Complex alloy phases for binary hard-disc mixtures

Abstract

We investigate the phase diagram of two-dimensional binary mixtures of hard dises. There are two parameters in the problem, the ratio r of the radii of the two dises, and the concentration p of smali dises. We determine the possible phases by trying different periodic structures and minimizing the area per particle of the alloy for given r and p. We discover over ten distinct pure phases, along with large regions of the phase diagram which are oceupied by ‘lattice gas’ and ‘random tiling’ phases. The system tends to separate into two coexisting triangular lattices for r⋧ 0.5. The phase diagram becomes increasingly complicated at small size ratio and large concentrations of small discs.