Theory of divalent ions in crystals

Abstract

The divalent ions in alkaline earth chalcogenides are viewed as compressible objects and are treated within a purely ionic model. As in earlier studies on the alkali and ammonium halides, the ions are taken to be in the form of space-filling polyhedral cells and the compression energy, which is the source of repulsion, is written as a surface integral over the cell faces. A simple method of computing the repulsion energy in any crystal lattice of arbitrary symmetry is proposed and the repulsion parametersB andσ are refined for the divalent ions under study. The theory explains the predominant occurrence of the NaCl structure in the alkaline earth chalcogenides. Hard sphere radii are estimated for the tetravalent cations Ti⁴⁺, Sn⁴⁺ and Pb⁴⁺ using the repulsion parameters of O²⁻ ion and the data on the corresponding rutile structure oxides. These radii are seen to be consistent with the measured interionic distances in several compounds occurring in the perovskite structure. The free transfer of repulsion parameters among several structures, which is a key feature of the present approach to repulsion, is confirmed to be valid by the present study.