Probability, nucleation

The difficulties imposed by clay coatings on quartz nucleation probably explain why there are few reports of quartz cementation in shales. The oxygen in quartz silt is isotopically heavy (8 0 = 19%o) compared to sand-size quartz (5 0 = 14%o) (Blatt, 1987) suggesting that a substantial component of relatively low-temperature quartz resides in shales. The application of cathodoluminescence microscopy to shales has been quite limited. In Frio Formation shales of south Texas no convincing quartz cement is observed across a range of depths in which quartz cementation becomes important in associated... 

By inspecting Fig. 3.13, one can see how single clusters become less and less numbered with increasing p after having passed a maximum. In term of bubbles, this means that with increasing nucleation probability more and more bubbles are growing on the electrode surface until a maximum is reached. After this maximum the number of small bubbles decreases. Comparatively, the larger bubbles (the mutli-clusters) increase and become equal in number to the small ones. This is well confirmed by visual observations (compare with Fig. 3.10). 

In order to be able to apply this model, the nucleation probability p has to be linked to the electrochemical, electrode, and cell properties such as the current density and the terminal voltage. Due to the lack of knowledge in this field, in particular the knowledge about the activation of nucleation sites, this is not a straightforward task. In the next section, a simplified approach that is able to explain the important effects is presented. 

Numerical simulations are performed on a quadratical grid with discrete time steps, thus the nucleation probability at a given point is calculated by... 

In precipitation reactions, where is very small and where large supersaturation ratios can be generated rapidly, homogenous nucleation probably... 

Since the homogeneous nucleation probability cannot be measured for glass-forming liquids, it has not been possible to either prove or disprove this denial of an in-principle ground state for the hquid state of simple substances. The plausibility of Kauzmann s resolution, however, has suffered from the identity of behavior of crystallizable and atactic (noncrystalliz-able) polymers, and by the experimental contrasts in the composition dependencies of homogeneous nucleation temperatures and glass transition temperatures (7 and T ) observed in binary solutions. 

We note that such a transition from a circular to a quadratic envelope of the crystals has also been reproduced by computer simulations [13,14]. There, this transition is due to the reduction of the growth front nucleation probability. Wliile the disk-like pattern consists of multiple crystals, the square-shaped pattern represents a single crystal. We thus assume that, for the given film thickness, we observed a transition from a poly crystalline structure to a single crystal within the temperature interval from 45 to 50°C. 

If it is assumed that nucleation of phase B is equally probable on all inner and outer surfaces of the crystal of A, and that the rate of the phase boundary reaction for the growth of phase B is constant, then the rate law for the dissociation reaction can be calculated, provided that the nucleation probability is known as a function of time. In the simplest case, there will be An possible nucleation sites, each of which has an equal a priori probability of becoming an actual nucleus. If n is the number of nuclei already present, then the rate of nucleation is ... 

To control the size and geometry of the prepared nanoparticles, another important parameter is the kind of substrate used. According to Markov et al. when metal crystallites or drops nucleate or grow onto a foreign substrate, in their immediate vicinity zones of zero nucleation probability exist [30]. Nucleation under these conditions occurs under the influence of the external electrical field. The growth of nuclei causes deformations in the field, resulting in an overpotential drop in the screened surface segments. When the overpotential is lower than the minimum value for nucleation, further nucleation is impossible. It was shown that for a hemispherical drop on a flat substrate, nucleation is impossible inside a zone of radius r, defined as... 

A rather convincing justification of the catalytic mechanism is reached in terms of atomistic events, at least on conveniently oriented crystal faces. Now, in turn, the problem remains of understanding the pH dependence of the step nucleation probability [31], Further investigation of iron dissolution by impedance analysis has clearly proved that both catalytic and consecutive mechanisms are operative with a relative contribution depending upon electrode potential and solution pH. 

Pit nucleation, which leads to the formation of a small area of bare, un-filmed, metal (pit "nucleus") and is considered as a random process. We note G (cm s ) the nucleation probability per unit of time and area. 

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