Nucleation rate-overvoltage dependence

In a nucleation rate-overvoltage study, the current following a nucleation pulse can be used as a criterion for nucleation. The voltage pulse, of amplitude //nuc, and duration fnuc. is of such a magnitude that in half of the trials a current is observed indicating nucleation. Then a 50% probability of formation of at least one nucleus can be ascribed to the duration fnuc = ro.s of that pulse. 

The probability P of nucleation, which can be identified with the reciprocal of the average nucleation period, in a sequence of nucleation events, is obviously 

For the initial period, i.e., for the period immediately following the nucleation pulse excitation, the probability of observing at least one nucleation event, fm i. is equal to the complementary probability, Pni=o = (1 - Fm i), that zero nucleation events are observed. Hence, 

The time lapse ro.s can be determined at different amplitudes of the nucleation pulse, so that the/- 7 dependence is easily found. Fig. 5.8 shows a In /vs. 1/171 plot obtained in this way. The relation is linear in this representation, as expected from eq. (5.2). The contributions of the overvoltage dependence of the Zeldovich factor Tand the attachment fi-equency att,ycrit obviously small enough to produce an appreciable effect on the general In/- 1/171 relation. From the slope, the specific edge 

Overvoltage range (cathodic) Number of atoms in the 2D nucleus Gibbs energy of nucleus formation 

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This behavior is easily understood in view of the nucleation rate-overvoltage dependence of Fig. 5.2. 

Figure 5.6 Schematic representation of the potentiostatic double pulse technique for investigations of the nucleation rate-overvoltage dependence. nuc and T/growth denote the overvolt es of 2D nucleation and growth, respectively.

Fig. 7.136. Overvoltage dependence of the 2D nucleation rate J [cm-2 s-1]. Specific edge energy, e = 2 x 10-13 J cm-1 b=4 for a square form T= 318 K gmon = 2 x 10-4 A s cm-2 for a quasi-perfect Ag(100) face and = 2 x 1CT3 cm2 s 1. The data are taken as most probable values from nucleation rate experiments. (Reprinted from E. Budevski, G. Staikov, and W. J. Lorenz, Electrochemical Phase Formation and Growth, p. 203, copyright 1996 John Wiley Sons. Reproduced by permission of John Wiley Sons, Ltd.)...

The /- t] dependence according to eq. (4.32) or (4.33) is characterized by an overvoltage threshold, known as a critical overvoltage l77critl. The nucleation rate is... 

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