Anisotropic axis

This critical field called coercivity ff. or switching field Ff., is also equal to FF. If a field is applied in between 0 and 90° the coercivity varies from maximum to zero. In the case of this special example the applied field Ha = Hs = Hc = Hk. Based on the classical theory, Stoner-Wohlfarth (33) considered the rotation unison for noninteracted, randomly oriented, elongated particles. The anisotropic axis can be due to the shape anisotropy (depending on the size and shape of the particle) or to the crystalline anisotropy. In the prolate ellipsoids b is the short axis and a the longest axis. The demagnetizing factors are IV (in the easy direction) and The demagnetizing fields can then be calculated by Hda = — Na Ms, and Hdb = — Nb Ms. The shape anisotropy field is Hd = (Na — Nb)Ms. Then the switching field Hs = Hd = (Na — Nb)Ms. 

Anisotropy in the molecular reorientation of a disaccharide molecule is to be expected when a C—H bond vector of the molecule lies on or near a preferred axis of rotation. This results in a shorter 7, value for carbons whose C—H bonds lie along the anisotropic axis than for those having other orientations. 

A nuclear magnetic relaxation study85 of lactose (17), which is a basic constituent disaccharide unit of all gangliosides, demonstrates that this molecule reorients anisotropically. The favored axis of molecular reorientation appears to lie along the axis of the molecule and therefore is reflected in the shorter T, value at C-4 of the galactose residue. The apparent differences between the relaxation times observed for the C-l resonances of the a (17a) and /3 (17b) isomers may also be reflected in their differing C—H orientations relative to the anisotropic axis. Similar anisotropic motion was observed for methyl /3-lactoside,85 methyl /3-cellobioside,84 and other disaccharide derivatives in solution. 

Figure 6.5. Use of O DAS NMR to determine details of the bridging oxygen resonance in K2Si409 glass. Slices taken parallel to the u>2 anisotropic axis are shown at the right, together with multi-parameter least-squares fits (broken lines) giving the variation of the magnitude and asymmetry of the electric field gradient across the isotropic lineshape (oji). From Faman eta/. (1992) by permission of MacMillan Magazines Ltd.

Since Eq. (29) is orientation independent, all crystallites are refocused at the same time t2e=R I,p)ti, giving rise to an isotropic echo. After a double Fourier transform in and tj.the NMR resonances appear along the anisotropic axis A with direction Vi=R(f,pjv2, where V2 and Vj are the single- and multiple-quantum dimensions frequencies, respectively. The projection of the spectrum onto an axis perpendicular to A yields an isotropic, highly resolved, spectrum. 

As stated above, the second-order broadened ridges appear in the two-dimensional MQMAS spectrum along the anisotropic axis A with direction Vi=R(I,p)v2. Therefore, the projection of the two-dimensional spectrum onto the Vi axis (Ei) does not yield an isotropic spectrum. In order to obtain a two-dimensional spectrum with an isotropic projection a shearing operation has to... 

For pure elemental semiconductors like silicon, the strong electronic absorption at energies above Eg produces a small non-linear dispersion of the refractive index below Eg in silicon, n = 3.57 near Eg at room temperature (RT) and it steadily decreases to 3.42 for wavelengths near 12 pm and stays close to this value down to radio frequency energies (see also [20]). For these elemental crystals, the dielectric constant at energies below Eg is real and equal to n2. The refractive index is isotropic for cubic crystals, but for crystals with one anisotropic axis, like those of the wurtzite type, the refractive index for the electric field component of the radiation parallel to this axis (n//) is slightly different from that for the component perpendicular to this axis (njJ. 

Figure 16 2D 3Q/MAS NMR spectrum of l anite measured by the three-pulse sequence with z-filter. No shearing transformation was applied. Labels "A," "CS," and "QiS" describe anisotropic axis, isotropic chemical shift axis and axis of quadrupole-induced isotropic shift, respectively. Three different AlOg structural units are clearly defined.

Continuum theory generally employs a unit vector field n(x) to describe the alignment of the anisotropic axis in nematic liquid crystals, this essentially ignoring variations in degrees of alignment which appear to be unimportant in many macroscopic effects. This unit vector field is frequently referred to as a director. In addition, following Oseen [1] and Frank [4], it commonly assumes the existence of a stored energy density W such that at any point... 

Given that nematics tend to align uniformly with the anisotropic axis everywhere parallel, Ericksen [18] argues that this must represent a state of minimum energy, and thus assumes that... 

To derive a dynamic theory one can of course extend the above formulation of equilibrium theory employing generalized body and surface forces as in the initial derivation [7,15]. Here, however, we prefer a different approach [46], which, besides providing an alternative, is more direct in that it follows traditional continuum mechanics more closely, although introducing body and surface moments usually excluded, as well as a new kinematic variable to describe alignment of the anisotropic axis. 

Figture 1.2 A schematic representation of a nematic liquid crystal phase where the short bold lines represent the molecules. A unit vector n, called the director, describes the average direction of the molecular alignment along what is commonly called, in uniaxial nematics, the anisotropic axis. 

This alignment displays a certain elasticity and it is known that an initial uniform alignment of a nematic liquid crystal commonly returns after the removal of any disturbing influences. It is therefore assumed that there is a free energy density, also called the free energy integrand, associated with distortions of the anisotropic axis of the form... 

A fast and highly practical photoinduced switching liquid crystal device is provided. In the photoinduced switching liquid crystal device, in-plane switching of an optical anisotropic axis of dichroic nematic liquid crystal is performed at a high speed by light. 

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