Modeling the shape of ions in pyrite-type crystals

Abstract

The geometrical shape of ions in crystals and the concept of ionic radii are re-considered. The re-investigation is motivated by the fact that a spherical modelling is justified for p valence shell ions on cubic lattice sites only. For the majority of point groups, however, the ionic radius must be assumed to be an anisotropic quantity. An appropriate modelling of p valence ions then has to be performed by ellipsoids. The approach is tested for pyrite-structured dichalcogenides MX2, with chalcogen ions X = O, S, Se and Te. The latter are found to exhibit the shape of ellipsoids being compressed along the <111> symmetry axes, with two radii r and r⊥ describing their spatial extension. Based on this ansatz, accurate interatomic M–X distances can be derived and a consistent geometrical model emerges for pyrite-structured compounds. Remarkably, the volumes of chalcogen ions are found to vary only little in different MX2 compounds, suggesting the ionic volume rather than the ionic radius to behave as a crystal-chemical constant.