Lattice-gas melting of two-dimensional alloys: Application to ternary graphite intercalation compounds

A Monte Carlo (spin exchange) method is used to study a spin-1 Ising (lattice-gas) model appropriate for ternary graphite intercalation compounds. In this paper we consider stage-1 $A_x$$B_{1\mathrm{-}x}$${\mathrm{C}}_8$ compounds. Monte Carlo results are compared with the molecular field results obtained within a two-sublattice model. The concentration (x) dependence of the lattice-gas melting temperature $T_m$ is studied for different strengths of interaction parameters. We find that the melting temperature $T_m$ for the ternaries under consideration is always greater than that predicted by Vegard’s law. A simple physical argument for this behavior within a Landau expansion is given. We have also investigated the order-disorder phase transition at temperature lower than $T_m$ on the 2×2 superlattice for the ternary alloy $A_{1/3}$$B_{2/3}$${\mathrm{C}}_8$. The appearance of (2 √3 ×2 √3 ) clusters above the transition temperature and its possible relationship with the experiment in ${\mathrm{K}}_{1/3}$${\mathrm{Rb}}_{2/3}$${\mathrm{C}}_8$ is briefly discussed.