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

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.