numerically.