Destruction of Solitons in Frenkel — Kontorova Models with Anharmonic Interactions

Abstract

The stability of moving topological solitons is investigated in the framework of a Frenkel - Kontorova model with anharmonic (e.g. Morse, Toda,etc.) interactions between the atoms and a lattice misfit between overlayer and substrate. The numerical simulations confirm the analytically derived misfit-and velocity-dependent critical ratio of periodic vs. interatomic potential strength, which determines the existence region of rarefaction 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 qualitatively these results.