Structural Diversity in Lithium Carbides

The lithium-carbon binary system possesses a broad range of chemical compounds, which exhibit fascinating chemical bonding characteristics that give rise diverse and technologically important properties. While lithium carbides with various compositions have been studied or suggested previously, the crystal structures of these compounds are far from well understood. In this work we present the first comprehensive survey of all ground state (GS) structures of lithium carbides over a broad range of thermodynamic conditions, using \textit{ab initio} density functional theory (DFT) crystal structure searching methods. Thorough searches were performed for 29 stoichiometries ranging from Li$_{12}$C to LiC$_{12}$ at 0 GPa as well as 40 GPa. Based on formation enthalpies from optimized van der Waals density functional calculations, three thermodynamically stable phases (Li$_4$C$_3$, Li$_2$C$_2$ and LiC$_{12}$) were identified at 0 GPa, and seven thermodynamically stable phases (Li$_8$C, Li$_6$C, Li$_4$C, Li$_8$C$_3$, Li$_2$C, Li$_3$C$_4$, and Li$_2$C$_3$) were predicted at 40 GPa. A rich diversity of carbon bonding, including monomers, dimers, trimers, nanoribbons, sheets and frameworks, was found within these structures, and the dimensionality of carbon connectivity existing within each phase was observed to increase with increasing carbon concentration. Of particular interest, we find that the well-known composition LiC$_6$ is actually a metastable one. We also find a unique coexistence of carbon monomers and dimers within the predicted thermodynamically stable phase Li$_8$C$_3$, and different widths of carbon nanoribbons coexist in a metastable phase of Li$_2$C$_2$ (\textit{Imm}2). Interesting mixed \textit{sp}$^2$-\textit{sp}$^3$ carbon frameworks are predicted in metastable phases with composition LiC$_6$.