Bloch lines

The dark-held method was hrst applied to study magnetic media in reference 73, where the domain structure was visualized in ferrite-garnet hlms. A signihcant contribuhon to the development of MO dark-held microscopy was made by Thiaville and co-workers [74,75], who ophcally detected the vertical Bloch lines (VBLs) in iron-garnet hlms and described the visualization mechanism. 

Figure 7.11. Observation of the VBLs in the ADFM. (a. b) Two main observation configurations, (c, e) Typicai images of domain walls and Bloch lines (marked by arrows) obtained in observation configurations corresponding to (a) and (b), respec-tiveiy (contrast is inverted), (d) Magnetic structure of the sample. The Bloch lines are indicated by arrows.

Hischii et al. (1977) have prepared by rf sputtering a specimen with a perpendicular uniaxial anisotropy. They observed various kinds of bubble domains under a bias field unichiral bubbles, bubbles with two or four Bloch lines, and also maze domains for thicker films, and white and black bubbles for higher bias field. They discussed the variation of the intensity of the wall image as a function of the angle between the easy axis and the film normal. 

The spin-spin relaxation time, T, defined in the Bloch equations, is simply related to the width Av 2 Lorentzian line at the half-height T. Thus, it is in principle possible to detennine by measuring... 

The relationship between the line shape of an NMR spectrum and the lifetime of chemical processes is provided by the Bloch equations. Let us imagine that there is a chemical equilibrium... 

The size-dependence of the intensity of single shake-up lines is dictated by the squares of the coupling amplitudes between the Ih and 2h-lp manifolds, which by definition (22) scale like bielectron integrals. Upon a development based on Bloch functions ((t>n(k)), a LCAO expansion over atomic primitives (y) and lattice summations over cell indices (p), these, in the limit of a stereoregular polymer chain consisting of a large number (Nq) of cells of length ao, take the form (31) ... 

Figure 2. Calculated CBED rocking curves for Si[ 110], a primary beam energy of 193.35 keV and a crystal thickness of 369nm. The three curves shown in the figure were calculated using 80 Bloch waves (circle+solid line) 20 Bloch waves (star solid line) and 5 Bloch waves (dotted line) and the curves correspond to the line of Figure 1 along A-D.

The phenomenological equations proposed by Felix Bloch in 19462 have had a profound effect on the development of magnetic resonance, both ESR and NMR, on the ways in which the experiments are described (particularly in NMR), and on the analysis of line widths and saturation behavior. Here we will describe the phenomenological model, derive the Bloch equations and solve them for steady-state conditions. We will also show how the Bloch equations can be extended to treat inter- and intramolecular exchange phenomena and give examples of applications. 

Lorentzian line shapes are expected in magnetic resonance spectra whenever the Bloch phenomenological model is applicable, i.e., when the loss of magnetization phase coherence in the xy-plane is a first-order process. As we have seen, a chemical reaction meets this criterion, but so do several other line broadening mechanisms such as averaging of the g- and hyperfine matrix anisotropies through molecular tumbling (rotational diffusion) in solution. 

A very similar application of the modified Bloch equations was based in the work of Adams and Connelly.4 ESR spectra (Figure 5.8) of [Mo P(0 Me)3 2(MeC = CMc)Cp] show the expected triplet (two equivalent 31P nuclei) at 280 K, but only a doublet at 160 K. At intermediate temperatures, the lines broaden. The interpretation is that the alkyne undergoes a pendulum oscillation, which in the extrema diverts spin density from one or the other phosphite. Interestingly, the diamagnetic cation undergoes a similar motion on the NMR time scale, but then the alkyne undergoes a complete rotation. Thus, analysis of the effect leads to a measure of the rate of the oscillation. The... 

A. Meissner, P. Bloch, E. Humpfer, M. Spraul and O. W. Sorensen, Reduction of inhomogeneous line broadening in two-dimensional high-resolution MAS NMR spectra of molecules attached to swelled resins in solid-phase synthesis, J. Am. Chem. Soc., 1997, 119, 1787-1788. 

For biased equilibria, Anet10 5 developed a method of estimating k and the population of the least stable conformer from line-broadening measurements. This method uses the expression developed by Gutowsky and Holm106 from the Bloch equations... 

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