Multisublattice cluster expansion study of short-range ordering in iron-substituted strontium titanate

Abstract

Owing to the challenges in obtaining realistic atomic configurations in large chemical phase spaces, it is not straightforward to describe structure–property relations in materials exhibiting configurational disorder. One example is iron-substituted strontium titanate (SrTi1−xFexO3−d, STF), a promising perovskite-derivative cathode material in solid oxide fuel cells that exhibits full solid solubility 0≤x≤1 and a tendency to exhibit short-range order. Here we demonstrate a multisublattice cluster expansion (CE) framework and apply it to STF across the full composition range. The CE approach is distinct from more traditional CE formulations in that clusters are defined explicitly by the chemical species distributed among multiple sublattices, rather than via cluster functions of occupation variables with decoration. The modified CE approach makes it easy to distinguish meaningful chemical interactions that are harder to extract from conventional CE, since for the latter chemical identity in a cluster is expressed as a product of site occupations. The least absolute shrinkage and selection operator (LASSO) is implemented as a regression analysis tool to select key clusters and avoid overfitting. We demonstrate this formulation on STF, and show that it can accurately predict configurational energies in comparison to conventional CE. From the key clusters, we identify that short-range ordering between substitutional Fe and oxygen vacancies (VO) results in the formation of Fe–VO strings. In addition, we consider the stability of STF through CE-based Monte Carlo (MC) simulations and confirm the presence of superstructures that were previously observed in transmission electron microscopy. Analysis of atomic configurations from MC samples reveals variations in the oxidation state of Fe atoms, which can be explained by the ordering tendency of Fe and VO. The cluster description and selection formalism described here may be applied to other disordered multisublattice systems for accurate and efficient material modeling.