Nucleation critical nuclei size

The resistance to nucleation is associated with the surface energy of forming small clusters. Once beyond a critical size, the growth proceeds with the considerable driving force due to the supersaturation or subcooling. It is the definition of this critical nucleus size that has consumed much theoretical and experimental research. We present a brief description of the classic nucleation theory along with some examples of crystal nucleation and growth studies. 

The models incorporate two microscopic parameters, the site density and the critical nucleus size. A fit of experimental current transients to the models allows conclusions, for example, concerning the effect of additives on nucleation rate. Fabricus et al. found by analysis of current transients that thiourea increases the nucleation density of copper deposited on glassy carbon at low concentration, but decreases it at higher concentration [112], Schmidt et al. found that Gold nucleation on pyrolytic graphite is limited by the availability of nucleation sites [113], Nucleation density and rate were found to depend on applied potential as was the critical nucleus size. Depending on concentration, critical nuclei as small as one atom have been estimated from current transient measurements. Michailova et al. found a critical nucleus of 11 atoms for copper nucleation on platinum [114], These numbers are typical, and they are comparable to the thermodynamic critical radii [86],... 

The definitive hydrate kinetic inhibition mechanism is not yet available. Some work suggests that the mechanism is to prevent hydrate nucleation (Kelland, 2006). However, a significant amount of evidence suggests that hydrate kinetic inhibitors inhibit the growth (Larsen et al., 1996). However, this apparent conflict is due to the definition of the size at which crystal nucleation stops and growth begins. To resolve this confusion, one may consider growth to occur after the critical nucleus size is achieved. 

Figure 4.6 shows the dependence on r for both contributions with small values of r its square is predominant and AG increases with increasing r the nucleus will stop growing and (with homogeneous nucleation) it disappears. From a certain value of r, the critical nucleus size, rk, AG decreases upon growth the nucleus is then stable and continues growing. The value of rk can be easily calculated at rk ... 

Nucleation — Atomistic theory of nucleation — Figure 1. Dependence of the nucleation work AG (ft) on the cluster size n (a) and dependence of the critical nucleus size nc on the supersaturation Ap (b) according to the atomistic nucleation theory (a schematic representation)... 

Hence, in this approximation, the critical nucleus size may be estimated from the slope of plots of the logarithm of the nucleation rate as a function of the logarithm of the supersaturation. 

FIGURE 7.5 Nucleation rate as a fimction of P/P(, and also as a function of critical nucleus size. From Nielsen [25]. 

The carbon atoms arriving at the substrate surface must exceed a certain concentration at the solid-gas interface to reach and exceed the critical nucleus size. Therefore the diamond nucleation density as well as the growth rate are dependent on the relative rates of bulk and surface diffusion of carbon atoms. ° These are different for different substrates. Thus, the nucleation process needs a temperature dependent incubation time which is related to the time required to form critical size diamond clusters on the substrate surface. The nucleation rate, which is initially negligible, reaches a maximum after a certain time period and tends to zero for longer deposition times. ... 

For the initial formation of a solid phase on a substrate surface from vapor precursors through heterogeneous nucleation, as is schematically illustrated in Figure 20.2, the critical nucleus size, r, and the corresponding energy barrier, AG, are given by the following equations ... 

As the gas is cooled, it becomes supersaturated, leading to the nucleation of particles. This nucleation is a result of molecules colliding and agglomerating until a critical nucleus size is reached and a panicle is formed. As these particles move down, the supersaturated gas molecules conden.se on the particles causing them to grow in size and then to flocculate. In the development on the CD-ROM. w c will model the formation and growth of aluminum nanoparticles in an, AFPR. 

It should be noted, however, that most conditions of deposition from the vapor phase have been shown to be such that classical nucleation theory is not well-suited to describe the nucleation kinetics of diamond, since the critical nucleus size is on the order of a few atoms.P The small size of the critical nucleus makes it quite inappropriate to use the classical thermodynamic variables to describe the nucleation processes. Under such conditions, the Gibbs free-energy of the formation of a critical nucleus carmot be expressed... 

The nucleation process has been discussed above in terms of the so-called classical theories stemming from the thermodynamic approach of Gibbs and Volmer, with the modifications of Becker, Doring and later workers. The main criticism of these theories is their dependence on the interfacial tension (surface energy), 7, e.g. in the Gibbs-Thomson equation, and this term is probably meaningless when applied to clusters of near critical nucleus size. 

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