Interface chevron

Theories of the oxidation of tantalum in the presence of suboxide have been developed by Stringer. By means of single-crystal studies he has been able to show that a rate anisotropy stems from the orientation of the suboxide which is precipitated in the form of thin plates. Their influence on the oxidation rate is least when they lie parallel to the metal interface, since the stresses set up by their oxidation to the pentoxide are most easily accommodated. By contrast, when the plates are at 45° to the surface, complex stresses are established which create characteristic chevron markings and cracks in the oxide. The cracks in this case follow lines of pores generated by oxidation of the plates. This behaviour is also found with niobium, but surprisingly, these pores are not formed when Ta-Nb alloys are oxidised, and the rate anisotropy disappears. However, the rate remains linear it seems that this is another case in which molecular oxygen travels by sub-microscopic routes. 

It is interesting to point out here that with all of the theoretical speculation in the literature about polar order (both ferroelectric and antiferroelectric) in bilayer chevron smectics, and about reflection symmetry breaking by formation of a helical structure in a smectic with anticlinic layer interfaces, the first actual LC structure proven to exhibit spontaneous reflection symmetry breaking, the SmCP structure, was never, to our knowledge, suggested prior to its discovery. 

It is assumed that 0 at the bottom surface is tt/2 and 0 at the top surface is —7t/2 for a high pretilt angle C2U. The azimuthal angle at the chevron interface is expressed as... 

In Fig. 5.1.25, the director twist angle 4> is plotted as a function of the cell thickness direction Y at various surface pretilt angles, where represents the director twist angle at the chevron interface and is expressed as... 

Another reason for this is the complexity of molecular orientation in FLC devices. FLC devices have layered structures, three surfaces (that is, two substrate surfaces and a chevron interface), tilt angles, spontaneous polarization, etc. These features lead to more complex phenomena such as layer leaning, twisted orientations, low shock stability, layer rotation, etc. 

The textures described above belong to the same phase and are not separated by sharp interfaces. The frontiers are fuzzy and are often the sites of hybrid, but interesting, textures. Among these, at the limit between polygons and fans, one finds occasional chevrons, the organization of which is shown in Fig. 35 [93]. 

After the discovery of the chevron structures, a number of complexities in observed optical and electrooptical phenomena could be interpreted in these new terms. For a more thorough discussion in this matter, we refer to references [166-168]. Our emphasis will be on the important consequences for the physics due to the presence of chevrons, but even this requires dealing with at least some structural details. First of all, the chevron fold forces the director n to be in the interface, i.e., to be parallel to the plane of the sample in this region, regardless of how n (r) may vary through the rest of the sample and independent of the surface conditions. Although the director n is continuous at the chevron interface, the local polarization field P cannot be, as shown in Fig. 96. It makes a jump in direction at the interface, nevertheless, in such a way that... 

Figure 96. (a) At the chevron interface the local polarization P is discontinuous, making a jump in direction. (b) When switching from the down to the up state, P rotates everywhere anticlockwise above and clockwise below the chevron interface (time axis to the right). The director is locked in the chevron plane and can move between n and nj. 

So far we have described the switching concentrating on the chevron interface, completely disregarding what could happen at the two bounding (electrode) surfaces. In fact, if the anchoring condition on the surfaces is very strong, switching between up and down states of polarization will only... 

It should be pointed out that the uniqueness of director rotation during the switching process is not a feature related to the chevron per se, but only to the fact that the chevron creates a certain P-tilt at the chevron interface. If the boundary conditions of the glass surfaces involved a similar P-tilt, this will have the same effect. 

Let us now extract the physical consequences contained in all these relations and start with the last one. As numerical examples we will use the data from Rieker and Clark [168] on the mixture W7-W82, for which the tilt angle 0 saturates at about 21° at low temperature, and the corresponding saturation value for the chevron angle 5 has been measured as 18°. To begin with we see that Eq. (412) sets an upper limit to the layer kink p, because of the requirement of uniqueness of the director n at each chevron interface. Figure 96a illustrates the fact... 

We mentioned that T- P=0 at the chevron interface, which means that even if P changes direction abruptly, Pj, (as well as any other component) is continuous across that surface (Fig. 96). As the boundary conditions at the substrates do not normally correspond to the director condition at the chevron, dPJdx is nonzero between the chevron and the substrates, but is small enough to be ignored. That this is not true when we have polar boundary conditions, is shown in Fig. 107. Let us, for instance, assume that the polarization P prefers to be directed from the boundary into the liquid crystal. Whether we have a chevron or not, we will have a splay state P x) corresponding to a splay-twist state in the director. With a chevron the splay is taking place in the upper or lower half of the cell when this is in its... 

Figure 109. Effective switching angle in a C2 structure as a function of the amplitude Vj of the applied data pulses for the so-called Malvern-3 scheme. The switching pulse amplitude is 30 V. Vd=0 corresponds to the memorized states as latched by the chevron interface. The value of the material is 4.4 nC/cm (after 171).

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