Melting Line of Graphite

A thin plate of highly oriented pyrolytic graphite (HOPG) with the hexagonal axis ($c$ axis) perpendicular to its surface was sandwiched between two plates of the window material and heated by an electric current pulse. The quasistatic heating process has been affected, in which the graphite sample undergoes thermal expansion only along the $c$ axis and is melted at a pressure of 0.3–2 GPa. The set of thermodynamic quantities characterizing completely the thermodynamic states of the sample in such a process (specific volume, enthalpy, temperature, and pressure) as well as the electrical resistivity, were measured with an uncertainty $<5\%$. It has been found that under the above pressures the HOPG melts at the temperatures of 6.3 to 6.7 kK, which are substantially higher than the literature values derived from indirect measurements. The jumps in the volume, resistivity and enthalpy of carbon on melting have been determined as well as values of the isochoric heat capacity and the sound velocity of the graphite and liquid carbon. The heat capacities in the vicinity of the melting line turned out to be close to the Dulong-Petit value while the sound velocity of liquid carbon clearly demonstrates an increase with volume indicating a change from the planar $s{p}^2$ to tetrahedral $s{p}^3$ covalent bonding.

Figure 1

Schematic diagram of the experiments. The HOPG sample ($S$) is placed between two plates of the window material ($P$ is the left plate) and two electrodes ($E$ is the high-potential electrode). To heat the sample the electric circuit is used which contains a capacitor ($C$), a ballast resistor ($R$), an inductance ($L$) and a current switch ($T$).

Figure 2

The experimental paths in the pressure-density plane which go from the normal state (NS). The hatched area designates the melting region; the two pairs of the experiments indicated with the thick red and black lines (solid and dashed) represent the experiments with relatively low pressures (1) and the higher pressures (2). The error bars show uncertainties of our measurements.

Figure 3

The temperature dependencies of enthalpy (a), resistivity (b), and density (c), measured in four experiments of this work (black and red lines) are compared with the literature data [15, 22, 23, 24, 25, 27]. The error bars show uncertainties of our measurements. The notations of the lines are the same as in Fig. 2.

Figure 4

Segment of the melting line of graphite determined in this work (thick blue line) is compared with that of Ref. [14] (green line), [11] (gray solid line), [28] (yellow circles), [4] (black short dashed lines), [6] (blue triangle), [29] (violet dashed dotted line); the dependencies measured in our four experiments (1,2) are shown with the thin lines which go from the normal state.

Figure 5

Density of liquid carbon as a function of pressure along the isotherm $T=7\mathrm{kK}$. Density values determined in these experiments (marks) are compared with the MD simulations results [32] performed using the local density approximation (black dash line) and the PBE functional [33] (red dashed line); the empirically corrected MD results are shown with the solid lines.