Two state model for critical points and the negative slope of the melting-curve

TL;DR

This paper introduces a two-state thermodynamic model explaining the negative slope of melting curves and associated anomalies in high-pressure systems like alkali metals and hydrogen.

Contribution

The model provides a unified explanation for negative Clapeyron slope phenomena and predicts features like melt curve maxima and thermodynamic anomalies.

Findings

Model reproduces observed negative slope in melting curves.

Predicts thermodynamic anomalies along Widom lines.

Fits well with experimental data on potassium electride transition.

Abstract

We present a thermodynamic model which explains the presence of a negative slope in the melt curve, as observed in systems as diverse as the alkali metals and molecular hydrogen at high pressure. We assume that components of the system can be in one of two well defined states - one associated with low energy, the other with low volume. The model exhibits a number of measurable features which are also observed in these systems and are therefore expected to be associated with all negative Clapeyron-slope systems: first order phase transitions, thermodynamic anomalies along Widom lines. The melt curve maximum is a feature of the model, but appears well below the pressures where the change in state occurs in the solid: the solid-solid transition is related to the melt line minimum. An example of the model fitted to the electride transition in potassium is discussed.