Comparative analysis of crystal-field parameters for rare-earth ions at monoclinic sites in AB(WO4)2 crystals: II. Pr3+ and Nd3+ ions in KRE(WO4)2 (RE = Y or Gd), Pr3+ ions in M+Bi(XO4)2 (M+ = Li or Na and X = W or Mo), and Nd3+ ions in NaBi(WO4)2 and AgNd(WO4)2

Abstract

In part I, the crystal-field (CF) parameter (CFP) sets for important potential solid state laser systems Tm3+, Ho3+, and Er3+ ions in KGd(WO4)2 and Tm3+ ions in KLu(WO4)2 were thoroughly revisited using a general framework for the analysis of CF levels and CFP modeling. In this part the non-standard CFP sets for Pr3+ and Nd3+ ions in KR(WO4)2 (R = Y or Gd) and the standard CFP sets for Pr3+ ions in M+Bi(XO4)2 (M+ = Li or Na and X = W or Mo) and Nd3+ ions in the related systems NaBi(WO4)2 and AgNd(WO4)2 are analyzed. Due to structural similarity of the hosts, the CFP values for a given trivalent rare-earth (RE3+) ion should be quite close in these systems. However, the fitted (and model) CFP sets appear disparate for the systems in question. The standardization criteria are utilized to ensure direct comparability of the apparently disparate CFP sets reported in the literature. The CFP sets standardized by us are compared with the originally standard CFP sets for Pr3+ and Nd3+ ions in related AB(XO4)2 systems. Following part I, we argue that meaningful analysis of the mixed CFP sets, i.e. standard and non-standard ones, must take into account the intrinsic features of CF Hamiltonians for orthorhombic and lower symmetry cases, which have not been fully recognized in the literature as yet. The model or fitted CFP sets that belong to disparate regions in the CFP space are intrinsically incompatible, i.e. such sets should not be directly compared. The correlated alternative CFP sets are calculated using monoclinic standardization transformations. The closeness of the standardized CFP sets is assessed in a quantitative way using the closeness factors and the norms ratios. Comparative analysis of the monoclinic CFP sets reported for the titled ion–host systems is carried out and several inconsistencies in the previous studies are clarified. The CFP sets determined by standardization are utilized as starting sets for applications of the multiple correlated fitting technique to independently obtain and additionally verify the fitted CFPs based on published energy levels data. Multiple correlated fittings offer an advantage over the single-fitting tactics by enabling an improved fine-tuning of the final fitted CFPs as well as their interpretation and comparability with the sets obtained by others. The present consistent methodology may enable better understanding of the intricate aspects inherent in the spectroscopic studies for other ion–host systems exhibiting orthorhombic, monoclinic, and triclinic site symmetry.