Top step annihilation

An intriguing complication arises when a series, say, of uphill steps is followed by an equal number of downhill steps, forming a one-dimensional wire on the surface. Below roughening, the thermal flattening of the wire proceeds through the top step annihilation mechanism -. By that, the amplitude of the wire is reduced by one lattice... 

Additional insight may be gained by considering the time scales introduced by the meandering of isolated top steps, by the step-step repulsion stemming from the steps below and by the top step annihilation. Indeed, in the evaporation case, the top step annihilation seems to determine the scaling behavior, with the step-step repulsion acting on the same time scale. 

In this subsection we describe a discrete model for vacancy-mediated diffusion of embedded atoms, solve it numerically for the case of In/Cu(0 0 1), and present the results. Our model is defined on a two-dimensional simple square lattice of size / x / (typically, l = 401) centered around the origin. This corresponds to the top layer of a terrace of the Cu(00 1) surface, with borders representing steps. The role of steps in the creation/annihilation of vacancies will be discussed in more detail in the next section. All sites but two are occupied by substrate atoms. At zero time the two remaining sites are the impurity (or tracer) atom, located at the origin, and a vacancy at position (1,0). This corresponds to the situation immediately after the impurity atom has changed places with the vacancy. 

Fig. 3.7 Top the diagonal SW wave for the JV = 200 dual closed grapheme at the last diffusion step b ore the annihilation of the 5j7 pairs, it has W = 113,925. Bottom Diagonal dislocations at the annihilation point W = 114,000 when only rotated txmds (the bold-blue ones) populate the region modified by the diffusiem process. UndCTlined vtntices evidtmee the ptaiodic imposed conditirais...

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