A multiphase equation of state for cerium (IV) oxide

I describe the construction of a theoretical equation of state (EOS) for cerium (IV) oxide, CeO$_{2}$, that includes a low- and high-pressure solid phase and the liquid. After quickly summarizing the standard models we use in each phase, I discuss challenges unique to the multiphase construction. I also describe some physical issues that appear in the Ce$_{x}$O$_{y}$ group of materials, including the possibility that CeO$_{2}$ changes chemical identity before melt. Finally, I briefly consider the challenge of comparing a full-density EOS to highly porous Hugoniot data.