the phase transition is of first order because quantities such as surface energy, the structure factor change discontinuously as temperature reaches the transition point. Moreover the hysteresis effects are observed when system is warming up and then cooling down. We can analyze the structure of the surface in disordered phase as well as in the coexistence of the faceted and disorder phase close to the transition temperature. We found that the disordered phase consists of many small {211} facets randomly distributed. Hence it is not planar bcc(111) surface. It would be interesting to check experimentally this prediction. It was suggested [@song95] that coexistence of faceted and disordered phases is due to the inhomogeneity of the adsorbate coverage but we have demonstrated that the coexistence could also exist for homogeneous coverage.

It seems that this model can be applied to study reconstruction of curved bcc surfaces where reconstructed surface has different structure than faceted bcc(111) surface. In case of Pd deposited on a needle-shaped tungsten [@sczep02], step like {211} microfacets has been observed. Using the present model we have not obtained the faceted phase with large {211} pyramids and small {011} pyramids as observed in Pd/W(111) [@mad99b] for prolonged annealing time. 