NMR of quadrupolar nuclei

For an ensemble of nuclei with spin / 1/2 experiencing no quadrupolar interaction, such as in an isotropic liquid or a crystal with cubic symmetry, the equations describing the time evolution of the density matrix under action of static and RF magnetic fields are a natural extension of the / = 1/2 case. The Hamiltonian contains only the Zeeman and RF terms the effects of RF pulses are described by rotations of the spin operators around the transverse axes in the rotating frame, whereas free evolution corresponds to rotations around the z-axis. 

To be more specific, let us detail the / = 3/2 case. The matrix representations of the nuclear spin operators in the m) basis are given by  

And the deviation density matrix corresponding to an ensemble of identical nuclei at thermal equilibrium is  

The effects of RF pulses are analysed in the rotating frame, precessing around the z-axis with frequency The effective Hamiltonian for a RF pulse applied along the x-direction in this case is given simply by  

On resonance, i.e., when = coi, we have Heg = —hco Ix and the time-evolution is accomplished by the operator U = = gico tph Rx(- p), associated with 

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Earlier sections of this review have already discussed results for quadrupolar nuclei in certain connections for Knight shifts (Sects. 3.4.3 and 3.4.4), for electric-field (Stark) effects upon NQCCs (Sect. 3.1), for measurements of NQCCs in GaN by static NMR and the effects of strain upon NQCCs (Sect. 3.2.1), for obtaining exchange couplings by MAS-NMR (Sect. 3.2.2), and for characterizing polytypes and defects in cubic polytypes by chemical shifts and NQCCs obtained from MAS-NMR (Sect. 3.3.2). This section will give some further examples of information about semiconductors obtained from the NMR of quadrupolar nuclei (see also [18]). 

S. P. Brown and S. Wimperis, Two-dimensional multiple-quantum MAS NMR of quadrupolar nuclei a comparison of methods. /. Magn. Reson., 1997,128,42-61. 

S. E. Ashbrook and S. Wimperis, Fligh-resolution NMR of quadrupolar nuclei in solids the satellite-transition magic angle spinning (STMAS) experiment. Prog. Nucl. Magn. Reson. Spectrosc., 2004, 45,53-108. 

The main progresses in NMR since now more than 10 years concern NMR of quadrupolar nuclei,12 in particular, with the MQMAS method introduced by L. Frydman and J. Harwood in 1995,74 and subsequent... 

It must be stressed that there are fundamental differences in the natures of the different nuclei discussed above. Si and P are spin 1/2 nuclei, and MAS yields particularly simple spectra with complete averaging of the chemical shift tensor components. The average isotropic shift values are field independent and correspond to the solution chemical shifts. AI and O, however, are quadrupolar nuclei with nonintegral spins greater than 1, and their solid-state spectra are often much more complex. Since the quadrupolar interaction depends on local electric field gradients at the nucleus studied, solid-state NMR of quadrupolar nuclei can yield further information about the local environment. More complicated spinning techniques have been introduced to average the anisotropies in the spectra of quadrupolar systems, and these new methods have increased interest in the use of such nuclei as probes of local microstructure. 

Although we will not discuss the solid-state NMR of quadrupolar nuclei, some interesting features of their presence should be mentioned. If the rare spin 14 nuclei are coupled to a quadrupole moment-bearing nucleus, characteristic splittings are observed as a consequence of the fact that the or coupling is not completely averaged... 

R 77 M. Pruski, J.P. Amoureux and C. Fernandez, Progress in High Resolution Solid State NMR of Quadrupolar Nuclei. Applications to Porous Materials and Catalysts , p. 107... 

THEORY OF NMR OF QUADRUPOLAR NUCLEI IN FREE RADICAL SOLUTIONS... 

P.A. Perras, J. Viger-Gravel, K.M.N. Burgess, D.L. Bryce, Signal enhancement in solid-state NMR of quadrupolar nuclei. Solid State Nucl. Magn. Reson. 51 (2013) 1-15. 

T. Polenova, A.S. Lipton, P.D. EUis, Quadrupolar NMR of metal nuchdes in biological materials, in R.E. Wasyhshen, S.E. Ashbrook, S. Wimperis (Eds.), NMR of Quadrupolar Nuclei in Solid Materials, Wiley, Chichester, West Sussex, England, 2012, pp. 439-452, (Chapter 25). 

A. Samoson, E. Kundla, E. Lippmaa, High resolntion MAS-NMR of quadrupolar nuclei in powders, J. Magn. Reson. 49 (1982) 350-357. 

S.P. Brown, S.J. Heyes, S. Wimperis, Two-dimensional MAS multiple-quantum NMR of quadrupolar nuclei, removal of inhomogeneous second-order broadening, J. Magn. Reson. Ser. A 119 (1996) 280-284. 

A. Jerschow, J.W. Logan, A. Pines, High-resolution NMR of quadrupolar nuclei using mixed multiple-quantum coherences, J. Magn. Reson. 149 (2001) 268-270. 

S.E. Ashbrook, S.P. Brown, S. Wimperis, Multiple-quantum cross-polarization in MAS NMR of quadrupolar nuclei, Chem. Phys. Lett. 288 (1998) 509-517. 

In solid-state NMR of quadrupolar nuclei, Hq often represents a perturbation of the Zeeman interaction. It is then natural to choose the quantization axis z along the direction of the external magnetic field and rewrite Equation [8] in a convenient form ... 

Table 6 Chemical shift range in solid materials studied by solid-state NMR of quadrupolar nuclei ...

Dey KK, Prasad S, Ash JT, Deschamps M, Grandinelti PJ (2007) Spectral editing in solid-state MAS NMR of quadrupolar nuclei using selective satellite inversion. J Magn Reson 185 326-330... 

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