Thermodynamically Stable Phases of Carbon at Multiterapascal Pressures

Phases of carbon are studied up to pressures of 1 petapascal (PPa) using first-principles density-functional-theory methods and a structure searching algorithm. Our extensive search over the potential energy surface supports the sequence of transitions $\mathrm{\text{diamond}}\to \mathrm{BC}8\to \mathrm{\text{simple}}$ cubic under increasing pressure found in previous theoretical studies. At higher pressures we predict a soft-phonon driven transition to a simple hexagonal structure at 6.4 terapascals (TPa), and further transitions to the face centered cubic electride structure at 21 TPa, a double hexagonal close packed structure at 270 TPa, and the body centered cubic structure at 650 TPa.

Figure 1

Variation of the enthalpies of the phases with pressure. The enthalpy of sh carbon is taken as reference in the main graph while the fcc structure is the reference for the inset showing the ultrahigh pressure regime.

Figure 2

Evolution of the phonon dispersion relations of sc carbon with pressure. As the pressure is increased the acoustic phonon branch becomes unstable at $X$ and a phase transition to the sh structure occurs.

Figure 3

Phase diagram of carbon. The solid lines were obtained from our static lattice DFT and vibrational data while the dashed line shows results from molecular dynamics simulations [29]. The dotted lines are estimates based on the DFT data and the Lindemann criterion.

Figure 4

Crystal structure and ELF isosurface of fcc carbon at 25 TPa. The carbon atoms are depicted in grey while the green pockets enclose the maximally localized electrons. Taken together, the positions of the carbon atoms and the maxima in the ELF form the ${\mathrm{CaF}}_2$ structure.