Nucleation exclusion zones

Nucleation — Exclusion zones — Figure. Nucleation exclusion zones formed around growing (a) Ag [i] and (b) Ag7NOn single crystals [ii]... 

As already stated, the nuclei behave as microelectrodes in the initial stage of electrodeposition of metals onto inert substrates.33 If nucleation exclusion zones around nuclei are formed,35,36 an inert substrate can be partially covered even at long deposition times, due to the nucleation exclusion zones overlapping, which results in the formation of granular electrodeposits.37,38 In this way, a granular... 

On the other hand, due to the overlapping of the nucleation exclusion zones,7,35,36 deposition on the partially covered graphite electrode is an excellent illustration of the above discussion. Namely, the diffusion layer on the inert electrode partially covered with grains of active metal can be formed and diffusion control established in the same way as on an electrode of massive active metal if the deposition process is characterized by a large jo/jh-1 If dendrites are formed on the grains, their tips enter the bulk solution and overall control of the deposition process becomes activation or mixed controlled. 

Figure 7.5 Copper crystals electrodeposited through galvanostatic reduction of Cu on PEDOT. Dark areas - nucleation exclusion zones bright areas - nanoscale fine copper deposits.

The radius of a nucleation exclusion zone can be calculated on the basis of the following discussion, taking into account the charge transfer overpotential also. If there is a half-spherical nucleus on a flat electrode, the extent of the deviation in the shape of the equipotential surfaces which occurs around it depends on the crystallization overpotential, current density, a resistivity of the solution and on the radius of the nucleus, r. If the distance from the flat part of the substrate surface to the equipotential surface which corresponds to the critical nucleation overpotential, rj, is /n, then this changes around defect to the extent where A is a number, as is presented in Fig. 2.18. 

The radius of the nucleation exclusion zone, corresponds to the distance between the edge of a nucleus and the first current line which not deviates (when k-rj becomes equal to /n). Accordingly, nucleation will occur at distances from the edge of a nucleus equal or larger than r z, which can be calculated as ... 

In the case of electrodeposition from the solution containing P04 -ions, almost complete surface coverage was achieved even with a charge quantity of 2 mA h cm at a current density of 30 mA cm (i.e., under the optimal film deposition conditions, as determined in Ref. [65]). This is probably due to the possibility of further nucleation occurring immediately next to the already existing nuclei, as a result of the smaller values of the radii of the nucleation exclusion zones caused by the decrease of the exchange current density for the deposition process by the addition of P04 -ions. For comparison, in phosphate-free nitrate solution, a compact Ag film had not been deposited even after 100 mA h cm had been passed through the cell, as can be seen from Fig. 2.23a [65]. 

The surface of completely covered graphite electrode by deposition from ammonium bath is shown in Fig. 2.38a, while the silver deposit obtained after polarization measurement up to an overpotential of 120 mV on an uncovered graphite electrode is shown in Fig. 2.38b. This electrode surface is partially covered because of the overlapping of the nucleation exclusion zones, being the ideal physical model of a partially covered inert electrode. The regular crystal form of the grains in Fig. 2.38b confirms that the deposition on the microelectrodes is not under diffusion control [16, 106], despite the overall deposition rate that is determined by diffusion to the macroelectrode. 

Figure 19.11 shows the natural logarithm of the fraction of residual nucleus sites of (Ng-N)/Ns based on Eq. (19.9) as a function of time. The residual fraction decreases linearlj with time giving the rate constant of Jq. The straight line can be applied up to 90-95% of the active sites, whereas the non-crystallized area remains about 90%. These results clearly indicate that almost all the active sites with the limited number are controlled by the heterogeneous nucleation mechanism. These characteristics of the active sites are not known. In the other explanation for the saturation density, there is a nucleation exclusion zone [58]. The nucleation will stop and reaches to the saturation density when the exclusion zone is overlap on the whole substrate surface. The zone might be associated with the density fluctuation around the... 

Nucleation exclusion zones modeling particle growth... 

The production of single nuclei is somewhat helped by the formation of nucleation exclusion zones around the growing particles (43 5). In the area surrounding a growing particle, there will be a reduction in the concentration of precursor, and this will reduce the probability of nucleating a new particle. Milchev et al. have derived an equation for the stationary nucleation rate around a growing stable cluster (46,47). 

Figure 163A Variation of the size of a growing particle as a function of applied overpotential and time calculated using equation (16.3.4) (a). Lines corresponding to the limiting cases of diffusion limiting growth (r

For most applicable overpotentials, the numerator becomes 1 and the nucleation exclusion zone extends a distance particle radii from the growing particle—that... 

In the very initial stage of the phase transition the appearance of a nucleus on the substrate does not change the conditions for subsequent nucleus formation, the growing supercritical clusters do not interact with one another and the actual surface fraction u) covered by nucleation exclusion zones (or by the growing nuclei themselves) is negligibly small. Thus the current density I t) is given by ... 

The evaluation of the actual volume or the actual surface area occupied by growing clusters or by nucleation exclusion zones, respectively is a most important point in the kinetic theory of the first order phase transitions. Several authors [5.11-5.17] have considered the problem and among them the name of Avrami [5.14-5.16] seems to be the most popular one. However, the stochastic approach proposed by Kolmogoroff [5.12] is undoubtedly the most rigorous one (see e.g. the critical analysis of Belen ky [5.18]) and here we describe this approach. 

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