Homogeneous solution, nucleation

In the homogeneous solution, nucleation is accompanied by the formation of an interface between solution and crystal at the cost of an increase in the free energy. On the other hand, the monomer in crystal has a smaller free energy than that in solution if the solution is supersaturated (S > 1). Therefore, there are two opposite tendencies in the nucleation reaction. The first is the increase in the free energy caused by the formation of the interface, which is reflected in the first term on the right-hand side of Equation (6.2). This term is always positive. The other tendency is the decrease in the free energy caused by the formation of the crystal, which is shown in the second term, which is negative when 5 > 1. 

The decomposition of a solution with composition outside the spinodal region but within the metastable region can be analyzed in a similar way. Let us assume that a sample with composition in this region is cooled to low temperatures. Small fluctuations in composition now initially lead to an increase in the Gibbs energy and the separation of the original homogeneous solution must occur by nucleation of a new phase. The formation of this phase is thermally activated. Two solutions with different composition appear, but in this case the composition of the nucleated phase is well defined at all times and only the relative amount of the two phases varies with time. 

In discussing the mechanisms of the formation of monodispersed colloids by precipitation in homogeneous solutions, it is necessary to consider both the chemical and physical aspects of the processes involved. The former require information on the composition of all species in solution, and especially of those that directly lead to the solid phase formation, while the latter deal with the nucleation, particle growth, and/or aggregation stages of the systems under investigation. In both instances, the kinetics of these processes play an essential role in defining the properties of the final products. 

The necessary condition to have a NG mechanism is that the second phase can nucleate from the homogeneous solution. The nucleation rate depends on interaction parameter, interfacial tension between both phases, and diffusion coefficient. 

The importance of polysulfides in the pyrite formation process was outlined by several studies (37, 38). Schoonen and Barnes (37) showed that no precipitation from homogeneous solution can be observed within a reasonable time scale, even in solutions highly supersaturated with respect to pyrite, unless pyrite seeds are already existing. Therefore future studies should address the role of ferric oxide surfaces in promoting the nucleation of pyrite. 

The existence of the phase boundary between the solid and liquid phase complicates matters, since a phase boundary is associated with an increase in free energy of the system which must be offset by the overall loss of free energy. For this reason the magnitudes of the activated barriers are dependent on the size (i.e. the surface to volume ratio of the new phase) of the supramolecular assembly (crystal nucleus). This was recognized in 1939 by Volmer in his development of the kinetic theory of nucleation from homogeneous solutions and remains our best model today (Volmer 1939). 

There are several other points of view regarding the definition of the nucleus of zeolite. For example, it was suggested that some primary structural units of the framework, such as rings and basic cages, could be defined as the nucleus of zeolites and other microporous crystals. It was also proposed that the nucleus of zeolite could be defined as particles with critical size. These particles should be stable under crystallization conditions. Compared with the classical theory of nucleation from homogeneous solution, the theory developed by Pope could well explain the significant decrease of the free-energy barrier of nucleation for zeolites and other microporous compounds.[43] This... 

Supersaturated homogeneous solutions are thus metastable, and the metastability decreases with increasing supersaturation. In other words, nucleation starts after the solute concentration has exceeded a definite value, and then solute molecules form aggregates or clusters. If, however, the crystals are placed in a supersaturated solution, the solution eventually attains equilibrium after the growth of the crystals upon crystallization. 

In the HDP procedure, the desired metal ion deposits in the form of the hydroxide. To obtain a homogeneous distribution, nucleation of the hydroxide must occur uniformly on the surface of the support particles, and not in the bulk solution. To prevent the latter, the suspension must... 

Nucleation and Growth. A common situation is when a homogeneous solution (or melt) is rapidly cooled to a constant temperature where In/I is large enough to induce nucleation. Then the semiempirical Avrami equation often applies ... 

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