Orientational Modulated Structures

Whenever a crystal transforms (usually on cooling) to a lower symmetry structure in which a number of orientational variants are possible, transformation twins are an almost invariable consequence if the new phase is nucleated at several different places in the original structure. The formation of Dauphine twins at the jS-to-a transformation in quartz is a classic example, which has already been mentioned briefly in Section 8.6. We now consider the twins and modulated structures associated with the monoclinic-to-triclinic transformation in the K feldspars, KAlSisOg. 

Mifepristone effectively competes with both progesterone and glucocorticoids for binding to their respective receptors. Mifepristone is considered a PR modulator (PRM) due to its context-dependent antagonist/agonist activity. Another antiprogestin is onapristone, which contains a methyl substituent in the 13a rather than 13 orientation. The structures of mifepristone and onapristone are shown in the 11th edition of the parent text. 

The BOg octahedra can not only deform but may also tilt and rotate along their fourfold or twofold axes, giving rise to different superstmctures or modulated structures. Besides, there is a strong dependence of structural symmetry on temperature at lower temperatures, numerous modifications or structural distortions from the ideal perovskite stmcture exist [43—45], and all of these causes lower the symmetry of the structure from cubic to tetragonal, orthorhombic, rhombohedral, or monoclinic. A lowering in symmetry will introduce different orientation variants (twins) and translation variants (antiphase boundaries). Stmctures with a lower symmetry, derived from the cubic structure by tilting and/or deformation of the BOg octahedra, become stable such that one (or several) phase transformation(s) may take place. 

Classification of the domain structures according to the physical origin of their appearance and the nature of the domain patterns. Two main types of modulated structures are discussed [4] orientational domains with pure director rotation without fluid motion, and electrohydrodynamic domains when the collective effect of the periodic director reorientation is observed together with regular vortices of the moving liquid. 

The flexoelectric modulated structure does not arise for homeotropic orientation Oq = tt/2, since its threshold voltage varies as... 

In Chapter 4 we considered the Frederiks transition of the ordinary type, when the director orientation depends only on one coordinate z, measured along the normal to the substrate plane. In some cases, however, the Frederiks transition, leading to modulated structures, seems to be more energetically favorable. 

FIGURE 5.3. Experimental frequency dependence (x) of the threshold voltage for the Prederiks modulated structure appearing from the initial homeotropic director orientation [17] (o) denotes the corresponding threshold for the uniform Frederiks transition C/p = Tr AnKzz/ i. -... 

The physical origin of these phenomena could be explained by faster response times of the modulated structures, as compared with uniform ones. When the equilibrium director distribution is approached, i.e., a relaxation process is over, the transient structures disappear. The emergence and subsequent evolution of the spatial periodicity of the transient structures were considered theoretically in [26] for different domain orientations with respect to the initial homogeneous and twisted director structure. 

Kini [29] considered the electric field-induced static modulated structures of nematic liquid crystals. The electric field E was applied parallel to the sample, and the initial uniform director orientation was tilted with respect to the sample boundaries in the plane normal to E. The formation of modulated structures was shown to be favored when a stabilizing magnetic field H of sufficient strength was applied along the initial director orientation. This type of modulated instability was observed in experiment [30]. 

From the curve CR in Fig. 13.8b we see that at larger e a short wavelength instability comes into play, i.e. a roll system with a different wave-vector, particular in different orientation, starts growing. This may saturate the often-observed rectangular patterns or, for a non-symmetric superposition, lead to the sometimes-observed oblique modulated structures [17, 105]. In order to examine this possibility one would have to test the stability of such patterns by a suitable Galerkin procedure, which was done for normal rolls. However, since there are other possibilities, in particular turbulent states, this approach is not exhaustive and has to be complemented by simulations of the dynamics. 

Field effects on chiral nematics can be interpreted by adding a pitch term to the free energy, so it might be expected that the Fr6edericksz transitions observed for chiral nematics will be similar to those described above for achiral nematics. In reality this is not the case because the helical structure in chiral phases prevents the formation of uniformly aligned films, and so defects and defect-modulated structures are unavoidable in many field-induced orientational changes. The effects of external fields on chiral ne-... 

The steady-state modulated structure is also observed in homogeneously oriented nematic layers at frequencies of the applied... 

Polyimide films are used in a variety of interconnect and packaging applications including passivation layers and stress buffers on integrated circuits and interlayer dielectrics in high density thin film interconnects on multi-chip modules and in flexible printed circuit boards. Performance differences between poly-imides are often discussed solely in terms of differences in chemistry, wiAout reference to the anisotropic nature of these films. Many of the polyimide properties important to the microelectronics industry are influenced not only by the polymer chemistry but also by the orientation and structure. Properties such as the linear coefficient of thermal expansion (CTE), dielectric constant, modulus, strength, elongation, stress and thermal conductivity are affected by molecular orientation. To a lesser extent, these properties as well as properties such as density and volumetric CTE are also influenced by crystdlinity (molecular ordering). 

Let us consider smectic A phases in which the molecules form a regular stack of infinite 2D liquid-like ordered layers with their director perpendicular to the layer the presence of longitudinal dipoles raises the question of their orientation within each layer. Over the past few years five Sa modifications have been defined which involve different overlapping structures of the molecules e.g. A (monolayer), A2 (bilayer), A (interdigitated bilayer) and A and A (antiphase and crenelated phase, in-plane modulated structuring) (Fig. 2.12). In the A phase the dipoles are randomly oriented in each layer, the period is then equal to the molecular length. In the Sa phase, the dipoles are all in the same... 

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