Instantaneous and progressive nucleation

The many defects on the surface of a real crystal form nucleation centers. After switching to a potential in the deposition region, there will already be a fixed density of defects Nq where local growth can start. 

As an example, diffusion-controlled hemispherical growths will be described. Hills, Schiffiin, and Thomson calculated the current of Nq individual nuclei that grow independently of each other.  

Schiffrin, and Thomson also calculated an equation for a progressive increase of the number of nucleation centers that occur after switching to a potential in the deposition region. This is called progressive nucleation. The density of nuclei as a linear function of time is described by the equation 

The area of the diffusion zone projected on the surface plane can be described by the equation 

An equation given by Avrami can be used to relate the real surface coverage with diffusion zones to the surface coverage, if the growth of the diffusion zones is unlimited, = NnkDt. 

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Fig. 10). With the completion of the structure transition, the current should drop to zero, which is indeed the case except for peak B, where a slight leak current is seen (ascribed to the side reaction Cu++ I c > Cu+). According to the theory by Bewick, Fleischmann and Thirsk (BFT) the transients can be used to distinguish between instantaneous and progressive nucleation [45], A corresponding analysis revealed that the falling part of the transients agrees well with the model for instantaneous nucleation, while the rising part shows a systematic deviation. This was explained by the existence of surface defects on a real electrode in contrast to the ideal case of a defect-free surface assumed in the theoretical model. By including an adsorption term in the BFT theory to account for Cu deposition at defects, the experimentally obtained transients could indeed be reproduced very well [44], We shall return to the important role of surface defects in metal deposition later (sec. 3.2).

Figure 10.6 Normalized current transients for instantaneous and progressive nucleation.

Deposition of mercury at boron-doped diamond (BDD) and platinum electrodes has also been studied [33]. Deposition and oxidation of mercury was performed by cyclic voltammetry from the solution of 1 mM Hg2 ( 104)2 in 1 M Na l04. In order to learn more about this deposition, it was carried out also under chronoamperometric conditions. The results obtained are shown in Fig. 2 in the form of dimensionless current-time transients. Experimental curves obtained at two different overpotentials were compared with the theoretical curves calculated for instantaneous and progressive nucleation. A good agreement of experimental plots with the instantaneous nucleation mechanism was... 

In Figure 7.9, current transients for instantaneous and progressive nucleation are shown in a reduced presentation, plotting versus Work on nucleation and current transients is continuously being developed. Examples are the papers of Scharifker and Mostany or of Heermann and Tarallo. Liu and Fenner... 

Figure 7.9 Instantaneous and progressive nucleation, according to Eqs. (7.16) and (7.18), reduced presentation versus (a) instantaneous nucleation, (b) progressive nucleation.

The distinction between instantaneous and progressive nucleation often merely reflects the experimental protocol used [17, 31]. 

In these expressions is the first order nucleation rate constant, and the limiting cases described by Equations (9.21) and (9.22) are referred to instantaneous and progressive nucleation respectively. They have been used extensively as part of the description of nucleation and growth on foreign substrates (discussed in sections 9.3 and 9.4). 

Fig. 9.16 - Dimensionless plots according to Equations (9.46) and (9.47) for the growth of monolayer deposits by the instantaneous and progressive nucleation mechanisms respectively.

Hills, Schiffrin, Thompson [22] have derived expressions for the current transients in the two limiting cases of instantaneous and progressive nucleation by the following argument. The instanteous current is related to the rate of change of volume of the centre, since... 

Figure 9.8. Reduced variable plots of electrochemical reduction of Pt metal onto (a) freshly cleaved, and (b) O3 oxidized (0.15 ppm O3, 300 °C) HOPG. The solid lines represent experimental data. The long and short dashed lines represent theoretical curves for instantaneous and progressive nucleation, respectively [78], (Reproduced by permission of ECS—The Electrochemical Society, from Halvorsen H, Bock C, MacDougall B, Wang D, Potentiostatic deposition of platinum clusters onto freshly cleaved and ozone oxidized highly ordered pyrol5dic graphite.)...

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