A unified equation was presented, for dislocations, based upon lattice statics and symmetry principles. The equation satisfied by the displacement field, defined on the two-dimensional misfit-plane, could be applied to curved dislocations as well as to straight dislocations. The correction for discreteness, which was important for the core structure, was included in the equation and was related to the acoustic phonon velocity and lattice geometry structure. The dislocation equation of the new theory could be viewed as being a unification of the Peierls–Nabarro and Frenkel–Kontorva models for dislocations.

A Unified Dislocation Equation from Lattice Statics. S.F.Wang: Journal of Physics A, 2009, 42[2], 025208