On the Lennard-Jones and Devonshire theory for solid state thermodynamics

ABSTRACT

The Lennard-Jones and Devonshire theory is developed into a self-consistent scheme for essentially complete thermodynamic information. The resulting methodology is compared with molecular simulation of the Lennard-Jones system in the face-centred-cubic solid state over an excessive range of state points. The thermal and caloric equations of state are in almost perfect agreement along the entire fluid–solid coexistence lines over more than six orders of magnitude in pressure. For homogeneous densities greater than twice the solid triple point density, the theory is essentially exact for derivatives of the Helmholtz energy. However, the fluid–solid phase equilibria are in disagreement with simulation. It is shown that the theory is in error by an additive constant to the Helmholtz energy A/(Nk_BT). Empirical inclusion of the error term makes all fluid–solid equilibria indistinguishable from exact results. Some arguments about the origin of the error are given.

KEYWORDS:

• Lennard-Jones and Devonshire
• solid-state thermodynamics
• fluid–solid phase equilibrium

Acknowledgements

I dedicate this work to Professor Johann Fischer, who never failed to give me exceptional advice. I thank Andreas Köster for his help with the ms2 molecular simulations.

Disclosure statement

No potential conflict of interest was reported by the author.