Metastable Phases

It is well known that the saturation evaporation pressure P' of a small liquid droplet with a radius r is larger than P of a liquid surface with an infinite radius, which is described by the famous Kelvin equation [79]

where a is the surface tension, M is the molecular weight, p is the density of the liquid, and R is the Avogadro constant. A similar conclusion could be derived for the crystals. Namely, the saturation evaporation pressure of a small crystallite is larger than that of a bulk crystal. The saturation evaporation pressure affects the melting point and the solubility of the crystals. The smaller the crystallite, the lower the melting point and the higher the solubility. In saturated liquid, small crystallites can be spontaneously dissolved or melted, while large ones can spontaneously grow. On the contrary, it is easy to understand that the process of solidification or crystallization can be more difficult for the smaller crystallites. It is difficult to form a new phase out of a phase, which results in different kinds of supersaturation phenomena, like the supersaturation of a gas or a solution, the superheating or the supercooling of a liquid or a solid, etc. From the thermodynamic point of view, all types of supersaturated systems are in the nonequilibrium state. The matter formed during such procedures should be in the nonequilibrium state. Of course, the phases could remain in such a state for a long period, which could be defined as metastable. A metastable phase is a phase that does not exist in equilibrium conditions. It is not the thermodynamically most stable phase but rather a temporarily stable one in a certain condition. The metastable phase forms under conditions corresponding to a local minimum of the free energy. The large energy barrier between this local energy minimum and the lowest energy minimum hinders the formation of the equilibrium phase in the sense of the dynamics. Nano-particles as well as nanocapsules usually form in nonequilib-rium conditions and consequently the phases formed can be metastable. It was found that in rare-earth transition-metal systems, the formation and phase transformation of rare-earth metastable phases depend sensitively on the structural symmetry of the metastable phases [84]. It is understandable that the structural symmetry of the metastable phases would be one of the most important factors that govern the formation and the phase transformation of the metastable phases in nanocapsules/nanoparticles.

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