Thermoelasticity of the Hard Sphere Crystal in Relation to the Melting

Abstract

The elastic constants of the hard sphere crystal near the melting point are investigated. The assumption in Born’s theory that the elastic constant of shear should vanish at the melting point is examined. In place of his theory which cannot be applied to the hard sphere crystal straightforwardly, the effective potential method developed in a previous paper by one of the present authors (K.H.) is employed. The important effect of atomic ordering in long range in the crystal is taken into account. As an effect of fluctuation in this order parameter, certain elastic constants in particular the bulk modulus diverge to minus infinity at a threshold of the specific volume. In spite of difficulty that the Fourier components of the second derivative of interaction potential is indefinite, the velocities of the lattice wave in the limit of long wave length can be obtained.