First-order quadrupole powder

In contrast, soft magnetic solids and paramagnetic systems with weak anisotropy may be completely polarized by an applied field, that is, the effective field at the Mossbauer nucleus is along the direction of the applied field, whereas the EFG is powder-distributed as in the case of crystallites or molecules. In this case, first-order quadrupole shifts cannot be observed in the magnetic Mossbauer spectra because they are symmetrically smeared out around the unperturbed positions of hyperfine fines, as given by the powder average of EQ mj, d, in (4.51). The result is a symmetric broadening of all hyperfine fines (however, distinct asymmetries arise if the first-order condition is violated). 

Figure 12 Offset dependence of the intensity of the CT resonance in MAS NMR spectra of Na2MgEDTA-4H20, recorded with a single HS pulse placed before the spin-echo sequence. The experimental data (square points) were recorded using a 7mm probe (with 7kHz MAS rate) the solid red line is just a guide for the eyes. Also shown (blue line) is the simulated first-order quadrupole static powder pattern for the single Mg site in this compound.

Fig. 7.2. Powder patterns for I = 3/2 showing (a) NMR spectrum in the presence of first-order quadrupole effects and (b) the effect on the central component in the spectrum of second-order effects. The spectra are shown relative to the central point, with Ap and denoting first- and second-order quadrupole splittings,...

Distinct quadrupole shifts do occur as well in magnetically split spectra of single-crystals, poly crystalline powder or frozen solution samples. In all three cases, the line shifts obey the simple first-order expression at high-field condition. 

Fig. 14. The pulse sequence for recording the double-quantum 2H experiment.37 The entire experiment is conducted under magic-angle spinning. This two-dimensional experiment separates 2H spinning sideband patterns (or alternatively, static-like 2H quadrupole powder patterns) according to the 2H double-quantum chemical shift, so improving the resolution over a single-quantum experiment. In addition, the doublequantum transition frequency has no contribution from quadrupole coupling (to first order) so, the double-quantum spectrum is not complicated by spinning sidebands. Details of molecular motion are then extracted from the separated 2H spinning sideband patterns by simulation.37 All pulses in the sequence are 90° pulses with the phases shown (the first two pulses are phase cycled to select double-quantum coherence in q). The r delay is of the order 10 gs. The q period is usually rotor-synchronized.

There is a redeeming instance that often makes partial spectra of quadrupolar nuclei observable. For odd-half integral nuclei, such as 23Na (7=2), the mz = to m. = -2 transition is not affected by the quadrupolar interaction to first order and remains relatively sharp, while the satellite transitions, such as mz = to mz = 2 and m. = —2 to mz = -2, are broadened by the powder distribution. There is a substantial second-order effect of the quadrupole coupling that broadens even the central transition, but this broadening is often only a few kilohertz to a few tens of kilohertz—large but much smaller than Megahertz. 

Figure 2.9. The quadrupole perturbed powder patterns for an I = nucleus. A. The outer satellite transitions to first-order. B. The second-order quadrupolar broadening of the central transition with...

This term is anisotropic and produces a powder pattern. It has been derived under the assumptions that first-order perturbation of the S-states is sufficient, that the J tensor is axially symmetric and that the unique axis of J is aligned with the intemuclear vector. Under MAS this term will be scaled but, as it is not proportional to P2(cos0), it cannot be completely removed. Hence the MAS spectrum will still have some residual width, but the most profound effect is to leave an isotropic term which can be calculated by averaging the powder lineshape. Hence for a J-coupled system with an axially symmetric quadrupole interaction, the spectrum is shifted from the isotropic chemical shift by ... 

It should be noted that for anisotropic liquid crystals the NMR signal is split into 21 component signals due to first-order static quadrupole interactions but that, in the absence of second-order quadrupole effects, the width of the central line gives the transverse relaxation rate both for powder samples and for macroscopically aligned samples (see further Chapter 7). 

---