  In this paper we have considered a simple lattice gas model of chemisorbed
monolayer which allows for the harmonic fluctuations of the bond length between
the adsorbate atom and the surface site. The model also involves a short-ranged
attractive potential acting between the adsorbed atoms as well as the surface
periodic corrugation potential. It has been assumed that the adsorbed atoms are
bonded to the uppermost layer of the substrate atoms. In particular, using
Monte Carlo simulation method we have focused on the orderings appearing in the
dense monolayer formed on the (111) face of an fcc solid. Within the lattice
gas limit, the chemisorbed layer forms a (1x1) structure. On the other hand,
when the bonds are allowed to fluctuate, three other different ordered phases
have been found to be stable in the ground state. One of them has been found to
be stable at finite temperatures and to undergo a phase transition to the
disordered state. The remaining two ordered states have been found to be stable
in the ground state only. At finite temperatures, the ordering has been
demonstrated to be destroyed due to large entropic effects.
