Surface diffusion jump lengths

The diffusion of the embedded atoms in the surface proceeds through multi-lattice-spacing jumps separated by long time intervals. The multi-lattice-spacing nature of the diffusion is illustrated by the jump length distributions which are plotted in Fig. 6. 

Our measurements indeed show the expected logarithmic increase in mean square jump length with increasing distance away from a step, and provide confirmation that steps are indeed the sole sources and sinks for surface vacancies. Having established the role of the steps as sources and sinks for vacancies we speculate on how the vacancies are formed at the steps. One can envision several different mechanisms at steps that lead to the formation of a surface vacancy. All of them involve removing an atom from a kink, a step or (least likely) from the terrace itself. Since the attachment and detachment of atoms from kinks is often the energetically least costly way to detach an atom from a step, this appears to be the most likely initial process in the formation of a surface vacancy. Calculations on this problem have been performed in the context of the observations on Mn/Cu(00 1) that were mentioned previously [48-50]. In these calculations it was indeed found that the formation of step vacancies at kinks and the subsequent diffusion of these vacancies along a step and their release into the terrace is the most likely scenario for the creation of surface vacancies in a terrace. 

Surface vacancies were shown to be responsible for the motion of embedded In and Pd atoms in the Cu(00 1) surface. The density of surface vacancies at room temperature is extremely low, but they diffuse through the surface at an extremely high rate leading to significant diffusion rates of Cu(00 1) terrace atoms. In the STM measurements the rapid diffusion of these vacancies leads to long jumps of embedded tracer atoms. Measurements of the jump length distribution show a shape of the distribution that is consistent with the model that we discussed in Section 3. In turn, this shows that the vacancy-mediated diffusion process can be accurately described with the model that is presented in Section 3, provided that the interaction between the tracer atom and the surface vacancy is properly taken into... 

Surface diffusion may be treated by a random-walk analysis. We assume that the molecular motion is completely random and that the jumps from site to site are of equal length, which is equal to the nearest-neighbor distance d. With these assumptions, the preexponential factor for diffusion is (23). 

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