How To Determine Limiting Velocities Of Dislocations In Anisotropic Crystals

In the continuum limit, the theory of dislocations in crystals predicts a divergence in the elastic energy of the host material at a crystal geometry dependent limiting (or critical) velocity v (c). Explicit expressions for v (c) are scattered throughout the literature and are available in analytic form only for special cases with a high degree of symmetry. The fact that in some cases (like pure edge dislocations in fcc) v (c) happens to coincide with the lowest shear wave speed of a sound wave traveling parallel to the dislocation's gliding direction has led to further confusion in the more recent literature. The aim of this short review therefore is to provide a concise overview of the limiting velocities for dislocations of arbitrary character in general anisotropic crystals, and how to efficiently compute them, either analytically or numerically.