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A unified dislocation equation from lattice statics

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