Hexagonal graphite to cubic diamond transition from equilibrium lines and barrier calculations

Abstract

Phase equilibrium lines of hexagonal graphite (hg) and cubic diamond (cd) phases of carbon as well as a saddle-point equilibrium line between the two phase equilibrium lines are studied by first-principles total-energy calculations. The Gibbs free energies (G) of the three equilibrium lines determine the transition pressure p t = 70 kbar (0.070 Mbar) from hg phase to cd phase and the barrier height at p t of ΔG = 178 mRy/atom that stabilizes the two phases against a phase transition. The cd phase becomes unstable at V = 13.6 au3/atom (p = 26 Mbar) where the curvature at the equilibrium point of the energy curve (denoted E V (c/a) curve) goes to zero. The hg and cd phase equilibrium lines cross at V = 14.5 au3/atom where the regular hg phase (with one minimum in each E V (c/a) curve) ends and the irregular hg phase (with two minima in each E V (c/a) curve) develops. The feature of “two phase equilibrium lines cross” was not observed in our previous work [S.L. Qiu, P.M. Marcus, J. Phys.: Condens. Matter 24, 225501 (2012); S.L. Qiu, P.M. Marcus, Eur. Phys. J. B 86, 425 (2013)] where the two interacting crystal phases have a common unit cell with different c/a ratios. This work demonstrates that the saddle-point equilibrium line along with the two phase equilibrium lines are all needed for a complete description of crystal phases and their transitions under pressure.