Analysis of the Cubic Crystal-Field Parameters for Gd3+ in the Alkaline Earth Fluorides

The optical spectra of the alkaline‐earth fluorides doped with Ge³⁺ (MeF₂:Gd³⁺, where Me represents Ca, Sr, or Ba) at octahedral sites are analyzed to determine the effect of lattice size on the cubic crystal‐field parameters. The point‐charge model predicts a linear dependence of the first‐order crystal‐field splitting on $B_0^4$ which in turn varies inversely with the Gd³⁺–F⁻ separation to the fifth power ${\mathrm{(R}}^{\text{−5}})$ . The slopes of plots of $\log b_4^0$ vs $\log R$ yield values of − 2.1, − 2.7, and 0 for the ${}^8{S}_{\text{7\hspace{0.17em}/\hspace{0.17em}2}}{,}^6{P}_{\text{7\hspace{0.17em}/\hspace{0.17em}2}}$ , and ${}^6{P}_{\text{5\hspace{0.17em}/\hspace{0.17em}2}}$ multiplets, respectively. This apparent discrepancy is resolved by the inclusion of crystal‐field interactions in all orders between the ${}^{8}S$ and ${}^6\mathrm{(P,\; I,\; D)}$ multiplets. The $\log {\mathrm{(A}}_4^0〈{{r}}^4\mathrm{〉)}$ vs $\log R$ plot is found to be − 1.8 which agrees with the EPR result to within experimental error. The disagreement with the point‐charge model is examined.