Lanthanide Contraction in LnF₃ (Ln = Ce-Lu) and Its Chemical and Structural Consequences: Part 2: Specialized Empirical System of R³⁺ (R = Y, La, and 14 Ln) and F¹⁻ Ionic Radii for RF₃ Series

A specialized empirical (Spec-zd Emp) system of ionic radii (SIR) for R = Y³⁺, La³⁺, Ln³⁺, and F¹⁻ (R rare earth elements (REE)) was derived from the dependence of lanthanide contraction (LC) on the atomic number (Z) of lanthanides (Ln). LC decreased the radius of the cation with increasing Z. The structures of t-RF₃ (LaF₃-NdF₃, “pseudo t-SmF₃”) of the LaF₃ type, 11 β-LnF₃ (Ln = Sm-Lu), and β-YF₃ of the β-YF₃ type were studied. The empirical basis of the shortest (F-F)_min and (R-F)_min distances was calculated from the structural data for the RF₃ complete series. The dependence of (F-F)_min on Z reached saturation at Z = 67 (Ho). The base F¹⁻ radius r₋ = 1.2539(16) Å was calculated as the arithmetic mean of five (F-F)_min in LnF₃ with Ln = Ho-Lu. For the LnF₃ series with Ln contributions up to 75 % wt., the dependence of (Ln-F)_min on Z reflected the non-uniformity of the 4f orbital filling. SIR was calculated as the difference in the empirical constants of RF₃ (ionic radii of (R,Ln)³⁺ (r₊) and F¹⁻ (r₋)), the change in which was continuous over the series and did not depend on the type of structure: r₊ = (_ZR-F)_min − ½(F-F)_min (Z = 57–71). The changes in LC in the LnF₃ series were described by a third-degree polynomial. LC reduced r₊ by 24% (percentage relative to less) from 1.1671(16) Å (La³⁺) to 0.9439(17) Å (Lu³⁺). In the Spec-zd Emp SIR, r₊ were constants that did not require corrections for a coordination number (CN). A comparison of r₊ in the Spec-zd Emp SIR with other SIRs was performed.