Quadrupolar magnetic field

NMR spectroscopy is a powerful technique to study molecular structure, order, and dynamics. Because of the anisotropy of the interactions of nuclear spins with each other and with their environment via dipolar, chemical shift, and quadrupolar interactions, the NMR frequencies depend on the orientation of a given molecular unit relative to the external magnetic field. NMR spectroscopy is thus quite valuable to characterize partially oriented systems. Solid-state NMR... 

Since the second-order quadrupolar broadening is inversely proportional to the Larmor frequency [(35) and (36)], one obvious means for improving the resolution is to employ the highest available magnetic field strength [94], The use of several spectrometers operated at different magnetic field strengths can be helpful in... 

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]. 

Vosegaard and Massiot [144] showed that it is possible to create a high-resolution 2D spectrum correlating the chemical shifts with the second-order quadrupolar lineshapes from several spectra recorded at different magnetic field strengths using a projection-reconstruction method called chemical shift-quadrupolar projection-reconstruction of one-dimensional spectra (CQ-PRODI). 

Here, the two Euler angles ak and flk define the orientation of the quadrupolar tensor with respect to the static magnetic field ... 

The complications that arise in solid state NMR spectra as compared to NMR spectra in solution are the consequence of the fixed orientation of the sample relative to the external magnetic field Bq. Mainly three interactions are responsible for the enormous linebroadening that can be observed for solid powder samples. These are (1) the shielding or chemical shift, including the chemical shift or shielding anisotropy CSA or Acr Hqsa) (2) homo- and/or heteronuclear dipole-dipole coupling (ffoo) and (3) in addition, for nuclei with spin >1/2, the quadrupolar interactions (Hq). 

Figure 4 Schematic representation of the populations of the nuclear spin energy levels of a quadrupolar nucleus with spin 5/2 (such as Mg) under a strong magnetic field and a perturbative quadrupole coupling showing (A) populations at thermal equilibrium, (B) populations after complete saturation of the satellite transitions, and (C) populations after complete inversion of the satellite transitions, following the order first, inversion of STl and ST4 and then inversion of ST2 and ST3. The numbers at left of each level (named pj in the text) are proportional to the population of that level, with —hVl/ 2k T= 0. ...

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