Propagation rate of monatomic steps

From the initial linear slope of the current transients, the propagation rate of monatomic steps can easily be determined as a function of overvoltage. Fig. 5.13 shows that this function is linear in the range 0 mV 6 mV, giving a propagation rate constant k -v/ tj = 2.2 cm s V  

Knowing the forms and orientations of the growing steps, very exact values of the propagation rate constants, /cy. were found for monatomic steps on Ag(lOO) and Ag(lll) faces by this technique. Both constants have the same value within experimental error xv = (1.0 0.05) cm s V 

Under certain conditions, particularly at higher voltage pulses of longer duration, an activation of the surface is observed [5.24]. The activation is connected with the deposition of a polyatomic layer of silver. On an activated, fresh surface, the value of xy is roughly twice as high. Fig. 5.13, and decreases slowly with time to the normal 

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Figure 5.13 Propagation rate of monatomic steps, v, on a rectangular quasi-perfect Ag (100) face as a function of overvoltage in the standard system Ag (100)/AgNO3 [5.22]. Face dimensions 125 X 102 pm. Growth-activated surface. Calculated propagation rate constant /Cy = 2.2 cm s V. ...

A rather unexpected result is that the rate of propagation is independent of the step height, giving a value of kv = 1.9 cm s V which is very close to that found for monatomic layers on activated surfaces. This finding holds at least up to step heights of 5-10 nm, corresponding to about 25 - 50 monatomic layers. Above this thickness the observed deviations can be attributed to local concentration polarization in the solution. 

This current-overvoltage squared relation has been experimentally investigated in the case of silver deposition on (100) faces of Ag crystals by Vitanov et al From the experimental i-r]l plot shown in Figure 16, e = 2.4 X 10 J cm" has been found. The spiral steps have been assumed to be monatomic (i.e., v = ) and has been taken from propagation rate measurements of single monatomic steps (Section 3.2.1) or from the spiral step propagation rate directly (Section 4.2.2). 

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