# Tetrahedrality dictates dynamics in hard spheres

## TL;DR

This paper demonstrates that in a fundamental glass model, the number of tetrahedral structures directly predicts the slowdown in dynamics, suggesting tetrahedra are key to understanding glass behavior.

## Contribution

It reveals that tetrahedrality, rather than icosahedral structures, governs the dynamics of glasses, providing a new structural perspective.

## Key findings

- Tetrahedral count predicts dynamical slowdown.
- Tetrahedra are more relevant than icosahedra for glass dynamics.
- Structural analysis links local geometry to glass behavior.

## Abstract

Glasses are ubiquitous amorphous solids that remain one of the big mysteries in condensed matter. Despite the vast body of literature on glasses, a unifying approach to link the structure and dynamics of glasses is still missing. A growing set of evidence, however, indicates the microscopic local geometry as a key ingredient. This originated from the seminal work of Frank, who conjectured that glasses may be the result of the local tendency of liquids to form icosahedral structures, which are not capable of globally filling space regularly. Here, we show that, for a fundamental glass model, dynamics can be fully understood by simply counting the number of tetrahedra. Both globally and locally, these local structures directly predict dynamical slowdown. After more than 60 years of Frank's Conjecture, it might not be the icosahedra that matter for glasses, but rather the tetrahedra inside them.