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The local angular distortions around the impurity Co2+ in CdCl2, CdBr2 and PbI2 are theoretically studied from the perturbation formulas of the electron paramagnetic resonance (EPR) parameters, the g factors g(//) and g(perpendicular to) and the hyperfine structure constants A(//) and A(perpendicular to) for a 3d(7) ion in trigonal symmetry. In these formulas, the contributions from the s-orbitals of the ligands, which were often ignored, are taken into account based on the cluster approach. By analyzing the EPR spectra, we find that the impurity-ligand bonding angles beta related to the C-3 axis in the Co2+ impurity centers are different from the corresponding metal-ligand bonding angles beta(H) in the hosts, characterized by the local angular distortions Delta beta (=beta - beta(H)). The calculated EPR parameters, especially the anisotropies of the g and A factors for the studied systems based on the local angular distortions Delta beta, show reasonable agreement with the observed values.