Crystal radii and effective ionic radii of the rare earth ions

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There exist some relationships between the crystal radii of the rare earth ions, the 4 f electron number, and the coordination number. On the basis of these relationships, two empirical formulas have been proposed to calculate the unknown crystal radii of the rare earth ions from the known crystal radii of the trivalent rare earth ions. The crystal radii and effective ionic radii of all the rare earth ions (trivalent and divalent) with different coordination number ( N = 6–12) have been evaluated. The calculated results are very satisfactory, and for most of examples the relative error is less than 1.0%.