Dislocation line vector

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 4.1 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.

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 disruption to the crystal introduced by a dislocation is characterized by the Burgers vector, b (see Supplementary Material SI for information on directions in crystals). During dislocation motion individual atoms move in a direction parallel to b, and the dislocation itself moves in a direction perpendicular to the dislocation line. As the energy of a dislocation is proportional to b2, dislocations with small Burgers vectors form more readily. 

The Burgers vector of a dislocation can lie at any angle to the dislocation line. Although there are many different types of dislocations, they can all be thought of as combinations of two fundamental types, edge dislocations, which have Burgers vectors perpendicular to the dislocation line, and screw dislocations, with Burgers vectors parallel to the dislocation line. 

Burgers vector of the dislocation (Fig. 3.7c). It is found that the Burgers vector of a screw dislocation is parallel to the dislocation line. 

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,... 

The Burgers vector and dislocation line are normal to each other in ... 

The reflections include a particular g in which the dislocation is invisible (i.e., g b = 0 when b is normal to the reflecting plane). With these criteria in diffraction contrast, one can determine the character of the defect, e.g., screw (where b is parallel to the screw dislocation line or axis), edge (with b normal to the line), or partial (incomplete) dislocations. The dislocations are termed screw or edge, because in the former the displacement vector forms a helix and in the latter the circuit around the dislocation exhibits its most characteristic feature, the half-plane edge. By definition, a partial dislocation has a stacking fault on one side of it, and the fault is terminated by the dislocation (23-25). The nature of dislocations is important in understanding how defects form and grow at a catalyst surface, as well as their critical role in catalysis (3,4). 

As seen in the last chapter, the image width is easy to quantify for a screw dislocation, where the diffraction vector is parallel to the dislocation line. Around a screw dislocation, the misorientation at a distance r from the core is given by... 

In dynamic ETEM studies, to determine the nature of the high temperature CS defects formed due to the anion loss of catalysts at the operating temperature, the important g b criteria for analysing dislocation displacement vectors are used as outlined in chapter 2. (HRTEM lattice images under careful conditions may also be used.) They show that the defects are invisible in the = 002 reflection suggesting that b is normal to the dislocation line. Further sample tilting in the ETEM to analyse their habit plane suggests the displacement vector b = di aj2, b/1, 0) and the defects are in the (120) planes (as determined in vacuum studies by Bursill (1969) and in dynamic catalysis smdies by Gai (1981)). In simulations of CS defect contrast, surface relaxation effects and isotropic elasticity theory of dislocations (Friedel 1964) are incorporated (Gai 1981). 

Trace out a clockwise path around the dislocation line moving n lattice vectors in each of the four mutually perpendicular directions. 

The second type of line defect, the screw dislocation, occurs when the Burger s vector is parallel to the dislocation line (OC in Figure 1.33). This type of defect is called a screw dislocation because the atomic structure that results is similar to a screw. The Burger s vector for a screw dislocation is constructed in the same fashion as with the edge dislocation. When a line defect has both an edge and screw dislocation... 

Edge L to dislocation line II to dislocation line, to Bnrger s vector... 

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. 

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

The vector form of Eq. 11.9 is readily obtained. If r is the position vector tracing out the dislocation line in space and ds is the increment of arc length traversed along the dislocation when r increased by dr,4... 

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 vector d is given by Eq. 11.3, and because the six stresses are independent of each other, a value of the stress tensor may be found so that d is parallel to the dislocation line. As shown in Exercise 11.3, a solution of Eq. 11.54 corresponding to a helix with its axis along d can then be found. 

Figure 10.8. The two extreme types of dislocations. In the edge dislocation (a), the Burgers vector is perpendicular to the dislocation line. In the screw dislocation (b), the Burgers vector is parallel to the dislocation line.

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