1 geometric monolayers of adsorbate on bcc (111), (211), and (011) surfaces, respectively. A second assumption is that substrate atoms (B) can take position in discrete bcc lattice. It has been shown [@mad99b], in the case of Pd/W(111), that both $\{011\}$ facets and $\{112\}$ facets of W are covered by pseudomorphic monolayer of Pd. Therefore we assume that adsorbate atoms (A) are also located in positions of the bcc structure. There are three types of interaction energies in this SOS model: adsorbate-adsorbate interaction $\epsilon^{AA}_{i}$, adsorbate-substrate interaction $ \epsilon^{AB}_{i}$, and substrate-substrate interaction $\epsilon^{BB}_{i}$, with the range of interaction up to forth neighbors (i =1, 2, 3, 4).

![ Schematic view of the bcc(111) surface. Sites of the sublattices $l=0, 1, 2$ are denoted by squares, triangles, crosses, respectively. The Z axis is normal to the plane and $a_x=a\sqrt{2}/2$, $a_y=a\sqrt{6}/6$.[]{data-label="figure1"}](fig1){width="6cm"}

It is convenient to chose the coordinate system with the $Z$ axis parallel to $[1 1 1]$ direction and $X$, $Y$ axes along $[\bar{1} 0 1]$, $[1 \bar{2} 1]$ directions in the (111) plane. Atoms along the closed packed direction ( parallel to the z axis) form columns which positions in the (x, y) plane are described by three triangular sublattices $l=0, 