A Theory of Dislocation Motion in a Crystal. II. Two-Dimensional Lattice and on the Lorentz Force

Abstract

A theory of dislocation motion in a two-dimensional lattice is developed by introducing the dislocation coordinates which describe collective motion of atoms in the dislocation core. Because the displacements of atoms are dependent on dislocation path, the dislocation coordinates are quasi-coordinates. The equation of motions for the dislocation are obtained from those for individual atoms. Lagrangian formalism is also discussed. A usual form of Lagrange’s equation of motion is shown to contain a spurious term, which corresponds to a so-called Lorentz force.