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Theoretical absorption line shapes are presented for Zeeman perturbed nuclear quadrupole resonance transitions (I = 3/2) in polycrystalline materials for the case in which the rf field is parallel to the Zeeman field. For a nuclear spin of 3/2, the pure quadrupole transition frequency νQ(1+η2/3)1/2 is insufficient to independently determine either νQ, the strength of the quadrupole interaction, or η, the asymmetry in the electric field gradient tensor. Application of a magnetic field removes the degeneracy of the energy levels producing, in general, four orientation dependent transition frequencies from which the quadrupole parameters can be determined. Computer simulated powder lineshapes are presented which are exact in η and are to first order in applied magnetic field strength. Frequencies of the features of the line shape are plotted as a function of η. The features of the line shape are due to crystallites aligned such that the applied field is parallel to one of the principal axes of the electric field gradient tensor. The combined nuclear electric quadrupole and nuclear Zeeman Hamiltonian has been solved exactly for these special orientations. Exact frequency expressions are calculated for these orientations of field with respect to sample. These correspond to the frequencies of the features of the line shape.

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