Structural and electronic properties of carbon in hybrid diamond-graphite structures

In this paper we report on ab initio pseudopotential density-functional calculations of some possible high-pressure phases of carbon. The total energies of several hybrid diamond-graphite structures were calculated as a function of volume using density-functional theory and the local density approximation. The lowest calculated transition pressures between hexagonal-graphite and hybrid structures were 17 and $20\mathrm{GPa}$, which compare well with the experimental value of $14\mathrm{GPa}$ for the transition at low temperatures between graphite and a still unidentified hard transparent phase. The electronic densities of states for the different structures are presented. Also, the x-ray powder diffraction patterns for a few structures were simulated and qualitatively compared to published experimental diffraction patterns.

Figure 1

Top views of (a) hexagonal-graphite, (b) orthorhombic-graphite, and (c) the layered-diamond structure obtained directly from hexagonal-graphite through buckling and without any graphene plane sliding.

Figure 2

The honeycomb structures: (a) all $s{p}^3$ (3,0) honeycomb structure (hexagonal-diamond), (b) mixed (3,0) and (4,0) structure, (c) mixed (3,0) and (4,0)ab structure, (d) (4,0) structure, (e) AB-stacked (4,0)ab structure, (f) (5,0) structure, and (g) (6,0) hexagonal structure. All except (6,0) can be obtained from buckling orthorhombic-graphite.

Figure 3

Calculated (a) energy versus volume, (b) enthalpy versus pressure, and (c) bulk modulus versus pressure for the honeycomb structures and layered-diamond compared to graphite and diamond. In (a) and (b), the symbols represent calculated data points and the lines are numerical fits, and in (c) the bulk modulus is obtained from the second derivative of the numerical fit to the energy and the pressure from the first derivative of the same fit. In (b) the enthalpy is plotted relative to the enthalpy at the graphite to diamond transition and the line defined by $H=40a_0^3\times p$ has been subtracted for clarity.

Figure 4

Calculated electronic density of states for all the studied carbon structures. The top two plots show the density of states of hexagonal-graphite and layered-diamond at the transition pressure, $120\mathrm{GPa}$, while all the other plots are at zero pressure. The Fermi level is at $0\mathrm{eV}$.

Figure 5

Comparison between (a) calculated graphite, $(3,0)∕(4,0)\mathrm{ab}$, $(3,0)∕(4,0)$, hexagon and cubic-diamond, and (b) experimental graphite powder X-ray diffraction patterns adapted from Ref. 8 (x-ray energy of $37.45\mathrm{KeV}$) for different pressures. The calculated patterns are based on a simple model, and therefore, only the position of the peaks should be trusted, not the amplitude.