Thermal behavior ofc(2×2)layers in the Pb/Cu(110) system and the influence of surface defects on the order-disorder transition

The thermal behavior of a $c(2\ifmmode\times\else\texttimes\fi{}2)$ Pb overlayer on Cu(110) surface is studied by thermal energy atom scattering. Diffraction analysis reveals a continuous reversible order-disorder transition with temperature at $437\ifmmode\pm\else\textpm\fi{}2.5$ K. Two of the extracted critical exponents, $\ensuremath{\gamma}$ and $\ensuremath{\nu},$ are in good agreement with those of the two-dimensional Ising universality class. The third, $\ensuremath{\beta},$ associated with the disappearance of long-range order in the layer, is, however, smaller than the theoretical expectations. The observed transition is discussed in a framework of model, where the deviation of one of the exponents $\ensuremath{\beta},$ $\ensuremath{\gamma},$ and $\ensuremath{\nu}$ from its exact value depends in a different way on the kind of ``imperfection'' (mean terrace width, domain boundaries, ``frozen-in'' surface defects, local distortions, and surface alloying) in the real physical system. The annihilation of domain walls, created during the simultaneous growth of $c(2\ifmmode\times\else\texttimes\fi{}2)$ phase on two equivalent sublattices of ${$110$}$ fcc surface, is found at 310 K. The experimental findings indicate also a noticeable change in the surface corrugation during the observed order-disorder transition.