A Theory of Dislocation Motion in a Crystal. I. General and Application to One-Dimensional Lattice

Abstract

A theory of dislocation motion in a crystal is developed by introducing the dislocation coordinate which describes collective motion of atoms in the dislocation core associated with dislocation motion. The other degrees of freedom are shown to give a phonon field. An explicit formulation is given for a one-dimensional lattice (Frenkel-Kontorova model). The equation of motion obtained based on Lagrangian formalism shows that the dislocation behaves as if it has an eigenmass which gives the kinetic energy of the dislocation core. The eigenmass vanishes for a core much wider than the lattice constant and this case corresponds to a continuum. In Appendix quantization of the dislocation motion is discussed.