Local deformation and the structure of the Stark splitting of rare-earth ions

A model for describing the relaxation of ligand ions close to a defect when impurity ions are introduced into a crystal is proposed and verified. The approach assumes that ionic displacements into new equilibrium positions can be regarded as fundamental parameters of impurity crystals that can be determined from experimental data concerning the energy structure of the impurity ion. Direct calculations for rare-earth impurity ions using crystal-field theory showed that the energy spectrum of these ions strongly depends on the equilibrium positions of the nearest matrix ions surrounding them. The results of the calculations are compared with the available experimental data. The parameters of the theory are determined. The possibility of applying this approach to the study of other systems is discussed.