Title: Assessing Local Structure Motifs Using Order Parameters for Motif Recognition, Interstitial Identification, and Diffusion Path Characterization

Structure–property relationships form the basis of many design rules in materials science, including synthesizability and long-term stability of catalysts, control of electrical and optoelectronic behavior in semiconductors, as well as the capacity of and transport properties in cathode materials for rechargeable batteries. The immediate atomic environments (i.e., the first coordination shells) of a few atomic sites are often a key factor in achieving a desired property. Some of the most frequently encountered coordination patterns are tetrahedra, octahedra, body and face-centered cubic as well as hexagonal close packed-like environments. Here, we showcase the usefulness of local order parameters to identify these basic structural motifs in inorganic solid materials by developing classification criteria. We introduce a systematic testing framework, the Einstein crystal test rig, that probes the response of order parameters to distortions in perfect motifs to validate our approach. Subsequently, we highlight three important application cases. First, we map basic crystal structure information of a large materials database in an intuitive manner by screening the Materials Project (MP) database (61,422 compounds) for element-specific motif distributions. Second, we use the structure-motif recognition capabilities to automatically find interstitials in metals, semiconductor, and insulator materials. Our Interstitialcy Finding Tool (InFiT) facilitates high-throughput screenings of defect properties. Third, the order parameters are reliable and compact quantitative structure descriptors for characterizing diffusion hops of intercalants as our example of magnesium in MnO₂-spinel indicates. Finally, the tools developed in our work are readily and freely available as software implementations in the pymatgen library, and we expect them to be further applied to machine-learning approaches for emerging applications in materials science.