LAUSR

The (Li,Al)-codoped magnesium spinel $({\mathrm{Li}}_{x}{\mathrm{Mg}}_{1\ensuremath{-}2x}{\mathrm{Al}}_{2+x}{\mathrm{O}}_{4})$ is a solid lithium-ion electrolyte with potential use in all-solid-state lithium-ion batteries. The spinel structure means that interfaces with spinel electrodes, such as ${\mathrm{Li}}_{y}{\mathrm{Mn}}_{2}{\mathrm{O}}_{4}$ and ${\mathrm{Li}}_{4+3z}{\mathrm{Ti}}_{5}{\mathrm{O}}_{12}$, may be lattice matched, with potentially low interfacial resistances. Small lattice parameter differences across a lattice-matched interface are unavoidable, causing residual epitaxial strain. This strain potentially modifies lithium diffusion near the electrolyte-electrode interface, contributing to interfacial resistance. Here, we report a density functional theory study of strain effects on lithium diffusion pathways for (Li,Al)-codoped magnesium spinel, for ${x}_{\mathrm{Li}}=0.25$ and ${x}_{\mathrm{Li}}=0.5$. We have calculated diffusion profiles for the unstrained materials, and for isotropic and biaxial tensile strains of up to $6%$, corresponding to $\left\{100\right\}$ epitaxial interfaces with ${\mathrm{Li}}_{y}{\mathrm{Mn}}_{2}{\mathrm{O}}_{4}$ and ${\mathrm{Li}}_{4+3z}{\mathrm{Ti}}_{5}{\mathrm{O}}_{12}$. We find that isotropic tensile strain reduces lithium diffusion barriers by as much as $0.32\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$, with typical barriers reduced by $\ensuremath{\sim}0.1$ eV. This effect is associated with increased volumes of transitional octahedral sites, and broadly follows qualitative changes in local electrostatic potentials. For biaxial (epitaxial) strain, which more closely approximates strain at a lattice-matched electrolyte-electrode interface, changes in octahedral site volumes and in lithium diffusion barriers are much smaller than under isotropic strain. Typical barriers are reduced by only $\ensuremath{\sim}0.05$ eV. Individual effects, however, depend on the pathway considered and the relative strain orientation. These results predict that isotropic strain strongly affects ionic conductivities in (Li,Al)-codoped magnesium spinel electrolytes, and that tensile strain is a potential route to enhanced lithium transport. For a lattice-matched interface with candidate spinel-structured electrodes, however, epitaxial strain has a small, but complex, effect on lithium diffusion barriers.