  We present a 5-phase equation of state (EOS) for elemental carbon. The phases
considered are: diamond, BC8, simple-cubic, simple-hexagonal, and the
liquid/plasma state. The solid phase free energies are constrained by density
functional theory (DFT) calculations. Vibrational contributions to the free
energy of each solid phase are treated within the quasiharmonic framework. The
liquid free energy model is constrained by fitting to a combination of DFT
molecular dynamics performed over the range 10,000 K < T < 100,000 K, and path
integral quantum Monte Carlo calculations for T > 100,000 K (both for {\rho}
between 3 and 12 g/cc, with select higher-{\rho} DFT calculations as well). The
liquid free energy model includes an atom-in-jellium approach to account for
the effects of ionization due to temperature and pressure in the plasma state,
and an ion-thermal model which includes the approach to the ideal gas limit.
The precise manner in which the ideal gas limit is reached is greatly
constrained by both the highest temperature DFT data and the path integral
data, forcing us to discard an ion-thermal model we had used previously in
favor of a new one. Predictions are made for the principal Hugoniot and the
room-temperature isotherm, and comparisons are made to recent experimental
results.
