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Similar variations in individual particle ripening rates have also been directly observed by P.W. Voorhees and R.J. Schaefer, Acta Metall. 35, 327 (1987).
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In making this estimate we assume that the individual dimers are randomly attaching and detaching from the step edge. At low temperature, STM observations suggest that dimers attach and detach from the step edge in pairs (Refs. 25, 27, and 28). If this behavior persisted to high temperature, then only the random attachment rate of pairs of dimers would be random. To explain the observed values of Γ, the dimer attachment rates would have to be a factor of 2(Formula presented) lower than given in the text because the mobility is proportional to the cube of the size of the entity, which is randomly attaching and detaching. This difference has no qualitative affect on our conclusions. If the coordinated participation of pairs of dimers were required to change the step edge position, it might account for attachment-limited step edge kinetics. For the case of Ag islands on Ag(111), where there is no such complexity associated with step edge attachment and detachment, diffusion-limited dissolution of islands has recently been observed [K. Morgenstern, G. Rosenfeld and G. Comsa, Phys. Rev. Lett. 76, 2113 (1996)].
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See F.-P. Ludwig, J. Schmelzer and J. Bartels, J. Mater. Sci. 29, 4852 (1994) for a discussion of the effects of thermal noise on the ripening.
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The large diffusion length does not imply that the adatom chemical potential should be in equilibrium with the bounding step edge. This issue is addressed theoretically by C.W.J. Beenakker and J. Ross, J. Chem. Phys. 83, 4710 (1985), and experimentally by G.R. Carlow and M. Zinke-Allmang, Can. J. Phys. 72, 812 (1994).
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