Structural Diversity from Anion Order in Heteroanionic Materials

Heteroanionic materials leverage the advantages offered by two different anions coordinating the same or different cations to realize unanticipated or enhanced electronic, optical, and magnetic responses. Beyond chemical variations offered by the anions, the ability to control the anion order present within a single transition metal polyhedron via anion-sublattice engineering offers a potentially transformative strategy in tuning material properties. The set of design rules for realizing and controlling anion order, however, are incomplete, which is due in part to the limited anion-ordered diversity in known structures. This aspect makes formulating such principles from experiment alone challenging. Here, we demonstrate how computational methods at multiple levels of theory are effective at investigating the anion site order dependencies in heteroanionic materials, HAMs, and enable the construction of crystal-chemistry principles. Our approach relies on a database of anion ordered structure variants in which we manipulate the lattice degrees of freedom through the incorporation of structural distortions. Structure-property relationships and anion-order descriptors are data mined from group theoretical techniques and density functional theory calculations. Using our combined computational scheme, we uncover a hybrid improper mechanism to stabilize polar phases, propose the chemical link between local and long ranger anion order, and detail the sequence of order-disorder/displacive transitions observed experimentally in the oxyfluoride Na₃MoO₃F₃. Our method is scalable and transferable to many heteroanionic chemistries and crystal families, facilitating the construction of heteroanionic materials design principles.