Defects Burgers vector

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. 

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.)...

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. 

Show that regardless of the orientation of a straight dislocation line and its Burgers vector, there will exist a stress system that will convert the dislocation line into a helix whose axis is along the position of the original dislocation when the point-defect concentration is at the equilibrium value characteristic of the stress-free crystal. Use the simple line-tension approximation leading to Eq. 11.12. 

The line defects which are either dislocations or dislocation/ledges may be further classified as intrinsic or extrinsic. So far, only intrinsic line defects have been considered. These line defects are arranged in uniform arrays and accommodate deviations of interface misorientation and/or inclination from certain reference structures. As part of the minimum-energy equilibrium structure of the interfaces, they are termed intrinsic. On the other hand, similar line defects can be present in interfaces in a more or less random fashion, so that their Burgers vectors cancel. In... 

Burgers vector and -> defects in solids). In realistic systems, the grains are often separated by a thin amorphous layer, which may also comprise inclusions of secondary phases. 

Another effect of hydrogen in crystalline silicon is to break Si—Si bonds. After exposure of the surface to atomic hydrogen, extended defects are found in the surface region, typically to a depth of about 1000 A (Johnson, Ponce, Street and Nemanich 1987). These defects have no Burgers vector and are therefore not dislocations, but rather appear to be microcracks, in which the (111) planes of the crystal are pushed apart. A plausible explanation of the crack is that the silicon atoms are terminated by hydrogen and so are pushed apart. The presence of Si—H bonds is confirmed by Raman scattering. Hydrogen therefore can break Si—Si bonds and has a tendency to disorder the crystal. 

Molecule Crystal lattice Homogeneous surface Lattice defect Irregular structure Rotation/reflection Spatial translation Surface translation Homotopy Dilation (self-similarity) Molecular point group Space group 2-dimensional unit cell Burgers vector Fractal dimension Spectroscopy X-ray analysis Adsorption studies Crysttd properties Scaling laws... 

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.)...

The helical structure of the c-director in the smectic C phase makes the defects different from those in the smectic C phase. As the Volterra process produces a screw dislocation, for example, along the z axis and the Burger vector b = d, it must be accompanied by a parallel wedge disclination in the c-director, in the form... 

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