Critical scattering at the order-disorder phase transition of Si(111)-3×3

The Si(111)-$\sqrt{3}$\ifmmode\times\else\texttimes\fi{}$\sqrt{3}$-Au phase, which coexists with three-dimensional islands of excess Au at coverages above 1 monolayer and at temperatures above 700 K, is shown to undergo a temperature driven order-disorder phase transition at 1057 K. The islands act as a reservoir of Au atoms and adjust the chemical potential for the two-dimensional layer during the transition. Due to this particle exchange, the phase transition within the $\sqrt{3}$\ifmmode\times\else\texttimes\fi{}$\sqrt{3}$R30\ifmmode^\circ\else\textdegree\fi{}-Au has been observed for a chemisorbed layer which is not under the usual constraint of constant coverage, but controlled by the chemical potential. We quantitatively analyzed the critical scattering and experimentally determined its critical exponents \ensuremath{\mathrm{B}}, \ensuremath{\gamma}, and \ensuremath{\nu} by high-resolution low-energy electron diffraction. Their values are in good agreement with the expected values of the three-state Potts model, which shows that the transition is continuous without any finite-size effects detectable.