Tilt and Twist Boundaries

For tilt boundaries, the value of E can also be calculated if the plane of the boundary is specified in the coordinate systems for both adjoining grains. This method is called the interface-plane scheme (Wolfe and Lutsko, 1989). In a crystal, lattice planes are imaginary sets of planes that intersect the unit cell edges. The tilt and twist boundaries can be defined in terms of the Miller indices for each of the adjoining lattices and the twist angle, , of both plane stacks normal to the boundary plane, as follows ... 

A crystal grown in a solvent medium may have hollow dislocations filled with solvent, since the crystal-solvent interfacial energy may be substantially lower than y. For metals, an unusual effect may occur (37). The chemisorption of certain gases onto some metals leads to an appreciable reduction in the value of y. For example (37), y for silver is decreased from 1140 erg cm 2 in vacuo to 450 erg cm 2 ir. Consequently, a dislocation which terminates flush with the surface in vacuo may, at equilibrium in the presence of an adsorbed gas, develop a pit. By the same token, emergent dislocations in tilt and twist boundaries would develop arrays of pits in the surface. 

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.

Fig. 9.43. Distribution of grain boundaries in polycrystals (adapted from Randle (1997)). The numbers on the vertical axis refer to the coordinates of the boundary plane, while ATGB and TWGB refer to the asymmetric tilt boundaries and twist boundaries, respectively.

Fig. 10.8. HREM images of various 90° grain boundaries in YBCO (a) [100] tilt, a and b interchanged across boundary (b) [100] tilt grain boundary showing two distinct facets, the (013) symmetric boundary with the CuOi planes joining at the interface and the (010)(001) asymmetric grain boundary (c) same as the asymmetric boundary in (b), but viewed at 90°, with one grain in the [001] projection (d) tilt and twist facets combined (continues overleaf).

Fig. 12.7. Schematic of a 90° boundary with mixed tilt and twist character, designated (110)(103) for the planes that meet at the boundary plane. This type of boundary is not observed to occur systematically in these films, but may occur as facets.

Small-angle boundaries are ones across which the difference in orientation is small. They are also called subgrain boundaries. There are two general classes of small-angle houndaries tilt boundaries, which comprise an array of edge dislocations, and twist boundaries, which comprise two or more arrays of screw dislocations. (The reader who is unfamiliar with the line defects known as dislocations will find a clear and readable description in Reference [6].)... 

N. A. Gjostein and F. N. Rhines, Absolute interfacial energies of [001] tilt and twist grain boundaries in copper, Acta Met. 1, 319 (1959). 

Tilt boundaries occur if the axis of rotation between the two grains is located in the boundary (interface). In contrast, if the axis of rotation is perpendicular to the boundary, the boundary is called a twist boundary and consists of a collection of screw dislocations (Fig. 3-6b). An equation similar to Eqn. (3.14) holds for twist (and mixed) boundaries. Since dislocation theory is well understood, it is possible to quantitatively treat small-angle grain boundaries [J.P. Hirth, J. Lothe (1982)]. 

Grain boundaries can also be classified as tilt boundaries, twist boundaries, and mixed boundaries. A tilt boundary s plane is parallel to the rotation axis used to define its crystal misorientation, as in Fig. B.4c. The crystals adjoining the boundary are related by a simple tilt around this axis. A twist boundary, as in Fig. B.56, is a boundary whose plane is perpendicular to the rotation axis. The two crystals adjoining the boundary are then related by a simple twist around this axis. All other types of boundaries are considered to be mixed. 

In addition to the tilt boundaries shown in Fig. 12.2, 90° [100] or [010] twist bormdaries, shown schematically in Fig. 12.3(a), also occur in a-axis and (103) films. A schematic of the (103) grain structure, showing the formation of twist boundaries along the [010] direction, as well as the tilt boundaries along the [301] direction is shown in Fig. 12.5. In a plan-view (103) film the twist boundaries are parallel to the viewing direction but are not readily visible because the projected orientation of both grains is the same. 

Facetting of the twist boundary must also be considered. In this case, BPF and symmetrical tilt facets do not intersect the macroscopic current path. Since we already have indication from the (103) films that the twist boundary does not degrade current, we do not expect that indirect paths crossing these boundaries will be preferred. However, when the nominal twist boundary deviates from its macroscopic direction it may form (110)(103) facets which do... 

It is significant that the fpL,max calculated above occurred for pinning by a twist boundary, where the grain boundary and H are parallel to the [111] direction of one grain and the [100] direction of the other. But these specimens contain tilt boundaries with the [111] tilt axis. The condition for the peak in these... 

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