Small data-driven study of two-dimensional ordering in rutile oxyfluorides

The fundamental properties of heteroanionic materials (HAMs) comprising more than one anion are governed by the structural arrangement of the anions within the parent crystal structure motifs, both at local and medium-range length scales. Less unexplored ordering pattern in these compounds that could prove to be important for materials design applications is the presence of extended correlations across two dimensions (2D). Here, we report robust 2D ordering patterns in the rutile oxyfluorides TiOF and FeOF. We train a cluster expansion model to perform large-size finite-temperature Monte-Carlo simulations from which we filter out low-energy supercells and subsequently compare their simulated structural and electronic property characterization to that obtained experimentally. Our computational data predicts that the ordering pattern in rutile oxyfluorides is dictated by the electronic configuration of the transition metal cation. The short-range order is influenced by the different degrees of ionicity of the M-O and M-F bonds, while the long-range order is determined by the number of valence d electrons in the cation, leading to distinct 2D ordering patterns along the <110> planes in TiOF and FeOF. We also observe good agreement between our simulated data for the Monte-Carlo structural model and diffuse X-Ray scattering results, thereby showcasing the merit of such a combined approach in resolving the structures of 2D ordered materials systems.