Lanthanide-Dependent Clustering in Yb$^{3+}$/Ln$^{3+}$ Co-Doped CaF$_2$ Nanocrystals: Correlating Spectroscopic Signatures with DFT Insights

Abstract

The formation of heterogeneous lanthanide-ion clusters in CaF$_2$ was investigated experimentally and computationally. CaF$_2$ nanoparticles co-doped with 20~mol\% Yb$^{3+}$ and 2~mol\% Ln$^{3+}$ (Ln$^{3+}$ = Ce$^{3+}$, Pr$^{3+}$, Nd$^{3+}$, Sm$^{3+}$, Eu$^{3+}$, Gd$^{3+}$, Ho$^{3+}$, Er$^{3+}$, and Tm$^{3+}$) were synthesized via a hydrothermal method. The structural and morphological properties were characterized using powder X-ray diffraction, dynamic light scattering, and transmission electron microscopy techniques. High-resolution Fourier transform infra-red spectroscopy revealed the presence of Yb$^{3+}$ isolated cubic centers and various cluster sites. The relative concentration of the clusters varied with the choice of the co-doping ion. Calculations based on density functional theory were used to estimate the formation energies and local coordination structures of different clusters. The calculations indicate that the neutral $C_{4v}$ aggregations containing Ln$^{3+}$ tend to decrease across the lanthanide series, while the negatively charged derivatives of hexameric clusters are relatively constant. This variation matches the experimental results. This study advances understanding of the clustering mechanisms in lanthanide-doped CaF$_2$ nanoparticles and has implications for luminescence optimization in advanced nanomaterials.