Charge ordering and self-assembled nanostructures in a fcc Coulomb lattice gas

The compositional ordering of Ag, Pb, Sb, Te ions in ${(\mathrm{Ag}\mathrm{Sb}{\mathrm{Te}}_{2})}_{x}{(\mathrm{Pb}\mathrm{Te})}_{2(1\ensuremath{-}x)}$ systems possessing a NaCl structure is studied using a Coulomb lattice gas (CLG) model on a face-centered cubic (fcc) lattice and Monte Carlo simulations. Our results show different possible microstructural orderings. Ordered superlattice structures formed out of $\mathrm{Ag}\mathrm{Sb}{\mathrm{Te}}_{2}$ layers separated by ${\mathrm{Pb}}_{2}{\mathrm{Te}}_{2}$ layers are observed for a large range of $x$ values. For $x=0.5$, we see an array of tubular structures formed by $\mathrm{Ag}\mathrm{Sb}{\mathrm{Te}}_{2}$ and ${\mathrm{Pb}}_{2}{\mathrm{Te}}_{2}$ blocks. For $x=1$, $\mathrm{Ag}\mathrm{Sb}{\mathrm{Te}}_{2}$ has a body-centered tetragonal (bct) structure which is in agreement with previous Monte Carlo simulation results for restricted primitive model (RPM) at closed packed density. The phase diagram of this frustrated CLG system is discussed.