A tunnel theory of melting

A crystal is divided into infinite strings of molecules assembled on a two-dimensional lattice, each string occupying a 'tunnel' formed by neighbouring strings. Molecular motion along the string direction only is considered. In a mean-field approximation, the positional correlation of a molecule with its neighbours within the string and those in different strings are separated. The resulting equations allow a smooth variation from a harmonic crystal to a 'tunnel' model of a liquid. Approximate solutions of these equations allow the melting temperature, if any, of this system to be predicted from intermolecular force constants of the crystal with no adjustable parameters. Melting occurs when the crystal becomes unstable to large-amplitude transverse shear waves (motions corresponding roughly to phonons of small longitudinal and large transverse wavevector). The theory has been tested by use of the elastic constants and melting temperatures of 51 crystals, metallic and molecular, of six crystal classes. The ratio of agreement between theory and observations is 0.98+or-0.22.