| The EPR study of the crystal KZnF3 doped with the transition-metal ion Fe3+ has caused considerable interest of people in the recent years. However, the EPR Ground-state Zero-field Splitting of KZnF3: Fe3+ system hasn't got satisfactory explanation in the previous theoretical calculations, so it's still a problem how to construct a reasonable physical model in accounting for the local structure of Fe3+ in KZnF3: Fe3+ system. In the present paper, we first introduce method of building complete energy matrix of d5 configuration ion in trigonal symmetry as well as EPR theory. Then we propose a two-layer-ligand model, in which the ligands consist of six nearest-neighbor F~ ions in the first layer and eight next nearest-neighbor K+ ions in the second layer. Based on this model, we construct two different theoretical models, i.e. Vk-Vacancy model and displacement model, to describe lattice local structure distortion of KZnF3:Fe3+ system and by diagonlizing the complete energy matrix, we make an analysis of the relationship between the EPR trigonal-field parameters and the local crystal structure of KZnF3:Fe3+system. By contrasting two models, we find that only displacement model can satisfactorily explained all the EPR parameters simultaneously. Therefore , we get an important conclusion from the displacement model that the local structure distortion of KZnF3:Fe3+system is due to the displacement of a K+ ion along C3 axis towards the Fe3+ ion, which leads to the shift of the F- ions away from C3 axis and this local structure distortion scheme supports the viewpoint of the charge compensation.
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