Order-disorder phase transition in Au2Fe on Ru(0001)

Order-disorder transition of the epitaxial surface alloy of bulk immiscible elements ${\mathrm{Au}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}$ on Ru(0001) is studied using complementary experiments of scanning tunneling microscopy and grazing incidence x-ray diffraction. For $x\ensuremath{\simeq}1/3$, we evidence an apparent continuous transition towards disorder with increasing temperature from 550 to 700 K. An ordered ${\mathrm{Au}}_{2}\mathrm{Fe}$ two-dimensional alloy is found to be composed of nanometer size domains of the three variants that switch to a two-dimensional solid solution with temperature. A two-levels model is developed to analyze those results which conducts to interpret this phase transition as the result of an order-disorder transition within two dimensional uncorrelated grains, or domains, with nearly fixed size. This system is a good candidate in order to study two-dimensional phase transitions of surface alloy, a largely unexplored domain but crucial to understanding thermal stability of bimetallic nanoparticles.