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 r\^ole as Li-ion battery (LIB) anodes. The
calculations comprise structural optimisations 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={Li,Na,K,Rb,Cs} and
Y={Si,Ge,Sn,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 Li17​Si4​
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 Li1​Si1​ and Li1​Ge1​P4/mmm layered phases which become the ground state above 2.5 and 5 GPa
respectively and reveal silicon and germanium's propensity to form dumbbells in
the Lix​Si, x=2.33−3.25 stoichiometry range. DFT predicts the stability of
the Li11​Ge6​Cmmm, Li12​Ge7​Pnma and Li7​Ge3​P321​2
phases and several new Li-Ge compounds, with stoichiometries Li5​Ge2​,
Li13​Ge5​, Li8​Ge3​ and Li13​Ge4​.Comment: 10 pages, 5 figure