Ledge effects on dislocation emission from a crack tip: A first-principles study for silicon

Extensive recent efforts to understand the intrinsic brittleness or ductility of materials have focused on crack-blunting mechanisms using the Peierls stress concept. So far, the effects due to newly created ledge surface during crack propagation have been either ignored or included within some semiempirical approximation. Using silicon as a prototypical brittle solid, we show that the energy associated with a newly created ledge surface at a crack tip can be obtained from first-principles calculations. We incorporate these results into a continuum theory of critical loading of cracks by assuming an evanescent force law for the surface effects. Our results indicate that inclusion of surface ledge effects can change the values of the critical load by up to 20%.