Dislocation cores

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. 

Fast diffusion paths grain boundary and dislocation core diffusion... 

Diffusion in the bulk crystals may sometimes be short circuited by diffusion down grain boundaries or dislocation cores. The boundary acts as a planar channel, about two atoms wide, with a local diffusion rate which can be as much as 10 times greater than in the bulk (Figs. 18.8 and 10.4). The dislocation core, too, can act as a high conductivity wire of cross-section about (2b), where b is the atom size (Fig. 18.9). Of course, their contribution to the total diffusive flux depends also on how many grain boundaries or dislocations there are when grains are small or dislocations numerous, their contribution becomes important. 

However, it is not yet clear why the ener es of the SISF and the twin boundary increase with increasing A1 concentration. To find a clue to the problem, it would be needed to make out the effects of the short-range ordering of A1 atoms in excess of the stoichiometric composition of the HAl phase on the energies of planar faults and the stmcture of dislocation cores in the Al-rich HAl phase. 

Exactly the same procedure can be followed to define the free energy of a dislocation core. It should be surrounded by a box, the terminating planes of which can be dealt with exactly as above. Special attention has to be given to the atoms at the comers of the box, but this presents no particular problems their weights are simply a oroduct of the weights generated by the planar terminations which they share. 

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.

Dislocation core structures of (100), (110) and (111) dislocations in NiAl have been studied by molecular statics calculations using a new many-body embedded atom potential. They... 

Similarly, in studies of lamellar interfaces the calculations using the central-force potentials predict correctly the order of energies for different interfaces but their ratios cannot be determined since the energy of the ordered twin is unphysically low, similarly as that of the SISF. Notwithstcinding, the situation is more complex in the case of interfaces. It has been demonstrated that the atomic structure of an ordered twin with APB type displacement is not predicted correctly in the framework of central-forces and that it is the formation of strong Ti-Ti covalent bonds across the interface which dominates the structure. This character of bonding in TiAl is likely to be even more important in more complex interfaces and it cannot be excluded that it affects directly dislocation cores. 

Kuhlmann-Wilsdorf [7] provided a new theoretical approach in which melting was ascribed to the unrestricted proliferation of dislocations at the temperature for which the free energy of formation of glide dislocation cores becomes negative. Several physicists have shown interest in this model which has not so far been accorded similar attention in the chemical literature. 

Clarity requires that a distinction be made between elastic strain and plastic deformation. They both have units of length/length, but they are physically different entities. Elastic strain is recoverable (conservative) plastic deformation is not (non-conservative). At a dislocation core, where atoms exchange places via shear, the plastic displacement gradient is a maximum as it passes from zero some distance ahead of the core, up to the maximum, and then back to zero some distance back of the core. In crystals with distinct bonds, the gradient becomes indefinite (infinite) at the core center. 

The viscosity coefficients at dislocation cores can be measured either from direct observations of dislocation motion, or from ultrasonic measurements of internal friction. Some directly measured viscosities for pure metals are given in Table 4.1. Viscosities can also be measured indirectly from internal friction studies. There is consistency between the two types of measurement, and they are all quite small, being 1-10% of the viscosities of liquid metals at their melting points. It may be concluded that hardnesses (flow stresses) of pure... 

Figure 5.10 Schematic dislocation core. Arrangement at kink on screw dislocation line.

Another special factor in ionic crystals is that dislocation cores in them acquire net charge. As a result, plastic bending of an ionic crystal causes the top and bottom regions to become charged relative to the middle. This is easily demonstrated because such specimens preferentially attract fine insulating powders. It has been studied in some detail by Li (2000). 

Dislocations can attract a population of impurities, vacancies, or self-interstitials that are bound to the dislocation core by a binding energy Agb. These will be liberated and become free to contribute to the overall diffusion at higher temperatures, so that it is possible to write... 

Values of r satisfying Equation 3 (corresponding to the minimum and maximum points in Ag) will yield steady state solutions where a pit radius should remain constant, while the rest of the crystal grows or dissolves depending on the chemical affinity (Equation 2). If the term t b2g /2Tt2Y2 > 1, there are no real solutions to Equation 3 and there is no steady state value of r, which indicates that a small pit nucleated at a dislocation core should spontaneously open up to form a macroscopic etch pit. The critical concentration at which this occurs (setting the above term equal to one) is ... 

Although, Kato has shown that the ray theory breaks down approximately 10 fjm from a dislocation core and we caimot apply it to compute the contrast of a dislocation in a quantitative way, it is possible to obtain a large amoimt of qualitative information. 

Figure 10.15 Simulated image width as a function of deviation parameter in Bragg case weak beam topographs. Here, the specimen is set off the Bragg peak and an image of the defect occurs only when the lattice planes are locally rotated or dilated back into the Bragg condition. As this occurs only close to the dislocation core, the images are narrowed from those under strong beam conditions...

As mentioned before and assuming the vahdity of the continuum elasticity theory at the dislocation core, F. C. Frank derived the expression for the characteristic radius of a hollow core (Frank, 1951) ... 

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