Diffusion at surfaces

Our present task is to build on the foundations laid in chap. 7, but now with special reference to the diffusive processes that take place at extended defects. The basic argument will be that by virtue of the more open atomic-level environments near extended defects, the activation energy both for point defect formation and migration will often be reduced relative to bulk values. We will build our case around a fundamental case study through the consideration of diffusion at surfaces. The surface diffusion example will illustrate not only how diffusive processes are amended at extended defects, but will also illustrate the shortcomings of the transition state formalism when the detailed atomic-level mechanisms are not known a priori. 

Because of the widespread interest in growth of material systems by deposition, the subject of surface diffusion is one of enormous current interest. The example of surface diffusion being taken up here is of interest to our overall mission for several different reasons. First, as noted above, surfaces are one of the most important sites of communication between a given material and the rest of the world. Whether we interest ourselves in oxidation and corrosion, catalysis, the crystal surface is the seat of tremendous activity, most of which is mediated by diffusion. A second reason that we have deemed it important to consider the role of surface diffusion is that our analysis will reveal the dangers that attend the use of transition state theory. In particular, we will appeal to the existence of exchange mechanisms for diffusion that reveal that the diffusion pathways adopted on some crystal surfaces are quite different than those that might be suggested by intuition. 

Exchange Mechanisms for Surface Diffusion. Our discussion of transition state theory in chap. 7 showed that in those cases when we are lucky enough to know the details of the transition pathway associated with a given diffusion mechanism, atomic-level analysis can shed important light on the process of diffusion. On the other hand, as we have already emphasized, the successful application of the ideas of transition state theory ultimately requires a knowledge of the transition pathway. Field-ion microscopy in conjunction with first-principles analysis of the energetics of metal surfaces has led to a convincing picture of surface diffusion in some instances that is entirely contrary to the ideas built around intuition. 

The simplest picture of diffusion on the (001) surface of an fee metal such as A1 or Pt would hold that atomic jumps take place from one binding site to the next via 

One of the key reasons we have considered the exchange mechanism for surface diffusion is as a reminder of the inherent difficulties in using transition state theory. 

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Given the uncertainties indicated by Niedermann, this value is subject to an error of -20%. The vast majority of this is not preserved because it is produced in minerals that have high He diffusivities at surface conditions even those minerals that do preserve... 

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