Formation of cracks from kinks in a Frenkel-Kontorova model with anharmonic interactions

The stability of moving topological solitons is investigated using the framework of a Frenkel-Kontorova model with Morse interactions between the atoms and a lattice misfit between overlayer and substrate. The numerical simulations confirm the analytically predicted misfit- and velocity-dependent critical ratio: the periodic-substrate-potential amplitude to the dissociation energy of the Morse potential, which determines the existence region of kinks. No such limit exists for antikinks. The maximal propagation velocity of solitary excitations increases monotonically from zero with growing misfit and becomes supersonic at positive misfit. The destruction of kinks beyond their stability limits and the resulting formation of cracks are demonstrated numerically in cases of kink collisions with antikinks or with lattice defects. Extension of the model to long-range interactions beyond first neighbors does not change these results qualitatively.