Evidence for multiple Liquid-liquid phase transitions in carbon, and the Friedel-ordering of its liquid state

Carbon, the fourth most abundant element in the Universe forms a metallic fluid with transient covalent bonds on melting. Its liquid-liquid phase transitions, intensely sought using simulations had been elusive. Here we use density functional theory (DFT) simulations with up to 108 atoms using molecular dynamics, as well as one-atom DFT as implemented in the neutral pseudo-atom method where multi-atom effects are treated by ion-ion correlation functionals. Both methods use electron-electron exchange correlation functionals for electron many-body effects. Here we show using both methods, that liquid carbon displays multiple liquid-liquid transitions linked to changes in coordination number in the density range 3 g/cm$^3$, to $\sim$ 6 g/cm$^3$ when a coordination number of 12 is reached. The transitions disappear by 4 eV in temperature. The calculated pressures and transition densities are shown to be sensitive to the exchange-correlation functionals used. Significantly, we find that a simple metallic model yields the structure factors and thermodynamics with quantitative accuracy, without invoking any covalent-bonding features. The ion-ion structure factor for these densities and temperatures is found to have a subpeak tied to twice the Fermi wavevector, constraining the fluid in momentum space. The dominant Friedel oscillations forming the pair interactions correlate the ions and drive the multiple liquid-liquid phase transitions. Our results suggest that liquid carbon typifies a class of fluids whose structure is ordered by the long-range Friedel oscillations in the pair-potentials. These results are critical to terrestrial and astrophysical studies, inertial fusion using carbon drivers, refined shock experiments, and in seeking new carbon-based materials.