Pulse FT NMR of non-equilibrium states of half-integer spin quadrupolar nuclei in single crystals

For quadrupolar nuclei with spin quantum numbers equal to 3/2, 5/2 and 7/2, the intensities of the NMR transitions in a single crystal are examined as a function of the rf excitation flip angle. Single-quantum NMR intensities are calculated using density matrix theory beginning under various non-equilibrium conditions and are compared with those determined experimentally. As a representative spin-3/2 system, the flip-angle dependence of the 23Na NMR intensities of a single crystal of NaNO3 was investigated beginning with the inversion of the populations associated with one of the satellite transitions. Subsequently, the populations of both satellite transitions were inverted using highly frequency-selective hyperbolic secant pulses. Calculated and experimental intensities are in good agreement. As an example of a spin-5/2 system, the flip-angle dependence of the 27Al NMR transition intensities was determined using a single crystal of sapphire, Al2O3, starting under different nuclear spin population conditions. The experimental trends mimicked those predicted by the density matrix calculations but the agreement was not as good as for the spin-3/2 case. Some SIMPSON simulations were also carried out to confirm the results generated by our density matrix calculations. The theoretical flip-angle behavior of the NMR transition intensities obtained from a spin-7/2 spin system is also discussed.