Equation of State Model for the $\gamma-\alpha$ Transition in Ce

TL;DR

This paper presents a physics-based empirical equation of state model for cerium's $ ext{γ-} ext{α}$ phase transition, capturing the volume change, phase boundary, and electronic contributions based on many-body calculations and experimental data.

Contribution

It introduces a novel EOS model for Ce that incorporates a variable degree of 4f electron localization, supported by many-body calculations and experimental parameters.

Findings

The model accurately describes the phase transition and volume change.

Electronic entropy significantly influences thermodynamic properties.

The static lattice energy has two minima corresponding to different phases.

Abstract

The element Ce exhibits an isostructural $\gamma-\alpha$ phase transition with a 15\% volume change at room temperature. The phase boundary ends in a critical point at 1.5 GPa and 480 K. We describe a model for the equation of state of Ce in the $\gamma-\alpha$ transition region. The model is based on the idea, supported by modern many-body calculations, of a continuously varying degree of localization of the $4f$ electrons as a function of compression. The functional forms used are motivated by many-body calculations, with parameters determined by experiments, resulting in a physics-based empirical EOS. In the large-volume $\gamma$ phase, degeneracy of the $j = 5/2$ state of the localized $4f$ electron makes a large contribution to the entropy. Rapid variation of the thermal electronic free energy with volume leads to unusually large electronic contributions to the pressure and thermodynamic Gr\"{u}neisen parameter. The static lattice energy has two local minima, with the $\alpha$-like minimum lower than the $\gamma$-like one by 6.3 meV/atom.