Phase states of dynamically compressed cerium

Abstract

This paper presents a multiphase equation of state for cerium, which includes the $\ensuremath{\gamma}$, $\ensuremath{\alpha}$, $\ensuremath{\varepsilon}$, and liquid phases. The $\ensuremath{\alpha}$ and $\ensuremath{\gamma}$ phases are described with the Aptekar-Ponyatovsky model for pseudobinary solutions, while the $\ensuremath{\varepsilon}$ and liquid phases are treated as pure phases. The Hugoniot and release isentropes are calculated for the solid $\ensuremath{\gamma}$, $\ensuremath{\alpha}$, liquid, and mixed phases. Based on the model developed, the Hugoniot does not cross the line of the $\ensuremath{\alpha}$-$\ensuremath{\varepsilon}$ transition and melting occurs directly from the $\ensuremath{\alpha}$ 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 $\ensuremath{\gamma}$-$\ensuremath{\alpha}$ transition as a result of cerium's abnormal compressibility in the region of the $\ensuremath{\gamma}$-$\ensuremath{\alpha}$ 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 $\ensuremath{\gamma}$-$\ensuremath{\alpha}$ transition and smoothly varies through the region of melting.