First-order quadrupole effect

This expression is the same as that for the first-order quadrupole effect in high-field NMR spectra [4, 66]. The angular variation of (4.51) is visualized in Fig. 4.11. The graph on the left shows the contour of the function (3cos 0 1 ... 

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,...

A conplication arises for quadrupole nuclei which constitute around three quarters of the NMR-active nuclei in the Periodic Table. For non-integer spin quadrupole nuclei the central (1/2, -1/2) transition does not experience any first-order quadrupole effects, then the interaction has to be considered to higher order perturbation, which has a much more complex angular dependence, which in turn has consequences for the line narrowing techniques that are employed. The quadmpole interaction is described by the quadrupole coupling constant Xq = 90/ and the asymmetry parameter (ri). 

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). 

Blinc et al.4 in a classic paper on the NMR line shapes in PGs have presented the relation between the RF distribution and the quadrupole-perturbed NMR line shape for both first-order and second-order quadrupole effects. Static as well as time fluctuating RFs have been considered. By evaluating the local RF distribution, Blinc et al.4 have evaluated the Edwards-Anderson (qEA) order parameter. 

MQMAS was first proposed in 1995 by Harwood and Frydman [22, 23]. The aim of the technique is to refocus the second-order quadrupole effects, which otherwise... 

MAS of second-order quadrupole effects. The same type of rotations using Wigner rotation matrices can be applied to the second-order effects as for the first-order interaction which leads to a second-order quadrupole energy of interaction such that... 

It has been pointed out that the central ( 2, transition does not experience any first-order quadrupole interaction. The absence of first-order broadening effects is a general property of symmetric (m, - m) transitions. There are cases where this can be a distinct advantage, the most direct instance being for integer spin nuclei (e.g. D and both 1=1) where there is no ( /2, — /2) transition. The main problem is to excite and detect such higher-order transitions, for which there are two separate approaches. The sample may either be irradiated and detected at the multiple quantum frequency (called overtone spectroscopy) or the MQ transition can be excited and a 2D sequence used to detect the effect on the observable magnetisation. 

A composite-pulse sequence to cancel the spurious signals has been described. " The main advantage of this sequence over the Hahn echo sequence has been shown to be 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. The effects of the first-order quadrupole interaction during the pulses have been considered (spin I = 3/2 nuclei). It has been shown that the size of the sample must be much smaller than that of the r.f. coil in order for the r.f. magnetic field to become homogeneous for the sample. 

Fig. 3.5 The effect of a first-order quadrupole perturbation on a magnetic hyper-fine spectrum for a f transition. Lines 1,2 and 5,6 have equal separations only when there is no quadrupole effect acting, or when cos 0 =- 1 / 3.

In practical applications it may happen that the magnetic and quadrupole hyperfine interactions occur simultaneously and the spectra are superimposed on one another. Such a case for iron is presented in Fig. 11 where the effect of first-order quadrupole perturbation on a magnetic hyperfine spectrum is shown. It is evident that the detailed interpretation of this Mossbauer spectrum is quite complex. 

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). 

First-order static quadrupole effects give for the chlorine and bromine nuclei rise to spectra analogous to that shown in Fig. 7.4. First-order quadrupole splittings have been determined for Cl in the hexagonal mesophase of the dodecyltrimethylammonium chloride-water system [1Z6 405] and for Br in the hexagonal mesophase of the hexadecyltrimethyl-ammonium bromide-water system [Z21], (The hexagonal mesophase is built... 

It has recently been demonstrated that the analysis of MAS sidebands patterns can be used to study molecular dynamics in the solid state [85-88]. Indeed, the line narrowing effect of MAS can be partly offset, or completely eliminated, if the 2H quadrupole tensor is reoriented due to motion on a time scale comparable to (first-order quadrupolar broadening, such motion-induced effects should be less evident in the DQMAS spectrum, as has indeed been observed by Wimperis and colleagues in several deuterated solids [87, 88]. For example, the simulation of the SQ spectrum of tetrathionate dihydrate-cfi yielded the same reorientational rate constant as the previously described quadrupolar echo approach (Fig. 6). 

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