We have performed ab-initio molecular dynamics simulations to elucidate the mechanism of the phase transition at high pressure from hexagonal graphite (HG) to hexagonal diamond (HD) or to cubic diamond (CD). The transition from HG to HD is found to occur swiftly in very small time of 0.2 ps, with large cooperative displacements of all the atoms. We observe that alternate layers of atoms in HG slide in opposite directions by (1/3, 1/6, 0) and (-1/3, -1/6, 0), respectively, which is about 0.7 {AA} along the pm[2, 1, 0] direction, while simultaneously puckering by about pm0.25 {AA} perpendicular to the a-b plane. The transition from HG to CD occurred with more complex cooperative displacements. In this case, six successive HG layers slide in pairs by 1/3 along [0, 1, 0], [-1, -1, 0] and [1, 0, 0], respectively along with the puckering as above. We have also performed calculations of the phonon spectrum in HG at high pressure, which reveal soft phonon modes that may facilitate the phase transition involving the sliding and puckering of the HG layers. The zero-point vibrational energy and the vibrational entropy are found to have important role in stabilizing HG up to higher pressures (>10 GPa) and temperatures than that estimated (<6 GPa) from previous enthalpy calculations.
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