The Diminishing Role of the Nucleation Rate as Crystallization Develops in Avrami-Type Models

Abstract

By making use of an isothermal crystallization kinetics formulation in which growth and nucleation rates are functions of the degree of crystallization, we describe a process consisting of birth and growth of spherical crystalline domains. It is found that beyond the early stages of crystallization, the role played by the nucleation rate becomes quite insignificant as compared to the role of the crystalline domain growth rate. This is in contrast to what we would expect from the simplified Avrami exponential equation, where both rates play a symmetrical role. We argue that the asymmetric roles of the growth and nucleation rates greatly contribute to the wide applicability of Avrami-type expressions. A geometric explanation of the diminishing role of nucleation in the later stages of transformation is given. Future theoretical developments might benefit from the arguments and results presented.

Keywords

• crystallization
• Avrami equation
• KJMA model
• nucleation rate