Twist boundary

D. Udler, D. N. Seidman, Solute-Atom Segregation/structure Relations at High.Angle (002) Twist Boundaries in Dilute Ni-Pt Alloys, Interface Sci., 3 41 (1995). 

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)]. 

Figure 3-6. a) Small-angle lilt boundary wiih edge dislocations, b) Small-angle twist boundary formation of a screw dislocation network. 

A, B, and C in vicinal (001) twist grain boundary in Au. Static array of screw dislocations in background accommodates the twist deviation of the vicinal boundary shown from the crystal misorientation of the nearby singular twist boundary to which it is vicinal. Excess selfinterstitial defects were produced m the specimen by fast-ion irradiation and were destroyed at the grain-boundary dislocations by climb, causing the boundary to act as a defect sink, (a) Prior to irradiation, (b) Same area as in (a) after irradiation, (c) Diagram showing the extent of the climb. From Komer et al. [24],... 

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. 

Another simple type of grain boundary is the twist boundary, where the lattice planes of the grains are rotated relative to each other. In this case the interface consists of a cross grid of screw dislocations. In the more general case, combinations of these two simple types of dislocation will occur. 

At low angles, y is proportional to 9, but at higher angles, ytO decreases, as illustrated in Figure 12.8. Screw dislocations onaplane form twist boundaries. The misorientation across a low-angle twist boundary and its energy are proportional to the number of dislocations. 

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 ... 

Figure 2.5. (a) A low-angle twist boundary, (b) Representation as a screw dislocation. 

Figure 8.34. Network of dislocations forming a low-angle twist boundary in quartz from the Saxony granulites.

Bristowe, P. D., Sass, S. L. (1980). The atomic structure of a large angle (001) twist boundary in gold determined by a joint computer modelling and x-ray diffraction study. Acta Metall., 28, 575-88. 

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. 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.

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. 

Fig. 12.5. Schematic of the (103) domain structure on the (101) cubic substrate. Tilt boundaries occur along the [301] direction twist boundaries occur along the [010] direction.

Fig. 12.6. Twist boundary in a planar (103) sample tilted 45° to show the c-axis fringes of one grain. Microdiffraction confirms that there is a 90° misorientation of the c-axis about the twist axis the 45° specimen tilt is not compatible with lattice imaging of the a, 6-plane.

Fig. 12.11. Schematic of the planes which meet at a [100] twist boundary and at a (110)(103) facet. The similarities are in the connectivity of the Cu02 planes and the change in ordering of the Y and Ba atoms across the boundary as illustrated. These similarities suggest similarities in properties. For the twist boundary the lattice is approximately square and the Y, Ba positions are not coplanar with the Cu atoms, whereas for the (110)(103) facet the lattice is rectangular and the atoms are coplanar.

Facetting may also occur in the macroscopic twist boundaries along the... 

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