Informatics-based learning of oxygen vacancy ordering principles in oxygen-deficient perovskites

Ordered oxygen vacancies (OOVs) in perovskites can exhibit long-range order and may be used to direct materials properties through modifications in electronic structures and broken symmetries. Based on the various vacancy patterns observed in previously known compounds, we explore the ordering principles of OOVs in oxygen-deficient perovskite oxides with $AB\mathrm{O}_{2.5}$ stoichiometry to identify other OOV variants. We performed first-principles calculations to assess the OOV stability on a dataset of 50 OOV structures generated from our bespoke algorithm. The algorithm employs uniform planar vacancy patterns on (111) pseudocubic perovskite layers and the approach proves effective for generating stable OOV patterns with minimal computational loads. We find as expected that the major factors determining the stability of OOV structures include coordination preferences of transition metals and elastic penalties resulting from the assemblies of polyhedra. Cooperative rotational modes of polyhedra within OOV structures reduce elastic instabilities by optimizing the bond valence of $A$- and $B$-cations. This finding explains the observed formation of vacancy channels along low-index crystallographic directions in prototypical OOV phases. The identified ordering principles enable us to devise other stable vacancy patterns with longer periodicity for targeted property design in yet to be synthesized compounds.