Monomer Adsorption on 6-Atoms Wide Zigzag (111) Terracess

We study monomer adsorption on six-atoms wide, zigzag ($111$) terraces, with first- ($V$), second- ($W$), and third-neighbor ($U$) interactions, specializing to repulsive first-neighbors. All possible crystallization patterns, or phases, that may exist are expected to occur at relatively low temperatures. Under these conditions, the energy phase diagram is three-dimensional and depends on the dimensionless variables, $v = \mu/|V|$, $u = U/|V|$, and $w = W/|V|$. The chemical potential energy of the monomers, $\mu$, in the medium to which the terrace is exposed depends on the pressure, if the medium is a gas, or the concentration if the medium is solution. There are $95$ phases, or crystallization patterns, of the adsorbates with coverages ranging from $1/5$ to $8/9$. In particular, we find that there are $10$ distinct $1/2$, $2/3$, and $4/9$ coverage phases, and $9$ distinct $1/3$ coverage phases.