Formation of hexagonal binary crystals in additive hard disk mixtures

The hard disk model is a foundational system for understanding two-dimensional phase behavior. Its extension to binary mixtures introduces additional structural complexity and kinetic constraints that hinder the formation of ordered phases. Although geometric constructions predict a variety of binary crystals at high densities, these phases often fail to self-assemble in simulations due to slow dynamics and competing phase separation. Here, we investigate the spontaneous formation of the H2 hexagonal binary hard disk crystal in additive mixtures using event-driven molecular dynamics. We show that crystallization is highly sensitive to thermodynamic conditions, requires long equilibration, and is facilitated by particle swap moves. Despite its high packing fraction, the H2 crystal forms spontaneously at equimolar composition and near-ideal size ratio but is kinetically hindered at intermediate densities by the formation of competing one-component hexagonal phases. Our results identify the conditions under which H2 binary crystals spontaneously form and show that their emergence can proceed through non-classical nucleation pathways involving metastable intermediates. These findings offer new insights into entropy-driven self-assembly in two-dimensional mixtures and inform strategies for realizing complex order in colloidal and granular materials.