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

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 <Subscript> t </Subscript>=70 kbar (0.070 Mbar) from hg phase to cd phase and the barrier height at p <Subscript> t </Subscript> of ΔG=178 mRy/atom that stabilizes the two phases against a phase transition. The cd phase becomes unstable at V=13.6 au<Superscript>3</Superscript>/atom (p=26 Mbar) where the curvature at the equilibrium point of the energy curve (denoted E <Subscript> V </Subscript>(c/a) curve) goes to zero. The hg and cd phase equilibrium lines cross at V=14.5 au<Superscript>3</Superscript>/atom where the regular hg phase (with one minimum in each E <Subscript> V </Subscript>(c/a) curve) ends and the irregular hg phase (with two minima in each E <Subscript> V </Subscript>(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 <Emphasis Type="Bold">24, 225501 (2012); S.L. Qiu, P.M. Marcus, Eur. Phys. J. B <Emphasis Type="Bold">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. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014