How inversion relates to disordering tendencies in complex oxides

Complex oxides exhibit great functionality due to their varied chemistry and structures. They are quite flexible in terms of the ordering of cations, which can also impact their functional properties to a large extent. Thus, the propensity for a complex oxide to disorder is a key factor in optimizing and discovering new materials. Here, we show that the propensity to disorder cations in perovskites, pyrochlores, and spinels correlates with the energy to "invert" the structure - to directly swap the cations across the sublattices. This relatively simple metric, involving only two energetic calculations per compound, qualitatively captures disordering trends amongst compounds across these three families of materials and is quantitative in several cases. This provides a fast and robust metric to determine those complex oxides that are easy or hard to disorder, providing new avenues for quick screening of compounds for cation-ordering-dependent functionalities.