Categorization of inorganic crystal structures by Delaunay tetrahedralization

Abstract

Crystal structure prediction is demanding in two senses: this is a difficult problem, both experimentally and computationally, yet we want to find new materials with new properties that take unknown crystal structures. Using statistical information on the local environment of already reported stable crystal structures would be helpful when, for instance, finding new crystal structures through visually adding atoms sequentially to a cluster of atoms, which is an intuitive procedure that does not require substantial computational resources. This study conducted hierarchical classification of frequently appearing structure types in the ICSD database by comparing the occurrence ratios of H, B, C, N, O, F, and transition metals (TM) in binary, ternary, and quaternary crystals. The bond angle and solid angle distributions of Delaunay polyhedra with atoms as vertices were considered as descriptors of the local environment for each structure type. Hierarchical clustering of structure types based on bond angle or solid angle distributions revealed that the structure types can be broadly categorized into those favoring TM oxides, having low TM occurrence, and having high TM occurrence. Our results indicate that the anion, or lack of, plays a key role in determining the crystal structure type, and structure types strongly preferred by TM oxides can accommodate a broad range of angles.

Keywords

• bond angle
• crystal structure type
• delaunay polyhedra
• hierarchical classification
• solid angle