Cahn–Hilliard theory with triple-parabolic free energy. II. Nucleation and growth in the presence of a metastable crystalline phase

Abstract

Nucleation and growth of stable and metastable crystalline phases are described in the framework of a single-order parameter Cahn–Hilliard theory. A piecewise parabolic free-energy order parameter relationship composed of three parabolas of positive curvature coefficient has been adopted. The analytical solution of the problem is presented. It is found that above a critical (bifurcation) temperature the interface is layered; a metastable layer is sandwiched between the initial and the stable phases. Above the bifurcation point, two solutions exist, one with a sharper interface and another with an extended metastable layer, of which the latter has a larger free energy of formation. The two solutions converge to each other at the bifurcation temperature. At lower temperatures only the metastable phase is able to nucleate from the liquid. In the parameter space we investigated, the growth rate of the stable phase exceeds that of the metastable one. The nucleation and growth rates are sensitive to the features (curvature and position) of the parabola for the metastable phase.