Nucleation step

Single-step nucleation, (ii) above, requires the unsatisfactory assumption that the generation of a single molecule (atom, ion-pair, etc.) of product constitutes the establishment of a nucleus. (It would seem to be more realistic to regard this as the outcome of several distinct chemical steps.) The mathematical treatment expressing the probability of the occurrence of this unimolecular process is... 

Fig. 11 Craze in commercial polystyrene showing the characteristic steps nucleation through void formation in a pre-craze zone, growth of the fibrillar structure of the widening craze by drawing-in of new matrix material in the process zone, and final breakdown of the fibrillar matter transforming a craze into a crack (the crack front is more advanced in the center of the specimen, shielded by a curtain of unbroken fibrils marked by the arrow). The fibril thickness depends—of course—on the molecular variables, the strain rate-stress-temperature regime of the crazing sample and on its treatment (preparation, annealing) and geometry (solid, thin film) for PS typical values of between 2.5 and 30 nm are found [1,60,61]...

Essentially, the key process in the preparation of ultrafine powders by reaction-precipitation is crystallization from a solution. As mentioned in the previous chapter, crystallization from a solution includes two steps nucleation and crystal-growth. Both can occur only in a supersaturated solution and spontaneous nucleation can occur only when the concentration of the solute in the solution is over the super solubility of the substance involved. The rate equation for nucleation derived from the principles of thermodynamics is represented by [ 182]... 

The extensive series of studies on in vitro core formation reported by Harrison and co-workers (32, 63, 82, 140) and others (133) has led to the development of a three-step hypothesis for iron uptake. In the first step, iron entry through the channels, Fe + passes from the outside of the protein through the channels in the apoferritin coat to the interior cavity. The second step, nucleation, involves iron binding to groups on the inner surface of the protein in such a way that a small cluster of coupled Fe ions is formed. The final step, formation of the core, involves the extension of a small nucleating cluster by the addition and oxidation of Fe +. This stage is characterized by an initial catalytic phase, during which the small cluster rapidly expands, followed by a reduced rate of expansion once the core has attained a particular size (—1000-1500 iron atoms per molecule). 

In a more general analysis, Allnatt and Jacobs [8,12] removed the restriction of single-step nucleation. 

The role of the iron-oxygen cluster in ferritin is not clear, but it is suggested that it plays a role in the first step (nucleation) of the multiiron aggregate in ferritin. Ferritin has an important role as a transport and storage protein for iron in many organisms 1, 22). 

Pellet formation essentially involves three steps nucleation (consolidation of several grains into a nucleus), transition (joining of several nuclei to form larger entities), and ball growth (growth... 

By combining the general form of the nucleation rate which applies to multi-step nucleation (Equation 5) with Equation (6) and assuming a constant growth rate (r increases linearly with time), it is possible to express the decomposition rate in terms of the fraction decomposed as [45] ... 

Fleischmann and coworkers [17, 133] and Retter [134] pointed out that the combination of active intermediates to form a critical nucleus at a specific site may lead to the power law of n-step nucleation... 

The same strategy was applied in the derivation of rate equations for w-step nucleation according to a power law (cf. Eq. (21)) [133, 134], the combination of nucleation laws with anisotropic growth regimes [153], as well as truncated nucleation due to time-dependent concentration gradients of monomers [136]. MC simulations verified that the Avrami theorem is valid for instantaneous [184], progressive [185], and n-step nucleation according to a power law [184-187]. 

Fig. 13 Current transients i(t) for Au (111), miscut < 0.5°, in 0.05 M H2SO4 obtained after a singie potentiai step from 1 = 0.75 V (region II) to various final potentials in region iii. The experimentai traces are given as individual data points, the solid lines represent theoretical curves calculated with the parameters of the numerical fit to a model combining (a) an adsorption process (Eq. 7) and (b) one-step nucleation according to an exponential law with surface diffusion-controlled growth (Eq. 34), (reprinted from Ref. [299]. Copyright 1997 by VCH Verlagsgesellschaft mbH Weinheim).

Phosphate crystals are carefully grown from the solution with final size in the mm range. The typical dimension of phosphate crystal should be about 2-20 pm. The size of the crystal and the growth procedure differ depending on the technological process occurring at the interface between steel and electrolyte solution. The next step, nucleation density of phosphate crystal, is adjusted to the technical system. The layer properties are improved by microscopic local elements in the technical process of... 

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