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

Geometry explains the large difference in the elastic properties of fcc and hcp crystals of hard spheres