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

Abstract

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 3–6 g/cm3 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-ranged 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.