Homogeneous nucleation embryo concentrations

Homogeneous nucleation of particles from solution has been observed in various methods that are used to synthesize ceramic powders [113-116]. For example, in aqueous solutions, metal ions are usually hydrated [117,118]. Embryos of hydrated metal ions are formed by progressive accumulation of ions to one another through a polymerization process. These polynuclear ions are the precursors for nucleation. When the concentration of the polynuclear ions is above some minimum supersaturation level, homogeneous nucleation starts to form solid nuclei. The nucleation rate of particles from solution can be expressed as [113] ... 

In a homogeneous system, i.e., in the absence of phase boundaries, nucleation is said to be homogeneous. A new phase (I can form if conditions (temperature, pressure, or solute concentration) are such that its chemical potential is smaller than that of phase a. It will then frequently happen that a cluster of molecules in phase a orient themselves by chance as they would be in phase (3. If the new phase is a liquid, the solute (or vapor) molecules have merely to associate to form such an embryo if the new phase is a solid, the molecules also have to attain a mutual orientation as in the crystals to be formed. 

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