Abstract
It is shown that, due to the existence of an inflection point in any interatomic potential that defines the energy bonds of a chain of atoms within the framework of Frenkel-Kontorova model, kinks (misfit dislocations) may exist only if the effective amplitude of the sinusoidal potential does not exceed a certain critical value. Exact analytic expressions for the dependence of this threshold value on the lattice mismatch in the system and on the velocity of the kinks are derived for the case of a Morse and of a model symmetric nonconvex potential.
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