Edge energy specific

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.)...

According to Eq. (3.126), B is a linear function of T2 provided % and A0 do not change appreciably with temperature. The B(T) dependence from Table 3.13 obeys this law [414] and yields hole specific edge energy % = 3.1 -10 11 J m1, when A0 = 4.2-10 19 m2 [332,366] is used. This % value coincides with the values given in Table 3.12. 

If i is constant for all sides considered, or if an averaged value, e, is taken for the specific edge energy,... 

At lower overvoltages, with increasing A/criti the rj intervals come closer, and the A/crit( 7)-function becomes smoother. The atomistic approach becomes cumbersome and can be reasonably replaced by the classical approach using bulk properties such as specific surface and edge energies as already discussed above. 

Most probable values of the specific edge energy and the pre-exponential factor obtained by the potentiostatic double pulse technique on quasi-perfect cubic and octahedral faces of silver in the standard system Ag (M/)/AgN03 are listed in Table 5.3. 

Table 5.3 Specific edge energies and pre-exponential factors in the standard system Ag (/ife/)/j N03.

Table 5.4 Experimental values of the specific edge energy, e, and the propagation rate constant, v of spiral growth steps obtained by electrocrystallization of silver in different stemsl5.67,5.74,5.75].

From current density transients the values of f(0) and I ss can directly be obtained. The propagation rate, v, and the propagation rate constant, k, of the spiral steps can be derived from the slope of experimental i vs. t dependencies. The kv values are used for an estimation of the specific edge energy efrom /gs and eq. (5.28). The values for Kv and e obtained in this way from the analysis of experimental current density transients in the system standard Ag(M0/AgNO3 [5.83] have been found to be in good agreement with those determined by other methods (cf. Table 5.4). 

More recently, Schaarwachter 45, 46) has argued that the formation energy of a nucleus at a dislocation is less than the corresponding formation energy at a perfect surface by a factor which is determined by the ration, [ibja, where a is the specific edge energy of the nucleus. 

Owing to the solid-solvent phase boundary interaction, however, this density may be increased significantly. A more reasonable value in such a case may be obtained when if/i is calculated from the specific surface energy o- or the specific edge energy e, e.g.J... 

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