Nucleation progressive

By electrodeposition of CuInSe2 thin films on glassy carbon disk substrates in acidic (pH 2) baths of cupric ions and sodium citrate, under potentiostatic conditions [176], it was established that the formation of tetragonal chalcopyrite CIS is entirely prevalent in the deposition potential interval -0.7 to -0.9 V vs. SCE. Through analysis of potentiostatic current transients, it was concluded that electrocrystallization of the compound proceeds according to a 3D progressive nucleation-growth model with diffusion control. 

This relationship is valid when the growing nuclei do not overlap. Otherwise, the rate of growth of the surface gradually decreases. However, usually the dependence of the current on time in the initial stage is used as a diagnostic criterium for the type of nucleus and nucleation. The simplest case of progressive nucleation with a constant rate k, Eq. (5.8.1) then gives... 

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.

In the case of progressive nucleation, new clusters are born at a constant rate fcjvMo- From Eq. (10.23) the area covered by a cluster born at a time t is ... 

Both Eqs. (10.28) and (10.31) predict a current density which first rises as the perimeters of the clusters grow, and then decreases rapidly as the clusters begin to overlap. They can be cast into a convenient dimensionless form by introducing the maximum current density jmax and the time fmax at which it is attained. A straightforward calculation gives for instantaneous nucleation and progressive nucleation, respectivly,... 

The two current transients are shown in Fig. 10.6. The curve for progressive nucleation rises faster at the beginning because not only the perimeter of the clusters increases but also their number it drops off faster after the maximum. Such dimensionless plots are particularly useful as a diagnostic criterion to determine the growth mechanism. Real current transients may fit neither of these curves for a number of reasons, for example, if the growth starts from steps rather than from circular clusters. 

The inverse of the time corresponding to the current maximum can be taken as a measure of the reaction rate [16-18]. For a reaction controlled by progressive nucleation and growth tmax is given by the expression ... 

A kinetic study of Cu underpotential deposition was carried out to determine if it is best described by adsorption processes or by nucleation processes. The nucleation growth process is classified into two categories instantaneous nucleation growth and progressive nucleation growth. In the case of instantaneous nucleation growth, where nucleation site formation is so fast that no other following nucleation sites are created, the number of nucleation sites N(t) is expressed as... 

It can be seen that Eqs. (7.9) and (7.10) represent the same type of current-time transient, iocl. Thus, to distinguish between 2D growth (progressive nucleation) and 3D growth (instantaneous nucleation), it is necessary to perform additional optical microscopic or electron microscopic experiments. These experiments can provide information enabling one to distinguish between progressive nucleation [Eq. (7.9)] and instantaneous nucleation [Eq. (7.10)]. 

There are two mechanisms for formation of a monolayer (1) the instantaneous nucleation mechanism according to Eq. (7.12)— in this case the monolayer is spreading out on the substrate from nuclei formed at time t = 0 and (2) the progressive nucleation mechanism, in which, according to Eq. (7.13), nuclei appear randomly in space and time. The current-time relationships for these two mechanisms are shown in Figure 7.5. In both cases the current passes through a maximum. 

Figure 7.7. Potentiostatic current-time transient for the metal deposition together with theoretical currents for individual layers (1-5). Two-dimensional progressive nucleation taking overlap into account. (From Ref. 13, with permission from the Electrochemical Society.)...

Figure 7.7 also shows the theoretical i-t transients for the formation of successive layers under conditions of progressive nucleation. The theoretical current-time transient for three-dimensional nucleation is shown in Figure 7.8. The difference between 2D and 3D nucleation (Fig. 7.7 and 7.8) is in the absence of damped oscillations in the latter case. A comparison between the theoretical and experimental transients for the 2D polynuclear multilayer growth is shown in Figure 7.9. 

Equations (7.16) and (7.17) are used in an analysis of experimental data. Eor example, R5mders and AUdre (32) used these equations to analyze copper electrodeposition on platinum. They concluded that at the intermediate overpotentials (120 and 170 mV), the dimensionless current transients are consistent with the theoretical predictions for progressive nucleation, Eq. (7.17). At overpotentials higher than 220mV, nucleation shifted to the instantaneous nucleation theory. 

Si(lll) plane [300]. Because the redox potential of the Cd +/Cd couple is much lower than the flat band potential of Si substrate, the surface electron concentration is sufficiently high. Thus the process occurs similarly as on a metal surface at relatively low cathodic overpotentials. The initial stages of Cd deposition were explained by progressive nucleation and cluster growth controlled by hemispherical diffusion. CdTe deposition on Si was also studied due to interest in application in IR radiation detectors. Mechanisms of this process on different planes of n-Si(lOO) was also discussed ([203, 301, 302] and references given therein). 

PbO reduction process to Pb has been postulated to occur according to progressive nucleation and growth path [132,... 

Properties of thin layers of lead electrodeposited on vitreous carbon have been found identical with that of metallic lead [304]. Therefore Pb and Pb02 coated reticulated vitreous carbon (RVC) electrodes [185] can be applied as electrodes in lead-acid batteries, as reviewed in [305]. The deposition of lead on carbon is through the diffusion-controlled process with instantaneous or progressive nucleation, for high and low Pb + concentration, respectively, and three-dimensional growth mechanism. The number of nucleation sites increases with deposition overpotential, as shown for vitreous [306] and glassy carbon [307] electrodes. The concentration dependence of the nucleation... 

On highly ordered pyrolytic graphite, HOPG(OOOl) electrodes, no UPD has been detected owing to weak carbon-lead interactions [311]. Deposition occurs by three-dimensional island growth according to Volmer-Weber mechanism. Initial steps are controlled by progressive nucleation on active sites and hemispherical diffusion. 

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... 

Philipp and Retter [151] have studied the formation of the first monolayer of adenine on mercury electrode in borate solutions. Applying potential-step method, they have proposed to explain the observed transients in terms of two-dimensional (2D) truncated progressive nucleation and constant growth of monolayer islands. 

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