Large difference in the elastic properties of fcc and hcp hard-sphere crystals

TL;DR

This study numerically compares the elastic properties of fcc and hcp hard-sphere crystals, revealing significant differences in elastic constants despite similar free energies, which impacts colloidal crystal stability and design.

Contribution

It provides the first detailed numerical comparison of elastic constants for fcc and hcp hard-sphere colloids, highlighting differences with practical implications.

Findings

Elastic constants differ by up to 20% between fcc and hcp phases.

Moderate deformation can favor hcp stability over fcc.

Small but significant differences in layer spacing (c/a ratios) below close packing.

Abstract

We report a numerical calculation of the elastic constants of the fcc and hcp crystal phases of monodisperse hard-sphere colloids. Surprisingly, some of these elastic constants are very different (up to 20%), even though the free energy, pressure and bulk compressibility of the two crystal structures are very nearly equal. As a consequence, a moderate deformation of a hard-sphere crystal may make the hcp phase more stable than the fcc phase. This finding has implications for the design of patterned templates to grow colloidal hcp crystals. We also find that, below close packing, there is a small, but significant, difference between the distances between hexagonal layers (c/a ratios) of fcc and hcp crystals.