Nuclear electric quadrupolar interaction

Serious complications arise, however, if the spins are subject to strong nuclear electric quadrupolar interactions, which tend to modify the echo amplitudes measured. In such cases, it is still possible to extract dipole-dipole coupling information from spin echo decay spectroscopy, if the 71-pulses are applied entirely selectively to the central l/2>o -l/2> transition [6]. If the resonance frequencies between the coupled nuclei are sufficiently similar to allow for spin-exchange via the flip-flop mechanism, Eq. (5) turns into... 

Finally, a few words remain to be said about case (d) (S>l/2,I>l/2). At the present stage of knowledge, this case remains seemingly intractable for quantitative applications outside the non-selective excitation limit Vj/Vq l. The chief problem in applying pulse sequence at Fig. 8b) arises from the nuclear electric quadrupolar interactions affecting the S spins, which interfere with the ability of the 71-pulse trains to refocus the transverse magnetization. In contrast, pulse sequence at Fig. 8a) is able to produce experimental REDOR curves, which are, however, difficult to interpret quantitatively. As a best-effort solution, one may resort to sample-to-sample comparisons on a relative basis and the use of empirical calibration procedures with closely related model compounds [32]. Alternatively, the SEDOR approach, which does not suffer from these restrictions, would be preferable. 

For Zn SSNMR spectroscopy, the observed spectrum is usually dominated by the nuclear electric quadrupolar interaction unless the zinc sits at a site with spherical symmetry (such as tetrahedral, octahedral and cubic sites). This anisotropic interaction originates from the coupfing between the quadrupole moment (eQ) of the nucleus and the electric field gradient (EFG) at the nuclear site. The EFG is described by a second-rank tensor that can be diagonalized in a principal axis system (PAS). In the PAS, the EFG is described by three components, which are ordered in such that I Fxx I kVy I ud they satisfy FxxT TyyT Tzz fi-The quadrupolar interaction is characterized by two parameters one is quadrupolar coupling constant ... 

The nuclear electric quadrupole interaction (QI) results from the coupling between Q and the EFG at the nuclear site. The EFG is a symmetric tensor quantity of zero trace and may be described by five independent parameters. When in its principal axis system (PAS), the off-diagonal matrix elements equal zero, and two parameters can fully describe the diagonal elements. The diagonal elements of a tensor in its PAS (Pn, P22/ and 1 33 in this case) are called the principal components. In practice, the SSNMR spectrum is usually described by the nuclear quadrupolar coupling constant, Cq, and quadrupolar asymmetry parameter, rj which are related to the principal components of the EFG tensor as follows ... 

Mentioned briefly here are some highlights of the most recent developments relating to the quadrupolar halogens. Cederberg has investigated the potential evidence for a non-zero nuclear electric hexadecapole interaction by analysirw... 

The magnetically induced electric quadrupolar interaction was recently observed in several cubic, ferromagnetically ordered intermetallic compounds at the nucleus of the rare-earth S-state ions Gd and Eu, despite the fact that the nuclei are residing on nominally cubic lattice sites e.g., nuclear quadrupole... 

The strength of the quadrupolar interaction is proportional to the quadrupole moment Q of a nucleus and the electric field gradient (EFG) [21-23]. The size of Q depends on the effective shape of the ellipsoid of nuclear charge distribution, and a non-zero value indicates that it is not spherically symmetric (Fig. 1). 

Extraframework cations are needed in anionic zeolites for charge balance, and for several zeolite topologies their locations are well investigated [281, 282]. Different cations have been investigated by solid state NMR in the past with different NMR properties and different project targets. We restrict this section to a tutorial example on sodium cation motion in sodalite and cancrinite structures [283-285], 23Na has a nuclear electric quadrupole moment, and quadrupolar interaction is useful to investigate jump processes, especially when they are well defined. 

The quadrupolar interaction in term (Id) applies to nuclei having nuclear spin I > 1/2, the so-called quadrupolar nuclei. Such nuclei have a nonspherical distribution of positive electric charge that can be expanded in terms of moments, with... 

When the electric field gradient at the nucleus exerted by the electrons is nonzero, the nuclear levels will be split. The eigenvalues of the quadrupolar interaction Hamiltonian are given by... 

Fig. 4. Quadrupolar powder patterns (a) Spin NMR powder pattern showing that the central -)<- ) transition is broadened only by dipolar coupling, chemical shift anisotropy, and the second-order quadrupolar interactions, (b) Spin 1 NMR powder pattern for a nucleus in an axially symmetric electric field gradient (see text). The central doublet corresponds to 6 = 90° in Eq. (10). The other features of low intensity correspond to 6 = 0° and 6 = 180°. (c) Theoretical line shape of the ) - -) transition of a quadrupolar nuclear spin in a powder with fast magic-angle spinning for different values of the asymmetry parameter t (IS) ...

NMR spectra of quadrupolar nuclei are influenced by the interaction of the nuclear electric quadrupole moment with electrostatic field gradients generated at the nuclear sites by asymmetric electron distributions due to chemical bonding. To a first order... 

In case of a deuterated sample (spin 1 case), the spectra are usually dominated by the quadrupolar interaction, that is, the coupling of the nuclear quadrupole moment with the electric field gradient of the C-2H bond. For deuterons in C-2H bonds this can lead to a splitting of about 250 kHz. As in the case of dipolar interaction, a Pake spectrum is obtained for a powder sample. The z-principal axis of the quadrupolar interaction is oriented along the bond axis which makes deuteron NMR particularly useful for studies of segmental orientations and molecular dynamics (reorientation) [1],... 

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