Shock Compressing Diamond to a Conducting Fluid

Abstract

Laser generated shock reflectance data show that diamond undergoes a continuous transition from optically absorbing to reflecting between Hugoniot pressures 600<P(H)<1000 GPa. The data are consistent with diamond having a thermal population of carriers at P(H) approximately 600 GPa, undergoing band overlap metallization at P(H) approximately 1000 GPa and melting at 800<P(H)<1000 GPa. The results agree well with an equation of state model that predicts that elemental carbon remains solid throughout the interior of Neptune.

Multiphase equation of state for carbon addressing high pressures and temperatures

“…Also shown on this figure are data from static compression measurements of the room-temperature isotherm [82] (green circles at the lowest P ), magnetically driven flyer plate studies [8] (dense set of magenta + symbols with ρ ∼ 6-7 g/cc), and multiple sets of laser-shock data on the principal Hugoniot of diamond (symbols with error bars) [1][2][3][4][5]. Note that much of the highest-P Hugoniot data [1] seems to straddle the 300 K isotherm, even well above P = 1000 GPa; indeed, the data of Brygoo et al [4] even fall below our prediction of the room-T isotherm. This is very puzzling in light of our theoretical results which suggest that the Hugoniot should be much stiffer than the isotherm at these larger compressions.…”

“…Our computational results fall into two categories: (1) calculations of the EOS, by which we mean internal energy E and pressure P as functions of density ρ and temperature T , and (2) calculations of intermediate quantities which we use to build the EOS. These include cold compression curves (E and P as functions of ρ, for ions fixed in position [18]), phonon densities of states (PDOSs), and electronic excitation contributions to the free energy.…”

“…The EOS of the high-temperature liquid is elucidated by performing DFT-MD for C up to 100 000 K and PIMC calculations [14] from ∼200 000 K (depending on the density) to over 10 8 K. We establish that the best fit to these EOS predictions requires a liquid free energy model in which (1) electronic excitations are treated in an average-atom picture which includes atomic shell structure, and (2) the decay of the ion-thermal specific heat from 3k B /atom to 3k B /2/atom as T → ∞ is much faster than previously expected. In what follows, we describe the details of our DFT and PIMC calculations of the EOS of C, present the models we use to fit these ab initio data, and compare various thermodynamic tracks through our resulting EOS with the findings of recent experiments performed on high-energy laser platforms [1,6,7].…”

“…Since the final multiphase EOS model was designed to be used in continuum dynamics (hydrocode) simulations spanning a wider range of conditions, these researchers embedded their detailed three-phase EOS model into a more coarse-grained model [17] that respected the ideal gas limits at high T and low ρ and the Thomas-Fermi limit [12] at high ρ. While satisfactory in a broad sense, this older EOS model suffers from three main drawbacks: (1) The embedding of the DFT-based 3-phase model into the coarsegrained model created kinks in the thermodynamic functions, even though an attempt was made to smooth out such features by interpolation. (2) There are no solid phases beyond BC8; sc and sh phases, for instance, are not included.…”

“…Recent laser-shock and ramp-compression studies [1][2][3][4][5][6][7], together with shock measurements performed with magnetically driven flyer plates [8], have produced data in the range from P = 0-50 Mbar. In addition, theoretical work on the EOS and phase diagram in this same range has yielded predictions which are largely (though not completely) in accord with these experimental data [8,9].…”