Reanalysis of energy levels and crystal field parameters for Er³⁺ and Tm³⁺ ions at C2 symmetry sites in hexahydrated trichloride crystals-Intricate aspects of multiple solutions for monoclinic symmetry

Authors:

• M. Karbowiak,
• P. Gnutek,
• Czesław Zygmunt Rudowicz

Abstract

Crystal-field splittings of lanthanide Ln³⁺ (Ln=Er, Tm) ions in hexahydrated Ln-trichlorides LnCl₃·6H₂O are re-analyzed in order to obtain consistent and standardized crystal-field parameter (CFP) sets. Experimental energy levels obtained by others were fitted to Hamiltonian parameters representing the combined free-ion and crystal-field interactions for Er³⁺ and Tm³⁺ ions in the actual monoclinic C₂ symmetry sites. The reliable starting values of the CFPs were obtained from superposition model calculations. Analysis of multiple solutions with relatively low r.m.s. deviation poses a dilemma arising from intricate aspects of fitted CFPs for low site symmetry systems. In order to solve this dilemma we propose a comprehensive procedure consisting in (i) model calculations of CFPs, (ii) scanning of the CF parameter space using values of the starting 2nd-rank CFPs in reasonable ranges, (iii) using starting CFP sets located in different regions of the CF parameter space for fittings, (iv) considering the effect of sign changes in CFPs on the fitted solutions, and (v) comparative analysis of the transformation properties of all fitted CFP sets based on the monoclinic standardization approach and the multiple correlated fitting technique. An important finding is that some of the multiple and seemingly comparable solutions for fitted CFP sets turn out to be spurious solutions. The nature of these computer artifacts is elucidated. Such artifacts occur when the descent in symmetry method is applied for initial evaluation of the starting CFPs, while the approximated higher symmetry axes do not coincide with the actual symmetry axes. Wider applications of the proposed procedure in CF studies of low site symmetry systems may improve the reliability of the CFP sets reported in literature. © 2010 Elsevier B.V. All rights reserved.