Pseudo-symmetries of crystallographic coordination polyhedra. Application to forsterite and comparison with some EPR results

A quantitative analysis of the distortion of octahedral and tetrahedral coordination polyhedra with respect to perfect symmetry in crystal structures is presented. The distortion of a polyhedron is defined by all the fourfold and threefold pseudo-symmetries. Tests on the significance of the pseudo-symmetries are presented. In forsterite the results are compared to ones previously proposed, based on the pseudo-symmetry of fourth order expansion of the crystal field, and also compared to the pseudo-symmetries of the environment of Mn²⁺ and Gd³⁺ that were determined by electron paramagnetic resonance (EPR) measurements. Agreements and differences between these results are given.