J. Appl. Cryst. (2023). 56, 884-888, https://doi.org/10.1107/S160057672300328X

Polyhedron ligands have been frequently used to characterize the ligand environment in inorganic materials. With a cation or anion as the central atom, its bonded counterparts are set as the vertices of the polyhedron. Generally, a series of geometrical parameters of the polyhedron, such as the average bond length and volumetric size, are extracted to illustrate the subtle change of local structure on compositional substitution. Polyhedral distortion analysis is widely adopted in research fields relying on a strong structure–property relationship. For example, in rare-earth or transition-metal element doped luminescent materials, the energy levels of the excited d electrons are highly dependent on the polyhedral distortion of the ligand. As a result, the spectral excitation/emission peaks of the luminescence center can be modulated by composition substitution, which usually induces polyhedral distortion due to the mismatch between ionic radii (Wang et al., 2016; Chen et al., 2017; Zhao et al., 2022). Therefore, characterization of polyhedral distortion constitutes an important part in the crystal structure analysis of inorganic materials.