The influence of the interatomic force law and of kinks on the propagation of brittle cracks

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Abstract
Cracks in brittle crystals can be lattice-trapped, as dislocations are by the Peierls barrier. Previous estimates of the range of loads within which a crack will not propagate more than one atomic spacing have varied greatly. The author's earlier computer model is extended to examine the effects of varying the shape of the interatomic force law and of the introduction of kinks in the crack edge. The system studied is a (111) cleavage crack in silicon, with edge either parallel to [OT1], or at a small angle to this direction, so that a series of kinks forms. The boundary conditions, being derived from a general continuum theory solution containing variable terms dependent on the core conditions, are ‘flexible’, allowing free motion of the crack inside the crystallite. The numerical relaxation method allows energy minima or saddle points to be located, thus making possible the calculation of migration activation energies. Several non-central interatomic force laws are employed, all matched to the elastic constants and cohesive energy of silicon, but varying in shape at long range. The calculations determine the atomic structure of the crack tip, the tensions in bonds crossing the crack plane, the potential energy barriers to crack propagation at various loads, and the range of loads for stability. A short-ranged force law is found to lead to much greater lattice trapping than one with a long attractive tail. The fractional range of loads Kmax/. Kmin is found to vary from 1-1 to 1-4 for a straight crack with realistic force laws in use, but to be about 7 when a law of the linear-spring type with sudden snapping point is used. In general, as the load is varied from Kmin to Kmax, the energy barrier to crack extension decreases from a maximum to zero, and vice versa for the crack-closure energy. The lattice trapping of a crack edge containing kinks is found to be only about one-tenth as strong as that experienced by a straight crack edge. The predicted kink motion energies are in the range 0.01 to 0.03 eV at the neutral load at which forward and reverse motion are equally favoured. A discussion is given of crack creep by thermally-activated kink pair nucleation and drift diffusion of kinks along the crack edge. A stress- and temperature-dependent creep law is obtained.