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

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.