Anisotropy origin

We noted in the preceding section that the polarizability of an ellipsoid is anisotropic the dipole moment induced by an applied uniform field is not, in general, parallel to that field. This anisotropy originates in the shape anisotropy of the ellipsoid. However, ellipsoids are not the only particles with an anisotropic polarizability in fact, all the expressions above for cross sections are valid regardless of the origin of the anisotropy provided that there exists a coordinate system in which the polarizability tensor is diagonal. 

We have discussed intrinsically anisotropic particles—ones with anisotropy originating in their optical constants rather than their shape—in previous chapters. In Section 5.6 we gave the solution to the problem of scattering by an anisotropic sphere in the Rayleigh approximation. From the results of that section and Section 5.5 it follows that the average cross section (C) (scattering or absorption) of a collection of randomly oriented, sufficiently small, anisotropic spheres is... 

Where does such a strong scattering anisotropy originate from It is evident that the optical anisotropy of nematic hquid crystals plays the crucial role. In fact, the scattering is caused by fluctuations of the director n, i.e. the local orientation of the order parameter tensor. The local changes in orientation of n imply local changes in orientation of the optical indicatrix. 

V.I. Goldanskii, E.F. Makarov, I.P. Suzdalev, LA. Vinogradov, Quantitative test of the vibrational anisotropy origin of the asymmetry of quadmpole Mossbauer doublets. Phys. Rev. Lett. 20, 137-140 (1968)... 

Tensorial character is relevant for rocks with an anisotropy (originated by lamination, preferred direction of fractures, grain axis or mineral orientation, etc.). The terms isotropy and anisotropy refer to the directional dependence of considered (tensorial) properties. Isotropic expresses that a vectorial property has at any point the same magnitude for all directions if the magnitude shows a directional dependence, then the material is anisotropic. 

Coercivity of Thin-Film Media. The coercivity ia a magnetic material is an important parameter for appHcations but it is difficult to understand its physical background. It can be varied from nearly zero to more than 2000 kA/m ia a variety of materials. For thin-film recording media, values of more than 250 kA / m have been reported. First of all the coercivity is an extrinsic parameter and is strongly iafluenced by the microstmctural properties of the layer such as crystal size and shape, composition, and texture. These properties are directly related to the preparation conditions. Material choice and chemical inborn ogeneties are responsible for the Af of a material and this is also an influencing parameter of the final In crystalline material, the crystalline anisotropy field plays an important role. It is difficult to discriminate between all these parameters and to understand the coercivity origin ia the different thin-film materials ia detail. 

Some materials that are atomically ordered also develop a sHp-iaduced anisotropy as a result of plastic deformation. The origin is thought to be identical to that of thermomagnetic anisotropy, ie, short-range directional order, except that the order is brought on by deformation rather than by heat treatment ia a field (3,4). 

To find the equilibrium form of a crystal, the following Wullf construction [20] can be used, which will be explained here, for simplicity, in two dimensions. Set the centre of the crystal at the origin of a polar coordinate system r,6. The radius r is assumed proportional to the surface tension 7( ), where 6 defines the angle between the coordinate system of the crystal lattice and the normal direction of a point at the surface. The anisotropy here is given through the angular dependence. A cubic crystal, for example, shows in a two-dimensional cut a clover-leaf shape for 7( ). Now draw everywhere on this graph the normals to the radius vector r = The... 

Gelbart (1974) has reviewed a number of theories of the origins of the depolarized spectrum. One of the simplest models is the isolated binary collision (IBC) model of McTague and Bimbaum (1968). All effects due to the interaction of three or more particles are ignored, and the scattering is due only to diatomic collision processes. In the case that the interacting particles A and B are atoms or highly symmetrical molecules then there are only two unique components of the pair polarizability tensor, and attention focuses on the anisotropy and the incremental mean pair polarizability... 

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