Direct mapping of Li-enabled octahedral tilt ordering and associated strain in nanostructured perovskites

Self-assembled nanostructures with periodic phase separation hold great promise for creating two-and three-dimensional superlattices with extraordinary physical properties. Understanding the mechanism(s) driving the formation of such superlattices demands an understanding of their underlying atomic structure. However, the nanoscale structural fluctuations intrinsic to these superlattices pose a new challenge for structure determination methods. Here we develop an optimized atomic-level imaging condition to measure TiO₆ octahedral tilt angles, unit-cell-by-unit-cell, in perovskite-based Li_0.5-3xNd_0.5+xTiO₃, and thereby determine the mathematical formula governing this nanoscale superstructure. We obtain a direct real-space correlation of the octahedral tilt modulation with the superstructure geometry and lattice-parameter variations. This reveals a composition-dependent, self-ordered octahedral superlattice. Amazingly, we observe a reversible annihilation/reconstruction of the octahedral superlattice correlated with the delithiation/lithiation process in this promising Li-ion conductor. This approach to quantify local octahedral tilt and correlate it with strain can be applied to characterize complex octahedral behaviours in other advanced oxide systems.