Most stable structure for hard spheres

TL;DR

This paper investigates the most stable crystal structure for hard spheres during the liquid-solid phase transition, comparing face centered cubic and hexagonal close packed arrangements.

Contribution

It contrasts various methods used to determine the more stable structure and extends one of these approaches.

Findings

Identifies the subtle free energy differences between FCC and HCP structures.

Provides a comparative analysis of different stability determination methods.

Extends an existing approach to better assess the stability of sphere packings.

Abstract

The hard sphere model is known to show a liquid-solid phase transition, with the solid expected to be either face centered cubic or hexagonal close packed. The difference in free energy between the two structures is very small and various attempts have been made to determine which one is the more stable. We contrast the different approaches and extend one.