Unstable Dislocations in Anisotropic Crystals

Dislocations are line-like objects with an associated elastic energy proportional to their length. Therefore, it would seem sensible to consider a positive line tension encoding their resistance to elongation. If we confine the dislocation to a plane, this tension is given by E + E", where E is the energy per unit length and the derivatives are taken with respect to the angle in the plane. When the crystal is isotropic, this quantity is always positive, and dislocations will assume a smooth elliptical shape at equilibrium. In highly anisotropic crystals, however, E + E" can become negative for certain orientations. This counter-intuitive notion (a dislocation can reduce its energy by increasing its length) leads to unusual cusped dislocation configurations, which have been observed in the electron microscope. It may also provide a possible explanation for the observed plastic weakness of iron and ferritic steels in the highly anisotropic (high temperature) regime.