Shape of hollow dislocation cores: anisotropic surface energy and elastic effects

Equilibrium morphologies are frequently determined by a competition between interfacial and elastic energies. Holes at the cores of dislocations in materials with large Burgers vectors are a prime example of this type of competition because their existence is solely due to this type of competition. In this paper, we presented an approach for addressing these issues both in terms of determination of morphologies for which the energy is an extremum and a procedure for examining the stability of those solutions. We found that the cricular core holes around screw dislocations predicted by Frank are stable in an isotropic material. Core holes around edge dislocations are stable, but are not circular because of the symmetry of their elastic field even in isotropic materials. Even isotropic elastic energy leads to core shapes in which the effect of surface anisotropy is exaggerated over what it would be in the Wulff shape. Most of the present results were derived on the basis of a parametric form for the hole shape and as an expansion of the energies valid for small perturbations about a circular cross-section. Calculations based upon a completely different proposed shape with exact elasticity results led to predictions of hole shapes which are nearly identical.