Ductile versus brittle behaviour of crystals

A necessary criterion for brittle fracture in crystals is established, in terms of the spontaneous emission of dislocations from an atomically sharp cleavage crack. We have calculated the stability of a sharp crack against emission of a blunting dislocation for a number of crystals and crystal types in two dimensions and the energy to form a stable loop of dislocation from the crack tip in three dimensions. We find that contrary to previous expectations, an atomically sharp cleavage crack is stable in a wide range of crystal types, but that in the face centred cubic metals investigated, blunting reactions occur spontaneously. Of the body centred metals investigated, iron is an intermediate case between the brittle and ductile cases, and the ionic and covalent crystals investigated are all stable against dislocation emission. Qualitatively, we find that crystals whose dislocations have wide cores, and small values of the parameter μb/γ (μb/γ⋦7·5 to 10) are ductile while crystals with narrow cores and large values of μb/r are brittle.