Determination of quadrupole parameters with a composite pulse for spurious signal suppression.

Spurious signals such as the piezoelectric signal from a ferroelectric crystal or the ringing signal from the NMR probe head tuned for low gyromagnetic ratio nuclei are often observed in pulsed NMR. Both signals are cancelled using the Hahn echo sequence with appropriate phase cyclings. The present paper applies a composite-pulse sequence to cancel the ringing signal. The main advantage of this sequence over the Hahn echo sequence is in the simplicity of optimizing the line intensity: the optimization of only one pulse duration for this sequence but of two pulse durations and the interpulse delay for the Hahn echo sequence. We are interested in half-integer quadrupole spins (I = 3/2, 5/2, 7/2, and 9/2), which means that we must consider the first-order quadrupole interaction during the pulses. For simplicity, we deal mainly with spin I = 3/2 nuclei. Since the central-line intensity depends on the ratio of the quadrupole coupling constant (QCC) to the amplitude of the RF pulse, we can determine the QCC from a featureless lineshape by fitting the variation of the experimental central-line intensity for increasing pulse duration with theoretical results. Contrary to the one-pulse sequence where the central-line intensity is proportional to the pulse duration if the latter is short, there is no such condition with the composite-pulse sequence. In other words, this sequence does not allow us to quantify the relative spin populations in powders. The size of the sample must be much smaller than that of the RF coil in order for the RF magnetic field to become homogeneous for the sample. We used (87)Rb (I = 3/2) in an aqueous solution of RbCl and in RbNb2O5F powder, (131)Xe (I = 3/2) of xenon gas physisorbed in Na-Y zeolite, and (23)Na (I = 3/2) in two well-known powders (NaNO3 and NaNO2) to support our theoretical result.

Determination of spin-5/2 quadrupolar coupling with two-pulse sequences.

The density matrix of a spin-5/2 system excited by two in-phase pulses separated by a delay tau 2 is calculated from the equilibrium state to the end of the second pulse. The interaction involved throughout the computation is the first-order quadrupolar interaction. Consequently, the results are valid for any ratio of the quadrupolar coupling to the amplitude of the radio-frequency pulse. It is shown that single- and multi-quantum coherences developed during the first pulse are detected at the end of the second pulse through single-quantum coherences. Other two-pulse sequences with various phase cyclings as well as the rotary echo sequence are also discussed and illustrated with the nuclei 27Al in a single crystal of corundum Al2O3.

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.

Application of one-dimensional nutation nuclear magnetic resonance to 51V in ferroelastic BiVO4.

The central line intensity of a spin I = 7/2, excited by a radio frequency (rf) pulse, is calculated by taking into account the first-order quadrupolar interaction during excitation. Thus, the result is valid for any ratio of quadrupolar coupling to pulse amplitude. The quadrupolar coupling of the nuclei vanadium 51V in a single crystal of ferroelastic BiVO4 is determined using this one-dimensional (1D) mutation method.

Spin-5/2 Hahn echoes in solids.

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.