Pb atoms deposited on Cu(111) form a Pb-poor surface-alloy phase and a Pb-rich overlayer phase which spontaneously order into nanoscale domain patterns.@footnote 1@ The thermodynamic forces responsible for the self-assembly have been determined in previous studies with the LEEM.@footnote 2@. In this talk I will describe recent studies of the atomic mechanisms underlying the remarkable cooperative motion that allows these patterns to form and evolve. For example, the ordering of Pb overlayer islands occurs by islands containing 10's of thousands of atoms moving 100's of nm's is a few minutes. To help understand the atomic processes responsible for such motion, we measured the thermal decay of pure Cu, Pb-overlayer, and Pb/Cu surface-alloy islands using both STM and LEEM.@footnote 3@ The results indicate that the diffusion of Cu atoms over the Pb-Cu surface alloy is rate-determining for the decay both Pb overlayer and Pb-Cu alloy islands and that slower diffusion on the surface alloy is due to path blocking by embedded Pb atoms. Additional LEEM studies of Cu island nucleation within the Pb overlayer strongly suggest that the large-scale mobility of overlayer islands is accomplished by fast migration of Cu atoms within the overlayer. Thus, the rapid self-assembly in this system can, surprisingly, be traced to the existence of a low energy Cu thermal defect within the Pb overlayer. Sandia is operated by Sandia Corporation, a Lockheed Martin company, for the U. S. Department of Energy under Contract #DE-AC04-94AL85000. @FootnoteText@ @footnote 1@ R. Plass, J. A. Last, N. C. Bartelt, and G. L. Kellogg, Nature 412, 875 (2001).@footnote 2@ R. van Gastel, R. Plass, N. C. Bartelt, and G. L. Kellogg, Phys. Rev. Lett. 91, #55503 (2003); R. van Gastel, N. C. Bartelt, P. J. Feibelman, Francois Leonard, and G. L. Kellogg, Phys. Rev. B, submitted.@footnote 3@ M. L. Anderson, N. C. Bartelt, P. J. Feibelman, G. L. Kellogg, and B. S. Swartzentruber, in preparation.