Elasticity in Rigid-Disk and -Sphere Crystals

Abstract

Our previously developed product representation for the partition function of rigid molecules under high compression is generalized to include distorted reference lattices. The resulting strain component variations of free energy then permit extraction of elastic constants, both linear and nonlinear. The high‐compression elastic behavior of the two‐dimensional rigid‐disk crystal is explicitly evaluated through triplet cluster contributions. For rigid spheres in three dimensions in the face‐centered‐cubic lattice, singlet and pair cluster contributions have been evaluated, and the sound velocity ratio is reported for propagation along the 〈100〉 directions. Consideration of singlet and pair contributions for hexagonal packing suggests not only that this structure is more stable than the face‐centered‐cubic case, but that it exhibits a spontaneous small contraction along the c axis.