Nature of dislocations

The simplest way to visualize a dislocation is to consider a simple cubic crystal consisting of two halves that meet on a horizontal plane, with the upper half containing one more vertical plane of atoms than the lower half. This is called an edge dislocation and is shown in Fig. 10.1. The points on the horizontal plane where the extra vertical plane of atoms ends form the dislocation line. The region around the 

There are different types of dislocations, depending on the crystal structure and the Burgers vector. Another characteristic example is a screw dislocation, which has a Burgers vector parallel to its line, as shown in Fig. 10.2. Dislocations in which the Burgers vector lies between the two extremes (parallel or perpendicular to the dislocation line) are called mixed dislocations. A dislocation is characterized by the direction of the dislocation line, denoted by and its Burgers vector b. For the two extreme cases, edge and screw dislocation, the following relations hold between 

Individual dislocations cannot begin or end within the solid without introducing additional defects. As a consequence, dislocations in a real solid must extend all the way to the surface, or form a closed loop, or form nodes at which they meet with other dislocations. Examples of a dislocation loop and dislocation nodes are shown in Fig. 10.3. Since a dislocation is characterized by a unique Burgers vector, in a 

Within the idealized situation of a single dislocation in an infinite crystal, it is possible to obtain the force per unit length of the dislocation due to the presence of external stress. If the width of the crystal is w and the length of the dislocation is I, then the work AW done by an external shear stress r to deform the crystal by moving an edge dislocation through it, in the configuration of Fig. 10.4, is 

If we assume that this is accomplished by a constant force, called the Peach-Koehler force Fpk, acting uniformly along the dislocation line, then the work done by this force will be given by 

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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). 

A detailed discussion of the consequences of the Hall-Petch equation in terms of the nature of dislocations is outside the scope of this work. Readers are directed to the many excellent texts and monographs dealing with solids in general and dislocations in particular (e.g.. Ref. 11). 

Crystallization Regime. This has been discussed in the previous section. It should be realized that properties of the crystal primarily determine which regime applies. This concerns (a) the magnitude of the various bond energies between the molecules in the crystal and (b) the concentration and the nature of dislocations present, screw dislocations in particular. The latter greatly depends on the impurities present. The density of screw dislocations tends to vary between crystal faces. 

The general need is to understand the response of a material to an applied stress. The stress may be applied externally or induced by altering other parameters such as temperature (which can cause a phase transformation). The fundamental idea is the link to bonding. In Chapter 4 we described how the Young s modulus is related directly to the bond-energy curve. In Chapter 12 we described the nature of dislocations in ceramics. 

With knowledge of the nature of dislocations and the role they play in the plastic deformation process, we are able to understand the underlying mechanisms of the techniques that are used to strengthen and... 

Fig. 1.5 A bubble raft illustrating the nature of a dislocation. The region of misfit near Y can be seen. (After Bragg and Nye )...

Climb unlocks dislocations from the precipitates which pin them and further slip (or glide ) can then take place (Fig. 19.3). Similar behaviour takes place for pinning by solute, and by other dislocations. After a little glide, of course, the unlocked dislocations bump into the next obstacles, and the whole cycle repeats itself. This explains the progressive, continuous, nature of creep, and the role of diffusion, with diffusion coefficient... 

The sequence just outlined provides a salutary lesson in the nature of explanation in materials science. At first the process was a pure mystery. Then the relationship to the shape of the solid-solubility curve was uncovered that was a partial explanation. Next it was found that the microstructural process that leads to age-hardening involves a succession of intermediate phases, none of them in equilibrium (a very common situation in materials science as we now know). An understanding of how these intermediate phases interact with dislocations was a further stage in explanation. Then came an nnderstanding of the shape of the GP zones (planar in some alloys, globniar in others). Next, the kinetics of the hardening needed to be... 

It is partly because of the variable effect of hydrogen (giving both softening and hardening, according to the nature of the slip) that the extrapolation of model experiments on very pure iron to predict the behaviour of commercial materials is so difficult. It is further hindered by the ability of dissolved hydrogen to modify the dislocation structure of a straining material. 

Obviously this model is very simplified, compared with the real crystal which contains many defects, dislocations and entanglements. In particular, it neglects many aspects of the true three-dimensional nature of the lamella which one may have thought to be important the influence of the stacking of folds, which is... 

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