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

Equations of state for ruthenium and rhodium