Melting Points and Formation Free Energies of Carbon Compounds with Sodalite Structure

TL;DR

This work investigates the stability and superconducting potential of sodalite-structured carbon compounds, XC$_6$, XC$_{10}$, and XC$_{12}$, using first-principles molecular dynamics to map melting behavior under pressure and to estimate formation energetics. By combining the Z-method with ab initio MD, the authors relate the melting temperature $T_m$ to the dynamical instability temperature $T_u$ via $T_m \simeq T_u/1.23$, and compute the superconducting transition temperature $T_c$ from DFPT-derived electron-phonon properties within the Allen–Dynes framework. They find that FC$_6$, FC$_{10}$, and ClC$_{10}$ can remain stable up to high temperatures at modest pressures with $T_c$ approaching 100 K, while NaC$_6$ requires very high pressure to be stable, though high-$T$ synthesis is potentially feasible as suggested by the finite-temperature free-energy analysis. The formation enthalpies at $P=0$ are generally positive, signaling synthesis challenges at ambient conditions; nevertheless, the introduction of a phenomenological free-energy correction $\tilde{F}(T)$ reveals possible synthesis windows under high $P$ and $T$, highlighting the nuanced balance between thermodynamics and kinetics in realizing these superconducting carbon sodalites.

Abstract

Using first-principles calculations, we investigate the melting temperatures $T_{\rm m}$ and formation free energy of carbon compounds with sodalite structures, $X$C$ _6$, $X$C$ _{10}$, and $X$C$ _{12}$, where $X$ is F, Na, Cl, and so on. These compounds are expected to be phonon-mediated superconductors exhibiting high transition temperatures $T_{\rm c}$ of up to about 100 K. We estimate $T_{\rm m}$ as a function of pressure $P$ by using the first-principles molecular dynamics method and show the results as phase diagrams on the $P$-$T$ plane together with the results of $T_{\rm c}$. It indicates that the $T_{\rm m}$ of NaC$_{\rm 6}$, which has a $T_{\rm c}$ up to about 100 K, is about $1300$ K or more at $P=30$ GPa. Furthermore, the $T_{\rm m}$ of FC$_{\rm 6}$ is about 2200 K even at $P=0$ GPa, where its $T_{\rm c}$ is about 80 K. Similar results are obtained for FC$_{\rm 10}$ and ClC$_{\rm 10}$ systems. These results suggest that some compounds can stably exist as high-temperature superconductors even at room temperature and pressure. To examine the feasibility of synthesizing these compounds, we estimate the formation enthalpies and formation free energies. These results suggest that NaC$_6$ could be formed under a sufficiently high pressure of about 300 GPa and a high temperature of about 6500 K.

Figures (18)

• Figure 1: (Color online) Structures of the sodalite-type compounds (a) $X$C$_6$ and (b) $X$C$_{10}$, where large spheres represent $X$-atoms and small spheres are carbon. Here, the crystal structure of $X$C$_{12}$ corresponds to (a) with one $X$ atom removed.
• Figure 2: Lindemann parameter $L_p$ as a function of simulation time $t$, where solid circles and empty circles represent the results for $T=6000$ and $7000$ K, respectively. $\bar{L_p}$ represents the average of the last four points of $L_p$.
• Figure 3: $\bar{L_p}$ as a function of $T$, where solid circles and empty circles represent the results for $N=8$ and 64, respectively. $T_u$ is determined by the condition $\bar{L_p}=0.3$.
• Figure 4: Melting points of diamond as a function of pressure $P$, where empty circles and empty squares represent $T_{\rm m}$ for the $N=8$ and 64 systems, respectively. Solid squares, solid circles, and solid triangles represent the results of Liang et al. Liang2019, Correa et al.Correa2006, and Wang et al, respectivelyWang2005. The light and broken lines show the result of Bundy et al. Bundy1996, where the broken line indicates the phase boundary between graphite and diamond. The inset shows the $k$-dependence of $T_{\rm m}$ at $P=0$ GPa, where $k$ is the mesh number in wavenumber space.
• Figure 5: (a) $T_{\rm m}$ of C$_6$ as a function of $P$, where empty circles, empty squares, and solid triangles represent $T_{\rm m}$ for the $N=12$, 48, and 96 systems, respectively. (b) $T_{\rm m}$ of C$_{10}$ as a function of $P$, where solid circles and solid squares represent $T_{\rm m}$ for the $N=10$ and 40 systems, respectively.