Dislocation core energy

Fig. 28. Dislocation core energies of a screw dislocation as a function of an applied pressure, for shuffle A and glide C2 cores. Values were determined from tight-binding DFTB (full lines) and DFT-GGA (dashed line) calculations, assuming that the core radius is equal to one Burgers vector b.

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. 

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. 

The average value of A must be conserved over long distances to minimize both the elastic energy and the chemical (core) energy. Also, there will be little tendency for a dislocation line to remain in a single plane. It will tend to follow the plane of maximum shear stress. This is observed experimentally. 

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... 

Next, let us compile some quantitative relations which concern the stress field and the energy of dislocations. Using elastic continuum theory and disregarding the dislocation core, the elastic energy, diS, of a screw dislocation per unit length for isotropic crystals is found to be... 

In many cases, vacancies are bound to the dislocation core by an attractive binding energy and diffuse along the dislocation more rapidly than in the crystal. Many more vacancies may therefore reach jogs by fast diffusion along the dislocation core than by diffusion directly to them through the crystal. 

It is well-known that it is more difficult to etch dislocations in metal crystals than in ionic and covalent ones. The cause might be poor techniques, but a relatively low energy increment for metal atoms near a dislocation core could also be... 

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