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

Nucleation and growth of stable and metastable crystalline phases are descr ibed in the framework of a single-order parameter Cahn-Hilliard theory. A p iecewise parabolic free-energy order parameter relationship composed of thr ee parabolas of positive curvature coefficient has been adopted. The analyt ical solution of the problem is presented. It is found that above a critica l (bifurcation) temperature the interface is layered; a metastable layer is sandwiched between the initial and the stable phases. Above the bifurcatio n 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 nuc leate from the liquid. In the parameter space we investigated, the growth r ate 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. (C) 2000 American Institute of Physi cs. [S0021-9606(00)52705-6].