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 $X-Y$ structures in the International Crystal Structure Database, where $X=\left\{\text{Li,}\text{Na,}\text{K,}\text{Rb,}\text{Cs}\right\}$ and $Y=\left\{\text{Si,}\text{Ge,}\text{Sn,}\text{Pb}\right\}$. 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 ${\mathrm{Li}}_x\mathrm{Si}$, $x=2.33$–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 ${\mathrm{Li}}_{13}{\mathrm{Ge}}_4$.

• Received 25 February 2014
• Revised 1 August 2014

DOI:https://doi.org/10.1103/PhysRevB.90.054111