Uniaxial materials

Meridian is the name for the principal axis found in the scattering patterns of uniaxial materials. 

On the other hand, strong SAXS reflections of uniaxial material are, in general, found on the meridian8. So be sure that a SAXS detector covers the meridian whenever fiber material or strained polymers are studied. 

Let us consider for simplicity a sphere composed of a uniaxial material (see Section 9.3). We denote by k ( and kx the wave numbers corresponding to the two principal values of the dielectric function tensor. It is reasonable to assert on physical grounds that anisotropy is only a perturbation if... 

The reason for the intractability of the anisotropic sphere scattering problem is the fundamental mismatch between the symmetry of the optical constants and the shape of the particle. For example, the vector wave equation for a uniaxial material is separable in cylindrical coordinates that is, the solutions to the field equations are cylindrical waves. But the bounding surface of the... 

Scattering problems in which the particle is composed of an anisotropic material are generally intractable. One of the few exceptions to this generalization is a normally illuminated cylinder composed of a uniaxial material, where the cylinder axis coincides with the optic axis. That is, if the constitutive relation connecting D and E is... 

In optics, the optical indicatrix (Figures 9 and 12) is a useful construct that ch aracterizes the birefringence of materials. The indicatrix is a surface that specifies the refractive indices of both the O and E rays traveling in any direction through the material. The indicatrix for a uniaxial material is defined by the equation... 

Figure 11. Schematic representation of the refractive index ellipsoid for a positive uniaxial material at frequency w. (Reprinted with permission from Williams, D. J. Atigew. Chem. Int. Ed. Engl 1984,23,690. Copyright VCH Publishers.)...

In 2-D and 1-D systems even in non-uniaxial materials, the Neel model can still be used since the anisotropic field in the plane where the moments can rotate is small compared with the exchange field in the perpendicular direction. After first considering the particular case of CsNiF3, we will described several 2-D and 1-D Heisenberg fluorides showing spin-flop behavior. 

A more sophisticated retardation plate is a film consisting of the perpendicular arranged combination of two optical uniaxial materials, e g., uniaxially stretched polycarbonate foil with a homeotropic oriented LC siloxane layer [18]. The purpose of such a foil is the improvement of the optical properties of LC displays, especially the viewing angle dependence of the contrast. 

Fig. 16. Combination of two optical uniaxial materials The figure shows the optical indicatrix of an uniaxially stretched plastic foil with horizontal direction of Ue and the indicatrix of a homeotropic oriented LC siloxane with horizontal direction of n (schematically).

IR or UV reflecting cholesterics are colorless in the visible region of the spectrum. Therefore, retardation plates can be realized for STN displays using a long pitch material. Also UV reflecting LC siloxanes are of interest for retardation plates because they exhibit behavior like an optical negative uniaxial material. 

Figure 4. A practical distinction between optically uniaxial and optically biaxial drawn (or extruded) material. For optically uniaxial material, the area fraction exhibiting extinction between crossed circular polars is greatest when the normal to the plane of the thin section is parallel to the draw axis. For optically biaxial material, the greatest area fraction is observed in a section cut so that the angle between its normal and the draw axis is equal to half the optic axial angle of a monodomain.

In most hexagonal ferrites, the easy direction is the unique crystallographic axis, or c-axis. A crystal with only one easy direction is known as a uniaxial material, and its anisotropy energy expression is then ... 

Domain structures can be complex in non-uniaxial materials. In addition to 180° walls, closure domain walls in materials with OH) anisotropy are expected to make angles of 71° and/or 109°, which are the angles between adjacent <111> directions. 

The magnetisation mechanism with the highest coercive force is domain rotation (or coherent rotation), in which all the spins within the sample are collectively reoriented in the field direction. In uniaxial materials. 

El-Diasly, E, Soliman, M. A., Elgendy, A. F. T, and Ashour, A. (2007). Birefringence dispersion in uniaxial material irradiated by gamma rays Cellulose triacetate films, OgtA ureAggl jjJ., 9, 247-252. 

The dependence of mean polarization (P3) on the applied electric field in shown in Fig. 4.38a for uniaxial material (Rochelle Salt) parameters, Dirac-delta distribution [T(7 ) = 8(7 — Rq) of particle sizes, fixed freezing radius Rf(T) at temperature 7 = 0 °C and different average nanoparticle radii Rq. Curves 1 for Rq < Rf correspond to Langevin law, while curves 5-7 for Rq > Rf indicate the hysteresis loop appearance. 

Fig. 4.28. Simulated Mossbauer spectra for microcrystalline samples of the uniaxial material a-FeOOH with a broad particle size distribution. The effect of pronounced collective excitations are seen in (a) where the mean value of 1cbT/XF 0.1S while the effect is much reduced in (h) where the mean value of kBT/KF-0.04.

The Berek (or Ehringhaus) rotary compensator is a disc of uniaxial material cut on the basal plane (normal to the optic axis) and mounted on a ring which can be tilted about a horizontal axis. The retardation increases with tilt. Range is 2000 nm if quartz, over 50 000 nm if calcite. 

It is well known that nematic liquid crystals are nonpolar. However, for a certain asymmetrical shape of the molecules, splay or bend deformations of the director field lead to an electrical polarization [87]. This feature is known as the flexoelectric effect. Theoretically, the influence of an electric field on CLCs for the case where the helical axis is oriented parallel to the plane of the sample was first considered by Goossens [88]. Experimentally, the flexoelectric electro-optic effect in CLCs can be observed in conventional sandwich cells with transparent electrodes when the helix axis of the CLC lies parallel to the glass surfaces [89]. In the absence of an electric field, the CLC behaves as a uniaxial material with its optic axis perpendicular to the director and parallel to the helix axis. When an electric field is applied normal to the pitch axis, the helix distorts, as shown in Figure 6.6. Thus, the optical axis is reoriented and the medium becomes biaxial. The deviation direction... 

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