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The anisotropic g factors g(//) and g(perpendicular to) for the tetragonal Er3+ center associated with Er3+ on y(3+) site in YBa2Cu3Oy(6 < y < 7) superconductor are investigated by using the second-order perturbation formulas of g factors for a 4f(11) ion in tetragonal symmetry. In these formulas, the contributions to the g factors from the second-order perturbation and the admixture of different energy levels are considered. The related crystal field parameters are calculated from the superposition model parameters obtained for similar tetragonal [ErOs](13-) clusters in some zircon compounds. The reasonableness of the results is discussed. (C) 2003 Published by Elsevier B.V.