Energetics for dislocation motion in a Peierls potential

In dealing with the kinetics of dislocation motion in a Peierls potential it would be desirable to have at hand analytic formulae for the energies and configurations involved. This is achieved here by applying an approximation procedure based on averaging out the periodic nature of the Peierls potential in an appropriate way and reintroducing it at a later stage. In this way an approximate analytic expression is obtained for the energy profile as seen by a dislocation of finite length moving in a sinusoidal Peierls potential. The results are in good agreement with recent numerical calculations.