Study of a spin-3/2 system by a quadrupolar-echo sequence: suppression of spurious signals

The density matrix describing the evolution of a spin-3/2 system excited by a quadrupolar-echo sequence consisting of two rf pulses in quadrature phase, {X}-tau(2)-{Y}-tau(4)-[acquisition(y)], is calculated from the equilibrium state to the acquisition period. The interactions involved are the first-order quadrupolar interaction throughout the experiment and a local heteronuclear magnetic dipolar term between the two pulses and during the acquisition period. Three echoes, one due to a satellite transition at tau(4) = tau(2) and two due to the central transition at tau(4) = tau(2) and tau(4) = 3 tau(2), are predicted. They have similar expressions than those obtained with two rf pulses of the same phase, {X}-tau(2)-{X)-tau(4)-[acquisition(y)], except the signs. Moreover, it is shown experimentally that a combination of these two sequences, namely: (X}-tau(2)-{X)-tau(4)-[acquisition(y)]-recycle delay-(X)-tau(2)-{-X}-tau(4)-[acquisition(y)]-recycle delay-(X)-tau(2)-{Y}-tau(4)-[acquisition(- y)]-recycle delay-{X}-tau(2)-{-Y}-tau(4)-[acquisition(- y)]-recycle delay, cancels the spurious piezo-electric signals when studying a ferroelectric material in the single-crystal form.