Magnetic isotropy

For an oriented polymer, the magnitude of the observed second moment static magnetic field H0, which can be conveniently defined by the polar and azimuthal angles A, transverse isotropy, to which the following discussion is limited, the observed second moment will depend only on the angle A, there being no preferred orientation in the plane normal to the 3 direction. The treatment follows that originally presented by McBrierty and Ward 9>. 

Use of high-frequency/high-magnetic field techniques to resolve y-an isotropy... 

As a particular example of materials with high spatial symmetry, we consider first an isotropic chiral bulk medium. Such a medium is, for example, an isotropic solution of enantiomerically pure molecules. Such material has arbitrary rotations in three dimensions as symmetry operations. Under rotations, the electric and magnetic quantities transform similarly. As a consequence, the nonvanishing components of y(2),eee, y 2)-een and y,2)jnee are the same. Due to the isotropy of the medium, each tensor has only one independent component of the xyz type ... 

The anisotropic nature of the dipolar, quadrupolar and chemical shift anisotropy interactions requires that the isotropy of molecular orientation relative to the applied magnetic field be broken in order to allow their direct observation in terms of shifts in the frequencies of resonances.20,32,38 40 For high resolution NMR studies this has meant, thus far, that some degree of alignment of the molecule needs to be established. Almost all molecules will align to a small extent due to the anisotropy of their magnetic... 

One of the features of the derivation of the emission rate for y rays that we glossed over is that the angular distribution of the emitted radiation from a single state must be isotropic. The isotropy comes from the fact that the nuclei are oriented at random, and the process sums over all the internal magnetic substates and thus includes all... 

From the point of view of the solvent influenee, there are three features of an electron spin resonance (ESR) speetrum of interest for an organic radical measured in solution the gf-factor of the radical, the isotropie hyperfine splitting (HFS) constant a of any nucleus with nonzero spin in the moleeule, and the widths of the various lines in the spectrum [2, 183-186, 390]. The g -faetor determines the magnetic field at which the unpaired electron of the free radieal will resonate at the fixed frequency of the ESR spectrometer (usually 9.5 GHz). The isotropie HFS constants are related to the distribution of the Ti-electron spin density (also ealled spin population) of r-radicals. Line-width effects are correlated with temperature-dependent dynamic processes such as internal rotations and electron-transfer reaetions. Some reviews on organic radicals in solution are given in reference [390]. 

The classical ideas about the isotropy of electrical properties of spherical-top molecules are usually extrapolated to the magnetic properties. This leads to the conclusion about the isotropy of the magnetic susceptibility in high-symmetry molecules and hence about the disappearance of the orientational contribution to the birefringence in magnetic fields (the Cotton-Mouton effect). In the case of degenerate electronic terms or in the pseudodegeneracy situation, these conclusions are incorrect and have to be reconsidered. 

The traditional definitions of the three principal value components (5i 1, 22, and 533), isotropy 5iso, anisotropy and asymmetry of the chemical shift are equivalent to those of the magnetic shielding. This traditional scheme is indefinite. It leads to a loss of physical and chemical generality which is disadvantageous. Therefore, besides the isotropy two new parameters, span Q and skew k, are often introduced and used instead of the anisotropy A3 and... 

Similarly, the magnetic hyperfine interaction [Eq. (1)] can be written as AI S if the A tensor is isotropic although anisotropy can arise from non-zero orbital and dipole contributions due to admixtures with higher electronic states. Only small departures from isotropy have been found in A for one of iron transport compounds (28) with the spherically symmetric 6S state. 

S.J. Glaser and J.J. Quant, Homonuclear and heteronuclear Hartmann-Hahn transfer in isotropie liquids, in W.S Warren (ed). Advances in Magnetic and Optical Resonance, vol. 19, 1996, pp. 59-252. 

Stark and Zeeman polarization quantum beats are discussed in Section 6.5.3. An external electric or magnetic field destroys the isotropy of space. As a result, the amplitudes for two transition sequences J", M" — J, M = M" 1 —> J ", M" interfere, and the intensity of X or Y (but not Z) polarized fluorescence is modulated at (Fj M =M"+i — Ejim =M"-i)/h. However, it is not necessary to destroy the isotropy of space in order to observe polarization quantum beats. 

Figure 15.6 Schematic showing how formation of domains lowers the energy of the system, (o) No domains, h) Two domains separated by a 180 wall, (c) The 90 domains are called closure domains because they result in the flux lines being completely enclosed within the solid. Closure domains are much more common in cubic crystals than in hexagonal ones because of the isotropy of the former, d) Alignment of individual magnetic dipoles within a 180 wall.

Finally, it may be noted that alloying Fe and Co with precious metals leads to the phases FePt, CoPt, and FePd with an LIq structure, which is an ordered f.c.c. structure with tetragonal distortion (see Fig. 1). These phases have been of importance for applications as permanent magnetic materials, and in particular CoPt, which is used in the only partially ordered state, excels because of isotropy, ductility, easy machinability and resistance to corrosion and high temperatures (Jellinghaus, 1936 Kouvel, 1967 Chin and Wernick,... 

The chaotic behavior reflected in the disordered patterns can be suppressed if the initial isotropy of the homeotropic alignment is broken by applying a magnetic field H parallel to x as shown in Fig. 8 [40]. The azimuthal angle of n is then singled out by the magnetic field, and the patterns become nicely ordered and exhibit similar morphologies as shown in Fig. 4 for the case A (e.g. the disordered pattern of Fig. 9a becomes similar to that in Fig. 4a). 

The C2 coefficient is of special interest since it controls the only octahedral term in the linear Zeeman effect. If this coefficient vanishes, the splitting will be completely isotropic and does not depend on the orientation of the magnetic field in the octahedron. There are three possible isotropies [13]. 

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