# Solid phase crystallization under continuous heating: kinetic and microstructure scaling laws Source: [Solid phase crystallization under continuous heating: kinetic and microstructure scaling laws]() Collection index: [llms.txt]() Data updated: 2025-10-28T13:53:55.438Z Authors: J. Farjas, P. Roura Published: 2008-11-14T10:40:55.000Z ## 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()