Ionic radii and the method of the undetermined parameter

Abstract

The basis on which values may be assigned to the radii of ions in crystals is examined. A set of radii in terms of one undetermined parameter (Li⁺, 2.581–δ; Na⁺, 2.851–δ; K⁺, 3.162–δ; Rb⁺, 3.302–δ; F^–,δ–0.520; Cl^–, δ–0.020; Br^–, δ+0.141; I^–, δ+0.399) is obtained for the alkali metal halides, which best satisfies the additivity criterion. The value assigned to the undetermined parameter δ in no way affects the accuracy of the additivity of the radii. Methods of finding δ based on the Landé assumptions, on screening constant calculations, on absolute molar refractions of the ions, and on absolute molar diamagnetic susceptibilities of the ions are in good agreement, but values of δ from measurements of electron density in crystals are at variance with them.

The following absolute scale is proposed for the alkali halides: Li⁺, 0.73₉; Na⁺, 1.00₉; K⁺, 1.32₀; Rb⁺, 1.46₀; F^–, 1.32₂; Cl^–, 1.82₂; Br^–, 1.98₃; I^–, 2.24₁Å. Absolute scales of values for single ion molar refractions and single ion diamagnetic susceptibilities are obtained.

For the alkaline earth chalcogenides a set of radii in terms of one undetermined parameter, which best satisfy the additivity criterion is produced. The agreement between the values of the undetermined parameter obtained by various methods is poor. For the alkali metal chalcogenides a set of radii in terms of one undetermined parameter, is also produced. Again the agreement between the values of the undetermined parameter obtained by various methods is poor.