Burger vector

Dislocations are characterized by the Burgers vector, which is the exua distance covered in traversing a closed loop around die core of the dislocation, compared with the conesponding distance traversed in a normal lattice, and is equal to about one lattice spacing. This circuit is made at right angles to the dislocation core of an edge dislocation, but parallel to the core of a screw dislocation. 

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... 

The Burgers vectors, glide plane and ine direction of the dislocations studied in this paper are given in table 1. Included in this table are also the results for the Peierls stresses as calculated here and, for comparison, those determined previously [6] with a different interatomic interaction model [16]. In the following we give for each of the three Burgers vectors under consideration a short description of the results. 

Table 1 Summary of the calculated properties of the various dislocations in NiAl. Dislocations are grouped together for different glide planes. The dislocation character, edge (E), screw (S) or mixed type (M) is indicated together with Burgers vector and line direction. The Peierls stresses for the (111) dislocations on the 211 plane correspond to the asymmetry in twinning and antitwinning sense respectively.

Figure 2 Core configuration and Burgers vector distribution of the (111) 211 edge dislocation display separation into two superpartials.

Figure 3 Core configuration of the (111) screw dislocation. The Burgers vector distribution is calculated for a 211 cut and clearly shows a compact dislocation core.

Fig. 20.32 Schematic illustration of a mixed dislocation as the boundary between slippted and unslipped crystal. The arrow shows the Burgers vector...

Hill et al. [117] extended the lower end of the temperature range studied (383—503 K) to investigate, in detail, the kinetic characteristics of the acceleratory period, which did not accurately obey eqn. (9). Behaviour varied with sample preparation. For recrystallized material, most of the acceleratory period showed an exponential increase of reaction rate with time (E = 155 kJ mole-1). Values of E for reaction at an interface and for nucleation within the crystal were 130 and 210 kJ mole-1, respectively. It was concluded that potential nuclei are not randomly distributed but are separated by a characteristic minimum distance, related to the Burgers vector of the dislocations present. Below 423 K, nucleation within crystals is very slow compared with decomposition at surfaces. Rate measurements are discussed with reference to absolute reaction rate theory. 

Fig. 13—Normalized o>/b as function of tglb, cta/b is the critical shear stress to move a dislocation from the B layer into the A layer, Q=(G -Gb)/(G +Gg), G and Gg are the shear moduli of A and B, b is the Burgers vector, fg is the thickness of one single B layer, and e is the angle between the A/B interfaces and the dislocation glide plane.

Figure 4.1 Schematic dislocation line a simple cubic crystal structure. The line enters the crystal at the center of the left-front face. It emerges at the center of the right-front face. The shortest translation vector of the structure is the Burgers Vector, b. The line bounds the glided area of the glide plane (100) from the unglided area.

Being the edge of a sheared area, a dislocation is a line, but does not, in general, lie on one plane, so its motion is usually three-dimensional. Since shear has two signs (plus and minus) so do dislocations and dislocations of like signs repel, while those of opposite signs attract. In some structures, the Burgers vector is an axial vector, so plus shear differs from minus shear (like a ratchet). 

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.

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