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By analyzing EPR and optical spectra, the local lattice structures of (NiF6)(4-) clusters in perovskite fluorides RbMF(3) (M = Cd(2+), Ca(2+), Mg(2+)) series in tetragonal and trigonal ligand field are studied. A compression distortion relative to the regular octahedron for the RbCdF(3): Ni(2+) and RbCaF(3): Ni(2+) systems is determined. Furthermore, on the basis of the complete energy matrices we found that ZFS parameter D dependence on spin-orbit coupling coefficient zeta is not a strictly quadratic relation as shown by the fourth-order perturbation formula. Finally, the curves of g(parallel to) versus k and g(perpendicular to) versus k for these three systems are plotted which satisfy an approximately linear relation. (c) 2008 Elsevier B. V. All rights reserved.