Equations of state for ruthenium and rhodium

Ru and Rh are interesting cases for comparing equations of state (EOS), because most general purpose EOS are semi-empirical, relying heavily on shock data, and none has been reported for Ru. EOS were calculated for both elements using all-electron atom-in-jellium theory, and cold compression curves were calculated for the common crystal types using the multi-ion pseudopotential approach. Previous EOS constructed for these elements used Thomas-Fermi (TF) theory for the electronic behavior at high temperatures, which neglects electronic shell structure; the atom-in-jellium EOS exhibited pronounced features from the excitation of successive electron shells. Otherwise, the EOS matched surprisingly well, especially considering the lack of experimental data for Ru. The TF-based EOS for Ru may however be inaccurate in the multi-terapascal range needed for some high energy density experiments. The multi-ion calculations predicted that the hexagonal close-packed phase of Ru remains stable to at least 2.5 TPa and possibly 10 TPa, and that its c/a should gradually increase to the ideal value. A method was devised to estimate the variation in Debye temperature from the cold curve, and thus estimate the ion-thermal EOS without requiring relatively expensive dynamical force calculations, in a form convenient for adjusting EOS or phase boundaries. The Debye temperature estimated in this way was similar to the result from atom-in-jellium calculations. We also predict the high-pressure melt loci of both elements.