RESUMO
The Hahn echoes for a spin I = 5/2 system were derived by considering the first-order quadrupole interaction throughout the experiment. Consequently, our results are valid for any ratio of the quadrupole coupling, omega Q, to the amplitude of the RF pulse, omega RF. The use of simplified density operators reduced the computation time dramatically. Furthermore, this approach allows a better understanding of the origin of the Hahn echoes in half-integer quadrupole spins. The tau 4 = tau 2 Hahn echoes were illustrated with the 27Al nucleus in a polycrystalline sample of KAl(SO4)2.12H2O. The quadrupole coupling constant and the asymmetry parameter of 27Al were determined by two methods: from the lineshape of the powder pattern and from the variation of the central line integrated intensity as a function of the second pulse duration.
