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. 2006 Jan 31;103(5):1204-8.
doi: 10.1073/pnas.0510489103. Epub 2006 Jan 23.

Carbon under extreme conditions: phase boundaries and electronic properties from first-principles theory

Alfredo A Correa  1 , Stanimir A Bonev, Giulia Galli
Affiliations

Carbon under extreme conditions: phase boundaries and electronic properties from first-principles theory

Alfredo A Correa et al. Proc Natl Acad Sci U S A. .

Abstract

At high pressure and temperature, the phase diagram of elemental carbon is poorly known. We present predictions of diamond and BC8 melting lines and their phase boundary in the solid phase, as obtained from first-principles calculations. Maxima are found in both melting lines, with a triple point located at approximately 850 GPa and approximately 7,400 K. Our results show that hot, compressed diamond is a semiconductor that undergoes metalization upon melting. In contrast, in the stability range of BC8, an insulator to metal transition is likely to occur in the solid phase. Close to the diamond/liquid and BC8/liquid boundaries, molten carbon is a low-coordinated metal retaining some covalent character in its bonding up to extreme pressures. Our results provide constraints on the carbon equation of state, which is of critical importance for devising models of Neptune, Uranus, and white dwarf stars, as well as of extrasolar carbon-rich planets.

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Figures

Fig. 1.
Fig. 1.
Calculated phase diagram of carbon at high pressure omitting the graphite stability region for clarity. Points indicate the final two-phase simulation data used to bracket the melting temperatures. The plotted melting lines are a fit to the melting points by using the three-parameter Kechin melting equation (34). For a consistency check, the slopes of the melting curves (marked with short dotted segments) were computed independently from the Clapeyron equation (35). The phase boundary between diamond and BC8 is calculated within the quasiharmonic approximation at low temperature and from the three-phase Clapeyron identity Eq. 1 near the triple point. The triple point is located at T = 7,445 K and P = 850 GPa; metastable extensions of melting lines of BC8 and diamond are calculated and presented for illustrative purposes. The diamond Hugoniot (dashed line) is shown for comparison with experimental results (see text).
Fig. 2.
Fig. 2.
Phonon dispersion curves of diamond calculated at different pressures; transverse acoustic branches are highlighted. (Inset) Pressure dependence of transverse acoustic phonon at the L point. Note the maximum in phonon frequency at 250 GPa (see text).
Fig. 3.
Fig. 3.
Coordination and pair correlation function in liquid carbon. (a) Fraction of threefold, fourfold, fivefold, and sixfold coordinated atoms as a function of pressure at T = 9,000 K in liquid carbon. The coordination of each atom is computed by counting the number of its neighbors within a distance less than the first minimum of the pair correlation function. (b) Average coordination in the liquid phase as a function of pressure (T = 9,000 K) obtained by integrating the normalized pair correlation function up to its first minimum. (c) Pair correlation function together with histograms of distances of the first 24 neighbors, at P = 1,000 GPa and T = 9,000 K. At this pressure and temperature, the maximum of the histogram curve for the fifth neighbor is shown to be just inside the first peak of the pair correlation function.
Fig. 4.
Fig. 4.
Maximally localized Wannier function spreads for diamond (T = 6,000 K), BC8 (T = 6,000 K), and liquid (T = 9,000 K) phases at selected pressures. Although in insulating diamond the maximally localized Wannier function spread is significantly reduced with pressure (gap of diamond increases with pressure), the metallic liquid maintains larger spreads across a broad range of pressures. BC8, being a semiconductor with a small gap (≈ 0.4 eV at T ≃ 0), is an intermediate case.
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