Relationship between domain-boundary free energy and the temperature dependence of stress-domain patterns

Pb deposition on Cu(111) causes the surface to self-assemble into periodically arranged domains of a Pb-rich phase and a Pb-poor phase. Using low-energy electron microscopy (LEEM) we provide evidence that the observed temperature-dependent periodicity of these self-assembled domain patterns is the result of changing domain-boundary free energy. We determine the free energy of boundaries at different temperatures from a capillary wave analysis of the thermal fluctuations of the boundaries and find that it varies from 22 meV/nm at 600 K to 8 meV/nm at 650 K. Combining this result with previous measurements of the surface stress difference between the two phases we find that the theory of surface-stress-induced domain formation can quantitatively account for the observed periodicities.