Orientational disordering in crystals—I: A model for the evaluation of thermodynamic properties of melting transitions in atomic and plastic crystals

Abstract

A generalisation of two-sublattice models of melting transitions in atomic and molecular crystals (Lennard-Jones and Devonshire; Pople and Karasz; Amzel and Becka) has been attempted. The intention was to develop a scheme by which parameters, such as the number of sublattices and distinguishable molecular orientations can be selected. It is found that the choice of these parameters made by Lennard Jones and Devonshire, and by Pople and Karasz, protects the theory to some extent from some of the more difficult physical issues. A single-lattice model also emerges as another possibility in the series of models that may be called upon. Thus a single-lattice model, based on concepts from Eyring's Significant Structure Theory of Liquids for the melt, and standard thermodynamic functions for the solid, has been developed to evaluate thermodynamic properties of melting transitions in atomic and molecular crystals. Despite the remarkable simplicity of the model predicted values of entropy of fusion for both argon and methane are in good agreement with experimental data. Mean positional disordering energies for the same substances have also been computed.