Surface diffusion of ad-atoms

Each ad-atom has a certain lifetime on the substrate surface called the residence time of the ad-atom. The equation for the residence time of the ad-atoms is obtained by the reciprocal value of the rate constant of dissolution of the ad-atoms. 

During the residence time ad-atoms are subject to a random walk on the surface with an average displacement which is the square root of the product of the residence time and the surface diffusion coefficient 

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Figure 4.25 Surface diffusion of ad-atoms on step terraces. The ad-atoms are deposited at a distance X from the step and carry out a random walk. Durins the time, the ad-atoms stay on the surface (residence time x ) they walk a distance = io x - (Reproduced with permission from Ref. [59], 1996, Wiley-VCH.)...

Figure 7.10 Model of an electrochemical deposition process (1) charge transfer of an ion in the electrolyte to an ad-atom position, (2) surface diffusion of ad-atoms, and (3) transfer of an ad-atom into a step or kink position.

Figure 6.5 Concentration-distance and energy-distance diagram for the surface diffusion of ad-atoms. (Wynblatt and Gjostein 1975. Reprinted with permission from Progress in Solid State Chemistry. Copyright by Pergamon Press, Inc.)...

The screening distance L is typically 2 to 3 times r sin d, making (In /) close to unity. The surface diffusivity of ad-atoms on the substrate is given by ... 

If 2D nuclei are formed through surface diffusion of ad-atoms on the foreign substrate what does change is only the frequency of single atoms attachment to the critical cluster. Similarly to the case of 3D nucleation... 

The surface diffusion of crystallites is more complicated than the diffusion of ad-atoms due to the dependence of surface diffusivity on crystallite size. A review on this subject can be found in the article by Kashchiev (1979). Theoretical models available for crystallite migration predict power or exponential dependence of the diffusivity on the size r (or the number of atoms fte making up the crystallite). The activation energy for the diffusion can be either size-dependent or size-indepen-... 

In the first case, the rate of deposition depends on the equilibrium concentration of ad-atoms, on their diffusion coefficient, on the exchange current density and on the overpotential. In the second case, the rate of deposition is a function, besides of the geometric factors of the surface, of the exchange current and the overpotential. This mechanism is valid, for example, in the deposition of silver from a AgN03 solution. 

This diffusion process is described in the hterature and will therefore not be discussed here in greater detail. The equivalent circuit used for the simulation of the deposition process on a stepped surface is shown in Figure 4.26 and gives a rough impression of the complex experimental problems in the investigation of ad-atoms and ad-atom diffusion. 

Porous metallic gas diffusion electrodes are used in these fuel cells. The anode consists of a nickel alloy with 2% of chromium. Chromium that is added prevents recrystallization and sintering of the porous nickel though it works as an electrode. This action is based on chromium forming a thin layer of chromium oxide at the nickel grain boundaries, which interferes with the surface diffusion of the nickel atoms. 

A surface phase of CU2O, not too thick to inhibit the reaction but thicker as a surface oxide ad-layer is the active phase for total oxidation. Its formation requires a bulk process, be it either segregation of oxygen or diffusion of copper atoms. 

Fig. 9.11 - (a) Distribution of ad-atom concentration between two parallel steps at a distance 2Xq from each other as a function of the penetration, X/jcq, of surface diffusion. Overpotential —30 mV. (b) Distribution of ad-atom concentration between two parallel steps at a distance 2ofo from each other for different values of the overpotential. X/x = 1. 

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