Walls between domains

In five nematic liquids investigated, the domain structure is similar to that shown in Figure 1. This structure persists indefinitely as long as the field is applied. The behavior of nematic p-methoxycinnamic acid (3) is different and illustrates some interesting features of the interface or wall between domains. 

When the dipoles in a crystal are randomly oriented there is no net P. When a field is applied, the dipoles begin to line up with the electric field. The total dipole moment changes either by the movement of the walls between domains or by the nucleation of new domains. Eventually the field aligns all of the dipoles and Ps is obtained. When all the dipoles are aligned in the same direction the material is poled. ... 

Figure 3-2. Soliion a domain wall between the two different dimerized phases shown in Figure 3-1. The dot indicates the unpaired electron which is localized near the domain wall in case it is neutral.

In dielectric materials there can be both permanent and induced polarization domains. The walls between these domains may also act as barriers to dislocation motion. They tend to have larger energies than magnetic domain walls so they may have more effect on hardness (McColm, 1990). 

The starting system is achiral (plates at 90° with isotropic fluid between), but leads to the formation of a chiral TN structure when the fluid becomes nematic. In this case, enantiomeric domains must be formed with equal likelihood and this is precisely what happens. The size of these domains is determined by the geometry and physics of the system, but they are macroscopic. Though the output polarization is identical for a pair of heterochiral domains, domain walls between them can be easily observed by polarized light microscopy. This system represents a type of spontaneous reflection symmetry breaking, leading to formation of a conglomerate of chiral domains. 

Since the walls between heterochiral domains are unacceptable defects in an LC display, enantiomericafly enriched dopants are added to the LC to favor one sign of twist over the other in actual devices, providing a monodomain in the TN cell. It should be noted, however, that the chirality of the structure derives from the interaction of the LC director with the surfaces the molecular chirality serving simply to break the degeneracy between mirror image domains to favor one over the other. 

Figure 8.34 Left Gold focal conics of MHOBOW coexisting with accordion domains in 4-p.m SSFLC cell. Cell has not seen electric field. Right Same area after brief application of field above threshold for causing textural change of focal conics from gold SmA-like to bistable blue SmC -like. Transition from gold to bistable blue is still incomplete in this photomicrograph clear domain walls between two textures are easily seen.

Pores may be present as structural features (e. g. between domains) or as a result of aggregation of particles. They may also be the result of partial dehydroxylation (oxide hydroxides) or dissolution. Although the shapes of pores can be quite variable, there are some definite, basic forms. The commonest of these are 1) slit shaped, the walls of which may or may not be parallel 2) ink bottle which are closed upon all sides but one from which a narrow neck opens and 3) cylindrical. Upon partial dissolution, pores bounded by well-defined crystal planes (e. g. 102 in goethite) develop (Chap. 12). 

Fig. 9 (a) Sketch of the structure of the hexagonal columnar phase of DNA, showing parallel molecules hexagonally packed in the plane perpendicular to their axis, a and 4 are the lattice parameters, (b) COL developable domains observed in polarized microscopy, w indicates defect walls between differently oriented domains, while 7t stands for point defect around which DNA molecules continuously bend (size bar is 10 pm). Adapted with permission from [27]... 

Note than typical domain-wall widths are much smaller than the domains themselves. When the size of a magnetic particle is smaller than the domain-wall width Sa, as encountered for example in small soft-magnetic nanodots, then the distinction between domains and domain walls blurrs, and the determination of the micromagnetic spin structure requires additional considerations [102], One example is curling-type flux-closure or vortex states. 

Figure 49 Possible arrangements of alkali-metal ions in the p-alumina structure, (a) and (b) show two alternative cation distributions, (c) and (d) show possible domain walls between these alternatives. Alkali-metal atoms are represented by filled circles and oxygen atoms by open circles...

The systems exhibiting the 1x2 structure are then also expected to show commensurate and incommensurate phases, quite similar to those observed for the ANNNI model [75]. In the lattice gas systems the presence of incommensurate phases is restricted to the situations in which the substrate lattice can be divided into a certain number of equivalent interpenetrating sublattices and the ordered state corresponds to the preferential occupation of one of those sublattices. Incommensurability is manifested by the presence of regions with different occupied sublattices and the formation of walls between the domains of commensurate phase. In the case of the discussed here systems exhibiting 1x2 ordered phase we have two sublattices, since particles occupy alternate rows. Figure 6 shows examples of equilibrium configurations demonstrating the formation of incommensurate structure when the ordered 1x2 phase is heated up. 

Figure 15.7 Relationship between domains and hysteresis, a) Typical hysteresis loop for a ferromagnet. h) For a virgin sample, // = 0 and M = 0 due to closure domains, (c) With increasing H, the shaded domain which was favorably oriented to H grows by the irreversible movement of domain walls up to point X. (d) Beyond point X, magnetization occurs only by the rotation of the moments, (e) Upon removal of the field, the irreversibility of the domain wall movement results in a remnant magnetization i.e., the solid is now a pennanent magnet.

Fig. 2a shows that some calculated positions of reflections from symmetry allowed domains do not coincide with observed reflections of domain TR4. Therefore, we proceed to calculate the orientation matrix of domain TR3 (previously determined with respects to TRI), and taking this domain as a reference . Positions of reflections are given in Fig. 2b which shows that the domain TR3 is connected with domain TRI via (121), and it is also coimected with the domain TR4 via the plane (110). However, there is no stress-free wall between the domains TR3 and TR2. Based on the identification of domain walls between 4 observed orientation states we can now assume that the domain pattern of LSGMO crystal has a chevron-like configuration in the trigonal phase (Fig. 3). 

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