Properties of graphite at melting from multilayer thermodynamic integration

Although the melting of graphite has been experimentally investigated for a long time, there is still much debate on the graphite melting properties, as studies show significant discrepancies. We calculate the melting line by means of LCBOPII, a state-of-the-art interaction potential for carbon. To this purpose, we developed a generalized thermodynamic integration scheme, suitable for layered crystals. We also investigate the structure of liquid carbon around the coexistence line, including the undercooled region, as well as its dynamic properties in a wide range of temperatures.

Figure 1

(Color online) Behavior of ${⟨\Delta u⟩}_{\lambda }$ as a function of $\lambda$. The red plus-symbols correspond to the thermodynamic integration of graphite from the multireference EC. Note the absence of any divergence at $\lambda =1$, despite the relative sliding of the graphite sheets. The blue crosses correspond to the thermodynamic integration of the liquid. The connecting solid and dashed lines are a guide to the eye. The error bars are smaller than the size of the symbols.

Figure 2

(Color online) Graphite melting line according to LCBOPII (red dots, solid line), compared to the ${\text{LCBOPI}}^{+}$ carbon phase diagram (blue diamonds, dashed lines).

Figure 3

(Color online) Volume per particle in liquid carbon (circles) and in graphite (diamonds) on the isotherms at $\text{T}=4250\text{K}$ (blue solid lines) and $\text{T}=4750\text{K}$ (red dashed lines). Error-bars are within the size of the symbols.

Figure 4

(Color online) LCBOPII radial distribution functions on the melting line at the densities of $1.94\text{g}{\text{cm}}^{-3}$ $\left(\text{T}=4250\text{K}\right)$ and $2.59\text{g}{\text{cm}}^{-3}$ $\left(\text{T}=4250\text{K}\right)$ (solid blue and dashed red lines, respectively).

Figure 5

(Color online) LCBOPII (solid blue) and AIMD (dashed red) radial distribution functions on the melting line $\left(\text{T}=4250\text{K}\right)$ at the density of $1.94{\text{cm}}^{-3}$.

Figure 6

(Color online) Coordination fractions in the undercooled liquid at $\text{T}=4000\text{K}$. The twofold coordination fractions are represented by circles, the threefold by triangles, and the fourfold by diamond. The one calculated according to LCBOPII are connected by solid lines, the one obtained with ab-initio simulations by dashed ones.

Figure 7

(Color online) Coordination fractions in the liquid carbon at low density $\left(1.94\text{g}{\text{cm}}^{-3}\right)$ as function of the temperature. The legend is the same as in Fig. 6. The AIMD results show that the liquid is mainly threefold coordinated, although the difference between twofold and threefold fractions becomes small around 7000 K. The LCBOPII model is able to reproduce qualitatively the trend.

Figure 8

(Color online) Mean square displacements for the LCBOPII-MD simulations for the temperatures $\text{T}=4250\text{K}$, 5000 K, 6000 K (blue, red, and green lines, respectively) at the density of $\rho =1.94\text{g}{\text{cm}}^{-3}$. The plot is truncated at the MSD of $20{\text{Å}}^2$.

Figure 9

(Color online) Arrhenius plot of the diffusivity of the liquid carbon at two different densities. The AIMD results at the lower density $\left(1.94\text{g}{\text{cm}}^{-3}\right)$ are represented by blue circles, the LCBOPII one by red diamonds. The green squares are the LCBOPII results at the density of $2.59\text{g}{\text{cm}}^{-3}$. On the $y$-axis we plot $\text{ln}\left(D/D_0\right)$, where $D_0=1{\text{cm}}^2{\text{s}}^{-1}$. On the $x$-axis we plot the inverse temperature $\beta$ for the temperature range 4000 K–7000 K. The lines are the linear fits of the shown data sets. The error bars provide a rough estimate for the statistical accuracy.