Monte Carlo simulations were used to study the assembly of model binary mixtures whose pure components have either distinct or similar crystal order symmetry. Specifically, we simulated mixtures of hard disks with either squares or hexagons, where the components have size ratios that optimize their co-assembly into compositionally disordered solids. For the disks + squares mixture, along with the enhanced regions of solid miscibility, we report a continuous-looking transition from the disklike to the squarelike behavior that occurs through a region that seamlessly bridges the regions of hexatic phase of disks and the tetratic phase of squares, which we term the mosaic ($M$) region. For the equimolar composition, this $M$ region is bound by the isotropic phase at low pressures and by the hexatic-tetratic (two-phase) macrophase segregated region above a critical transition pressure. Our analysis showed that the $M$ region lies in the vicinity of the critical point, manifesting local compositional fluctuations that give rise to microphase segregated regions of interspersed square-rich fourfold and rhombic lattice symmetry and disk-rich sixfold clusters that coexist across the system. The $M$ behavior is characterized by a short-ranged translational order and an algebraic decay of the correlation functions for sixfold and fourfold orientational order. A finite size scaling analysis was used to evaluate the dependence of the local compositional susceptibility with system size to extract the critical exponent associated with the approach of the critical point. For the disks + hexagons mixture, a fully mixed hexatic phase was observed for all compositions.

• Received 21 September 2020
• Revised 4 December 2020
• Accepted 22 January 2021

DOI:https://doi.org/10.1103/PhysRevMaterials.5.024003