Dislocations Burgers vector, defined

A unit, or perfect, dislocation is defined by a Burgers vector which regenerates the structure perfectly after passage along the slip plane. The dislocations defined above with respect to a simple cubic structure are perfect dislocations. Clearly, then, a unit dislocation is defined in terms of the crystal structure of the host crystal. Thus, there is no definition of a unit dislocation that applies across all structures, unlike the definitions of point defects, which generally can be given in terms of any structure. 

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. 

Screw dislocation. The simplest case to start with is that of a straight screw dislocation of Burgers vector b parallel to the surface of a thin parallel-sided crystal foil, as shown in Figure 5.10. Using the coordinate system defined there, the dislocation AB is parallel to y and at a depth z below the top surface. The dislocation causes a column CD of unit cells parallel to z in the perfect crystal to be deformed. If we assume that the atomic displacements around the dislocation are the same in the thin specimen as in an infinitely large, elastically isotropic crystal, then the components u, v, w of the deformation of the column along thex, y, and z directions will be... 

The symbols used to define a dislocation convey both the magnitude and the direction of the Burgers vector as well as the slip plane in which the dislocation moves. The slip plane is cited first followed by the strength and direction of the Burgers vector. For example, in the rock-salt structure, where the lattice constant is a, there exist dislocations which lie and move in the (ITO) slip plane, their Burgers vector being b = ( a)[110]. Such dislocations, schematized in Fig. 7, are symbolized thus (iTO) a [110]. This means that the strength b of the vector is... 

Mechanical properties of disordered alloys are also different to those of ordered alloys. This can have a bearing on the techniques used to prepare the alloys. Ordered structures are usually harder than disordered ones. In the former, dislocations have higher energy the Burgers vector is larger because it is defined on the basis of the superlattice. Ako, dislocation movement is hindered by antiphase domain boundaries which may be present in the ordered state. 

As indicated in Sect. 3.3.1, dislocations are line defects. The two basic types of dislocations are the edge and screw dislocations. A schematic three-dimensional (3D) illustration of an edge dislocation appears in Fig. 3.25. A (100) plane of Fig. 3.25 in a simple cubic crystal is illustrated schematically in Fig. 3.28. This illustration will help to define the Burgers vector later on. Figure 3.29 is a schematic view of edge and screw dislocations. 

Fig. 6.2. A long straight dislocation in an elastic solid is parallel to a traction-free surface and at a distance tf from it. The dislocation is formed by an offset of one side of the shaded plane with respect to the other side defined by the Burgers vector bi.

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