Critical and co-operative phenomena. III. A theory of melting and the structure of liquids

TLDR

Existing theories of melting, such as Lindemann’s criterion and later pressure‑minimum approaches, have offered only partial explanations of the solid‑to‑liquid transition based on interatomic forces. The authors determine a critical vibrational amplitude fraction from one crystal’s data and apply it universally to other crystals of the same type. This approach yields a surprisingly good correlation between the melting points of many solids and their characteristic vibrational frequencies.

Abstract

There have been many theories of the melting of solids but none has as yet given a satisfactory explanation of the change of phase from solid to liquid in terms of interatomic forces. They have usually been based on simple models and have attempted only to correlate the temperature of melting with other properties of the solid. Of the earlier theories the best known is that of Lindemann (1910), who made the assumption that melting takes place when the amplitude of the vibrations of the atoms in a crystal is a certain fraction of the distance between nearest neighbours. This fraction was determined from the data for one crystal and then applied to others of the same type. This effected a surprisingly good correlation between the melting-points of many solids and their characteristic frequencies. Raschevsky (1927) and later Herzfeld and Goeppert Mayer (1934) introduced another criterion for melting. The latter showed that if a lattice is expanded uniformly at constant temperature it reaches a state for which the pressure is a minimum with respect to changes of volume. This they associated with melting. Though the theory does not give the heat of fusion, it gives the temperature of melting as a function of pressure. On the other hand, Raschevsky’s theory gives the heat of fusion but not the temperature of melting.