Ostwald's step rule is widely known as an empirical rule that the thermodynamically less stable phase nucleates first, and then new phases are formed in order of increasing thermodynamic stability [1].

   Solvent-mediated transformation is a good example of this step rule. In that, the stable phase nucleates and grows separately from preexistent crystals of the metastable phase. On the other hand, the metastable phase provides a substrate for nucleation of the stable phase. Indeed, a scenario where the stable phase nucleates on the surfaces of the preexistent metastable crystal and grows has been presented as for the origin of polycrystals such as tetrapod-like polycrystals of ZnO [2,3,4] and CdS [5], and a combination of bullets of snow [6,7]. Although, there have been few theoretical and universal studies on this phenomenon. In the present study, the conditions for as transformation induced by heterogeneous nucleation of a stable phase on the surface of the preformed metastable phase, referred as “epitaxy-mediated transformation” is studied theoretically.

   We treated homogeneous 3D nucleation as the first process of Ostwald’s step rule and derived conditions for nucleation of the metastable phase from comparison of induction periods for nucleation and steady state nucleation rates of two crystal phases. It was revealed that if the surface free energy of critical 3D nucleus of the metastable phase is small enough and its shape is less anisotropic, nucleation of the metastable phase becomes dominant. The stable phase dominantly nucleates under the adverse conditions.

   If any nuclei of the metastable phase are formed, three competitive following processes: growth of the metastable phase, solvent-mediated transformation, and epitaxy-mediated transformation, are envisioned. It was revealed that the later homogeneous nucleation of the stable phase, which accompanies solvent-mediated transformation, is possible only near the equilibrium concentration for the metastable phase. In contrast, epitaxy-mediated transformation arises under a high degree of concentration as well as near the equilibrium concentration of the metastable phase. The smaller edge energy and less anisotropy of a 2D nucleus of the stable phase work to the advantage of hetero-epitaxial nucleation. And, the orientation giving the minimum value of the interfacial energy is selectively chosen for hetero-epitaxial nucleation. It should be noted that 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.

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1. Composition of a binary regular solid solution during its growth studied by the Monte Carlo simulation and the mean field approximation