The Pb/Si(111) phase diagram and the thermal stability of a ``Devil's Staircase''

The T-$\theta $ phase diagram for Pb/Si(111) was determined in the range 6/5$<\theta <$4/3ML from complementary STM and SPA-LEED experiments. Within this coverage a ``Devil's Staircase'' (DS) was found with numerous phases formed as a result of the long range elastic Pb interactions. The presence of the DS phases can account for previous contradictory observations in the literature about the Pb/Si(111) phases. In addition we study the thermal stability of the different linear DS phases and determine that the transition temperature is a monotonic function of the phase periodicity. Because of additional complexity in the experimental system (i.e. 2-dimensionality and 3-fold symmetry) the DS phases transform at higher temperature into commensurate phases of 3-fold symmetry ``HIC''. Different types of ``HIC'' phases have been discovered differing in the size of their supercell within $\sim $0.04ML coverage variation. The presence of such large number of different ordered phases within a very small range of control parameters demonstrate the unusual degree of self organization in Pb/Si(111).