Ionic radii of the REE, 2: A practical revision to REE3+ radii in common minerals

Nearly all geochemical applications of ionic radii appeal to the classic tabulation of Shannon (1976; Acta Crystallographica, A32, 751-767). In that work, smoothing was applied to the crystallographic systematics of lanthanides to ensure consistent decreases in cationic radii with increasing atomic number – the lanthanide contraction. Recent work of Hawthorne and Gagné (2024; Acta Crystallographica, B80, 326-339) has now updated preferred radii, based on a vastly larger database of crystal structures. However, values have not been smoothed, and several average radii violate the lanthanide contraction principle. Here, we propose a set of effective ionic radii for trivalent lanthanides using simple regressions, based in part on atomic theory, and verify that these radii satisfy theoretical principles of lattice strain:

r = 1/(0.0235·n_e - 0.035·CN – 0.0015·n_e·CN + 1.150)

where n_e is electron number (0 to 14 for La to Lu) and CN is coordination number (6 to 12). Expressions for ionic radii of lanthanides in xenotime, zircon, monazite, and apatite are:

r = 1/(0.01593·n_e + 0.8773) [xenotime and zircon

r = 1/(0.01148·n_e + 0.8270) [monazite]

r = 1/(0.01143·n_e + 0.8344) [apatite]

The ionic radius of Y³⁺ can be refined to high precision using partitioning data (= 0.999·r_Ho; see Schwartz and Kohn, this session), but the ionic radius of Sc³⁺ cannot because its ionic radius is so different from lanthanides, and because it does not necessarily substitute equivalently into mineral structures.