Free-energy functional for freezing transitions: Hard sphere systems freezing into crystalline and amorphous structures

TL;DR

This paper develops a free-energy functional approach to study the freezing of hard spheres into crystalline and amorphous states, showing good agreement with simulations and revealing stable supercooled amorphous structures.

Contribution

It introduces a free-energy functional incorporating symmetry aspects to analyze both crystalline and amorphous freezing transitions in hard sphere systems.

Findings

Freezing parameters match simulation results.

Identifies stable amorphous structures at certain densities.

Reveals supercooled amorphous states with heterogeneous density profiles.

Abstract

A free-energy functional that contains both the symmetry conserved and symmetry broken parts of the direct pair correlation function has been used to investigate the freezing of a system of hard spheres into crystalline and amorphous structures. The freezing parameters for fluid-crystal transition have been found to be in very good agreement with the results found from simulations. We considered amorphous structures found from the molecular dynamics simulations at packing fractions $\eta$ lower than the glass close packing fraction $\eta_{J}$ and investigated their stability compared to that of a homogeneous fluid. The existence of free-energy minimum corresponding to a density distribution of overlapping Gaussians centered around an amorphous lattice depicts the deeply supercooled state with a heterogeneous density profile.