From glass formation to icosahedral ordering by curving three-dimensional space

TL;DR

This study demonstrates that curving three-dimensional space onto a hypersphere reduces geometric frustration in glass-forming liquids, enabling a transition to icosahedral order and revealing insights into glassy dynamics and fragility.

Contribution

It introduces a novel approach of curving space to control frustration and study structural transitions in glass-forming liquids, linking geometry to glassy behavior.

Findings

Frustration vanishes at high curvature, leading to a sharp transition to icosahedral order.

Reducing curvature increases frustration and smoothens the transition, inducing glassy dynamics.

Decreased curvature causes decoupling of structural and dynamical length scales, reducing fragility.

Abstract

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 3-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 emerges. 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 the Euclidean space.