Density of binary disc packings: Playing with stoichiometry

We root 2consider hard-disc mixtures with disc sizes within ratio - 1, that is, the small disc exactly fits in the hole between four large discs. For each prescribed stoichiometry of large and small discs, the densest packings are rigorously determined via a computer-assisted proof. The density is maximal for the 1:1 stoichiometry: the large discs then form a square grid in each interstitial site of which a small disc nests. When there is an excess of large discs, the densest packings are made of a single phase which mixes the two types of discs in a chaotic way (it can be described by square-triangle tilings). When there is an excess of small discs, on the contrary, a phenomenon of phase separation appears: the large discs are involved in the densest 1:1 stoichiometry phases while the excess of small discs form compact hexagonal phases.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

The study investigates the densest packings of hard-disc mixtures with a ratio of 1, where the small discs fit perfectly into the gaps between four large discs. The maximum density is achieved in a 1:1 stoichiometry, where the large discs form a square grid and the small discs nest in the interstitial sites. Excess large discs result in chaotic mixtures, while excess small discs exhibit a phenomenon of phase separation.