Vacancy current density

In this case, the strain rate is determined by the rate of emission or absorption of vacancies. Figure 11.5 shows the example of two edge dislocations pinned at two obstacles. Dislocation 1 has to absorb vacancies to climb dislocation 2 needs to emit them. Thus, vacancies can be transported from one dislocation to the other, with one dislocation acting as vacancy source, the other as vacancy sink. The vacancy current density, j, determines the rate of deformation. This quantity can be estimated. 

According to Pick s law, the vacancy current density is proportional to the gradient of the vacancy concentration ... 

Here we used the approximation formula exp 1 + a for a 1. We finally find the vacancy current density as... 

According to this calculation, the vacancy current density is... 

The derivation of the strain rate in diffusion creep is analogous to that of the previous section. Again, the vacancy current density is calculated and related to the strain rate. 

The vacancy concentration gradient can be estimated, according to equation (11.10), as (ni — n2)/d, with the grain size d replacing the dislocation distance. Thus, a vacancy current density... 

The creep rate e is proportional to the vacancy current density divided by the... 

As before, the vacancy current density j is inversely proportional to the grain size. The derivation of the current density in the bulk material can thus be copied exactly, simply replacing the activation energy with... 

Alloying of Pt with transition elements increases the Pt /-band vacancy/ atom and decreases the Pt-Pt bond distance. The extent of the change is shown to be dependent on the electronegativity of the transition element. Correlation of the ORR activity in terms of current density at 0.9 V with the /-band vacancy/atom of Pt and the Pt-Pt bond distance shows a familiar volcano-type behavior with respect to the various binary alloys. This clearly indicates the importance of both these parameters in the rate-determining step of ORR. 

Nmax would be the theoretical density of the "perfect" metal (i.e., without vacancies). Then we could define the time to failure, tf, such that nj (0, tf) = 0. In other words, tf would be the time for all the metal ions initially at x = 0 to migrate to vacancies somewhere to the right. Since the number of vacancies available per cm would be proportional to L, we would expect that tf would be inversely proportional to L, as was experimentally observed by Blech (10). If we imagine that the current density je is produced by a pulsed dc technique, so that joule heating is slight, then dissolution of silicon at the interface could be prevented. Then u(L,t) = 0 would be an appropriate boundary condition. 

Attempts to verify the above volume diffusion mechanism experimentally included X-ray and electron diffraction experiments with electrodes that were corroded at > Ec, as well as investigations by positron annihilation spectroscopy (PAS). In the former case, the occurrence of broadened diffraction lines at Bragg angles between those of the bulk alloy and the pure, noble component was taken as a confirmation of the volume diffusion mechanism [54, 120, 131]. More direct evidence was obtained from the PAS experiments with dezincified brass, where experimental positron Kfetimes correlated well with calculated values in vacancies or vacancy aggregates [78-80]. On the other hand, it has been objected that Eq. (20) predicts a dependence of the current density, which is in contradiction to many experimental results. It has been shown, however, that this particular problem may... 

Figure 6.10 Fraction of Ni vacancies and surface coverage CO at the three-phase boundary as a function of current density for different operating temperatures.

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