Boundary twisted periodic

MBCB [30] 32 NpT MD 230 K, 10 ps with/without twisted periodic boundaries... 

The use of twisted boundary conditions is commonplace for the solution of the band structure problem for a periodic solid, particularly for metals. In order to calculate properties of an infinite periodic solid, properties must be averaged by integrating over the first Brillouin zone. 

Fig. 12.25. Higher-magnification of the twist boundary. Periodic stacking faults occur near or at the boundary they are distinct from the stacking faults due to misregistry of nucleation. These faults occur every 13 c-axis lattice fringes along, with missing fringes on the c-axis oriented side of the boundary.

Fig. 6. However, these two structures are incompatible with one another and cannot co-exist and the molecules still fill space uniformly without forming defects. The matter is resolved by the formation of a periodic ordering of screw dislocations which enables a quasi-helical structure to co-exist with a layered structure. This is achieved by having small blocks/sheets of molecules, which have a local smectic structure, being rotated with respect to one another by a set of screw dislocations, thereby forming a helical structure [15]. As the macroscopic helix is formed with the aid of screw dislocations, the dislocations themselves must be periodic. It is predicted that rows of screw dislocations in the lattice will form grain boundaries in the phase, see Fig. 7, and hence this structurally frustrated phase, which was theoretically predicted by Renn and Lubensky [15], was called the twist grain boundary (TGB).

Fig. 12.11 Calculated director azimuth (p for the last two periods of the helix adjacent to the top boundary of the cell (see Fig. 12.10). It repeatedly increases from 0° to 360° within each period Pq. Without field the dependence cp (z) is linear. With increasing voltage the director is progressively reoriented but the period remains unchanged. Cell parameters thickness d = 4 pm, pitch Fq = 2.5 pm, Ea = 7.8, twist elastic modulus K22 = 9 x 10 dyn...

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.

The solution of the Euler equation with the splay and twist distortion allowed results in a bifurcation point for the threshold voltage plotted as a function of K22/K11, Fig. 4.44 [243]. The curves shown in the figure were calculated numerically for weak anchoring at both boundaries. It is seen that for K22IK11 < 0.303 the periodic splay-twist distortion is more favorable than a uniform splay. 

A low angle tilt boundary is a special type of grain boundary in which a portion of the grain is tilted as a result of a periodic array of edge dislocations as shown in Figure 8.11. Similarly, a low angle twist boimdary can be formed by an ordered array of screw dislocations. 

Sugimura A, Luckhurst GR, On-Yang Z (1995) Director deformation of a twisted chiral nematic liquid crystal cell with weak anchraing boundaries. Phys Rev E 52(l) 681-689 Torrent MC, Sagues F, Arias F, San Miguel M (1988) Freedericksz transition in a periodic magnetic field. Phys Rev A 38(5) 2641-2649... 

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