Theory of Melting

Abstract

A theory of melting is presented. It is based on the contention that melting occurs when the free energy of glide dislocation cores becomes negative. When this happens, dislocation cores are generated to fill the crystal to capacity. In the process the crystal absorbs a considerable amount of latent heat and loses all permanent resistance against shear forces. Equations are derived to relate the temperature of melting as well as the latent heat of fusion to known crystal properties, in addition to two parameters, $\alpha$ and $X$. These are related to the energy and dilatation of dislocation cores, respectively. Quantitative comparison of the theory with experimental data allows evaluating not $\alpha$ and $X$ directly, but $\frac{\alpha }{q}$ and $\frac{X}{q}$, with $q^{-1\mathrm{}}$ the highest shear strain that can be supported by a defect-free crystal of the substance considered. From the geometry of dislocation cores, $\frac{X}{q}$ can be calculated independently within rather narrow limits. For a wide variety of elements, including argon, typical fcc, hcp, alkali and bcc metals, silicon, and germanium, the values of $\frac{X}{q}$ derived from the present theory agree very well with the values derived from core geometry. The data for $\frac{\alpha }{q}$ indicate that the latent heat of melting is nearly the same multiple of modulus of rigidity times the atomic volume, independent of crystal type. It is shown that the theory predicts a first-order transition. Suggestions are made of how the theory could be employed in investigations into properties of ideal crystals, crystal defects, liquids, and the electronic structure of atoms.