Nuclei, growth model

Summary of the n Values Found in the Diffusion-Controlled Nuclei Growth Model for Different Growth Geometries and Nucleation Rates. 

Table 1 Nuclei growth models for solid state reactions. Values possible for intercalation into a layered host are highlighted in bold ...

The aim of this study was to develop a kinetic model for the reduction of a supported chromia catalyst. The reduction rate data was examined by various methods and typical kinetic models were tested. Based on the information obtained, the nucleation/nuclei growth models were investigated more closely and derived in a revised form. 

The re-derived nuclei growth model (2) was able to describe the experimental data (nns<3e-4 pmol/s). The parameter estimation with the model (2) clearly suggested that fire reduction of CrOx might proceed rather by 2-dimensional than by 3-dimensional nuclei growth. The model solution (2) with the optimal parameters and the experimental data are illustrated in Figure 1. 

There is increasing interest in nucleus growth mechanisms and many mathematical models have been advanced relating nucleation and nuclei growth rates to the kinetics of solid-state reactions (22-28 general form of the kinetic equations for nuclei growth models is... 

The Ginstling-Brounshtein model was used in constructing an Arrhenius plot for the reaction between strontium carbonate and anatase. Arrhenius plots were constructed for the reaction between strontium carbonate and rutile (see Fig. 8) using both the contracting cylinder model and the nucleus growth model with m = Activation energies calculated from the two reac-... 

It is seen in Table I that the effects of deviation from stoichiometry on the kinetics of the reaction between rutile and strontium carbonate are very pronounced. On the basis of the applicability of the nucleus growth models it appears that increasing the defect concentration lowers the frequency factor as well as the activation energy for diffusion of the rate-con-... 

In the mononuclear model, the limiting step is the formation of a nucleus. Once one is formed, the subsequent growth spreading across the crystal surface is infinitely rapid. For the polynuclear model, the spreading velocity is taken as zero and the crystal surface can only be covered by the accumulation of a sufficient number of nuclei. These two growth models represent two extreme cases. A third model, known as the birth-and-spread model, allows for formation of nuclei and their subsequent growth at a finite rate. In this case, new nuclei can form on top of uncompleted layers. 

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. 

Figure 14 Model of monomolecular growth of bundle-like nucleus. (From Refs. 104, 110, and 111.)...

Supramolecular structures formed during the crystallization of the melt under a tensile stress have already been described by Keller and Machin25. These authors have proposed a model for the formation of structures of the shish-kebab type according to which crystallization occurs in two stages in the first stage, the application of tensile stress leads to the extension of the molecules and the formation of a nucleus from ECC and the second stage involves epitaxial growth of folded-chain lamellae. 

Knowledge concerning the mechanism of hydrates formation is important in designing inhibitor systems for hydrates. The process of formation is believed to occur in two steps. The first step is a nucleation step and the second step is a growth reaction of the nucleus. Experimental results of nucleation are difficult to reproduce. Therefore, it is assumed that stochastic models would be useful in the mechanism of formation. Hydrate nucleation is an intrinsically stochastic process that involves the formation and growth of gas-water clusters to critical-sized, stable hydrate nuclei. The hydrate growth process involves the growth of stable hydrate nuclei as solid hydrates [129]. 

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