Solid phase crystallization under continuous heating: kinetic and microstructure scaling laws

TL;DR

This paper develops scaling laws for the kinetics and microstructure of solid-phase crystallization under continuous heating, revealing how these properties depend on temperature, time, and heating rate, and providing analytical and numerical tools for analysis.

Contribution

It introduces a scaling law framework that simplifies the analysis of crystallization kinetics and microstructure evolution under continuous heating conditions.

Findings

The extended volume follows a specific exponential growth law.

A length scaling factor allows prediction of grain-size distribution.

Final grain size can be analytically related to kinetic parameters.

Abstract

The kinetics and microstructure of solid-phase crystallization under continuous heating conditions and random distribution of nuclei are analyzed. An Arrhenius temperature dependence is assumed for both nucleation and growth rates. Under these circumstances, the system has a scaling law such that the behavior of the scaled system is independent of the heating rate. Hence, the kinetics and microstructure obtained at different heating rates differ only in time and length scaling factors.Concerning the kinetics, it is shown that the extended volume evolves with time according to alpha_ex=[exp(kappa Ct)]^m+1, where t' is the dimensionless time. This scaled solution not only represents a significant simplification of the system description, it also provides new tools for its analysis. For instance, it has been possible to find an analytical dependence of the final average grain size on kinetic parameters. Concerning the microstructure, the existence of a length scaling factor has allowed the grain-size distribution to be numerically calculated as a function of the kinetic parameters.