From Glass Formation to Icosahedral Ordering by Curving Three-Dimensional Space.

Geometric frustration describes the inability of a local molecular arrangement, such as icosahedra found in metallic glasses and in model atomic glass formers, to tile space. Local icosahedral order, however, is strongly frustrated in Euclidean space, which obscures any causal relationship with the observed dynamical slowdown. Here we relieve frustration in a model glass-forming liquid by curving three-dimensional space onto the surface of a 4-dimensional hypersphere. For sufficient curvature, frustration vanishes and the liquid "freezes" in a fully icosahedral structure via a sharp "transition." Frustration increases upon reducing the curvature, and the transition to the icosahedral state smoothens while glassy dynamics emerge. Decreasing the curvature leads to decoupling between dynamical and structural length scales and the decrease of kinetic fragility. This sheds light on the observed glass-forming behavior in Euclidean space.