Emergent rigidity percolation of five-fold aggregates enables controllable glass properties

Abstract: Metallic glasses possess outstanding mechanical and physical properties, making them promising candidates for advanced structural and functional applications; however, the lack of understanding and control over their glass transition and solidification processes remains a significant barrier to practical design. The glass transition from liquid to amorphous solid has remained an open problem in physics despite many theories and recent advances in computational efforts. The question of identifying a clear and well-defined diverging length scale accompanying the glass transition has remained unanswered, as has the nature of the transition and, indeed, the presence of a transition at all, as opposed to a mere dynamical crossover. Here we answer these questions using numerical results and theoretical analysis showing that, in atomic (metallic) glass formers, the glass transition coincides with, and is caused by, a continuous rigidity percolation transition from a liquid-like to a solid-like material. The transition occurs as five-fold symmetric atomic clusters progressively aggregate, forming a system-spanning rigid network that marks the onset of mechanical stability. This percolation-driven rigidity growth is accompanied by a sharp increase in the shear modulus G', indicating the emergence of macroscopic solid-like behavior. Beyond this point, which coincides with the Maxwell isostatic point of the percolating structure, dynamical arrest or "freezing-in" prevents further evolution. The long-sought diverging length scale is thus identified as the percolation-driven growth of rigid five-fold clusters, providing a direct link between local structural motifs and macroscopic mechanical properties at the glass transition. These insights offer practical routes to rationally engineer metallic glasses with targeted mechanical stiffness, hardness, and toughness.