Lattice trapping barriers to brittle fracture.

We present a multiscale simulation of a crack in silicon under tensile loading that is consistent with experiment; fracture is brittle with a modest lattice-trapping energy barrier to crack propagation. Our multiscale molecular-dynamics simulation has a tight-binding description of bonding near the crack tip embedded in an empirical-potential (EP) region. Forces on atoms in the tight-binding region are computed using a Green's function method. Comparing our multiscale simulation with EP simulations shows that the EP models severely overestimate lattice trapping, explaining the failure of the Griffith criterion and the dramatic differences in crack morphology. A two-length-scale model for the lattice-trapping energy barrier correctly predicts the critical load for brittle fracture. We argue that lattice trapping plays an important role in the brittle-to-ductile transition.