Anisotropy
Anisotropy refers to the property of a material exhibiting different physical characteristics when measured in different directions. In physics, anisotropy can manifest in various forms, such as electrical, thermal, or magnetic anisotropy, and is commonly observed in crystals, liquid crystals, and some composite materials. This directional dependence plays a crucial role in understanding the behavior and properties of these materials.
4 Key excerpts on "Anisotropy"
eBook - ePub- Dennis H. Goldstein(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
...By its very nature, light is asymmetrical. Considering light as a wave, it is a transverse oscillation in which the oscillating quantity, the electric field vector, is oriented in a particular direction in space perpendicular to the propagation direction. Light that crosses the boundary between two materials, isotropic or not, at any angle other than normal to the boundary, will produce an anisotropic result. The Fresnel equations illustrate this, as we saw in Chapter 7. Once light has crossed a boundary separating materials, it experiences the bulk properties of the material through which it is currently traversing, and we are concerned with the effects of those bulk properties on the light. The study of Anisotropy in materials is important to understanding the results of the interaction of light with matter. For example, the principle of operation of many solid state and liquid crystal spatial light modulators is based on polarization modulation. Modulation is accomplished by altering the refractive index of the modulator material, usually with an electric or magnetic field. Crystalline materials are an especially important class of modulator materials because of their use in electro-optics and in ruggedized or space-worthy systems, and also because of the potential for putting optical systems on integrated circuit chips. We will briefly review the electromagnetics necessary to the understanding of anisotropic materials, and show the source and form of the electro-optic tensor. We will discuss crystalline materials and their properties, and introduce the concept of the index ellipsoid. We will show how the application of electric and magnetic fields alters the properties of materials and give examples...
eBook - ePubCrystal Plasticity Finite Element Methods
in Materials Science and Engineering
- Franz Roters, Philip Eisenlohr, Thomas R. Bieler, Dierk Raabe(Authors)
- 2011(Publication Date)
- Wiley-VCH(Publisher)
...1 Introduction to Crystalline Anisotropy and the Crystal Plasticity Finite Element Method Crystalline matter is mechanically anisotropic. This means that the instantaneous and time-dependent deformation of crystalline aggregates depends on the direction of the mechanical loads and geometrical constraints imposed. This phenomenon is due to the Anisotropy of the elastic tensor, Figure 1.1, and to the orientation dependence of the activation of the crystallographic deformation mechanisms (dislocations, twins, martensitic transformations), Figure 1.2. Figure 1.1 Elastic Anisotropy in a polycrystal resulting from superposition of single-crystal Anisotropy. Figure 1.2 Plastic Anisotropy in a single crystal due to distinct crystallography. An essential consequence of this crystalline Anisotropy is that the associated mechanical phenomena such as material strength, shape change, ductility, strain hardening, deformation-induced surface roughening, damage, wear, and abrasion are also orientation-dependent. This is not a trivial statement as it implies that mechanical parameters of crystalline matter are generally tensor-valued quantities. Another major consequence of the single-crystal elastic-plastic Anisotropy is that it adds up to produce also macroscopically directional properties when the orientation distribution (crystallographic texture) of the grains in a polycrystal is not random. Figure 1.3a, b shows such an example of a plain carbon steel sheet with a preferred crystal orientation (here high probability for a crystallographic {111} plane being parallel to the sheet surface) after cup drawing. Plastic Anisotropy leads to the formation of an uneven rim (referred to as ears or earing) and a heterogeneous distribution of material thinning during forming. It must be emphasized in that context that a random texture is not the rule but a rare exception in real materials...
eBook - ePub- Bahaa E. A. Saleh, Malvin Carl Teich(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
...21.1 ; polarization and anisotropic effects were either ignored or introduced only generically. In this section a more complete analysis of the electro-optics of anisotropic media is presented. A brief refresher of some of the important properties of anisotropic media set forth in Sec. 6.3 is provided below. Crystal Optics: A Brief Refresher The optical properties of an anisotropic medium are characterized by a geometric construction called the index ellipsoid, where are elements of the impermeability tensor. If the axes of the ellipsoid correspond to the principal axes of the medium, its dimensions along these axes are the principal refractive indices,, and (Fig. 21.2-1): Figure 21.2-1 The index ellipsoid. The coordinates are the principal axes and are the principal refractive indices. The refractive indices of the normal modes of a wave traveling in the direction are and. The index ellipsoid may be used to determine the polarizations and refractive indices and of the two normal modes of a wave traveling in an arbitrary direction in the anisotropic medium. This is accomplished by drawing a plane perpendicular to the direction of propagation that passes through the center of the ellipsoid. Its intersection with the ellipsoid is an ellipse whose major and minor axes have half-lengths equal to and, as described in Sec. 6.3C. A. Pockels and Kerr Effects When a steady electric field with components is applied to a crystal, the elements of the impermeability tensor are altered. Each of the nine elements becomes a function of,, and, i.e.,, so that the index ellipsoid is modified (Fig. 21.2-2). Once we know the functions, we can determine the index ellipsoid and the optical properties for an arbitrary applied electric field...
eBook - ePubLiquid Crystal Displays
Fundamental Physics and Technology
- Robert H. Chen(Author)
- 2011(Publication Date)
- Wiley(Publisher)
...6 Thermodynamics for Liquid Crystals In the preceding chapters, the polarization of light as an electromagnetic wave resulting from the interaction with crystal structures was described, with the light electric vector in an anisotropic medium analyzed as ordinary and extraordinary waves that travel at different speeds through the crystal, resulting in a phase lag that produces crystal birefringence. The mesophases of liquid crystals then were introduced as having a crystal-like fluid structure characterized by the different degrees of positional and orientational order of the different mesophases. That order created structural anisotropies that would produce different optical effects in light passing through much as crystals do, but owing to the fluid nature of liquid crystals, the birefringence was alterable by applying an electric field. An orientational order parameter was then devised to parameterize that fluid molecular order for use in theoretical studies. Finally, the liquid crystal as a material medium responsive to stresses was characterized by its viscosity and elasticity. A theory of the behavior of liquid crystals at the very least must be able to physically and quantitatively describe the dielectric Anisotropy that produces birefringence and the subsequent controllable interaction with light that forms the basis of liquid crystal displays. The theory also must address the solid, mesophase, and liquid phase transitions that are the essence of the liquid crystals themselves. Models are formulated from constructs based on physics, such as an electric dipole moment field, and results are produced from the models by solving the model equations using mathematical techniques, for example, finding the states of lowest orientational potential energy through minimization of the Helmholtz free energy using the calculus of variations...
