Role of epitaxy-mediated transformation in Ostwald's step rule: a theoretical study

Abstract

Crystallization following Ostwald's step rule is given theoretical consideration on the basis of the classical nucleation and growth theory. Conditions for homogeneous 3D nucleation of the thermodynamically metastable crystal, for that of the stable crystal, and for co-precipitation of them are derived from comparison of induction periods for nucleation and steady state nucleation rates of both crystal phases. It is shown that if the surface free energy of a critical 3D nucleus of the metastable phase is small enough and its shape is less anisotropic, homogeneous 3D nucleation of the metastable phase rather than the stable phase dominates. After nucleation, the metastable phase should undergo transformation to the stable phase. In addition to two familiar types of transformation, solvent-mediated transformation and direct transformation, we propose a new type of transformation, epitaxy-mediated transformation, which is induced by heterogeneous nucleation and growth of the stable phase on the preexistent crystal of the metastable phase. The general conditions for three competitive processes, growth of the metastable phase, solvent-mediated transformation and epitaxy-mediated transformation, are obtained on the assumption that transformation and growth proceed by 2D nucleation. The result shows that except for the case of co-precipitation, 3D nucleation of the stable phase in solvent-mediated transformation is possible only near or below the equilibrium concentration for the metastable phase. Also, the smaller edge energy of a 2D nucleus of the stable phase and its less anisotropy are more advantageous to epitaxy-mediated transformation. Epitaxy-mediated transformation sometimes results in a polycrystal whose arrangement of components is dominated by the symmetry of the metastable phase. In parallel, heterogeneous nucleation on the metastable phase can act as a trigger of direct transformation, as transformation proceeds from the surface to the center of the crystal.