Surface nucleation frequency

Figure 9.7 presents the time variations of the supersaturation profiles relatively for the CBZ and CBZ/NCT solid phases. The primary nucleation of CBZ/NCT first occurred at a supersaturation ratio 15% lower than the CBZ supersaturation ratio. A possible explanation lies in the fact that there may be a better affinity with the solvent of the CBZ/NCT nuclei than with that of the CBZ nuclei leading to a higher nucleation frequency of CBZ/NCT than CBZ. Ten minutes later, CBZ primary nucleation occurred. One could assume that the presence of the co-crystal form in suspension may favour a nucleation of CBZ crystals on the surface of CBZ/NCT solid form. 

Ultimately, if we stick to the simple laws of nucleation, we will be satisfied with the law at constant specific frequency, the exponential law of Avrami [8.64], or possibly with the law power [8.55] or [8.70]. We will study in Chapter 11 heterogenous reactions with surface nucleation using a constant specific frequency. In Appendix A. 9, we will use the various laws to discuss reactions with nucleation in the bulk. 

We will see later (section 14.6) that if y and Sj x) respectively represent the frequency of the surface nucleation (independent of time in a pseudo-steady state mode) and the spatial function of nucleation (which is the area of the free surface of solid A), the frequency of nucleation is always ... 

When the primary facets of ice are defect free, the relevant step generation mechanism is the formation of two-dimensional nuclei. The process is driven by thermally activated fluctuations of the liquid phase that create two-dimensional heterophase clusters with solid-like structure. The most probable cluster geometry is tiiat of a pillbox, for which the edge-to-surface free energy ratio will favor spreading at a given drive. In analogy with three-dimensions, the nucleation frequency /per unit facet area. 4 is of a Maxwell-Boltzmann form, / exp - n cr /Ap kbT), where [Pg.47]

The stationary nucleation rate is 1st where No/cra is the number density of active sites on the electrode surface and K /s is the 2D nucleation frequency (or the nucleation rate constant) per site given by the general formula (2.126). 

A pre-factor 1/r contains a time scale r or a frequency which for instance corresponds to the hard phonon or to an atomic frequency. The growth rate of the crystal is proportional to this rate (23). As will be shown later, the nucleus once formed expands in a time scale shorter than the one necessary for nucleation. If the process consists of a series of sequential subprocesses, the global velocity is governed by the slowest one. Therefore, this nucleation process determines the growth rate of a faceted surface. 

The frequency-dependent spectroscopic capabilities of SPFM are ideally suited for studies of ion solvation and mobility on surfaces. This is because the characteristic time of processes involving ionic motion in liquids ranges from seconds (or more) to fractions of a millisecond. Ions at the surface of materials are natural nucleation sites for adsorbed water. Solvation increases ionic mobility, and this is reflected in their response to the electric field around the tip of the SPFM. The schematic drawing in Figure 29 illustrates the situation in which positive ions accumulate under a negatively biased tip. If the polarity is reversed, the positive ions will diffuse away while negative ions will accumulate under the tip. Mass transport of ions takes place over distances of a few tip radii or a few times the tip-surface distance. 

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