Crystallographic and spectroscopic evidence for intrinsic distortion in the disordered crystal β-NaGdF₄

β-NaREF4 (RE: rare earth metals) is a peculiar crystal due to its intriguing disordered structure. This crystal is usually considered to have an average structure with a space group of P-6 (174). However, a long-term contradiction existing in this system is that the luminescence characteristics do not match the corresponding theoretical predictions based on the average structure. To resolve this contradiction, we proposed a reasonable local structure model clearly showing the local symmetry of the cations based on the measurement of the extended X-ray absorption fine structure of β-NaGdF4. We also observed an intrinsic distortion in the disordered structure that resulted from the disordered arrangement of the Na+ and Gd3+ cations. Furthermore, using Eu3+ as a photoluminescence probe, we concluded that the breakdown in the crystallographic site symmetry originated from the intrinsic distortion of these crystals. This work provides a comprehensive explanation for the contradiction observed in this system and a foundation for further investigations to understand such disordered structures.