Interaction of dislocations with a local defect in an atomic chain with a nonconvex interparticle potential

It is known that in a Frenkel-Kontorova-type model with nonconvex interactions between closest neighbors a breakup of a dislocation (kink) takes place when an effective amplitude of the sinusoidal substrate potential exceeds a certain critical value. We consider (in the continuum limit) the same model with a local inhomogeneity, i.e., a narrow region where the substrate-potential amplitude is increased or decreased. While the former case results in an effective repulsion of the kink, we demonstrate that in the latter case, when the kink is attracted by the inhomogeneity, the breakup threshold for a kink pinned by the inhomogeneity is higher than for a free kink in the homogeneous system. Thus the local inhomogeneities of the latter type may trap and stabilize the kinks beyond the point of their breakup in the homogeneous system. These results suggest a possible explanation of recent experiments with formation of cracks out of misfit dislocation in adsorbed layers. We also derive a universal dynamic equation describing the kinks destruction in the homogeneous system at the breakup threshold, and we find its self-similar solutions, which demonstrate explicitly different modes of the destruction. Finally, all the static and dynamic results obtained for a single kink are extended to cases of periodic kink arrays with an arbitrary spacing.