Gyromagnetic effect

It is also interesting to point to the so-called gyromagnetic effect, observed in Fe-Si-B amorphous wires with a particular magnetic-domain structure (Chiriac et al. 2000b). 

Compare this with Eq. (4.329), where Jn = (n x 9/0u) is the operator of infinitesimal rotations over n. We mention that, in our attempts to obtain low-frequency susceptibilities, we have omitted in Eq. (4.332) the term responsible for gyromagnetic effects. 

Table CLXVIII.LandS Splitting Factor from Gyromagnetic Effect...

As an example, a precession of an unbalanced gyroscope (a top) in a uniform gravity field is considered in Appendix 2. Many physical events, such as diamagnetism, precession of magnetic moments (atomic and nuclear) in the external magnetic field and others are based on gyromagnetic effects (refer to Chapter 8 and Appendix 2). 

Figure 8 Effects of spin diffusion. The NOE between two protons (indicated by the solid line) may be altered by the presence of alternative pathways for the magnetization (dashed lines). The size of the NOE can be calculated for a structure from the experimental mixing time, and the complete relaxation matrix, (Ry), which is a function of all mterproton distances d j and functions describing the motion of the protons, y is the gyromagnetic ratio of the proton, ti is the Planck constant, t is the rotational correlation time, and O) is the Larmor frequency of the proton m the magnetic field. The expression for (Rjj) is an approximation assuming an internally rigid molecule.

As stated earlier, since tt]/ = yff2yr and since the gyromagnetic ratio of proton is about fourfold greater than that of carbon, then if C is observed and H is irradiated (expressed as C H ), at the extreme narrowing limit Ti, = 198.8% i.e., the C signal appears with a threefold enhancement of intensity due to the nOe effect. This is a very useful feature. For instance, in noise-decoupled C spectra in which C-H couplings are removed, the C signals appear with enhanced intensities due to nOe effects. 

The effect of deuteration, for the needs of sequence-specific resonance assignments using triple-resonance experiments, was first demonstrated by Bax and co-workers on the 19.7 kDa protein calcineurin B in 1993.56 By replacing the H spin with deuterium, the transverse relaxation time of 13C spin is increased by nearly an order of magnitude due to the 6.5 times smaller gyromagnetic ratio of 2H in comparison to in.52,56 Not surprisingly, deuteration was utilized for the aid of structure determination of several... 

At this point, it is appropriate to present a brief discussion on the origin of the FC operator (d function) in the two-component form (Pauli form) of the molecular relativistic Hamiltonian. Many textbooks adopt the point of view that the FC is a relativistic effect, which must be derived from the Dirac equation [50,51]. In other textbooks or review articles it is stressed that the FC is not a relativistic effect and that it can be derived from classical electrodynamics [52,53] disregarding the origin of the gyromagnetic factor g—2. In some textbooks both derivations are presented [54]. The relativistic derivations suffer from the inherent drawbacks in the Pauli expansion, in particular that the Pauli Hamiltonian can only be used in the context of the first-order perturbation theory. Moreover, the origin of the FC term appears to be different depending on whether one uses the ESC method or FW transformation. 

Here, rodu is the effective distance between the gadolinium electronic spin and the water protons, ys (yi) is the electron (proton) gyromagnetic ratio and Tci is the correlation time, defined by... 

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... 

Yi and Ys - gyromagnetic ratio of spin 1 and spin S nuclear spin, rJS = intemuclear distance, tr= rotational correlation time, x< = reorientation correlation time, xj = angular momentum correlation time, Cs = concentration of spin S, Cq = e2qzzQ/h = quadrupole coupling constant, qzz = the electric field gradient, Q = nuclear electric quadrupole moment in 10 24 cm2, Ceff = effective spin-rotational coupling constant, a = closest distance of appropriate of spin 1 and spin S, D = (DA+DB)/2 = mutual translational self diffusion coefficient of the molecules containing I and S, Ij = moment of inertia of the molecule, Ao = a// - ol-... 

If the primary isotopic effect is neglected, very accurate values may be obtained for the gyromagnetic constant ratio y("7Sn)/y(119Sn) [equation (10)1 from the ratio of the tin resonance frequencies, vTMs(U7Sn)/vTMs(U9Sn)- The ratios of resonance frequencies measured for pairs of tin isotopes with different accuracies by various authors are compared in Table XIV. 

The Overhauser effect has been widely employed as an NMR analysis method in many disciplines ranging from medical to chemical sciences, and broadly refers to the motion-mediated transfer of spin polarization from a species with a higher gyromagnetic ratio (y) to one with a lower gyromagnetic ratio. Because molecular motion is critical for efficient transfer, the Overhauser effect is most commonly observed in liquid samples. The Overhauser effect can be divided into two categories the nuclear Overhauser effect (NOE), where both species are nuclear spins, and Overhauser DNP, where the higher y spin is an unpaired electron. As Overhauser DNP is the focus of this review, some of the terminology and equations are specific to the Overhauser DNP effect. 

The precessional motion can be maintained by a suitable radio frequency field superimposed on the steady field. For example, in Fig. 9.38(b), when a steady field Hz is applied along the z axis and a radiofrequency field //,., is applied in the x-y plane and rotates in the same sense and at the same frequency as the precession, resonance occurs. Gyromagnetic resonance as outlined above is in principle the same as ferrimagnetic resonance referred to earlier (Section 9.3.1), except that in the former case the material is magnetically saturated by a strong applied field. In practice the steady field, which determines the Larmor frequency, is made up of the externally applied field, the demagnetizing field and the anisotropy field, and is termed the effective field He. Figure 9.39 shows the He values at which resonance occurs in some of the important communications and radar frequency bands. 

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