Burgers circuit

The Burgers vector of a screw dislocation can be determined in exactly the same way as an edge dislocation, following the FS/RH (perfect crystal) convention. A closed Burgers circuit is completed in a clockwise direction around the dislocation (Fig. 3.7a). An identical circuit in both direction and number of steps is completed in a perfect crystal (Fig. 3.7b). This will not close. The vector needed to close the circuit in the perfect crystal, running from the finish atom to the start atom, is the... 

In extended defects, the displacement vector b (or R) associated with them can be defined from the Burgers Circuit shown in figure 2.4(a), for a simple cubic system (Frank 1951, Cottrell 1971, Amelinckx et al 1978). In the defective crystal (A), a sequence of lattice vectors forms a clockwise ring around the dislocation precisely the same set of lattice vectors is then used to make a second... 

Figure 5.7 Burgers circuit for (a) an edge dislocation and (b) a screw dislocation. By moving a certain number of lattice distances to the right and down followed by a corresponding number of distances to the left and up, we get a closed path in the lower portion of (a) in the upper portion containing an edge dislocation, we have the misfit given by T. In (a), T is perpendicular to the dislocation line, while it is parallel in (b).

Figure 3-1. a) Edge dislocation model b) Burgers vector h with Burgers circuit and glide plane indicated. Dislocation motion during plastic deformation under the action of force F. Jog and kink. 

Figure 3-2. Screw dislocation Burgers vector b with Burgers circuit, s = direction of screw dislocation line.

The Burgers circuit is constructed so that it will close if mapped step by step into a perfect reference crystal. See Hirth and Lothe [2]. 

Figure 9.37. Schematic diagrams showing (a) a perfect edge dislocation in a structure consisting of alternating layers A and B, and (b) the climb dissociation of such a dislocation into two partial dislocations. As shown, the dissociation is due to the preferential precipitation of vacancies at A layers, or of interstitials at B layers. Burgers circuits are shown for the perfect dislocation (a) and the two par-tials (b). In BaTiOs, the A and B layers could correspond to BaO and Ti02 layers...

F re 5.26 Edge dislocation (a) and screw dislocation (b) in crystals with a simple cubic lattice. The symbol (-L) denotes the edge dislocation. The lattice atoms involved in a Burgers circuit construction are denoted as ( ). 

The Burgers circuit concept introduced above from the discrete perspective has a continuum analog. Mathematically, the origin of this analog is the fact that there is a jump in the continuum displacement fields used to characterize the geometric state of the body. Recall that above we described the Volterra procedure in which the body is cut and rejoined after a relative translation operation. The resulting displacement jump reveals itself upon consideration of the integral... 

Figure 4. Isolated topological defects in a triangular lattice, (a) Isolated -1 and +1 disclinations. A vector aligned along a local lattice direction is rotated by 60° upon parallel transport around a unit strength disclination. (6) An isolated dislocation. The heavy line represents a Burgers circuit around the dislocation, and the Burgers vector of the dislocation is the amount by which the circuit fails to close. The core of the dislocation is a tightly bound pair of +1 and -1 disclinations (Reproduced from [78] by permission of Oxford University Press.)...

Figure 3.20 (a) A Burgers circuit in a perfect crystal (heavy line) will be closed (b) the same circuit in a crystal containing a dislocation will remain open. The vector required to close the circuit, b, is the Burgers vector... 

Fig. 19. High resolution image of a type A step on a (313) twin, with Burgers circuit and vector, and plane directions of one crystal. (Photo B. Yangui.)... 

FIGURE 12.1 The Burgers circuit in the imperfect and perfect lattices for an edge dislocation in a simple-cubic crystal. 

TEM can be used to observe a periodic array of edge dislocations we use Burgers circuit to characterize the dislocations... 

Fig. 3.30 The Burgers circuits in a perfect crystal and in a faulted one. The steps of the circuit from one atomic position to the next must be the same in both lattices a the circuit in a dislocation-lree crystal b the circuit around a dislocation, b is the Burgers vector [14]...

Fig. 3.31 Burgers circuits to show the strength of vector b as having the magnitude of the distance between the atoms of the lattice a around a dislocation, b in the reference crystal (dislocation free) [14] and c a Burgers circuit around a screw dislocation (schematic). The Burgers vector b is required to complete the circuit...

Inset is the Burgers circuit around a dislocation, and the Burgers vector is /2[110] [50]. With kind permission of Professor Shibata... 

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