Density of binary disc packings: Playing with stoichiometry

We consider hard-disc mixtures with disc sizes within ratio 2?1, that is, the small exactly fits in hole between four large discs. For each prescribed stoichiometry of and discs, densest packings are rigorously determined via a computer-assisted proof. The density is maximal for 1:1 stoichiometry: discs then form square grid interstitial site which nests. When there an excess made single phase mixes two types chaotic way (it can be described by square-triangle tilings). on contrary, phenomenon separation appears: involved phases while compact hexagonal phases.