Metallization of Fluid Hydrogen at 140 GPA (1.4 Mbar)

Abstract

The properties of hydrogen at high pressures and temperatures are important for the interiors of giant planets, such as Jupiter and Saturn, and for Inertial Confinement Fusion. Electrical conductivity measurements indicate that hydrogen becomes a metallic fluid at 140 GPa, ninefold initial liquid-H₂ density, and 2600 K. Metallization density is defined to be that at which the electronic bandgap E_g is reduced by pressure to E_g — k_BT, at which point E_g is filled in by fluid disorder to produce a metallic density of states with a Fermi surface and the minimum conductivity of a metal. High pressures and temperatures were obtained with a two-stage gun, which accelerates an impactor up to 7 km/s. A strong shock wave is generated on impact with a holder containing liquid hydrogen at 20 K. The impact shock is split into a shock wave reverberating in hydrogen between stiff Al₂O₃ anvils. This dynamic compression heats hydrogen quasi-isentropically to about twice its melting temperature at 100 Gpa pressures and lasts ~100 ns, sufficiently long to achieve equilibrium and sufficiently short to preclude loss of hydrogen by mass diffusion and chemical reactions.

The measured electrical conductivity increases four orders of magnitude from 93 to 140 GPa and is constant at 2000 (Ω-cm)-1 from 140 to 180 GPa. This conductivity is the same as that of Cs and Rb undergoing the same transition from a semiconducting to metallic fluid at 2000 K. This measured value is also within factor of 5 or less of hydrogen conductivities calculated with the following models: (i) minimum conductivity of a metal, (ii) Ziman model of a liquid metal, and (iii) tight-binding molecular dynamics. At metallization this fluid is ç90 at.% H₂ and 10 at.% H with a Fermi energy of ç12 eV. Fluid hydrogen at finite temperature undergoes a Mott transition at D_m ¹⁰a^*=0.30, where D_m is the metallization density and a^* is the Bohr radius of the molecule. Metallization occurs at a lower pressure in the fluid than predicted for the solid probably because crystalline and orientational phase transitions, which occur in the ordered solid and inhibit metallization, do not occur in the fluid

Tight-binding molecular dynamics calculations by Lenosky et al suggest that fluid metallic hydrogen is a novel state of condensed matter. Protons are paired transiently and exchange on a timescale of a few molecular vibrational periods, ç10–14 s. Also, the kinetic, vibrational, and rotational energies of the dynamically paired protons are comparable. These tight-binding calculations indicate that the measured conductivity is the minimum conductivity of a metal.