Melting criterion for cubic crystals on the basis of the anisotropic dispersive continuum model

Abstract

The anisotropic dispersive continuum model for the lattice dynamics of solids is used to express the temperature dependence of the ratio γ of the mean square displacement of thermal vibrations and the square of interatomic spacing. The value of this ratio at the melting temperature, γ_m, for a number of elements crystallizing in the cubic system, is calculated from elastic data and is about 0.015. γ has nearly the same value for elements belonging to a particular group of the periodic table, but it exhibits wide variation as we go from one group of the periodic table to another. In the light of this study, Lindemann's criterion for melting based on the assumption of a fixed value for γ m for all solids looks no more impressive than it used to do.