First-principles equations of state for Al, Cu, Mo, and Pb to ultrahigh pressures

Abstract

Using accurate electronic-structure, interatomic-potential, and statistical methods, first-principles theoretical equations of state (EOSs) have been developed for the prototype metals Al, Cu, Mo, and Pb over wide ranges of volume and temperature. Emphasis is given to both the cold compressed solid, relevant to diamond-anvil-cell (DAC) experiments, and to the hot compressed liquid, relevant to multimegabar shock-wave experiments. The A1 EOS has recently been used to analyze nuclear-impedance-match (NIM) shock data on AI-Cu, AI-Mo, and A1-Pb sample pairs in the 5–30 Mbar regime [J. Appl. Phys. 69, 2981 (1991)]. Below 10 Mbar, calculated theoretical Hugoniots are in very good agreement with both absolute and NIM shock data for all four metals. Above 10 Mbar, some quantitative uncertainties remain, especially for Mo. Useful analytic representations of the calculated 300-K isotherms below 10 Mbar have also been developed for fcc Al, Cu, and Pb and for bcc Mo. The theoretical isotherms are in excellent agreement with a variety of ultrasonic, DAC, and reduced-shock data obtained in the assumed phases below 3 Mbar. At higher pressures complicating solid-solid phase transitions are expected and/or observed in Al, Mo, and Pb, but not in Cu, which is consequently a good candidate as a static ultrahigh-pressure EOS standard.