VOLUME 60, NUMBER 14 PHYSICAL REVIEW LETTERS 4 APRIL 1988 Metals Physics at Ultrahigh Pressure: Aluminum, Copper, and Lead as Prototypes W. J. Nellis, ' J. A. Moriarty, ' A. C. Mitchell, ' ' M. Ross, ' R. G. Dandrea, N. W. Ashcroft, N. C. Holmes, (') and G. R. Gathers ' "'Lawrence Livermore National Laboratory, University of California, Livermore, California 94550 t ~Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853 (Received 11 May 1987; revised manuscript received 9 February 1988) New shock compression data for Al, Cu, and Pb in the pressure range 0.3-1 TPa (3-10 Mbar) have been combined with first-principles theory and earlier equation-of-state data to give the first self-con- sistent description of the thermodynamic states of metals at ultrahigh pressures. No evidence is found for a break in the slope of the shock Hugoniot of A1 near 0.5 TPa, as claimed by Al'tshuler. PACS numbers: 64. 30. +t, 06.20.Hq, 62. 50.+p The physics of condensed matter at ultrahigh pres- sures is of considerable current interest. The first optical and x-ray-diffraction data in the 0. 1-0. 2-TPa (1-2 Mbar) range have been published recently for H2 and D2, ' N2, and Si. ' These static high-pressure data were obtained with diamond-anvil cells, and there are current- ly prospects for the extension of such measurements up to 0. 5 TPa. 4 At the same time, high dynamic shock pressures generated by chemical and nuclear explosives have also been used to measure equation-of-state (EOS) data for metals up to 1 TPa. ' Densities at these ex- tremes of pressure can be several times those at ambient conditions, leading to significant changes in atomic, elec- tronic, and chemical structure. In metals, a pressure- induced s d or d s transfer of electrons is expected to occur over a wide portion of the periodic table and this transfer is expected to modify physical properties in the 0. 1-1-TPa range. While it is of intrinsic interest to study various phe- nomena at ultrahigh pressures, it is also important to study prototypical systems in detail as a foundation for physical understanding in this rapidly expanding regime of experimentation. The metals Al, Cu, and Pb are espe- cially noteworthy for study in the 0. 1-1-TPa range be- cause of the following: (i) The s-d transfer can influ- ence the properties of these materials, yet their position outside of the normal transition metals in the periodic table makes them more amenable to an accurate theoret- ical description. (ii) The behavior of Al above 0. 5 TPa is currently controversial. Al'tshuler contends that there is a break in the slope of the shock Hugoniot near 0.5 TPa and a softening above, the anomaly possibly be- ing driven by an s d transition. (iii) Previous EOS data on these metals, ' ' when combined with the present experimental results, lead to the most extensive data base available for any materials in the 0. 1-1-TPa pressure range. (iv) The suitability of Al, Cu, and Pb as high-pressure EOS standards can now be objectively considered for the first time. In discussing experimental high-pressure EOS data, it is essential to distinguish between absolute and relative 1. 0 p O.s 4) CL 0. 2 0. 1 0. 3 0. 4 0. 5 Relative atomic volume VNO 0. 6 FIG. 1. Pressure-volume relations in Al. The filled and open circles are experimental single-shock (Hugoniot) and double- shock data, respectively, while the solid, dashed, and dotted curves represent the theoretical results derived from EOS 1, EOS 2, and EOS 3, respectively (1 TPa =10 Mbar). measurements. Absolute EOS data are independent of any theoretical model; relative EOS data, such as are ob- tained from shock-impedance-match experiments, de- pend on the EOS of a reference material, and often in a sensitive way. In the present paper, we utilize all previ- ously published absolute data on Al, s' ' Cu, ' ' and Pb. ' ' We also report here new absolute double-shock data on Al and new nuclear-driven shock-impedance- match (NIM) data on Cu and Pb. All of these results are summarized in Figs. 1 and 2. Our new double-shock EQS data for Al up to 0. 425 TPa (Fig. 1) were obtained with a two-stage light-gas gun. Double shocking achieves states closer to the room-temperature isotherm than single shocking, which yields the higher-temperature Hugoniot curve. The ex- periments are similar to the single-shock class, ' except that the target is a composite Al specimen and Ta or Pt anvil. Velocities for the impactors of up to 8 km/s are used: Both the impactor velocity and the shock velocity 1414