Dislocation pairs

Such a screw dislocation pair generates steps at twice the rate for a single screw dislocation, i.e., it has an activity twice that of a single screw dislocation. Similar behavior is shown by a group of n screw dislocations of same sign which are closer than the sixe of the 2D nucleus (Fig. 5.33b). The resultant activity of such a group is approximately n times that of the activity of a single dislocation. 

The full KTHNY theory improves upon the simple instability theory presented above in several respects. Kosterlitz and Thouless recognized that the elastic constants of a solid containing thermally excited dislocation pairs are renormalized by the presence of such excitations, so that the coupling constant that appears in the above formula for the transition... 

However, there is a small bump in the specific heat above [85], representing the entropy associated with unbinding dislocation pairs. This feature may be unobservably small, however, because the density of such pairs is assumed to be small. 

Numerical calculations of dislocation pair interactions have been carried out for systems of particles with / [89] and LJ [90] potentials. For the potential, Fisher et al. [89] find that the elastic dislocation interaction potential is accurate for dislocation separations as small as 3 lattice spacings, while Joos and Duesbery [90] find that separations of 30 lattice spacings are necessary to reach the asymptotic elastic limit. The adequacy of the continuum elastic approximation in describing the short-range interactions between defects is thus still something of an open question, and may depend on the range of the interparticle potential. 

It is interesting to contrast this melting model with the KTHNY theory. In the KTHNY theory, 2D melting is associated with the unbinding of a dilute gas of thermally generated, bound dislocation pairs,... 

At this point we also note the relation to the Halperin-Nelson (1978)-Young (1978) theory of continuous melting in two dimensions via an unbinding of dislocation pairs. Writing the Hamiltonian in terms of the strain tensor afi = J[dtip/dxa -(- < Uq/... 

Fig. 3.64 Dislocation pairs in a specimen deformed at — 196 °C. Dense dislocation substructure composed largely of close edge. Active slip plane is at 45 to plane of foil [23], With kind permission of John Wiley and Sons...

The Grist dislocation model [98] assumes die formation in polymers crystalline regions of screw dislocation (or such dislocation pair) with Bulgers vector b and the yield process is realized at the formation of critical nucleus domain with size u ... 

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