Nucleation in the bulk

Increasing the temperature or lowering the pressure on a superheated liquid will increase the probability of nucleation. Also, the presence of solid surfaces enhances the probability because it is often easier to form a critical-sized embryo at a solid-liquid interface than in the bulk of the liquid. Nucleation in the bulk is referred to as homogeneous nucleation whereas if the critical-sized embryo forms at a solid-liquid (or liquid-liquid) interface, it is termed heterogeneous nucleation. Normal boiling processes wherein heat transfer occurs through the container wall to the liquid always occur by heterogeneous nucleation. 

The critical radius given by Eq. 19.97 is equal to the critical radius for homogeneous nucleation in the bulk liquid. This result is similar to that obtained in Exercise 19.7... 

In all cases, though, the silver particle-size distribution turned out to be a bimodal one. It was suggested that next to nucleation at the support (leading to Ag particles 5 nm) nucleation in the bulk liquid (leading to Ag particles of 20-40 nm) also played a role. 

Fig. 10.23 Illustration of three basic situations of crystal nucleation. From left to right are primary nucleation in the bulk polymer phase, secondary nucleation on the smooth growth front, and tertiary nucleation at the terrace of the growth front...

Fig.2 Reduced location of crystallization front versus dimensionless contact times (Fourier numbers) for the wall temperatures indicated near the curves with unchanged bulk temperature of 180 C for an industrial polypropylene, according to ref.7. The short pieces of lines near the origin belong to = 100 C (O), 95°C ( D ) and 90 C (6 ). A farther growth was inhibited by diffuse nucleation in the bulk of the melt. Sample thickness - 0,7 mm.

The kinetics of the thermal decomposition of solids are reviewed, with emphasis on topological considerations. The general model of nucleation in the bulk of the reactant is explored in detail and the kinetic equations appropriate to this model are derived. It is pointed out that a multistage nucleation process leads to a power law whenever the characteristic time for nucleus formation is long compared with the observation time, and that the assumption of equal rate constants for successive steps is unnecessarily restrictive. The problem of the induction period is examined and two possible reasons for the critical time to, namely the use of an incorrect model, and time-dependent growth rates (including, as a special case, aggregation without chemical decomposition) are advanced. Finally, the consequences of nucleation only on the surface of the reactant are mentioned briefly. 

The next section, which introduces a mass distribution function Q N, i), also describes a new basic equation of the mass conservation law based on the introduction of the net flow j N, t). We directly observe Q N, i) and obtain the overall crystalUnify during nano-nucleation in the bulk melt, which confirms our proposed nucleation theory. 

Calculation of the probability for A to be occluded at time t by one spherulite nucleated either inside a polymer or on polymer boundaries leads to the equations describing the respective components of conversion rate. Integration over time allows derivation of the separate expressions for two contributions to cr. the contribution from spherulites nucleated in the bulk of a polymer, a , and the contribution from those nucleated on the sample boundaries, respectively ... 

The problem is also similar to that discussed in the preceding paragraph, but the nucleation on the surface must not be compared with the nucleation in the bulk of the hquid phase, with interfacial energy, but with nucleation in the bulk of the solid, with interfacial energy y. ... 

It is noted thus that the majority of heterogenous reactions lead to surface nucleations indeed, only some polymorphic transformations, that is, those not requiring any other reactant and not producing s phase, which would occur starting from defects of Frenkel or from defects of misplaced atoms, would be likely to lead to nucleation in the bulk. 

In the same way, if Fl represents the remaining volume of the initial solid, for a nucleation in the bulk, we would have... 

Ultimately, if we stick to the simple laws of nucleation, we will be satisfied with the law at constant specific frequency, the exponential law of Avrami [8.64], or possibly with the law power [8.55] or [8.70]. We will study in Chapter 11 heterogenous reactions with surface nucleation using a constant specific frequency. In Appendix A. 9, we will use the various laws to discuss reactions with nucleation in the bulk. 

The total transfonnation of an initial solid A into a new solid B involves the two processes of nucleation and growth. It is thus advisable to estabUsh laws of evolution that consider the two processes. We will examine the most frequent case, when the nuclei are formed on the surface of the initial soUd. We will see in Appendix 9 the case with nucleation in the bulk. 

In metal alloys, phase transformations and preeipitations at the grain boundaries are generally surface phenomena (on the surface of the grains) and do not apparently rise from the phenomena of nucleation in the bulk. However, if the grains are sufficiently numerous and about the same dimensions, we can make the approximation of a representation in volume of the grain boundaries, which are considered as potential sites. If these sites are located at random, it is possible to apply the whole of the volume of the alloy to the preceding models of Avrami and Erofeev, which one regularly finds in the literature (often without justification). 

---