  Capillarity approximation is used to study the free-energy landscape of
nucleation when an intermediate metastable phase exists. The critical nucleus
that corresponds to the saddle point of the free-energy landscape as well as
the whole free-energy landscape can be studied using this capillarity
approximation, and various scenarios of nucleation and growth can be
elucidated. In this study we consider a model in which a stable solid phase
nucleates within a metastable vapor phase when an intermediate metastable
liquid phase exists. We predict that a composite critical nucleus that consists
of a solid core and a liquid wetting layer as well as pure liquid and pure
solid critical nuclei can exist depending not only on the supersaturation of
the liquid phase relative to that of the vapor phase but also on the wetting
behavior of the liquid surrounding the solid. The existence of liquid critical
nucleus indicates that the phase transformation from metastable vapor to stable
solid occurs via the intermediate metastable liquid phase, which is quite
similar to the scenario of nucleation observed in proteins and colloidal
systems. By studying the minimum-free-energy path on the free-energy landscape,
we can study the evolution of the composition of solid and liquid within nuclei
not limited to the critical nucleus.
