The ionization of carbon at 10-100 times the diamond density and in the 10${}^6$ K temperature range

The behaviour of partially ionized hot compressed matter is critical to the study of planetary interiors as well as for nuclear fusion studies. A recent quantum study of carbon in the 10-70 Gbar range and at a temperature of 100 eV used $N$-atom density functional theory (DFT) with $N\sim 32$-64 and molecular dynamics (MD). This involves band-structure type electronic calculations and averaging over many MD generated ion configurations. The calculated average number of free electrons per ion, viz., $\bar{Z}$, was systematically higher than from a standard average atom (AA) quantum calculation. To clarify this offset, we examine (a) the effect of the self-interaction (SI) error in such estimates (b) the possibility of carbon being a granular plasma containing Coulomb crystals. The possibility of `magic-number’ bound states is considered. The electrical conductivity, pressure, and the compressibility of the carbon system are examined. The very low conductivity and the high $\bar{Z}$ results of DFT-MD point to the existence of carbon in a complex non-uniform low-conducting dispersed phase, possibly containing magic-number Coulomb crystals. The NPA estimate of $\bar{Z}$, conductivity, compressibility, and pressure reported here pertain to the {\it uniform liquid}.