Kinetics of Phase Change. II Transformation-Time Relations for Random Distribution of Nuclei

TLDR

The study introduces a simplification for modeling phase‑change kinetics when nuclei are randomly distributed, extending the theory presented in Part I. It derives a statistical relation between the actual transformed volume and an extended volume, applies it to various crystalline growth geometries, and reduces the problem to determining the extended volume, thereby linking to empirical formulas in the isokinetic range. The derived approximations reproduce the Austin–Rickett and Krainer empirical relations and yield isothermal transformation‑time curves that agree well with experimental observations.

Abstract

Following upon the general theory in Part I, a considerable simplification is here introduced in the treatment of the case where the grain centers of the new phase are randomly distributed. Also, the kinetics of the main types of crystalline growth, such as result in polyhedral, plate-like and lineal grains, are studied. A relation between the actual transformed volume V and a related extended volume V1 ex is derived upon statistical considerations. A rough approximation to this relation is shown to lead, under the proper conditions, to the empirical formula of Austin and Rickett. The exact relation is used to reduce the entire problem to the determination of V1 ex, in terms of which all other quantities are expressed. The approximate treatment of the beginning of transformation in the isokinetic range is shown to lead to the empirical formula of Krainer and to account quantitatively for certain relations observed in recrystallization phenomena. It is shown that the predicted shapes for isothermal transformation-time curves correspond well with the experimental data.