The Application of the Wulff Construction to Dislocation Problems

The Wulff construction in two dimensions which relates to the equilibrium shape of a closed glissile dislocation loop at equilibrium with an applied stress is described. Formulae are derived for the coordinates of the shape, for the average energy of a dislocation loop, and for the forces exerted on a dislocation segment. The geometry of the Wulff construction is used to describe the rotation of dislocations at a free surface and instabilities caused by high line energies. A formula is given for the effective line tension of a bent dislocation. The results are applied to instabilities observed in the electron microscope on dislocations in deformed f.c.c. crystals. The zig-zag configurations of Lomer-Cottrell/Lomer dislocations and of dipoles/faulted dipoles are analysed.