Nuclear magnetic resonance quadrupole interaction

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... 

As we shall see, each of these two terms, one for each nucleus, describes a second-rank scalar interaction between the electric field gradient at each nucleus and the nuclear quadrupole moment. De Santis, Lurio, Miller and Freund [44] included two other terms which involve the nuclear spins. One is the direct dipolar coupling of the 14N nuclear magnetic moments, an interaction which we discussed earlier in connection with the magnetic resonance spectrum of D2 its matrix elements were given in equation (8.33). The other is the nuclear spin-rotation interaction, also discussed in connection with H2 and its deuterium isotopes. It is represented by the term... 

The nuclear quadrupole interaction often produces measurable effects in electronic, rotational, atomic and molecular beam resonance, nuclear magnetic resonance, and MOssbauer spectra. In many cases it can be directly studied by nuclear quadrupole resonance (NQR). The magnitude of interaction is expressed by the nuclear quadrupole coupling constant, e2qQ/hy which is the product of Eq. (1) and (3) expressed as a frequency. 

Nuclear magnetic resonance (NMR) is perhaps the simplest technique for obtaining deuterium quadrupole coupling constants in solids or in liquid crystalline solutions. In ordinary NMR experiments with a magnetic field Hq > 104 gauss, the nuclear quadrupole interaction [Eq. (6)1 for deuterium is much smaller than the Zeeman interaction and can be treated as a perturbation to the Hamiltonian... 

W. H. Jones, Jr., T. P. Graham, and R G. Barnes, "Nuclear magnetic resonance line shapes resulting from the combined effects of nuclear quadrupole and anisotropic shift interactions," Phys. Rev. 132, 1898-1909, (1963). 

It can now be predicted with confidence that machine calculations will lead gradually toward a really fundamental quantitative understanding of the rules of valence and the exceptions to these toward a real understanding of the dimensions and detailed structures, force constants, dipole moments, ionization potentitils, and other properties of stable molecules and equally unstable radicals, anions, and cations, and chemical reaction intermediates toward a basic understanding of activated states in chemical reactions, and of triplet and other excited states which are important in combustion and explosion processes and in photochemistry and in radiation chemistry and also of intermolecular forces further, of the structure and stability of metals and other solids of those parts of molecular wave functions which are important in nuclear magnetic resonance, nuclear quadrupole coupling, and other interaction involving electrons and nuclei and of very many other aspects of the structure of matter which are now understood only qualitatively or semi-empirically. 

Very low-temperature calorimetiy measurements of Lounasmaa and Roach (1962) (0.37-4.2 K), Van Kempen et al. (1964) (0.05-0.89 K), Anderson et al. (1968), and Krusius et al. (1969) (0.03-0.5 K) as well as nuclear magnetic resonance (NMR) measurements by Kobayashi et al. (1967) and Sano and Itoh (1972) were used to derive the nuclear contribution to the heat capacity by determining the magnetic interaction parameter a and the quadrupole coupling constant P. Following the procedure described in Section 2.4, the selected values given in Part 13.12 were used to calculate the variation of the nuclear heat capacity with temperature. 

Nuclear magnetic resonance (NMR), in particular, deuterium NMR, has proven to be a valuable technique for determining the nature of molecular organization in liquid crystals. The utility of the NMR technique derives from the fact that the relevant NMR interactions are entirely intramolecular, i.e. the dominant interaction is that between the nuclear quadrupole moment of the deuteron and the local electric-field gradient (EFG) at the deuterium nucleus. The EFG tensor is a traceless, axially symmetric, second-rank tensor with its principal component along the C—D bond. In a nematic fluid rapid anisotropic reorientation incompletely averages the quadrupolar interaction tensor q, resulting in a nonzero projection similar to the result in Eq. (5.6) ... 

Park, K.D., Guo, K., Adebodun, F., Chiu, M.L., Sligar, S.G., et al. Distal and proximal ligand interactions in heme proteins correlations between C-O and Fe-C vibrational liequencies, oxygen-17 and carbon-13 nuclear magnetic resonance chemical shifts, and oxygen-17 nuclear quadrupole coupling constants in C O- and CO-labeled species. Biochemistry 30, 2333-2347 (1991)... 

A large variety of hyperfine spectroscopy methods exist that allow the detection of hyperfine and nuclear quadrupole interactions electron spin-echo envelope modulation (ESEEM), ENDOR, and ELDOR-detected NMR (electron-electron doubleresonance detected nuclear magnetic resonance) [13]. Although there are cases in which ESEEM and ENDOR perform equally well, ESEEM-like methods tend to be... 

In Equation (6) ge is the electronic g tensor, yn is the nuclear g factor (dimensionless), fln is the nuclear magneton in erg/G (or J/T), In is the nuclear spin angular momentum operator, An is the electron-nuclear hyperfine tensor in Hz, and Qn (non-zero for fn > 1) is the quadrupole interaction tensor in Hz. The first two terms in the Hamiltonian are the electron and nuclear Zeeman interactions, respectively the third term is the electron-nuclear hyperfine interaction and the last term is the nuclear quadrupole interaction. For the usual systems with an odd number of unpaired electrons, the transition moment is finite only for a magnetic dipole moment operator oriented perpendicular to the static magnetic field direction. In an ESR resonator in which the sample is placed, the microwave magnetic field must be therefore perpendicular to the external static magnetic field. The selection rules for the electron spin transitions are given in Equation (7)... 

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