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The local lattice structure and EPR, optical spectra for Cr(3+) doped in RbCdF(3) crystal have been studied by diagonalizing the complete energy matrices. The results show that the local structure of the Cr(3+) ions in RbCdF(3) exhibits a compressed distortion at the trigonal and tetragonal sites. The compressed distortion can be ascribed to the fact that the radius of Cr(3+) ion is smaller than that of Cd(2+) ion, and therefore Cr(3+) ion will draw the fluorin ligands inwards. The variational ranges of the local structural parameters for Cr(3+) doped in RbCdF(3) crystal R = 1.9491 angstrom similar to 1.9814 angstrom, theta = 55.234 degrees similar to 55.286 degrees at the trigonal site and R(1) = 1.8617 angstrom similar to 1.8928 angstrom, R(2) = 1.9527 angstrom similar to 1.9851 angstrom at tetragonal site are obtained respectively, and the EPR and optical spectra agree well with the experimental results.