Quadrupolar effects

The quadrupolar effects of order higher than two (7) are usually assumed to be negligible, especially at high magnetic fields. However, once the first- and second-order effects are removed, the measurement of third-order contributions becomes realistic. It can be easily shown that, similar to the first-order case, the CT and all symmetric MQ transitions (q = 0) are free of the third-order contribution, which thus can be safely ignored in DAS, DOR, and MQMAS experiments [161,162]. This is not the case for transitions between non-symmetric spin states, such as the STs. Indeed, numerical simulations of the third-order effect have explained the spectral features that have been observed in 27A1 STMAS spectra of andalusite mineral [161]. 

The usefulness of quadrupolar effects on the nuclear magnetic resonance c I 7 yi nuclei in the defect solid state arises from the fact that point defects, dislocations, etc., give rise to electric field gradients, which in cubic ciystals produce a large effect on the nuclear resonance line. In noncubic crystals defects of course produce an effect, but it may be masked by the already present quadrupole interaction. Considerable experimental data have been obtained by Reif (96,97) on the NMR of nuclei in doped, cubic, polycrystalline solids. The effect of defect-producing impurities is quite... 

The magnitude of the chemical shift anisotropy depends on the bonding situation and the nucleus gyromagnetic ratio. Since the bonds formed by lithium in organolithium compounds or other lithiated systems are mainly ionic, the anisotropy of the lithium chemical shift is generally small. It is more pronounced for Li than for Li. Li spectra are dominated by the quadrupolar effect and the CSA contribution to the Li lineshape is often negligible. Exceptions are compounds with poly-hapto bound lithium, such as... 

For 1 1 electrolytes the simplest choice for n is unity (as in Figure lb) and is shown to be appropriate by comparison with experiment. Thus we have n = 1, X = 1 (cos 0i = 1, 0i = 0), and can take any value, since m = 0 and does not depend on (p. Variants of Equation 39 are easily obtained for other than uni-univalent salts by choosing a structure for the reduced ionic atmosphere in the light of symmetry and chemical intuition. This is illustrated with reference to the divalent ion of a 1 2 electrolyte, where it is reasonable as a first approximation to suppose that the ionic cloud will have two diametrically opposed maxima, each at a distance 1 /k from the reference ion. It is easy to see that dipoles induced on the central ion by these two charge centers will cancel, as well all higher terms of odd Z, but that quadrupolar effects (Z = 2) and other terms of even Z will not. For the structure factor the coordinates of the two maxima in dq are 0i = 0 and 02 = 7r, while the atmosphere is still symmetrical with respect to the angular coordinate [Pg.211]

The following strategy therefore emerges for the study of quadrupolar nuclei observe the central transition of nuclei with noninteger spin, use MAS (to remove dipolar coupling, chemical shift anisotropy, and first-order quadrupolar effects), and work at high fields (to minimize second-order effects). 

Fig. 3. Energy level diagram for a spin f nucleus showing the effect of the first-order quadrupolar interaction on the Zeeman energy levels. Frequency of the central transition (shown in bold lines) is independent of the quadrupolar interaction to first order, but is subject to second-order quadrupolar effects (see text).

Because of the 100% isotopoic abundance of 27A1 and its very short spin-lattice relaxation time, even traces of aluminum are often detectable by MAS NMR. For example, Thomas et al. (156) were able to show that aluminum present as an impurity in soda glass is four-coordinated. However, quantitative determination of Al concentration in the sample is only possible when the quadrupolar effects are not so large as to affect significantly the apparent intensity of the 27A1 signal. 

H-ZSM-5 quadrupolar effects are always dominant. The same applies to both the hydrated and the dehydrated samples of zeolite H-Y (not shown). 

The authors of ref. 15 explain the observed strong quadrupolar effects by a distortion of A104 tetrahedra on dehydration, possibly caused by the closeness of the bare cation. They justify the postulate of a distribution of 27A1 chemical shifts with an observation of several aluminous species with distinct 7j values and chemical shifts. More work is needed to elucidate these important effects fully. 

Ref. 13 contains a more complete discussion of static quadrupolar effects for amphiphilic mesophases. That work also includes a treatment of counterion quadrupole relaxation for liquid crystalline systems a brief outline of this discussion is given in the next section. 

Most spectroscopic techniques (e.g. infrared and Raman spectroscopy) provide a snapshot view of the structure of a liquid because the timescale of the techniques is of the order of lattice vibration. However, NMR can probe much lower frequency motions, motions which are important in the glass transition and the viscosity of a silicate liquid. In addition, the timescale of the NMR experiment may be varied (by changing the magnetic field, or the type of experiment, T or T fJ, or observing quadrupolar effects) from a few hertz to several hundred megahertz. 

By using 15N-substituted ammine complexes, the broadening of 195Pt signals caused by the quadrupolar effects of 14N can be avoided. Both 15N-... 

From these results, it is evident that QCPMG experiments may be performed when the second-order quadrupolar effect is adequately small. In the present calculations, the CQ-limit for the QCPMG spectra is around 750 kHz at 14.1 T but this limit is of course higher at higher magnetic field strengths. 

Except for some quadrupolar effects, all the interactions mentioned are small compared with the Zeeman interaction between the nuclear spin and the applied magnetic field, which was discussed in detail in Chapter 2. Under these circumstances, the interaction may be treated as a perturbation, and the first-order modifications to energy levels then arise only from terms in the Hamiltonian that commute with the Zeeman Hamiltonian. This portion of the interaction Hamiltonian is often called the secular part of the Hamiltonian, and the Hamiltonian is said to be truncated when nonsecular terms are dropped. This secular approximation often simplifies calculations and is an excellent approximation except for large quadrupolar interactions, where second-order terms become important. 

The cliemical shifts reported here are only experimental values the correction of induced quadrupolar effect has not been taken into account. 

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