Variational Approach to Melting. II

Abstract

A variational approach to the equilibrium thermodynamic properties of an original system based upon an inequality for the Helmholtz free energy of that system is introduced. A system with molecules obeying the cell model of Lennard-Jones and Devonshire, and having a harmonic-oscillator-type potential function inside their cells, is used for a reference system to produce the inequality for the Helmholtz free energy of the original system. Optimization upon this inequality indicates that a variational calculation based on a reference system with highly ordered structure, as the cell model, predicts the properties of the solid phase better than the liquid phase. Also, it shows that by an ordered-structure reference model, it is possible to predict the liquid–solid phase transition. Equilibrium thermodynamic properties of the solid phase and liquid–solid phase equilibria are calculated and are compared with the machine-calculated and the experimental data.