Nucleation of a new phase

Figure 1.11 The formation of metal clusters during the nucleation of a new phase. The co-ordination is first tetrahedral, leading to 5-fold symmetry, until the 13-atom icosahedron is formed which transforms into the cubic icosahedron of the stable phase...

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. 

Heterogeneous reactions that do not require nucleation of a new phase. That is, all the phases involved in the reactions are initially present. Many of these reactions can be quantified well if the boundary conditions are simple. The following are some examples. 

The transforming material portion may be adjacent to its prospective phase, which is the case for growth of a new phase or the portion may be isolated, which is the case for nucleation of a new phase. In any case, the spatial variation of... 

Nucleation of a new phase in the solid state is more complicated than that of nucleation in freezing. Volume difference between the new and old phases causes an elastic misfit term that increases AG. Destruction of existing grain boundaries reduces AG. An expression for the free energy change during nucleation of 3 in a matrix of a is... 

The ratio of the activation energy for heterogeneous nucleation of a new phase on a grain boundary, AG hetero, to that for homogeneous nucleation,... 

Exclusion zones — Zones of reduced supersaturation in which nucleation of a new phase is fully arrested. Such zones appear around growing stable clusters due to reduced concentration of ionic species and/or reduced -> overpotential in the clusters vicinity. 

This is, however, not the whole of the matter. The superstructure ordering of point defects the collection of interstitial ions along certain fines or sheets, as in Magneli s model for the precursor of his shear structures the temperature-dependent adjustment of composition of a nonstoichiometric phase at the boundary of the bivariant range the nucleation of a new phase of different stoichiometry—these depend on accumulating vacancies or interstitials in some regions of the crystal lattice at the expense of others. 

Let us consider the thermodynamics of processes of the homogeneous nucleation of a new phase with the formation of fluid drops from the over saturated vapor as an example. While the chemical potential of the equihb rium substance vapor over spherical particles of its condensed phase is given by the Kelvin Thomson equation (5.2), only those drops that have the critical size r.. 

Because of the interplay between thermodynamic, kinetic, and molecular recognition factors (Fig. 1) in determining nucleation of a new phase, it is essential to consider the effects of these factors when using solvents to selectively nucleate polymorphs. Threlfall has thoroughly considered thermodynamic and kinetic factors and the conditions in which the solvent may or cannot affect polymorphic outcomes. The analysis is briefly summarized here. These concepts are also discussed extensively elsewhere. ... 

Fig. 2.22. Schematic illustration of the geometries for homogeneous and heterogeneous nucleation of a new phase, C, in a diffusion couple of A and B. See text for further explanation...

Crystallization results basically in the succession of two events the primary nucleation of a new phase and then the three-dimensional growth of lamellae these steps can be followed by lamellar thickening, fold surface smoothing, or reorganization into more perfect crystals. As reported by others, with increasing the annealing temperature in PVDF/PMMA blend film, the amount of a phase increases due to easier local internal chain rotation at higher temperature and most of p and y form convert to a form. 

The first indication of the nucleation of a new phase occurred immediately beyond itcAc)r indicated in Fig.4,and shown in Fig.5a. The domains observed were compact and had a monodisperse size distribution. Obviously, there is a minimum distance between then as no closely neighbouring dark spots (compared to their diameter) are observed. However, distances between nearest neighbours differ largely. 

It is significant that chemical waves originate from the point where specks are first formed. Bands appear at heterogeneous centres or dust particles or at glass surfaces. Nucleation of chemical wave and nucleation of a new phase have a formal similarity [27]. 

The vapor pressure is thus enhanced with decreasing drop radii, although the effect is appreciable only for extremely small drops (see calculation below). This effect is of importance in homogeneous nucleation of a new phase. 

The real nature of the very first stage of the nucleation of a new phase on the surface of an electrode. In most cases, either the classical or atomistic analyses of its kinetics indicate that single adatoms behave as thermodynamically stable entities that are able to grow irreversibly. 

Figure 2 The different classes of nucleation. (a) Homogeneous a pure clear solution spontaneously shows nuclei, (b) Heteoge-neous nucleation of a new phase on foreign particles, (c) Secondary the addition of seed particles results in new nuclei.

The temperature dependencies of both nucleation of a new phase and its rate of growth result in a strong temperature dependence of transformation rate. 

It is evident from Equation 7.114 that in the case when G > 1, nanoshell formation is impossible (taking into account that x and y start from almost 1). This means that, in very small particles, Tba < 2yS2/Ag, the reaction with void formation is impossible. It is interesting that this critical condition coincides with the critical radius for nucleation of a new phase. 

The highest possible degree of dispersion cannot be achieved by simple comminution and grinding, that is, by dispersion processes. It can only be achieved by condensation methods. The latter involve the nucleation of a new phase in the initial homogeneous system at high levels of supersaturation. 

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