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 ferro-electric material in the single-crystal form.