A melting criterion based on the dilatation dependence of shear moduli

Abstract

THE elastic instability theory of melting, proposed by Max Born¹, held that melting in a crystalline material occurs when one of the elastic shear moduli vanishes, so that the material can no longer sustain an infinitesimal shear stress without flowing. This explains the fluidity of a melt, but fails to account for several other important characteristics of melting. Melting is a transition between two independent phases, while Born's theory is a single-phase theory which contains no distinct description of the melt, and thus fails to account for the discontinuous, first order character of melting. Because it is an essentially homogeneous theory, it does not explain the occurrence of superheating, the metastability of the melt, and the heterogeneous nucleation and growth features of the melting process. Also, subsequent observations of elastic moduli showed that none of the shear moduli is zero or near zero in the solid at the melting point. Because of these defects Born's instability theory currently enjoys little credibility. We believe, however, that correct application of Born's hypothesis leads to a simple modification of his initial criterion for melting which satisfies all the requirements of a physically realistic theory of melting. We show here that the hypothesis does predict a first-order transition between two phases and that the transition has a nucleation barrier, thus dismissing some of the physical objections to the hypothesis. Moreover, the hypothesis applies in the alkali halides, in that in each case one of the shear moduli falls continuously to zero through the melting expansion.