Nucleation and growth of a core-shell composite nucleus by diffusion.

Abstract

The critical radius of a core-shell-type nucleus grown by diffusion in a phase-separated solution is studied. A kinetic critical radius rather than the thermodynamic critical radius of standard classical nucleation theory can be defined from the diffusional growth equations. It is shown that there exist two kinetic critical radii for the core-shell-type nucleus, for which both the inner-core radius and the outer-shell radius will be stationary. Therefore, these two critical radii correspond to a single critical point of the nucleation path with a single energy barrier even though the nucleation looks like a two-step process. The two radii are given by formulas similar to that of classical nucleation theory if the Ostwald-Freundlich boundary condition is imposed at the surface of the inner nucleus and that of the outer shell. The subsequent growth of a core-shell-type postcritical nucleus follows the classical picture of Ostwald's step rule. Our result is consistent with some of the experimental and numerical results which suggest the core-shell-type critical nucleus.