This paper presents a multiphase equation of state for cerium, which includes the $\gamma$, $\alpha$, $\varepsilon$, and liquid phases. The $\alpha$ and $\gamma$ phases are described with the Aptekar-Ponyatovsky model for pseudobinary solutions, while the $\varepsilon$ and liquid phases are treated as pure phases. The Hugoniot and release isentropes are calculated for the solid $\gamma$, $\alpha$, liquid, and mixed phases. Based on the model developed, the Hugoniot does not cross the line of the $\alpha$-$\varepsilon$ transition and melting occurs directly from the $\alpha$ phase. The equation of state developed shows reasonable agreement with the static measurements, the experimentally determined phase diagram, and the shock experimental data. Cerium compresses isentropically through the $\gamma$-$\alpha$ transition as a result of cerium’s abnormal compressibility in the region of the $\gamma$-$\alpha$ transition. The inclusion of the Aptekar-Ponyatovsky model assists in providing a way to handle both the abnormal compressibility and the anomalous melt boundary simultaneously. Experimentally under dynamic loading conditions, a three-wave structure is observed at stresses above the phase transition: an elastic wave, a phase transition wave (which appears as an isentropic compression wave), followed by a shock wave. For our model development we consider only the hydrostatic response and thus a two-wave structure would be anticipated. No phase precursor would be observed for melting. Sound velocity behind the shock front dramatically decreases in the region of the $\gamma$-$\alpha$ transition and smoothly varies through the region of melting.

• Received 10 September 2009

DOI:https://doi.org/10.1103/PhysRevB.84.094120