Thermodynamically stable lithium silicides and germanides from density functional theory calculations

High-throughput density functional theory (DFT) calculations have been performed on the Li-Si and Li-Ge systems. Lithiated Si and Ge, including their metastable phases, play an important technological role as Li-ion battery (LIB) anodes. The calculations comprise structural optimizations on crystal structures obtained by swapping atomic species to Li-Si and Li-Ge from the $X\ensuremath{-}Y$ structures in the International Crystal Structure Database, where $X={\text{Li,}\phantom{\rule{4.pt}{0ex}}\text{Na,}\phantom{\rule{4.pt}{0ex}}\text{K,}\phantom{\rule{4.pt}{0ex}}\text{Rb,}\phantom{\rule{4.pt}{0ex}}\text{Cs}}$ and $Y={\text{Si,}\phantom{\rule{4.pt}{0ex}}\text{Ge,}\phantom{\rule{4.pt}{0ex}}\text{Sn,}\phantom{\rule{4.pt}{0ex}}\text{Pb}}$. To complement this at various Li-Si and Li-Ge stoichiometries, ab initio random structure searching (AIRSS) was also performed. Between the ground-state stoichiometries, including the recently found ${\mathrm{Li}}_{17}{\mathrm{Si}}_{4}$ phase, the average voltages were calculated, indicating that germanium may be a safer alternative to silicon anodes in LIB due to its higher lithium insertion voltage. Calculations predict high-density ${\mathrm{Li}}_{1}{\mathrm{Si}}_{1}$ and ${\mathrm{Li}}_{1}{\mathrm{Ge}}_{1}$ $P4/mmm$ layered phases which become the ground states above 2.5 and 5 GPa, respectively, and reveal silicon and germanium's propensity to form dumbbells in the ${\mathrm{Li}}_{x}\mathrm{Si}$, $x=2.33$\char21{}3.25, stoichiometry range. DFT predicts the stability of the ${\mathrm{Li}}_{11}{\mathrm{Ge}}_{6}$ $Cmmm$, ${\mathrm{Li}}_{12}{\mathrm{Ge}}_{7}$ $Pnma$, and ${\mathrm{Li}}_{7}{\mathrm{Ge}}_{3}$ $P{32}_{1}2$ phases and several new Li-Ge compounds, with stoichiometries ${\mathrm{Li}}_{5}{\mathrm{Ge}}_{2}$, ${\mathrm{Li}}_{13}{\mathrm{Ge}}_{5}$, ${\mathrm{Li}}_{8}{\mathrm{Ge}}_{3}$ and ${\mathrm{Li}}_{13}{\mathrm{Ge}}_{4}$.