Kinetics of crystallization preceded by metastable-phase formation

Abstract

A theoretical description is proposed of the kinetics of overall crystallization when the appearance of the stable crystalline (SC) phase is preceded by the formation of a metastable phase. A general formula is derived for the fraction αs of volume of the SC phase crystallized at time t. This formula is used for obtaining the αs(t) function in the case of Kolmogorov–Johnson–Mehl–Avrami kinetics of overall crystallization. The time t1/2 at which half of the transformation of the parent phase into the SC one is accomplished is determined and it is found that this time is the sum of the times for half completion of the two successive phase transformations of the parent phase into the metastable one and of the latter into the SC phase. A general condition for formation of a long living metastable phase is formulated in terms of the nucleation and growth rates of the metastable and the SC phases. The general results are applied to melt crystallization and an expression for the temperature dependence of t1/2 is obtained. It is found that the presence of a metastable phase in the melt is easy to observe only below a certain critical temperature, because then the transformation of the metastable phase into the SC one is sufficiently delayed. In a supplementary analysis, an answer is given to the classical question about the possibility for formation of a metastable phase prior to the stable one in accordance with Ostwald’s Rule of Stages.