Dislocations Burgers vector

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.

Figure 3.17 Layer of the corundum (AI2O3) structure, projected down the c axis. The unit cell is marked. A unit dislocation, Burgers vector b, can be decomposed into four partial dislocations bl-b4.

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

It may be energetically favorable for a dislocation, b, to spht into two dislocations if the product dislocation Burgers vectors and satisfy the condition b >b -hb. Dislocation reactions can even produce stable imperfect dislocations, if they result... 

The TEM investigations were performed in a 200 keV Philips CM 200 FEG/ST microscope which is equipped with a field emission gun. Dislocation Burgers vectors b were analyzed on the basis of the b g = 0 extinction criterion using different imaging vectors g. The weak-beam... 

What are the two shortest (crystallographically different) perfect-dislocation Burgers vectors in the following materials (i) alumina, (ii) graphite, and (iii) M0S2. 

Fig. 3.69 Representative weak-beam dark-field (WBDF) images where dislocations Burgers vectors (b) and fault vector (Rp) of fault F were determined (transmission electron microscopy) [55], With kind permission of John Wiley and Sons...

The normalized critical thickness ha/b can be computed from the condition (6.16) assuming Tq = b/2 for the given conditions and for the dislocation Burgers vector whose components are listed in (6.18). Alternatively, it is readily noted from Figure 6.8 that ln(hcr/ ) 3.9 for jeml = 0.0062. With b k 0.4 nm, the critical thickness is estimated to be 19.8 nm. 

This explanation of the role of misfit dislocations seems to be a likely explanation, as conductivity enhancement has been seen in YSZ single crystals that have been plastically deformed at high temperatures. Otsuka and co-workers [24, 25] have shown that the conductivity of the material, plastically deformed, with dislocation densities of 8 xlO m or greater show an enhancement of the conductivity. This effect is shown in Fig. 5 where the enhancement seen is small, around 8 %, but they estimate that in order for this effect to be observable, the conductivity in the core region of the dislocation would need to be enhanced by a factor of 10 -10" at a temperature of 597 °C, depending upon the estimated size of the core region (radius 1-10 times the dislocation Burgers 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). 

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