Burgers displacement vector

Figure 1.17. (a) An HRTEM image of the intergrowths and dislocations in a complex block structure using GaNbn029 as an example (b) a schematic diagram of the structure in the area shown in (a) (c) a structural model of the misfit fault in D2 and (d) the idealized structure of the dislocation D6. The Burgers (displacement) vector and mismatch of cation levels due to the dislocation are shown (after Gai P L and Anderson J S 1976 Acta Cryst. A 32 157). 

Burger s vector A measure of the crystal lattice displacement resulting from the passage of a dislocation. 

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... 

Dislocations are line defects. They bound slipped areas in a crystal and their motion produces plastic deformation. They are characterized by two geometrical parameters 1) the elementary slip displacement vector b (Burgers vector) and 2) the unit vector that defines the direction of the dislocation line at some point in the crystal, s. Figures 3-1 and 3-2 show the two limiting cases of a dislocation. If b is perpendicular to s, the dislocation is named an edge dislocation. The screw dislocation has b parallel to v. Often one Finds mixed dislocations. Dislocation lines close upon themselves or they end at inner or outer surfaces of a solid. 

Edge dislocation. The displacement vector R for an edge dislocation of Burgers vector b parallel to the surface of a thin foil, as shown in Figure 5.12, is given by... 

Figure6.7 Dislocations can have various widths depending on the atomic bonding. The dislocation displacement is spread over several atoms. The motion of the dislocation involves individual atomic displacements less than the Burger s vector. The shaded atoms indicate the position of the atoms after a small displacement.

Third, dislocations may be of mixed character — partially screw-like and partially edge-like. In this case the Burger s vector is neither perpendicular to nor parallel to the dislocation line. One can see how this can happen as follows. Slicing the sohd and moving an irregularly-shaped plane of atoms to form a dislocation has the same displacement, and hence the same Burger s vector across its entire surface. However, the line of the dislocation is forced to follow the edges of the plane, wherever they... 

Dislocation motion produces plastic strain. Figure 9.4 shows how the atoms rearrange as the dislocation moves through the crystal, and that, when one dislocation moves entirely through a crystal, the lower part is displaced under the upper by the distance b (called the Burgers vector). The same process is drawn, without the atoms, and using the symbol 1 for the position of the dislocation line, in Fig. 9.5. The way in... 

Figure 4.2 Quasi-hexagonal dislocation loop lying on the (111) glide plane of the diamond crystal structure. The <110> Burgers vector is indicated. A segment, displaced by one atomic plane, with a pair of kinks, is shown a the right-hand screw orientation of the loop. As the kinks move apart along the screw dislocation, more of it moves to the right.

Figure 14.1 Schematic comparison of dislocation lines in a crystalline and a glassy structure. Dashed line indicates the center of a dislocation line. The vectors indicate the displacement of the atoms in the next level above the plane of the figure. At (a) the displacement (Burgers) vectors In the periodic crystal have a constant value. At (b) the displacements in the glass fluctuate in both magnitude and direction.

The Burgers vector of most dislocations is neither perpendicular nor parallel to the dislocation line. Such a dislocation has an intermediate character and is called a mixed dislocation. In this case the atom displacements in the region of the dislocation are a complicated combination of edge and screw components. The mixed edge and screw nature of a dislocation can be illustrated by the structure of a dislocation loop,... 

To illustrate this, take the situation in a very common and relatively simple metal structure, that of copper. A crystal of copper adopts the face-centered cubic (fee) structure (Fig. 2.8). In all crystals with this structure slip takes place on one of the equivalent 111 planes, in one of the compatible <110> directions. The shortest vector describing this runs from an atom at the comer of the unit cell to one at a face center (Fig. 3.10). A dislocation having Burgers vector equal to this displacement, i <110>, is thus a unit dislocation in the structure. 

Figure 3.12 Partial dislocations in copper (a) a unit dislocation, Burgers vector bl (b) initially slip is easier in the direction represented by the Burgers vector of the partial dislocation b2 than bl (c) the result of the movement in (h) is to generate a stacking fault and (d) the combined effect of displacements by the two partial dislocations b2 and b3 is identical to that of the unit dislocation, but the partials are separated by a stacking fault.

Stack of lamellar crystals generated by spiral growth at one or more screw dislocations. Note The axial displacement over a full turn of the screw (Burgers vector) is usually equal to one lamellar thickness. 

Figure 2.4. Definition of a displacement (Burgers or shear) vector b (a) a Burgers vector around a dislocation (defect) A in a perfect crystal there is a closure failure unless completed by b (b) a schematic diagram of a screw dislocation—segments of crystals displace or shear relative to each other (c) a three-dimensional view of edge dislocation DC formed by inserting an extra half-plane of atoms in ABCD (d) a schematic diagram of a stacking fault. (Cottrell 1971 reproduced by the courtesy of Arnold Publishers.)...

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