Two-dimensional discrete Coulomb alloy

Abstract

We study an ${A}_{1\ensuremath{-}x}{B}_{x}$ alloy on a two-dimensional triangular lattice. The ions A and B have different charges, with a background charge to ensure neutrality, and are constrained to lie at the discrete sites defined by a fixed triangular lattice. We study the various structures formed at different compositions x by doing computer simulations to find the lowest energy, using an energy minimization scheme, together with simulated annealing. Like ions try to avoid each other because of charge repulsion, which leads to structures, which are very different from those in a random alloy. At low concentrations, a triangular Wigner lattice is formed, which evolves continuously up to a concentration of $x=1/3.$ For higher concentrations, $1/3<~x<~1/2$ there are long polymer chains, with occasional branches. We show that there is a symmetry about $x=1/2,$ which is the percolation point for nearest neighbors on the triangular lattice. At certain special stoichiometries, regular superlattices are formed, which usually have a slightly lower energy than a disordered configuration. The powder-diffraction patterns are calculated. The magnetic properties of this structure are also studied, and it is shown that the high-temperature susceptibility could be a useful diagnostic tool, in that it is very sensitive to the number of nearest-neighbor magnetic pairs. This work contributes to a better understanding of layered double hydroxides like ${\mathrm{Ni}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}(\mathrm{OH}{)}_{2}({\mathrm{CO}}_{3}{)}_{x/2}\ensuremath{\cdot}y{\mathrm{H}}_{2}\mathrm{O}.$