Surface nucleation model

A surface nucleation model in which attachment sites exist as molecular clusters that, like nuclei, must reach a critical size to be stable and support subsequent crystal growth. Here,... 

Models used to describe the growth of crystals by layers call for a two-step process (/) formation of a two-dimensional nucleus on the surface and (2) spreading of the solute from the two-dimensional nucleus across the surface. The relative rates at which these two steps occur give rise to the mononuclear two-dimensional nucleation theory and the polynuclear two-dimensional nucleation theory. In the mononuclear two-dimensional nucleation theory, the surface nucleation step occurs at a finite rate, whereas the spreading across the surface is assumed to occur at an infinite rate. The reverse is tme for the polynuclear two-dimensional nucleation theory. Erom the mononuclear two-dimensional nucleation theory, growth is related to supersaturation by the equation. 

J. W. Evans, T. R. Ray. Interface propagation and nucleation phenomena for discontinuous poisoning transitions in surface reaction models. Phys Rev E 50 4302 314, 1994. 

Fig. 3.4. A simple nucleation model for long chains. The first stem is of length l and attaches to the surface. Subsequent stems are deposited adjacent to attached stems, so that the patch spreads in either direction with velocity g...

As shown in 4.4.1., two stages usually occur in surface nucleation, nucleation and then nuclei growth. If surface nucleation is fast (Model C) it is likely due to reaction of a gas with the solid particle. The reaction of a liquid is the other possibility, i.e.-... 

Adsorption and Precipitation vs heterogeneous Nucleation and Surface Precipitation. There is not only a continuum between surface complexation (adsorption) and precipitation, but there is also obiously a continuum from heterogeneous nucleation to surface precipitation. The two models are two limiting cases for the initiation of precipitation. In the heterogeneous nucleation model, the interface is fixed and no mixing of ions occurs across the interface. As a consequence precipi-... 

By use of the proper experimental conditions and Ltting the four models described above, it may be possible to arrive at a reasonable mechanistic interpretation of the experimental data. As an example, the crystal growth kinetics of theophylline monohydrate was studied by Rodriguez-Hornedo and Wu (1991). Their conclusion was that the crystal growth of theophylline monohydrate is controlled by a surface reaction mechanism rather than by solute diffusion in the bulk. Further, they found that the data was described by the screw-dislocation model and by the parabolic law, and they concluded that a defect-mediated growth mechanism occurred rather than a surface nucleation mechanism. 

The nucleation model represents the other extreme. Here, the dissociation of hydrogen is the slow step. Once a nucleus of reduced metal exists, it acts as a catalyst for further reduction, as it provides a site where H2 is dissociated. Atomic hydrogen diffuses to adjacent sites on the surface or into the lattice and reduces the oxide. As a result, the nuclei grow in three dimensions until the whole surface is reduced, after which further reduction takes place, as in the shrinking core model. The extent of reduction (see Fig. 2.3a) shows an induction period, but then increases rapidly and slows down again when the reduction enters the shrinking core regime. 

The droplet current / calculated by nucleation models represents a limit of initial new phase production. The initiation of condensed phase takes place rapidly once a critical supersaturation is achieved in a vapor. The phase change occurs in seconds or less, normally limited only by vapor diffusion to the surface. In many circumstances, we are concerned with the evolution of the particle size distribution well after the formation of new particles or the addition of new condensate to nuclei. When the growth or evaporation of particles is limited by vapor diffusion or molecular transport, the growth law is expressed in terms of vapor flux equation, given by Maxwell s theory, or... 

Bubble nucleation model uses a vapour bubble growing on a heater surface with heat diffusion in the vapour phase. This corresponds to post-CHF heat transfer and is an inaccurate model of heat transfer during nucleation and bubble growth. 

The core of the nucleation model proposed in Refs. [362, 363] is an assumption based on the experimental data that epitaxially oriented nucleation sites are formed in the SiC layer of about 10-nm thickness during the bias treatment. These sites are exposed at the SiC surface, while plasma etching of SiC is occurring during both the BEN treatment and the successive diamond growth process. The model of nucleation process is schematically depicted in Figure 11.57 ... 

New kinetic models were developed to incorporate interface nucleation (Zhang and Banfield 1999) and surface nucleation (Zhang and Banfield 2000), thus to quantitatively interpret the kinetic behavior in the nanocrystalline anatase-rutile system. Surface nucleation and bulk nucleation come into play as temperature increases (Zhang and Banfield 2000). Particle size has been explicitly incorporated into the kinetic equations. The transformation rate scales with the square of the number of anatase nanoparticles in the case of interface nucleation (Zhang and Banfield 1999), or with the number of anatase nanoparticles in the case of surface nucleation (Zhang and Banfield 2000). If the transformation is governed only by interface nucleation, the kinetic equation is ... 

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