Comment on "Large Difference in the Elastic Properties of fcc and hcp Hard-Sphere Crystals"

TL;DR

This paper explains the differences in elastic properties between fcc and hcp hard-sphere crystals by using symmetry considerations, showing that their elastic constants can be accurately mapped onto each other through geometric arguments.

Contribution

It demonstrates that the elastic constants of fcc and hcp hard-sphere crystals are closely related and can be predicted from one another using symmetry-based geometric mappings.

Findings

Elastic constants of fcc and hcp crystals are highly similar when mapped via symmetry.

Simulation and density functional theory predictions align closely for both structures.

Symmetry considerations effectively explain the elastic property differences.

Abstract

As is well known, hard-sphere crystals of the fcc and hcp type differ very little in their thermodynamic properties. Nonetheless, recent computer simulations by Pronk and Frenkel indicate that the elastic response to mechanical deformation of the two types of crystal should be quite different. By invoking a geometrical argument put forward by R. Martin some time ago, we suggest that this is largely due to the different symmetries of the fcc and hcp crystal structures. Indeed, we find that elastic constants obtained by means of computer simulations for the fcc hard-sphere crystal can be mapped onto the equivalent ones of the hcp crystal to very high accuracy. The same procedure applied to density functional theoretical predictions for the elastic properties of the fcc hard-sphere crystal also produces remarkably accurate predictions for those of the hcp hard-sphere crystal.