Loss-Free Dislocation Motion in a Lattice Model

It is shown that a mode of dislocation motion exists in the modified Frenkel-Kontorova model in which the dislocation moves at a high constant speed without exciting any lattice waves and with no applied stress required to maintain the motion. The Peierls stress, ${\sigma }_{\mathrm{p}}$, for the model parameters employed has the value ${\sigma }_{\mathrm{p}}=0.0506\mathrm{}\mu$, with $\mu$ the shear modulus, so that this result provides an example of a dislocation subject to a periodic Peierls potential in its steady motion, without this fact giving rise to radiation losses.