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

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 these two types of crystal are quite different [S. Pronk and D. Frenkel, Phys. Rev. Lett. 90, 255501 (2003)]. By invoking a geometrical argument put forward by Martin some time ago [R. M. Martin, Phys. Rev. B 6, 4546 (1972)], we suggest that this is largely due to the different symmetries of the fcc and hcp crystal structures. Indeed, we find that elastic constants of the fcc hard-sphere crystal can be mapped onto the equivalent ones of the hcp crystal to very high accuracy, as a comparison with the computer simulation data of Pronk and Frenkel shows. 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.