The EPR zero-field splitting of Fe3+in a trigonal-symmetry crystal field has been calculated on the basis of the complete matrices for ligand-field spin-orbit coupling of the d~configuration with C3 symmetry. The absorption spectrum, the EPR zero-field-splitting axial parameters D and F, and the cubic parameter a for the Fc3+ ion in sapphire have been interpreted uniformly.

The relationship between the EPR cubic-field parameter 10g(a), the covalence factor N, and the crystal-field strength Dq has been established by diagonalizing the complete matrices for ligand-field and spin-orbit coupling. A general method for calculating the local thermal-expansion coefficient of the im-purity ion has been proposed. It is shown that the experiment of Rubio and Medrano is in agreement with the infrared and Raman spectra.

A theoretical method for studying the inter-relation between electronic and molecular structure has been proposed by diagonalizingthe complete energy matrices for a d5 configuration ion in a trigonal ligand field. As for ZnO: Fe3+system, the local lattice distortion forthe tetrahedral Fe3+ centers in zinc oxide has been investigated by considering the second-order and fourth-order EPR parameters D and (a-F) simultaneously. The results indicate that the local lattice structure around tetrahedral Fe3+ centers exhibits a compression distortion, i.e., the (FeO4) 5 entity in ZnO: Fe3+ system is smaller than the (ZnO) 6entity in ZnO crystal. The local lattice structure distortionparameters DR =0.119 A and Dh=0.339for Fe3+ion in ZnO: Fe3+ system are determined. Furthermore, thedisplacements DZ1=0.050 A for transition-metal ion along the C3 axis, and DZ2=0.169 A for the distance variation between theO2 along the C3 axis and the lower oxygen plane are obtained.

By diagonalizing the complete energy matrices for a d5 configuration ion in a trigonal ligand-field and considering the second-order,fourth-order EPR parameters D and (a-F) simultaneously, the substitution position of Mn2+ion in the CaCO3: Mn2+system has beenstudied by analyzing the optical absorption and EPR spectra of single crystal and the ostracum layer of operculum of fresh water snailPila globosa. The results show that in the single crystal there is an obvious compressed distortion DR=0.158A and Dh=0.70, and thedistortion in P. globosa is DR=0.107A and Dh=0.34～0.23. Meanwhile the EPR parameters 104(a-F)=7.02-7.29cm 1 and104a=6.35cm 1 are predicted in P.globosa.

The EPR spectra of octahedral Fe3+ center in lutetium aluminum garnet have been studied by means of the complete energy matricesfor a d5 configuration ion in a trigonal ligand–field. It is manifested that the local lattice structure around an octahedrally coordinatedFe3+ center has an expansion distortion from that of undistorted host Al3+ ion. The expansion distortion can be ascribed to the fact thatthe radius of Fe3+ ion is bigger than that of Al3+ion, and consequently the Fe3+ ion pushes the oxygen ligands outwards. Simultaneously,for the octahedral Fe3+ center in the crystal, the local lattice structure parameters, R=(2.007±0.022)A andh=(52.708 ± 0.032), which reflect the interactions between impurity and crystal lattice, are determined from our calculation, andEPR parameters a, D, and (a-F) also get a unified explanation.