Tilt grain boundary phases

Figure 11.10. Blocks of hexagonally ordered columns are helically stacked to form a tilt grain boundary phase. (Reprinted with permission from J. Physique 47, 1813 1986, edp-sciences [18].)...

Figure 11.11. A single screw disclination in a tilt grain boundary phase.

Sinusoidal undulations of the optical axis, thin cholesteric layers between columnar domains, and nested-arc textures are all strong indications of a helical structure (Figures 11.18 and 11.19). The nested-arc texture shows the structure of the tilt grain boundary phase particularly well. 

Fig. 10.12. Resistance-temperature relationship for a 45°/[001] tilt grain boundary in YBCO. In contrast to the grain characteristics, the grain boundary shows a foot structure, which is due to thermally activated phase slippage [10.17, 10.59].

Figures 3.89 and 3.90 show twist boundaries in SiAlON and in sapphire ceramics, respectively. In Fig. 3.89, both tilt and twist boundaries are indicated. Rows of parallel and more complex dislocations are observed. These dislocation structures are periodic. The Burgers vector determined for the dislocations are of type b = a/3 (110). The experimental results show that these twist boundaries are stable without an amorphous grain-boundary phase. It appears, according to the experimental results, that boundaries with low L misorientation possess relatively low energies and, therefore, are formed favorably during a sintering process.

A helical director field also occurs in the chiral smectic-C phase and those smectic phases where the director is tilted with respect to the layer normal (Figure 1.13(c)). In these cases, the pitch axis is parallel to the layer normal and the director inclined with respect to the pitch axis. Very complicated defect structures can occur in the temperature range between the cholesteric (or isotropic) phase and a smectic phase. The incompatibility between a cholesteric-like helical director field (with the director perpendicular to the pitch axis) and a smectic layer structure (with the layer normal parallel or almost parallel to the director) leads to the appearance of grain boundaries which in turn consist of a regular lattice of screw dislocations. The resulting structures of twist grain boundary phases are currently extensively studied. The state of the art in this topical field is summarized in Chapter 10. 

The situation is simpler if the column lattice is helically distorted perpendicular to the column axes blocks of parallel columns are stacked on top of each other with a finite angle between the columns of adjacent blocks (Figure 11.10) [18], The blocks are thus separated by planar tilt grain boundaries, and parallel linear screw disclinations lie within these boundary planes (Figure 11.11). This structure is perfectly analogous to the twist grain boundary phases of chiral smectic liquid crystals. 

Incorporating a chiral center into a molecule confers chirality to it, and in solution it will display conventional optical activity. However, this does not necessarily mean that liquid crystal phases composed of chiral molecules will display optical activity. If the liquid crystal phase does exhibit optical activity, this is denoted with an asterisk, e.g., N or S. Of the smectic phases only those with molecules tilted within the layers exhibit optical activity. In some rare cases an orthogonal smectic phase can exhibit features not seen in the achiral version, e.g., the 5 phase exhibited by some chiral compounds exhibits a twist grain boundary phase. ... 

The HREM image in Fig. 10.8(d) shows a curved boundary between the grain on the top and the grain on the bottom. The boundary has a 90°/[100] misorientation and, like the 90° [100] tilt boundaries, this boundary is structurally coherent and free of any second phase. A grain boundary along a horizontal plane in this image would be a pure twist grain boundary. 

There are a number of possible structures for TGBC phases. The following structural features need to be considered with respect to each possibility. Firstly, the orientation of the layers can be either tilted with respect to the heli-axis or parallel, secondly, the local spontaneous polarization of the smectic layers can be either parallel or perpendicular to the heli-axis, thirdly, the smectic blocks can have a local helical structure caused by a precession in the tilt of the molecules perpendicular to the layers or alternatively the twist can be expelled to the grain boundaries, and fourthly, the rotation of the blocks about the heli-axis can be either rational (commensurate) or irrational (incommensurate). 

Renn and Lubensy have also proposed the structure of tilted twist grain boundary (TGBC and TGBC ) phases. The existence of the TGBC phase was demonstrated by Nguyen et al. ... 

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