Mechanisms of Surface Diffusion

The changes in slope indicate changes in the mechanism of surface diffusion. While, at low temperatures, adatom diffusion or adatom-surface atom exchange appears to be the dominant atom-transport mechanism, the diffusion of surface vacancies created by thermal roughening is likely to be dominant at high temperatures to account for the increased activation energies. For example, copper adatom and vacancy diffusion rates in the Cu(l 10) crystal face are given by 

The collective diffusion of dimers and clusters of atoms has also been observed [52, 54, 55]. The diffusion rates of dimers can be greater (Re2 on Re) or smaller 

The presence of coadsorbates can markedly influence surface diffusion. On the one hand, the presence of Bi, Pb, Tl, and S can greatly increase the surface selfdiffusion of Cu and Ag. Elements that reduce the melting point of the substrate can cause an increase in surface diffusion rates and a decrease in activation energies for diffusion in general. On the other hand, carbon markedly decreases the diffusion rate of copper. 

In Tables 4.5 and 4.6, surface self-diffusion and adsorbate diffusion data are plotted. The diffusion coefficient Dq and the activation energy AEq are given, along with the temperature range of the study. 

A closely related and frequently observed phenomenon is the spillover of adsorbed species. In a multiphase system such as metal islands dispersed on an oxide, it is possible for molecules to adsorb or even react on one of the constituents (the metal, for example) before diffusing over onto the second phase (the oxide in this 

---

At the same time, mechanisms of the solid-state diffusion of ions in the intercalation electrodes are numerous and more complicated than the mechanisms of surface diffusion. Crystallographic fea-... 

The effect of undercutting the sphere svirface just at the edge of the neck has been shown to have a major effect on the mechanisms of surface diffusion. 

Selective surface flow is, as Knudsen diffusion, associated with transport through microporous membranes, usually inorganic materials. The mechanism of surface diffusion is disputed and several different approaches have been proposed in the literature. 

The mechanism of surface diffusion has been much studied by Miyabe and Guiochon [116-122]. These authors showed that the activation energy of surface diffusion can be considered as the sum of two terms. The first one is the energy needed to make a hole in the mobile phase. It is independent of the adsorption energy of the solute considered but depends only on the nature of the mobile phase. The second contribution is the energy needed for the molecule of adsorbate to jump from the monolayer into this hole. This activation energy is proportional to the isosteric heat of adsorption. Experimental results confirmed that the values of the surface diffusion coefficients of several series of compounds are related to those of their bulk diffusivities through the equation ... 

As discussed before, the free surface of a crystalline solid is not a perfectly flat plane, which could contain vacancies, terraces, kinks, edges, and adatoms. The migration of vacancies and the movement of adatoms facilitate the mechanisms of surface diffusion. The diffusion process is usually confined to a thin layer near the surface with a thickness of 0.5-1 nm. 

In this section, situations are considered for which the surface of a stressed solid is initially flat, or nearly so, and for which the slope of the evolving surface is everywhere small in magnitude throughout the evolution process. Chemical potential for a one-dimensional sinusoidal surface shape was developed in Section 8.4.1, for a two-dimensional sinusoidal shape in Section 8.5.3, and for a general small amplitude surface profile in Section 8.5.2. These results are used to examine surface evolution by either the mechanism of surface diffusion or condensation, as described in Section 9.1. In all cases considered in this section, surface energy is assumed to have the constant value 70, independent of surface orientation and surface strain. Implications of surface energy anisotropy and strain dependence are examined subsequently. 

Thermal grooving on alumina occurs by a mechanism of surface diffusion. 

---