Extended Defects in Graphene and Their Contribution to the Excess Specific Heat at High Temperatures

The recent experiments on fast (microsecond) pulse heating of graphite suggest the existence of sharp maximum (6500 K at 1–2 GPa) on its melting curve. To check the validity of these findings, we propose to investigate the accumulation of extended in-plane defects in graphene. Such defects would contribute to thermodynamic properties of graphene and impose the upper limit on its melting temperature. We propose a type of extended defect of graphene, consisting of pentagonal and heptagonal rings with record low formation energy, whose accumulation leads to the loss of shear rigidity of graphene at temperatures above 6400 K, thus setting the upper limit on its melting temperature. We found that this model satisfactorily explains the increase of specific heat observed in the premelting region of graphite in slow (millisecond) pulse heating experiments. However, in fast (microsecond) pulse heating experiments such an increase of specific heat was not observed, which is a strong indication of overheating that takes place in these experiments.

Figure 1

Phase diagram of graphite in a low-pressure region. Solid lines designate the vapor phase boundary according to Leider et al. [16]. (Black filled circle) triple point vapor-solid-liquid, which corresponds to experimental results obtained by Savvatimskiy et al. [1].(White filled circle) melting points of graphite obtained by Togaya [7]. (Black filled square) melting point of graphite, registered in experiments of Kondratyev and Rakhel [8].

Figure 2

Zigzag (a) and armchair (b) extended defects in graphene considered in the Letter. In (c) the artificially created extended defect in graphene [20] is shown. Solid green color depicts domains of pristine graphene. The translucent gray color marks interfacial carbon layers.

Figure 3

Comparison (not a fit) of experimental excess specific heat with theoretical dependence obtained for extended zigzag defects with specific formation energy $0.57\mathrm{eV}/\mathrm{atom}$. Experimental data of graphite specific heat were obtained in the millisecond pulse heating experiment of Savvatimskiy et al. [1] (Plus symbol) and Sheindlin and Senchenko [28] (White filled circle). Dashed line—theoretical curve of specific heat calculated according to Eq. (1) with the Dulong-Petit “3R” additive term (the Debye temperature of graphite is $\approx 400\mathrm{K}$).